Repository: zcash/zcash (language: rust)

Issue:
Remove insecurely-downloaded dependencies that we don't currently use.
Closes #898.



Discussion / hints:
ACK that this can safely be merged. I have _not_ checked that these are the only packages for which hashes were not verified.

Is there a way we can avoid removing these dependencies but still ensure they are verified? We don't use them because we don't yet use Qt.

Yes, but it's more work, so I vote we just remove them for now.

ACK.

@zkbot r+

:pushpin: Commit 5b2e61e has been approved by `ebfull`

<!-- @zkbot r=ebfull 5b2e61ecef8a09f1b514855b77358cc865cdee70 -->

:umbrella: The latest upstream changes (presumably #1089) made this pull request unmergeable. Please resolve the merge conflicts.

:lock: Merge conflict

This needs to be rebased. :)

ACK.

@zkbot r+

:pushpin: Commit 86551dc has been approved by `ebfull`

<!-- @zkbot r=ebfull 86551dcb182f5179475f3872ad153300d2feb248 -->

:hourglass: Testing commit 86551dc with merge b5dfcd0...

:sunny: Test successful - [zcash](http://ci.leastauthority.com:8010/builders/zcash/builds/257)


Fix patch:
diff --git a/.cargo/config.offline b/.cargo/config.offline
index 8b7762d20bf..ca836a44ac9 100644
--- a/.cargo/config.offline
+++ b/.cargo/config.offline
@@ -4,5 +4,10 @@ linker = "aarch64-linux-gnu-gcc"
 [source.crates-io]
 replace-with = "vendored-sources"
 
+[source."https://github.com/zcash/librustzcash.git"]
+git = "https://github.com/zcash/librustzcash.git"
+rev = "ec1c1bcf21c43b0736d298d3a437162253946a8a"
+replace-with = "vendored-sources"
+
 [source.vendored-sources]
 # The directory for this source is set to RUST_VENDORED_SOURCES by src/Makefile.am
diff --git a/Cargo.lock b/Cargo.lock
index bddc5c7bb5e..0ef1f8225e9 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -517,8 +517,7 @@ checksum = "7fcaabb2fef8c910e7f4c7ce9f67a1283a1715879a7c230ca9d6d1ae31f16d91"
 [[package]]
 name = "equihash"
 version = "0.2.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ab579d7cf78477773b03e80bc2f89702ef02d7112c711d54ca93dcdce68533d5"
+source = "git+https://github.com/zcash/librustzcash.git?rev=ec1c1bcf21c43b0736d298d3a437162253946a8a#ec1c1bcf21c43b0736d298d3a437162253946a8a"
 dependencies = [
  "blake2b_simd",
  "byteorder",
@@ -527,8 +526,7 @@ dependencies = [
 [[package]]
 name = "f4jumble"
 version = "0.1.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "0a83e8d7fd0c526af4aad893b7c9fe41e2699ed8a776a6c74aecdeafe05afc75"
+source = "git+https://github.com/zcash/librustzcash.git?rev=ec1c1bcf21c43b0736d298d3a437162253946a8a#ec1c1bcf21c43b0736d298d3a437162253946a8a"
 dependencies = [
  "blake2b_simd",
 ]
@@ -725,14 +723,15 @@ dependencies = [
 
 [[package]]
 name = "hdwallet"
-version = "0.3.1"
+version = "0.4.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9cd89bf343be18dbe1e505100e48168bbd084760e842a8fed0317d2361470193"
+checksum = "5a03ba7d4c9ea41552cd4351965ff96883e629693ae85005c501bb4b9e1c48a7"
 dependencies = [
  "lazy_static",
  "rand_core 0.6.4",
  "ring",
  "secp256k1",
+ "thiserror",
 ]
 
 [[package]]
@@ -1696,18 +1695,18 @@ checksum = "d29ab0c6d3fc0ee92fe66e2d99f700eab17a8d57d1c1d3b748380fb20baa78cd"
 
 [[package]]
 name = "secp256k1"
-version = "0.21.3"
+version = "0.26.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9c42e6f1735c5f00f51e43e28d6634141f2bcad10931b2609ddd74a86d751260"
+checksum = "4124a35fe33ae14259c490fd70fa199a32b9ce9502f2ee6bc4f81ec06fa65894"
 dependencies = [
  "secp256k1-sys",
 ]
 
 [[package]]
 name = "secp256k1-sys"
-version = "0.4.2"
+version = "0.8.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "957da2573cde917463ece3570eab4a0b3f19de6f1646cde62e6fd3868f566036"
+checksum = "70a129b9e9efbfb223753b9163c4ab3b13cff7fd9c7f010fbac25ab4099fa07e"
 dependencies = [
  "cc",
 ]
@@ -2315,8 +2314,7 @@ dependencies = [
 [[package]]
 name = "zcash_address"
 version = "0.2.1"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "52be35a205369d480378646bff9c9fedafd8efe8af1e0e54bb858f405883f2b2"
+source = "git+https://github.com/zcash/librustzcash.git?rev=ec1c1bcf21c43b0736d298d3a437162253946a8a#ec1c1bcf21c43b0736d298d3a437162253946a8a"
 dependencies = [
  "bech32",
  "bs58",
@@ -2327,8 +2325,7 @@ dependencies = [
 [[package]]
 name = "zcash_encoding"
 version = "0.2.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f03391b81727875efa6ac0661a20883022b6fba92365dc121c48fa9b00c5aac0"
+source = "git+https://github.com/zcash/librustzcash.git?rev=ec1c1bcf21c43b0736d298d3a437162253946a8a#ec1c1bcf21c43b0736d298d3a437162253946a8a"
 dependencies = [
  "byteorder",
  "nonempty",
@@ -2337,8 +2334,7 @@ dependencies = [
 [[package]]
 name = "zcash_history"
 version = "0.3.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "eb611a28a4e13ac715ee712f4344d6b279b767daf6345dafefb2c4bf582b6679"
+source = "git+https://github.com/zcash/librustzcash.git?rev=ec1c1bcf21c43b0736d298d3a437162253946a8a#ec1c1bcf21c43b0736d298d3a437162253946a8a"
 dependencies = [
  "blake2b_simd",
  "byteorder",
@@ -2348,8 +2344,7 @@ dependencies = [
 [[package]]
 name = "zcash_note_encryption"
 version = "0.3.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "2eb2149e6cd5fbee36c5b87c601715a8c35554602f7fe84af38b636afa2db318"
+source = "git+https://github.com/zcash/librustzcash.git?rev=ec1c1bcf21c43b0736d298d3a437162253946a8a#ec1c1bcf21c43b0736d298d3a437162253946a8a"
 dependencies = [
  "chacha20",
  "chacha20poly1305",
@@ -2361,8 +2356,7 @@ dependencies = [
 [[package]]
 name = "zcash_primitives"
 version = "0.11.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "914d2195a478d5b63191584dff126f552751115181857b290211ec88e68acc3e"
+source = "git+https://github.com/zcash/librustzcash.git?rev=ec1c1bcf21c43b0736d298d3a437162253946a8a#ec1c1bcf21c43b0736d298d3a437162253946a8a"
 dependencies = [
  "aes",
  "bip0039",
@@ -2397,8 +2391,7 @@ dependencies = [
 [[package]]
 name = "zcash_proofs"
 version = "0.11.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "e5c8147884952748b00aa443d36511ae2d7b49acfec74cfd39c0959fbb61ef14"
+source = "git+https://github.com/zcash/librustzcash.git?rev=ec1c1bcf21c43b0736d298d3a437162253946a8a#ec1c1bcf21c43b0736d298d3a437162253946a8a"
 dependencies = [
  "bellman",
  "blake2b_simd",
diff --git a/Cargo.toml b/Cargo.toml
index 5425c03f064..3151df92f97 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -51,7 +51,7 @@ jubjub = "0.10"
 memuse = "0.2"
 nonempty = "0.7"
 orchard = "0.4"
-secp256k1 = "0.21"
+secp256k1 = "0.26"
 subtle = "2.2"
 rand_core = "0.6"
 tracing = "0.1"
@@ -112,3 +112,12 @@ features = ["ansi", "env-filter", "fmt", "time"]
 lto = 'thin'
 panic = 'abort'
 codegen-units = 1
+
+[patch.crates-io]
+equihash = { git = "https://github.com/zcash/librustzcash.git", rev = "ec1c1bcf21c43b0736d298d3a437162253946a8a" }
+zcash_address = { git = "https://github.com/zcash/librustzcash.git", rev = "ec1c1bcf21c43b0736d298d3a437162253946a8a" }
+zcash_encoding = { git = "https://github.com/zcash/librustzcash.git", rev = "ec1c1bcf21c43b0736d298d3a437162253946a8a" }
+zcash_history = { git = "https://github.com/zcash/librustzcash.git", rev = "ec1c1bcf21c43b0736d298d3a437162253946a8a" }
+zcash_note_encryption = { git = "https://github.com/zcash/librustzcash.git", rev = "ec1c1bcf21c43b0736d298d3a437162253946a8a" }
+zcash_primitives = { git = "https://github.com/zcash/librustzcash.git", rev = "ec1c1bcf21c43b0736d298d3a437162253946a8a" }
+zcash_proofs = { git = "https://github.com/zcash/librustzcash.git", rev = "ec1c1bcf21c43b0736d298d3a437162253946a8a" }
diff --git a/configure.ac b/configure.ac
index 4a88acac738..96fb6acbb47 100644
--- a/configure.ac
+++ b/configure.ac
@@ -1188,15 +1188,7 @@ LIBS_TEMP="$LIBS"
 unset LIBS
 LIBS="$LIBS_TEMP"
 
-PKGCONFIG_PATH_TEMP="$PKG_CONFIG_PATH"
-unset PKG_CONFIG_PATH
-PKG_CONFIG_PATH="$PKGCONFIG_PATH_TEMP"
-
-PKGCONFIG_LIBDIR_TEMP="$PKG_CONFIG_LIBDIR"
-unset PKG_CONFIG_LIBDIR
-PKG_CONFIG_LIBDIR="$PKGCONFIG_LIBDIR_TEMP"
-
-ac_configure_args="${ac_configure_args} --disable-shared --with-pic --enable-benchmark=no --enable-module-recovery --disable-openssl-tests"
+ac_configure_args="${ac_configure_args} --disable-shared --with-pic --enable-benchmark=no --enable-module-recovery"
 AC_CONFIG_SUBDIRS([src/secp256k1 src/univalue])
 
 AC_OUTPUT
diff --git a/qa/supply-chain/audits.toml b/qa/supply-chain/audits.toml
index d0dda94f2d4..07bc25e4c46 100644
--- a/qa/supply-chain/audits.toml
+++ b/qa/supply-chain/audits.toml
@@ -634,6 +634,11 @@ The ECC core team maintains this crate, and we have reviewed every line.
 The crate has `deny(unsafe_code)`.
 """
 
+[[audits.hdwallet]]
+who = "Jack Grigg <jack@electriccoin.co>"
+criteria = "safe-to-deploy"
+delta = "0.3.1 -> 0.4.1"
+
 [[audits.http]]
 who = "Jack Grigg <jack@electriccoin.co>"
 criteria = "safe-to-deploy"
diff --git a/qa/supply-chain/config.toml b/qa/supply-chain/config.toml
index 19a81f95b6e..832857961a4 100644
--- a/qa/supply-chain/config.toml
+++ b/qa/supply-chain/config.toml
@@ -19,6 +19,30 @@ url = "https://raw.githubusercontent.com/divviup/libprio-rs/main/supply-chain/au
 [imports.mozilla]
 url = "https://raw.githubusercontent.com/mozilla/supply-chain/main/audits.toml"
 
+[policy.equihash]
+audit-as-crates-io = false
+
+[policy.f4jumble]
+audit-as-crates-io = false
+
+[policy.zcash_address]
+audit-as-crates-io = false
+
+[policy.zcash_encoding]
+audit-as-crates-io = false
+
+[policy.zcash_history]
+audit-as-crates-io = false
+
+[policy.zcash_note_encryption]
+audit-as-crates-io = false
+
+[policy.zcash_primitives]
+audit-as-crates-io = false
+
+[policy.zcash_proofs]
+audit-as-crates-io = false
+
 [[exemptions.addr2line]]
 version = "0.17.0"
 criteria = "safe-to-deploy"
@@ -524,11 +548,11 @@ version = "1.1.0"
 criteria = "safe-to-deploy"
 
 [[exemptions.secp256k1]]
-version = "0.21.3"
+version = "0.26.0"
 criteria = "safe-to-deploy"
 
 [[exemptions.secp256k1-sys]]
-version = "0.4.2"
+version = "0.8.1"
 criteria = "safe-to-deploy"
 
 [[exemptions.secrecy]]
diff --git a/src/bench/bench_bitcoin.cpp b/src/bench/bench_bitcoin.cpp
index 39a983edcda..dc87d20ef66 100644
--- a/src/bench/bench_bitcoin.cpp
+++ b/src/bench/bench_bitcoin.cpp
@@ -20,7 +20,6 @@ main(int argc, char** argv)
 {
     SHA256AutoDetect();
     ECC_Start();
-    auto globalVerifyHandle = new ECCVerifyHandle();
     SetupEnvironment();
     fPrintToDebugLog = false; // don't want to write to debug log file
 
diff --git a/src/bitcoin-tx.cpp b/src/bitcoin-tx.cpp
index f6acf9d0587..b60131e3907 100644
--- a/src/bitcoin-tx.cpp
+++ b/src/bitcoin-tx.cpp
@@ -499,8 +499,6 @@ static void MutateTxSign(CMutableTransaction& tx, const std::string& strInput)
 
 class Secp256k1Init
 {
-    ECCVerifyHandle globalVerifyHandle;
-
 public:
     Secp256k1Init() {
         ECC_Start();
diff --git a/src/init.cpp b/src/init.cpp
index 207369b25bf..7073d14eeb8 100644
--- a/src/init.cpp
+++ b/src/init.cpp
@@ -175,7 +175,6 @@ class CCoinsViewErrorCatcher : public CCoinsViewBacked
 
 static CCoinsViewDB *pcoinsdbview = NULL;
 static CCoinsViewErrorCatcher *pcoinscatcher = NULL;
-static boost::scoped_ptr<ECCVerifyHandle> globalVerifyHandle;
 
 void Interrupt(boost::thread_group& threadGroup)
 {
@@ -269,7 +268,6 @@ void Shutdown()
     delete pwalletMain;
     pwalletMain = NULL;
 #endif
-    globalVerifyHandle.reset();
     ECC_Stop();
     TracingInfo("main", "done");
     if (pTracingHandle) {
@@ -1417,7 +1415,6 @@ bool AppInit2(boost::thread_group& threadGroup, CScheduler& scheduler)
     std::string sha256_algo = SHA256AutoDetect();
     LogPrintf("Using the '%s' SHA256 implementation\n", sha256_algo);
     ECC_Start();
-    globalVerifyHandle.reset(new ECCVerifyHandle());
 
     // Sanity check
     if (!InitSanityCheck())
diff --git a/src/key.cpp b/src/key.cpp
index 19de17e431f..7cbc3a34a6c 100644
--- a/src/key.cpp
+++ b/src/key.cpp
@@ -33,46 +33,46 @@ static secp256k1_context* secp256k1_context_sign = NULL;
  *
  * out32 must point to an output buffer of length at least 32 bytes.
  */
-static int ec_privkey_import_der(const secp256k1_context* ctx, unsigned char *out32, const unsigned char *privkey, size_t privkeylen) {
-    const unsigned char *end = privkey + privkeylen;
+static int ec_seckey_import_der(const secp256k1_context* ctx, unsigned char *out32, const unsigned char *seckey, size_t seckeylen) {
+    const unsigned char *end = seckey + seckeylen;
     memset(out32, 0, 32);
     /* sequence header */
-    if (end - privkey < 1 || *privkey != 0x30u) {
+    if (end - seckey < 1 || *seckey != 0x30u) {
         return 0;
     }
-    privkey++;
+    seckey++;
     /* sequence length constructor */
-    if (end - privkey < 1 || !(*privkey & 0x80u)) {
+    if (end - seckey < 1 || !(*seckey & 0x80u)) {
         return 0;
     }
-    size_t lenb = *privkey & ~0x80u; privkey++;
+    size_t lenb = *seckey & ~0x80u; seckey++;
     if (lenb < 1 || lenb > 2) {
         return 0;
     }
-    if (end - privkey < lenb) {
+    if (end - seckey < lenb) {
         return 0;
     }
     /* sequence length */
-    size_t len = privkey[lenb-1] | (lenb > 1 ? privkey[lenb-2] << 8 : 0u);
-    privkey += lenb;
-    if (end - privkey < len) {
+    size_t len = seckey[lenb-1] | (lenb > 1 ? seckey[lenb-2] << 8 : 0u);
+    seckey += lenb;
+    if (end - seckey < len) {
         return 0;
     }
     /* sequence element 0: version number (=1) */
-    if (end - privkey < 3 || privkey[0] != 0x02u || privkey[1] != 0x01u || privkey[2] != 0x01u) {
+    if (end - seckey < 3 || seckey[0] != 0x02u || seckey[1] != 0x01u || seckey[2] != 0x01u) {
         return 0;
     }
-    privkey += 3;
+    seckey += 3;
     /* sequence element 1: octet string, up to 32 bytes */
-    if (end - privkey < 2 || privkey[0] != 0x04u) {
+    if (end - seckey < 2 || seckey[0] != 0x04u) {
         return 0;
     }
-    size_t oslen = privkey[1];
-    privkey += 2;
-    if (oslen > 32 || end - privkey < oslen) {
+    size_t oslen = seckey[1];
+    seckey += 2;
+    if (oslen > 32 || end - seckey < oslen) {
         return 0;
     }
-    memcpy(out32 + (32 - oslen), privkey, oslen);
+    memcpy(out32 + (32 - oslen), seckey, oslen);
     if (!secp256k1_ec_seckey_verify(ctx, out32)) {
         memset(out32, 0, 32);
         return 0;
@@ -85,17 +85,17 @@ static int ec_privkey_import_der(const secp256k1_context* ctx, unsigned char *ou
  * <https://www.secg.org/sec1-v2.pdf>. The optional parameters and publicKey fields are
  * included.
  *
- * privkey must point to an output buffer of length at least CKey::PRIVATE_KEY_SIZE bytes.
- * privkeylen must initially be set to the size of the privkey buffer. Upon return it
+ * seckey must point to an output buffer of length at least CKey::PRIVATE_KEY_SIZE bytes.
+ * seckeylen must initially be set to the size of the seckey buffer. Upon return it
  * will be set to the number of bytes used in the buffer.
  * key32 must point to a 32-byte raw private key.
  */
-static int ec_privkey_export_der(const secp256k1_context *ctx, unsigned char *privkey, size_t *privkeylen, const unsigned char *key32, int compressed) {
-    assert(*privkeylen >= CKey::PRIVATE_KEY_SIZE);
+static int ec_seckey_export_der(const secp256k1_context *ctx, unsigned char *seckey, size_t *seckeylen, const unsigned char *key32, int compressed) {
+    assert(*seckeylen >= CKey::PRIVATE_KEY_SIZE);
     secp256k1_pubkey pubkey;
     size_t pubkeylen = 0;
     if (!secp256k1_ec_pubkey_create(ctx, &pubkey, key32)) {
-        *privkeylen = 0;
+        *seckeylen = 0;
         return 0;
     }
     if (compressed) {
@@ -113,15 +113,15 @@ static int ec_privkey_export_der(const secp256k1_context *ctx, unsigned char *pr
             0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
             0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x24,0x03,0x22,0x00
         };
-        unsigned char *ptr = privkey;
+        unsigned char *ptr = seckey;
         memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
         memcpy(ptr, key32, 32); ptr += 32;
         memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
         pubkeylen = CPubKey::COMPRESSED_PUBLIC_KEY_SIZE;
         secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED);
         ptr += pubkeylen;
-        *privkeylen = ptr - privkey;
-        assert(*privkeylen == CKey::COMPRESSED_PRIVATE_KEY_SIZE);
+        *seckeylen = ptr - seckey;
+        assert(*seckeylen == CKey::COMPRESSED_PRIVATE_KEY_SIZE);
     } else {
         static const unsigned char begin[] = {
             0x30,0x82,0x01,0x13,0x02,0x01,0x01,0x04,0x20
@@ -139,15 +139,15 @@ static int ec_privkey_export_der(const secp256k1_context *ctx, unsigned char *pr
             0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
             0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x44,0x03,0x42,0x00
         };
-        unsigned char *ptr = privkey;
+        unsigned char *ptr = seckey;
         memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
         memcpy(ptr, key32, 32); ptr += 32;
         memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
         pubkeylen = CPubKey::PUBLIC_KEY_SIZE;
         secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_UNCOMPRESSED);
         ptr += pubkeylen;
-        *privkeylen = ptr - privkey;
-        assert(*privkeylen == CKey::PRIVATE_KEY_SIZE);
+        *seckeylen = ptr - seckey;
+        assert(*seckeylen == CKey::PRIVATE_KEY_SIZE);
     }
     return 1;
 }
@@ -166,9 +166,9 @@ CKey CKey::TestOnlyRandomKey(bool fCompressedIn) {
     return key;
 }
 
-std::optional<CKey> CKey::FromPrivKey(const CPrivKey &privkey, bool fCompressedIn) {
+std::optional<CKey> CKey::FromPrivKey(const CPrivKey &seckey, bool fCompressedIn) {
     CKey key;
-    if (!ec_privkey_import_der(secp256k1_context_sign, (unsigned char*)key.begin(), &privkey[0], privkey.size()))
+    if (!ec_seckey_import_der(secp256k1_context_sign, (unsigned char*)key.begin(), &seckey[0], seckey.size()))
         return std::nullopt;
     key.fCompressed = fCompressedIn;
     key.fValid = true;
@@ -177,15 +177,15 @@ std::optional<CKey> CKey::FromPrivKey(const CPrivKey &privkey, bool fCompressedI
 
 CPrivKey CKey::GetPrivKey() const {
     assert(fValid);
-    CPrivKey privkey;
+    CPrivKey seckey;
     int ret;
-    size_t privkeylen;
-    privkey.resize(PRIVATE_KEY_SIZE);
-    privkeylen = PRIVATE_KEY_SIZE;
-    ret = ec_privkey_export_der(secp256k1_context_sign, privkey.data(), &privkeylen, begin(), fCompressed ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED);
+    size_t seckeylen;
+    seckey.resize(PRIVATE_KEY_SIZE);
+    seckeylen = PRIVATE_KEY_SIZE;
+    ret = ec_seckey_export_der(secp256k1_context_sign, seckey.data(), &seckeylen, begin(), fCompressed ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED);
     assert(ret);
-    privkey.resize(privkeylen);
-    return privkey;
+    seckey.resize(seckeylen);
+    return seckey;
 }
 
 CPubKey CKey::GetPubKey() const {
@@ -245,8 +245,8 @@ bool CKey::SignCompact(const uint256 &hash, std::vector<unsigned char>& vchSig)
     return true;
 }
 
-bool CKey::Load(CPrivKey &privkey, CPubKey &vchPubKey, bool fSkipCheck=false) {
-    if (!ec_privkey_import_der(secp256k1_context_sign, (unsigned char*)begin(), privkey.data(), privkey.size()))
+bool CKey::Load(CPrivKey &seckey, CPubKey &vchPubKey, bool fSkipCheck=false) {
+    if (!ec_seckey_import_der(secp256k1_context_sign, (unsigned char*)begin(), seckey.data(), seckey.size()))
         return false;
     fCompressed = vchPubKey.IsCompressed();
     fValid = true;
@@ -271,7 +271,7 @@ bool CKey::Derive(CKey& keyChild, ChainCode &ccChild, unsigned int nChild, const
     }
     memcpy(ccChild.begin(), vout.data()+32, 32);
     memcpy((unsigned char*)keyChild.begin(), begin(), 32);
-    bool ret = secp256k1_ec_privkey_tweak_add(secp256k1_context_sign, (unsigned char*)keyChild.begin(), vout.data());
+    bool ret = secp256k1_ec_seckey_tweak_add(secp256k1_context_sign, (unsigned char*)keyChild.begin(), vout.data());
     keyChild.fCompressed = true;
     keyChild.fValid = ret;
     return ret;
@@ -346,7 +346,7 @@ bool CKey::ECC_InitSanityCheck() {
 void ECC_Start() {
     assert(secp256k1_context_sign == NULL);
 
-    secp256k1_context *ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
+    secp256k1_context *ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
     assert(ctx != NULL);
 
     {
diff --git a/src/pubkey.cpp b/src/pubkey.cpp
index dc3e6742104..366dc44c0d6 100644
--- a/src/pubkey.cpp
+++ b/src/pubkey.cpp
@@ -8,32 +8,37 @@
 #include <secp256k1.h>
 #include <secp256k1_recovery.h>
 
-namespace
+namespace {
+
+struct Secp256k1SelfTester
 {
-/* Global secp256k1_context object used for verification. */
-secp256k1_context* secp256k1_context_verify = NULL;
-}
+    Secp256k1SelfTester() {
+        /* Run libsecp256k1 self-test before using the secp256k1_context_static. */
+        secp256k1_selftest();
+    }
+} SECP256K1_SELFTESTER;
 
+} // namespace
 
 bool CPubKey::Verify(const uint256 &hash, const std::vector<unsigned char>& vchSig) const {
     if (!IsValid())
         return false;
     secp256k1_pubkey pubkey;
     secp256k1_ecdsa_signature sig;
-    if (!secp256k1_ec_pubkey_parse(secp256k1_context_verify, &pubkey, &(*this)[0], size())) {
+    if (!secp256k1_ec_pubkey_parse(secp256k1_context_static, &pubkey, &(*this)[0], size())) {
         return false;
     }
     if (vchSig.size() == 0) {
         return false;
     }
     /* Zcash, unlike Bitcoin, has always enforced strict DER signatures. */
-    if (!secp256k1_ecdsa_signature_parse_der(secp256k1_context_verify, &sig, &vchSig[0], vchSig.size())) {
+    if (!secp256k1_ecdsa_signature_parse_der(secp256k1_context_static, &sig, &vchSig[0], vchSig.size())) {
         return false;
     }
     /* libsecp256k1's ECDSA verification requires lower-S signatures, which have
      * not historically been enforced in Bitcoin or Zcash, so normalize them first. */
-    secp256k1_ecdsa_signature_normalize(secp256k1_context_verify, &sig, &sig);
-    return secp256k1_ecdsa_verify(secp256k1_context_verify, &sig, hash.begin(), &pubkey);
+    secp256k1_ecdsa_signature_normalize(secp256k1_context_static, &sig, &sig);
+    return secp256k1_ecdsa_verify(secp256k1_context_static, &sig, hash.begin(), &pubkey);
 }
 
 bool CPubKey::RecoverCompact(const uint256 &hash, const std::vector<unsigned char>& vchSig) {
@@ -43,15 +48,15 @@ bool CPubKey::RecoverCompact(const uint256 &hash, const std::vector<unsigned cha
     bool fComp = ((vchSig[0] - 27) & 4) != 0;
     secp256k1_pubkey pubkey;
     secp256k1_ecdsa_recoverable_signature sig;
-    if (!secp256k1_ecdsa_recoverable_signature_parse_compact(secp256k1_context_verify, &sig, &vchSig[1], recid)) {
+    if (!secp256k1_ecdsa_recoverable_signature_parse_compact(secp256k1_context_static, &sig, &vchSig[1], recid)) {
         return false;
     }
-    if (!secp256k1_ecdsa_recover(secp256k1_context_verify, &pubkey, &sig, hash.begin())) {
+    if (!secp256k1_ecdsa_recover(secp256k1_context_static, &pubkey, &sig, hash.begin())) {
         return false;
     }
     unsigned char pub[PUBLIC_KEY_SIZE];
     size_t publen = PUBLIC_KEY_SIZE;
-    secp256k1_ec_pubkey_serialize(secp256k1_context_verify, pub, &publen, &pubkey, fComp ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED);
+    secp256k1_ec_pubkey_serialize(secp256k1_context_static, pub, &publen, &pubkey, fComp ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED);
     Set(pub, pub + publen);
     return true;
 }
@@ -60,19 +65,19 @@ bool CPubKey::IsFullyValid() const {
     if (!IsValid())
         return false;
     secp256k1_pubkey pubkey;
-    return secp256k1_ec_pubkey_parse(secp256k1_context_verify, &pubkey, &(*this)[0], size());
+    return secp256k1_ec_pubkey_parse(secp256k1_context_static, &pubkey, &(*this)[0], size());
 }
 
 bool CPubKey::Decompress() {
     if (!IsValid())
         return false;
     secp256k1_pubkey pubkey;
-    if (!secp256k1_ec_pubkey_parse(secp256k1_context_verify, &pubkey, &(*this)[0], size())) {
+    if (!secp256k1_ec_pubkey_parse(secp256k1_context_static, &pubkey, &(*this)[0], size())) {
         return false;
     }
     unsigned char pub[PUBLIC_KEY_SIZE];
     size_t publen = PUBLIC_KEY_SIZE;
-    secp256k1_ec_pubkey_serialize(secp256k1_context_verify, pub, &publen, &pubkey, SECP256K1_EC_UNCOMPRESSED);
+    secp256k1_ec_pubkey_serialize(secp256k1_context_static, pub, &publen, &pubkey, SECP256K1_EC_UNCOMPRESSED);
     Set(pub, pub + publen);
     return true;
 }
@@ -85,15 +90,15 @@ bool CPubKey::Derive(CPubKey& pubkeyChild, ChainCode &ccChild, unsigned int nChi
     BIP32Hash(cc, nChild, *begin(), begin()+1, out);
     memcpy(ccChild.begin(), out+32, 32);
     secp256k1_pubkey pubkey;
-    if (!secp256k1_ec_pubkey_parse(secp256k1_context_verify, &pubkey, &(*this)[0], size())) {
+    if (!secp256k1_ec_pubkey_parse(secp256k1_context_static, &pubkey, &(*this)[0], size())) {
         return false;
     }
-    if (!secp256k1_ec_pubkey_tweak_add(secp256k1_context_verify, &pubkey, out)) {
+    if (!secp256k1_ec_pubkey_tweak_add(secp256k1_context_static, &pubkey, out)) {
         return false;
     }
     unsigned char pub[COMPRESSED_PUBLIC_KEY_SIZE];
     size_t publen = COMPRESSED_PUBLIC_KEY_SIZE;
-    secp256k1_ec_pubkey_serialize(secp256k1_context_verify, pub, &publen, &pubkey, SECP256K1_EC_COMPRESSED);
+    secp256k1_ec_pubkey_serialize(secp256k1_context_static, pub, &publen, &pubkey, SECP256K1_EC_COMPRESSED);
     pubkeyChild.Set(pub, pub + publen);
     return true;
 }
@@ -138,10 +143,10 @@ bool CExtPubKey::Derive(CExtPubKey &out, unsigned int _nChild) const {
     secp256k1_ecdsa_signature sig;
 
     /* Zcash, unlike Bitcoin, has always enforced strict DER signatures. */
-    if (!secp256k1_ecdsa_signature_parse_der(secp256k1_context_verify, &sig, &vchSig[0], vchSig.size())) {
+    if (!secp256k1_ecdsa_signature_parse_der(secp256k1_context_static, &sig, &vchSig[0], vchSig.size())) {
         return false;
     }
-    return (!secp256k1_ecdsa_signature_normalize(secp256k1_context_verify, NULL, &sig));
+    return (!secp256k1_ecdsa_signature_normalize(secp256k1_context_static, NULL, &sig));
 }
 
 /* static */ std::optional<CChainablePubKey> CChainablePubKey::FromParts(ChainCode chaincode, CPubKey pubkey) {
@@ -151,25 +156,3 @@ bool CExtPubKey::Derive(CExtPubKey &out, unsigned int _nChild) const {
         return std::nullopt;
     }
 }
-
-/* static */ int ECCVerifyHandle::refcount = 0;
-
-ECCVerifyHandle::ECCVerifyHandle()
-{
-    if (refcount == 0) {
-        assert(secp256k1_context_verify == NULL);
-        secp256k1_context_verify = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
-        assert(secp256k1_context_verify != NULL);
-    }
-    refcount++;
-}
-
-ECCVerifyHandle::~ECCVerifyHandle()
-{
-    refcount--;
-    if (refcount == 0) {
-        assert(secp256k1_context_verify != NULL);
-        secp256k1_context_destroy(secp256k1_context_verify);
-        secp256k1_context_verify = NULL;
-    }
-}
diff --git a/src/pubkey.h b/src/pubkey.h
index 3f99095d903..5a0e391bdc6 100644
--- a/src/pubkey.h
+++ b/src/pubkey.h
@@ -304,15 +304,4 @@ struct CExtPubKey {
     }
 };
 
-/** Users of this module must hold an ECCVerifyHandle. The constructor and
- *  destructor of these are not allowed to run in parallel, though. */
-class ECCVerifyHandle
-{
-    static int refcount;
-
-public:
-    ECCVerifyHandle();
-    ~ECCVerifyHandle();
-};
-
 #endif // BITCOIN_PUBKEY_H
diff --git a/src/script/zcash_script.cpp b/src/script/zcash_script.cpp
index e34d2454985..ae3e80484b2 100644
--- a/src/script/zcash_script.cpp
+++ b/src/script/zcash_script.cpp
@@ -64,13 +64,6 @@ inline int set_error(zcash_script_error* ret, zcash_script_error serror)
     return 0;
 }
 
-struct ECCryptoClosure
-{
-    ECCVerifyHandle handle;
-};
-
-ECCryptoClosure instance_of_eccryptoclosure;
-
 // Copy of GetLegacySigOpCount from main.cpp commit c4b2ef7c4.
 // Replace with the copy from src/consensus/tx_verify.{cpp,h} after backporting that refactor.
 unsigned int GetLegacySigOpCount(const CTransaction& tx)
diff --git a/src/secp256k1/.cirrus.yml b/src/secp256k1/.cirrus.yml
index 6d63511e6d3..51e3bc94849 100644
--- a/src/secp256k1/.cirrus.yml
+++ b/src/secp256k1/.cirrus.yml
@@ -1,21 +1,35 @@
 env:
-  WIDEMUL: auto
-  STATICPRECOMPUTATION: yes
+  ### compiler options
+  HOST:
+  # Specific warnings can be disabled with -Wno-error=foo.
+  # -pedantic-errors is not equivalent to -Werror=pedantic and thus not implied by -Werror according to the GCC manual.
+  WERROR_CFLAGS: -Werror -pedantic-errors
+  MAKEFLAGS: -j4
+  BUILD: check
+  ### secp256k1 config
+  ECMULTWINDOW: auto
   ECMULTGENPRECISION: auto
   ASM: no
-  BUILD: check
+  WIDEMUL: auto
   WITH_VALGRIND: yes
   EXTRAFLAGS:
-  HOST:
+  ### secp256k1 modules
+  EXPERIMENTAL: no
   ECDH: no
   RECOVERY: no
   SCHNORRSIG: no
-  EXPERIMENTAL: no
-  CTIMETEST: yes
+  ### test options
+  SECP256K1_TEST_ITERS:
   BENCH: yes
-  TEST_ITERS:
-  BENCH_ITERS: 2
-  MAKEFLAGS: -j2
+  SECP256K1_BENCH_ITERS: 2
+  CTIMETEST: yes
+  # Compile and run the tests
+  EXAMPLES: yes
+
+# https://cirrus-ci.org/pricing/#compute-credits
+credits_snippet: &CREDITS
+  # Don't use any credits for now.
+  use_compute_credits: false
 
 cat_logs_snippet: &CAT_LOGS
   always:
@@ -27,7 +41,6 @@ cat_logs_snippet: &CAT_LOGS
       - cat valgrind_ctime_test.log || true
     cat_bench_log_script:
       - cat bench.log || true
-  on_failure:
     cat_config_log_script:
       - cat config.log || true
     cat_test_env_script:
@@ -43,28 +56,33 @@ merge_base_script_snippet: &MERGE_BASE
     - git config --global user.name "ci"
     - git merge FETCH_HEAD  # Merge base to detect silent merge conflicts
 
-task:
-  name: "x86_64: Linux (Debian stable)"
+linux_container_snippet: &LINUX_CONTAINER
   container:
     dockerfile: ci/linux-debian.Dockerfile
     # Reduce number of CPUs to be able to do more builds in parallel.
     cpu: 1
+    # Gives us more CPUs for free if they're available.
+    greedy: true
     # More than enough for our scripts.
     memory: 1G
+
+task:
+  name: "x86_64: Linux (Debian stable)"
+  << : *LINUX_CONTAINER
   matrix: &ENV_MATRIX
     - env: {WIDEMUL:  int64,  RECOVERY: yes}
-    - env: {WIDEMUL:  int64,                 ECDH: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes}
+    - env: {WIDEMUL:  int64,                 ECDH: yes, SCHNORRSIG: yes}
     - env: {WIDEMUL: int128}
-    - env: {WIDEMUL: int128,  RECOVERY: yes,            EXPERIMENTAL: yes, SCHNORRSIG: yes}
-    - env: {WIDEMUL: int128,                 ECDH: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes}
+    - env: {WIDEMUL: int128_struct}
+    - env: {WIDEMUL: int128,  RECOVERY: yes,            SCHNORRSIG: yes}
+    - env: {WIDEMUL: int128,                 ECDH: yes, SCHNORRSIG: yes}
     - env: {WIDEMUL: int128,  ASM: x86_64}
-    - env: {                  RECOVERY: yes,            EXPERIMENTAL: yes, SCHNORRSIG: yes}
-    - env: {                  STATICPRECOMPUTATION: no}
+    - env: {                  RECOVERY: yes,            SCHNORRSIG: yes}
     - env: {BUILD: distcheck, WITH_VALGRIND: no, CTIMETEST: no, BENCH: no}
     - env: {CPPFLAGS: -DDETERMINISTIC}
     - env: {CFLAGS: -O0, CTIMETEST: no}
-    - env: { ECMULTGENPRECISION: 2 }
-    - env: { ECMULTGENPRECISION: 8 }
+    - env: { ECMULTGENPRECISION: 2, ECMULTWINDOW: 2 }
+    - env: { ECMULTGENPRECISION: 8, ECMULTWINDOW: 4 }
   matrix:
     - env:
         CC: gcc
@@ -77,15 +95,11 @@ task:
 
 task:
   name: "i686: Linux (Debian stable)"
-  container:
-    dockerfile: ci/linux-debian.Dockerfile
-    cpu: 1
-    memory: 1G
+  << : *LINUX_CONTAINER
   env:
     HOST: i686-linux-gnu
     ECDH: yes
     RECOVERY: yes
-    EXPERIMENTAL: yes
     SCHNORRSIG: yes
   matrix:
     - env:
@@ -98,78 +112,43 @@ task:
   << : *CAT_LOGS
 
 task:
-  name: "x86_64: macOS Catalina"
+  name: "arm64: macOS Ventura"
   macos_instance:
-    image: catalina-base
+    image: ghcr.io/cirruslabs/macos-ventura-base:latest
   env:
     HOMEBREW_NO_AUTO_UPDATE: 1
     HOMEBREW_NO_INSTALL_CLEANUP: 1
-    # Cirrus gives us a fixed number of 12 virtual CPUs. Not that we even have that many jobs at the moment...
-    MAKEFLAGS: -j13
+    # Cirrus gives us a fixed number of 4 virtual CPUs. Not that we even have that many jobs at the moment...
+    MAKEFLAGS: -j5
   matrix:
     << : *ENV_MATRIX
+  env:
+    ASM: no
+    WITH_VALGRIND: no
+    CTIMETEST: no
   matrix:
     - env:
-        CC: gcc-9
+        CC: gcc
     - env:
         CC: clang
-  # Update Command Line Tools
-  # Uncomment this if the Command Line Tools on the CirrusCI macOS image are too old to brew valgrind.
-  # See https://apple.stackexchange.com/a/195963 for the implementation.
-  ## update_clt_script:
-  ##   - system_profiler SPSoftwareDataType
-  ##   - touch /tmp/.com.apple.dt.CommandLineTools.installondemand.in-progress
-  ##   - |-
-  ##     PROD=$(softwareupdate -l | grep "*.*Command Line" | tail -n 1 | awk -F"*" '{print $2}' | sed -e 's/^ *//' | sed 's/Label: //g' | tr -d '\n')
-  ##   # For debugging
-  ##   - softwareupdate -l && echo "PROD: $PROD"
-  ##   - softwareupdate -i "$PROD" --verbose
-  ##   - rm /tmp/.com.apple.dt.CommandLineTools.installondemand.in-progress
-  ##
-  brew_valgrind_pre_script:
-    - brew config
-    - brew tap --shallow LouisBrunner/valgrind
-    # Fetch valgrind source but don't build it yet.
-    - brew fetch --HEAD LouisBrunner/valgrind/valgrind
-  brew_valgrind_cache:
-    # This is $(brew --cellar valgrind) but command substition does not work here.
-    folder: /usr/local/Cellar/valgrind
-    # Rebuild cache if ...
-    fingerprint_script:
-      # ... macOS version changes:
-      - sw_vers
-      # ... brew changes:
-      - brew config
-      # ... valgrind changes:
-      - git -C "$(brew --cache)/valgrind--git" rev-parse HEAD
-    populate_script:
-      # If there's no hit in the cache, build and install valgrind.
-      - brew install --HEAD LouisBrunner/valgrind/valgrind
-  brew_valgrind_post_script:
-    # If we have restored valgrind from the cache, tell brew to create symlink to the PATH.
-    # If we haven't restored from cached (and just run brew install), this is a no-op.
-    - brew link valgrind
   brew_script:
-    - brew install automake libtool gcc@9
+    - brew install automake libtool gcc
   << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
+  << : *CREDITS
 
 task:
   name: "s390x (big-endian): Linux (Debian stable, QEMU)"
-  container:
-    dockerfile: ci/linux-debian.Dockerfile
-    cpu: 1
-    memory: 1G
+  << : *LINUX_CONTAINER
   env:
     WRAPPER_CMD: qemu-s390x
-    TEST_ITERS: 16
+    SECP256K1_TEST_ITERS: 16
     HOST: s390x-linux-gnu
     WITH_VALGRIND: no
     ECDH: yes
     RECOVERY: yes
-    EXPERIMENTAL: yes
     SCHNORRSIG: yes
     CTIMETEST: no
   << : *MERGE_BASE
@@ -181,23 +160,19 @@ task:
 
 task:
   name: "ARM32: Linux (Debian stable, QEMU)"
-  container:
-    dockerfile: ci/linux-debian.Dockerfile
-    cpu: 1
-    memory: 1G
+  << : *LINUX_CONTAINER
   env:
     WRAPPER_CMD: qemu-arm
-    TEST_ITERS: 16
+    SECP256K1_TEST_ITERS: 16
     HOST: arm-linux-gnueabihf
     WITH_VALGRIND: no
     ECDH: yes
     RECOVERY: yes
-    EXPERIMENTAL: yes
     SCHNORRSIG: yes
     CTIMETEST: no
   matrix:
     - env: {}
-    - env: {ASM: arm}
+    - env: {EXPERIMENTAL: yes, ASM: arm}
   << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
@@ -205,18 +180,14 @@ task:
 
 task:
   name: "ARM64: Linux (Debian stable, QEMU)"
-  container:
-    dockerfile: ci/linux-debian.Dockerfile
-    cpu: 1
-    memory: 1G
+  << : *LINUX_CONTAINER
   env:
     WRAPPER_CMD: qemu-aarch64
-    TEST_ITERS: 16
+    SECP256K1_TEST_ITERS: 16
     HOST: aarch64-linux-gnu
     WITH_VALGRIND: no
     ECDH: yes
     RECOVERY: yes
-    EXPERIMENTAL: yes
     SCHNORRSIG: yes
     CTIMETEST: no
   << : *MERGE_BASE
@@ -226,18 +197,14 @@ task:
 
 task:
   name: "ppc64le: Linux (Debian stable, QEMU)"
-  container:
-    dockerfile: ci/linux-debian.Dockerfile
-    cpu: 1
-    memory: 1G
+  << : *LINUX_CONTAINER
   env:
     WRAPPER_CMD: qemu-ppc64le
-    TEST_ITERS: 16
+    SECP256K1_TEST_ITERS: 16
     HOST: powerpc64le-linux-gnu
     WITH_VALGRIND: no
     ECDH: yes
     RECOVERY: yes
-    EXPERIMENTAL: yes
     SCHNORRSIG: yes
     CTIMETEST: no
   << : *MERGE_BASE
@@ -246,21 +213,63 @@ task:
   << : *CAT_LOGS
 
 task:
-  name: "x86_64 (mingw32-w64): Windows (Debian stable, Wine)"
-  container:
-    dockerfile: ci/linux-debian.Dockerfile
-    cpu: 1
-    memory: 1G
+  << : *LINUX_CONTAINER
   env:
-    WRAPPER_CMD: wine64-stable
-    TEST_ITERS: 16
-    HOST: x86_64-w64-mingw32
+    WRAPPER_CMD: wine
+    WITH_VALGRIND: no
+    ECDH: yes
+    RECOVERY: yes
+    SCHNORRSIG: yes
+    CTIMETEST: no
+  matrix:
+    - name: "x86_64 (mingw32-w64): Windows (Debian stable, Wine)"
+      env:
+        HOST: x86_64-w64-mingw32
+    - name: "i686 (mingw32-w64): Windows (Debian stable, Wine)"
+      env:
+        HOST: i686-w64-mingw32
+  << : *MERGE_BASE
+  test_script:
+    - ./ci/cirrus.sh
+  << : *CAT_LOGS
+
+task:
+  << : *LINUX_CONTAINER
+  env:
+    WRAPPER_CMD: wine
+    WERROR_CFLAGS: -WX
     WITH_VALGRIND: no
     ECDH: yes
     RECOVERY: yes
     EXPERIMENTAL: yes
     SCHNORRSIG: yes
     CTIMETEST: no
+    # Use a MinGW-w64 host to tell ./configure we're building for Windows.
+    # This will detect some MinGW-w64 tools but then make will need only
+    # the MSVC tools CC, AR and NM as specified below.
+    HOST: x86_64-w64-mingw32
+    CC: /opt/msvc/bin/x64/cl
+    AR: /opt/msvc/bin/x64/lib
+    NM: /opt/msvc/bin/x64/dumpbin -symbols -headers
+    # Set non-essential options that affect the CLI messages here.
+    # (They depend on the user's taste, so we don't want to set them automatically in configure.ac.)
+    CFLAGS: -nologo -diagnostics:caret
+    LDFLAGS: -XCClinker -nologo -XCClinker -diagnostics:caret
+  matrix:
+    - name: "x86_64 (MSVC): Windows (Debian stable, Wine)"
+    - name: "x86_64 (MSVC): Windows (Debian stable, Wine, int128_struct)"
+      env:
+        WIDEMUL: int128_struct
+    - name: "x86_64 (MSVC): Windows (Debian stable, Wine, int128_struct with __(u)mulh)"
+      env:
+        WIDEMUL: int128_struct
+        CPPFLAGS: -DSECP256K1_MSVC_MULH_TEST_OVERRIDE
+    - name: "i686 (MSVC): Windows (Debian stable, Wine)"
+      env:
+        HOST: i686-w64-mingw32
+        CC: /opt/msvc/bin/x86/cl
+        AR: /opt/msvc/bin/x86/lib
+        NM: /opt/msvc/bin/x86/dumpbin -symbols -headers
   << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
@@ -268,40 +277,37 @@ task:
 
 # Sanitizers
 task:
-  container:
-    dockerfile: ci/linux-debian.Dockerfile
-    cpu: 1
-    memory: 1G
+  << : *LINUX_CONTAINER
   env:
     ECDH: yes
     RECOVERY: yes
-    EXPERIMENTAL: yes
     SCHNORRSIG: yes
     CTIMETEST: no
-    EXTRAFLAGS: "--disable-openssl-tests"
   matrix:
     - name: "Valgrind (memcheck)"
+      container:
+        cpu: 2
       env:
         # The `--error-exitcode` is required to make the test fail if valgrind found errors, otherwise it'll return 0 (https://www.valgrind.org/docs/manual/manual-core.html)
         WRAPPER_CMD: "valgrind --error-exitcode=42"
-        TEST_ITERS: 16
+        SECP256K1_TEST_ITERS: 2
     - name: "UBSan, ASan, LSan"
+      container:
+        memory: 2G
       env:
-        CFLAGS: "-fsanitize=undefined,address"
-        CFLAGS_FOR_BUILD: "-fsanitize=undefined,address"
+        CFLAGS: "-fsanitize=undefined,address -g"
         UBSAN_OPTIONS: "print_stacktrace=1:halt_on_error=1"
         ASAN_OPTIONS: "strict_string_checks=1:detect_stack_use_after_return=1:detect_leaks=1"
         LSAN_OPTIONS: "use_unaligned=1"
-        TEST_ITERS: 32
+        SECP256K1_TEST_ITERS: 32
   # Try to cover many configurations with just a tiny matrix.
   matrix:
     - env:
         ASM: auto
-        STATICPRECOMPUTATION: yes
     - env:
         ASM: no
-        STATICPRECOMPUTATION: no
         ECMULTGENPRECISION: 2
+        ECMULTWINDOW: 2
   matrix:
     - env:
         CC: clang
@@ -313,3 +319,59 @@ task:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
 
+# Memory sanitizers
+task:
+  << : *LINUX_CONTAINER
+  name: "MSan"
+  env:
+    ECDH: yes
+    RECOVERY: yes
+    SCHNORRSIG: yes
+    CTIMETEST: no
+    CC: clang
+    SECP256K1_TEST_ITERS: 32
+    ASM: no
+  container:
+    memory: 2G
+  matrix:
+    - env:
+        CFLAGS: "-fsanitize=memory -g"
+    - env:
+        ECMULTGENPRECISION: 2
+        ECMULTWINDOW: 2
+        CFLAGS: "-fsanitize=memory -g -O3"
+  << : *MERGE_BASE
+  test_script:
+    - ./ci/cirrus.sh
+  << : *CAT_LOGS
+
+task:
+  name: "C++ -fpermissive (entire project)"
+  << : *LINUX_CONTAINER
+  env:
+    CC: g++
+    CFLAGS: -fpermissive -g
+    CPPFLAGS: -DSECP256K1_CPLUSPLUS_TEST_OVERRIDE
+    WERROR_CFLAGS:
+    ECDH: yes
+    RECOVERY: yes
+    SCHNORRSIG: yes
+  << : *MERGE_BASE
+  test_script:
+    - ./ci/cirrus.sh
+  << : *CAT_LOGS
+
+task:
+  name: "C++ (public headers)"
+  << : *LINUX_CONTAINER
+  test_script:
+    - g++ -Werror include/*.h
+    - clang -Werror -x c++-header include/*.h
+    - /opt/msvc/bin/x64/cl.exe -c -WX -TP include/*.h
+
+task:
+  name: "sage prover"
+  << : *LINUX_CONTAINER
+  test_script:
+    - cd sage
+    - sage prove_group_implementations.sage
diff --git a/src/secp256k1/.gitattributes b/src/secp256k1/.gitattributes
new file mode 100644
index 00000000000..30efb2244fe
--- /dev/null
+++ b/src/secp256k1/.gitattributes
@@ -0,0 +1,2 @@
+src/precomputed_ecmult.c linguist-generated
+src/precomputed_ecmult_gen.c linguist-generated
diff --git a/src/secp256k1/.gitignore b/src/secp256k1/.gitignore
index b62055a39bc..80c646b7719 100644
--- a/src/secp256k1/.gitignore
+++ b/src/secp256k1/.gitignore
@@ -1,19 +1,21 @@
-bench_inv
-bench_ecdh
+bench
 bench_ecmult
-bench_schnorrsig
-bench_sign
-bench_verify
-bench_recover
 bench_internal
 tests
 exhaustive_tests
-gen_context
+precompute_ecmult_gen
+precompute_ecmult
 valgrind_ctime_test
+ecdh_example
+ecdsa_example
+schnorr_example
 *.exe
 *.so
 *.a
-!.gitignore
+*.csv
+*.log
+*.trs
+*.sage.py
 
 Makefile
 configure
@@ -23,6 +25,7 @@ aclocal.m4
 autom4te.cache/
 config.log
 config.status
+conftest*
 *.tar.gz
 *.la
 libtool
@@ -31,8 +34,6 @@ libtool
 *.lo
 *.o
 *~
-*.log
-*.trs
 
 coverage/
 coverage.html
@@ -43,7 +44,7 @@ coverage.*.html
 
 src/libsecp256k1-config.h
 src/libsecp256k1-config.h.in
-src/ecmult_static_context.h
+build-aux/ar-lib
 build-aux/config.guess
 build-aux/config.sub
 build-aux/depcomp
diff --git a/src/secp256k1/CHANGELOG.md b/src/secp256k1/CHANGELOG.md
new file mode 100644
index 00000000000..74434834233
--- /dev/null
+++ b/src/secp256k1/CHANGELOG.md
@@ -0,0 +1,28 @@
+# Changelog
+
+The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/).
+
+## [Unreleased]
+
+## [0.2.0] - 2022-12-12
+
+### Added
+ - Added `secp256k1_selftest`, to be used in conjunction with `secp256k1_context_static`.
+
+### Changed
+ - Enabled modules schnorrsig, extrakeys and ECDH by default in `./configure`.
+
+### Deprecated
+ - Deprecated context flags `SECP256K1_CONTEXT_VERIFY` and `SECP256K1_CONTEXT_SIGN`. Use `SECP256K1_CONTEXT_NONE` instead.
+ - Renamed `secp256k1_context_no_precomp` to `secp256k1_context_static`.
+
+### ABI Compatibility
+
+Since this is the first release, we do not compare application binary interfaces.
+However, there are unreleased versions of libsecp256k1 that are *not* ABI compatible with this version.
+
+## [0.1.0] - 2013-03-05 to 2021-12-25
+
+This version was in fact never released.
+The number was given by the build system since the introduction of autotools in Jan 2014 (ea0fe5a5bf0c04f9cc955b2966b614f5f378c6f6).
+Therefore, this version number does not uniquely identify a set of source files.
diff --git a/src/secp256k1/Makefile.am b/src/secp256k1/Makefile.am
index 23b29281df8..ad50504f7e5 100644
--- a/src/secp256k1/Makefile.am
+++ b/src/secp256k1/Makefile.am
@@ -1,5 +1,11 @@
+.PHONY: clean-precomp precomp
+
 ACLOCAL_AMFLAGS = -I build-aux/m4
 
+# AM_CFLAGS will be automatically prepended to CFLAGS by Automake when compiling some foo
+# which does not have an explicit foo_CFLAGS variable set.
+AM_CFLAGS = $(SECP_CFLAGS)
+
 lib_LTLIBRARIES = libsecp256k1.la
 include_HEADERS = include/secp256k1.h
 include_HEADERS += include/secp256k1_preallocated.h
@@ -20,10 +26,14 @@ noinst_HEADERS += src/eckey.h
 noinst_HEADERS += src/eckey_impl.h
 noinst_HEADERS += src/ecmult.h
 noinst_HEADERS += src/ecmult_impl.h
+noinst_HEADERS += src/ecmult_compute_table.h
+noinst_HEADERS += src/ecmult_compute_table_impl.h
 noinst_HEADERS += src/ecmult_const.h
 noinst_HEADERS += src/ecmult_const_impl.h
 noinst_HEADERS += src/ecmult_gen.h
 noinst_HEADERS += src/ecmult_gen_impl.h
+noinst_HEADERS += src/ecmult_gen_compute_table.h
+noinst_HEADERS += src/ecmult_gen_compute_table_impl.h
 noinst_HEADERS += src/field_10x26.h
 noinst_HEADERS += src/field_10x26_impl.h
 noinst_HEADERS += src/field_5x52.h
@@ -34,8 +44,16 @@ noinst_HEADERS += src/modinv32.h
 noinst_HEADERS += src/modinv32_impl.h
 noinst_HEADERS += src/modinv64.h
 noinst_HEADERS += src/modinv64_impl.h
+noinst_HEADERS += src/precomputed_ecmult.h
+noinst_HEADERS += src/precomputed_ecmult_gen.h
 noinst_HEADERS += src/assumptions.h
 noinst_HEADERS += src/util.h
+noinst_HEADERS += src/int128.h
+noinst_HEADERS += src/int128_impl.h
+noinst_HEADERS += src/int128_native.h
+noinst_HEADERS += src/int128_native_impl.h
+noinst_HEADERS += src/int128_struct.h
+noinst_HEADERS += src/int128_struct_impl.h
 noinst_HEADERS += src/scratch.h
 noinst_HEADERS += src/scratch_impl.h
 noinst_HEADERS += src/selftest.h
@@ -50,13 +68,19 @@ noinst_HEADERS += contrib/lax_der_parsing.h
 noinst_HEADERS += contrib/lax_der_parsing.c
 noinst_HEADERS += contrib/lax_der_privatekey_parsing.h
 noinst_HEADERS += contrib/lax_der_privatekey_parsing.c
+noinst_HEADERS += examples/random.h
+
+PRECOMPUTED_LIB = libsecp256k1_precomputed.la
+noinst_LTLIBRARIES = $(PRECOMPUTED_LIB)
+libsecp256k1_precomputed_la_SOURCES =  src/precomputed_ecmult.c src/precomputed_ecmult_gen.c
+libsecp256k1_precomputed_la_CPPFLAGS = $(SECP_INCLUDES)
 
 if USE_EXTERNAL_ASM
 COMMON_LIB = libsecp256k1_common.la
-noinst_LTLIBRARIES = $(COMMON_LIB)
 else
 COMMON_LIB =
 endif
+noinst_LTLIBRARIES += $(COMMON_LIB)
 
 pkgconfigdir = $(libdir)/pkgconfig
 pkgconfig_DATA = libsecp256k1.pc
@@ -68,8 +92,9 @@ endif
 endif
 
 libsecp256k1_la_SOURCES = src/secp256k1.c
-libsecp256k1_la_CPPFLAGS = -I$(top_srcdir)/include -I$(top_srcdir)/src $(SECP_INCLUDES)
-libsecp256k1_la_LIBADD = $(SECP_LIBS) $(COMMON_LIB)
+libsecp256k1_la_CPPFLAGS = $(SECP_INCLUDES)
+libsecp256k1_la_LIBADD = $(SECP_LIBS) $(COMMON_LIB) $(PRECOMPUTED_LIB)
+libsecp256k1_la_LDFLAGS = -no-undefined -version-info $(LIB_VERSION_CURRENT):$(LIB_VERSION_REVISION):$(LIB_VERSION_AGE)
 
 if VALGRIND_ENABLED
 libsecp256k1_la_CPPFLAGS += -DVALGRIND
@@ -77,18 +102,14 @@ endif
 
 noinst_PROGRAMS =
 if USE_BENCHMARK
-noinst_PROGRAMS += bench_verify bench_sign bench_internal bench_ecmult
-bench_verify_SOURCES = src/bench_verify.c
-bench_verify_LDADD = libsecp256k1.la $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
-# SECP_TEST_INCLUDES are only used here for CRYPTO_CPPFLAGS
-bench_verify_CPPFLAGS = $(SECP_TEST_INCLUDES)
-bench_sign_SOURCES = src/bench_sign.c
-bench_sign_LDADD = libsecp256k1.la $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
+noinst_PROGRAMS += bench bench_internal bench_ecmult
+bench_SOURCES = src/bench.c
+bench_LDADD = libsecp256k1.la $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
 bench_internal_SOURCES = src/bench_internal.c
-bench_internal_LDADD = $(SECP_LIBS) $(COMMON_LIB)
+bench_internal_LDADD = $(SECP_LIBS) $(COMMON_LIB) $(PRECOMPUTED_LIB)
 bench_internal_CPPFLAGS = $(SECP_INCLUDES)
 bench_ecmult_SOURCES = src/bench_ecmult.c
-bench_ecmult_LDADD = $(SECP_LIBS) $(COMMON_LIB)
+bench_ecmult_LDADD = $(SECP_LIBS) $(COMMON_LIB) $(PRECOMPUTED_LIB)
 bench_ecmult_CPPFLAGS = $(SECP_INCLUDES)
 endif
 
@@ -96,7 +117,7 @@ TESTS =
 if USE_TESTS
 noinst_PROGRAMS += tests
 tests_SOURCES = src/tests.c
-tests_CPPFLAGS = -I$(top_srcdir)/src -I$(top_srcdir)/include $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
+tests_CPPFLAGS = $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
 if VALGRIND_ENABLED
 tests_CPPFLAGS += -DVALGRIND
 noinst_PROGRAMS += valgrind_ctime_test
@@ -106,7 +127,7 @@ endif
 if !ENABLE_COVERAGE
 tests_CPPFLAGS += -DVERIFY
 endif
-tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
+tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB) $(PRECOMPUTED_LIB)
 tests_LDFLAGS = -static
 TESTS += tests
 endif
@@ -114,38 +135,96 @@ endif
 if USE_EXHAUSTIVE_TESTS
 noinst_PROGRAMS += exhaustive_tests
 exhaustive_tests_SOURCES = src/tests_exhaustive.c
-exhaustive_tests_CPPFLAGS = -I$(top_srcdir)/src $(SECP_INCLUDES)
+exhaustive_tests_CPPFLAGS = $(SECP_INCLUDES)
 if !ENABLE_COVERAGE
 exhaustive_tests_CPPFLAGS += -DVERIFY
 endif
+# Note: do not include $(PRECOMPUTED_LIB) in exhaustive_tests (it uses runtime-generated tables).
 exhaustive_tests_LDADD = $(SECP_LIBS) $(COMMON_LIB)
 exhaustive_tests_LDFLAGS = -static
 TESTS += exhaustive_tests
 endif
 
-if USE_ECMULT_STATIC_PRECOMPUTATION
-CPPFLAGS_FOR_BUILD +=-I$(top_srcdir) -I$(builddir)/src
-
-gen_context_OBJECTS = gen_context.o
-gen_context_BIN = gen_context$(BUILD_EXEEXT)
-gen_%.o: src/gen_%.c src/libsecp256k1-config.h
-	$(CC_FOR_BUILD) $(DEFS) $(CPPFLAGS_FOR_BUILD) $(CFLAGS_FOR_BUILD) -c $< -o $@
-
-$(gen_context_BIN): $(gen_context_OBJECTS)
-	$(CC_FOR_BUILD) $(CFLAGS_FOR_BUILD) $(LDFLAGS_FOR_BUILD) $^ -o $@
-
-$(libsecp256k1_la_OBJECTS): src/ecmult_static_context.h
-$(tests_OBJECTS): src/ecmult_static_context.h
-$(bench_internal_OBJECTS): src/ecmult_static_context.h
-$(bench_ecmult_OBJECTS): src/ecmult_static_context.h
-
-src/ecmult_static_context.h: $(gen_context_BIN)
-	./$(gen_context_BIN)
-
-CLEANFILES = $(gen_context_BIN) src/ecmult_static_context.h
+if USE_EXAMPLES
+noinst_PROGRAMS += ecdsa_example
+ecdsa_example_SOURCES = examples/ecdsa.c
+ecdsa_example_CPPFLAGS = -I$(top_srcdir)/include
+ecdsa_example_LDADD = libsecp256k1.la
+ecdsa_example_LDFLAGS = -static
+if BUILD_WINDOWS
+ecdsa_example_LDFLAGS += -lbcrypt
+endif
+TESTS += ecdsa_example
+if ENABLE_MODULE_ECDH
+noinst_PROGRAMS += ecdh_example
+ecdh_example_SOURCES = examples/ecdh.c
+ecdh_example_CPPFLAGS = -I$(top_srcdir)/include
+ecdh_example_LDADD = libsecp256k1.la
+ecdh_example_LDFLAGS = -static
+if BUILD_WINDOWS
+ecdh_example_LDFLAGS += -lbcrypt
+endif
+TESTS += ecdh_example
+endif
+if ENABLE_MODULE_SCHNORRSIG
+noinst_PROGRAMS += schnorr_example
+schnorr_example_SOURCES = examples/schnorr.c
+schnorr_example_CPPFLAGS = -I$(top_srcdir)/include
+schnorr_example_LDADD = libsecp256k1.la
+schnorr_example_LDFLAGS = -static
+if BUILD_WINDOWS
+schnorr_example_LDFLAGS += -lbcrypt
+endif
+TESTS += schnorr_example
+endif
 endif
 
-EXTRA_DIST = autogen.sh src/gen_context.c src/basic-config.h
+### Precomputed tables
+EXTRA_PROGRAMS = precompute_ecmult precompute_ecmult_gen
+CLEANFILES = $(EXTRA_PROGRAMS)
+
+precompute_ecmult_SOURCES = src/precompute_ecmult.c
+precompute_ecmult_CPPFLAGS = $(SECP_INCLUDES)
+precompute_ecmult_LDADD = $(SECP_LIBS) $(COMMON_LIB)
+
+precompute_ecmult_gen_SOURCES = src/precompute_ecmult_gen.c
+precompute_ecmult_gen_CPPFLAGS = $(SECP_INCLUDES)
+precompute_ecmult_gen_LDADD = $(SECP_LIBS) $(COMMON_LIB)
+
+# See Automake manual, Section "Errors with distclean".
+# We don't list any dependencies for the prebuilt files here because
+# otherwise make's decision whether to rebuild them (even in the first
+# build by a normal user) depends on mtimes, and thus is very fragile.
+# This means that rebuilds of the prebuilt files always need to be
+# forced by deleting them, e.g., by invoking `make clean-precomp`.
+src/precomputed_ecmult.c:
+	$(MAKE) $(AM_MAKEFLAGS) precompute_ecmult$(EXEEXT)
+	./precompute_ecmult$(EXEEXT)
+src/precomputed_ecmult_gen.c:
+	$(MAKE) $(AM_MAKEFLAGS) precompute_ecmult_gen$(EXEEXT)
+	./precompute_ecmult_gen$(EXEEXT)
+
+PRECOMP = src/precomputed_ecmult_gen.c src/precomputed_ecmult.c
+precomp: $(PRECOMP)
+
+# Ensure the prebuilt files will be build first (only if they don't exist,
+# e.g., after `make maintainer-clean`).
+BUILT_SOURCES = $(PRECOMP)
+
+maintainer-clean-local: clean-precomp
+
+clean-precomp:
+	rm -f $(PRECOMP)
+
+EXTRA_DIST = autogen.sh CHANGELOG.md SECURITY.md
+EXTRA_DIST += doc/release-process.md doc/safegcd_implementation.md
+EXTRA_DIST += examples/EXAMPLES_COPYING
+EXTRA_DIST += sage/gen_exhaustive_groups.sage
+EXTRA_DIST += sage/gen_split_lambda_constants.sage
+EXTRA_DIST += sage/group_prover.sage
+EXTRA_DIST += sage/prove_group_implementations.sage
+EXTRA_DIST += sage/secp256k1_params.sage
+EXTRA_DIST += sage/weierstrass_prover.sage
 
 if ENABLE_MODULE_ECDH
 include src/modules/ecdh/Makefile.am.include
diff --git a/src/secp256k1/README.md b/src/secp256k1/README.md
index a7eb2b0e894..ffdc9aeaee5 100644
--- a/src/secp256k1/README.md
+++ b/src/secp256k1/README.md
@@ -2,6 +2,8 @@ libsecp256k1
 ============
 
 [![Build Status](https://api.cirrus-ci.com/github/bitcoin-core/secp256k1.svg?branch=master)](https://cirrus-ci.com/github/bitcoin-core/secp256k1)
+![Dependencies: None](https://img.shields.io/badge/dependencies-none-success)
+[![irc.libera.chat #secp256k1](https://img.shields.io/badge/irc.libera.chat-%23secp256k1-success)](https://web.libera.chat/#secp256k1)
 
 Optimized C library for ECDSA signatures and secret/public key operations on curve secp256k1.
 
@@ -15,10 +17,10 @@ Features:
 * Derandomized ECDSA (via RFC6979 or with a caller provided function.)
 * Very efficient implementation.
 * Suitable for embedded systems.
+* No runtime dependencies.
 * Optional module for public key recovery.
 * Optional module for ECDH key exchange.
-
-Experimental features have not received enough scrutiny to satisfy the standard of quality of this library but are made available for testing and review by the community. The APIs of these features should not be considered stable.
+* Optional module for Schnorr signatures according to [BIP-340](https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki).
 
 Implementation details
 ----------------------
@@ -34,6 +36,7 @@ Implementation details
   * Optimized implementation of arithmetic modulo the curve's field size (2^256 - 0x1000003D1).
     * Using 5 52-bit limbs (including hand-optimized assembly for x86_64, by Diederik Huys).
     * Using 10 26-bit limbs (including hand-optimized assembly for 32-bit ARM, by Wladimir J. van der Laan).
+      * This is an experimental feature that has not received enough scrutiny to satisfy the standard of quality of this library but is made available for testing and review by the community.
 * Scalar operations
   * Optimized implementation without data-dependent branches of arithmetic modulo the curve's order.
     * Using 4 64-bit limbs (relying on __int128 support in the compiler).
@@ -65,17 +68,19 @@ libsecp256k1 is built using autotools:
     $ ./autogen.sh
     $ ./configure
     $ make
-    $ make check
+    $ make check  # run the test suite
     $ sudo make install  # optional
 
-Exhaustive tests
------------
-
-    $ ./exhaustive_tests
+To compile optional modules (such as Schnorr signatures), you need to run `./configure` with additional flags (such as `--enable-module-schnorrsig`). Run `./configure --help` to see the full list of available flags.
 
-With valgrind, you might need to increase the max stack size:
+Usage examples
+-----------
+Usage examples can be found in the [examples](examples) directory. To compile them you need to configure with `--enable-examples`.
+  * [ECDSA example](examples/ecdsa.c)
+  * [Schnorr signatures example](examples/schnorr.c)
+  * [Deriving a shared secret (ECDH) example](examples/ecdh.c)
 
-    $ valgrind --max-stackframe=2500000 ./exhaustive_tests
+To compile the Schnorr signature and ECDH examples, you also need to configure with `--enable-module-schnorrsig` and `--enable-module-ecdh`.
 
 Test coverage
 -----------
@@ -99,6 +104,18 @@ To create a HTML report with coloured and annotated source code:
     $ mkdir -p coverage
     $ gcovr --exclude 'src/bench*' --html --html-details -o coverage/coverage.html
 
+Benchmark
+------------
+If configured with `--enable-benchmark` (which is the default), binaries for benchmarking the libsecp256k1 functions will be present in the root directory after the build.
+
+To print the benchmark result to the command line:
+
+    $ ./bench_name
+
+To create a CSV file for the benchmark result :
+
+    $ ./bench_name | sed '2d;s/ \{1,\}//g' > bench_name.csv
+
 Reporting a vulnerability
 ------------
 
diff --git a/src/secp256k1/SECURITY.md b/src/secp256k1/SECURITY.md
index 0e4d5880302..b515cc1c8e2 100644
--- a/src/secp256k1/SECURITY.md
+++ b/src/secp256k1/SECURITY.md
@@ -9,7 +9,7 @@ The following keys may be used to communicate sensitive information to developer
 | Name | Fingerprint |
 |------|-------------|
 | Pieter Wuille | 133E AC17 9436 F14A 5CF1  B794 860F EB80 4E66 9320 |
-| Andrew Poelstra | 699A 63EF C17A D3A9 A34C  FFC0 7AD0 A91C 40BD 0091 |
+| Jonas Nick | 36C7 1A37 C9D9 88BD E825  08D9 B1A7 0E4F 8DCD 0366 |
 | Tim Ruffing | 09E0 3F87 1092 E40E 106E  902B 33BC 86AB 80FF 5516 |
 
-You can import a key by running the following command with that individual’s fingerprint: `gpg --recv-keys "<fingerprint>"` Ensure that you put quotes around fingerprints containing spaces.
+You can import a key by running the following command with that individual’s fingerprint: `gpg --keyserver hkps://keys.openpgp.org --recv-keys "<fingerprint>"` Ensure that you put quotes around fingerprints containing spaces.
diff --git a/src/secp256k1/build-aux/m4/ax_prog_cc_for_build.m4 b/src/secp256k1/build-aux/m4/ax_prog_cc_for_build.m4
deleted file mode 100644
index 7bcbf3200cf..00000000000
--- a/src/secp256k1/build-aux/m4/ax_prog_cc_for_build.m4
+++ /dev/null
@@ -1,125 +0,0 @@
-# ===========================================================================
-#   https://www.gnu.org/software/autoconf-archive/ax_prog_cc_for_build.html
-# ===========================================================================
-#
-# SYNOPSIS
-#
-#   AX_PROG_CC_FOR_BUILD
-#
-# DESCRIPTION
-#
-#   This macro searches for a C compiler that generates native executables,
-#   that is a C compiler that surely is not a cross-compiler. This can be
-#   useful if you have to generate source code at compile-time like for
-#   example GCC does.
-#
-#   The macro sets the CC_FOR_BUILD and CPP_FOR_BUILD macros to anything
-#   needed to compile or link (CC_FOR_BUILD) and preprocess (CPP_FOR_BUILD).
-#   The value of these variables can be overridden by the user by specifying
-#   a compiler with an environment variable (like you do for standard CC).
-#
-#   It also sets BUILD_EXEEXT and BUILD_OBJEXT to the executable and object
-#   file extensions for the build platform, and GCC_FOR_BUILD to `yes' if
-#   the compiler we found is GCC. All these variables but GCC_FOR_BUILD are
-#   substituted in the Makefile.
-#
-# LICENSE
-#
-#   Copyright (c) 2008 Paolo Bonzini <bonzini@gnu.org>
-#
-#   Copying and distribution of this file, with or without modification, are
-#   permitted in any medium without royalty provided the copyright notice
-#   and this notice are preserved. This file is offered as-is, without any
-#   warranty.
-
-#serial 8
-
-AU_ALIAS([AC_PROG_CC_FOR_BUILD], [AX_PROG_CC_FOR_BUILD])
-AC_DEFUN([AX_PROG_CC_FOR_BUILD], [dnl
-AC_REQUIRE([AC_PROG_CC])dnl
-AC_REQUIRE([AC_PROG_CPP])dnl
-AC_REQUIRE([AC_EXEEXT])dnl
-AC_REQUIRE([AC_CANONICAL_HOST])dnl
-
-dnl Use the standard macros, but make them use other variable names
-dnl
-pushdef([ac_cv_prog_CPP], ac_cv_build_prog_CPP)dnl
-pushdef([ac_cv_prog_gcc], ac_cv_build_prog_gcc)dnl
-pushdef([ac_cv_prog_cc_works], ac_cv_build_prog_cc_works)dnl
-pushdef([ac_cv_prog_cc_cross], ac_cv_build_prog_cc_cross)dnl
-pushdef([ac_cv_prog_cc_g], ac_cv_build_prog_cc_g)dnl
-pushdef([ac_cv_exeext], ac_cv_build_exeext)dnl
-pushdef([ac_cv_objext], ac_cv_build_objext)dnl
-pushdef([ac_exeext], ac_build_exeext)dnl
-pushdef([ac_objext], ac_build_objext)dnl
-pushdef([CC], CC_FOR_BUILD)dnl
-pushdef([CPP], CPP_FOR_BUILD)dnl
-pushdef([CFLAGS], CFLAGS_FOR_BUILD)dnl
-pushdef([CPPFLAGS], CPPFLAGS_FOR_BUILD)dnl
-pushdef([LDFLAGS], LDFLAGS_FOR_BUILD)dnl
-pushdef([host], build)dnl
-pushdef([host_alias], build_alias)dnl
-pushdef([host_cpu], build_cpu)dnl
-pushdef([host_vendor], build_vendor)dnl
-pushdef([host_os], build_os)dnl
-pushdef([ac_cv_host], ac_cv_build)dnl
-pushdef([ac_cv_host_alias], ac_cv_build_alias)dnl
-pushdef([ac_cv_host_cpu], ac_cv_build_cpu)dnl
-pushdef([ac_cv_host_vendor], ac_cv_build_vendor)dnl
-pushdef([ac_cv_host_os], ac_cv_build_os)dnl
-pushdef([ac_cpp], ac_build_cpp)dnl
-pushdef([ac_compile], ac_build_compile)dnl
-pushdef([ac_link], ac_build_link)dnl
-
-save_cross_compiling=$cross_compiling
-save_ac_tool_prefix=$ac_tool_prefix
-cross_compiling=no
-ac_tool_prefix=
-
-AC_PROG_CC
-AC_PROG_CPP
-AC_EXEEXT
-
-ac_tool_prefix=$save_ac_tool_prefix
-cross_compiling=$save_cross_compiling
-
-dnl Restore the old definitions
-dnl
-popdef([ac_link])dnl
-popdef([ac_compile])dnl
-popdef([ac_cpp])dnl
-popdef([ac_cv_host_os])dnl
-popdef([ac_cv_host_vendor])dnl
-popdef([ac_cv_host_cpu])dnl
-popdef([ac_cv_host_alias])dnl
-popdef([ac_cv_host])dnl
-popdef([host_os])dnl
-popdef([host_vendor])dnl
-popdef([host_cpu])dnl
-popdef([host_alias])dnl
-popdef([host])dnl
-popdef([LDFLAGS])dnl
-popdef([CPPFLAGS])dnl
-popdef([CFLAGS])dnl
-popdef([CPP])dnl
-popdef([CC])dnl
-popdef([ac_objext])dnl
-popdef([ac_exeext])dnl
-popdef([ac_cv_objext])dnl
-popdef([ac_cv_exeext])dnl
-popdef([ac_cv_prog_cc_g])dnl
-popdef([ac_cv_prog_cc_cross])dnl
-popdef([ac_cv_prog_cc_works])dnl
-popdef([ac_cv_prog_gcc])dnl
-popdef([ac_cv_prog_CPP])dnl
-
-dnl Finally, set Makefile variables
-dnl
-BUILD_EXEEXT=$ac_build_exeext
-BUILD_OBJEXT=$ac_build_objext
-AC_SUBST(BUILD_EXEEXT)dnl
-AC_SUBST(BUILD_OBJEXT)dnl
-AC_SUBST([CFLAGS_FOR_BUILD])dnl
-AC_SUBST([CPPFLAGS_FOR_BUILD])dnl
-AC_SUBST([LDFLAGS_FOR_BUILD])dnl
-])
diff --git a/src/secp256k1/build-aux/m4/bitcoin_secp.m4 b/src/secp256k1/build-aux/m4/bitcoin_secp.m4
index e57888ca189..98be915b67a 100644
--- a/src/secp256k1/build-aux/m4/bitcoin_secp.m4
+++ b/src/secp256k1/build-aux/m4/bitcoin_secp.m4
@@ -1,7 +1,7 @@
 dnl escape "$0x" below using the m4 quadrigaph @S|@, and escape it again with a \ for the shell.
 AC_DEFUN([SECP_64BIT_ASM_CHECK],[
 AC_MSG_CHECKING(for x86_64 assembly availability)
-AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
+AC_LINK_IFELSE([AC_LANG_PROGRAM([[
   #include <stdint.h>]],[[
   uint64_t a = 11, tmp;
   __asm__ __volatile__("movq \@S|@0x100000000,%1; mulq %%rsi" : "+a"(a) : "S"(tmp) : "cc", "%rdx");
@@ -9,76 +9,47 @@ AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
 AC_MSG_RESULT([$has_64bit_asm])
 ])
 
-dnl
-AC_DEFUN([SECP_OPENSSL_CHECK],[
-  has_libcrypto=no
-  m4_ifdef([PKG_CHECK_MODULES],[
-    PKG_CHECK_MODULES([CRYPTO], [libcrypto], [has_libcrypto=yes],[has_libcrypto=no])
-    if test x"$has_libcrypto" = x"yes"; then
-      TEMP_LIBS="$LIBS"
-      LIBS="$LIBS $CRYPTO_LIBS"
-      AC_CHECK_LIB(crypto, main,[AC_DEFINE(HAVE_LIBCRYPTO,1,[Define this symbol if libcrypto is installed])],[has_libcrypto=no])
-      LIBS="$TEMP_LIBS"
-    fi
-  ])
-  if test x$has_libcrypto = xno; then
-    AC_CHECK_HEADER(openssl/crypto.h,[
-      AC_CHECK_LIB(crypto, main,[
-        has_libcrypto=yes
-        CRYPTO_LIBS=-lcrypto
-        AC_DEFINE(HAVE_LIBCRYPTO,1,[Define this symbol if libcrypto is installed])
-      ])
-    ])
-    LIBS=
-  fi
-if test x"$has_libcrypto" = x"yes" && test x"$has_openssl_ec" = x; then
-  AC_MSG_CHECKING(for EC functions in libcrypto)
-  CPPFLAGS_TEMP="$CPPFLAGS"
-  CPPFLAGS="$CRYPTO_CPPFLAGS $CPPFLAGS"
-  AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
-    #include <openssl/bn.h>
-    #include <openssl/ec.h>
-    #include <openssl/ecdsa.h>
-    #include <openssl/obj_mac.h>]],[[
-    # if OPENSSL_VERSION_NUMBER < 0x10100000L
-    void ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **pr, const BIGNUM **ps) {(void)sig->r; (void)sig->s;}
-    # endif
-
-    unsigned int zero = 0;
-    const unsigned char *zero_ptr = (unsigned char*)&zero;
-    EC_KEY_free(EC_KEY_new_by_curve_name(NID_secp256k1));
-    EC_KEY *eckey = EC_KEY_new();
-    EC_GROUP *group = EC_GROUP_new_by_curve_name(NID_secp256k1);
-    EC_KEY_set_group(eckey, group);
-    ECDSA_sign(0, NULL, 0, NULL, &zero, eckey);
-    ECDSA_verify(0, NULL, 0, NULL, 0, eckey);
-    o2i_ECPublicKey(&eckey, &zero_ptr, 0);
-    d2i_ECPrivateKey(&eckey, &zero_ptr, 0);
-    EC_KEY_check_key(eckey);
-    EC_KEY_free(eckey);
-    EC_GROUP_free(group);
-    ECDSA_SIG *sig_openssl;
-    sig_openssl = ECDSA_SIG_new();
-    d2i_ECDSA_SIG(&sig_openssl, &zero_ptr, 0);
-    i2d_ECDSA_SIG(sig_openssl, NULL);
-    ECDSA_SIG_get0(sig_openssl, NULL, NULL);
-    ECDSA_SIG_free(sig_openssl);
-    const BIGNUM *bignum = BN_value_one();
-    BN_is_negative(bignum);
-    BN_num_bits(bignum);
-    if (sizeof(zero) >= BN_num_bytes(bignum)) {
-        BN_bn2bin(bignum, (unsigned char*)&zero);
-    }
-  ]])],[has_openssl_ec=yes],[has_openssl_ec=no])
-  AC_MSG_RESULT([$has_openssl_ec])
-  CPPFLAGS="$CPPFLAGS_TEMP"
-fi
-])
-
 AC_DEFUN([SECP_VALGRIND_CHECK],[
+AC_MSG_CHECKING([for valgrind support])
 if test x"$has_valgrind" != x"yes"; then
   CPPFLAGS_TEMP="$CPPFLAGS"
   CPPFLAGS="$VALGRIND_CPPFLAGS $CPPFLAGS"
-  AC_CHECK_HEADER([valgrind/memcheck.h], [has_valgrind=yes; AC_DEFINE(HAVE_VALGRIND,1,[Define this symbol if valgrind is installed])])
+  AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
+    #include <valgrind/memcheck.h>
+  ]], [[
+    #if defined(NVALGRIND)
+    #  error "Valgrind does not support this platform."
+    #endif
+  ]])], [has_valgrind=yes; AC_DEFINE(HAVE_VALGRIND,1,[Define this symbol if valgrind is installed, and it supports the host platform])])
 fi
+AC_MSG_RESULT($has_valgrind)
+])
+
+dnl SECP_TRY_APPEND_CFLAGS(flags, VAR)
+dnl Append flags to VAR if CC accepts them.
+AC_DEFUN([SECP_TRY_APPEND_CFLAGS], [
+  AC_MSG_CHECKING([if ${CC} supports $1])
+  SECP_TRY_APPEND_CFLAGS_saved_CFLAGS="$CFLAGS"
+  CFLAGS="$1 $CFLAGS"
+  AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])], [flag_works=yes], [flag_works=no])
+  AC_MSG_RESULT($flag_works)
+  CFLAGS="$SECP_TRY_APPEND_CFLAGS_saved_CFLAGS"
+  if test x"$flag_works" = x"yes"; then
+    $2="$$2 $1"
+  fi
+  unset flag_works
+  AC_SUBST($2)
+])
+
+dnl SECP_SET_DEFAULT(VAR, default, default-dev-mode)
+dnl Set VAR to default or default-dev-mode, depending on whether dev mode is enabled
+AC_DEFUN([SECP_SET_DEFAULT], [
+  if test "${enable_dev_mode+set}" != set; then
+    AC_MSG_ERROR([[Set enable_dev_mode before calling SECP_SET_DEFAULT]])
+  fi
+  if test x"$enable_dev_mode" = x"yes"; then
+    $1="$3"
+  else
+    $1="$2"
+  fi
 ])
diff --git a/src/secp256k1/ci/cirrus.sh b/src/secp256k1/ci/cirrus.sh
index 27db1e6779f..fb5854a777e 100755
--- a/src/secp256k1/ci/cirrus.sh
+++ b/src/secp256k1/ci/cirrus.sh
@@ -5,19 +5,58 @@ set -x
 
 export LC_ALL=C
 
+# Print relevant CI environment to allow reproducing the job outside of CI.
+print_environment() {
+    # Turn off -x because it messes up the output
+    set +x
+    # There are many ways to print variable names and their content. This one
+    # does not rely on bash.
+    for i in WERROR_CFLAGS MAKEFLAGS BUILD \
+            ECMULTWINDOW ECMULTGENPRECISION ASM WIDEMUL WITH_VALGRIND EXTRAFLAGS \
+            EXPERIMENTAL ECDH RECOVERY SCHNORRSIG \
+            SECP256K1_TEST_ITERS BENCH SECP256K1_BENCH_ITERS CTIMETEST\
+            EXAMPLES \
+            WRAPPER_CMD CC AR NM HOST
+    do
+        eval 'printf "%s %s " "$i=\"${'"$i"'}\""'
+    done
+    echo "$0"
+    set -x
+}
+print_environment
+
+# Start persistent wineserver if necessary.
+# This speeds up jobs with many invocations of wine (e.g., ./configure with MSVC) tremendously.
+case "$WRAPPER_CMD" in
+    *wine*)
+        # This is apparently only reliable when we run a dummy command such as "hh.exe" afterwards.
+        wineserver -p && wine hh.exe
+        ;;
+esac
+
 env >> test_env.log
 
-$CC -v || true
-valgrind --version || true
+if [ -n "$CC" ]; then
+    # The MSVC compiler "cl" doesn't understand "-v"
+    $CC -v || true
+fi
+if [ "$WITH_VALGRIND" = "yes" ]; then
+    valgrind --version
+fi
+if [ -n "$WRAPPER_CMD" ]; then
+    $WRAPPER_CMD --version
+fi
 
 ./autogen.sh
 
 ./configure \
     --enable-experimental="$EXPERIMENTAL" \
     --with-test-override-wide-multiply="$WIDEMUL" --with-asm="$ASM" \
-    --enable-ecmult-static-precomputation="$STATICPRECOMPUTATION" --with-ecmult-gen-precision="$ECMULTGENPRECISION" \
+    --with-ecmult-window="$ECMULTWINDOW" \
+    --with-ecmult-gen-precision="$ECMULTGENPRECISION" \
     --enable-module-ecdh="$ECDH" --enable-module-recovery="$RECOVERY" \
     --enable-module-schnorrsig="$SCHNORRSIG" \
+    --enable-examples="$EXAMPLES" \
     --with-valgrind="$WITH_VALGRIND" \
     --host="$HOST" $EXTRAFLAGS
 
@@ -26,16 +65,12 @@ make
 
 # Print information about binaries so that we can see that the architecture is correct
 file *tests* || true
-file bench_* || true
+file bench* || true
 file .libs/* || true
 
 # This tells `make check` to wrap test invocations.
 export LOG_COMPILER="$WRAPPER_CMD"
 
-# This limits the iterations in the tests and benchmarks.
-export SECP256K1_TEST_ITERS="$TEST_ITERS"
-export SECP256K1_BENCH_ITERS="$BENCH_ITERS"
-
 make "$BUILD"
 
 if [ "$BENCH" = "yes" ]
@@ -49,23 +84,25 @@ then
     {
         $EXEC ./bench_ecmult
         $EXEC ./bench_internal
-        $EXEC ./bench_sign
-        $EXEC ./bench_verify
+        $EXEC ./bench
     } >> bench.log 2>&1
-    if [ "$RECOVERY" = "yes" ]
-    then
-        $EXEC ./bench_recover >> bench.log 2>&1
-    fi
-    if [ "$ECDH" = "yes" ]
-    then
-        $EXEC ./bench_ecdh >> bench.log 2>&1
-    fi
-    if [ "$SCHNORRSIG" = "yes" ]
-    then
-        $EXEC ./bench_schnorrsig >> bench.log 2>&1
-    fi
 fi
+
 if [ "$CTIMETEST" = "yes" ]
 then
     ./libtool --mode=execute valgrind --error-exitcode=42 ./valgrind_ctime_test > valgrind_ctime_test.log 2>&1
 fi
+
+# Rebuild precomputed files (if not cross-compiling).
+if [ -z "$HOST" ]
+then
+    make clean-precomp
+    make precomp
+fi
+
+# Shutdown wineserver again
+wineserver -k || true
+
+# Check that no repo files have been modified by the build.
+# (This fails for example if the precomp files need to be updated in the repo.)
+git diff --exit-code
diff --git a/src/secp256k1/ci/linux-debian.Dockerfile b/src/secp256k1/ci/linux-debian.Dockerfile
index 6def91333dc..a83a4e36db0 100644
--- a/src/secp256k1/ci/linux-debian.Dockerfile
+++ b/src/secp256k1/ci/linux-debian.Dockerfile
@@ -1,24 +1,37 @@
 FROM debian:stable
 
-RUN dpkg --add-architecture i386
-RUN dpkg --add-architecture s390x
-RUN dpkg --add-architecture armhf
-RUN dpkg --add-architecture arm64
-RUN dpkg --add-architecture ppc64el
-RUN apt-get update
+RUN dpkg --add-architecture i386 && \
+    dpkg --add-architecture s390x && \
+    dpkg --add-architecture armhf && \
+    dpkg --add-architecture arm64 && \
+    dpkg --add-architecture ppc64el
 
 # dkpg-dev: to make pkg-config work in cross-builds
 # llvm: for llvm-symbolizer, which is used by clang's UBSan for symbolized stack traces
-RUN apt-get install --no-install-recommends --no-upgrade -y \
+RUN apt-get update && apt-get install --no-install-recommends -y \
         git ca-certificates \
         make automake libtool pkg-config dpkg-dev valgrind qemu-user \
         gcc clang llvm libc6-dbg \
-        gcc-i686-linux-gnu libc6-dev-i386-cross libc6-dbg:i386 libubsan1:i386 libasan5:i386 \
+        g++ \
+        gcc-i686-linux-gnu libc6-dev-i386-cross libc6-dbg:i386 libubsan1:i386 libasan6:i386 \
         gcc-s390x-linux-gnu libc6-dev-s390x-cross libc6-dbg:s390x \
         gcc-arm-linux-gnueabihf libc6-dev-armhf-cross libc6-dbg:armhf \
         gcc-aarch64-linux-gnu libc6-dev-arm64-cross libc6-dbg:arm64 \
         gcc-powerpc64le-linux-gnu libc6-dev-ppc64el-cross libc6-dbg:ppc64el \
-        wine gcc-mingw-w64-x86-64
+        gcc-mingw-w64-x86-64-win32 wine64 wine \
+        gcc-mingw-w64-i686-win32 wine32 \
+        sagemath
 
-# Run a dummy command in wine to make it set up configuration
-RUN wine64-stable xcopy || true
+WORKDIR /root
+# The "wine" package provides a convience wrapper that we need
+RUN apt-get update && apt-get install --no-install-recommends -y \
+        git ca-certificates wine64 wine python3-simplejson python3-six msitools winbind procps && \
+    git clone https://github.com/mstorsjo/msvc-wine && \
+    mkdir /opt/msvc && \
+    python3 msvc-wine/vsdownload.py --accept-license --dest /opt/msvc Microsoft.VisualStudio.Workload.VCTools && \
+    msvc-wine/install.sh /opt/msvc
+
+# Initialize the wine environment. Wait until the wineserver process has
+# exited before closing the session, to avoid corrupting the wine prefix.
+RUN wine64 wineboot --init && \
+    while (ps -A | grep wineserver) > /dev/null; do sleep 1; done
diff --git a/src/secp256k1/configure.ac b/src/secp256k1/configure.ac
index 9200c498fdc..1c9749adc31 100644
--- a/src/secp256k1/configure.ac
+++ b/src/secp256k1/configure.ac
@@ -1,180 +1,196 @@
 AC_PREREQ([2.60])
-AC_INIT([libsecp256k1],[0.1])
+
+# The package (a.k.a. release) version is based on semantic versioning 2.0.0 of
+# the API. All changes in experimental modules are treated as
+# backwards-compatible and therefore at most increase the minor version.
+define(_PKG_VERSION_MAJOR, 0)
+define(_PKG_VERSION_MINOR, 2)
+define(_PKG_VERSION_PATCH, 0)
+define(_PKG_VERSION_IS_RELEASE, true)
+
+# The library version is based on libtool versioning of the ABI. The set of
+# rules for updating the version can be found here:
+# https://www.gnu.org/software/libtool/manual/html_node/Updating-version-info.html
+# All changes in experimental modules are treated as if they don't affect the
+# interface and therefore only increase the revision.
+define(_LIB_VERSION_CURRENT, 1)
+define(_LIB_VERSION_REVISION, 0)
+define(_LIB_VERSION_AGE, 0)
+
+AC_INIT([libsecp256k1],m4_join([.], _PKG_VERSION_MAJOR, _PKG_VERSION_MINOR, _PKG_VERSION_PATCH)m4_if(_PKG_VERSION_IS_RELEASE, [true], [], [-dev]),[https://github.com/bitcoin-core/secp256k1/issues],[libsecp256k1],[https://github.com/bitcoin-core/secp256k1])
+
 AC_CONFIG_AUX_DIR([build-aux])
 AC_CONFIG_MACRO_DIR([build-aux/m4])
 AC_CANONICAL_HOST
 AH_TOP([#ifndef LIBSECP256K1_CONFIG_H])
 AH_TOP([#define LIBSECP256K1_CONFIG_H])
 AH_BOTTOM([#endif /*LIBSECP256K1_CONFIG_H*/])
-AM_INIT_AUTOMAKE([foreign subdir-objects])
 
-# Set -g if CFLAGS are not already set, which matches the default autoconf
-# behavior (see PROG_CC in the Autoconf manual) with the exception that we don't
-# set -O2 here because we set it in any case (see further down).
-: ${CFLAGS="-g"}
-LT_INIT
+# Require Automake 1.11.2 for AM_PROG_AR
+AM_INIT_AUTOMAKE([1.11.2 foreign subdir-objects])
 
 # Make the compilation flags quiet unless V=1 is used.
 m4_ifdef([AM_SILENT_RULES], [AM_SILENT_RULES([yes])])
 
-PKG_PROG_PKG_CONFIG
-
-AC_PATH_TOOL(AR, ar)
-AC_PATH_TOOL(RANLIB, ranlib)
-AC_PATH_TOOL(STRIP, strip)
-
-# Save definition of AC_PROG_CC because AM_PROG_CC_C_O in automake<=1.13 will
-# redefine AC_PROG_CC to exit with an error, which avoids the user calling it
-# accidently and screwing up the effect of AM_PROG_CC_C_O. However, we'll need
-# AC_PROG_CC later on in AX_PROG_CC_FOR_BUILD, where its usage is fine, and
-# we'll carefully make sure not to call AC_PROG_CC anywhere else.
-m4_copy([AC_PROG_CC], [saved_AC_PROG_CC])
-AM_PROG_CC_C_O
-# Restore AC_PROG_CC
-m4_rename_force([saved_AC_PROG_CC], [AC_PROG_CC])
-
-AC_PROG_CC_C99
-if test x"$ac_cv_prog_cc_c99" = x"no"; then
-  AC_MSG_ERROR([c99 compiler support required])
-fi
+AC_PROG_CC
 AM_PROG_AS
+AM_PROG_AR
+
+# Clear some cache variables as a workaround for a bug that appears due to a bad
+# interaction between AM_PROG_AR and LT_INIT when combining MSVC's archiver lib.exe.
+# https://debbugs.gnu.org/cgi/bugreport.cgi?bug=54421
+AS_UNSET(ac_cv_prog_AR)
+AS_UNSET(ac_cv_prog_ac_ct_AR)
+LT_INIT([win32-dll])
+
+build_windows=no
 
 case $host_os in
   *darwin*)
      if  test x$cross_compiling != xyes; then
-       AC_PATH_PROG([BREW],brew,)
-       if test x$BREW != x; then
+       AC_CHECK_PROG([BREW], brew, brew)
+       if test x$BREW = xbrew; then
          # These Homebrew packages may be keg-only, meaning that they won't be found
          # in expected paths because they may conflict with system files. Ask
          # Homebrew where each one is located, then adjust paths accordingly.
-         openssl_prefix=`$BREW --prefix openssl 2>/dev/null`
-         valgrind_prefix=`$BREW --prefix valgrind 2>/dev/null`
-         if test x$openssl_prefix != x; then
-           PKG_CONFIG_PATH="$openssl_prefix/lib/pkgconfig:$PKG_CONFIG_PATH"
-           export PKG_CONFIG_PATH
-           CRYPTO_CPPFLAGS="-I$openssl_prefix/include"
-         fi
-         if test x$valgrind_prefix != x; then
+         if $BREW list --versions valgrind >/dev/null; then
+           valgrind_prefix=$($BREW --prefix valgrind 2>/dev/null)
            VALGRIND_CPPFLAGS="-I$valgrind_prefix/include"
          fi
        else
-         AC_PATH_PROG([PORT],port,)
+         AC_CHECK_PROG([PORT], port, port)
          # If homebrew isn't installed and macports is, add the macports default paths
          # as a last resort.
-         if test x$PORT != x; then
+         if test x$PORT = xport; then
            CPPFLAGS="$CPPFLAGS -isystem /opt/local/include"
            LDFLAGS="$LDFLAGS -L/opt/local/lib"
          fi
        fi
      fi
    ;;
+   cygwin*|mingw*)
+     build_windows=yes
+   ;;
 esac
 
-CFLAGS="-W $CFLAGS"
-
-warn_CFLAGS="-std=c99 -pedantic -Wall -Wextra -Wcast-align -Wnested-externs -Wshadow -Wstrict-prototypes -Wundef -Wno-unused-function -Wno-long-long -Wno-overlength-strings"
-saved_CFLAGS="$CFLAGS"
-CFLAGS="$warn_CFLAGS $CFLAGS"
-AC_MSG_CHECKING([if ${CC} supports ${warn_CFLAGS}])
-AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
-    [ AC_MSG_RESULT([yes]) ],
-    [ AC_MSG_RESULT([no])
-      CFLAGS="$saved_CFLAGS"
-    ])
-
-saved_CFLAGS="$CFLAGS"
-CFLAGS="-Wconditional-uninitialized $CFLAGS"
-AC_MSG_CHECKING([if ${CC} supports -Wconditional-uninitialized])
-AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
-    [ AC_MSG_RESULT([yes]) ],
-    [ AC_MSG_RESULT([no])
-      CFLAGS="$saved_CFLAGS"
-    ])
-
-saved_CFLAGS="$CFLAGS"
-CFLAGS="-fvisibility=hidden $CFLAGS"
-AC_MSG_CHECKING([if ${CC} supports -fvisibility=hidden])
-AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
-    [ AC_MSG_RESULT([yes]) ],
-    [ AC_MSG_RESULT([no])
-      CFLAGS="$saved_CFLAGS"
-    ])
+# Try if some desirable compiler flags are supported and append them to SECP_CFLAGS.
+#
+# These are our own flags, so we append them to our own SECP_CFLAGS variable (instead of CFLAGS) as
+# recommended in the automake manual (Section "Flag Variables Ordering"). CFLAGS belongs to the user
+# and we are not supposed to touch it. In the Makefile, we will need to ensure that SECP_CFLAGS
+# is prepended to CFLAGS when invoking the compiler so that the user always has the last word (flag).
+#
+# Another advantage of not touching CFLAGS is that the contents of CFLAGS will be picked up by
+# libtool for compiling helper executables. For example, when compiling for Windows, libtool will
+# generate entire wrapper executables (instead of simple wrapper scripts as on Unix) to ensure
+# proper operation of uninstalled programs linked by libtool against the uninstalled shared library.
+# These executables are compiled from C source file for which our flags may not be appropriate,
+# e.g., -std=c89 flag has lead to undesirable warnings in the past.
+#
+# TODO We should analogously not touch CPPFLAGS and LDFLAGS but currently there are no issues.
+AC_DEFUN([SECP_TRY_APPEND_DEFAULT_CFLAGS], [
+    # GCC and compatible (incl. clang)
+    if test "x$GCC" = "xyes"; then
+      # Try to append -Werror=unknown-warning-option to CFLAGS temporarily. Otherwise clang will
+      # not error out if it gets unknown warning flags and the checks here will always succeed
+      # no matter if clang knows the flag or not.
+      SECP_TRY_APPEND_DEFAULT_CFLAGS_saved_CFLAGS="$CFLAGS"
+      SECP_TRY_APPEND_CFLAGS([-Werror=unknown-warning-option], CFLAGS)
+
+      SECP_TRY_APPEND_CFLAGS([-std=c99 -pedantic -Wno-long-long -Wnested-externs -Wshadow -Wstrict-prototypes -Wundef], $1) # GCC >= 3.0, -Wlong-long is implied by -pedantic.
+      SECP_TRY_APPEND_CFLAGS([-Wno-overlength-strings], $1) # GCC >= 4.2, -Woverlength-strings is implied by -pedantic.
+      SECP_TRY_APPEND_CFLAGS([-Wall], $1) # GCC >= 2.95 and probably many other compilers
+      SECP_TRY_APPEND_CFLAGS([-Wno-unused-function], $1) # GCC >= 3.0, -Wunused-function is implied by -Wall.
+      SECP_TRY_APPEND_CFLAGS([-Wextra], $1) # GCC >= 3.4, this is the newer name of -W, which we don't use because older GCCs will warn about unused functions.
+      SECP_TRY_APPEND_CFLAGS([-Wcast-align], $1) # GCC >= 2.95
+      SECP_TRY_APPEND_CFLAGS([-Wcast-align=strict], $1) # GCC >= 8.0
+      SECP_TRY_APPEND_CFLAGS([-Wconditional-uninitialized], $1) # Clang >= 3.0 only
+      SECP_TRY_APPEND_CFLAGS([-fvisibility=hidden], $1) # GCC >= 4.0
+
+      CFLAGS="$SECP_TRY_APPEND_DEFAULT_CFLAGS_saved_CFLAGS"
+    fi
+
+    # MSVC
+    # Assume MSVC if we're building for Windows but not with GCC or compatible;
+    # libtool makes the same assumption internally.
+    # Note that "/opt" and "-opt" are equivalent for MSVC; we use "-opt" because "/opt" looks like a path.
+    if test x"$GCC" != x"yes" && test x"$build_windows" = x"yes"; then
+      SECP_TRY_APPEND_CFLAGS([-W2 -wd4146], $1) # Moderate warning level, disable warning C4146 "unary minus operator applied to unsigned type, result still unsigned"
+      SECP_TRY_APPEND_CFLAGS([-external:anglebrackets -external:W0], $1) # Suppress warnings from #include <...> files
+    fi
+])
+SECP_TRY_APPEND_DEFAULT_CFLAGS(SECP_CFLAGS)
 
 ###
 ### Define config arguments
 ###
 
+# In dev mode, we enable all binaries and modules by default but individual options can still be overridden explicitly.
+# Check for dev mode first because SECP_SET_DEFAULT needs enable_dev_mode set.
+AC_ARG_ENABLE(dev_mode, [], [],
+    [enable_dev_mode=no])
+
 AC_ARG_ENABLE(benchmark,
-    AS_HELP_STRING([--enable-benchmark],[compile benchmark [default=yes]]),
-    [use_benchmark=$enableval],
-    [use_benchmark=yes])
+    AS_HELP_STRING([--enable-benchmark],[compile benchmark [default=yes]]), [],
+    [SECP_SET_DEFAULT([enable_benchmark], [yes], [yes])])
 
 AC_ARG_ENABLE(coverage,
-    AS_HELP_STRING([--enable-coverage],[enable compiler flags to support kcov coverage analysis [default=no]]),
-    [enable_coverage=$enableval],
-    [enable_coverage=no])
+    AS_HELP_STRING([--enable-coverage],[enable compiler flags to support kcov coverage analysis [default=no]]), [],
+    [SECP_SET_DEFAULT([enable_coverage], [no], [no])])
 
 AC_ARG_ENABLE(tests,
-    AS_HELP_STRING([--enable-tests],[compile tests [default=yes]]),
-    [use_tests=$enableval],
-    [use_tests=yes])
-
-AC_ARG_ENABLE(openssl_tests,
-    AS_HELP_STRING([--enable-openssl-tests],[enable OpenSSL tests [default=auto]]),
-    [enable_openssl_tests=$enableval],
-    [enable_openssl_tests=auto])
+    AS_HELP_STRING([--enable-tests],[compile tests [default=yes]]), [],
+    [SECP_SET_DEFAULT([enable_tests], [yes], [yes])])
 
 AC_ARG_ENABLE(experimental,
-    AS_HELP_STRING([--enable-experimental],[allow experimental configure options [default=no]]),
-    [use_experimental=$enableval],
-    [use_experimental=no])
+    AS_HELP_STRING([--enable-experimental],[allow experimental configure options [default=no]]), [],
+    [SECP_SET_DEFAULT([enable_experimental], [no], [yes])])
 
 AC_ARG_ENABLE(exhaustive_tests,
-    AS_HELP_STRING([--enable-exhaustive-tests],[compile exhaustive tests [default=yes]]),
-    [use_exhaustive_tests=$enableval],
-    [use_exhaustive_tests=yes])
+    AS_HELP_STRING([--enable-exhaustive-tests],[compile exhaustive tests [default=yes]]), [],
+    [SECP_SET_DEFAULT([enable_exhaustive_tests], [yes], [yes])])
 
-AC_ARG_ENABLE(ecmult_static_precomputation,
-    AS_HELP_STRING([--enable-ecmult-static-precomputation],[enable precomputed ecmult table for signing [default=auto]]),
-    [use_ecmult_static_precomputation=$enableval],
-    [use_ecmult_static_precomputation=auto])
+AC_ARG_ENABLE(examples,
+    AS_HELP_STRING([--enable-examples],[compile the examples [default=no]]), [],
+    [SECP_SET_DEFAULT([enable_examples], [no], [yes])])
 
 AC_ARG_ENABLE(module_ecdh,
-    AS_HELP_STRING([--enable-module-ecdh],[enable ECDH shared secret computation]),
-    [enable_module_ecdh=$enableval],
-    [enable_module_ecdh=no])
+    AS_HELP_STRING([--enable-module-ecdh],[enable ECDH module [default=yes]]), [],
+    [SECP_SET_DEFAULT([enable_module_ecdh], [yes], [yes])])
 
 AC_ARG_ENABLE(module_recovery,
-    AS_HELP_STRING([--enable-module-recovery],[enable ECDSA pubkey recovery module [default=no]]),
-    [enable_module_recovery=$enableval],
-    [enable_module_recovery=no])
+    AS_HELP_STRING([--enable-module-recovery],[enable ECDSA pubkey recovery module [default=no]]), [],
+    [SECP_SET_DEFAULT([enable_module_recovery], [no], [yes])])
 
 AC_ARG_ENABLE(module_extrakeys,
-    AS_HELP_STRING([--enable-module-extrakeys],[enable extrakeys module (experimental)]),
-    [enable_module_extrakeys=$enableval],
-    [enable_module_extrakeys=no])
+    AS_HELP_STRING([--enable-module-extrakeys],[enable extrakeys module [default=yes]]), [],
+    [SECP_SET_DEFAULT([enable_module_extrakeys], [yes], [yes])])
 
 AC_ARG_ENABLE(module_schnorrsig,
-    AS_HELP_STRING([--enable-module-schnorrsig],[enable schnorrsig module (experimental)]),
-    [enable_module_schnorrsig=$enableval],
-    [enable_module_schnorrsig=no])
+    AS_HELP_STRING([--enable-module-schnorrsig],[enable schnorrsig module [default=yes]]), [],
+    [SECP_SET_DEFAULT([enable_module_schnorrsig], [yes], [yes])])
 
 AC_ARG_ENABLE(external_default_callbacks,
-    AS_HELP_STRING([--enable-external-default-callbacks],[enable external default callback functions [default=no]]),
-    [use_external_default_callbacks=$enableval],
-    [use_external_default_callbacks=no])
+    AS_HELP_STRING([--enable-external-default-callbacks],[enable external default callback functions [default=no]]), [],
+    [SECP_SET_DEFAULT([enable_external_default_callbacks], [no], [no])])
 
 # Test-only override of the (autodetected by the C code) "widemul" setting.
-# Legal values are int64 (for [u]int64_t), int128 (for [unsigned] __int128), and auto (the default).
+# Legal values are:
+#  * int64 (for [u]int64_t),
+#  * int128 (for [unsigned] __int128),
+#  * int128_struct (for int128 implemented as a structure),
+#  *  and auto (the default).
 AC_ARG_WITH([test-override-wide-multiply], [] ,[set_widemul=$withval], [set_widemul=auto])
 
 AC_ARG_WITH([asm], [AS_HELP_STRING([--with-asm=x86_64|arm|no|auto],
-[assembly optimizations to use (experimental: arm) [default=auto]])],[req_asm=$withval], [req_asm=auto])
+[assembly optimizations to use (experimental: arm) [default=auto]])],[req_asm=$withval], [req_asm=auto])
 
 AC_ARG_WITH([ecmult-window], [AS_HELP_STRING([--with-ecmult-window=SIZE|auto],
 [window size for ecmult precomputation for verification, specified as integer in range [2..24].]
 [Larger values result in possibly better performance at the cost of an exponentially larger precomputed table.]
 [The table will store 2^(SIZE-1) * 64 bytes of data but can be larger in memory due to platform-specific padding and alignment.]
+[A window size larger than 15 will require you delete the prebuilt precomputed_ecmult.c file so that it can be rebuilt.]
+[For very large window sizes, use "make -j 1" to reduce memory use during compilation.]
 ["auto" is a reasonable setting for desktop machines (currently 15). [default=auto]]
 )],
 [req_ecmult_window=$withval], [req_ecmult_window=auto])
@@ -213,10 +229,13 @@ AM_CONDITIONAL([VALGRIND_ENABLED],[test "$enable_valgrind" = "yes"])
 
 if test x"$enable_coverage" = x"yes"; then
     AC_DEFINE(COVERAGE, 1, [Define this symbol to compile out all VERIFY code])
-    CFLAGS="-O0 --coverage $CFLAGS"
+    SECP_CFLAGS="-O0 --coverage $SECP_CFLAGS"
     LDFLAGS="--coverage $LDFLAGS"
 else
-    CFLAGS="-O2 $CFLAGS"
+    # Most likely the CFLAGS already contain -O2 because that is autoconf's default.
+    # We still add it here because passing it twice is not an issue, and handling
+    # this case would just add unnecessary complexity (see #896).
+    SECP_CFLAGS="-O2 $SECP_CFLAGS"
 fi
 
 if test x"$req_asm" = x"auto"; then
@@ -247,14 +266,14 @@ else
 fi
 
 # Select assembly optimization
-use_external_asm=no
+enable_external_asm=no
 
 case $set_asm in
 x86_64)
   AC_DEFINE(USE_ASM_X86_64, 1, [Define this symbol to enable x86_64 assembly optimizations])
   ;;
 arm)
-  use_external_asm=yes
+  enable_external_asm=yes
   ;;
 no)
   ;;
@@ -263,13 +282,16 @@ no)
   ;;
 esac
 
-if test x"$use_external_asm" = x"yes"; then
+if test x"$enable_external_asm" = x"yes"; then
   AC_DEFINE(USE_EXTERNAL_ASM, 1, [Define this symbol if an external (non-inline) assembly implementation is used])
 fi
 
 
 # Select wide multiplication implementation
 case $set_widemul in
+int128_struct)
+  AC_DEFINE(USE_FORCE_WIDEMUL_INT128_STRUCT, 1, [Define this symbol to force the use of the structure for simulating (unsigned) int128 based wide multiplication])
+  ;;
 int128)
   AC_DEFINE(USE_FORCE_WIDEMUL_INT128, 1, [Define this symbol to force the use of the (unsigned) __int128 based wide multiplication implementation])
   ;;
@@ -321,114 +343,14 @@ case $set_ecmult_gen_precision in
   ;;
 esac
 
-if test x"$use_tests" = x"yes"; then
-  SECP_OPENSSL_CHECK
-  if test x"$enable_openssl_tests" != x"no" && test x"$has_openssl_ec" = x"yes"; then
-      enable_openssl_tests=yes
-      AC_DEFINE(ENABLE_OPENSSL_TESTS, 1, [Define this symbol if OpenSSL EC functions are available])
-      SECP_TEST_INCLUDES="$SSL_CFLAGS $CRYPTO_CFLAGS $CRYPTO_CPPFLAGS"
-      SECP_TEST_LIBS="$CRYPTO_LIBS"
-
-      case $host in
-      *mingw*)
-        SECP_TEST_LIBS="$SECP_TEST_LIBS -lgdi32"
-        ;;
-      esac
-  else
-    if test x"$enable_openssl_tests" = x"yes"; then
-      AC_MSG_ERROR([OpenSSL tests requested but OpenSSL with EC support is not available])
-    fi
-    enable_openssl_tests=no
-  fi
-else
-  if test x"$enable_openssl_tests" = x"yes"; then
-    AC_MSG_ERROR([OpenSSL tests requested but tests are not enabled])
-  fi
-  enable_openssl_tests=no
-fi
-
 if test x"$enable_valgrind" = x"yes"; then
   SECP_INCLUDES="$SECP_INCLUDES $VALGRIND_CPPFLAGS"
 fi
 
-# Handle static precomputation (after everything which modifies CFLAGS and friends)
-if test x"$use_ecmult_static_precomputation" != x"no"; then
-  if test x"$cross_compiling" = x"no"; then
-    set_precomp=yes
-    if test x"${CC_FOR_BUILD+x}${CFLAGS_FOR_BUILD+x}${CPPFLAGS_FOR_BUILD+x}${LDFLAGS_FOR_BUILD+x}" != x; then
-      AC_MSG_WARN([CC_FOR_BUILD, CFLAGS_FOR_BUILD, CPPFLAGS_FOR_BUILD, and/or LDFLAGS_FOR_BUILD is set but ignored because we are not cross-compiling.])
-    fi
-    # If we're not cross-compiling, simply use the same compiler for building the static precompation code.
-    CC_FOR_BUILD="$CC"
-    CFLAGS_FOR_BUILD="$CFLAGS"
-    CPPFLAGS_FOR_BUILD="$CPPFLAGS"
-    LDFLAGS_FOR_BUILD="$LDFLAGS"
-  else
-    AX_PROG_CC_FOR_BUILD
-
-    # Temporarily switch to an environment for the native compiler
-    save_cross_compiling=$cross_compiling
-    cross_compiling=no
-    SAVE_CC="$CC"
-    CC="$CC_FOR_BUILD"
-    SAVE_CFLAGS="$CFLAGS"
-    CFLAGS="$CFLAGS_FOR_BUILD"
-    SAVE_CPPFLAGS="$CPPFLAGS"
-    CPPFLAGS="$CPPFLAGS_FOR_BUILD"
-    SAVE_LDFLAGS="$LDFLAGS"
-    LDFLAGS="$LDFLAGS_FOR_BUILD"
-
-    warn_CFLAGS_FOR_BUILD="-Wall -Wextra -Wno-unused-function"
-    saved_CFLAGS="$CFLAGS"
-    CFLAGS="$warn_CFLAGS_FOR_BUILD $CFLAGS"
-    AC_MSG_CHECKING([if native ${CC_FOR_BUILD} supports ${warn_CFLAGS_FOR_BUILD}])
-    AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
-        [ AC_MSG_RESULT([yes]) ],
-        [ AC_MSG_RESULT([no])
-          CFLAGS="$saved_CFLAGS"
-        ])
-
-    AC_MSG_CHECKING([for working native compiler: ${CC_FOR_BUILD}])
-    AC_RUN_IFELSE(
-      [AC_LANG_PROGRAM([], [])],
-      [working_native_cc=yes],
-      [working_native_cc=no],[:])
-
-    CFLAGS_FOR_BUILD="$CFLAGS"
-
-    # Restore the environment
-    cross_compiling=$save_cross_compiling
-    CC="$SAVE_CC"
-    CFLAGS="$SAVE_CFLAGS"
-    CPPFLAGS="$SAVE_CPPFLAGS"
-    LDFLAGS="$SAVE_LDFLAGS"
-
-    if test x"$working_native_cc" = x"no"; then
-      AC_MSG_RESULT([no])
-      set_precomp=no
-      m4_define([please_set_for_build], [Please set CC_FOR_BUILD, CFLAGS_FOR_BUILD, CPPFLAGS_FOR_BUILD, and/or LDFLAGS_FOR_BUILD.])
-      if test x"$use_ecmult_static_precomputation" = x"yes";  then
-        AC_MSG_ERROR([native compiler ${CC_FOR_BUILD} does not produce working binaries. please_set_for_build])
-      else
-        AC_MSG_WARN([Disabling statically generated ecmult table because the native compiler ${CC_FOR_BUILD} does not produce working binaries. please_set_for_build])
-      fi
-    else
-      AC_MSG_RESULT([yes])
-      set_precomp=yes
-    fi
-  fi
-
-  AC_SUBST(CC_FOR_BUILD)
-  AC_SUBST(CFLAGS_FOR_BUILD)
-  AC_SUBST(CPPFLAGS_FOR_BUILD)
-  AC_SUBST(LDFLAGS_FOR_BUILD)
-else
-  set_precomp=no
-fi
-
-if test x"$set_precomp" = x"yes"; then
-  AC_DEFINE(USE_ECMULT_STATIC_PRECOMPUTATION, 1, [Define this symbol to use a statically generated ecmult table])
-fi
+# Add -Werror and similar flags passed from the outside (for testing, e.g., in CI).
+# We don't want to set the user variable CFLAGS in CI because this would disable
+# autoconf's logic for setting default CFLAGS, which we would like to test in CI.
+SECP_CFLAGS="$SECP_CFLAGS $WERROR_CFLAGS"
 
 ###
 ### Handle module options
@@ -453,7 +375,7 @@ if test x"$enable_module_extrakeys" = x"yes"; then
   AC_DEFINE(ENABLE_MODULE_EXTRAKEYS, 1, [Define this symbol to enable the extrakeys module])
 fi
 
-if test x"$use_external_default_callbacks" = x"yes"; then
+if test x"$enable_external_default_callbacks" = x"yes"; then
   AC_DEFINE(USE_EXTERNAL_DEFAULT_CALLBACKS, 1, [Define this symbol if an external implementation of the default callbacks is used])
 fi
 
@@ -465,16 +387,8 @@ if test x"$enable_experimental" = x"yes"; then
   AC_MSG_NOTICE([******])
   AC_MSG_NOTICE([WARNING: experimental build])
   AC_MSG_NOTICE([Experimental features do not have stable APIs or properties, and may not be safe for production use.])
-  AC_MSG_NOTICE([Building extrakeys module: $enable_module_extrakeys])
-  AC_MSG_NOTICE([Building schnorrsig module: $enable_module_schnorrsig])
   AC_MSG_NOTICE([******])
 else
-  if test x"$enable_module_extrakeys" = x"yes"; then
-    AC_MSG_ERROR([extrakeys module is experimental. Use --enable-experimental to allow.])
-  fi
-  if test x"$enable_module_schnorrsig" = x"yes"; then
-    AC_MSG_ERROR([schnorrsig module is experimental. Use --enable-experimental to allow.])
-  fi
   if test x"$set_asm" = x"arm"; then
     AC_MSG_ERROR([ARM assembly optimization is experimental. Use --enable-experimental to allow.])
   fi
@@ -490,33 +404,32 @@ AC_SUBST(SECP_INCLUDES)
 AC_SUBST(SECP_LIBS)
 AC_SUBST(SECP_TEST_LIBS)
 AC_SUBST(SECP_TEST_INCLUDES)
+AC_SUBST(SECP_CFLAGS)
 AM_CONDITIONAL([ENABLE_COVERAGE], [test x"$enable_coverage" = x"yes"])
-AM_CONDITIONAL([USE_TESTS], [test x"$use_tests" != x"no"])
-AM_CONDITIONAL([USE_EXHAUSTIVE_TESTS], [test x"$use_exhaustive_tests" != x"no"])
-AM_CONDITIONAL([USE_BENCHMARK], [test x"$use_benchmark" = x"yes"])
-AM_CONDITIONAL([USE_ECMULT_STATIC_PRECOMPUTATION], [test x"$set_precomp" = x"yes"])
+AM_CONDITIONAL([USE_TESTS], [test x"$enable_tests" != x"no"])
+AM_CONDITIONAL([USE_EXHAUSTIVE_TESTS], [test x"$enable_exhaustive_tests" != x"no"])
+AM_CONDITIONAL([USE_EXAMPLES], [test x"$enable_examples" != x"no"])
+AM_CONDITIONAL([USE_BENCHMARK], [test x"$enable_benchmark" = x"yes"])
 AM_CONDITIONAL([ENABLE_MODULE_ECDH], [test x"$enable_module_ecdh" = x"yes"])
 AM_CONDITIONAL([ENABLE_MODULE_RECOVERY], [test x"$enable_module_recovery" = x"yes"])
 AM_CONDITIONAL([ENABLE_MODULE_EXTRAKEYS], [test x"$enable_module_extrakeys" = x"yes"])
 AM_CONDITIONAL([ENABLE_MODULE_SCHNORRSIG], [test x"$enable_module_schnorrsig" = x"yes"])
-AM_CONDITIONAL([USE_EXTERNAL_ASM], [test x"$use_external_asm" = x"yes"])
+AM_CONDITIONAL([USE_EXTERNAL_ASM], [test x"$enable_external_asm" = x"yes"])
 AM_CONDITIONAL([USE_ASM_ARM], [test x"$set_asm" = x"arm"])
-
-# Make sure nothing new is exported so that we don't break the cache.
-PKGCONFIG_PATH_TEMP="$PKG_CONFIG_PATH"
-unset PKG_CONFIG_PATH
-PKG_CONFIG_PATH="$PKGCONFIG_PATH_TEMP"
+AM_CONDITIONAL([BUILD_WINDOWS], [test "$build_windows" = "yes"])
+AC_SUBST(LIB_VERSION_CURRENT, _LIB_VERSION_CURRENT)
+AC_SUBST(LIB_VERSION_REVISION, _LIB_VERSION_REVISION)
+AC_SUBST(LIB_VERSION_AGE, _LIB_VERSION_AGE)
 
 AC_OUTPUT
 
 echo
 echo "Build Options:"
-echo "  with ecmult precomp     = $set_precomp"
-echo "  with external callbacks = $use_external_default_callbacks"
-echo "  with benchmarks         = $use_benchmark"
-echo "  with tests              = $use_tests"
-echo "  with openssl tests      = $enable_openssl_tests"
+echo "  with external callbacks = $enable_external_default_callbacks"
+echo "  with benchmarks         = $enable_benchmark"
+echo "  with tests              = $enable_tests"
 echo "  with coverage           = $enable_coverage"
+echo "  with examples           = $enable_examples"
 echo "  module ecdh             = $enable_module_ecdh"
 echo "  module recovery         = $enable_module_recovery"
 echo "  module extrakeys        = $enable_module_extrakeys"
@@ -532,13 +445,7 @@ fi
 echo
 echo "  valgrind                = $enable_valgrind"
 echo "  CC                      = $CC"
-echo "  CFLAGS                  = $CFLAGS"
 echo "  CPPFLAGS                = $CPPFLAGS"
+echo "  SECP_CFLAGS             = $SECP_CFLAGS"
+echo "  CFLAGS                  = $CFLAGS"
 echo "  LDFLAGS                 = $LDFLAGS"
-echo
-if test x"$set_precomp" = x"yes"; then
-echo "  CC_FOR_BUILD            = $CC_FOR_BUILD"
-echo "  CFLAGS_FOR_BUILD        = $CFLAGS_FOR_BUILD"
-echo "  CPPFLAGS_FOR_BUILD      = $CPPFLAGS_FOR_BUILD"
-echo "  LDFLAGS_FOR_BUILD       = $LDFLAGS_FOR_BUILD"
-fi
diff --git a/src/secp256k1/contrib/lax_der_parsing.c b/src/secp256k1/contrib/lax_der_parsing.c
index 885a817169a..bf562303edd 100644
--- a/src/secp256k1/contrib/lax_der_parsing.c
+++ b/src/secp256k1/contrib/lax_der_parsing.c
@@ -120,7 +120,7 @@ int ecdsa_signature_parse_der_lax(const secp256k1_context* ctx, secp256k1_ecdsa_
     /* Copy R value */
     if (rlen > 32) {
         overflow = 1;
-    } else {
+    } else if (rlen) {
         memcpy(tmpsig + 32 - rlen, input + rpos, rlen);
     }
 
@@ -132,7 +132,7 @@ int ecdsa_signature_parse_der_lax(const secp256k1_context* ctx, secp256k1_ecdsa_
     /* Copy S value */
     if (slen > 32) {
         overflow = 1;
-    } else {
+    } else if (slen) {
         memcpy(tmpsig + 64 - slen, input + spos, slen);
     }
 
diff --git a/src/secp256k1/contrib/lax_der_privatekey_parsing.c b/src/secp256k1/contrib/lax_der_privatekey_parsing.c
index 372e84ea4eb..a1b8200079e 100644
--- a/src/secp256k1/contrib/lax_der_privatekey_parsing.c
+++ b/src/secp256k1/contrib/lax_der_privatekey_parsing.c
@@ -44,7 +44,7 @@ int ec_privkey_import_der(const secp256k1_context* ctx, unsigned char *out32, co
     if (end < privkey+2 || privkey[0] != 0x04 || privkey[1] > 0x20 || end < privkey+2+privkey[1]) {
         return 0;
     }
-    memcpy(out32 + 32 - privkey[1], privkey + 2, privkey[1]);
+    if (privkey[1]) memcpy(out32 + 32 - privkey[1], privkey + 2, privkey[1]);
     if (!secp256k1_ec_seckey_verify(ctx, out32)) {
         memset(out32, 0, 32);
         return 0;
diff --git a/src/secp256k1/contrib/lax_der_privatekey_parsing.h b/src/secp256k1/contrib/lax_der_privatekey_parsing.h
index 1a8ad8ae0c3..3749e418fe3 100644
--- a/src/secp256k1/contrib/lax_der_privatekey_parsing.h
+++ b/src/secp256k1/contrib/lax_der_privatekey_parsing.h
@@ -43,8 +43,7 @@ extern "C" {
 /** Export a private key in DER format.
  *
  *  Returns: 1 if the private key was valid.
- *  Args: ctx:        pointer to a context object, initialized for signing (cannot
- *                    be NULL)
+ *  Args: ctx:        pointer to a context object (not secp256k1_context_static).
  *  Out: privkey:     pointer to an array for storing the private key in BER.
  *                    Should have space for 279 bytes, and cannot be NULL.
  *       privkeylen:  Pointer to an int where the length of the private key in
diff --git a/src/secp256k1/doc/release-process.md b/src/secp256k1/doc/release-process.md
new file mode 100644
index 00000000000..91e3616915a
--- /dev/null
+++ b/src/secp256k1/doc/release-process.md
@@ -0,0 +1,52 @@
+# Release Process
+
+This document outlines the process for releasing versions of the form `$MAJOR.$MINOR.$PATCH`.
+
+We distinguish between two types of releases: *regular* and *maintenance* releases.
+Regular releases are releases of a new major or minor version as well as patches of the most recent release.
+Maintenance releases, on the other hand, are required for patches of older releases.
+
+You should coordinate with the other maintainers on the release date, if possible.
+This date will be part of the release entry in [CHANGELOG.md](../CHANGELOG.md) and it should match the dates of the remaining steps in the release process (including the date of the tag and the GitHub release).
+It is best if the maintainers are present during the release, so they can help ensure that the process is followed correctly and, in the case of a regular release, they are aware that they should not modify the master branch between merging the PR in step 1 and the PR in step 3.
+
+This process also assumes that there will be no minor releases for old major releases.
+
+## Regular release
+
+1. Open a PR to the master branch with a commit (using message `"release: prepare for $MAJOR.$MINOR.$PATCH"`, for example) that
+   * finalizes the release notes in [CHANGELOG.md](../CHANGELOG.md) (make sure to include an entry for `### ABI Compatibility`) and
+   * updates `_PKG_VERSION_*`, `_LIB_VERSION_*`, and sets `_PKG_VERSION_IS_RELEASE` to `true` in `configure.ac`.
+2. After the PR is merged, tag the commit and push it:
+   ```
+   RELEASE_COMMIT=<merge commit of step 1>
+   git tag -s v$MAJOR.$MINOR.$PATCH -m "libsecp256k1 $MAJOR.$MINOR.$PATCH" $RELEASE_COMMIT
+   git push git@github.com:bitcoin-core/secp256k1.git v$MAJOR.$MINOR.$PATCH
+   ```
+3. Open a PR to the master branch with a commit (using message `"release: bump version after $MAJOR.$MINOR.$PATCH"`, for example) that sets `_PKG_VERSION_IS_RELEASE` to `false` and `_PKG_VERSION_PATCH` to `$PATCH + 1` and increases `_LIB_VERSION_REVISION`. If other maintainers are not present to approve the PR, it can be merged without ACKs.
+4. Create a new GitHub release with a link to the corresponding entry in [CHANGELOG.md](../CHANGELOG.md).
+
+## Maintenance release
+
+Note that bugfixes only need to be backported to releases for which no compatible release without the bug exists.
+
+1. If `$PATCH = 1`, create maintenance branch `$MAJOR.$MINOR`:
+   ```
+   git checkout -b $MAJOR.$MINOR v$MAJOR.$MINOR.0
+   git push git@github.com:bitcoin-core/secp256k1.git $MAJOR.$MINOR
+   ```
+2. Open a pull request to the `$MAJOR.$MINOR` branch that
+   * includes the bugfixes,
+   * finalizes the release notes,
+   * bumps `_PKG_VERSION_PATCH` and `_LIB_VERSION_REVISION` in `configure.ac` (with commit message `"release: update PKG_ and LIB_VERSION for $MAJOR.$MINOR.$PATCH"`, for example).
+3. After the PRs are merged, update the release branch and tag the commit:
+   ```
+   git checkout $MAJOR.$MINOR && git pull
+   git tag -s v$MAJOR.$MINOR.$PATCH -m "libsecp256k1 $MAJOR.$MINOR.$PATCH"
+   ```
+4. Push tag:
+   ```
+   git push git@github.com:bitcoin-core/secp256k1.git v$MAJOR.$MINOR.$PATCH
+   ```
+5. Create a new GitHub release with a link to the corresponding entry in [CHANGELOG.md](../CHANGELOG.md).
+6. Open PR to the master branch that includes a commit (with commit message `"release notes: add $MAJOR.$MINOR.$PATCH"`, for example) that adds release notes to [CHANGELOG.md](../CHANGELOG.md).
diff --git a/src/secp256k1/doc/safegcd_implementation.md b/src/secp256k1/doc/safegcd_implementation.md
index 3ae556f9a72..063aa8efae0 100644
--- a/src/secp256k1/doc/safegcd_implementation.md
+++ b/src/secp256k1/doc/safegcd_implementation.md
@@ -569,8 +569,14 @@ bits efficiently, which is possible on most platforms; it is abstracted here as
 
 ```python
 def count_trailing_zeros(v):
-    """For a non-zero value v, find z such that v=(d<<z) for some odd d."""
-    return (v & -v).bit_length() - 1
+    """
+    When v is zero, consider all N zero bits as "trailing".
+    For a non-zero value v, find z such that v=(d<<z) for some odd d.
+    """
+    if v == 0:
+        return N
+    else:
+        return (v & -v).bit_length() - 1
 
 i = N # divsteps left to do
 while True:
@@ -601,7 +607,7 @@ becomes negative, or when *i* reaches *0*. Combined, this is equivalent to addin
 It is easy to find what that multiple is: we want a number *w* such that *g+w&thinsp;f* has a few bottom
 zero bits. If that number of bits is *L*, we want *g+w&thinsp;f mod 2<sup>L</sup> = 0*, or *w = -g/f mod 2<sup>L</sup>*. Since *f*
 is odd, such a *w* exists for any *L*. *L* cannot be more than *i* steps (as we'd finish the loop before
-doing more) or more than *&eta;+1* steps (as we'd run `eta, f, g = -eta, g, f` at that point), but
+doing more) or more than *&eta;+1* steps (as we'd run `eta, f, g = -eta, g, -f` at that point), but
 apart from that, we're only limited by the complexity of computing *w*.
 
 This code demonstrates how to cancel up to 4 bits per step:
@@ -618,7 +624,7 @@ while True:
         break
     # We know g is odd now
     if eta < 0:
-        eta, f, g = -eta, g, f
+        eta, f, g = -eta, g, -f
     # Compute limit on number of bits to cancel
     limit = min(min(eta + 1, i), 4)
     # Compute w = -g/f mod 2**limit, using the table value for -1/f mod 2**4. Note that f is
diff --git a/src/secp256k1/examples/EXAMPLES_COPYING b/src/secp256k1/examples/EXAMPLES_COPYING
new file mode 100644
index 00000000000..0e259d42c99
--- /dev/null
+++ b/src/secp256k1/examples/EXAMPLES_COPYING
@@ -0,0 +1,121 @@
+Creative Commons Legal Code
+
+CC0 1.0 Universal
+
+    CREATIVE COMMONS CORPORATION IS NOT A LAW FIRM AND DOES NOT PROVIDE
+    LEGAL SERVICES. DISTRIBUTION OF THIS DOCUMENT DOES NOT CREATE AN
+    ATTORNEY-CLIENT RELATIONSHIP. CREATIVE COMMONS PROVIDES THIS
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+    REGARDING THE USE OF THIS DOCUMENT OR THE INFORMATION OR WORKS
+    PROVIDED HEREUNDER, AND DISCLAIMS LIABILITY FOR DAMAGES RESULTING FROM
+    THE USE OF THIS DOCUMENT OR THE INFORMATION OR WORKS PROVIDED
+    HEREUNDER.
+
+Statement of Purpose
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+vii. other similar, equivalent or corresponding rights throughout the
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+2. Waiver. To the greatest extent permitted by, but not in contravention
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+partial invalidity or ineffectiveness shall not invalidate the remainder
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+will not (i) exercise any of his or her remaining Copyright and Related
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+
+4. Limitations and Disclaimers.
+
+ a. No trademark or patent rights held by Affirmer are waived, abandoned,
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+ c. Affirmer disclaims responsibility for clearing rights of other persons
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+ d. Affirmer understands and acknowledges that Creative Commons is not a
+    party to this document and has no duty or obligation with respect to
+    this CC0 or use of the Work.
diff --git a/src/secp256k1/examples/ecdh.c b/src/secp256k1/examples/ecdh.c
new file mode 100644
index 00000000000..027d52fd5fe
--- /dev/null
+++ b/src/secp256k1/examples/ecdh.c
@@ -0,0 +1,123 @@
+/*************************************************************************
+ * Written in 2020-2022 by Elichai Turkel                                *
+ * To the extent possible under law, the author(s) have dedicated all    *
+ * copyright and related and neighboring rights to the software in this  *
+ * file to the public domain worldwide. This software is distributed     *
+ * without any warranty. For the CC0 Public Domain Dedication, see       *
+ * EXAMPLES_COPYING or https://creativecommons.org/publicdomain/zero/1.0 *
+ *************************************************************************/
+
+#include <stdio.h>
+#include <assert.h>
+#include <string.h>
+
+#include <secp256k1.h>
+#include <secp256k1_ecdh.h>
+
+#include "random.h"
+
+
+int main(void) {
+    unsigned char seckey1[32];
+    unsigned char seckey2[32];
+    unsigned char compressed_pubkey1[33];
+    unsigned char compressed_pubkey2[33];
+    unsigned char shared_secret1[32];
+    unsigned char shared_secret2[32];
+    unsigned char randomize[32];
+    int return_val;
+    size_t len;
+    secp256k1_pubkey pubkey1;
+    secp256k1_pubkey pubkey2;
+
+    /* Before we can call actual API functions, we need to create a "context". */
+    secp256k1_context* ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+    if (!fill_random(randomize, sizeof(randomize))) {
+        printf("Failed to generate randomness\n");
+        return 1;
+    }
+    /* Randomizing the context is recommended to protect against side-channel
+     * leakage See `secp256k1_context_randomize` in secp256k1.h for more
+     * information about it. This should never fail. */
+    return_val = secp256k1_context_randomize(ctx, randomize);
+    assert(return_val);
+
+    /*** Key Generation ***/
+
+    /* If the secret key is zero or out of range (bigger than secp256k1's
+     * order), we try to sample a new key. Note that the probability of this
+     * happening is negligible. */
+    while (1) {
+        if (!fill_random(seckey1, sizeof(seckey1)) || !fill_random(seckey2, sizeof(seckey2))) {
+            printf("Failed to generate randomness\n");
+            return 1;
+        }
+        if (secp256k1_ec_seckey_verify(ctx, seckey1) && secp256k1_ec_seckey_verify(ctx, seckey2)) {
+            break;
+        }
+    }
+
+    /* Public key creation using a valid context with a verified secret key should never fail */
+    return_val = secp256k1_ec_pubkey_create(ctx, &pubkey1, seckey1);
+    assert(return_val);
+    return_val = secp256k1_ec_pubkey_create(ctx, &pubkey2, seckey2);
+    assert(return_val);
+
+    /* Serialize pubkey1 in a compressed form (33 bytes), should always return 1 */
+    len = sizeof(compressed_pubkey1);
+    return_val = secp256k1_ec_pubkey_serialize(ctx, compressed_pubkey1, &len, &pubkey1, SECP256K1_EC_COMPRESSED);
+    assert(return_val);
+    /* Should be the same size as the size of the output, because we passed a 33 byte array. */
+    assert(len == sizeof(compressed_pubkey1));
+
+    /* Serialize pubkey2 in a compressed form (33 bytes) */
+    len = sizeof(compressed_pubkey2);
+    return_val = secp256k1_ec_pubkey_serialize(ctx, compressed_pubkey2, &len, &pubkey2, SECP256K1_EC_COMPRESSED);
+    assert(return_val);
+    /* Should be the same size as the size of the output, because we passed a 33 byte array. */
+    assert(len == sizeof(compressed_pubkey2));
+
+    /*** Creating the shared secret ***/
+
+    /* Perform ECDH with seckey1 and pubkey2. Should never fail with a verified
+     * seckey and valid pubkey */
+    return_val = secp256k1_ecdh(ctx, shared_secret1, &pubkey2, seckey1, NULL, NULL);
+    assert(return_val);
+
+    /* Perform ECDH with seckey2 and pubkey1. Should never fail with a verified
+     * seckey and valid pubkey */
+    return_val = secp256k1_ecdh(ctx, shared_secret2, &pubkey1, seckey2, NULL, NULL);
+    assert(return_val);
+
+    /* Both parties should end up with the same shared secret */
+    return_val = memcmp(shared_secret1, shared_secret2, sizeof(shared_secret1));
+    assert(return_val == 0);
+
+    printf("Secret Key1: ");
+    print_hex(seckey1, sizeof(seckey1));
+    printf("Compressed Pubkey1: ");
+    print_hex(compressed_pubkey1, sizeof(compressed_pubkey1));
+    printf("\nSecret Key2: ");
+    print_hex(seckey2, sizeof(seckey2));
+    printf("Compressed Pubkey2: ");
+    print_hex(compressed_pubkey2, sizeof(compressed_pubkey2));
+    printf("\nShared Secret: ");
+    print_hex(shared_secret1, sizeof(shared_secret1));
+
+    /* This will clear everything from the context and free the memory */
+    secp256k1_context_destroy(ctx);
+
+    /* It's best practice to try to clear secrets from memory after using them.
+     * This is done because some bugs can allow an attacker to leak memory, for
+     * example through "out of bounds" array access (see Heartbleed), Or the OS
+     * swapping them to disk. Hence, we overwrite the secret key buffer with zeros.
+     *
+     * TODO: Prevent these writes from being optimized out, as any good compiler
+     * will remove any writes that aren't used. */
+    memset(seckey1, 0, sizeof(seckey1));
+    memset(seckey2, 0, sizeof(seckey2));
+    memset(shared_secret1, 0, sizeof(shared_secret1));
+    memset(shared_secret2, 0, sizeof(shared_secret2));
+
+    return 0;
+}
diff --git a/src/secp256k1/examples/ecdsa.c b/src/secp256k1/examples/ecdsa.c
new file mode 100644
index 00000000000..7e4f1b13ac8
--- /dev/null
+++ b/src/secp256k1/examples/ecdsa.c
@@ -0,0 +1,133 @@
+/*************************************************************************
+ * Written in 2020-2022 by Elichai Turkel                                *
+ * To the extent possible under law, the author(s) have dedicated all    *
+ * copyright and related and neighboring rights to the software in this  *
+ * file to the public domain worldwide. This software is distributed     *
+ * without any warranty. For the CC0 Public Domain Dedication, see       *
+ * EXAMPLES_COPYING or https://creativecommons.org/publicdomain/zero/1.0 *
+ *************************************************************************/
+
+#include <stdio.h>
+#include <assert.h>
+#include <string.h>
+
+#include <secp256k1.h>
+
+#include "random.h"
+
+
+
+int main(void) {
+    /* Instead of signing the message directly, we must sign a 32-byte hash.
+     * Here the message is "Hello, world!" and the hash function was SHA-256.
+     * An actual implementation should just call SHA-256, but this example
+     * hardcodes the output to avoid depending on an additional library.
+     * See https://bitcoin.stackexchange.com/questions/81115/if-someone-wanted-to-pretend-to-be-satoshi-by-posting-a-fake-signature-to-defrau/81116#81116 */
+    unsigned char msg_hash[32] = {
+        0x31, 0x5F, 0x5B, 0xDB, 0x76, 0xD0, 0x78, 0xC4,
+        0x3B, 0x8A, 0xC0, 0x06, 0x4E, 0x4A, 0x01, 0x64,
+        0x61, 0x2B, 0x1F, 0xCE, 0x77, 0xC8, 0x69, 0x34,
+        0x5B, 0xFC, 0x94, 0xC7, 0x58, 0x94, 0xED, 0xD3,
+    };
+    unsigned char seckey[32];
+    unsigned char randomize[32];
+    unsigned char compressed_pubkey[33];
+    unsigned char serialized_signature[64];
+    size_t len;
+    int is_signature_valid;
+    int return_val;
+    secp256k1_pubkey pubkey;
+    secp256k1_ecdsa_signature sig;
+    /* Before we can call actual API functions, we need to create a "context". */
+    secp256k1_context* ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+    if (!fill_random(randomize, sizeof(randomize))) {
+        printf("Failed to generate randomness\n");
+        return 1;
+    }
+    /* Randomizing the context is recommended to protect against side-channel
+     * leakage See `secp256k1_context_randomize` in secp256k1.h for more
+     * information about it. This should never fail. */
+    return_val = secp256k1_context_randomize(ctx, randomize);
+    assert(return_val);
+
+    /*** Key Generation ***/
+
+    /* If the secret key is zero or out of range (bigger than secp256k1's
+     * order), we try to sample a new key. Note that the probability of this
+     * happening is negligible. */
+    while (1) {
+        if (!fill_random(seckey, sizeof(seckey))) {
+            printf("Failed to generate randomness\n");
+            return 1;
+        }
+        if (secp256k1_ec_seckey_verify(ctx, seckey)) {
+            break;
+        }
+    }
+
+    /* Public key creation using a valid context with a verified secret key should never fail */
+    return_val = secp256k1_ec_pubkey_create(ctx, &pubkey, seckey);
+    assert(return_val);
+
+    /* Serialize the pubkey in a compressed form(33 bytes). Should always return 1. */
+    len = sizeof(compressed_pubkey);
+    return_val = secp256k1_ec_pubkey_serialize(ctx, compressed_pubkey, &len, &pubkey, SECP256K1_EC_COMPRESSED);
+    assert(return_val);
+    /* Should be the same size as the size of the output, because we passed a 33 byte array. */
+    assert(len == sizeof(compressed_pubkey));
+
+    /*** Signing ***/
+
+    /* Generate an ECDSA signature `noncefp` and `ndata` allows you to pass a
+     * custom nonce function, passing `NULL` will use the RFC-6979 safe default.
+     * Signing with a valid context, verified secret key
+     * and the default nonce function should never fail. */
+    return_val = secp256k1_ecdsa_sign(ctx, &sig, msg_hash, seckey, NULL, NULL);
+    assert(return_val);
+
+    /* Serialize the signature in a compact form. Should always return 1
+     * according to the documentation in secp256k1.h. */
+    return_val = secp256k1_ecdsa_signature_serialize_compact(ctx, serialized_signature, &sig);
+    assert(return_val);
+
+
+    /*** Verification ***/
+
+    /* Deserialize the signature. This will return 0 if the signature can't be parsed correctly. */
+    if (!secp256k1_ecdsa_signature_parse_compact(ctx, &sig, serialized_signature)) {
+        printf("Failed parsing the signature\n");
+        return 1;
+    }
+
+    /* Deserialize the public key. This will return 0 if the public key can't be parsed correctly. */
+    if (!secp256k1_ec_pubkey_parse(ctx, &pubkey, compressed_pubkey, sizeof(compressed_pubkey))) {
+        printf("Failed parsing the public key\n");
+        return 1;
+    }
+
+    /* Verify a signature. This will return 1 if it's valid and 0 if it's not. */
+    is_signature_valid = secp256k1_ecdsa_verify(ctx, &sig, msg_hash, &pubkey);
+
+    printf("Is the signature valid? %s\n", is_signature_valid ? "true" : "false");
+    printf("Secret Key: ");
+    print_hex(seckey, sizeof(seckey));
+    printf("Public Key: ");
+    print_hex(compressed_pubkey, sizeof(compressed_pubkey));
+    printf("Signature: ");
+    print_hex(serialized_signature, sizeof(serialized_signature));
+
+
+    /* This will clear everything from the context and free the memory */
+    secp256k1_context_destroy(ctx);
+
+    /* It's best practice to try to clear secrets from memory after using them.
+     * This is done because some bugs can allow an attacker to leak memory, for
+     * example through "out of bounds" array access (see Heartbleed), Or the OS
+     * swapping them to disk. Hence, we overwrite the secret key buffer with zeros.
+     *
+     * TODO: Prevent these writes from being optimized out, as any good compiler
+     * will remove any writes that aren't used. */
+    memset(seckey, 0, sizeof(seckey));
+
+    return 0;
+}
diff --git a/src/secp256k1/examples/random.h b/src/secp256k1/examples/random.h
new file mode 100644
index 00000000000..439226f09f5
--- /dev/null
+++ b/src/secp256k1/examples/random.h
@@ -0,0 +1,73 @@
+/*************************************************************************
+ * Copyright (c) 2020-2021 Elichai Turkel                                *
+ * Distributed under the CC0 software license, see the accompanying file *
+ * EXAMPLES_COPYING or https://creativecommons.org/publicdomain/zero/1.0 *
+ *************************************************************************/
+
+/*
+ * This file is an attempt at collecting best practice methods for obtaining randomness with different operating systems.
+ * It may be out-of-date. Consult the documentation of the operating system before considering to use the methods below.
+ *
+ * Platform randomness sources:
+ * Linux   -> `getrandom(2)`(`sys/random.h`), if not available `/dev/urandom` should be used. http://man7.org/linux/man-pages/man2/getrandom.2.html, https://linux.die.net/man/4/urandom
+ * macOS   -> `getentropy(2)`(`sys/random.h`), if not available `/dev/urandom` should be used. https://www.unix.com/man-page/mojave/2/getentropy, https://opensource.apple.com/source/xnu/xnu-517.12.7/bsd/man/man4/random.4.auto.html
+ * FreeBSD -> `getrandom(2)`(`sys/random.h`), if not available `kern.arandom` should be used. https://www.freebsd.org/cgi/man.cgi?query=getrandom, https://www.freebsd.org/cgi/man.cgi?query=random&sektion=4
+ * OpenBSD -> `getentropy(2)`(`unistd.h`), if not available `/dev/urandom` should be used. https://man.openbsd.org/getentropy, https://man.openbsd.org/urandom
+ * Windows -> `BCryptGenRandom`(`bcrypt.h`). https://docs.microsoft.com/en-us/windows/win32/api/bcrypt/nf-bcrypt-bcryptgenrandom
+ */
+
+#if defined(_WIN32)
+#include <windows.h>
+#include <ntstatus.h>
+#include <bcrypt.h>
+#elif defined(__linux__) || defined(__APPLE__) || defined(__FreeBSD__)
+#include <sys/random.h>
+#elif defined(__OpenBSD__)
+#include <unistd.h>
+#else
+#error "Couldn't identify the OS"
+#endif
+
+#include <stddef.h>
+#include <limits.h>
+#include <stdio.h>
+
+
+/* Returns 1 on success, and 0 on failure. */
+static int fill_random(unsigned char* data, size_t size) {
+#if defined(_WIN32)
+    NTSTATUS res = BCryptGenRandom(NULL, data, size, BCRYPT_USE_SYSTEM_PREFERRED_RNG);
+    if (res != STATUS_SUCCESS || size > ULONG_MAX) {
+        return 0;
+    } else {
+        return 1;
+    }
+#elif defined(__linux__) || defined(__FreeBSD__)
+    /* If `getrandom(2)` is not available you should fallback to /dev/urandom */
+    ssize_t res = getrandom(data, size, 0);
+    if (res < 0 || (size_t)res != size ) {
+        return 0;
+    } else {
+        return 1;
+    }
+#elif defined(__APPLE__) || defined(__OpenBSD__)
+    /* If `getentropy(2)` is not available you should fallback to either
+     * `SecRandomCopyBytes` or /dev/urandom */
+    int res = getentropy(data, size);
+    if (res == 0) {
+        return 1;
+    } else {
+        return 0;
+    }
+#endif
+    return 0;
+}
+
+static void print_hex(unsigned char* data, size_t size) {
+    size_t i;
+    printf("0x");
+    for (i = 0; i < size; i++) {
+        printf("%02x", data[i]);
+    }
+    printf("\n");
+}
diff --git a/src/secp256k1/examples/schnorr.c b/src/secp256k1/examples/schnorr.c
new file mode 100644
index 00000000000..207c45c4222
--- /dev/null
+++ b/src/secp256k1/examples/schnorr.c
@@ -0,0 +1,148 @@
+/*************************************************************************
+ * Written in 2020-2022 by Elichai Turkel                                *
+ * To the extent possible under law, the author(s) have dedicated all    *
+ * copyright and related and neighboring rights to the software in this  *
+ * file to the public domain worldwide. This software is distributed     *
+ * without any warranty. For the CC0 Public Domain Dedication, see       *
+ * EXAMPLES_COPYING or https://creativecommons.org/publicdomain/zero/1.0 *
+ *************************************************************************/
+
+#include <stdio.h>
+#include <assert.h>
+#include <string.h>
+
+#include <secp256k1.h>
+#include <secp256k1_extrakeys.h>
+#include <secp256k1_schnorrsig.h>
+
+#include "random.h"
+
+int main(void) {
+    unsigned char msg[12] = "Hello World!";
+    unsigned char msg_hash[32];
+    unsigned char tag[17] = "my_fancy_protocol";
+    unsigned char seckey[32];
+    unsigned char randomize[32];
+    unsigned char auxiliary_rand[32];
+    unsigned char serialized_pubkey[32];
+    unsigned char signature[64];
+    int is_signature_valid;
+    int return_val;
+    secp256k1_xonly_pubkey pubkey;
+    secp256k1_keypair keypair;
+    /* Before we can call actual API functions, we need to create a "context". */
+    secp256k1_context* ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+    if (!fill_random(randomize, sizeof(randomize))) {
+        printf("Failed to generate randomness\n");
+        return 1;
+    }
+    /* Randomizing the context is recommended to protect against side-channel
+     * leakage See `secp256k1_context_randomize` in secp256k1.h for more
+     * information about it. This should never fail. */
+    return_val = secp256k1_context_randomize(ctx, randomize);
+    assert(return_val);
+
+    /*** Key Generation ***/
+
+    /* If the secret key is zero or out of range (bigger than secp256k1's
+     * order), we try to sample a new key. Note that the probability of this
+     * happening is negligible. */
+    while (1) {
+        if (!fill_random(seckey, sizeof(seckey))) {
+            printf("Failed to generate randomness\n");
+            return 1;
+        }
+        /* Try to create a keypair with a valid context, it should only fail if
+         * the secret key is zero or out of range. */
+        if (secp256k1_keypair_create(ctx, &keypair, seckey)) {
+            break;
+        }
+    }
+
+    /* Extract the X-only public key from the keypair. We pass NULL for
+     * `pk_parity` as the parity isn't needed for signing or verification.
+     * `secp256k1_keypair_xonly_pub` supports returning the parity for
+     * other use cases such as tests or verifying Taproot tweaks.
+     * This should never fail with a valid context and public key. */
+    return_val = secp256k1_keypair_xonly_pub(ctx, &pubkey, NULL, &keypair);
+    assert(return_val);
+
+    /* Serialize the public key. Should always return 1 for a valid public key. */
+    return_val = secp256k1_xonly_pubkey_serialize(ctx, serialized_pubkey, &pubkey);
+    assert(return_val);
+
+    /*** Signing ***/
+
+    /* Instead of signing (possibly very long) messages directly, we sign a
+     * 32-byte hash of the message in this example.
+     *
+     * We use secp256k1_tagged_sha256 to create this hash. This function expects
+     * a context-specific "tag", which restricts the context in which the signed
+     * messages should be considered valid. For example, if protocol A mandates
+     * to use the tag "my_fancy_protocol" and protocol B mandates to use the tag
+     * "my_boring_protocol", then signed messages from protocol A will never be
+     * valid in protocol B (and vice versa), even if keys are reused across
+     * protocols. This implements "domain separation", which is considered good
+     * practice. It avoids attacks in which users are tricked into signing a
+     * message that has intended consequences in the intended context (e.g.,
+     * protocol A) but would have unintended consequences if it were valid in
+     * some other context (e.g., protocol B). */
+    return_val = secp256k1_tagged_sha256(ctx, msg_hash, tag, sizeof(tag), msg, sizeof(msg));
+    assert(return_val);
+
+    /* Generate 32 bytes of randomness to use with BIP-340 schnorr signing. */
+    if (!fill_random(auxiliary_rand, sizeof(auxiliary_rand))) {
+        printf("Failed to generate randomness\n");
+        return 1;
+    }
+
+    /* Generate a Schnorr signature.
+     *
+     * We use the secp256k1_schnorrsig_sign32 function that provides a simple
+     * interface for signing 32-byte messages (which in our case is a hash of
+     * the actual message). BIP-340 recommends passing 32 bytes of randomness
+     * to the signing function to improve security against side-channel attacks.
+     * Signing with a valid context, a 32-byte message, a verified keypair, and
+     * any 32 bytes of auxiliary random data should never fail. */
+    return_val = secp256k1_schnorrsig_sign32(ctx, signature, msg_hash, &keypair, auxiliary_rand);
+    assert(return_val);
+
+    /*** Verification ***/
+
+    /* Deserialize the public key. This will return 0 if the public key can't
+     * be parsed correctly */
+    if (!secp256k1_xonly_pubkey_parse(ctx, &pubkey, serialized_pubkey)) {
+        printf("Failed parsing the public key\n");
+        return 1;
+    }
+
+    /* Compute the tagged hash on the received messages using the same tag as the signer. */
+    return_val = secp256k1_tagged_sha256(ctx, msg_hash, tag, sizeof(tag), msg, sizeof(msg));
+    assert(return_val);
+
+    /* Verify a signature. This will return 1 if it's valid and 0 if it's not. */
+    is_signature_valid = secp256k1_schnorrsig_verify(ctx, signature, msg_hash, 32, &pubkey);
+
+
+    printf("Is the signature valid? %s\n", is_signature_valid ? "true" : "false");
+    printf("Secret Key: ");
+    print_hex(seckey, sizeof(seckey));
+    printf("Public Key: ");
+    print_hex(serialized_pubkey, sizeof(serialized_pubkey));
+    printf("Signature: ");
+    print_hex(signature, sizeof(signature));
+
+    /* This will clear everything from the context and free the memory */
+    secp256k1_context_destroy(ctx);
+
+    /* It's best practice to try to clear secrets from memory after using them.
+     * This is done because some bugs can allow an attacker to leak memory, for
+     * example through "out of bounds" array access (see Heartbleed), Or the OS
+     * swapping them to disk. Hence, we overwrite the secret key buffer with zeros.
+     *
+     * TODO: Prevent these writes from being optimized out, as any good compiler
+     * will remove any writes that aren't used. */
+    memset(seckey, 0, sizeof(seckey));
+
+    return 0;
+}
diff --git a/src/secp256k1/include/secp256k1.h b/src/secp256k1/include/secp256k1.h
index c05a06d29dd..826ab75850c 100644
--- a/src/secp256k1/include/secp256k1.h
+++ b/src/secp256k1/include/secp256k1.h
@@ -7,7 +7,7 @@ extern "C" {
 
 #include <stddef.h>
 
-/* Unless explicitly stated all pointer arguments must not be NULL.
+/** Unless explicitly stated all pointer arguments must not be NULL.
  *
  * The following rules specify the order of arguments in API calls:
  *
@@ -24,15 +24,19 @@ extern "C" {
  * 5. Opaque data pointers follow the function pointer they are to be passed to.
  */
 
-/** Opaque data structure that holds context information (precomputed tables etc.).
+/** Opaque data structure that holds context information
  *
- *  The purpose of context structures is to cache large precomputed data tables
- *  that are expensive to construct, and also to maintain the randomization data
- *  for blinding.
+ *  The primary purpose of context objects is to store randomization data for
+ *  enhanced protection against side-channel leakage. This protection is only
+ *  effective if the context is randomized after its creation. See
+ *  secp256k1_context_create for creation of contexts and
+ *  secp256k1_context_randomize for randomization.
  *
- *  Do not create a new context object for each operation, as construction is
- *  far slower than all other API calls (~100 times slower than an ECDSA
- *  verification).
+ *  A secondary purpose of context objects is to store pointers to callback
+ *  functions that the library will call when certain error states arise. See
+ *  secp256k1_context_set_error_callback as well as
+ *  secp256k1_context_set_illegal_callback for details. Future library versions
+ *  may use context objects for additional purposes.
  *
  *  A constructed context can safely be used from multiple threads
  *  simultaneously, but API calls that take a non-const pointer to a context
@@ -45,7 +49,7 @@ extern "C" {
  */
 typedef struct secp256k1_context_struct secp256k1_context;
 
-/** Opaque data structure that holds rewriteable "scratch space"
+/** Opaque data structure that holds rewritable "scratch space"
  *
  *  The purpose of this structure is to replace dynamic memory allocations,
  *  because we target architectures where this may not be available. It is
@@ -130,7 +134,7 @@ typedef int (*secp256k1_nonce_function)(
 #  define SECP256K1_INLINE inline
 # endif
 
-/** When this header is used at build-time the SECP256K1_BUILD define needs to be set
+/*  When this header is used at build-time the SECP256K1_BUILD define needs to be set
  *  to correctly setup export attributes and nullness checks.  This is normally done
  *  by secp256k1.c but to guard against this header being included before secp256k1.c
  *  has had a chance to set the define (e.g. via test harnesses that just includes
@@ -141,9 +145,13 @@ typedef int (*secp256k1_nonce_function)(
 # define SECP256K1_NO_BUILD
 #endif
 
+/** At secp256k1 build-time DLL_EXPORT is defined when building objects destined
+ *  for a shared library, but not for those intended for static libraries.
+ */
+
 #ifndef SECP256K1_API
 # if defined(_WIN32)
-#  ifdef SECP256K1_BUILD
+#  if defined(SECP256K1_BUILD) && defined(DLL_EXPORT)
 #   define SECP256K1_API __declspec(dllexport)
 #  else
 #   define SECP256K1_API
@@ -155,9 +163,9 @@ typedef int (*secp256k1_nonce_function)(
 # endif
 #endif
 
-/**Warning attributes
-  * NONNULL is not used if SECP256K1_BUILD is set to avoid the compiler optimizing out
-  * some paranoid null checks. */
+/* Warning attributes
+ * NONNULL is not used if SECP256K1_BUILD is set to avoid the compiler optimizing out
+ * some paranoid null checks. */
 # if defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4)
 #  define SECP256K1_WARN_UNUSED_RESULT __attribute__ ((__warn_unused_result__))
 # else
@@ -169,22 +177,37 @@ typedef int (*secp256k1_nonce_function)(
 #  define SECP256K1_ARG_NONNULL(_x)
 # endif
 
-/** All flags' lower 8 bits indicate what they're for. Do not use directly. */
+/* Attribute for marking functions, types, and variables as deprecated */
+#if !defined(SECP256K1_BUILD) && defined(__has_attribute)
+# if __has_attribute(__deprecated__)
+#  define SECP256K1_DEPRECATED(_msg) __attribute__ ((__deprecated__(_msg)))
+# else
+#  define SECP256K1_DEPRECATED(_msg)
+# endif
+#else
+# define SECP256K1_DEPRECATED(_msg)
+#endif
+
+/* All flags' lower 8 bits indicate what they're for. Do not use directly. */
 #define SECP256K1_FLAGS_TYPE_MASK ((1 << 8) - 1)
 #define SECP256K1_FLAGS_TYPE_CONTEXT (1 << 0)
 #define SECP256K1_FLAGS_TYPE_COMPRESSION (1 << 1)
-/** The higher bits contain the actual data. Do not use directly. */
+/* The higher bits contain the actual data. Do not use directly. */
 #define SECP256K1_FLAGS_BIT_CONTEXT_VERIFY (1 << 8)
 #define SECP256K1_FLAGS_BIT_CONTEXT_SIGN (1 << 9)
 #define SECP256K1_FLAGS_BIT_CONTEXT_DECLASSIFY (1 << 10)
 #define SECP256K1_FLAGS_BIT_COMPRESSION (1 << 8)
 
-/** Flags to pass to secp256k1_context_create, secp256k1_context_preallocated_size, and
+/** Context flags to pass to secp256k1_context_create, secp256k1_context_preallocated_size, and
  *  secp256k1_context_preallocated_create. */
+#define SECP256K1_CONTEXT_NONE (SECP256K1_FLAGS_TYPE_CONTEXT)
+
+/** Deprecated context flags. These flags are treated equivalent to SECP256K1_CONTEXT_NONE. */
 #define SECP256K1_CONTEXT_VERIFY (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_VERIFY)
 #define SECP256K1_CONTEXT_SIGN (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_SIGN)
+
+/* Testing flag. Do not use. */
 #define SECP256K1_CONTEXT_DECLASSIFY (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_DECLASSIFY)
-#define SECP256K1_CONTEXT_NONE (SECP256K1_FLAGS_TYPE_CONTEXT)
 
 /** Flag to pass to secp256k1_ec_pubkey_serialize. */
 #define SECP256K1_EC_COMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION | SECP256K1_FLAGS_BIT_COMPRESSION)
@@ -197,23 +220,66 @@ typedef int (*secp256k1_nonce_function)(
 #define SECP256K1_TAG_PUBKEY_HYBRID_EVEN 0x06
 #define SECP256K1_TAG_PUBKEY_HYBRID_ODD 0x07
 
-/** A simple secp256k1 context object with no precomputed tables. These are useful for
- *  type serialization/parsing functions which require a context object to maintain
- *  API consistency, but currently do not require expensive precomputations or dynamic
- *  allocations.
+/** A built-in constant secp256k1 context object with static storage duration, to be
+ *  used in conjunction with secp256k1_selftest.
+ *
+ *  This context object offers *only limited functionality* , i.e., it cannot be used
+ *  for API functions that perform computations involving secret keys, e.g., signing
+ *  and public key generation. If this restriction applies to a specific API function,
+ *  it is mentioned in its documentation. See secp256k1_context_create if you need a
+ *  full context object that supports all functionality offered by the library.
+ *
+ *  It is highly recommended to call secp256k1_selftest before using this context.
+ */
+SECP256K1_API extern const secp256k1_context *secp256k1_context_static;
+
+/** Deprecated alias for secp256k1_context_static. */
+SECP256K1_API extern const secp256k1_context *secp256k1_context_no_precomp
+SECP256K1_DEPRECATED("Use secp256k1_context_static instead");
+
+/** Perform basic self tests (to be used in conjunction with secp256k1_context_static)
+ *
+ *  This function performs self tests that detect some serious usage errors and
+ *  similar conditions, e.g., when the library is compiled for the wrong endianness.
+ *  This is a last resort measure to be used in production. The performed tests are
+ *  very rudimentary and are not intended as a replacement for running the test
+ *  binaries.
+ *
+ *  It is highly recommended to call this before using secp256k1_context_static.
+ *  It is not necessary to call this function before using a context created with
+ *  secp256k1_context_create (or secp256k1_context_preallocated_create), which will
+ *  take care of performing the self tests.
+ *
+ *  If the tests fail, this function will call the default error handler to abort the
+ *  program (see secp256k1_context_set_error_callback).
  */
-SECP256K1_API extern const secp256k1_context *secp256k1_context_no_precomp;
+SECP256K1_API void secp256k1_selftest(void);
+
 
 /** Create a secp256k1 context object (in dynamically allocated memory).
  *
  *  This function uses malloc to allocate memory. It is guaranteed that malloc is
  *  called at most once for every call of this function. If you need to avoid dynamic
- *  memory allocation entirely, see the functions in secp256k1_preallocated.h.
+ *  memory allocation entirely, see secp256k1_context_static and the functions in
+ *  secp256k1_preallocated.h.
  *
  *  Returns: a newly created context object.
- *  In:      flags: which parts of the context to initialize.
+ *  In:      flags: Always set to SECP256K1_CONTEXT_NONE (see below).
  *
- *  See also secp256k1_context_randomize.
+ *  The only valid non-deprecated flag in recent library versions is
+ *  SECP256K1_CONTEXT_NONE, which will create a context sufficient for all functionality
+ *  offered by the library. All other (deprecated) flags will be treated as equivalent
+ *  to the SECP256K1_CONTEXT_NONE flag. Though the flags parameter primarily exists for
+ *  historical reasons, future versions of the library may introduce new flags.
+ *
+ *  If the context is intended to be used for API functions that perform computations
+ *  involving secret keys, e.g., signing and public key generation, then it is highly
+ *  recommended to call secp256k1_context_randomize on the context before calling
+ *  those API functions. This will provide enhanced protection against side-channel
+ *  leakage, see secp256k1_context_randomize for details.
+ *
+ *  Do not create a new context object for each operation, as construction and
+ *  randomization can take non-negligible time.
  */
 SECP256K1_API secp256k1_context* secp256k1_context_create(
     unsigned int flags
@@ -226,7 +292,7 @@ SECP256K1_API secp256k1_context* secp256k1_context_create(
  *  memory allocation entirely, see the functions in secp256k1_preallocated.h.
  *
  *  Returns: a newly created context object.
- *  Args:    ctx: an existing context to copy (cannot be NULL)
+ *  Args:    ctx: an existing context to copy
  */
 SECP256K1_API secp256k1_context* secp256k1_context_clone(
     const secp256k1_context* ctx
@@ -247,7 +313,7 @@ SECP256K1_API secp256k1_context* secp256k1_context_clone(
  */
 SECP256K1_API void secp256k1_context_destroy(
     secp256k1_context* ctx
-);
+) SECP256K1_ARG_NONNULL(1);
 
 /** Set a callback function to be called when an illegal argument is passed to
  *  an API call. It will only trigger for violations that are mentioned
@@ -264,7 +330,7 @@ SECP256K1_API void secp256k1_context_destroy(
  *  undefined.
  *
  *  When this function has not been called (or called with fn==NULL), then the
- *  default handler will be used. The library provides a default handler which
+ *  default handler will be used. The library provides a default handler which
  *  writes the message to stderr and calls abort. This default handler can be
  *  replaced at link time if the preprocessor macro
  *  USE_EXTERNAL_DEFAULT_CALLBACKS is defined, which is the case if the build
@@ -278,11 +344,11 @@ SECP256K1_API void secp256k1_context_destroy(
  *  fails. In this case, the corresponding default handler will be called with
  *  the data pointer argument set to NULL.
  *
- *  Args: ctx:  an existing context object (cannot be NULL)
+ *  Args: ctx:  an existing context object.
  *  In:   fun:  a pointer to a function to call when an illegal argument is
  *              passed to the API, taking a message and an opaque pointer.
  *              (NULL restores the default handler.)
- *        data: the opaque pointer to pass to fun above.
+ *        data: the opaque pointer to pass to fun above, must be NULL for the default handler.
  *
  *  See also secp256k1_context_set_error_callback.
  */
@@ -293,7 +359,10 @@ SECP256K1_API void secp256k1_context_set_illegal_callback(
 ) SECP256K1_ARG_NONNULL(1);
 
 /** Set a callback function to be called when an internal consistency check
- *  fails. The default is crashing.
+ *  fails.
+ *
+ *  The default callback writes an error message to stderr and calls abort
+ *  to abort the program.
  *
  *  This can only trigger in case of a hardware failure, miscompilation,
  *  memory corruption, serious bug in the library, or other error would can
@@ -302,12 +371,12 @@ SECP256K1_API void secp256k1_context_set_illegal_callback(
  *  for that). After this callback returns, anything may happen, including
  *  crashing.
  *
- *  Args: ctx:  an existing context object (cannot be NULL)
+ *  Args: ctx:  an existing context object.
  *  In:   fun:  a pointer to a function to call when an internal error occurs,
  *              taking a message and an opaque pointer (NULL restores the
  *              default handler, see secp256k1_context_set_illegal_callback
  *              for details).
- *        data: the opaque pointer to pass to fun above.
+ *        data: the opaque pointer to pass to fun above, must be NULL for the default handler.
  *
  *  See also secp256k1_context_set_illegal_callback.
  */
@@ -320,7 +389,7 @@ SECP256K1_API void secp256k1_context_set_error_callback(
 /** Create a secp256k1 scratch space object.
  *
  *  Returns: a newly created scratch space.
- *  Args: ctx:  an existing context object (cannot be NULL)
+ *  Args: ctx:  an existing context object.
  *  In:   size: amount of memory to be available as scratch space. Some extra
  *              (<100 bytes) will be allocated for extra accounting.
  */
@@ -411,8 +480,8 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_cmp(
  *  encoding is invalid. R and S with value 0 are allowed in the encoding.
  *
  *  After the call, sig will always be initialized. If parsing failed or R or
- *  S are zero, the resulting sig value is guaranteed to fail validation for any
- *  message and public key.
+ *  S are zero, the resulting sig value is guaranteed to fail verification for
+ *  any message and public key.
  */
 SECP256K1_API int secp256k1_ecdsa_signature_parse_compact(
     const secp256k1_context* ctx,
@@ -432,7 +501,7 @@ SECP256K1_API int secp256k1_ecdsa_signature_parse_compact(
  *  encoded numbers are out of range.
  *
  *  After the call, sig will always be initialized. If parsing failed or the
- *  encoded numbers are out of range, signature validation with it is
+ *  encoded numbers are out of range, signature verification with it is
  *  guaranteed to fail for every message and public key.
  */
 SECP256K1_API int secp256k1_ecdsa_signature_parse_der(
@@ -479,9 +548,9 @@ SECP256K1_API int secp256k1_ecdsa_signature_serialize_compact(
  *
  *  Returns: 1: correct signature
  *           0: incorrect or unparseable signature
- *  Args:    ctx:       a secp256k1 context object, initialized for verification.
- *  In:      sig:       the signature being verified (cannot be NULL)
- *           msghash32: the 32-byte message hash being verified (cannot be NULL).
+ *  Args:    ctx:       a secp256k1 context object.
+ *  In:      sig:       the signature being verified.
+ *           msghash32: the 32-byte message hash being verified.
  *                      The verifier must make sure to apply a cryptographic
  *                      hash function to the message by itself and not accept an
  *                      msghash32 value directly. Otherwise, it would be easy to
@@ -489,14 +558,14 @@ SECP256K1_API int secp256k1_ecdsa_signature_serialize_compact(
  *                      secret key. See also
  *                      https://bitcoin.stackexchange.com/a/81116/35586 for more
  *                      background on this topic.
- *           pubkey:    pointer to an initialized public key to verify with (cannot be NULL)
+ *           pubkey:    pointer to an initialized public key to verify with.
  *
  * To avoid accepting malleable signatures, only ECDSA signatures in lower-S
  * form are accepted.
  *
  * If you need to accept ECDSA signatures from sources that do not obey this
  * rule, apply secp256k1_ecdsa_signature_normalize to the signature prior to
- * validation, but be aware that doing so results in malleable signatures.
+ * verification, but be aware that doing so results in malleable signatures.
  *
  * For details, see the comments for that function.
  */
@@ -515,8 +584,7 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_verify(
  *                or copy if the input was already normalized. (can be NULL if
  *                you're only interested in whether the input was already
  *                normalized).
- *  In:   sigin:  a pointer to a signature to check/normalize (cannot be NULL,
- *                can be identical to sigout)
+ *  In:   sigin:  a pointer to a signature to check/normalize (can be identical to sigout)
  *
  *  With ECDSA a third-party can forge a second distinct signature of the same
  *  message, given a single initial signature, but without knowing the key. This
@@ -568,12 +636,16 @@ SECP256K1_API extern const secp256k1_nonce_function secp256k1_nonce_function_def
  *
  *  Returns: 1: signature created
  *           0: the nonce generation function failed, or the secret key was invalid.
- *  Args:    ctx:       pointer to a context object, initialized for signing (cannot be NULL)
- *  Out:     sig:       pointer to an array where the signature will be placed (cannot be NULL)
- *  In:      msghash32: the 32-byte message hash being signed (cannot be NULL)
- *           seckey:    pointer to a 32-byte secret key (cannot be NULL)
- *           noncefp:   pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used
- *           ndata:     pointer to arbitrary data used by the nonce generation function (can be NULL)
+ *  Args:    ctx:       pointer to a context object (not secp256k1_context_static).
+ *  Out:     sig:       pointer to an array where the signature will be placed.
+ *  In:      msghash32: the 32-byte message hash being signed.
+ *           seckey:    pointer to a 32-byte secret key.
+ *           noncefp:   pointer to a nonce generation function. If NULL,
+ *                      secp256k1_nonce_function_default is used.
+ *           ndata:     pointer to arbitrary data used by the nonce generation function
+ *                      (can be NULL). If it is non-NULL and
+ *                      secp256k1_nonce_function_default is used, then ndata must be a
+ *                      pointer to 32-bytes of additional data.
  *
  * The created signature is always in lower-S form. See
  * secp256k1_ecdsa_signature_normalize for more details.
@@ -596,8 +668,8 @@ SECP256K1_API int secp256k1_ecdsa_sign(
  *
  *  Returns: 1: secret key is valid
  *           0: secret key is invalid
- *  Args:    ctx: pointer to a context object (cannot be NULL)
- *  In:      seckey: pointer to a 32-byte secret key (cannot be NULL)
+ *  Args:    ctx: pointer to a context object.
+ *  In:      seckey: pointer to a 32-byte secret key.
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_verify(
     const secp256k1_context* ctx,
@@ -606,11 +678,11 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_verify(
 
 /** Compute the public key for a secret key.
  *
- *  Returns: 1: secret was valid, public key stores
- *           0: secret was invalid, try again
- *  Args:   ctx:        pointer to a context object, initialized for signing (cannot be NULL)
- *  Out:    pubkey:     pointer to the created public key (cannot be NULL)
- *  In:     seckey:     pointer to a 32-byte secret key (cannot be NULL)
+ *  Returns: 1: secret was valid, public key stores.
+ *           0: secret was invalid, try again.
+ *  Args:    ctx:    pointer to a context object (not secp256k1_context_static).
+ *  Out:     pubkey: pointer to the created public key.
+ *  In:      seckey: pointer to a 32-byte secret key.
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create(
     const secp256k1_context* ctx,
@@ -626,8 +698,7 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create(
  *  In/Out: seckey: pointer to the 32-byte secret key to be negated. If the
  *                  secret key is invalid according to
  *                  secp256k1_ec_seckey_verify, this function returns 0 and
- *                  seckey will be set to some unspecified value. (cannot be
- *                  NULL)
+ *                  seckey will be set to some unspecified value.
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_negate(
     const secp256k1_context* ctx,
@@ -639,13 +710,14 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_negate(
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_negate(
     const secp256k1_context* ctx,
     unsigned char *seckey
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2)
+  SECP256K1_DEPRECATED("Use secp256k1_ec_seckey_negate instead");
 
 /** Negates a public key in place.
  *
  *  Returns: 1 always
  *  Args:   ctx:        pointer to a context object
- *  In/Out: pubkey:     pointer to the public key to be negated (cannot be NULL)
+ *  In/Out: pubkey:     pointer to the public key to be negated.
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_negate(
     const secp256k1_context* ctx,
@@ -657,15 +729,15 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_negate(
  *  Returns: 0 if the arguments are invalid or the resulting secret key would be
  *           invalid (only when the tweak is the negation of the secret key). 1
  *           otherwise.
- *  Args:    ctx:   pointer to a context object (cannot be NULL).
+ *  Args:    ctx:   pointer to a context object.
  *  In/Out: seckey: pointer to a 32-byte secret key. If the secret key is
  *                  invalid according to secp256k1_ec_seckey_verify, this
  *                  function returns 0. seckey will be set to some unspecified
- *                  value if this function returns 0. (cannot be NULL)
+ *                  value if this function returns 0.
  *  In:    tweak32: pointer to a 32-byte tweak. If the tweak is invalid according to
  *                  secp256k1_ec_seckey_verify, this function returns 0. For
  *                  uniformly random 32-byte arrays the chance of being invalid
- *                  is negligible (around 1 in 2^128) (cannot be NULL).
+ *                  is negligible (around 1 in 2^128).
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_tweak_add(
     const secp256k1_context* ctx,
@@ -679,21 +751,21 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add(
     const secp256k1_context* ctx,
     unsigned char *seckey,
     const unsigned char *tweak32
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3)
+  SECP256K1_DEPRECATED("Use secp256k1_ec_seckey_tweak_add instead");
 
 /** Tweak a public key by adding tweak times the generator to it.
  *
  *  Returns: 0 if the arguments are invalid or the resulting public key would be
  *           invalid (only when the tweak is the negation of the corresponding
  *           secret key). 1 otherwise.
- *  Args:    ctx:   pointer to a context object initialized for validation
- *                  (cannot be NULL).
+ *  Args:    ctx:   pointer to a context object.
  *  In/Out: pubkey: pointer to a public key object. pubkey will be set to an
- *                  invalid value if this function returns 0 (cannot be NULL).
+ *                  invalid value if this function returns 0.
  *  In:    tweak32: pointer to a 32-byte tweak. If the tweak is invalid according to
  *                  secp256k1_ec_seckey_verify, this function returns 0. For
  *                  uniformly random 32-byte arrays the chance of being invalid
- *                  is negligible (around 1 in 2^128) (cannot be NULL).
+ *                  is negligible (around 1 in 2^128).
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add(
     const secp256k1_context* ctx,
@@ -704,15 +776,15 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add(
 /** Tweak a secret key by multiplying it by a tweak.
  *
  *  Returns: 0 if the arguments are invalid. 1 otherwise.
- *  Args:   ctx:    pointer to a context object (cannot be NULL).
+ *  Args:   ctx:    pointer to a context object.
  *  In/Out: seckey: pointer to a 32-byte secret key. If the secret key is
  *                  invalid according to secp256k1_ec_seckey_verify, this
  *                  function returns 0. seckey will be set to some unspecified
- *                  value if this function returns 0. (cannot be NULL)
+ *                  value if this function returns 0.
  *  In:    tweak32: pointer to a 32-byte tweak. If the tweak is invalid according to
  *                  secp256k1_ec_seckey_verify, this function returns 0. For
  *                  uniformly random 32-byte arrays the chance of being invalid
- *                  is negligible (around 1 in 2^128) (cannot be NULL).
+ *                  is negligible (around 1 in 2^128).
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_tweak_mul(
     const secp256k1_context* ctx,
@@ -726,19 +798,19 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul(
     const secp256k1_context* ctx,
     unsigned char *seckey,
     const unsigned char *tweak32
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3)
+  SECP256K1_DEPRECATED("Use secp256k1_ec_seckey_tweak_mul instead");
 
 /** Tweak a public key by multiplying it by a tweak value.
  *
  *  Returns: 0 if the arguments are invalid. 1 otherwise.
- *  Args:    ctx:   pointer to a context object initialized for validation
- *                  (cannot be NULL).
+ *  Args:    ctx:   pointer to a context object.
  *  In/Out: pubkey: pointer to a public key object. pubkey will be set to an
- *                  invalid value if this function returns 0 (cannot be NULL).
+ *                  invalid value if this function returns 0.
  *  In:    tweak32: pointer to a 32-byte tweak. If the tweak is invalid according to
  *                  secp256k1_ec_seckey_verify, this function returns 0. For
  *                  uniformly random 32-byte arrays the chance of being invalid
- *                  is negligible (around 1 in 2^128) (cannot be NULL).
+ *                  is negligible (around 1 in 2^128).
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul(
     const secp256k1_context* ctx,
@@ -746,30 +818,41 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul(
     const unsigned char *tweak32
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
-/** Updates the context randomization to protect against side-channel leakage.
- *  Returns: 1: randomization successfully updated or nothing to randomize
+/** Randomizes the context to provide enhanced protection against side-channel leakage.
+ *
+ *  Returns: 1: randomization successful (or called on copy of secp256k1_context_static)
  *           0: error
- *  Args:    ctx:       pointer to a context object (cannot be NULL)
+ *  Args:    ctx:       pointer to a context object.
  *  In:      seed32:    pointer to a 32-byte random seed (NULL resets to initial state)
  *
- * While secp256k1 code is written to be constant-time no matter what secret
- * values are, it's possible that a future compiler may output code which isn't,
+ * While secp256k1 code is written and tested to be constant-time no matter what
+ * secret values are, it is possible that a compiler may output code which is not,
  * and also that the CPU may not emit the same radio frequencies or draw the same
- * amount power for all values.
- *
- * This function provides a seed which is combined into the blinding value: that
- * blinding value is added before each multiplication (and removed afterwards) so
- * that it does not affect function results, but shields against attacks which
- * rely on any input-dependent behaviour.
- *
- * This function has currently an effect only on contexts initialized for signing
- * because randomization is currently used only for signing. However, this is not
- * guaranteed and may change in the future. It is safe to call this function on
- * contexts not initialized for signing; then it will have no effect and return 1.
- *
- * You should call this after secp256k1_context_create or
- * secp256k1_context_clone (and secp256k1_context_preallocated_create or
- * secp256k1_context_clone, resp.), and you may call this repeatedly afterwards.
+ * amount of power for all values. Randomization of the context shields against
+ * side-channel observations which aim to exploit secret-dependent behaviour in
+ * certain computations which involve secret keys.
+ *
+ * It is highly recommended to call this function on contexts returned from
+ * secp256k1_context_create or secp256k1_context_clone (or from the corresponding
+ * functions in secp256k1_preallocated.h) before using these contexts to call API
+ * functions that perform computations involving secret keys, e.g., signing and
+ * public key generation. It is possible to call this function more than once on
+ * the same context, and doing so before every few computations involving secret
+ * keys is recommended as a defense-in-depth measure.
+ *
+ * Currently, the random seed is mainly used for blinding multiplications of a
+ * secret scalar with the elliptic curve base point. Multiplications of this
+ * kind are performed by exactly those API functions which are documented to
+ * require a context that is not the secp256k1_context_static. As a rule of thumb,
+ * these are all functions which take a secret key (or a keypair) as an input.
+ * A notable exception to that rule is the ECDH module, which relies on a different
+ * kind of elliptic curve point multiplication and thus does not benefit from
+ * enhanced protection against side-channel leakage currently.
+ *
+ * It is safe call this function on a copy of secp256k1_context_static in writable
+ * memory (e.g., obtained via secp256k1_context_clone). In that case, this
+ * function is guaranteed to return 1, but the call will have no effect because
+ * the static context (or a copy thereof) is not meant to be randomized.
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_context_randomize(
     secp256k1_context* ctx,
@@ -780,18 +863,42 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_context_randomize(
  *
  *  Returns: 1: the sum of the public keys is valid.
  *           0: the sum of the public keys is not valid.
- *  Args:   ctx:        pointer to a context object
- *  Out:    out:        pointer to a public key object for placing the resulting public key
- *                      (cannot be NULL)
- *  In:     ins:        pointer to array of pointers to public keys (cannot be NULL)
- *          n:          the number of public keys to add together (must be at least 1)
+ *  Args:   ctx:        pointer to a context object.
+ *  Out:    out:        pointer to a public key object for placing the resulting public key.
+ *  In:     ins:        pointer to array of pointers to public keys.
+ *          n:          the number of public keys to add together (must be at least 1).
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_combine(
     const secp256k1_context* ctx,
     secp256k1_pubkey *out,
     const secp256k1_pubkey * const * ins,
     size_t n
-) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Compute a tagged hash as defined in BIP-340.
+ *
+ *  This is useful for creating a message hash and achieving domain separation
+ *  through an application-specific tag. This function returns
+ *  SHA256(SHA256(tag)||SHA256(tag)||msg). Therefore, tagged hash
+ *  implementations optimized for a specific tag can precompute the SHA256 state
+ *  after hashing the tag hashes.
+ *
+ *  Returns: 1 always.
+ *  Args:    ctx: pointer to a context object
+ *  Out:  hash32: pointer to a 32-byte array to store the resulting hash
+ *  In:      tag: pointer to an array containing the tag
+ *        taglen: length of the tag array
+ *           msg: pointer to an array containing the message
+ *        msglen: length of the message array
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_tagged_sha256(
+    const secp256k1_context* ctx,
+    unsigned char *hash32,
+    const unsigned char *tag,
+    size_t taglen,
+    const unsigned char *msg,
+    size_t msglen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(5);
 
 #ifdef __cplusplus
 }
diff --git a/src/secp256k1/include/secp256k1_ecdh.h b/src/secp256k1/include/secp256k1_ecdh.h
index 4058e9c0436..c8577984b1a 100644
--- a/src/secp256k1/include/secp256k1_ecdh.h
+++ b/src/secp256k1/include/secp256k1_ecdh.h
@@ -37,14 +37,15 @@ SECP256K1_API extern const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_func
  *
  *  Returns: 1: exponentiation was successful
  *           0: scalar was invalid (zero or overflow) or hashfp returned 0
- *  Args:    ctx:        pointer to a context object (cannot be NULL)
- *  Out:     output:     pointer to an array to be filled by hashfp
- *  In:      pubkey:     a pointer to a secp256k1_pubkey containing an
- *                       initialized public key
- *           seckey:     a 32-byte scalar with which to multiply the point
- *           hashfp:     pointer to a hash function. If NULL, secp256k1_ecdh_hash_function_sha256 is used
- *                       (in which case, 32 bytes will be written to output)
+ *  Args:    ctx:        pointer to a context object.
+ *  Out:     output:     pointer to an array to be filled by hashfp.
+ *  In:      pubkey:     a pointer to a secp256k1_pubkey containing an initialized public key.
+ *           seckey:     a 32-byte scalar with which to multiply the point.
+ *           hashfp:     pointer to a hash function. If NULL,
+ *                       secp256k1_ecdh_hash_function_sha256 is used
+ *                       (in which case, 32 bytes will be written to output).
  *           data:       arbitrary data pointer that is passed through to hashfp
+ *                       (can be NULL for secp256k1_ecdh_hash_function_sha256).
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdh(
   const secp256k1_context* ctx,
diff --git a/src/secp256k1/include/secp256k1_extrakeys.h b/src/secp256k1/include/secp256k1_extrakeys.h
index 0a37fb6b9d3..3591bc0012c 100644
--- a/src/secp256k1/include/secp256k1_extrakeys.h
+++ b/src/secp256k1/include/secp256k1_extrakeys.h
@@ -39,11 +39,10 @@ typedef struct {
  *  Returns: 1 if the public key was fully valid.
  *           0 if the public key could not be parsed or is invalid.
  *
- *  Args:   ctx: a secp256k1 context object (cannot be NULL).
+ *  Args:   ctx: a secp256k1 context object.
  *  Out: pubkey: pointer to a pubkey object. If 1 is returned, it is set to a
  *               parsed version of input. If not, it's set to an invalid value.
- *               (cannot be NULL).
- *  In: input32: pointer to a serialized xonly_pubkey (cannot be NULL)
+ *  In: input32: pointer to a serialized xonly_pubkey.
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_parse(
     const secp256k1_context* ctx,
@@ -55,11 +54,9 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_parse(
  *
  *  Returns: 1 always.
  *
- *  Args:     ctx: a secp256k1 context object (cannot be NULL).
- *  Out: output32: a pointer to a 32-byte array to place the serialized key in
- *                 (cannot be NULL).
- *  In:    pubkey: a pointer to a secp256k1_xonly_pubkey containing an
- *                 initialized public key (cannot be NULL).
+ *  Args:     ctx: a secp256k1 context object.
+ *  Out: output32: a pointer to a 32-byte array to place the serialized key in.
+ *  In:    pubkey: a pointer to a secp256k1_xonly_pubkey containing an initialized public key.
  */
 SECP256K1_API int secp256k1_xonly_pubkey_serialize(
     const secp256k1_context* ctx,
@@ -84,16 +81,14 @@ SECP256K1_API int secp256k1_xonly_pubkey_cmp(
 
 /** Converts a secp256k1_pubkey into a secp256k1_xonly_pubkey.
  *
- *  Returns: 1 if the public key was successfully converted
- *           0 otherwise
+ *  Returns: 1 always.
  *
- *  Args:         ctx: pointer to a context object (cannot be NULL)
- *  Out: xonly_pubkey: pointer to an x-only public key object for placing the
- *                     converted public key (cannot be NULL)
- *          pk_parity: pointer to an integer that will be set to 1 if the point
- *                     encoded by xonly_pubkey is the negation of the pubkey and
- *                     set to 0 otherwise. (can be NULL)
- *  In:        pubkey: pointer to a public key that is converted (cannot be NULL)
+ *  Args:         ctx: pointer to a context object.
+ *  Out: xonly_pubkey: pointer to an x-only public key object for placing the converted public key.
+ *          pk_parity: Ignored if NULL. Otherwise, pointer to an integer that
+ *                     will be set to 1 if the point encoded by xonly_pubkey is
+ *                     the negation of the pubkey and set to 0 otherwise.
+ *  In:        pubkey: pointer to a public key that is converted.
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_from_pubkey(
     const secp256k1_context* ctx,
@@ -113,18 +108,14 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_from_pubke
  *           invalid (only when the tweak is the negation of the corresponding
  *           secret key). 1 otherwise.
  *
- *  Args:           ctx: pointer to a context object initialized for verification
- *                       (cannot be NULL)
+ *  Args:           ctx: pointer to a context object.
  *  Out:  output_pubkey: pointer to a public key to store the result. Will be set
- *                       to an invalid value if this function returns 0 (cannot
- *                       be NULL)
+ *                       to an invalid value if this function returns 0.
  *  In: internal_pubkey: pointer to an x-only pubkey to apply the tweak to.
- *                       (cannot be NULL).
  *              tweak32: pointer to a 32-byte tweak. If the tweak is invalid
  *                       according to secp256k1_ec_seckey_verify, this function
  *                       returns 0. For uniformly random 32-byte arrays the
- *                       chance of being invalid is negligible (around 1 in
- *                       2^128) (cannot be NULL).
+ *                       chance of being invalid is negligible (around 1 in 2^128).
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_tweak_add(
     const secp256k1_context* ctx,
@@ -146,17 +137,15 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_tweak_add(
  *
  *  Returns: 0 if the arguments are invalid or the tweaked pubkey is not the
  *           result of tweaking the internal_pubkey with tweak32. 1 otherwise.
- *  Args:            ctx: pointer to a context object initialized for verification
- *                       (cannot be NULL)
- *  In: tweaked_pubkey32: pointer to a serialized xonly_pubkey (cannot be NULL)
+ *  Args:            ctx: pointer to a context object.
+ *  In: tweaked_pubkey32: pointer to a serialized xonly_pubkey.
  *     tweaked_pk_parity: the parity of the tweaked pubkey (whose serialization
  *                        is passed in as tweaked_pubkey32). This must match the
  *                        pk_parity value that is returned when calling
  *                        secp256k1_xonly_pubkey with the tweaked pubkey, or
  *                        this function will fail.
- *       internal_pubkey: pointer to an x-only public key object to apply the
- *                        tweak to (cannot be NULL)
- *               tweak32: pointer to a 32-byte tweak (cannot be NULL)
+ *       internal_pubkey: pointer to an x-only public key object to apply the tweak to.
+ *               tweak32: pointer to a 32-byte tweak.
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_tweak_add_check(
     const secp256k1_context* ctx,
@@ -170,9 +159,9 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_tweak_add_
  *
  *  Returns: 1: secret was valid, keypair is ready to use
  *           0: secret was invalid, try again with a different secret
- *  Args:    ctx: pointer to a context object, initialized for signing (cannot be NULL)
- *  Out: keypair: pointer to the created keypair (cannot be NULL)
- *  In:   seckey: pointer to a 32-byte secret key (cannot be NULL)
+ *  Args:    ctx: pointer to a context object (not secp256k1_context_static).
+ *  Out: keypair: pointer to the created keypair.
+ *  In:   seckey: pointer to a 32-byte secret key.
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_create(
     const secp256k1_context* ctx,
@@ -182,10 +171,10 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_create(
 
 /** Get the secret key from a keypair.
  *
- *  Returns: 0 if the arguments are invalid. 1 otherwise.
- *  Args:   ctx: pointer to a context object (cannot be NULL)
- *  Out: seckey: pointer to a 32-byte buffer for the secret key (cannot be NULL)
- *  In: keypair: pointer to a keypair (cannot be NULL)
+ *  Returns: 1 always.
+ *  Args:   ctx: pointer to a context object.
+ *  Out: seckey: pointer to a 32-byte buffer for the secret key.
+ *  In: keypair: pointer to a keypair.
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_sec(
     const secp256k1_context* ctx,
@@ -195,12 +184,11 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_sec(
 
 /** Get the public key from a keypair.
  *
- *  Returns: 0 if the arguments are invalid. 1 otherwise.
- *  Args:    ctx: pointer to a context object (cannot be NULL)
+ *  Returns: 1 always.
+ *  Args:    ctx: pointer to a context object.
  *  Out: pubkey: pointer to a pubkey object. If 1 is returned, it is set to
  *               the keypair public key. If not, it's set to an invalid value.
- *               (cannot be NULL)
- *  In: keypair: pointer to a keypair (cannot be NULL)
+ *  In: keypair: pointer to a keypair.
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_pub(
     const secp256k1_context* ctx,
@@ -213,15 +201,14 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_pub(
  *  This is the same as calling secp256k1_keypair_pub and then
  *  secp256k1_xonly_pubkey_from_pubkey.
  *
- *  Returns: 0 if the arguments are invalid. 1 otherwise.
- *  Args:   ctx: pointer to a context object (cannot be NULL)
+ *  Returns: 1 always.
+ *  Args:   ctx: pointer to a context object.
  *  Out: pubkey: pointer to an xonly_pubkey object. If 1 is returned, it is set
  *               to the keypair public key after converting it to an
- *               xonly_pubkey. If not, it's set to an invalid value (cannot be
- *               NULL).
- *    pk_parity: pointer to an integer that will be set to the pk_parity
- *               argument of secp256k1_xonly_pubkey_from_pubkey (can be NULL).
- *  In: keypair: pointer to a keypair (cannot be NULL)
+ *               xonly_pubkey. If not, it's set to an invalid value.
+ *    pk_parity: Ignored if NULL. Otherwise, pointer to an integer that will be set to the
+ *               pk_parity argument of secp256k1_xonly_pubkey_from_pubkey.
+ *  In: keypair: pointer to a keypair.
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_xonly_pub(
     const secp256k1_context* ctx,
@@ -241,15 +228,13 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_xonly_pub(
  *           invalid (only when the tweak is the negation of the keypair's
  *           secret key). 1 otherwise.
  *
- *  Args:       ctx: pointer to a context object initialized for verification
- *                   (cannot be NULL)
+ *  Args:       ctx: pointer to a context object.
  *  In/Out: keypair: pointer to a keypair to apply the tweak to. Will be set to
- *                   an invalid value if this function returns 0 (cannot be
- *                   NULL).
+ *                   an invalid value if this function returns 0.
  *  In:     tweak32: pointer to a 32-byte tweak. If the tweak is invalid according
  *                   to secp256k1_ec_seckey_verify, this function returns 0. For
  *                   uniformly random 32-byte arrays the chance of being invalid
- *                   is negligible (around 1 in 2^128) (cannot be NULL).
+ *                   is negligible (around 1 in 2^128).
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_xonly_tweak_add(
     const secp256k1_context* ctx,
diff --git a/src/secp256k1/include/secp256k1_preallocated.h b/src/secp256k1/include/secp256k1_preallocated.h
index a9ae15d5ae8..ed846f75f9d 100644
--- a/src/secp256k1/include/secp256k1_preallocated.h
+++ b/src/secp256k1/include/secp256k1_preallocated.h
@@ -55,9 +55,11 @@ SECP256K1_API size_t secp256k1_context_preallocated_size(
  *  Returns: a newly created context object.
  *  In:      prealloc: a pointer to a rewritable contiguous block of memory of
  *                     size at least secp256k1_context_preallocated_size(flags)
- *                     bytes, as detailed above (cannot be NULL)
+ *                     bytes, as detailed above.
  *           flags:    which parts of the context to initialize.
  *
+ *  See secp256k1_context_create (in secp256k1.h) for further details.
+ *
  *  See also secp256k1_context_randomize (in secp256k1.h)
  *  and secp256k1_context_preallocated_destroy.
  */
@@ -70,7 +72,7 @@ SECP256K1_API secp256k1_context* secp256k1_context_preallocated_create(
  *  caller-provided memory.
  *
  *  Returns: the required size of the caller-provided memory block.
- *  In:      ctx: an existing context to copy (cannot be NULL)
+ *  In:      ctx: an existing context to copy.
  */
 SECP256K1_API size_t secp256k1_context_preallocated_clone_size(
     const secp256k1_context* ctx
@@ -87,10 +89,10 @@ SECP256K1_API size_t secp256k1_context_preallocated_clone_size(
  *  secp256k1_context_preallocated_create for details.
  *
  *  Returns: a newly created context object.
- *  Args:    ctx:      an existing context to copy (cannot be NULL)
+ *  Args:    ctx:      an existing context to copy.
  *  In:      prealloc: a pointer to a rewritable contiguous block of memory of
  *                     size at least secp256k1_context_preallocated_size(flags)
- *                     bytes, as detailed above (cannot be NULL)
+ *                     bytes, as detailed above.
  */
 SECP256K1_API secp256k1_context* secp256k1_context_preallocated_clone(
     const secp256k1_context* ctx,
@@ -115,11 +117,11 @@ SECP256K1_API secp256k1_context* secp256k1_context_preallocated_clone(
  *
  *  Args:   ctx: an existing context to destroy, constructed using
  *               secp256k1_context_preallocated_create or
- *               secp256k1_context_preallocated_clone (cannot be NULL)
+ *               secp256k1_context_preallocated_clone.
  */
 SECP256K1_API void secp256k1_context_preallocated_destroy(
     secp256k1_context* ctx
-);
+) SECP256K1_ARG_NONNULL(1);
 
 #ifdef __cplusplus
 }
diff --git a/src/secp256k1/include/secp256k1_recovery.h b/src/secp256k1/include/secp256k1_recovery.h
index aa16532ce86..824c604025d 100644
--- a/src/secp256k1/include/secp256k1_recovery.h
+++ b/src/secp256k1/include/secp256k1_recovery.h
@@ -43,8 +43,9 @@ SECP256K1_API int secp256k1_ecdsa_recoverable_signature_parse_compact(
 /** Convert a recoverable signature into a normal signature.
  *
  *  Returns: 1
- *  Out: sig:    a pointer to a normal signature (cannot be NULL).
- *  In:  sigin:  a pointer to a recoverable signature (cannot be NULL).
+ *  Args: ctx:    a secp256k1 context object.
+ *  Out:  sig:    a pointer to a normal signature.
+ *  In:   sigin:  a pointer to a recoverable signature.
  */
 SECP256K1_API int secp256k1_ecdsa_recoverable_signature_convert(
     const secp256k1_context* ctx,
@@ -55,10 +56,10 @@ SECP256K1_API int secp256k1_ecdsa_recoverable_signature_convert(
 /** Serialize an ECDSA signature in compact format (64 bytes + recovery id).
  *
  *  Returns: 1
- *  Args: ctx:      a secp256k1 context object
- *  Out:  output64: a pointer to a 64-byte array of the compact signature (cannot be NULL)
- *        recid:    a pointer to an integer to hold the recovery id (can be NULL).
- *  In:   sig:      a pointer to an initialized signature object (cannot be NULL)
+ *  Args: ctx:      a secp256k1 context object.
+ *  Out:  output64: a pointer to a 64-byte array of the compact signature.
+ *        recid:    a pointer to an integer to hold the recovery id.
+ *  In:   sig:      a pointer to an initialized signature object.
  */
 SECP256K1_API int secp256k1_ecdsa_recoverable_signature_serialize_compact(
     const secp256k1_context* ctx,
@@ -71,12 +72,14 @@ SECP256K1_API int secp256k1_ecdsa_recoverable_signature_serialize_compact(
  *
  *  Returns: 1: signature created
  *           0: the nonce generation function failed, or the secret key was invalid.
- *  Args:    ctx:       pointer to a context object, initialized for signing (cannot be NULL)
- *  Out:     sig:       pointer to an array where the signature will be placed (cannot be NULL)
- *  In:      msghash32: the 32-byte message hash being signed (cannot be NULL)
- *           seckey:    pointer to a 32-byte secret key (cannot be NULL)
- *           noncefp:   pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used
- *           ndata:     pointer to arbitrary data used by the nonce generation function (can be NULL)
+ *  Args:    ctx:       pointer to a context object (not secp256k1_context_static).
+ *  Out:     sig:       pointer to an array where the signature will be placed.
+ *  In:      msghash32: the 32-byte message hash being signed.
+ *           seckey:    pointer to a 32-byte secret key.
+ *           noncefp:   pointer to a nonce generation function. If NULL,
+ *                      secp256k1_nonce_function_default is used.
+ *           ndata:     pointer to arbitrary data used by the nonce generation function
+ *                      (can be NULL for secp256k1_nonce_function_default).
  */
 SECP256K1_API int secp256k1_ecdsa_sign_recoverable(
     const secp256k1_context* ctx,
@@ -91,10 +94,10 @@ SECP256K1_API int secp256k1_ecdsa_sign_recoverable(
  *
  *  Returns: 1: public key successfully recovered (which guarantees a correct signature).
  *           0: otherwise.
- *  Args:    ctx:       pointer to a context object, initialized for verification (cannot be NULL)
- *  Out:     pubkey:    pointer to the recovered public key (cannot be NULL)
- *  In:      sig:       pointer to initialized signature that supports pubkey recovery (cannot be NULL)
- *           msghash32: the 32-byte message hash assumed to be signed (cannot be NULL)
+ *  Args:    ctx:       pointer to a context object.
+ *  Out:     pubkey:    pointer to the recovered public key.
+ *  In:      sig:       pointer to initialized signature that supports pubkey recovery.
+ *           msghash32: the 32-byte message hash assumed to be signed.
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_recover(
     const secp256k1_context* ctx,
diff --git a/src/secp256k1/include/secp256k1_schnorrsig.h b/src/secp256k1/include/secp256k1_schnorrsig.h
index 0150cd33953..e579e1b1d83 100644
--- a/src/secp256k1/include/secp256k1_schnorrsig.h
+++ b/src/secp256k1/include/secp256k1_schnorrsig.h
@@ -23,24 +23,29 @@ extern "C" {
  *
  *  Returns: 1 if a nonce was successfully generated. 0 will cause signing to
  *           return an error.
- *  Out:     nonce32:   pointer to a 32-byte array to be filled by the function.
- *  In:      msg32:     the 32-byte message hash being verified (will not be NULL)
- *           key32:     pointer to a 32-byte secret key (will not be NULL)
- *      xonly_pk32:     the 32-byte serialized xonly pubkey corresponding to key32
- *                      (will not be NULL)
- *           algo16:    pointer to a 16-byte array describing the signature
- *                      algorithm (will not be NULL).
- *           data:      Arbitrary data pointer that is passed through.
+ *  Out:  nonce32: pointer to a 32-byte array to be filled by the function
+ *  In:       msg: the message being verified. Is NULL if and only if msglen
+ *                 is 0.
+ *         msglen: the length of the message
+ *          key32: pointer to a 32-byte secret key (will not be NULL)
+ *     xonly_pk32: the 32-byte serialized xonly pubkey corresponding to key32
+ *                 (will not be NULL)
+ *           algo: pointer to an array describing the signature
+ *                 algorithm (will not be NULL)
+ *        algolen: the length of the algo array
+ *           data: arbitrary data pointer that is passed through
  *
  *  Except for test cases, this function should compute some cryptographic hash of
  *  the message, the key, the pubkey, the algorithm description, and data.
  */
 typedef int (*secp256k1_nonce_function_hardened)(
     unsigned char *nonce32,
-    const unsigned char *msg32,
+    const unsigned char *msg,
+    size_t msglen,
     const unsigned char *key32,
     const unsigned char *xonly_pk32,
-    const unsigned char *algo16,
+    const unsigned char *algo,
+    size_t algolen,
     void *data
 );
 
@@ -50,59 +55,125 @@ typedef int (*secp256k1_nonce_function_hardened)(
  *
  *  If a data pointer is passed, it is assumed to be a pointer to 32 bytes of
  *  auxiliary random data as defined in BIP-340. If the data pointer is NULL,
- *  schnorrsig_sign does not produce BIP-340 compliant signatures. The algo16
- *  argument must be non-NULL, otherwise the function will fail and return 0.
- *  The hash will be tagged with algo16 after removing all terminating null
- *  bytes. Therefore, to create BIP-340 compliant signatures, algo16 must be set
- *  to "BIP0340/nonce\0\0\0"
+ *  the nonce derivation procedure follows BIP-340 by setting the auxiliary
+ *  random data to zero. The algo argument must be non-NULL, otherwise the
+ *  function will fail and return 0. The hash will be tagged with algo.
+ *  Therefore, to create BIP-340 compliant signatures, algo must be set to
+ *  "BIP0340/nonce" and algolen to 13.
  */
 SECP256K1_API extern const secp256k1_nonce_function_hardened secp256k1_nonce_function_bip340;
 
+/** Data structure that contains additional arguments for schnorrsig_sign_custom.
+ *
+ *  A schnorrsig_extraparams structure object can be initialized correctly by
+ *  setting it to SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT.
+ *
+ *  Members:
+ *      magic: set to SECP256K1_SCHNORRSIG_EXTRAPARAMS_MAGIC at initialization
+ *             and has no other function than making sure the object is
+ *             initialized.
+ *    noncefp: pointer to a nonce generation function. If NULL,
+ *             secp256k1_nonce_function_bip340 is used
+ *      ndata: pointer to arbitrary data used by the nonce generation function
+ *             (can be NULL). If it is non-NULL and
+ *             secp256k1_nonce_function_bip340 is used, then ndata must be a
+ *             pointer to 32-byte auxiliary randomness as per BIP-340.
+ */
+typedef struct {
+    unsigned char magic[4];
+    secp256k1_nonce_function_hardened noncefp;
+    void* ndata;
+} secp256k1_schnorrsig_extraparams;
+
+#define SECP256K1_SCHNORRSIG_EXTRAPARAMS_MAGIC { 0xda, 0x6f, 0xb3, 0x8c }
+#define SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT {\
+    SECP256K1_SCHNORRSIG_EXTRAPARAMS_MAGIC,\
+    NULL,\
+    NULL\
+}
+
 /** Create a Schnorr signature.
  *
  *  Does _not_ strictly follow BIP-340 because it does not verify the resulting
  *  signature. Instead, you can manually use secp256k1_schnorrsig_verify and
  *  abort if it fails.
  *
- *  Otherwise BIP-340 compliant if the noncefp argument is NULL or
- *  secp256k1_nonce_function_bip340 and the ndata argument is 32-byte auxiliary
- *  randomness.
+ *  This function only signs 32-byte messages. If you have messages of a
+ *  different size (or the same size but without a context-specific tag
+ *  prefix), it is recommended to create a 32-byte message hash with
+ *  secp256k1_tagged_sha256 and then sign the hash. Tagged hashing allows
+ *  providing an context-specific tag for domain separation. This prevents
+ *  signatures from being valid in multiple contexts by accident.
  *
  *  Returns 1 on success, 0 on failure.
- *  Args:    ctx: pointer to a context object, initialized for signing (cannot be NULL)
- *  Out:   sig64: pointer to a 64-byte array to store the serialized signature (cannot be NULL)
- *  In:    msg32: the 32-byte message being signed (cannot be NULL)
- *       keypair: pointer to an initialized keypair (cannot be NULL)
- *       noncefp: pointer to a nonce generation function. If NULL, secp256k1_nonce_function_bip340 is used
- *         ndata: pointer to arbitrary data used by the nonce generation
- *                function (can be NULL). If it is non-NULL and
- *                secp256k1_nonce_function_bip340 is used, then ndata must be a
- *                pointer to 32-byte auxiliary randomness as per BIP-340.
+ *  Args:    ctx: pointer to a context object (not secp256k1_context_static).
+ *  Out:   sig64: pointer to a 64-byte array to store the serialized signature.
+ *  In:    msg32: the 32-byte message being signed.
+ *       keypair: pointer to an initialized keypair.
+ *    aux_rand32: 32 bytes of fresh randomness. While recommended to provide
+ *                this, it is only supplemental to security and can be NULL. A
+ *                NULL argument is treated the same as an all-zero one. See
+ *                BIP-340 "Default Signing" for a full explanation of this
+ *                argument and for guidance if randomness is expensive.
  */
-SECP256K1_API int secp256k1_schnorrsig_sign(
+SECP256K1_API int secp256k1_schnorrsig_sign32(
     const secp256k1_context* ctx,
     unsigned char *sig64,
     const unsigned char *msg32,
     const secp256k1_keypair *keypair,
-    secp256k1_nonce_function_hardened noncefp,
-    void *ndata
+    const unsigned char *aux_rand32
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
 
+/** Same as secp256k1_schnorrsig_sign32, but DEPRECATED. Will be removed in
+ *  future versions. */
+SECP256K1_API int secp256k1_schnorrsig_sign(
+    const secp256k1_context* ctx,
+    unsigned char *sig64,
+    const unsigned char *msg32,
+    const secp256k1_keypair *keypair,
+    const unsigned char *aux_rand32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4)
+  SECP256K1_DEPRECATED("Use secp256k1_schnorrsig_sign32 instead");
+
+/** Create a Schnorr signature with a more flexible API.
+ *
+ *  Same arguments as secp256k1_schnorrsig_sign except that it allows signing
+ *  variable length messages and accepts a pointer to an extraparams object that
+ *  allows customizing signing by passing additional arguments.
+ *
+ *  Creates the same signatures as schnorrsig_sign if msglen is 32 and the
+ *  extraparams.ndata is the same as aux_rand32.
+ *
+ *  In:     msg: the message being signed. Can only be NULL if msglen is 0.
+ *       msglen: length of the message
+ *  extraparams: pointer to a extraparams object (can be NULL)
+ */
+SECP256K1_API int secp256k1_schnorrsig_sign_custom(
+    const secp256k1_context* ctx,
+    unsigned char *sig64,
+    const unsigned char *msg,
+    size_t msglen,
+    const secp256k1_keypair *keypair,
+    secp256k1_schnorrsig_extraparams *extraparams
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(5);
+
 /** Verify a Schnorr signature.
  *
  *  Returns: 1: correct signature
  *           0: incorrect signature
- *  Args:    ctx: a secp256k1 context object, initialized for verification.
- *  In:    sig64: pointer to the 64-byte signature to verify (cannot be NULL)
- *         msg32: the 32-byte message being verified (cannot be NULL)
+ *  Args:    ctx: a secp256k1 context object.
+ *  In:    sig64: pointer to the 64-byte signature to verify.
+ *           msg: the message being verified. Can only be NULL if msglen is 0.
+ *        msglen: length of the message
  *        pubkey: pointer to an x-only public key to verify with (cannot be NULL)
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorrsig_verify(
     const secp256k1_context* ctx,
     const unsigned char *sig64,
-    const unsigned char *msg32,
+    const unsigned char *msg,
+    size_t msglen,
     const secp256k1_xonly_pubkey *pubkey
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(5);
 
 #ifdef __cplusplus
 }
diff --git a/src/secp256k1/sage/group_prover.sage b/src/secp256k1/sage/group_prover.sage
index b200bfeae3d..9305c215d59 100644
--- a/src/secp256k1/sage/group_prover.sage
+++ b/src/secp256k1/sage/group_prover.sage
@@ -164,6 +164,9 @@ class constraints:
   def negate(self):
     return constraints(zero=self.nonzero, nonzero=self.zero)
 
+  def map(self, fun):
+    return constraints(zero={fun(k): v for k, v in self.zero.items()}, nonzero={fun(k): v for k, v in self.nonzero.items()})
+
   def __add__(self, other):
     zero = self.zero.copy()
     zero.update(other.zero)
@@ -177,6 +180,30 @@ class constraints:
   def __repr__(self):
     return "%s" % self
 
+def normalize_factor(p):
+  """Normalizes the sign of primitive polynomials (as returned by factor())
+
+  This function ensures that the polynomial has a positive leading coefficient.
+
+  This is necessary because recent sage versions (starting with v9.3 or v9.4,
+  we don't know) are inconsistent about the placement of the minus sign in
+  polynomial factorizations:
+  ```
+  sage: R.<ax,bx,ay,by,Az,Bz,Ai,Bi> = PolynomialRing(QQ,8,order='invlex')
+  sage: R((-2 * (bx - ax)) ^ 1).factor()
+  (-2) * (bx - ax)
+  sage: R((-2 * (bx - ax)) ^ 2).factor()
+  (4) * (-bx + ax)^2
+  sage: R((-2 * (bx - ax)) ^ 3).factor()
+  (8) * (-bx + ax)^3
+  ```
+  """
+  # Assert p is not 0 and that its non-zero coeffients are coprime.
+  # (We could just work with the primitive part p/p.content() but we want to be
+  # aware if factor() does not return a primitive part in future sage versions.)
+  assert p.content() == 1
+  # Ensure that the first non-zero coefficient is positive.
+  return p if p.lc() > 0 else -p
 
 def conflicts(R, con):
   """Check whether any of the passed non-zero assumptions is implied by the zero assumptions"""
@@ -204,10 +231,10 @@ def get_nonzero_set(R, assume):
   nonzero = set()
   for nz in map(numerator, assume.nonzero):
     for (f,n) in nz.factor():
-      nonzero.add(f)
+      nonzero.add(normalize_factor(f))
     rnz = zero.reduce(nz)
     for (f,n) in rnz.factor():
-      nonzero.add(f)
+      nonzero.add(normalize_factor(f))
   return nonzero
 
 
@@ -222,27 +249,27 @@ def prove_nonzero(R, exprs, assume):
       return (False, [exprs[expr]])
   allexprs = reduce(lambda a,b: numerator(a)*numerator(b), exprs, 1)
   for (f, n) in allexprs.factor():
-    if f not in nonzero:
+    if normalize_factor(f) not in nonzero:
       ok = False
   if ok:
     return (True, None)
   ok = True
-  for (f, n) in zero.reduce(numerator(allexprs)).factor():
-    if f not in nonzero:
+  for (f, n) in zero.reduce(allexprs).factor():
+    if normalize_factor(f) not in nonzero:
       ok = False
   if ok:
     return (True, None)
   ok = True
   for expr in exprs:
     for (f,n) in numerator(expr).factor():
-      if f not in nonzero:
+      if normalize_factor(f) not in nonzero:
         ok = False
   if ok:
     return (True, None)
   ok = True
   for expr in exprs:
     for (f,n) in zero.reduce(numerator(expr)).factor():
-      if f not in nonzero:
+      if normalize_factor(f) not in nonzero:
         expl.add(exprs[expr])
   if expl:
     return (False, list(expl))
@@ -254,7 +281,7 @@ def prove_zero(R, exprs, assume):
   """Check whether all of the passed expressions are provably zero, given assumptions"""
   r, e = prove_nonzero(R, dict(map(lambda x: (fastfrac(R, x.bot, 1), exprs[x]), exprs)), assume)
   if not r:
-    return (False, map(lambda x: "Possibly zero denominator: %s" % x, e))
+    return (False, list(map(lambda x: "Possibly zero denominator: %s" % x, e)))
   zero = R.ideal(list(map(numerator, assume.zero)))
   nonzero = prod(x for x in assume.nonzero)
   expl = []
@@ -279,8 +306,8 @@ def describe_extra(R, assume, assumeExtra):
     if base not in zero:
       add = []
       for (f, n) in numerator(base).factor():
-        if f not in nonzero:
-          add += ["%s" % f]
+        if normalize_factor(f) not in nonzero:
+          add += ["%s" % normalize_factor(f)]
       if add:
         ret.add((" * ".join(add)) + " = 0 [%s]" % assumeExtra.zero[base])
   # Iterate over the extra nonzero expressions
@@ -288,8 +315,8 @@ def describe_extra(R, assume, assumeExtra):
     nzr = zeroextra.reduce(numerator(nz))
     if nzr not in zeroextra:
       for (f,n) in nzr.factor():
-        if zeroextra.reduce(f) not in nonzero:
-          ret.add("%s != 0" % zeroextra.reduce(f))
+        if normalize_factor(zeroextra.reduce(f)) not in nonzero:
+          ret.add("%s != 0" % normalize_factor(zeroextra.reduce(f)))
   return ", ".join(x for x in ret)
 
 
@@ -299,22 +326,21 @@ def check_symbolic(R, assumeLaw, assumeAssert, assumeBranch, require):
 
   if conflicts(R, assume):
     # This formula does not apply
-    return None
+    return (True, None)
 
   describe = describe_extra(R, assumeLaw + assumeBranch, assumeAssert)
+  if describe != "":
+    describe = " (assuming " + describe + ")"
 
   ok, msg = prove_zero(R, require.zero, assume)
   if not ok:
-    return "FAIL, %s fails (assuming %s)" % (str(msg), describe)
+    return (False, "FAIL, %s fails%s" % (str(msg), describe))
 
   res, expl = prove_nonzero(R, require.nonzero, assume)
   if not res:
-    return "FAIL, %s fails (assuming %s)" % (str(expl), describe)
+    return (False, "FAIL, %s fails%s" % (str(expl), describe))
 
-  if describe != "":
-    return "OK (assuming %s)" % describe
-  else:
-    return "OK"
+  return (True, "OK%s" % describe)
 
 
 def concrete_verify(c):
diff --git a/src/secp256k1/sage/prove_group_implementations.sage b/src/secp256k1/sage/prove_group_implementations.sage
index a97e732f7fa..652bd87f110 100644
--- a/src/secp256k1/sage/prove_group_implementations.sage
+++ b/src/secp256k1/sage/prove_group_implementations.sage
@@ -8,25 +8,20 @@ load("weierstrass_prover.sage")
 def formula_secp256k1_gej_double_var(a):
   """libsecp256k1's secp256k1_gej_double_var, used by various addition functions"""
   rz = a.Z * a.Y
-  rz = rz * 2
-  t1 = a.X^2
-  t1 = t1 * 3
-  t2 = t1^2
-  t3 = a.Y^2
-  t3 = t3 * 2
-  t4 = t3^2
-  t4 = t4 * 2
-  t3 = t3 * a.X
-  rx = t3
-  rx = rx * 4
-  rx = -rx
-  rx = rx + t2
-  t2 = -t2
-  t3 = t3 * 6
-  t3 = t3 + t2
-  ry = t1 * t3
-  t2 = -t4
-  ry = ry + t2
+  s = a.Y^2
+  l = a.X^2
+  l = l * 3
+  l = l / 2
+  t = -s
+  t = t * a.X
+  rx = l^2
+  rx = rx + t
+  rx = rx + t
+  s = s^2
+  t = t + rx
+  ry = t * l
+  ry = ry + s
+  ry = -ry
   return jacobianpoint(rx, ry, rz)
 
 def formula_secp256k1_gej_add_var(branch, a, b):
@@ -45,29 +40,26 @@ def formula_secp256k1_gej_add_var(branch, a, b):
   s2 = s2 * a.Z
   h = -u1
   h = h + u2
-  i = -s1
-  i = i + s2
+  i = -s2
+  i = i + s1
   if branch == 2:
     r = formula_secp256k1_gej_double_var(a)
     return (constraints(), constraints(zero={h : 'h=0', i : 'i=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}), r)
   if branch == 3:
     return (constraints(), constraints(zero={h : 'h=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={i : 'i!=0'}), point_at_infinity())
-  i2 = i^2
+  t = h * b.Z
+  rz = a.Z * t
   h2 = h^2
+  h2 = -h2
   h3 = h2 * h
-  h = h * b.Z
-  rz = a.Z * h
   t = u1 * h2
-  rx = t
-  rx = rx * 2
+  rx = i^2
   rx = rx + h3
-  rx = -rx
-  rx = rx + i2
-  ry = -rx
-  ry = ry + t
-  ry = ry * i
+  rx = rx + t
+  rx = rx + t
+  t = t + rx
+  ry = t * i
   h3 = h3 * s1
-  h3 = -h3
   ry = ry + h3
   return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
 
@@ -85,28 +77,25 @@ def formula_secp256k1_gej_add_ge_var(branch, a, b):
   s2 = s2 * a.Z
   h = -u1
   h = h + u2
-  i = -s1
-  i = i + s2
+  i = -s2
+  i = i + s1
   if (branch == 2):
     r = formula_secp256k1_gej_double_var(a)
     return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r)
   if (branch == 3):
     return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity())
-  i2 = i^2
-  h2 = h^2
-  h3 = h * h2
   rz = a.Z * h
+  h2 = h^2
+  h2 = -h2
+  h3 = h2 * h
   t = u1 * h2
-  rx = t
-  rx = rx * 2
+  rx = i^2
   rx = rx + h3
-  rx = -rx
-  rx = rx + i2
-  ry = -rx
-  ry = ry + t
-  ry = ry * i
+  rx = rx + t
+  rx = rx + t
+  t = t + rx
+  ry = t * i
   h3 = h3 * s1
-  h3 = -h3
   ry = ry + h3
   return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
 
@@ -114,14 +103,15 @@ def formula_secp256k1_gej_add_zinv_var(branch, a, b):
   """libsecp256k1's secp256k1_gej_add_zinv_var"""
   bzinv = b.Z^(-1)
   if branch == 0:
-    return (constraints(), constraints(nonzero={b.Infinity : 'b_infinite'}), a)
-  if branch == 1:
+    rinf = b.Infinity
     bzinv2 = bzinv^2
     bzinv3 = bzinv2 * bzinv
     rx = b.X * bzinv2
     ry = b.Y * bzinv3
     rz = 1
-    return (constraints(), constraints(zero={b.Infinity : 'b_finite'}, nonzero={a.Infinity : 'a_infinite'}), jacobianpoint(rx, ry, rz))
+    return (constraints(), constraints(nonzero={a.Infinity : 'a_infinite'}), jacobianpoint(rx, ry, rz, rinf))
+  if branch == 1:
+    return (constraints(), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a)
   azz = a.Z * bzinv
   z12 = azz^2
   u1 = a.X
@@ -131,29 +121,25 @@ def formula_secp256k1_gej_add_zinv_var(branch, a, b):
   s2 = s2 * azz
   h = -u1
   h = h + u2
-  i = -s1
-  i = i + s2
+  i = -s2
+  i = i + s1
   if branch == 2:
     r = formula_secp256k1_gej_double_var(a)
     return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r)
   if branch == 3:
     return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity())
-  i2 = i^2
+  rz = a.Z * h
   h2 = h^2
-  h3 = h * h2
-  rz = a.Z
-  rz = rz * h
+  h2 = -h2
+  h3 = h2 * h
   t = u1 * h2
-  rx = t
-  rx = rx * 2
+  rx = i^2
   rx = rx + h3
-  rx = -rx
-  rx = rx + i2
-  ry = -rx
-  ry = ry + t
-  ry = ry * i
+  rx = rx + t
+  rx = rx + t
+  t = t + rx
+  ry = t * i
   h3 = h3 * s1
-  h3 = -h3
   ry = ry + h3
   return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
 
@@ -197,7 +183,8 @@ def formula_secp256k1_gej_add_ge(branch, a, b):
     rr_alt = rr
     m_alt = m
   n = m_alt^2
-  q = n * t
+  q = -t
+  q = q * n
   n = n^2
   if degenerate:
     n = m
@@ -210,8 +197,6 @@ def formula_secp256k1_gej_add_ge(branch, a, b):
     zeroes.update({rz : 'r.z=0'})
   else:
     nonzeroes.update({rz : 'r.z!=0'})
-  rz = rz * 2
-  q = -q
   t = t + q
   rx = t
   t = t * 2
@@ -219,8 +204,7 @@ def formula_secp256k1_gej_add_ge(branch, a, b):
   t = t * rr_alt
   t = t + n
   ry = -t
-  rx = rx * 4
-  ry = ry * 4
+  ry = ry / 2
   if a_infinity:
     rx = b.X
     ry = b.Y
@@ -292,15 +276,18 @@ def formula_secp256k1_gej_add_ge_old(branch, a, b):
   return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), jacobianpoint(rx, ry, rz))
 
 if __name__ == "__main__":
-  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var)
-  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var)
-  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var)
-  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge)
-  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old)
+  success = True
+  success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var)
+  success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var)
+  success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var)
+  success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge)
+  success = success & (not check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old))
 
   if len(sys.argv) >= 2 and sys.argv[1] == "--exhaustive":
-    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var, 43)
-    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var, 43)
-    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var, 43)
-    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge, 43)
-    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old, 43)
+    success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var, 43)
+    success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var, 43)
+    success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var, 43)
+    success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge, 43)
+    success = success & (not check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old, 43))
+
+  sys.exit(int(not success))
diff --git a/src/secp256k1/sage/secp256k1_params.sage b/src/secp256k1/sage/secp256k1_params.sage
index 4e000726ed3..68f95adec4b 100644
--- a/src/secp256k1/sage/secp256k1_params.sage
+++ b/src/secp256k1/sage/secp256k1_params.sage
@@ -9,6 +9,9 @@ C = EllipticCurve([F(0), F(7)])
 
 """Base point of secp256k1"""
 G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
+if int(G[1]) & 1:
+    # G.y is even
+    G = -G
 
 """Prime order of secp256k1"""
 N = C.order()
diff --git a/src/secp256k1/sage/weierstrass_prover.sage b/src/secp256k1/sage/weierstrass_prover.sage
index b770c6dafe2..be9cfd4c76d 100644
--- a/src/secp256k1/sage/weierstrass_prover.sage
+++ b/src/secp256k1/sage/weierstrass_prover.sage
@@ -184,6 +184,7 @@ def check_exhaustive_jacobian_weierstrass(name, A, B, branches, formula, p):
       if r:
         points.append(point)
 
+  ret = True
   for za in range(1, p):
     for zb in range(1, p):
       for pa in points:
@@ -211,8 +212,11 @@ def check_exhaustive_jacobian_weierstrass(name, A, B, branches, formula, p):
                         match = True
                       r, e = concrete_verify(require)
                       if not r:
+                        ret = False
                         print("  failure in branch %i for (%s,%s,%s,%s) + (%s,%s,%s,%s) = (%s,%s,%s,%s): %s" % (branch, pA.X, pA.Y, pA.Z, pA.Infinity, pB.X, pB.Y, pB.Z, pB.Infinity, pC.X, pC.Y, pC.Z, pC.Infinity, e))
+
   print()
+  return ret
 
 
 def check_symbolic_function(R, assumeAssert, assumeBranch, f, A, B, pa, pb, pA, pB, pC):
@@ -244,15 +248,21 @@ def check_symbolic_jacobian_weierstrass(name, A, B, branches, formula):
 
   print("Formula " + name + ":")
   count = 0
+  ret = True
   for branch in range(branches):
     assumeFormula, assumeBranch, pC = formula(branch, pA, pB)
+    assumeBranch = assumeBranch.map(lift)
+    assumeFormula = assumeFormula.map(lift)
     pC.X = lift(pC.X)
     pC.Y = lift(pC.Y)
     pC.Z = lift(pC.Z)
     pC.Infinity = lift(pC.Infinity)
 
     for key in laws_jacobian_weierstrass:
-      res[key].append((check_symbolic_function(R, assumeFormula, assumeBranch, laws_jacobian_weierstrass[key], A, B, pa, pb, pA, pB, pC), branch))
+      success, msg = check_symbolic_function(R, assumeFormula, assumeBranch, laws_jacobian_weierstrass[key], A, B, pa, pb, pA, pB, pC)
+      if not success:
+        ret = False
+      res[key].append((msg, branch))
 
   for key in res:
     print("  %s:" % key)
@@ -262,3 +272,4 @@ def check_symbolic_jacobian_weierstrass(name, A, B, branches, formula):
         print("    branch %i: %s" % (x[1], x[0]))
 
   print()
+  return ret
diff --git a/src/secp256k1/src/assumptions.h b/src/secp256k1/src/assumptions.h
index 6dc527b2889..8ed04209e91 100644
--- a/src/secp256k1/src/assumptions.h
+++ b/src/secp256k1/src/assumptions.h
@@ -10,6 +10,9 @@
 #include <limits.h>
 
 #include "util.h"
+#if defined(SECP256K1_INT128_NATIVE)
+#include "int128_native.h"
+#endif
 
 /* This library, like most software, relies on a number of compiler implementation defined (but not undefined)
    behaviours. Although the behaviours we require are essentially universal we test them specifically here to
@@ -55,7 +58,7 @@ struct secp256k1_assumption_checker {
 
         /* To int64_t. */
         ((int64_t)(uint64_t)0xB123C456D789E012ULL == (int64_t)-(int64_t)0x4EDC3BA928761FEEULL) &&
-#if defined(SECP256K1_WIDEMUL_INT128)
+#if defined(SECP256K1_INT128_NATIVE)
         ((int64_t)(((uint128_t)0xA1234567B8901234ULL << 64) + 0xC5678901D2345678ULL) == (int64_t)-(int64_t)0x3A9876FE2DCBA988ULL) &&
         (((int64_t)(int128_t)(((uint128_t)0xB1C2D3E4F5A6B7C8ULL << 64) + 0xD9E0F1A2B3C4D5E6ULL)) == (int64_t)(uint64_t)0xD9E0F1A2B3C4D5E6ULL) &&
         (((int64_t)(int128_t)(((uint128_t)0xABCDEF0123456789ULL << 64) + 0x0123456789ABCDEFULL)) == (int64_t)(uint64_t)0x0123456789ABCDEFULL) &&
@@ -71,7 +74,7 @@ struct secp256k1_assumption_checker {
         ((((int16_t)0xE9AC) >> 4) == (int16_t)(uint16_t)0xFE9A) &&
         ((((int32_t)0x937C918A) >> 9) == (int32_t)(uint32_t)0xFFC9BE48) &&
         ((((int64_t)0xA8B72231DF9CF4B9ULL) >> 19) == (int64_t)(uint64_t)0xFFFFF516E4463BF3ULL) &&
-#if defined(SECP256K1_WIDEMUL_INT128)
+#if defined(SECP256K1_INT128_NATIVE)
         ((((int128_t)(((uint128_t)0xCD833A65684A0DBCULL << 64) + 0xB349312F71EA7637ULL)) >> 39) == (int128_t)(((uint128_t)0xFFFFFFFFFF9B0674ULL << 64) + 0xCAD0941B79669262ULL)) &&
 #endif
     1) * 2 - 1];
diff --git a/src/secp256k1/src/basic-config.h b/src/secp256k1/src/basic-config.h
deleted file mode 100644
index 6f7693cb8fd..00000000000
--- a/src/secp256k1/src/basic-config.h
+++ /dev/null
@@ -1,17 +0,0 @@
-/***********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille                              *
- * Distributed under the MIT software license, see the accompanying    *
- * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
- ***********************************************************************/
-
-#ifndef SECP256K1_BASIC_CONFIG_H
-#define SECP256K1_BASIC_CONFIG_H
-
-#ifdef USE_BASIC_CONFIG
-
-#define ECMULT_WINDOW_SIZE 15
-#define ECMULT_GEN_PREC_BITS 4
-
-#endif /* USE_BASIC_CONFIG */
-
-#endif /* SECP256K1_BASIC_CONFIG_H */
diff --git a/src/secp256k1/src/bench.c b/src/secp256k1/src/bench.c
new file mode 100644
index 00000000000..e68021aa284
--- /dev/null
+++ b/src/secp256k1/src/bench.c
@@ -0,0 +1,229 @@
+/***********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                    *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#include <stdio.h>
+#include <string.h>
+
+#include "../include/secp256k1.h"
+#include "util.h"
+#include "bench.h"
+
+void help(int default_iters) {
+    printf("Benchmarks the following algorithms:\n");
+    printf("    - ECDSA signing/verification\n");
+
+#ifdef ENABLE_MODULE_ECDH
+    printf("    - ECDH key exchange (optional module)\n");
+#endif
+
+#ifdef ENABLE_MODULE_RECOVERY
+    printf("    - Public key recovery (optional module)\n");
+#endif
+
+#ifdef ENABLE_MODULE_SCHNORRSIG
+    printf("    - Schnorr signatures (optional module)\n");
+#endif
+
+    printf("\n");
+    printf("The default number of iterations for each benchmark is %d. This can be\n", default_iters);
+    printf("customized using the SECP256K1_BENCH_ITERS environment variable.\n");
+    printf("\n");
+    printf("Usage: ./bench [args]\n");
+    printf("By default, all benchmarks will be run.\n");
+    printf("args:\n");
+    printf("    help              : display this help and exit\n");
+    printf("    ecdsa             : all ECDSA algorithms--sign, verify, recovery (if enabled)\n");
+    printf("    ecdsa_sign        : ECDSA siging algorithm\n");
+    printf("    ecdsa_verify      : ECDSA verification algorithm\n");
+
+#ifdef ENABLE_MODULE_RECOVERY
+    printf("    ecdsa_recover     : ECDSA public key recovery algorithm\n");
+#endif
+
+#ifdef ENABLE_MODULE_ECDH
+    printf("    ecdh              : ECDH key exchange algorithm\n");
+#endif
+
+#ifdef ENABLE_MODULE_SCHNORRSIG
+    printf("    schnorrsig        : all Schnorr signature algorithms (sign, verify)\n");
+    printf("    schnorrsig_sign   : Schnorr sigining algorithm\n");
+    printf("    schnorrsig_verify : Schnorr verification algorithm\n");
+#endif
+
+    printf("\n");
+}
+
+typedef struct {
+    secp256k1_context *ctx;
+    unsigned char msg[32];
+    unsigned char key[32];
+    unsigned char sig[72];
+    size_t siglen;
+    unsigned char pubkey[33];
+    size_t pubkeylen;
+} bench_verify_data;
+
+static void bench_verify(void* arg, int iters) {
+    int i;
+    bench_verify_data* data = (bench_verify_data*)arg;
+
+    for (i = 0; i < iters; i++) {
+        secp256k1_pubkey pubkey;
+        secp256k1_ecdsa_signature sig;
+        data->sig[data->siglen - 1] ^= (i & 0xFF);
+        data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
+        data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
+        CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->pubkey, data->pubkeylen) == 1);
+        CHECK(secp256k1_ecdsa_signature_parse_der(data->ctx, &sig, data->sig, data->siglen) == 1);
+        CHECK(secp256k1_ecdsa_verify(data->ctx, &sig, data->msg, &pubkey) == (i == 0));
+        data->sig[data->siglen - 1] ^= (i & 0xFF);
+        data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
+        data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
+    }
+}
+
+typedef struct {
+    secp256k1_context* ctx;
+    unsigned char msg[32];
+    unsigned char key[32];
+} bench_sign_data;
+
+static void bench_sign_setup(void* arg) {
+    int i;
+    bench_sign_data *data = (bench_sign_data*)arg;
+
+    for (i = 0; i < 32; i++) {
+        data->msg[i] = i + 1;
+    }
+    for (i = 0; i < 32; i++) {
+        data->key[i] = i + 65;
+    }
+}
+
+static void bench_sign_run(void* arg, int iters) {
+    int i;
+    bench_sign_data *data = (bench_sign_data*)arg;
+
+    unsigned char sig[74];
+    for (i = 0; i < iters; i++) {
+        size_t siglen = 74;
+        int j;
+        secp256k1_ecdsa_signature signature;
+        CHECK(secp256k1_ecdsa_sign(data->ctx, &signature, data->msg, data->key, NULL, NULL));
+        CHECK(secp256k1_ecdsa_signature_serialize_der(data->ctx, sig, &siglen, &signature));
+        for (j = 0; j < 32; j++) {
+            data->msg[j] = sig[j];
+            data->key[j] = sig[j + 32];
+        }
+    }
+}
+
+#ifdef ENABLE_MODULE_ECDH
+# include "modules/ecdh/bench_impl.h"
+#endif
+
+#ifdef ENABLE_MODULE_RECOVERY
+# include "modules/recovery/bench_impl.h"
+#endif
+
+#ifdef ENABLE_MODULE_SCHNORRSIG
+# include "modules/schnorrsig/bench_impl.h"
+#endif
+
+int main(int argc, char** argv) {
+    int i;
+    secp256k1_pubkey pubkey;
+    secp256k1_ecdsa_signature sig;
+    bench_verify_data data;
+
+    int d = argc == 1;
+    int default_iters = 20000;
+    int iters = get_iters(default_iters);
+
+    /* Check for invalid user arguments */
+    char* valid_args[] = {"ecdsa", "verify", "ecdsa_verify", "sign", "ecdsa_sign", "ecdh", "recover",
+                         "ecdsa_recover", "schnorrsig", "schnorrsig_verify", "schnorrsig_sign"};
+    size_t valid_args_size = sizeof(valid_args)/sizeof(valid_args[0]);
+    int invalid_args = have_invalid_args(argc, argv, valid_args, valid_args_size);
+
+    if (argc > 1) {
+        if (have_flag(argc, argv, "-h")
+           || have_flag(argc, argv, "--help")
+           || have_flag(argc, argv, "help")) {
+            help(default_iters);
+            return 0;
+        } else if (invalid_args) {
+            fprintf(stderr, "./bench: unrecognized argument.\n\n");
+            help(default_iters);
+            return 1;
+        }
+    }
+
+/* Check if the user tries to benchmark optional module without building it */
+#ifndef ENABLE_MODULE_ECDH
+    if (have_flag(argc, argv, "ecdh")) {
+        fprintf(stderr, "./bench: ECDH module not enabled.\n");
+        fprintf(stderr, "Use ./configure --enable-module-ecdh.\n\n");
+        return 1;
+    }
+#endif
+
+#ifndef ENABLE_MODULE_RECOVERY
+    if (have_flag(argc, argv, "recover") || have_flag(argc, argv, "ecdsa_recover")) {
+        fprintf(stderr, "./bench: Public key recovery module not enabled.\n");
+        fprintf(stderr, "Use ./configure --enable-module-recovery.\n\n");
+        return 1;
+    }
+#endif
+
+#ifndef ENABLE_MODULE_SCHNORRSIG
+    if (have_flag(argc, argv, "schnorrsig") || have_flag(argc, argv, "schnorrsig_sign") || have_flag(argc, argv, "schnorrsig_verify")) {
+        fprintf(stderr, "./bench: Schnorr signatures module not enabled.\n");
+        fprintf(stderr, "Use ./configure --enable-module-schnorrsig.\n\n");
+        return 1;
+    }
+#endif
+
+    /* ECDSA benchmark */
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+
+    for (i = 0; i < 32; i++) {
+        data.msg[i] = 1 + i;
+    }
+    for (i = 0; i < 32; i++) {
+        data.key[i] = 33 + i;
+    }
+    data.siglen = 72;
+    CHECK(secp256k1_ecdsa_sign(data.ctx, &sig, data.msg, data.key, NULL, NULL));
+    CHECK(secp256k1_ecdsa_signature_serialize_der(data.ctx, data.sig, &data.siglen, &sig));
+    CHECK(secp256k1_ec_pubkey_create(data.ctx, &pubkey, data.key));
+    data.pubkeylen = 33;
+    CHECK(secp256k1_ec_pubkey_serialize(data.ctx, data.pubkey, &data.pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
+
+    print_output_table_header_row();
+    if (d || have_flag(argc, argv, "ecdsa") || have_flag(argc, argv, "verify") || have_flag(argc, argv, "ecdsa_verify")) run_benchmark("ecdsa_verify", bench_verify, NULL, NULL, &data, 10, iters);
+
+    if (d || have_flag(argc, argv, "ecdsa") || have_flag(argc, argv, "sign") || have_flag(argc, argv, "ecdsa_sign")) run_benchmark("ecdsa_sign", bench_sign_run, bench_sign_setup, NULL, &data, 10, iters);
+
+    secp256k1_context_destroy(data.ctx);
+
+#ifdef ENABLE_MODULE_ECDH
+    /* ECDH benchmarks */
+    run_ecdh_bench(iters, argc, argv);
+#endif
+
+#ifdef ENABLE_MODULE_RECOVERY
+    /* ECDSA recovery benchmarks */
+    run_recovery_bench(iters, argc, argv);
+#endif
+
+#ifdef ENABLE_MODULE_SCHNORRSIG
+    /* Schnorr signature benchmarks */
+    run_schnorrsig_bench(iters, argc, argv);
+#endif
+
+    return 0;
+}
diff --git a/src/secp256k1/src/bench.h b/src/secp256k1/src/bench.h
index 63c55df44d0..611ba11f049 100644
--- a/src/secp256k1/src/bench.h
+++ b/src/secp256k1/src/bench.h
@@ -7,15 +7,31 @@
 #ifndef SECP256K1_BENCH_H
 #define SECP256K1_BENCH_H
 
+#include <stdlib.h>
 #include <stdint.h>
 #include <stdio.h>
 #include <string.h>
-#include "sys/time.h"
+
+#if (defined(_MSC_VER) && _MSC_VER >= 1900)
+#  include <time.h>
+#else
+#  include "sys/time.h"
+#endif
 
 static int64_t gettime_i64(void) {
+#if (defined(_MSC_VER) && _MSC_VER >= 1900)
+    /* C11 way to get wallclock time */
+    struct timespec tv;
+    if (!timespec_get(&tv, TIME_UTC)) {
+        fputs("timespec_get failed!", stderr);
+        exit(1);
+    }
+    return (int64_t)tv.tv_nsec / 1000 + (int64_t)tv.tv_sec * 1000000LL;
+#else
     struct timeval tv;
     gettimeofday(&tv, NULL);
     return (int64_t)tv.tv_usec + (int64_t)tv.tv_sec * 1000000LL;
+#endif
 }
 
 #define FP_EXP (6)
@@ -24,7 +40,7 @@ static int64_t gettime_i64(void) {
 /* Format fixed point number. */
 void print_number(const int64_t x) {
     int64_t x_abs, y;
-    int c, i, rounding;
+    int c, i, rounding, g; /* g = integer part size, c = fractional part size */
     size_t ptr;
     char buffer[30];
 
@@ -56,21 +72,27 @@ void print_number(const int64_t x) {
     /* Format and print the number. */
     ptr = sizeof(buffer) - 1;
     buffer[ptr] = 0;
-    if (c != 0) {
+    g = 0;
+    if (c != 0) { /* non zero fractional part */
         for (i = 0; i < c; ++i) {
             buffer[--ptr] = '0' + (y % 10);
             y /= 10;
         }
-        buffer[--ptr] = '.';
+    } else if (c == 0) { /* fractional part is 0 */
+        buffer[--ptr] = '0'; 
     }
+    buffer[--ptr] = '.';
     do {
         buffer[--ptr] = '0' + (y % 10);
         y /= 10;
+        g++;
     } while (y != 0);
     if (x < 0) {
         buffer[--ptr] = '-';
+        g++;
     }
-    printf("%s", &buffer[ptr]);
+    printf("%5.*s", g, &buffer[ptr]); /* Prints integer part */
+    printf("%-*s", FP_EXP, &buffer[ptr + g]); /* Prints fractional part */
 }
 
 void run_benchmark(char *name, void (*benchmark)(void*, int), void (*setup)(void*), void (*teardown)(void*, int), void* data, int count, int iter) {
@@ -97,22 +119,20 @@ void run_benchmark(char *name, void (*benchmark)(void*, int), void (*setup)(void
         }
         sum += total;
     }
-    printf("%s: min ", name);
+    /* ',' is used as a column delimiter */
+    printf("%-30s, ", name);
     print_number(min * FP_MULT / iter);
-    printf("us / avg ");
+    printf("   , ");
     print_number(((sum * FP_MULT) / count) / iter);
-    printf("us / max ");
+    printf("   , ");
     print_number(max * FP_MULT / iter);
-    printf("us\n");
+    printf("\n");
 }
 
 int have_flag(int argc, char** argv, char *flag) {
     char** argm = argv + argc;
     argv++;
-    if (argv == argm) {
-        return 1;
-    }
-    while (argv != NULL && argv != argm) {
+    while (argv != argm) {
         if (strcmp(*argv, flag) == 0) {
             return 1;
         }
@@ -121,6 +141,32 @@ int have_flag(int argc, char** argv, char *flag) {
     return 0;
 }
 
+/* takes an array containing the arguments that the user is allowed to enter on the command-line
+   returns:
+      - 1 if the user entered an invalid argument
+      - 0 if all the user entered arguments are valid */
+int have_invalid_args(int argc, char** argv, char** valid_args, size_t n) {
+    size_t i;
+    int found_valid;
+    char** argm = argv + argc;
+    argv++;
+
+    while (argv != argm) {
+        found_valid = 0;
+        for (i = 0; i < n; i++) {
+            if (strcmp(*argv, valid_args[i]) == 0) {
+                found_valid = 1; /* user entered a valid arg from the list */
+                break;
+            }
+        }
+        if (found_valid == 0) {
+            return 1; /* invalid arg found */
+        }
+        argv++;
+    }
+    return 0;
+}
+
 int get_iters(int default_iters) {
     char* env = getenv("SECP256K1_BENCH_ITERS");
     if (env) {
@@ -130,4 +176,13 @@ int get_iters(int default_iters) {
     }
 }
 
+void print_output_table_header_row(void) {
+    char* bench_str = "Benchmark";     /* left justified */
+    char* min_str = "    Min(us)    "; /* center alignment */
+    char* avg_str = "    Avg(us)    ";
+    char* max_str = "    Max(us)    ";
+    printf("%-30s,%-15s,%-15s,%-15s\n", bench_str, min_str, avg_str, max_str);
+    printf("\n");
+}
+
 #endif /* SECP256K1_BENCH_H */
diff --git a/src/secp256k1/src/bench_ecmult.c b/src/secp256k1/src/bench_ecmult.c
index 1d463f92d0b..9d0db340e12 100644
--- a/src/secp256k1/src/bench_ecmult.c
+++ b/src/secp256k1/src/bench_ecmult.c
@@ -84,9 +84,7 @@ static void bench_ecmult_teardown_helper(bench_data* data, size_t* seckey_offset
         }
     }
     secp256k1_ecmult_gen(&data->ctx->ecmult_gen_ctx, &tmp, &sum_scalars);
-    secp256k1_gej_neg(&tmp, &tmp);
-    secp256k1_gej_add_var(&tmp, &tmp, &sum_output, NULL);
-    CHECK(secp256k1_gej_is_infinity(&tmp));
+    CHECK(secp256k1_gej_eq_var(&tmp, &sum_output));
 }
 
 static void bench_ecmult_setup(void* arg) {
@@ -124,46 +122,46 @@ static void bench_ecmult_const_teardown(void* arg, int iters) {
     bench_ecmult_teardown_helper(data, &data->offset1, &data->offset2, NULL, iters);
 }
 
-static void bench_ecmult_1(void* arg, int iters) {
+static void bench_ecmult_1p(void* arg, int iters) {
     bench_data* data = (bench_data*)arg;
     int i;
 
     for (i = 0; i < iters; ++i) {
-        secp256k1_ecmult(&data->ctx->ecmult_ctx, &data->output[i], &data->pubkeys_gej[(data->offset1+i) % POINTS], &data->scalars[(data->offset2+i) % POINTS], NULL);
+        secp256k1_ecmult(&data->output[i], &data->pubkeys_gej[(data->offset1+i) % POINTS], &data->scalars[(data->offset2+i) % POINTS], NULL);
     }
 }
 
-static void bench_ecmult_1_teardown(void* arg, int iters) {
+static void bench_ecmult_1p_teardown(void* arg, int iters) {
     bench_data* data = (bench_data*)arg;
     bench_ecmult_teardown_helper(data, &data->offset1, &data->offset2, NULL, iters);
 }
 
-static void bench_ecmult_1g(void* arg, int iters) {
+static void bench_ecmult_0p_g(void* arg, int iters) {
     bench_data* data = (bench_data*)arg;
     secp256k1_scalar zero;
     int i;
 
     secp256k1_scalar_set_int(&zero, 0);
     for (i = 0; i < iters; ++i) {
-        secp256k1_ecmult(&data->ctx->ecmult_ctx, &data->output[i], NULL, &zero, &data->scalars[(data->offset1+i) % POINTS]);
+        secp256k1_ecmult(&data->output[i], NULL, &zero, &data->scalars[(data->offset1+i) % POINTS]);
     }
 }
 
-static void bench_ecmult_1g_teardown(void* arg, int iters) {
+static void bench_ecmult_0p_g_teardown(void* arg, int iters) {
     bench_data* data = (bench_data*)arg;
     bench_ecmult_teardown_helper(data, NULL, NULL, &data->offset1, iters);
 }
 
-static void bench_ecmult_2g(void* arg, int iters) {
+static void bench_ecmult_1p_g(void* arg, int iters) {
     bench_data* data = (bench_data*)arg;
     int i;
 
     for (i = 0; i < iters/2; ++i) {
-        secp256k1_ecmult(&data->ctx->ecmult_ctx, &data->output[i], &data->pubkeys_gej[(data->offset1+i) % POINTS], &data->scalars[(data->offset2+i) % POINTS], &data->scalars[(data->offset1+i) % POINTS]);
+        secp256k1_ecmult(&data->output[i], &data->pubkeys_gej[(data->offset1+i) % POINTS], &data->scalars[(data->offset2+i) % POINTS], &data->scalars[(data->offset1+i) % POINTS]);
     }
 }
 
-static void bench_ecmult_2g_teardown(void* arg, int iters) {
+static void bench_ecmult_1p_g_teardown(void* arg, int iters) {
     bench_data* data = (bench_data*)arg;
     bench_ecmult_teardown_helper(data, &data->offset1, &data->offset2, &data->offset1, iters/2);
 }
@@ -175,14 +173,14 @@ static void run_ecmult_bench(bench_data* data, int iters) {
     sprintf(str, "ecmult_const");
     run_benchmark(str, bench_ecmult_const, bench_ecmult_setup, bench_ecmult_const_teardown, data, 10, iters);
     /* ecmult with non generator point */
-    sprintf(str, "ecmult 1");
-    run_benchmark(str, bench_ecmult_1, bench_ecmult_setup, bench_ecmult_1_teardown, data, 10, iters);
+    sprintf(str, "ecmult_1p");
+    run_benchmark(str, bench_ecmult_1p, bench_ecmult_setup, bench_ecmult_1p_teardown, data, 10, iters);
     /* ecmult with generator point */
-    sprintf(str, "ecmult 1g");
-    run_benchmark(str, bench_ecmult_1g, bench_ecmult_setup, bench_ecmult_1g_teardown, data, 10, iters);
+    sprintf(str, "ecmult_0p_g");
+    run_benchmark(str, bench_ecmult_0p_g, bench_ecmult_setup, bench_ecmult_0p_g_teardown, data, 10, iters);
     /* ecmult with generator and non-generator point. The reported time is per point. */
-    sprintf(str, "ecmult 2g");
-    run_benchmark(str, bench_ecmult_2g, bench_ecmult_setup, bench_ecmult_2g_teardown, data, 10, 2*iters);
+    sprintf(str, "ecmult_1p_g");
+    run_benchmark(str, bench_ecmult_1p_g, bench_ecmult_setup, bench_ecmult_1p_g_teardown, data, 10, 2*iters);
 }
 
 static int bench_ecmult_multi_callback(secp256k1_scalar* sc, secp256k1_ge* ge, size_t idx, void* arg) {
@@ -207,7 +205,7 @@ static void bench_ecmult_multi(void* arg, int iters) {
     iters = iters / data->count;
 
     for (iter = 0; iter < iters; ++iter) {
-        data->ecmult_multi(&data->ctx->error_callback, &data->ctx->ecmult_ctx, data->scratch, &data->output[iter], data->includes_g ? &data->scalars[data->offset1] : NULL, bench_ecmult_multi_callback, arg, count - includes_g);
+        data->ecmult_multi(&data->ctx->error_callback, data->scratch, &data->output[iter], data->includes_g ? &data->scalars[data->offset1] : NULL, bench_ecmult_multi_callback, arg, count - includes_g);
         data->offset1 = (data->offset1 + count) % POINTS;
         data->offset2 = (data->offset2 + count - 1) % POINTS;
     }
@@ -266,11 +264,15 @@ static void run_ecmult_multi_bench(bench_data* data, size_t count, int includes_
             secp256k1_scalar_add(&total, &total, &tmp);
         }
         secp256k1_scalar_negate(&total, &total);
-        secp256k1_ecmult(&data->ctx->ecmult_ctx, &data->expected_output[iter], NULL, &zero, &total);
+        secp256k1_ecmult(&data->expected_output[iter], NULL, &zero, &total);
     }
 
     /* Run the benchmark. */
-    sprintf(str, includes_g ? "ecmult_multi %ig" : "ecmult_multi %i", (int)count);
+    if (includes_g) {
+        sprintf(str, "ecmult_multi_%ip_g", (int)count - 1);
+    } else {
+        sprintf(str, "ecmult_multi_%ip", (int)count);
+    }
     run_benchmark(str, bench_ecmult_multi, bench_ecmult_multi_setup, bench_ecmult_multi_teardown, data, 10, count * iters);
 }
 
@@ -288,7 +290,7 @@ int main(int argc, char **argv) {
            || have_flag(argc, argv, "--help")
            || have_flag(argc, argv, "help")) {
             help(argv);
-            return 1;
+            return 0;
         } else if(have_flag(argc, argv, "pippenger_wnaf")) {
             printf("Using pippenger_wnaf:\n");
             data.ecmult_multi = secp256k1_ecmult_pippenger_batch_single;
@@ -304,7 +306,7 @@ int main(int argc, char **argv) {
         }
     }
 
-    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
     scratch_size = secp256k1_strauss_scratch_size(POINTS) + STRAUSS_SCRATCH_OBJECTS*16;
     if (!have_flag(argc, argv, "simple")) {
         data.scratch = secp256k1_scratch_space_create(data.ctx, scratch_size);
@@ -333,6 +335,7 @@ int main(int argc, char **argv) {
     secp256k1_ge_set_all_gej_var(data.pubkeys, data.pubkeys_gej, POINTS);
 
 
+    print_output_table_header_row();
     /* Initialize offset1 and offset2 */
     hash_into_offset(&data, 0);
     run_ecmult_bench(&data, iters);
diff --git a/src/secp256k1/src/bench_internal.c b/src/secp256k1/src/bench_internal.c
index 161b1c4a476..2224058f64e 100644
--- a/src/secp256k1/src/bench_internal.c
+++ b/src/secp256k1/src/bench_internal.c
@@ -140,6 +140,15 @@ void bench_scalar_inverse_var(void* arg, int iters) {
     CHECK(j <= iters);
 }
 
+void bench_field_half(void* arg, int iters) {
+    int i;
+    bench_inv *data = (bench_inv*)arg;
+
+    for (i = 0; i < iters; i++) {
+        secp256k1_fe_half(&data->fe[0]);
+    }
+}
+
 void bench_field_normalize(void* arg, int iters) {
     int i;
     bench_inv *data = (bench_inv*)arg;
@@ -245,6 +254,15 @@ void bench_group_add_affine_var(void* arg, int iters) {
     }
 }
 
+void bench_group_add_zinv_var(void* arg, int iters) {
+    int i;
+    bench_inv *data = (bench_inv*)arg;
+
+    for (i = 0; i < iters; i++) {
+        secp256k1_gej_add_zinv_var(&data->gej[0], &data->gej[0], &data->ge[1], &data->gej[0].y);
+    }
+}
+
 void bench_group_to_affine_var(void* arg, int iters) {
     int i;
     bench_inv *data = (bench_inv*)arg;
@@ -325,56 +343,51 @@ void bench_rfc6979_hmac_sha256(void* arg, int iters) {
     }
 }
 
-void bench_context_verify(void* arg, int iters) {
-    int i;
-    (void)arg;
-    for (i = 0; i < iters; i++) {
-        secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_VERIFY));
-    }
-}
-
-void bench_context_sign(void* arg, int iters) {
+void bench_context(void* arg, int iters) {
     int i;
     (void)arg;
     for (i = 0; i < iters; i++) {
-        secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_SIGN));
+        secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_NONE));
     }
 }
 
 int main(int argc, char **argv) {
     bench_inv data;
     int iters = get_iters(20000);
-
-    if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "add")) run_benchmark("scalar_add", bench_scalar_add, bench_setup, NULL, &data, 10, iters*100);
-    if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "negate")) run_benchmark("scalar_negate", bench_scalar_negate, bench_setup, NULL, &data, 10, iters*100);
-    if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "mul")) run_benchmark("scalar_mul", bench_scalar_mul, bench_setup, NULL, &data, 10, iters*10);
-    if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "split")) run_benchmark("scalar_split", bench_scalar_split, bench_setup, NULL, &data, 10, iters);
-    if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse", bench_scalar_inverse, bench_setup, NULL, &data, 10, iters);
-    if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse_var", bench_scalar_inverse_var, bench_setup, NULL, &data, 10, iters);
-
-    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize", bench_field_normalize, bench_setup, NULL, &data, 10, iters*100);
-    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize_weak", bench_field_normalize_weak, bench_setup, NULL, &data, 10, iters*100);
-    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqr")) run_benchmark("field_sqr", bench_field_sqr, bench_setup, NULL, &data, 10, iters*10);
-    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "mul")) run_benchmark("field_mul", bench_field_mul, bench_setup, NULL, &data, 10, iters*10);
-    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse", bench_field_inverse, bench_setup, NULL, &data, 10, iters);
-    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse_var", bench_field_inverse_var, bench_setup, NULL, &data, 10, iters);
-    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqrt")) run_benchmark("field_sqrt", bench_field_sqrt, bench_setup, NULL, &data, 10, iters);
-
-    if (have_flag(argc, argv, "group") || have_flag(argc, argv, "double")) run_benchmark("group_double_var", bench_group_double_var, bench_setup, NULL, &data, 10, iters*10);
-    if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_var", bench_group_add_var, bench_setup, NULL, &data, 10, iters*10);
-    if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine", bench_group_add_affine, bench_setup, NULL, &data, 10, iters*10);
-    if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine_var", bench_group_add_affine_var, bench_setup, NULL, &data, 10, iters*10);
-    if (have_flag(argc, argv, "group") || have_flag(argc, argv, "to_affine")) run_benchmark("group_to_affine_var", bench_group_to_affine_var, bench_setup, NULL, &data, 10, iters);
-
-    if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("wnaf_const", bench_wnaf_const, bench_setup, NULL, &data, 10, iters);
-    if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("ecmult_wnaf", bench_ecmult_wnaf, bench_setup, NULL, &data, 10, iters);
-
-    if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "sha256")) run_benchmark("hash_sha256", bench_sha256, bench_setup, NULL, &data, 10, iters);
-    if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "hmac")) run_benchmark("hash_hmac_sha256", bench_hmac_sha256, bench_setup, NULL, &data, 10, iters);
-    if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "rng6979")) run_benchmark("hash_rfc6979_hmac_sha256", bench_rfc6979_hmac_sha256, bench_setup, NULL, &data, 10, iters);
-
-    if (have_flag(argc, argv, "context") || have_flag(argc, argv, "verify")) run_benchmark("context_verify", bench_context_verify, bench_setup, NULL, &data, 10, 1 + iters/1000);
-    if (have_flag(argc, argv, "context") || have_flag(argc, argv, "sign")) run_benchmark("context_sign", bench_context_sign, bench_setup, NULL, &data, 10, 1 + iters/100);
+    int d = argc == 1; /* default */
+    print_output_table_header_row();
+
+    if (d || have_flag(argc, argv, "scalar") || have_flag(argc, argv, "add")) run_benchmark("scalar_add", bench_scalar_add, bench_setup, NULL, &data, 10, iters*100);
+    if (d || have_flag(argc, argv, "scalar") || have_flag(argc, argv, "negate")) run_benchmark("scalar_negate", bench_scalar_negate, bench_setup, NULL, &data, 10, iters*100);
+    if (d || have_flag(argc, argv, "scalar") || have_flag(argc, argv, "mul")) run_benchmark("scalar_mul", bench_scalar_mul, bench_setup, NULL, &data, 10, iters*10);
+    if (d || have_flag(argc, argv, "scalar") || have_flag(argc, argv, "split")) run_benchmark("scalar_split", bench_scalar_split, bench_setup, NULL, &data, 10, iters);
+    if (d || have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse", bench_scalar_inverse, bench_setup, NULL, &data, 10, iters);
+    if (d || have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse_var", bench_scalar_inverse_var, bench_setup, NULL, &data, 10, iters);
+
+    if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "half")) run_benchmark("field_half", bench_field_half, bench_setup, NULL, &data, 10, iters*100);
+    if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize", bench_field_normalize, bench_setup, NULL, &data, 10, iters*100);
+    if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize_weak", bench_field_normalize_weak, bench_setup, NULL, &data, 10, iters*100);
+    if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "sqr")) run_benchmark("field_sqr", bench_field_sqr, bench_setup, NULL, &data, 10, iters*10);
+    if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "mul")) run_benchmark("field_mul", bench_field_mul, bench_setup, NULL, &data, 10, iters*10);
+    if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse", bench_field_inverse, bench_setup, NULL, &data, 10, iters);
+    if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse_var", bench_field_inverse_var, bench_setup, NULL, &data, 10, iters);
+    if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "sqrt")) run_benchmark("field_sqrt", bench_field_sqrt, bench_setup, NULL, &data, 10, iters);
+
+    if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "double")) run_benchmark("group_double_var", bench_group_double_var, bench_setup, NULL, &data, 10, iters*10);
+    if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_var", bench_group_add_var, bench_setup, NULL, &data, 10, iters*10);
+    if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine", bench_group_add_affine, bench_setup, NULL, &data, 10, iters*10);
+    if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine_var", bench_group_add_affine_var, bench_setup, NULL, &data, 10, iters*10);
+    if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_zinv_var", bench_group_add_zinv_var, bench_setup, NULL, &data, 10, iters*10);
+    if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "to_affine")) run_benchmark("group_to_affine_var", bench_group_to_affine_var, bench_setup, NULL, &data, 10, iters);
+
+    if (d || have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("wnaf_const", bench_wnaf_const, bench_setup, NULL, &data, 10, iters);
+    if (d || have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("ecmult_wnaf", bench_ecmult_wnaf, bench_setup, NULL, &data, 10, iters);
+
+    if (d || have_flag(argc, argv, "hash") || have_flag(argc, argv, "sha256")) run_benchmark("hash_sha256", bench_sha256, bench_setup, NULL, &data, 10, iters);
+    if (d || have_flag(argc, argv, "hash") || have_flag(argc, argv, "hmac")) run_benchmark("hash_hmac_sha256", bench_hmac_sha256, bench_setup, NULL, &data, 10, iters);
+    if (d || have_flag(argc, argv, "hash") || have_flag(argc, argv, "rng6979")) run_benchmark("hash_rfc6979_hmac_sha256", bench_rfc6979_hmac_sha256, bench_setup, NULL, &data, 10, iters);
+
+    if (d || have_flag(argc, argv, "context")) run_benchmark("context_create", bench_context, bench_setup, NULL, &data, 10, iters);
 
     return 0;
 }
diff --git a/src/secp256k1/src/bench_sign.c b/src/secp256k1/src/bench_sign.c
deleted file mode 100644
index f659c18c92d..00000000000
--- a/src/secp256k1/src/bench_sign.c
+++ /dev/null
@@ -1,58 +0,0 @@
-/***********************************************************************
- * Copyright (c) 2014 Pieter Wuille                                    *
- * Distributed under the MIT software license, see the accompanying    *
- * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
- ***********************************************************************/
-
-#include "../include/secp256k1.h"
-#include "util.h"
-#include "bench.h"
-
-typedef struct {
-    secp256k1_context* ctx;
-    unsigned char msg[32];
-    unsigned char key[32];
-} bench_sign_data;
-
-static void bench_sign_setup(void* arg) {
-    int i;
-    bench_sign_data *data = (bench_sign_data*)arg;
-
-    for (i = 0; i < 32; i++) {
-        data->msg[i] = i + 1;
-    }
-    for (i = 0; i < 32; i++) {
-        data->key[i] = i + 65;
-    }
-}
-
-static void bench_sign_run(void* arg, int iters) {
-    int i;
-    bench_sign_data *data = (bench_sign_data*)arg;
-
-    unsigned char sig[74];
-    for (i = 0; i < iters; i++) {
-        size_t siglen = 74;
-        int j;
-        secp256k1_ecdsa_signature signature;
-        CHECK(secp256k1_ecdsa_sign(data->ctx, &signature, data->msg, data->key, NULL, NULL));
-        CHECK(secp256k1_ecdsa_signature_serialize_der(data->ctx, sig, &siglen, &signature));
-        for (j = 0; j < 32; j++) {
-            data->msg[j] = sig[j];
-            data->key[j] = sig[j + 32];
-        }
-    }
-}
-
-int main(void) {
-    bench_sign_data data;
-
-    int iters = get_iters(20000);
-
-    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
-
-    run_benchmark("ecdsa_sign", bench_sign_run, bench_sign_setup, NULL, &data, 10, iters);
-
-    secp256k1_context_destroy(data.ctx);
-    return 0;
-}
diff --git a/src/secp256k1/src/bench_verify.c b/src/secp256k1/src/bench_verify.c
deleted file mode 100644
index 565ae4beec8..00000000000
--- a/src/secp256k1/src/bench_verify.c
+++ /dev/null
@@ -1,115 +0,0 @@
-/***********************************************************************
- * Copyright (c) 2014 Pieter Wuille                                    *
- * Distributed under the MIT software license, see the accompanying    *
- * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
- ***********************************************************************/
-
-#include <stdio.h>
-#include <string.h>
-
-#include "../include/secp256k1.h"
-#include "util.h"
-#include "bench.h"
-
-#ifdef ENABLE_OPENSSL_TESTS
-#include <openssl/bn.h>
-#include <openssl/ecdsa.h>
-#include <openssl/obj_mac.h>
-#endif
-
-
-typedef struct {
-    secp256k1_context *ctx;
-    unsigned char msg[32];
-    unsigned char key[32];
-    unsigned char sig[72];
-    size_t siglen;
-    unsigned char pubkey[33];
-    size_t pubkeylen;
-#ifdef ENABLE_OPENSSL_TESTS
-    EC_GROUP* ec_group;
-#endif
-} bench_verify_data;
-
-static void bench_verify(void* arg, int iters) {
-    int i;
-    bench_verify_data* data = (bench_verify_data*)arg;
-
-    for (i = 0; i < iters; i++) {
-        secp256k1_pubkey pubkey;
-        secp256k1_ecdsa_signature sig;
-        data->sig[data->siglen - 1] ^= (i & 0xFF);
-        data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
-        data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
-        CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->pubkey, data->pubkeylen) == 1);
-        CHECK(secp256k1_ecdsa_signature_parse_der(data->ctx, &sig, data->sig, data->siglen) == 1);
-        CHECK(secp256k1_ecdsa_verify(data->ctx, &sig, data->msg, &pubkey) == (i == 0));
-        data->sig[data->siglen - 1] ^= (i & 0xFF);
-        data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
-        data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
-    }
-}
-
-#ifdef ENABLE_OPENSSL_TESTS
-static void bench_verify_openssl(void* arg, int iters) {
-    int i;
-    bench_verify_data* data = (bench_verify_data*)arg;
-
-    for (i = 0; i < iters; i++) {
-        data->sig[data->siglen - 1] ^= (i & 0xFF);
-        data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
-        data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
-        {
-            EC_KEY *pkey = EC_KEY_new();
-            const unsigned char *pubkey = &data->pubkey[0];
-            int result;
-
-            CHECK(pkey != NULL);
-            result = EC_KEY_set_group(pkey, data->ec_group);
-            CHECK(result);
-            result = (o2i_ECPublicKey(&pkey, &pubkey, data->pubkeylen)) != NULL;
-            CHECK(result);
-            result = ECDSA_verify(0, &data->msg[0], sizeof(data->msg), &data->sig[0], data->siglen, pkey) == (i == 0);
-            CHECK(result);
-            EC_KEY_free(pkey);
-        }
-        data->sig[data->siglen - 1] ^= (i & 0xFF);
-        data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
-        data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
-    }
-}
-#endif
-
-int main(void) {
-    int i;
-    secp256k1_pubkey pubkey;
-    secp256k1_ecdsa_signature sig;
-    bench_verify_data data;
-
-    int iters = get_iters(20000);
-
-    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
-
-    for (i = 0; i < 32; i++) {
-        data.msg[i] = 1 + i;
-    }
-    for (i = 0; i < 32; i++) {
-        data.key[i] = 33 + i;
-    }
-    data.siglen = 72;
-    CHECK(secp256k1_ecdsa_sign(data.ctx, &sig, data.msg, data.key, NULL, NULL));
-    CHECK(secp256k1_ecdsa_signature_serialize_der(data.ctx, data.sig, &data.siglen, &sig));
-    CHECK(secp256k1_ec_pubkey_create(data.ctx, &pubkey, data.key));
-    data.pubkeylen = 33;
-    CHECK(secp256k1_ec_pubkey_serialize(data.ctx, data.pubkey, &data.pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
-
-    run_benchmark("ecdsa_verify", bench_verify, NULL, NULL, &data, 10, iters);
-#ifdef ENABLE_OPENSSL_TESTS
-    data.ec_group = EC_GROUP_new_by_curve_name(NID_secp256k1);
-    run_benchmark("ecdsa_verify_openssl", bench_verify_openssl, NULL, NULL, &data, 10, iters);
-    EC_GROUP_free(data.ec_group);
-#endif
-
-    secp256k1_context_destroy(data.ctx);
-    return 0;
-}
diff --git a/src/secp256k1/src/ecdsa.h b/src/secp256k1/src/ecdsa.h
index d5e54d8ce61..4441b083984 100644
--- a/src/secp256k1/src/ecdsa.h
+++ b/src/secp256k1/src/ecdsa.h
@@ -15,7 +15,7 @@
 
 static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *r, secp256k1_scalar *s, const unsigned char *sig, size_t size);
 static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar *r, const secp256k1_scalar *s);
-static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar* r, const secp256k1_scalar* s, const secp256k1_ge *pubkey, const secp256k1_scalar *message);
+static int secp256k1_ecdsa_sig_verify(const secp256k1_scalar* r, const secp256k1_scalar* s, const secp256k1_ge *pubkey, const secp256k1_scalar *message);
 static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid);
 
 #endif /* SECP256K1_ECDSA_H */
diff --git a/src/secp256k1/src/ecdsa_impl.h b/src/secp256k1/src/ecdsa_impl.h
index 156a33d1128..90b4b22b779 100644
--- a/src/secp256k1/src/ecdsa_impl.h
+++ b/src/secp256k1/src/ecdsa_impl.h
@@ -112,7 +112,7 @@ static int secp256k1_der_parse_integer(secp256k1_scalar *r, const unsigned char
     if (secp256k1_der_read_len(&rlen, sig, sigend) == 0) {
         return 0;
     }
-    if (rlen == 0 || *sig + rlen > sigend) {
+    if (rlen == 0 || rlen > (size_t)(sigend - *sig)) {
         /* Exceeds bounds or not at least length 1 (X.690-0207 8.3.1).  */
         return 0;
     }
@@ -140,7 +140,7 @@ static int secp256k1_der_parse_integer(secp256k1_scalar *r, const unsigned char
         overflow = 1;
     }
     if (!overflow) {
-        memcpy(ra + 32 - rlen, *sig, rlen);
+        if (rlen) memcpy(ra + 32 - rlen, *sig, rlen);
         secp256k1_scalar_set_b32(r, ra, &overflow);
     }
     if (overflow) {
@@ -204,7 +204,7 @@ static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const
     return 1;
 }
 
-static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar *sigs, const secp256k1_ge *pubkey, const secp256k1_scalar *message) {
+static int secp256k1_ecdsa_sig_verify(const secp256k1_scalar *sigr, const secp256k1_scalar *sigs, const secp256k1_ge *pubkey, const secp256k1_scalar *message) {
     unsigned char c[32];
     secp256k1_scalar sn, u1, u2;
 #if !defined(EXHAUSTIVE_TEST_ORDER)
@@ -221,7 +221,7 @@ static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const
     secp256k1_scalar_mul(&u1, &sn, message);
     secp256k1_scalar_mul(&u2, &sn, sigr);
     secp256k1_gej_set_ge(&pubkeyj, pubkey);
-    secp256k1_ecmult(ctx, &pr, &pubkeyj, &u2, &u1);
+    secp256k1_ecmult(&pr, &pubkeyj, &u2, &u1);
     if (secp256k1_gej_is_infinity(&pr)) {
         return 0;
     }
@@ -304,12 +304,12 @@ static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, sec
     high = secp256k1_scalar_is_high(sigs);
     secp256k1_scalar_cond_negate(sigs, high);
     if (recid) {
-            *recid ^= high;
+        *recid ^= high;
     }
     /* P.x = order is on the curve, so technically sig->r could end up being zero, which would be an invalid signature.
      * This is cryptographically unreachable as hitting it requires finding the discrete log of P.x = N.
      */
-    return !secp256k1_scalar_is_zero(sigr) & !secp256k1_scalar_is_zero(sigs);
+    return (int)(!secp256k1_scalar_is_zero(sigr)) & (int)(!secp256k1_scalar_is_zero(sigs));
 }
 
 #endif /* SECP256K1_ECDSA_IMPL_H */
diff --git a/src/secp256k1/src/eckey.h b/src/secp256k1/src/eckey.h
index 5be3a64b840..d54d44c997b 100644
--- a/src/secp256k1/src/eckey.h
+++ b/src/secp256k1/src/eckey.h
@@ -18,8 +18,8 @@ static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char
 static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed);
 
 static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak);
-static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_pubkey_tweak_add(secp256k1_ge *key, const secp256k1_scalar *tweak);
 static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak);
-static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_pubkey_tweak_mul(secp256k1_ge *key, const secp256k1_scalar *tweak);
 
 #endif /* SECP256K1_ECKEY_H */
diff --git a/src/secp256k1/src/eckey_impl.h b/src/secp256k1/src/eckey_impl.h
index a39cb79653c..e0506d3e2b7 100644
--- a/src/secp256k1/src/eckey_impl.h
+++ b/src/secp256k1/src/eckey_impl.h
@@ -57,12 +57,12 @@ static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp25
     return !secp256k1_scalar_is_zero(key);
 }
 
-static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) {
+static int secp256k1_eckey_pubkey_tweak_add(secp256k1_ge *key, const secp256k1_scalar *tweak) {
     secp256k1_gej pt;
     secp256k1_scalar one;
     secp256k1_gej_set_ge(&pt, key);
     secp256k1_scalar_set_int(&one, 1);
-    secp256k1_ecmult(ctx, &pt, &pt, &one, tweak);
+    secp256k1_ecmult(&pt, &pt, &one, tweak);
 
     if (secp256k1_gej_is_infinity(&pt)) {
         return 0;
@@ -79,7 +79,7 @@ static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp25
     return ret;
 }
 
-static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) {
+static int secp256k1_eckey_pubkey_tweak_mul(secp256k1_ge *key, const secp256k1_scalar *tweak) {
     secp256k1_scalar zero;
     secp256k1_gej pt;
     if (secp256k1_scalar_is_zero(tweak)) {
@@ -88,7 +88,7 @@ static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx,
 
     secp256k1_scalar_set_int(&zero, 0);
     secp256k1_gej_set_ge(&pt, key);
-    secp256k1_ecmult(ctx, &pt, &pt, tweak, &zero);
+    secp256k1_ecmult(&pt, &pt, tweak, &zero);
     secp256k1_ge_set_gej(key, &pt);
     return 1;
 }
diff --git a/src/secp256k1/src/ecmult.h b/src/secp256k1/src/ecmult.h
index 7ab617e20e4..e28c6025067 100644
--- a/src/secp256k1/src/ecmult.h
+++ b/src/secp256k1/src/ecmult.h
@@ -11,21 +11,37 @@
 #include "scalar.h"
 #include "scratch.h"
 
-typedef struct {
-    /* For accelerating the computation of a*P + b*G: */
-    secp256k1_ge_storage (*pre_g)[];    /* odd multiples of the generator */
-    secp256k1_ge_storage (*pre_g_128)[]; /* odd multiples of 2^128*generator */
-} secp256k1_ecmult_context;
-
-static const size_t SECP256K1_ECMULT_CONTEXT_PREALLOCATED_SIZE;
-static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx);
-static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, void **prealloc);
-static void secp256k1_ecmult_context_finalize_memcpy(secp256k1_ecmult_context *dst, const secp256k1_ecmult_context *src);
-static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx);
-static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx);
+#ifndef ECMULT_WINDOW_SIZE
+#  define ECMULT_WINDOW_SIZE 15
+#  ifdef DEBUG_CONFIG
+#     pragma message DEBUG_CONFIG_MSG("ECMULT_WINDOW_SIZE undefined, assuming default value")
+#  endif
+#endif
+
+#ifdef DEBUG_CONFIG
+#  pragma message DEBUG_CONFIG_DEF(ECMULT_WINDOW_SIZE)
+#endif
+
+/* Noone will ever need more than a window size of 24. The code might
+ * be correct for larger values of ECMULT_WINDOW_SIZE but this is not
+ * tested.
+ *
+ * The following limitations are known, and there are probably more:
+ * If WINDOW_G > 27 and size_t has 32 bits, then the code is incorrect
+ * because the size of the memory object that we allocate (in bytes)
+ * will not fit in a size_t.
+ * If WINDOW_G > 31 and int has 32 bits, then the code is incorrect
+ * because certain expressions will overflow.
+ */
+#if ECMULT_WINDOW_SIZE < 2 || ECMULT_WINDOW_SIZE > 24
+#  error Set ECMULT_WINDOW_SIZE to an integer in range [2..24].
+#endif
+
+/** The number of entries a table with precomputed multiples needs to have. */
+#define ECMULT_TABLE_SIZE(w) (1L << ((w)-2))
 
 /** Double multiply: R = na*A + ng*G */
-static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng);
+static void secp256k1_ecmult(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng);
 
 typedef int (secp256k1_ecmult_multi_callback)(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *data);
 
@@ -40,6 +56,6 @@ typedef int (secp256k1_ecmult_multi_callback)(secp256k1_scalar *sc, secp256k1_ge
  *          0 if there is not enough scratch space for a single point or
  *          callback returns 0
  */
-static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback, const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n);
+static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n);
 
 #endif /* SECP256K1_ECMULT_H */
diff --git a/src/secp256k1/src/ecmult_compute_table.h b/src/secp256k1/src/ecmult_compute_table.h
new file mode 100644
index 00000000000..665f87ff3d5
--- /dev/null
+++ b/src/secp256k1/src/ecmult_compute_table.h
@@ -0,0 +1,16 @@
+/*****************************************************************************************************
+ * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor *
+ * Distributed under the MIT software license, see the accompanying                                  *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.                              *
+ *****************************************************************************************************/
+
+#ifndef SECP256K1_ECMULT_COMPUTE_TABLE_H
+#define SECP256K1_ECMULT_COMPUTE_TABLE_H
+
+/* Construct table of all odd multiples of gen in range 1..(2**(window_g-1)-1). */
+static void secp256k1_ecmult_compute_table(secp256k1_ge_storage* table, int window_g, const secp256k1_gej* gen);
+
+/* Like secp256k1_ecmult_compute_table, but one for both gen and gen*2^128. */
+static void secp256k1_ecmult_compute_two_tables(secp256k1_ge_storage* table, secp256k1_ge_storage* table_128, int window_g, const secp256k1_ge* gen);
+
+#endif /* SECP256K1_ECMULT_COMPUTE_TABLE_H */
diff --git a/src/secp256k1/src/ecmult_compute_table_impl.h b/src/secp256k1/src/ecmult_compute_table_impl.h
new file mode 100644
index 00000000000..69d59ce5956
--- /dev/null
+++ b/src/secp256k1/src/ecmult_compute_table_impl.h
@@ -0,0 +1,49 @@
+/*****************************************************************************************************
+ * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor *
+ * Distributed under the MIT software license, see the accompanying                                  *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.                              *
+ *****************************************************************************************************/
+
+#ifndef SECP256K1_ECMULT_COMPUTE_TABLE_IMPL_H
+#define SECP256K1_ECMULT_COMPUTE_TABLE_IMPL_H
+
+#include "ecmult_compute_table.h"
+#include "group_impl.h"
+#include "field_impl.h"
+#include "ecmult.h"
+#include "util.h"
+
+static void secp256k1_ecmult_compute_table(secp256k1_ge_storage* table, int window_g, const secp256k1_gej* gen) {
+    secp256k1_gej gj;
+    secp256k1_ge ge, dgen;
+    int j;
+
+    gj = *gen;
+    secp256k1_ge_set_gej_var(&ge, &gj);
+    secp256k1_ge_to_storage(&table[0], &ge);
+
+    secp256k1_gej_double_var(&gj, gen, NULL);
+    secp256k1_ge_set_gej_var(&dgen, &gj);
+
+    for (j = 1; j < ECMULT_TABLE_SIZE(window_g); ++j) {
+        secp256k1_gej_set_ge(&gj, &ge);
+        secp256k1_gej_add_ge_var(&gj, &gj, &dgen, NULL);
+        secp256k1_ge_set_gej_var(&ge, &gj);
+        secp256k1_ge_to_storage(&table[j], &ge);
+    }
+}
+
+/* Like secp256k1_ecmult_compute_table, but one for both gen and gen*2^128. */
+static void secp256k1_ecmult_compute_two_tables(secp256k1_ge_storage* table, secp256k1_ge_storage* table_128, int window_g, const secp256k1_ge* gen) {
+    secp256k1_gej gj;
+    int i;
+
+    secp256k1_gej_set_ge(&gj, gen);
+    secp256k1_ecmult_compute_table(table, window_g, &gj);
+    for (i = 0; i < 128; ++i) {
+        secp256k1_gej_double_var(&gj, &gj, NULL);
+    }
+    secp256k1_ecmult_compute_table(table_128, window_g, &gj);
+}
+
+#endif /* SECP256K1_ECMULT_COMPUTE_TABLE_IMPL_H */
diff --git a/src/secp256k1/src/ecmult_const.h b/src/secp256k1/src/ecmult_const.h
index d6f0ea22275..f891f3f3067 100644
--- a/src/secp256k1/src/ecmult_const.h
+++ b/src/secp256k1/src/ecmult_const.h
@@ -14,6 +14,7 @@
  * Multiply: R = q*A (in constant-time)
  * Here `bits` should be set to the maximum bitlength of the _absolute value_ of `q`, plus
  * one because we internally sometimes add 2 to the number during the WNAF conversion.
+ * A must not be infinity.
  */
 static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q, int bits);
 
diff --git a/src/secp256k1/src/ecmult_const_impl.h b/src/secp256k1/src/ecmult_const_impl.h
index 0e1fb965cbd..12dbcc6c5b6 100644
--- a/src/secp256k1/src/ecmult_const_impl.h
+++ b/src/secp256k1/src/ecmult_const_impl.h
@@ -12,6 +12,19 @@
 #include "ecmult_const.h"
 #include "ecmult_impl.h"
 
+/** Fill a table 'pre' with precomputed odd multiples of a.
+ *
+ *  The resulting point set is brought to a single constant Z denominator, stores the X and Y
+ *  coordinates as ge_storage points in pre, and stores the global Z in globalz.
+ *  It only operates on tables sized for WINDOW_A wnaf multiples.
+ */
+static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) {
+    secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)];
+
+    secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), pre, zr, globalz, a);
+    secp256k1_ge_table_set_globalz(ECMULT_TABLE_SIZE(WINDOW_A), pre, zr);
+}
+
 /* This is like `ECMULT_TABLE_GET_GE` but is constant time */
 #define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
     int m = 0; \
@@ -40,7 +53,6 @@
     secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \
 } while(0)
 
-
 /** Convert a number to WNAF notation.
  *  The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val.
  *  It has the following guarantees:
@@ -56,7 +68,7 @@
  */
 static int secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar *scalar, int w, int size) {
     int global_sign;
-    int skew = 0;
+    int skew;
     int word = 0;
 
     /* 1 2 3 */
@@ -64,9 +76,7 @@ static int secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar *scalar, int w
     int u;
 
     int flip;
-    int bit;
-    secp256k1_scalar s;
-    int not_neg_one;
+    secp256k1_scalar s = *scalar;
 
     VERIFY_CHECK(w > 0);
     VERIFY_CHECK(size > 0);
@@ -74,33 +84,19 @@ static int secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar *scalar, int w
     /* Note that we cannot handle even numbers by negating them to be odd, as is
      * done in other implementations, since if our scalars were specified to have
      * width < 256 for performance reasons, their negations would have width 256
-     * and we'd lose any performance benefit. Instead, we use a technique from
-     * Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even)
-     * or 2 (for odd) to the number we are encoding, returning a skew value indicating
+     * and we'd lose any performance benefit. Instead, we use a variation of a
+     * technique from Section 4.2 of the Okeya/Tagaki paper, which is to add 1 to the
+     * number we are encoding when it is even, returning a skew value indicating
      * this, and having the caller compensate after doing the multiplication.
      *
      * In fact, we _do_ want to negate numbers to minimize their bit-lengths (and in
      * particular, to ensure that the outputs from the endomorphism-split fit into
-     * 128 bits). If we negate, the parity of our number flips, inverting which of
-     * {1, 2} we want to add to the scalar when ensuring that it's odd. Further
-     * complicating things, -1 interacts badly with `secp256k1_scalar_cadd_bit` and
-     * we need to special-case it in this logic. */
-    flip = secp256k1_scalar_is_high(scalar);
-    /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
-    bit = flip ^ !secp256k1_scalar_is_even(scalar);
-    /* We check for negative one, since adding 2 to it will cause an overflow */
-    secp256k1_scalar_negate(&s, scalar);
-    not_neg_one = !secp256k1_scalar_is_one(&s);
-    s = *scalar;
-    secp256k1_scalar_cadd_bit(&s, bit, not_neg_one);
-    /* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects
-     * that we added two to it and flipped it. In fact for -1 these operations are
-     * identical. We only flipped, but since skewing is required (in the sense that
-     * the skew must be 1 or 2, never zero) and flipping is not, we need to change
-     * our flags to claim that we only skewed. */
+     * 128 bits). If we negate, the parity of our number flips, affecting whether
+     * we want to add to the scalar to ensure that it's odd. */
+    flip = secp256k1_scalar_is_high(&s);
+    skew = flip ^ secp256k1_scalar_is_even(&s);
+    secp256k1_scalar_cadd_bit(&s, 0, skew);
     global_sign = secp256k1_scalar_cond_negate(&s, flip);
-    global_sign *= not_neg_one * 2 - 1;
-    skew = 1 << bit;
 
     /* 4 */
     u_last = secp256k1_scalar_shr_int(&s, w);
@@ -168,6 +164,7 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
      * that the Z coordinate was 1, use affine addition formulae, and correct
      * the Z coordinate of the result once at the end.
      */
+    VERIFY_CHECK(!a->infinity);
     secp256k1_gej_set_ge(r, a);
     secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r);
     for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
@@ -213,42 +210,22 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
         }
     }
 
-    secp256k1_fe_mul(&r->z, &r->z, &Z);
-
     {
         /* Correct for wNAF skew */
-        secp256k1_ge correction = *a;
-        secp256k1_ge_storage correction_1_stor;
-        secp256k1_ge_storage correction_lam_stor;
-        secp256k1_ge_storage a2_stor;
         secp256k1_gej tmpj;
-        secp256k1_gej_set_ge(&tmpj, &correction);
-        secp256k1_gej_double_var(&tmpj, &tmpj, NULL);
-        secp256k1_ge_set_gej(&correction, &tmpj);
-        secp256k1_ge_to_storage(&correction_1_stor, a);
-        if (size > 128) {
-            secp256k1_ge_to_storage(&correction_lam_stor, a);
-        }
-        secp256k1_ge_to_storage(&a2_stor, &correction);
 
-        /* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */
-        secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2);
-        if (size > 128) {
-            secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
-        }
-
-        /* Apply the correction */
-        secp256k1_ge_from_storage(&correction, &correction_1_stor);
-        secp256k1_ge_neg(&correction, &correction);
-        secp256k1_gej_add_ge(r, r, &correction);
+        secp256k1_ge_neg(&tmpa, &pre_a[0]);
+        secp256k1_gej_add_ge(&tmpj, r, &tmpa);
+        secp256k1_gej_cmov(r, &tmpj, skew_1);
 
         if (size > 128) {
-            secp256k1_ge_from_storage(&correction, &correction_lam_stor);
-            secp256k1_ge_neg(&correction, &correction);
-            secp256k1_ge_mul_lambda(&correction, &correction);
-            secp256k1_gej_add_ge(r, r, &correction);
+            secp256k1_ge_neg(&tmpa, &pre_a_lam[0]);
+            secp256k1_gej_add_ge(&tmpj, r, &tmpa);
+            secp256k1_gej_cmov(r, &tmpj, skew_lam);
         }
     }
+
+    secp256k1_fe_mul(&r->z, &r->z, &Z);
 }
 
 #endif /* SECP256K1_ECMULT_CONST_IMPL_H */
diff --git a/src/secp256k1/src/ecmult_gen.h b/src/secp256k1/src/ecmult_gen.h
index 539618dcbb8..a430e8d5d92 100644
--- a/src/secp256k1/src/ecmult_gen.h
+++ b/src/secp256k1/src/ecmult_gen.h
@@ -10,37 +10,35 @@
 #include "scalar.h"
 #include "group.h"
 
+#ifndef ECMULT_GEN_PREC_BITS
+#  define ECMULT_GEN_PREC_BITS 4
+#  ifdef DEBUG_CONFIG
+#     pragma message DEBUG_CONFIG_MSG("ECMULT_GEN_PREC_BITS undefined, assuming default value")
+#  endif
+#endif
+
+#ifdef DEBUG_CONFIG
+#  pragma message DEBUG_CONFIG_DEF(ECMULT_GEN_PREC_BITS)
+#endif
+
 #if ECMULT_GEN_PREC_BITS != 2 && ECMULT_GEN_PREC_BITS != 4 && ECMULT_GEN_PREC_BITS != 8
 #  error "Set ECMULT_GEN_PREC_BITS to 2, 4 or 8."
 #endif
-#define ECMULT_GEN_PREC_B ECMULT_GEN_PREC_BITS
-#define ECMULT_GEN_PREC_G (1 << ECMULT_GEN_PREC_B)
-#define ECMULT_GEN_PREC_N (256 / ECMULT_GEN_PREC_B)
+
+#define ECMULT_GEN_PREC_G(bits) (1 << bits)
+#define ECMULT_GEN_PREC_N(bits) (256 / bits)
 
 typedef struct {
-    /* For accelerating the computation of a*G:
-     * To harden against timing attacks, use the following mechanism:
-     * * Break up the multiplicand into groups of PREC_B bits, called n_0, n_1, n_2, ..., n_(PREC_N-1).
-     * * Compute sum(n_i * (PREC_G)^i * G + U_i, i=0 ... PREC_N-1), where:
-     *   * U_i = U * 2^i, for i=0 ... PREC_N-2
-     *   * U_i = U * (1-2^(PREC_N-1)), for i=PREC_N-1
-     *   where U is a point with no known corresponding scalar. Note that sum(U_i, i=0 ... PREC_N-1) = 0.
-     * For each i, and each of the PREC_G possible values of n_i, (n_i * (PREC_G)^i * G + U_i) is
-     * precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0 ... PREC_N-1).
-     * None of the resulting prec group elements have a known scalar, and neither do any of
-     * the intermediate sums while computing a*G.
-     */
-    secp256k1_ge_storage (*prec)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G]; /* prec[j][i] = (PREC_G)^j * i * G + U_i */
-    secp256k1_scalar blind;
-    secp256k1_gej initial;
+    /* Whether the context has been built. */
+    int built;
+
+    /* Blinding values used when computing (n-b)G + bG. */
+    secp256k1_scalar blind; /* -b */
+    secp256k1_gej initial;  /* bG */
 } secp256k1_ecmult_gen_context;
 
-static const size_t SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE;
-static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context* ctx);
-static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx, void **prealloc);
-static void secp256k1_ecmult_gen_context_finalize_memcpy(secp256k1_ecmult_gen_context *dst, const secp256k1_ecmult_gen_context* src);
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx);
 static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context* ctx);
-static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx);
 
 /** Multiply with the generator: R = a*G */
 static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context* ctx, secp256k1_gej *r, const secp256k1_scalar *a);
diff --git a/src/secp256k1/src/ecmult_gen_compute_table.h b/src/secp256k1/src/ecmult_gen_compute_table.h
new file mode 100644
index 00000000000..e577158d923
--- /dev/null
+++ b/src/secp256k1/src/ecmult_gen_compute_table.h
@@ -0,0 +1,14 @@
+/***********************************************************************
+ * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell       *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_ECMULT_GEN_COMPUTE_TABLE_H
+#define SECP256K1_ECMULT_GEN_COMPUTE_TABLE_H
+
+#include "ecmult_gen.h"
+
+static void secp256k1_ecmult_gen_compute_table(secp256k1_ge_storage* table, const secp256k1_ge* gen, int bits);
+
+#endif /* SECP256K1_ECMULT_GEN_COMPUTE_TABLE_H */
diff --git a/src/secp256k1/src/ecmult_gen_compute_table_impl.h b/src/secp256k1/src/ecmult_gen_compute_table_impl.h
new file mode 100644
index 00000000000..ff6a2992dc9
--- /dev/null
+++ b/src/secp256k1/src/ecmult_gen_compute_table_impl.h
@@ -0,0 +1,81 @@
+/***********************************************************************
+ * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell       *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H
+#define SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H
+
+#include "ecmult_gen_compute_table.h"
+#include "group_impl.h"
+#include "field_impl.h"
+#include "ecmult_gen.h"
+#include "util.h"
+
+static void secp256k1_ecmult_gen_compute_table(secp256k1_ge_storage* table, const secp256k1_ge* gen, int bits) {
+    int g = ECMULT_GEN_PREC_G(bits);
+    int n = ECMULT_GEN_PREC_N(bits);
+
+    secp256k1_ge* prec = checked_malloc(&default_error_callback, n * g * sizeof(*prec));
+    secp256k1_gej gj;
+    secp256k1_gej nums_gej;
+    int i, j;
+
+    /* get the generator */
+    secp256k1_gej_set_ge(&gj, gen);
+
+    /* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
+    {
+        static const unsigned char nums_b32[33] = "The scalar for this x is unknown";
+        secp256k1_fe nums_x;
+        secp256k1_ge nums_ge;
+        int r;
+        r = secp256k1_fe_set_b32(&nums_x, nums_b32);
+        (void)r;
+        VERIFY_CHECK(r);
+        r = secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0);
+        (void)r;
+        VERIFY_CHECK(r);
+        secp256k1_gej_set_ge(&nums_gej, &nums_ge);
+        /* Add G to make the bits in x uniformly distributed. */
+        secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, gen, NULL);
+    }
+
+    /* compute prec. */
+    {
+        secp256k1_gej gbase;
+        secp256k1_gej numsbase;
+        secp256k1_gej* precj = checked_malloc(&default_error_callback, n * g * sizeof(*precj));  /* Jacobian versions of prec. */
+        gbase = gj; /* PREC_G^j * G */
+        numsbase = nums_gej; /* 2^j * nums. */
+        for (j = 0; j < n; j++) {
+            /* Set precj[j*PREC_G .. j*PREC_G+(PREC_G-1)] to (numsbase, numsbase + gbase, ..., numsbase + (PREC_G-1)*gbase). */
+            precj[j*g] = numsbase;
+            for (i = 1; i < g; i++) {
+                secp256k1_gej_add_var(&precj[j*g + i], &precj[j*g + i - 1], &gbase, NULL);
+            }
+            /* Multiply gbase by PREC_G. */
+            for (i = 0; i < bits; i++) {
+                secp256k1_gej_double_var(&gbase, &gbase, NULL);
+            }
+            /* Multiply numbase by 2. */
+            secp256k1_gej_double_var(&numsbase, &numsbase, NULL);
+            if (j == n - 2) {
+                /* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
+                secp256k1_gej_neg(&numsbase, &numsbase);
+                secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL);
+            }
+        }
+        secp256k1_ge_set_all_gej_var(prec, precj, n * g);
+        free(precj);
+    }
+    for (j = 0; j < n; j++) {
+        for (i = 0; i < g; i++) {
+            secp256k1_ge_to_storage(&table[j*g + i], &prec[j*g + i]);
+        }
+    }
+    free(prec);
+}
+
+#endif /* SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H */
diff --git a/src/secp256k1/src/ecmult_gen_impl.h b/src/secp256k1/src/ecmult_gen_impl.h
index 384a67faeda..4f5ea9f3c08 100644
--- a/src/secp256k1/src/ecmult_gen_impl.h
+++ b/src/secp256k1/src/ecmult_gen_impl.h
@@ -12,130 +12,54 @@
 #include "group.h"
 #include "ecmult_gen.h"
 #include "hash_impl.h"
-#ifdef USE_ECMULT_STATIC_PRECOMPUTATION
-#include "ecmult_static_context.h"
-#endif
+#include "precomputed_ecmult_gen.h"
 
-#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
-    static const size_t SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE = ROUND_TO_ALIGN(sizeof(*((secp256k1_ecmult_gen_context*) NULL)->prec));
-#else
-    static const size_t SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE = 0;
-#endif
-
-static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context *ctx) {
-    ctx->prec = NULL;
-}
-
-static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx, void **prealloc) {
-#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
-    secp256k1_ge prec[ECMULT_GEN_PREC_N * ECMULT_GEN_PREC_G];
-    secp256k1_gej gj;
-    secp256k1_gej nums_gej;
-    int i, j;
-    size_t const prealloc_size = SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE;
-    void* const base = *prealloc;
-#endif
-
-    if (ctx->prec != NULL) {
-        return;
-    }
-#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
-    ctx->prec = (secp256k1_ge_storage (*)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G])manual_alloc(prealloc, prealloc_size, base, prealloc_size);
-
-    /* get the generator */
-    secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
-
-    /* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
-    {
-        static const unsigned char nums_b32[33] = "The scalar for this x is unknown";
-        secp256k1_fe nums_x;
-        secp256k1_ge nums_ge;
-        int r;
-        r = secp256k1_fe_set_b32(&nums_x, nums_b32);
-        (void)r;
-        VERIFY_CHECK(r);
-        r = secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0);
-        (void)r;
-        VERIFY_CHECK(r);
-        secp256k1_gej_set_ge(&nums_gej, &nums_ge);
-        /* Add G to make the bits in x uniformly distributed. */
-        secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g, NULL);
-    }
-
-    /* compute prec. */
-    {
-        secp256k1_gej precj[ECMULT_GEN_PREC_N * ECMULT_GEN_PREC_G]; /* Jacobian versions of prec. */
-        secp256k1_gej gbase;
-        secp256k1_gej numsbase;
-        gbase = gj; /* PREC_G^j * G */
-        numsbase = nums_gej; /* 2^j * nums. */
-        for (j = 0; j < ECMULT_GEN_PREC_N; j++) {
-            /* Set precj[j*PREC_G .. j*PREC_G+(PREC_G-1)] to (numsbase, numsbase + gbase, ..., numsbase + (PREC_G-1)*gbase). */
-            precj[j*ECMULT_GEN_PREC_G] = numsbase;
-            for (i = 1; i < ECMULT_GEN_PREC_G; i++) {
-                secp256k1_gej_add_var(&precj[j*ECMULT_GEN_PREC_G + i], &precj[j*ECMULT_GEN_PREC_G + i - 1], &gbase, NULL);
-            }
-            /* Multiply gbase by PREC_G. */
-            for (i = 0; i < ECMULT_GEN_PREC_B; i++) {
-                secp256k1_gej_double_var(&gbase, &gbase, NULL);
-            }
-            /* Multiply numbase by 2. */
-            secp256k1_gej_double_var(&numsbase, &numsbase, NULL);
-            if (j == ECMULT_GEN_PREC_N - 2) {
-                /* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
-                secp256k1_gej_neg(&numsbase, &numsbase);
-                secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL);
-            }
-        }
-        secp256k1_ge_set_all_gej_var(prec, precj, ECMULT_GEN_PREC_N * ECMULT_GEN_PREC_G);
-    }
-    for (j = 0; j < ECMULT_GEN_PREC_N; j++) {
-        for (i = 0; i < ECMULT_GEN_PREC_G; i++) {
-            secp256k1_ge_to_storage(&(*ctx->prec)[j][i], &prec[j*ECMULT_GEN_PREC_G + i]);
-        }
-    }
-#else
-    (void)prealloc;
-    ctx->prec = (secp256k1_ge_storage (*)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G])secp256k1_ecmult_static_context;
-#endif
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx) {
     secp256k1_ecmult_gen_blind(ctx, NULL);
+    ctx->built = 1;
 }
 
 static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx) {
-    return ctx->prec != NULL;
-}
-
-static void secp256k1_ecmult_gen_context_finalize_memcpy(secp256k1_ecmult_gen_context *dst, const secp256k1_ecmult_gen_context *src) {
-#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
-    if (src->prec != NULL) {
-        /* We cast to void* first to suppress a -Wcast-align warning. */
-        dst->prec = (secp256k1_ge_storage (*)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G])(void*)((unsigned char*)dst + ((unsigned char*)src->prec - (unsigned char*)src));
-    }
-#else
-    (void)dst, (void)src;
-#endif
+    return ctx->built;
 }
 
 static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context *ctx) {
+    ctx->built = 0;
     secp256k1_scalar_clear(&ctx->blind);
     secp256k1_gej_clear(&ctx->initial);
-    ctx->prec = NULL;
 }
 
+/* For accelerating the computation of a*G:
+ * To harden against timing attacks, use the following mechanism:
+ * * Break up the multiplicand into groups of PREC_BITS bits, called n_0, n_1, n_2, ..., n_(PREC_N-1).
+ * * Compute sum(n_i * (PREC_G)^i * G + U_i, i=0 ... PREC_N-1), where:
+ *   * U_i = U * 2^i, for i=0 ... PREC_N-2
+ *   * U_i = U * (1-2^(PREC_N-1)), for i=PREC_N-1
+ *   where U is a point with no known corresponding scalar. Note that sum(U_i, i=0 ... PREC_N-1) = 0.
+ * For each i, and each of the PREC_G possible values of n_i, (n_i * (PREC_G)^i * G + U_i) is
+ * precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0 ... PREC_N-1).
+ * None of the resulting prec group elements have a known scalar, and neither do any of
+ * the intermediate sums while computing a*G.
+ * The prec values are stored in secp256k1_ecmult_gen_prec_table[i][n_i] = n_i * (PREC_G)^i * G + U_i.
+ */
 static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp256k1_gej *r, const secp256k1_scalar *gn) {
+    int bits = ECMULT_GEN_PREC_BITS;
+    int g = ECMULT_GEN_PREC_G(bits);
+    int n = ECMULT_GEN_PREC_N(bits);
+
     secp256k1_ge add;
     secp256k1_ge_storage adds;
     secp256k1_scalar gnb;
-    int bits;
-    int i, j;
+    int i, j, n_i;
+    
     memset(&adds, 0, sizeof(adds));
     *r = ctx->initial;
     /* Blind scalar/point multiplication by computing (n-b)G + bG instead of nG. */
     secp256k1_scalar_add(&gnb, gn, &ctx->blind);
     add.infinity = 0;
-    for (j = 0; j < ECMULT_GEN_PREC_N; j++) {
-        bits = secp256k1_scalar_get_bits(&gnb, j * ECMULT_GEN_PREC_B, ECMULT_GEN_PREC_B);
-        for (i = 0; i < ECMULT_GEN_PREC_G; i++) {
+    for (i = 0; i < n; i++) {
+        n_i = secp256k1_scalar_get_bits(&gnb, i * bits, bits);
+        for (j = 0; j < g; j++) {
             /** This uses a conditional move to avoid any secret data in array indexes.
              *   _Any_ use of secret indexes has been demonstrated to result in timing
              *   sidechannels, even when the cache-line access patterns are uniform.
@@ -146,12 +70,12 @@ static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp25
              *    by Dag Arne Osvik, Adi Shamir, and Eran Tromer
              *    (https://www.tau.ac.il/~tromer/papers/cache.pdf)
              */
-            secp256k1_ge_storage_cmov(&adds, &(*ctx->prec)[j][i], i == bits);
+            secp256k1_ge_storage_cmov(&adds, &secp256k1_ecmult_gen_prec_table[i][j], j == n_i);
         }
         secp256k1_ge_from_storage(&add, &adds);
         secp256k1_gej_add_ge(r, r, &add);
     }
-    bits = 0;
+    n_i = 0;
     secp256k1_ge_clear(&add);
     secp256k1_scalar_clear(&gnb);
 }
@@ -164,31 +88,31 @@ static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const
     unsigned char nonce32[32];
     secp256k1_rfc6979_hmac_sha256 rng;
     int overflow;
-    unsigned char keydata[64] = {0};
+    unsigned char keydata[64];
     if (seed32 == NULL) {
         /* When seed is NULL, reset the initial point and blinding value. */
         secp256k1_gej_set_ge(&ctx->initial, &secp256k1_ge_const_g);
         secp256k1_gej_neg(&ctx->initial, &ctx->initial);
         secp256k1_scalar_set_int(&ctx->blind, 1);
+        return;
     }
     /* The prior blinding value (if not reset) is chained forward by including it in the hash. */
-    secp256k1_scalar_get_b32(nonce32, &ctx->blind);
+    secp256k1_scalar_get_b32(keydata, &ctx->blind);
     /** Using a CSPRNG allows a failure free interface, avoids needing large amounts of random data,
      *   and guards against weak or adversarial seeds.  This is a simpler and safer interface than
      *   asking the caller for blinding values directly and expecting them to retry on failure.
      */
-    memcpy(keydata, nonce32, 32);
-    if (seed32 != NULL) {
-        memcpy(keydata + 32, seed32, 32);
-    }
-    secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, seed32 ? 64 : 32);
+    VERIFY_CHECK(seed32 != NULL);
+    memcpy(keydata + 32, seed32, 32);
+    secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, 64);
     memset(keydata, 0, sizeof(keydata));
     /* Accept unobservably small non-uniformity. */
     secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
     overflow = !secp256k1_fe_set_b32(&s, nonce32);
     overflow |= secp256k1_fe_is_zero(&s);
     secp256k1_fe_cmov(&s, &secp256k1_fe_one, overflow);
-    /* Randomize the projection to defend against multiplier sidechannels. */
+    /* Randomize the projection to defend against multiplier sidechannels.
+       Do this before our own call to secp256k1_ecmult_gen below. */
     secp256k1_gej_rescale(&ctx->initial, &s);
     secp256k1_fe_clear(&s);
     secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
@@ -197,6 +121,7 @@ static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const
     secp256k1_scalar_cmov(&b, &secp256k1_scalar_one, secp256k1_scalar_is_zero(&b));
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
     memset(nonce32, 0, 32);
+    /* The random projection in ctx->initial ensures that gb will have a random projection. */
     secp256k1_ecmult_gen(ctx, &gb, &b);
     secp256k1_scalar_negate(&b, &b);
     ctx->blind = b;
diff --git a/src/secp256k1/src/ecmult_impl.h b/src/secp256k1/src/ecmult_impl.h
index 5c2edac68fc..3776fe73fc8 100644
--- a/src/secp256k1/src/ecmult_impl.h
+++ b/src/secp256k1/src/ecmult_impl.h
@@ -14,6 +14,7 @@
 #include "group.h"
 #include "scalar.h"
 #include "ecmult.h"
+#include "precomputed_ecmult.h"
 
 #if defined(EXHAUSTIVE_TEST_ORDER)
 /* We need to lower these values for exhaustive tests because
@@ -21,13 +22,10 @@
  * affine-isomorphism stuff which tracks z-ratios) */
 #  if EXHAUSTIVE_TEST_ORDER > 128
 #    define WINDOW_A 5
-#    define WINDOW_G 8
 #  elif EXHAUSTIVE_TEST_ORDER > 8
 #    define WINDOW_A 4
-#    define WINDOW_G 4
 #  else
 #    define WINDOW_A 2
-#    define WINDOW_G 2
 #  endif
 #else
 /* optimal for 128-bit and 256-bit exponents. */
@@ -41,34 +39,15 @@
  *  Two tables of this size are used (due to the endomorphism
  *  optimization).
  */
-#  define WINDOW_G ECMULT_WINDOW_SIZE
-#endif
-
-/* Noone will ever need more than a window size of 24. The code might
- * be correct for larger values of ECMULT_WINDOW_SIZE but this is not
- * not tested.
- *
- * The following limitations are known, and there are probably more:
- * If WINDOW_G > 27 and size_t has 32 bits, then the code is incorrect
- * because the size of the memory object that we allocate (in bytes)
- * will not fit in a size_t.
- * If WINDOW_G > 31 and int has 32 bits, then the code is incorrect
- * because certain expressions will overflow.
- */
-#if ECMULT_WINDOW_SIZE < 2 || ECMULT_WINDOW_SIZE > 24
-#  error Set ECMULT_WINDOW_SIZE to an integer in range [2..24].
 #endif
 
 #define WNAF_BITS 128
 #define WNAF_SIZE_BITS(bits, w) (((bits) + (w) - 1) / (w))
 #define WNAF_SIZE(w) WNAF_SIZE_BITS(WNAF_BITS, w)
 
-/** The number of entries a table with precomputed multiples needs to have. */
-#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
-
 /* The number of objects allocated on the scratch space for ecmult_multi algorithms */
 #define PIPPENGER_SCRATCH_OBJECTS 6
-#define STRAUSS_SCRATCH_OBJECTS 6
+#define STRAUSS_SCRATCH_OBJECTS 5
 
 #define PIPPENGER_MAX_BUCKET_WINDOW 12
 
@@ -77,14 +56,23 @@
 
 #define ECMULT_MAX_POINTS_PER_BATCH 5000000
 
-/** Fill a table 'prej' with precomputed odd multiples of a. Prej will contain
- *  the values [1*a,3*a,...,(2*n-1)*a], so it space for n values. zr[0] will
- *  contain prej[0].z / a.z. The other zr[i] values = prej[i].z / prej[i-1].z.
- *  Prej's Z values are undefined, except for the last value.
+/** Fill a table 'pre_a' with precomputed odd multiples of a.
+ *  pre_a will contain [1*a,3*a,...,(2*n-1)*a], so it needs space for n group elements.
+ *  zr needs space for n field elements.
+ *
+ *  Although pre_a is an array of _ge rather than _gej, it actually represents elements
+ *  in Jacobian coordinates with their z coordinates omitted. The omitted z-coordinates
+ *  can be recovered using z and zr. Using the notation z(b) to represent the omitted
+ *  z coordinate of b:
+ *  - z(pre_a[n-1]) = 'z'
+ *  - z(pre_a[i-1]) = z(pre_a[i]) / zr[i] for n > i > 0
+ *
+ *  Lastly the zr[0] value, which isn't used above, is set so that:
+ *  - a.z = z(pre_a[0]) / zr[0]
  */
-static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_gej *prej, secp256k1_fe *zr, const secp256k1_gej *a) {
-    secp256k1_gej d;
-    secp256k1_ge a_ge, d_ge;
+static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_ge *pre_a, secp256k1_fe *zr, secp256k1_fe *z, const secp256k1_gej *a) {
+    secp256k1_gej d, ai;
+    secp256k1_ge d_ge;
     int i;
 
     VERIFY_CHECK(!a->infinity);
@@ -92,279 +80,73 @@ static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_gej *prej, sec
     secp256k1_gej_double_var(&d, a, NULL);
 
     /*
-     * Perform the additions on an isomorphism where 'd' is affine: drop the z coordinate
-     * of 'd', and scale the 1P starting value's x/y coordinates without changing its z.
+     * Perform the additions using an isomorphic curve Y^2 = X^3 + 7*C^6 where C := d.z.
+     * The isomorphism, phi, maps a secp256k1 point (x, y) to the point (x*C^2, y*C^3) on the other curve.
+     * In Jacobian coordinates phi maps (x, y, z) to (x*C^2, y*C^3, z) or, equivalently to (x, y, z/C).
+     *
+     *     phi(x, y, z) = (x*C^2, y*C^3, z) = (x, y, z/C)
+     *   d_ge := phi(d) = (d.x, d.y, 1)
+     *     ai := phi(a) = (a.x*C^2, a.y*C^3, a.z)
+     *
+     * The group addition functions work correctly on these isomorphic curves.
+     * In particular phi(d) is easy to represent in affine coordinates under this isomorphism.
+     * This lets us use the faster secp256k1_gej_add_ge_var group addition function that we wouldn't be able to use otherwise.
      */
-    d_ge.x = d.x;
-    d_ge.y = d.y;
-    d_ge.infinity = 0;
-
-    secp256k1_ge_set_gej_zinv(&a_ge, a, &d.z);
-    prej[0].x = a_ge.x;
-    prej[0].y = a_ge.y;
-    prej[0].z = a->z;
-    prej[0].infinity = 0;
-
-    zr[0] = d.z;
-    for (i = 1; i < n; i++) {
-        secp256k1_gej_add_ge_var(&prej[i], &prej[i-1], &d_ge, &zr[i]);
-    }
+    secp256k1_ge_set_xy(&d_ge, &d.x, &d.y);
+    secp256k1_ge_set_gej_zinv(&pre_a[0], a, &d.z);
+    secp256k1_gej_set_ge(&ai, &pre_a[0]);
+    ai.z = a->z;
 
-    /*
-     * Each point in 'prej' has a z coordinate too small by a factor of 'd.z'. Only
-     * the final point's z coordinate is actually used though, so just update that.
+    /* pre_a[0] is the point (a.x*C^2, a.y*C^3, a.z*C) which is equvalent to a.
+     * Set zr[0] to C, which is the ratio between the omitted z(pre_a[0]) value and a.z.
      */
-    secp256k1_fe_mul(&prej[n-1].z, &prej[n-1].z, &d.z);
-}
-
-/** Fill a table 'pre' with precomputed odd multiples of a.
- *
- *  There are two versions of this function:
- *  - secp256k1_ecmult_odd_multiples_table_globalz_windowa which brings its
- *    resulting point set to a single constant Z denominator, stores the X and Y
- *    coordinates as ge_storage points in pre, and stores the global Z in rz.
- *    It only operates on tables sized for WINDOW_A wnaf multiples.
- *  - secp256k1_ecmult_odd_multiples_table_storage_var, which converts its
- *    resulting point set to actually affine points, and stores those in pre.
- *    It operates on tables of any size.
- *
- *  To compute a*P + b*G, we compute a table for P using the first function,
- *  and for G using the second (which requires an inverse, but it only needs to
- *  happen once).
- */
-static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) {
-    secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)];
-    secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)];
-
-    /* Compute the odd multiples in Jacobian form. */
-    secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), prej, zr, a);
-    /* Bring them to the same Z denominator. */
-    secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A), pre, globalz, prej, zr);
-}
-
-static void secp256k1_ecmult_odd_multiples_table_storage_var(const int n, secp256k1_ge_storage *pre, const secp256k1_gej *a) {
-    secp256k1_gej d;
-    secp256k1_ge d_ge, p_ge;
-    secp256k1_gej pj;
-    secp256k1_fe zi;
-    secp256k1_fe zr;
-    secp256k1_fe dx_over_dz_squared;
-    int i;
-
-    VERIFY_CHECK(!a->infinity);
-
-    secp256k1_gej_double_var(&d, a, NULL);
+    zr[0] = d.z;
 
-    /* First, we perform all the additions in an isomorphic curve obtained by multiplying
-     * all `z` coordinates by 1/`d.z`. In these coordinates `d` is affine so we can use
-     * `secp256k1_gej_add_ge_var` to perform the additions. For each addition, we store
-     * the resulting y-coordinate and the z-ratio, since we only have enough memory to
-     * store two field elements. These are sufficient to efficiently undo the isomorphism
-     * and recompute all the `x`s.
-     */
-    d_ge.x = d.x;
-    d_ge.y = d.y;
-    d_ge.infinity = 0;
-
-    secp256k1_ge_set_gej_zinv(&p_ge, a, &d.z);
-    pj.x = p_ge.x;
-    pj.y = p_ge.y;
-    pj.z = a->z;
-    pj.infinity = 0;
-
-    for (i = 0; i < (n - 1); i++) {
-        secp256k1_fe_normalize_var(&pj.y);
-        secp256k1_fe_to_storage(&pre[i].y, &pj.y);
-        secp256k1_gej_add_ge_var(&pj, &pj, &d_ge, &zr);
-        secp256k1_fe_normalize_var(&zr);
-        secp256k1_fe_to_storage(&pre[i].x, &zr);
+    for (i = 1; i < n; i++) {
+        secp256k1_gej_add_ge_var(&ai, &ai, &d_ge, &zr[i]);
+        secp256k1_ge_set_xy(&pre_a[i], &ai.x, &ai.y);
     }
 
-    /* Invert d.z in the same batch, preserving pj.z so we can extract 1/d.z */
-    secp256k1_fe_mul(&zi, &pj.z, &d.z);
-    secp256k1_fe_inv_var(&zi, &zi);
-
-    /* Directly set `pre[n - 1]` to `pj`, saving the inverted z-coordinate so
-     * that we can combine it with the saved z-ratios to compute the other zs
-     * without any more inversions. */
-    secp256k1_ge_set_gej_zinv(&p_ge, &pj, &zi);
-    secp256k1_ge_to_storage(&pre[n - 1], &p_ge);
-
-    /* Compute the actual x-coordinate of D, which will be needed below. */
-    secp256k1_fe_mul(&d.z, &zi, &pj.z);  /* d.z = 1/d.z */
-    secp256k1_fe_sqr(&dx_over_dz_squared, &d.z);
-    secp256k1_fe_mul(&dx_over_dz_squared, &dx_over_dz_squared, &d.x);
-
-    /* Going into the second loop, we have set `pre[n-1]` to its final affine
-     * form, but still need to set `pre[i]` for `i` in 0 through `n-2`. We
-     * have `zi = (p.z * d.z)^-1`, where
-     *
-     *     `p.z` is the z-coordinate of the point on the isomorphic curve
-     *           which was ultimately assigned to `pre[n-1]`.
-     *     `d.z` is the multiplier that must be applied to all z-coordinates
-     *           to move from our isomorphic curve back to secp256k1; so the
-     *           product `p.z * d.z` is the z-coordinate of the secp256k1
-     *           point assigned to `pre[n-1]`.
-     *
-     * All subsequent inverse-z-coordinates can be obtained by multiplying this
-     * factor by successive z-ratios, which is much more efficient than directly
-     * computing each one.
-     *
-     * Importantly, these inverse-zs will be coordinates of points on secp256k1,
-     * while our other stored values come from computations on the isomorphic
-     * curve. So in the below loop, we will take care not to actually use `zi`
-     * or any derived values until we're back on secp256k1.
+    /* Multiply the last z-coordinate by C to undo the isomorphism.
+     * Since the z-coordinates of the pre_a values are implied by the zr array of z-coordinate ratios,
+     * undoing the isomorphism here undoes the isomorphism for all pre_a values.
      */
-    i = n - 1;
-    while (i > 0) {
-        secp256k1_fe zi2, zi3;
-        const secp256k1_fe *rzr;
-        i--;
-
-        secp256k1_ge_from_storage(&p_ge, &pre[i]);
-
-        /* For each remaining point, we extract the z-ratio from the stored
-         * x-coordinate, compute its z^-1 from that, and compute the full
-         * point from that. */
-        rzr = &p_ge.x;
-        secp256k1_fe_mul(&zi, &zi, rzr);
-        secp256k1_fe_sqr(&zi2, &zi);
-        secp256k1_fe_mul(&zi3, &zi2, &zi);
-        /* To compute the actual x-coordinate, we use the stored z ratio and
-         * y-coordinate, which we obtained from `secp256k1_gej_add_ge_var`
-         * in the loop above, as well as the inverse of the square of its
-         * z-coordinate. We store the latter in the `zi2` variable, which is
-         * computed iteratively starting from the overall Z inverse then
-         * multiplying by each z-ratio in turn.
-         *
-         * Denoting the z-ratio as `rzr`, we observe that it is equal to `h`
-         * from the inside of the above `gej_add_ge_var` call. This satisfies
-         *
-         *    rzr = d_x * z^2 - x * d_z^2
-         *
-         * where (`d_x`, `d_z`) are Jacobian coordinates of `D` and `(x, z)`
-         * are Jacobian coordinates of our desired point -- except both are on
-         * the isomorphic curve that we were using when we called `gej_add_ge_var`.
-         * To get back to secp256k1, we must multiply both `z`s by `d_z`, or
-         * equivalently divide both `x`s by `d_z^2`. Our equation then becomes
-         *
-         *    rzr = d_x * z^2 / d_z^2 - x
-         *
-         * (The left-hand-side, being a ratio of z-coordinates, is unaffected
-         * by the isomorphism.)
-         *
-         * Rearranging to solve for `x`, we have
-         *
-         *     x = d_x * z^2 / d_z^2 - rzr
-         *
-         * But what we actually want is the affine coordinate `X = x/z^2`,
-         * which will satisfy
-         *
-         *     X = d_x / d_z^2 - rzr / z^2
-         *       = dx_over_dz_squared - rzr * zi2
-         */
-        secp256k1_fe_mul(&p_ge.x, rzr, &zi2);
-        secp256k1_fe_negate(&p_ge.x, &p_ge.x, 1);
-        secp256k1_fe_add(&p_ge.x, &dx_over_dz_squared);
-        /* y is stored_y/z^3, as we expect */
-        secp256k1_fe_mul(&p_ge.y, &p_ge.y, &zi3);
-        /* Store */
-        secp256k1_ge_to_storage(&pre[i], &p_ge);
-    }
+    secp256k1_fe_mul(z, &ai.z, &d.z);
 }
 
-/** The following two macro retrieves a particular odd multiple from a table
- *  of precomputed multiples. */
-#define ECMULT_TABLE_GET_GE(r,pre,n,w) do { \
+#define SECP256K1_ECMULT_TABLE_VERIFY(n,w) \
     VERIFY_CHECK(((n) & 1) == 1); \
     VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
-    VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
-    if ((n) > 0) { \
-        *(r) = (pre)[((n)-1)/2]; \
-    } else { \
-        *(r) = (pre)[(-(n)-1)/2]; \
-        secp256k1_fe_negate(&((r)->y), &((r)->y), 1); \
-    } \
-} while(0)
-
-#define ECMULT_TABLE_GET_GE_STORAGE(r,pre,n,w) do { \
-    VERIFY_CHECK(((n) & 1) == 1); \
-    VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
-    VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
-    if ((n) > 0) { \
-        secp256k1_ge_from_storage((r), &(pre)[((n)-1)/2]); \
-    } else { \
-        secp256k1_ge_from_storage((r), &(pre)[(-(n)-1)/2]); \
-        secp256k1_fe_negate(&((r)->y), &((r)->y), 1); \
-    } \
-} while(0)
-
-static const size_t SECP256K1_ECMULT_CONTEXT_PREALLOCATED_SIZE =
-    ROUND_TO_ALIGN(sizeof((*((secp256k1_ecmult_context*) NULL)->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G))
-    + ROUND_TO_ALIGN(sizeof((*((secp256k1_ecmult_context*) NULL)->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G))
-    ;
-
-static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx) {
-    ctx->pre_g = NULL;
-    ctx->pre_g_128 = NULL;
-}
-
-static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, void **prealloc) {
-    secp256k1_gej gj;
-    void* const base = *prealloc;
-    size_t const prealloc_size = SECP256K1_ECMULT_CONTEXT_PREALLOCATED_SIZE;
-
-    if (ctx->pre_g != NULL) {
-        return;
-    }
+    VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1));
 
-    /* get the generator */
-    secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
-
-    {
-        size_t size = sizeof((*ctx->pre_g)[0]) * ((size_t)ECMULT_TABLE_SIZE(WINDOW_G));
-        /* check for overflow */
-        VERIFY_CHECK(size / sizeof((*ctx->pre_g)[0]) == ((size_t)ECMULT_TABLE_SIZE(WINDOW_G)));
-        ctx->pre_g = (secp256k1_ge_storage (*)[])manual_alloc(prealloc, sizeof((*ctx->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G), base, prealloc_size);
-    }
-
-    /* precompute the tables with odd multiples */
-    secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g, &gj);
-
-    {
-        secp256k1_gej g_128j;
-        int i;
-
-        size_t size = sizeof((*ctx->pre_g_128)[0]) * ((size_t) ECMULT_TABLE_SIZE(WINDOW_G));
-        /* check for overflow */
-        VERIFY_CHECK(size / sizeof((*ctx->pre_g_128)[0]) == ((size_t)ECMULT_TABLE_SIZE(WINDOW_G)));
-        ctx->pre_g_128 = (secp256k1_ge_storage (*)[])manual_alloc(prealloc, sizeof((*ctx->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G), base, prealloc_size);
-
-        /* calculate 2^128*generator */
-        g_128j = gj;
-        for (i = 0; i < 128; i++) {
-            secp256k1_gej_double_var(&g_128j, &g_128j, NULL);
-        }
-        secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g_128, &g_128j);
+SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge(secp256k1_ge *r, const secp256k1_ge *pre, int n, int w) {
+    SECP256K1_ECMULT_TABLE_VERIFY(n,w)
+    if (n > 0) {
+        *r = pre[(n-1)/2];
+    } else {
+        *r = pre[(-n-1)/2];
+        secp256k1_fe_negate(&(r->y), &(r->y), 1);
     }
 }
 
-static void secp256k1_ecmult_context_finalize_memcpy(secp256k1_ecmult_context *dst, const secp256k1_ecmult_context *src) {
-    if (src->pre_g != NULL) {
-        /* We cast to void* first to suppress a -Wcast-align warning. */
-        dst->pre_g = (secp256k1_ge_storage (*)[])(void*)((unsigned char*)dst + ((unsigned char*)(src->pre_g) - (unsigned char*)src));
-    }
-    if (src->pre_g_128 != NULL) {
-        dst->pre_g_128 = (secp256k1_ge_storage (*)[])(void*)((unsigned char*)dst + ((unsigned char*)(src->pre_g_128) - (unsigned char*)src));
+SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge_lambda(secp256k1_ge *r, const secp256k1_ge *pre, const secp256k1_fe *x, int n, int w) {
+    SECP256K1_ECMULT_TABLE_VERIFY(n,w)
+    if (n > 0) {
+        secp256k1_ge_set_xy(r, &x[(n-1)/2], &pre[(n-1)/2].y);
+    } else {
+        secp256k1_ge_set_xy(r, &x[(-n-1)/2], &pre[(-n-1)/2].y);
+        secp256k1_fe_negate(&(r->y), &(r->y), 1);
     }
 }
 
-static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx) {
-    return ctx->pre_g != NULL;
-}
-
-static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx) {
-    secp256k1_ecmult_context_init(ctx);
+SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge_storage(secp256k1_ge *r, const secp256k1_ge_storage *pre, int n, int w) {
+    SECP256K1_ECMULT_TABLE_VERIFY(n,w)
+    if (n > 0) {
+        secp256k1_ge_from_storage(r, &pre[(n-1)/2]);
+    } else {
+        secp256k1_ge_from_storage(r, &pre[(-n-1)/2]);
+        secp256k1_fe_negate(&(r->y), &(r->y), 1);
+    }
 }
 
 /** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits),
@@ -418,35 +200,38 @@ static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a,
         bit += now;
     }
 #ifdef VERIFY
-    CHECK(carry == 0);
-    while (bit < 256) {
-        CHECK(secp256k1_scalar_get_bits(&s, bit++, 1) == 0);
+    {
+        int verify_bit = bit;
+
+        VERIFY_CHECK(carry == 0);
+
+        while (verify_bit < 256) {
+            VERIFY_CHECK(secp256k1_scalar_get_bits(&s, verify_bit, 1) == 0);
+            verify_bit++;
+        }
     }
 #endif
     return last_set_bit + 1;
 }
 
 struct secp256k1_strauss_point_state {
-    secp256k1_scalar na_1, na_lam;
     int wnaf_na_1[129];
     int wnaf_na_lam[129];
     int bits_na_1;
     int bits_na_lam;
-    size_t input_pos;
 };
 
 struct secp256k1_strauss_state {
-    secp256k1_gej* prej;
-    secp256k1_fe* zr;
+    /* aux is used to hold z-ratios, and then used to hold pre_a[i].x * BETA values. */
+    secp256k1_fe* aux;
     secp256k1_ge* pre_a;
-    secp256k1_ge* pre_a_lam;
     struct secp256k1_strauss_point_state* ps;
 };
 
-static void secp256k1_ecmult_strauss_wnaf(const secp256k1_ecmult_context *ctx, const struct secp256k1_strauss_state *state, secp256k1_gej *r, size_t num, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
+static void secp256k1_ecmult_strauss_wnaf(const struct secp256k1_strauss_state *state, secp256k1_gej *r, size_t num, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
     secp256k1_ge tmpa;
     secp256k1_fe Z;
-    /* Splitted G factors. */
+    /* Split G factors. */
     secp256k1_scalar ng_1, ng_128;
     int wnaf_ng_1[129];
     int bits_ng_1 = 0;
@@ -457,17 +242,19 @@ static void secp256k1_ecmult_strauss_wnaf(const secp256k1_ecmult_context *ctx, c
     size_t np;
     size_t no = 0;
 
+    secp256k1_fe_set_int(&Z, 1);
     for (np = 0; np < num; ++np) {
+        secp256k1_gej tmp;
+        secp256k1_scalar na_1, na_lam;
         if (secp256k1_scalar_is_zero(&na[np]) || secp256k1_gej_is_infinity(&a[np])) {
             continue;
         }
-        state->ps[no].input_pos = np;
         /* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */
-        secp256k1_scalar_split_lambda(&state->ps[no].na_1, &state->ps[no].na_lam, &na[np]);
+        secp256k1_scalar_split_lambda(&na_1, &na_lam, &na[np]);
 
         /* build wnaf representation for na_1 and na_lam. */
-        state->ps[no].bits_na_1   = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_1,   129, &state->ps[no].na_1,   WINDOW_A);
-        state->ps[no].bits_na_lam = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_lam, 129, &state->ps[no].na_lam, WINDOW_A);
+        state->ps[no].bits_na_1   = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_1,   129, &na_1,   WINDOW_A);
+        state->ps[no].bits_na_lam = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_lam, 129, &na_lam, WINDOW_A);
         VERIFY_CHECK(state->ps[no].bits_na_1 <= 129);
         VERIFY_CHECK(state->ps[no].bits_na_lam <= 129);
         if (state->ps[no].bits_na_1 > bits) {
@@ -476,40 +263,36 @@ static void secp256k1_ecmult_strauss_wnaf(const secp256k1_ecmult_context *ctx, c
         if (state->ps[no].bits_na_lam > bits) {
             bits = state->ps[no].bits_na_lam;
         }
-        ++no;
-    }
 
-    /* Calculate odd multiples of a.
-     * All multiples are brought to the same Z 'denominator', which is stored
-     * in Z. Due to secp256k1' isomorphism we can do all operations pretending
-     * that the Z coordinate was 1, use affine addition formulae, and correct
-     * the Z coordinate of the result once at the end.
-     * The exception is the precomputed G table points, which are actually
-     * affine. Compared to the base used for other points, they have a Z ratio
-     * of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same
-     * isomorphism to efficiently add with a known Z inverse.
-     */
-    if (no > 0) {
-        /* Compute the odd multiples in Jacobian form. */
-        secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), state->prej, state->zr, &a[state->ps[0].input_pos]);
-        for (np = 1; np < no; ++np) {
-            secp256k1_gej tmp = a[state->ps[np].input_pos];
+        /* Calculate odd multiples of a.
+         * All multiples are brought to the same Z 'denominator', which is stored
+         * in Z. Due to secp256k1' isomorphism we can do all operations pretending
+         * that the Z coordinate was 1, use affine addition formulae, and correct
+         * the Z coordinate of the result once at the end.
+         * The exception is the precomputed G table points, which are actually
+         * affine. Compared to the base used for other points, they have a Z ratio
+         * of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same
+         * isomorphism to efficiently add with a known Z inverse.
+         */
+        tmp = a[np];
+        if (no) {
 #ifdef VERIFY
-            secp256k1_fe_normalize_var(&(state->prej[(np - 1) * ECMULT_TABLE_SIZE(WINDOW_A) + ECMULT_TABLE_SIZE(WINDOW_A) - 1].z));
+            secp256k1_fe_normalize_var(&Z);
 #endif
-            secp256k1_gej_rescale(&tmp, &(state->prej[(np - 1) * ECMULT_TABLE_SIZE(WINDOW_A) + ECMULT_TABLE_SIZE(WINDOW_A) - 1].z));
-            secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), state->prej + np * ECMULT_TABLE_SIZE(WINDOW_A), state->zr + np * ECMULT_TABLE_SIZE(WINDOW_A), &tmp);
-            secp256k1_fe_mul(state->zr + np * ECMULT_TABLE_SIZE(WINDOW_A), state->zr + np * ECMULT_TABLE_SIZE(WINDOW_A), &(a[state->ps[np].input_pos].z));
+            secp256k1_gej_rescale(&tmp, &Z);
         }
-        /* Bring them to the same Z denominator. */
-        secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A) * no, state->pre_a, &Z, state->prej, state->zr);
-    } else {
-        secp256k1_fe_set_int(&Z, 1);
+        secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), state->pre_a + no * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), &Z, &tmp);
+        if (no) secp256k1_fe_mul(state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), &(a[np].z));
+
+        ++no;
     }
 
+    /* Bring them to the same Z denominator. */
+    secp256k1_ge_table_set_globalz(ECMULT_TABLE_SIZE(WINDOW_A) * no, state->pre_a, state->aux);
+
     for (np = 0; np < no; ++np) {
         for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
-            secp256k1_ge_mul_lambda(&state->pre_a_lam[np * ECMULT_TABLE_SIZE(WINDOW_A) + i], &state->pre_a[np * ECMULT_TABLE_SIZE(WINDOW_A) + i]);
+            secp256k1_fe_mul(&state->aux[np * ECMULT_TABLE_SIZE(WINDOW_A) + i], &state->pre_a[np * ECMULT_TABLE_SIZE(WINDOW_A) + i].x, &secp256k1_const_beta);
         }
     }
 
@@ -535,20 +318,20 @@ static void secp256k1_ecmult_strauss_wnaf(const secp256k1_ecmult_context *ctx, c
         secp256k1_gej_double_var(r, r, NULL);
         for (np = 0; np < no; ++np) {
             if (i < state->ps[np].bits_na_1 && (n = state->ps[np].wnaf_na_1[i])) {
-                ECMULT_TABLE_GET_GE(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A);
+                secp256k1_ecmult_table_get_ge(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A);
                 secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
             }
             if (i < state->ps[np].bits_na_lam && (n = state->ps[np].wnaf_na_lam[i])) {
-                ECMULT_TABLE_GET_GE(&tmpa, state->pre_a_lam + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A);
+                secp256k1_ecmult_table_get_ge_lambda(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A);
                 secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
             }
         }
         if (i < bits_ng_1 && (n = wnaf_ng_1[i])) {
-            ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
+            secp256k1_ecmult_table_get_ge_storage(&tmpa, secp256k1_pre_g, n, WINDOW_G);
             secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
         }
         if (i < bits_ng_128 && (n = wnaf_ng_128[i])) {
-            ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g_128, n, WINDOW_G);
+            secp256k1_ecmult_table_get_ge_storage(&tmpa, secp256k1_pre_g_128, n, WINDOW_G);
             secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
         }
     }
@@ -558,28 +341,24 @@ static void secp256k1_ecmult_strauss_wnaf(const secp256k1_ecmult_context *ctx, c
     }
 }
 
-static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
-    secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)];
-    secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)];
+static void secp256k1_ecmult(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
+    secp256k1_fe aux[ECMULT_TABLE_SIZE(WINDOW_A)];
     secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
     struct secp256k1_strauss_point_state ps[1];
-    secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
     struct secp256k1_strauss_state state;
 
-    state.prej = prej;
-    state.zr = zr;
+    state.aux = aux;
     state.pre_a = pre_a;
-    state.pre_a_lam = pre_a_lam;
     state.ps = ps;
-    secp256k1_ecmult_strauss_wnaf(ctx, &state, r, 1, a, na, ng);
+    secp256k1_ecmult_strauss_wnaf(&state, r, 1, a, na, ng);
 }
 
 static size_t secp256k1_strauss_scratch_size(size_t n_points) {
-    static const size_t point_size = (2 * sizeof(secp256k1_ge) + sizeof(secp256k1_gej) + sizeof(secp256k1_fe)) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar);
+    static const size_t point_size = (sizeof(secp256k1_ge) + sizeof(secp256k1_fe)) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar);
     return n_points*point_size;
 }
 
-static int secp256k1_ecmult_strauss_batch(const secp256k1_callback* error_callback, const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) {
+static int secp256k1_ecmult_strauss_batch(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) {
     secp256k1_gej* points;
     secp256k1_scalar* scalars;
     struct secp256k1_strauss_state state;
@@ -591,15 +370,16 @@ static int secp256k1_ecmult_strauss_batch(const secp256k1_callback* error_callba
         return 1;
     }
 
+    /* We allocate STRAUSS_SCRATCH_OBJECTS objects on the scratch space. If these
+     * allocations change, make sure to update the STRAUSS_SCRATCH_OBJECTS
+     * constant and strauss_scratch_size accordingly. */
     points = (secp256k1_gej*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(secp256k1_gej));
     scalars = (secp256k1_scalar*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(secp256k1_scalar));
-    state.prej = (secp256k1_gej*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_gej));
-    state.zr = (secp256k1_fe*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_fe));
+    state.aux = (secp256k1_fe*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_fe));
     state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge));
-    state.pre_a_lam = (secp256k1_ge*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge));
     state.ps = (struct secp256k1_strauss_point_state*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(struct secp256k1_strauss_point_state));
 
-    if (points == NULL || scalars == NULL || state.prej == NULL || state.zr == NULL || state.pre_a == NULL || state.pre_a_lam == NULL || state.ps == NULL) {
+    if (points == NULL || scalars == NULL || state.aux == NULL || state.pre_a == NULL || state.ps == NULL) {
         secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint);
         return 0;
     }
@@ -612,14 +392,14 @@ static int secp256k1_ecmult_strauss_batch(const secp256k1_callback* error_callba
         }
         secp256k1_gej_set_ge(&points[i], &point);
     }
-    secp256k1_ecmult_strauss_wnaf(ctx, &state, r, n_points, points, scalars, inp_g_sc);
+    secp256k1_ecmult_strauss_wnaf(&state, r, n_points, points, scalars, inp_g_sc);
     secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint);
     return 1;
 }
 
 /* Wrapper for secp256k1_ecmult_multi_func interface */
-static int secp256k1_ecmult_strauss_batch_single(const secp256k1_callback* error_callback, const secp256k1_ecmult_context *actx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) {
-    return secp256k1_ecmult_strauss_batch(error_callback, actx, scratch, r, inp_g_sc, cb, cbdata, n, 0);
+static int secp256k1_ecmult_strauss_batch_single(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) {
+    return secp256k1_ecmult_strauss_batch(error_callback, scratch, r, inp_g_sc, cb, cbdata, n, 0);
 }
 
 static size_t secp256k1_strauss_max_points(const secp256k1_callback* error_callback, secp256k1_scratch *scratch) {
@@ -866,7 +646,7 @@ static size_t secp256k1_pippenger_scratch_size(size_t n_points, int bucket_windo
     return (sizeof(secp256k1_gej) << bucket_window) + sizeof(struct secp256k1_pippenger_state) + entries * entry_size;
 }
 
-static int secp256k1_ecmult_pippenger_batch(const secp256k1_callback* error_callback, const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) {
+static int secp256k1_ecmult_pippenger_batch(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) {
     const size_t scratch_checkpoint = secp256k1_scratch_checkpoint(error_callback, scratch);
     /* Use 2(n+1) with the endomorphism, when calculating batch
      * sizes. The reason for +1 is that we add the G scalar to the list of
@@ -881,13 +661,16 @@ static int secp256k1_ecmult_pippenger_batch(const secp256k1_callback* error_call
     int i, j;
     int bucket_window;
 
-    (void)ctx;
     secp256k1_gej_set_infinity(r);
     if (inp_g_sc == NULL && n_points == 0) {
         return 1;
     }
-
     bucket_window = secp256k1_pippenger_bucket_window(n_points);
+
+    /* We allocate PIPPENGER_SCRATCH_OBJECTS objects on the scratch space. If
+     * these allocations change, make sure to update the
+     * PIPPENGER_SCRATCH_OBJECTS constant and pippenger_scratch_size
+     * accordingly. */
     points = (secp256k1_ge *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*points));
     scalars = (secp256k1_scalar *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*scalars));
     state_space = (struct secp256k1_pippenger_state *) secp256k1_scratch_alloc(error_callback, scratch, sizeof(*state_space));
@@ -895,7 +678,6 @@ static int secp256k1_ecmult_pippenger_batch(const secp256k1_callback* error_call
         secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint);
         return 0;
     }
-
     state_space->ps = (struct secp256k1_pippenger_point_state *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*state_space->ps));
     state_space->wnaf_na = (int *) secp256k1_scratch_alloc(error_callback, scratch, entries*(WNAF_SIZE(bucket_window+1)) * sizeof(int));
     buckets = (secp256k1_gej *) secp256k1_scratch_alloc(error_callback, scratch, (1<<bucket_window) * sizeof(*buckets));
@@ -941,8 +723,8 @@ static int secp256k1_ecmult_pippenger_batch(const secp256k1_callback* error_call
 }
 
 /* Wrapper for secp256k1_ecmult_multi_func interface */
-static int secp256k1_ecmult_pippenger_batch_single(const secp256k1_callback* error_callback, const secp256k1_ecmult_context *actx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) {
-    return secp256k1_ecmult_pippenger_batch(error_callback, actx, scratch, r, inp_g_sc, cb, cbdata, n, 0);
+static int secp256k1_ecmult_pippenger_batch_single(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) {
+    return secp256k1_ecmult_pippenger_batch(error_callback, scratch, r, inp_g_sc, cb, cbdata, n, 0);
 }
 
 /**
@@ -986,7 +768,7 @@ static size_t secp256k1_pippenger_max_points(const secp256k1_callback* error_cal
 
 /* Computes ecmult_multi by simply multiplying and adding each point. Does not
  * require a scratch space */
-static int secp256k1_ecmult_multi_simple_var(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points) {
+static int secp256k1_ecmult_multi_simple_var(secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points) {
     size_t point_idx;
     secp256k1_scalar szero;
     secp256k1_gej tmpj;
@@ -995,7 +777,7 @@ static int secp256k1_ecmult_multi_simple_var(const secp256k1_ecmult_context *ctx
     secp256k1_gej_set_infinity(r);
     secp256k1_gej_set_infinity(&tmpj);
     /* r = inp_g_sc*G */
-    secp256k1_ecmult(ctx, r, &tmpj, &szero, inp_g_sc);
+    secp256k1_ecmult(r, &tmpj, &szero, inp_g_sc);
     for (point_idx = 0; point_idx < n_points; point_idx++) {
         secp256k1_ge point;
         secp256k1_gej pointj;
@@ -1005,7 +787,7 @@ static int secp256k1_ecmult_multi_simple_var(const secp256k1_ecmult_context *ctx
         }
         /* r += scalar*point */
         secp256k1_gej_set_ge(&pointj, &point);
-        secp256k1_ecmult(ctx, &tmpj, &pointj, &scalar, NULL);
+        secp256k1_ecmult(&tmpj, &pointj, &scalar, NULL);
         secp256k1_gej_add_var(r, r, &tmpj, NULL);
     }
     return 1;
@@ -1031,11 +813,11 @@ static int secp256k1_ecmult_multi_batch_size_helper(size_t *n_batches, size_t *n
     return 1;
 }
 
-typedef int (*secp256k1_ecmult_multi_func)(const secp256k1_callback* error_callback, const secp256k1_ecmult_context*, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t);
-static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback, const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) {
+typedef int (*secp256k1_ecmult_multi_func)(const secp256k1_callback* error_callback, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t);
+static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) {
     size_t i;
 
-    int (*f)(const secp256k1_callback* error_callback, const secp256k1_ecmult_context*, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t, size_t);
+    int (*f)(const secp256k1_callback* error_callback, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t, size_t);
     size_t n_batches;
     size_t n_batch_points;
 
@@ -1045,11 +827,11 @@ static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback,
     } else if (n == 0) {
         secp256k1_scalar szero;
         secp256k1_scalar_set_int(&szero, 0);
-        secp256k1_ecmult(ctx, r, r, &szero, inp_g_sc);
+        secp256k1_ecmult(r, r, &szero, inp_g_sc);
         return 1;
     }
     if (scratch == NULL) {
-        return secp256k1_ecmult_multi_simple_var(ctx, r, inp_g_sc, cb, cbdata, n);
+        return secp256k1_ecmult_multi_simple_var(r, inp_g_sc, cb, cbdata, n);
     }
 
     /* Compute the batch sizes for Pippenger's algorithm given a scratch space. If it's greater than
@@ -1057,13 +839,13 @@ static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback,
      * As a first step check if there's enough space for Pippenger's algo (which requires less space
      * than Strauss' algo) and if not, use the simple algorithm. */
     if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_pippenger_max_points(error_callback, scratch), n)) {
-        return secp256k1_ecmult_multi_simple_var(ctx, r, inp_g_sc, cb, cbdata, n);
+        return secp256k1_ecmult_multi_simple_var(r, inp_g_sc, cb, cbdata, n);
     }
     if (n_batch_points >= ECMULT_PIPPENGER_THRESHOLD) {
         f = secp256k1_ecmult_pippenger_batch;
     } else {
         if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_strauss_max_points(error_callback, scratch), n)) {
-            return secp256k1_ecmult_multi_simple_var(ctx, r, inp_g_sc, cb, cbdata, n);
+            return secp256k1_ecmult_multi_simple_var(r, inp_g_sc, cb, cbdata, n);
         }
         f = secp256k1_ecmult_strauss_batch;
     }
@@ -1071,7 +853,7 @@ static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback,
         size_t nbp = n < n_batch_points ? n : n_batch_points;
         size_t offset = n_batch_points*i;
         secp256k1_gej tmp;
-        if (!f(error_callback, ctx, scratch, &tmp, i == 0 ? inp_g_sc : NULL, cb, cbdata, nbp, offset)) {
+        if (!f(error_callback, scratch, &tmp, i == 0 ? inp_g_sc : NULL, cb, cbdata, nbp, offset)) {
             return 0;
         }
         secp256k1_gej_add_var(r, r, &tmp, NULL);
diff --git a/src/secp256k1/src/field.h b/src/secp256k1/src/field.h
index 854aaebabc9..2584a494eeb 100644
--- a/src/secp256k1/src/field.h
+++ b/src/secp256k1/src/field.h
@@ -14,8 +14,8 @@
  *  - Each field element can be normalized or not.
  *  - Each field element has a magnitude, which represents how far away
  *    its representation is away from normalization. Normalized elements
- *    always have a magnitude of 1, but a magnitude of 1 doesn't imply
- *    normality.
+ *    always have a magnitude of 0 or 1, but a magnitude of 1 doesn't
+ *    imply normality.
  */
 
 #if defined HAVE_CONFIG_H
@@ -32,6 +32,12 @@
 #error "Please select wide multiplication implementation"
 #endif
 
+static const secp256k1_fe secp256k1_fe_one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+static const secp256k1_fe secp256k1_const_beta = SECP256K1_FE_CONST(
+    0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
+    0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
+);
+
 /** Normalize a field element. This brings the field element to a canonical representation, reduces
  *  its magnitude to 1, and reduces it modulo field size `p`.
  */
@@ -50,7 +56,9 @@ static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r);
  *  without constant-time guarantee. */
 static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r);
 
-/** Set a field element equal to a small integer. Resulting field element is normalized. */
+/** Set a field element equal to a small (not greater than 0x7FFF), non-negative integer.
+ *  Resulting field element is normalized; it has magnitude 0 if a == 0, and magnitude 1 otherwise.
+ */
 static void secp256k1_fe_set_int(secp256k1_fe *r, int a);
 
 /** Sets a field element equal to zero, initializing all fields. */
@@ -122,4 +130,13 @@ static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_f
 /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time.  Both *r and *a must be initialized.*/
 static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag);
 
+/** Halves the value of a field element modulo the field prime. Constant-time.
+ *  For an input magnitude 'm', the output magnitude is set to 'floor(m/2) + 1'.
+ *  The output is not guaranteed to be normalized, regardless of the input. */
+static void secp256k1_fe_half(secp256k1_fe *r);
+
+/** Sets each limb of 'r' to its upper bound at magnitude 'm'. The output will also have its
+ *  magnitude set to 'm' and is normalized if (and only if) 'm' is zero. */
+static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m);
+
 #endif /* SECP256K1_FIELD_H */
diff --git a/src/secp256k1/src/field_10x26_impl.h b/src/secp256k1/src/field_10x26_impl.h
index 7a38c117f19..21742bf6eb6 100644
--- a/src/secp256k1/src/field_10x26_impl.h
+++ b/src/secp256k1/src/field_10x26_impl.h
@@ -11,6 +11,15 @@
 #include "field.h"
 #include "modinv32_impl.h"
 
+/** See the comment at the top of field_5x52_impl.h for more details.
+ *
+ *  Here, we represent field elements as 10 uint32_t's in base 2^26, least significant first,
+ *  where limbs can contain >26 bits.
+ *  A magnitude M means:
+ *  - 2*M*(2^22-1) is the max (inclusive) of the most significant limb
+ *  - 2*M*(2^26-1) is the max (inclusive) of the remaining limbs
+ */
+
 #ifdef VERIFY
 static void secp256k1_fe_verify(const secp256k1_fe *a) {
     const uint32_t *d = a->n;
@@ -40,6 +49,26 @@ static void secp256k1_fe_verify(const secp256k1_fe *a) {
 }
 #endif
 
+static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m) {
+    VERIFY_CHECK(m >= 0);
+    VERIFY_CHECK(m <= 2048);
+    r->n[0] = 0x3FFFFFFUL * 2 * m;
+    r->n[1] = 0x3FFFFFFUL * 2 * m;
+    r->n[2] = 0x3FFFFFFUL * 2 * m;
+    r->n[3] = 0x3FFFFFFUL * 2 * m;
+    r->n[4] = 0x3FFFFFFUL * 2 * m;
+    r->n[5] = 0x3FFFFFFUL * 2 * m;
+    r->n[6] = 0x3FFFFFFUL * 2 * m;
+    r->n[7] = 0x3FFFFFFUL * 2 * m;
+    r->n[8] = 0x3FFFFFFUL * 2 * m;
+    r->n[9] = 0x03FFFFFUL * 2 * m;
+#ifdef VERIFY
+    r->magnitude = m;
+    r->normalized = (m == 0);
+    secp256k1_fe_verify(r);
+#endif
+}
+
 static void secp256k1_fe_normalize(secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
@@ -264,10 +293,11 @@ static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) {
 }
 
 SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
+    VERIFY_CHECK(0 <= a && a <= 0x7FFF);
     r->n[0] = a;
     r->n[1] = r->n[2] = r->n[3] = r->n[4] = r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
 #ifdef VERIFY
-    r->magnitude = 1;
+    r->magnitude = (a != 0);
     r->normalized = 1;
     secp256k1_fe_verify(r);
 #endif
@@ -390,6 +420,10 @@ SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k
 #ifdef VERIFY
     VERIFY_CHECK(a->magnitude <= m);
     secp256k1_fe_verify(a);
+    VERIFY_CHECK(0x3FFFC2FUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
+    VERIFY_CHECK(0x3FFFFBFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
+    VERIFY_CHECK(0x3FFFFFFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
+    VERIFY_CHECK(0x03FFFFFUL * 2 * (m + 1) >= 0x03FFFFFUL * 2 * m);
 #endif
     r->n[0] = 0x3FFFC2FUL * 2 * (m + 1) - a->n[0];
     r->n[1] = 0x3FFFFBFUL * 2 * (m + 1) - a->n[1];
@@ -1119,6 +1153,82 @@ static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_
 #endif
 }
 
+static SECP256K1_INLINE void secp256k1_fe_half(secp256k1_fe *r) {
+    uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
+             t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
+    uint32_t one = (uint32_t)1;
+    uint32_t mask = -(t0 & one) >> 6;
+
+#ifdef VERIFY
+    secp256k1_fe_verify(r);
+    VERIFY_CHECK(r->magnitude < 32);
+#endif
+
+    /* Bounds analysis (over the rationals).
+     *
+     * Let m = r->magnitude
+     *     C = 0x3FFFFFFUL * 2
+     *     D = 0x03FFFFFUL * 2
+     *
+     * Initial bounds: t0..t8 <= C * m
+     *                     t9 <= D * m
+     */
+
+    t0 += 0x3FFFC2FUL & mask;
+    t1 += 0x3FFFFBFUL & mask;
+    t2 += mask;
+    t3 += mask;
+    t4 += mask;
+    t5 += mask;
+    t6 += mask;
+    t7 += mask;
+    t8 += mask;
+    t9 += mask >> 4;
+
+    VERIFY_CHECK((t0 & one) == 0);
+
+    /* t0..t8: added <= C/2
+     *     t9: added <= D/2
+     *
+     * Current bounds: t0..t8 <= C * (m + 1/2)
+     *                     t9 <= D * (m + 1/2)
+     */
+
+    r->n[0] = (t0 >> 1) + ((t1 & one) << 25);
+    r->n[1] = (t1 >> 1) + ((t2 & one) << 25);
+    r->n[2] = (t2 >> 1) + ((t3 & one) << 25);
+    r->n[3] = (t3 >> 1) + ((t4 & one) << 25);
+    r->n[4] = (t4 >> 1) + ((t5 & one) << 25);
+    r->n[5] = (t5 >> 1) + ((t6 & one) << 25);
+    r->n[6] = (t6 >> 1) + ((t7 & one) << 25);
+    r->n[7] = (t7 >> 1) + ((t8 & one) << 25);
+    r->n[8] = (t8 >> 1) + ((t9 & one) << 25);
+    r->n[9] = (t9 >> 1);
+
+    /* t0..t8: shifted right and added <= C/4 + 1/2
+     *     t9: shifted right
+     *
+     * Current bounds: t0..t8 <= C * (m/2 + 1/2)
+     *                     t9 <= D * (m/2 + 1/4)
+     */
+
+#ifdef VERIFY
+    /* Therefore the output magnitude (M) has to be set such that:
+     *     t0..t8: C * M >= C * (m/2 + 1/2)
+     *         t9: D * M >= D * (m/2 + 1/4)
+     *
+     * It suffices for all limbs that, for any input magnitude m:
+     *     M >= m/2 + 1/2
+     *
+     * and since we want the smallest such integer value for M:
+     *     M == floor(m/2) + 1
+     */
+    r->magnitude = (r->magnitude >> 1) + 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
 static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
     uint32_t mask0, mask1;
     VG_CHECK_VERIFY(r->n, sizeof(r->n));
@@ -1162,6 +1272,7 @@ static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const se
 #ifdef VERIFY
     r->magnitude = 1;
     r->normalized = 1;
+    secp256k1_fe_verify(r);
 #endif
 }
 
diff --git a/src/secp256k1/src/field_5x52_impl.h b/src/secp256k1/src/field_5x52_impl.h
index 60ded927f6e..6bd202f5871 100644
--- a/src/secp256k1/src/field_5x52_impl.h
+++ b/src/secp256k1/src/field_5x52_impl.h
@@ -22,11 +22,18 @@
 #endif
 
 /** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F,
- *  represented as 5 uint64_t's in base 2^52. The values are allowed to contain >52 each. In particular,
- *  each FieldElem has a 'magnitude' associated with it. Internally, a magnitude M means each element
- *  is at most M*(2^53-1), except the most significant one, which is limited to M*(2^49-1). All operations
- *  accept any input with magnitude at most M, and have different rules for propagating magnitude to their
- *  output.
+ *  represented as 5 uint64_t's in base 2^52, least significant first. Note that the limbs are allowed to
+ *  contain >52 bits each.
+ *
+ *  Each field element has a 'magnitude' associated with it. Internally, a magnitude M means:
+ *  - 2*M*(2^48-1) is the max (inclusive) of the most significant limb
+ *  - 2*M*(2^52-1) is the max (inclusive) of the remaining limbs
+ *
+ *  Operations have different rules for propagating magnitude to their outputs. If an operation takes a
+ *  magnitude M as a parameter, that means the magnitude of input field elements can be at most M (inclusive).
+ *
+ *  Each field element also has a 'normalized' flag. A field element is normalized if its magnitude is either
+ *  0 or 1, and its value is already reduced modulo the order of the field.
  */
 
 #ifdef VERIFY
@@ -51,6 +58,21 @@ static void secp256k1_fe_verify(const secp256k1_fe *a) {
 }
 #endif
 
+static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m) {
+    VERIFY_CHECK(m >= 0);
+    VERIFY_CHECK(m <= 2048);
+    r->n[0] = 0xFFFFFFFFFFFFFULL * 2 * m;
+    r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * m;
+    r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * m;
+    r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * m;
+    r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * m;
+#ifdef VERIFY
+    r->magnitude = m;
+    r->normalized = (m == 0);
+    secp256k1_fe_verify(r);
+#endif
+}
+
 static void secp256k1_fe_normalize(secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 
@@ -227,10 +249,11 @@ static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) {
 }
 
 SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
+    VERIFY_CHECK(0 <= a && a <= 0x7FFF);
     r->n[0] = a;
     r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
 #ifdef VERIFY
-    r->magnitude = 1;
+    r->magnitude = (a != 0);
     r->normalized = 1;
     secp256k1_fe_verify(r);
 #endif
@@ -376,6 +399,9 @@ SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k
 #ifdef VERIFY
     VERIFY_CHECK(a->magnitude <= m);
     secp256k1_fe_verify(a);
+    VERIFY_CHECK(0xFFFFEFFFFFC2FULL * 2 * (m + 1) >= 0xFFFFFFFFFFFFFULL * 2 * m);
+    VERIFY_CHECK(0xFFFFFFFFFFFFFULL * 2 * (m + 1) >= 0xFFFFFFFFFFFFFULL * 2 * m);
+    VERIFY_CHECK(0x0FFFFFFFFFFFFULL * 2 * (m + 1) >= 0x0FFFFFFFFFFFFULL * 2 * m);
 #endif
     r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0];
     r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1];
@@ -466,6 +492,71 @@ static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_
 #endif
 }
 
+static SECP256K1_INLINE void secp256k1_fe_half(secp256k1_fe *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+    uint64_t one = (uint64_t)1;
+    uint64_t mask = -(t0 & one) >> 12;
+
+#ifdef VERIFY
+    secp256k1_fe_verify(r);
+    VERIFY_CHECK(r->magnitude < 32);
+#endif
+
+    /* Bounds analysis (over the rationals).
+     *
+     * Let m = r->magnitude
+     *     C = 0xFFFFFFFFFFFFFULL * 2
+     *     D = 0x0FFFFFFFFFFFFULL * 2
+     *
+     * Initial bounds: t0..t3 <= C * m
+     *                     t4 <= D * m
+     */
+
+    t0 += 0xFFFFEFFFFFC2FULL & mask;
+    t1 += mask;
+    t2 += mask;
+    t3 += mask;
+    t4 += mask >> 4;
+
+    VERIFY_CHECK((t0 & one) == 0);
+
+    /* t0..t3: added <= C/2
+     *     t4: added <= D/2
+     *
+     * Current bounds: t0..t3 <= C * (m + 1/2)
+     *                     t4 <= D * (m + 1/2)
+     */
+
+    r->n[0] = (t0 >> 1) + ((t1 & one) << 51);
+    r->n[1] = (t1 >> 1) + ((t2 & one) << 51);
+    r->n[2] = (t2 >> 1) + ((t3 & one) << 51);
+    r->n[3] = (t3 >> 1) + ((t4 & one) << 51);
+    r->n[4] = (t4 >> 1);
+
+    /* t0..t3: shifted right and added <= C/4 + 1/2
+     *     t4: shifted right
+     *
+     * Current bounds: t0..t3 <= C * (m/2 + 1/2)
+     *                     t4 <= D * (m/2 + 1/4)
+     */
+
+#ifdef VERIFY
+    /* Therefore the output magnitude (M) has to be set such that:
+     *     t0..t3: C * M >= C * (m/2 + 1/2)
+     *         t4: D * M >= D * (m/2 + 1/4)
+     *
+     * It suffices for all limbs that, for any input magnitude m:
+     *     M >= m/2 + 1/2
+     *
+     * and since we want the smallest such integer value for M:
+     *     M == floor(m/2) + 1
+     */
+    r->magnitude = (r->magnitude >> 1) + 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
 static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
     uint64_t mask0, mask1;
     VG_CHECK_VERIFY(r->n, sizeof(r->n));
@@ -496,6 +587,7 @@ static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const se
 #ifdef VERIFY
     r->magnitude = 1;
     r->normalized = 1;
+    secp256k1_fe_verify(r);
 #endif
 }
 
diff --git a/src/secp256k1/src/field_5x52_int128_impl.h b/src/secp256k1/src/field_5x52_int128_impl.h
index 314002ee395..18567b95f39 100644
--- a/src/secp256k1/src/field_5x52_int128_impl.h
+++ b/src/secp256k1/src/field_5x52_int128_impl.h
@@ -9,14 +9,18 @@
 
 #include <stdint.h>
 
+#include "int128.h"
+
 #ifdef VERIFY
 #define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
+#define VERIFY_BITS_128(x, n) VERIFY_CHECK(secp256k1_u128_check_bits((x), (n)))
 #else
 #define VERIFY_BITS(x, n) do { } while(0)
+#define VERIFY_BITS_128(x, n) do { } while(0)
 #endif
 
 SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
-    uint128_t c, d;
+    secp256k1_uint128 c, d;
     uint64_t t3, t4, tx, u0;
     uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
     const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
@@ -40,122 +44,119 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t
      *  Note that [x 0 0 0 0 0] = [x*R].
      */
 
-    d  = (uint128_t)a0 * b[3]
-       + (uint128_t)a1 * b[2]
-       + (uint128_t)a2 * b[1]
-       + (uint128_t)a3 * b[0];
-    VERIFY_BITS(d, 114);
+    secp256k1_u128_mul(&d, a0, b[3]);
+    secp256k1_u128_accum_mul(&d, a1, b[2]);
+    secp256k1_u128_accum_mul(&d, a2, b[1]);
+    secp256k1_u128_accum_mul(&d, a3, b[0]);
+    VERIFY_BITS_128(&d, 114);
     /* [d 0 0 0] = [p3 0 0 0] */
-    c  = (uint128_t)a4 * b[4];
-    VERIFY_BITS(c, 112);
+    secp256k1_u128_mul(&c, a4, b[4]);
+    VERIFY_BITS_128(&c, 112);
     /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
-    d += (c & M) * R; c >>= 52;
-    VERIFY_BITS(d, 115);
-    VERIFY_BITS(c, 60);
-    /* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
-    t3 = d & M; d >>= 52;
+    secp256k1_u128_accum_mul(&d, R, secp256k1_u128_to_u64(&c)); secp256k1_u128_rshift(&c, 64);
+    VERIFY_BITS_128(&d, 115);
+    VERIFY_BITS_128(&c, 48);
+    /* [(c<<12) 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    t3 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
     VERIFY_BITS(t3, 52);
-    VERIFY_BITS(d, 63);
-    /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    VERIFY_BITS_128(&d, 63);
+    /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
 
-    d += (uint128_t)a0 * b[4]
-       + (uint128_t)a1 * b[3]
-       + (uint128_t)a2 * b[2]
-       + (uint128_t)a3 * b[1]
-       + (uint128_t)a4 * b[0];
-    VERIFY_BITS(d, 115);
-    /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
-    d += c * R;
-    VERIFY_BITS(d, 116);
+    secp256k1_u128_accum_mul(&d, a0, b[4]);
+    secp256k1_u128_accum_mul(&d, a1, b[3]);
+    secp256k1_u128_accum_mul(&d, a2, b[2]);
+    secp256k1_u128_accum_mul(&d, a3, b[1]);
+    secp256k1_u128_accum_mul(&d, a4, b[0]);
+    VERIFY_BITS_128(&d, 115);
+    /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    secp256k1_u128_accum_mul(&d, R << 12, secp256k1_u128_to_u64(&c));
+    VERIFY_BITS_128(&d, 116);
     /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
-    t4 = d & M; d >>= 52;
+    t4 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
     VERIFY_BITS(t4, 52);
-    VERIFY_BITS(d, 64);
+    VERIFY_BITS_128(&d, 64);
     /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
     tx = (t4 >> 48); t4 &= (M >> 4);
     VERIFY_BITS(tx, 4);
     VERIFY_BITS(t4, 48);
     /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
 
-    c  = (uint128_t)a0 * b[0];
-    VERIFY_BITS(c, 112);
+    secp256k1_u128_mul(&c, a0, b[0]);
+    VERIFY_BITS_128(&c, 112);
     /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
-    d += (uint128_t)a1 * b[4]
-       + (uint128_t)a2 * b[3]
-       + (uint128_t)a3 * b[2]
-       + (uint128_t)a4 * b[1];
-    VERIFY_BITS(d, 115);
+    secp256k1_u128_accum_mul(&d, a1, b[4]);
+    secp256k1_u128_accum_mul(&d, a2, b[3]);
+    secp256k1_u128_accum_mul(&d, a3, b[2]);
+    secp256k1_u128_accum_mul(&d, a4, b[1]);
+    VERIFY_BITS_128(&d, 115);
     /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
-    u0 = d & M; d >>= 52;
+    u0 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
     VERIFY_BITS(u0, 52);
-    VERIFY_BITS(d, 63);
+    VERIFY_BITS_128(&d, 63);
     /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
     /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
     u0 = (u0 << 4) | tx;
     VERIFY_BITS(u0, 56);
     /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
-    c += (uint128_t)u0 * (R >> 4);
-    VERIFY_BITS(c, 115);
+    secp256k1_u128_accum_mul(&c, u0, R >> 4);
+    VERIFY_BITS_128(&c, 115);
     /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
-    r[0] = c & M; c >>= 52;
+    r[0] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
     VERIFY_BITS(r[0], 52);
-    VERIFY_BITS(c, 61);
+    VERIFY_BITS_128(&c, 61);
     /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
 
-    c += (uint128_t)a0 * b[1]
-       + (uint128_t)a1 * b[0];
-    VERIFY_BITS(c, 114);
+    secp256k1_u128_accum_mul(&c, a0, b[1]);
+    secp256k1_u128_accum_mul(&c, a1, b[0]);
+    VERIFY_BITS_128(&c, 114);
     /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
-    d += (uint128_t)a2 * b[4]
-       + (uint128_t)a3 * b[3]
-       + (uint128_t)a4 * b[2];
-    VERIFY_BITS(d, 114);
+    secp256k1_u128_accum_mul(&d, a2, b[4]);
+    secp256k1_u128_accum_mul(&d, a3, b[3]);
+    secp256k1_u128_accum_mul(&d, a4, b[2]);
+    VERIFY_BITS_128(&d, 114);
     /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
-    c += (d & M) * R; d >>= 52;
-    VERIFY_BITS(c, 115);
-    VERIFY_BITS(d, 62);
+    secp256k1_u128_accum_mul(&c, secp256k1_u128_to_u64(&d) & M, R); secp256k1_u128_rshift(&d, 52);
+    VERIFY_BITS_128(&c, 115);
+    VERIFY_BITS_128(&d, 62);
     /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
-    r[1] = c & M; c >>= 52;
+    r[1] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
     VERIFY_BITS(r[1], 52);
-    VERIFY_BITS(c, 63);
+    VERIFY_BITS_128(&c, 63);
     /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
 
-    c += (uint128_t)a0 * b[2]
-       + (uint128_t)a1 * b[1]
-       + (uint128_t)a2 * b[0];
-    VERIFY_BITS(c, 114);
+    secp256k1_u128_accum_mul(&c, a0, b[2]);
+    secp256k1_u128_accum_mul(&c, a1, b[1]);
+    secp256k1_u128_accum_mul(&c, a2, b[0]);
+    VERIFY_BITS_128(&c, 114);
     /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
-    d += (uint128_t)a3 * b[4]
-       + (uint128_t)a4 * b[3];
-    VERIFY_BITS(d, 114);
+    secp256k1_u128_accum_mul(&d, a3, b[4]);
+    secp256k1_u128_accum_mul(&d, a4, b[3]);
+    VERIFY_BITS_128(&d, 114);
     /* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
-    c += (d & M) * R; d >>= 52;
-    VERIFY_BITS(c, 115);
-    VERIFY_BITS(d, 62);
-    /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    secp256k1_u128_accum_mul(&c, R, secp256k1_u128_to_u64(&d)); secp256k1_u128_rshift(&d, 64);
+    VERIFY_BITS_128(&c, 115);
+    VERIFY_BITS_128(&d, 50);
+    /* [(d<<12) 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
 
-    /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
-    r[2] = c & M; c >>= 52;
+    r[2] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
     VERIFY_BITS(r[2], 52);
-    VERIFY_BITS(c, 63);
-    /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
-    c   += d * R + t3;
-    VERIFY_BITS(c, 100);
+    VERIFY_BITS_128(&c, 63);
+    /* [(d<<12) 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    secp256k1_u128_accum_mul(&c, R << 12, secp256k1_u128_to_u64(&d));
+    secp256k1_u128_accum_u64(&c, t3);
+    VERIFY_BITS_128(&c, 100);
     /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
-    r[3] = c & M; c >>= 52;
+    r[3] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
     VERIFY_BITS(r[3], 52);
-    VERIFY_BITS(c, 48);
+    VERIFY_BITS_128(&c, 48);
     /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
-    c   += t4;
-    VERIFY_BITS(c, 49);
-    /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
-    r[4] = c;
+    r[4] = secp256k1_u128_to_u64(&c) + t4;
     VERIFY_BITS(r[4], 49);
     /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
 }
 
 SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
-    uint128_t c, d;
+    secp256k1_uint128 c, d;
     uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
     int64_t t3, t4, tx, u0;
     const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
@@ -171,107 +172,105 @@ SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t
      *  Note that [x 0 0 0 0 0] = [x*R].
      */
 
-    d  = (uint128_t)(a0*2) * a3
-       + (uint128_t)(a1*2) * a2;
-    VERIFY_BITS(d, 114);
+    secp256k1_u128_mul(&d, a0*2, a3);
+    secp256k1_u128_accum_mul(&d, a1*2, a2);
+    VERIFY_BITS_128(&d, 114);
     /* [d 0 0 0] = [p3 0 0 0] */
-    c  = (uint128_t)a4 * a4;
-    VERIFY_BITS(c, 112);
+    secp256k1_u128_mul(&c, a4, a4);
+    VERIFY_BITS_128(&c, 112);
     /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
-    d += (c & M) * R; c >>= 52;
-    VERIFY_BITS(d, 115);
-    VERIFY_BITS(c, 60);
-    /* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
-    t3 = d & M; d >>= 52;
+    secp256k1_u128_accum_mul(&d, R, secp256k1_u128_to_u64(&c)); secp256k1_u128_rshift(&c, 64);
+    VERIFY_BITS_128(&d, 115);
+    VERIFY_BITS_128(&c, 48);
+    /* [(c<<12) 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    t3 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
     VERIFY_BITS(t3, 52);
-    VERIFY_BITS(d, 63);
-    /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    VERIFY_BITS_128(&d, 63);
+    /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
 
     a4 *= 2;
-    d += (uint128_t)a0 * a4
-       + (uint128_t)(a1*2) * a3
-       + (uint128_t)a2 * a2;
-    VERIFY_BITS(d, 115);
-    /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
-    d += c * R;
-    VERIFY_BITS(d, 116);
+    secp256k1_u128_accum_mul(&d, a0, a4);
+    secp256k1_u128_accum_mul(&d, a1*2, a3);
+    secp256k1_u128_accum_mul(&d, a2, a2);
+    VERIFY_BITS_128(&d, 115);
+    /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    secp256k1_u128_accum_mul(&d, R << 12, secp256k1_u128_to_u64(&c));
+    VERIFY_BITS_128(&d, 116);
     /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
-    t4 = d & M; d >>= 52;
+    t4 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
     VERIFY_BITS(t4, 52);
-    VERIFY_BITS(d, 64);
+    VERIFY_BITS_128(&d, 64);
     /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
     tx = (t4 >> 48); t4 &= (M >> 4);
     VERIFY_BITS(tx, 4);
     VERIFY_BITS(t4, 48);
     /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
 
-    c  = (uint128_t)a0 * a0;
-    VERIFY_BITS(c, 112);
+    secp256k1_u128_mul(&c, a0, a0);
+    VERIFY_BITS_128(&c, 112);
     /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
-    d += (uint128_t)a1 * a4
-       + (uint128_t)(a2*2) * a3;
-    VERIFY_BITS(d, 114);
+    secp256k1_u128_accum_mul(&d, a1, a4);
+    secp256k1_u128_accum_mul(&d, a2*2, a3);
+    VERIFY_BITS_128(&d, 114);
     /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
-    u0 = d & M; d >>= 52;
+    u0 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
     VERIFY_BITS(u0, 52);
-    VERIFY_BITS(d, 62);
+    VERIFY_BITS_128(&d, 62);
     /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
     /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
     u0 = (u0 << 4) | tx;
     VERIFY_BITS(u0, 56);
     /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
-    c += (uint128_t)u0 * (R >> 4);
-    VERIFY_BITS(c, 113);
+    secp256k1_u128_accum_mul(&c, u0, R >> 4);
+    VERIFY_BITS_128(&c, 113);
     /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
-    r[0] = c & M; c >>= 52;
+    r[0] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
     VERIFY_BITS(r[0], 52);
-    VERIFY_BITS(c, 61);
+    VERIFY_BITS_128(&c, 61);
     /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
 
     a0 *= 2;
-    c += (uint128_t)a0 * a1;
-    VERIFY_BITS(c, 114);
+    secp256k1_u128_accum_mul(&c, a0, a1);
+    VERIFY_BITS_128(&c, 114);
     /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
-    d += (uint128_t)a2 * a4
-       + (uint128_t)a3 * a3;
-    VERIFY_BITS(d, 114);
+    secp256k1_u128_accum_mul(&d, a2, a4);
+    secp256k1_u128_accum_mul(&d, a3, a3);
+    VERIFY_BITS_128(&d, 114);
     /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
-    c += (d & M) * R; d >>= 52;
-    VERIFY_BITS(c, 115);
-    VERIFY_BITS(d, 62);
+    secp256k1_u128_accum_mul(&c, secp256k1_u128_to_u64(&d) & M, R); secp256k1_u128_rshift(&d, 52);
+    VERIFY_BITS_128(&c, 115);
+    VERIFY_BITS_128(&d, 62);
     /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
-    r[1] = c & M; c >>= 52;
+    r[1] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
     VERIFY_BITS(r[1], 52);
-    VERIFY_BITS(c, 63);
+    VERIFY_BITS_128(&c, 63);
     /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
 
-    c += (uint128_t)a0 * a2
-       + (uint128_t)a1 * a1;
-    VERIFY_BITS(c, 114);
+    secp256k1_u128_accum_mul(&c, a0, a2);
+    secp256k1_u128_accum_mul(&c, a1, a1);
+    VERIFY_BITS_128(&c, 114);
     /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
-    d += (uint128_t)a3 * a4;
-    VERIFY_BITS(d, 114);
+    secp256k1_u128_accum_mul(&d, a3, a4);
+    VERIFY_BITS_128(&d, 114);
     /* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
-    c += (d & M) * R; d >>= 52;
-    VERIFY_BITS(c, 115);
-    VERIFY_BITS(d, 62);
-    /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
-    r[2] = c & M; c >>= 52;
+    secp256k1_u128_accum_mul(&c, R, secp256k1_u128_to_u64(&d)); secp256k1_u128_rshift(&d, 64);
+    VERIFY_BITS_128(&c, 115);
+    VERIFY_BITS_128(&d, 50);
+    /* [(d<<12) 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[2] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
     VERIFY_BITS(r[2], 52);
-    VERIFY_BITS(c, 63);
-    /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    VERIFY_BITS_128(&c, 63);
+    /* [(d<<12) 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
 
-    c   += d * R + t3;
-    VERIFY_BITS(c, 100);
+    secp256k1_u128_accum_mul(&c, R << 12, secp256k1_u128_to_u64(&d));
+    secp256k1_u128_accum_u64(&c, t3);
+    VERIFY_BITS_128(&c, 100);
     /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
-    r[3] = c & M; c >>= 52;
+    r[3] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
     VERIFY_BITS(r[3], 52);
-    VERIFY_BITS(c, 48);
+    VERIFY_BITS_128(&c, 48);
     /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
-    c   += t4;
-    VERIFY_BITS(c, 49);
-    /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
-    r[4] = c;
+    r[4] = secp256k1_u128_to_u64(&c) + t4;
     VERIFY_BITS(r[4], 49);
     /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
 }
diff --git a/src/secp256k1/src/field_impl.h b/src/secp256k1/src/field_impl.h
index 374284a1f4c..0a4a04d9ac2 100644
--- a/src/secp256k1/src/field_impl.h
+++ b/src/secp256k1/src/field_impl.h
@@ -135,6 +135,4 @@ static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a) {
     return secp256k1_fe_equal(&t1, a);
 }
 
-static const secp256k1_fe secp256k1_fe_one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
-
 #endif /* SECP256K1_FIELD_IMPL_H */
diff --git a/src/secp256k1/src/gen_context.c b/src/secp256k1/src/gen_context.c
deleted file mode 100644
index 8fab7aa49d8..00000000000
--- a/src/secp256k1/src/gen_context.c
+++ /dev/null
@@ -1,94 +0,0 @@
-/***********************************************************************
- * Copyright (c) 2013, 2014, 2015 Thomas Daede, Cory Fields            *
- * Distributed under the MIT software license, see the accompanying    *
- * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
- ***********************************************************************/
-
-/* Autotools creates libsecp256k1-config.h, of which ECMULT_GEN_PREC_BITS is needed.
-   ifndef guard so downstream users can define their own if they do not use autotools. */
-#if !defined(ECMULT_GEN_PREC_BITS)
-#include "libsecp256k1-config.h"
-#endif
-
-/* We can't require the precomputed tables when creating them. */
-#undef USE_ECMULT_STATIC_PRECOMPUTATION
-
-/* In principle we could use external ASM, but this yields only a minor speedup in
-   build time and it's very complicated. In particular when cross-compiling, we'd
-   need to build the external ASM for the build and the host machine. */
-#undef USE_EXTERNAL_ASM
-
-#include "../include/secp256k1.h"
-#include "assumptions.h"
-#include "util.h"
-#include "field_impl.h"
-#include "scalar_impl.h"
-#include "group_impl.h"
-#include "ecmult_gen_impl.h"
-
-static void default_error_callback_fn(const char* str, void* data) {
-    (void)data;
-    fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str);
-    abort();
-}
-
-static const secp256k1_callback default_error_callback = {
-    default_error_callback_fn,
-    NULL
-};
-
-int main(int argc, char **argv) {
-    secp256k1_ecmult_gen_context ctx;
-    void *prealloc, *base;
-    int inner;
-    int outer;
-    FILE* fp;
-
-    (void)argc;
-    (void)argv;
-
-    fp = fopen("src/ecmult_static_context.h","w");
-    if (fp == NULL) {
-        fprintf(stderr, "Could not open src/ecmult_static_context.h for writing!\n");
-        return -1;
-    }
-
-    fprintf(fp, "#ifndef SECP256K1_ECMULT_STATIC_CONTEXT_H\n");
-    fprintf(fp, "#define SECP256K1_ECMULT_STATIC_CONTEXT_H\n");
-    fprintf(fp, "#include \"src/group.h\"\n");
-    fprintf(fp, "#define SC SECP256K1_GE_STORAGE_CONST\n");
-    fprintf(fp, "#if ECMULT_GEN_PREC_N != %d || ECMULT_GEN_PREC_G != %d\n", ECMULT_GEN_PREC_N, ECMULT_GEN_PREC_G);
-    fprintf(fp, "   #error configuration mismatch, invalid ECMULT_GEN_PREC_N, ECMULT_GEN_PREC_G. Try deleting ecmult_static_context.h before the build.\n");
-    fprintf(fp, "#endif\n");
-    fprintf(fp, "static const secp256k1_ge_storage secp256k1_ecmult_static_context[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G] = {\n");
-
-    base = checked_malloc(&default_error_callback, SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE);
-    prealloc = base;
-    secp256k1_ecmult_gen_context_init(&ctx);
-    secp256k1_ecmult_gen_context_build(&ctx, &prealloc);
-    for(outer = 0; outer != ECMULT_GEN_PREC_N; outer++) {
-        fprintf(fp,"{\n");
-        for(inner = 0; inner != ECMULT_GEN_PREC_G; inner++) {
-            fprintf(fp,"    SC(%uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu)", SECP256K1_GE_STORAGE_CONST_GET((*ctx.prec)[outer][inner]));
-            if (inner != ECMULT_GEN_PREC_G - 1) {
-                fprintf(fp,",\n");
-            } else {
-                fprintf(fp,"\n");
-            }
-        }
-        if (outer != ECMULT_GEN_PREC_N - 1) {
-            fprintf(fp,"},\n");
-        } else {
-            fprintf(fp,"}\n");
-        }
-    }
-    fprintf(fp,"};\n");
-    secp256k1_ecmult_gen_context_clear(&ctx);
-    free(base);
-
-    fprintf(fp, "#undef SC\n");
-    fprintf(fp, "#endif\n");
-    fclose(fp);
-
-    return 0;
-}
diff --git a/src/secp256k1/src/group.h b/src/secp256k1/src/group.h
index b9cd334dae2..b79ba597dbb 100644
--- a/src/secp256k1/src/group.h
+++ b/src/secp256k1/src/group.h
@@ -9,7 +9,10 @@
 
 #include "field.h"
 
-/** A group element of the secp256k1 curve, in affine coordinates. */
+/** A group element in affine coordinates on the secp256k1 curve,
+ *  or occasionally on an isomorphic curve of the form y^2 = x^3 + 7*t^6.
+ *  Note: For exhaustive test mode, secp256k1 is replaced by a small subgroup of a different curve.
+ */
 typedef struct {
     secp256k1_fe x;
     secp256k1_fe y;
@@ -19,7 +22,9 @@ typedef struct {
 #define SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0}
 #define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
 
-/** A group element of the secp256k1 curve, in jacobian coordinates. */
+/** A group element of the secp256k1 curve, in jacobian coordinates.
+ *  Note: For exhastive test mode, secp256k1 is replaced by a small subgroup of a different curve.
+ */
 typedef struct {
     secp256k1_fe x; /* actual X: x/z^2 */
     secp256k1_fe y; /* actual Y: y/z^3 */
@@ -64,12 +69,24 @@ static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a);
 /** Set a batch of group elements equal to the inputs given in jacobian coordinates */
 static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len);
 
-/** Bring a batch inputs given in jacobian coordinates (with known z-ratios) to
- *  the same global z "denominator". zr must contain the known z-ratios such
- *  that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. The x and y
- *  coordinates of the result are stored in r, the common z coordinate is
- *  stored in globalz. */
-static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr);
+/** Bring a batch of inputs to the same global z "denominator", based on ratios between
+ *  (omitted) z coordinates of adjacent elements.
+ *
+ *  Although the elements a[i] are _ge rather than _gej, they actually represent elements
+ *  in Jacobian coordinates with their z coordinates omitted.
+ *
+ *  Using the notation z(b) to represent the omitted z coordinate of b, the array zr of
+ *  z coordinate ratios must satisfy zr[i] == z(a[i]) / z(a[i-1]) for 0 < 'i' < len.
+ *  The zr[0] value is unused.
+ *
+ *  This function adjusts the coordinates of 'a' in place so that for all 'i', z(a[i]) == z(a[len-1]).
+ *  In other words, the initial value of z(a[len-1]) becomes the global z "denominator". Only the
+ *  a[i].x and a[i].y coordinates are explicitly modified; the adjustment of the omitted z coordinate is
+ *  implicit.
+ *
+ *  The coordinates of the final element a[len-1] are not changed.
+ */
+static void secp256k1_ge_table_set_globalz(size_t len, secp256k1_ge *a, const secp256k1_fe *zr);
 
 /** Set a group element (affine) equal to the point at infinity. */
 static void secp256k1_ge_set_infinity(secp256k1_ge *r);
@@ -80,6 +97,9 @@ static void secp256k1_gej_set_infinity(secp256k1_gej *r);
 /** Set a group element (jacobian) equal to another which is given in affine coordinates. */
 static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a);
 
+/** Check two group elements (jacobian) for equality in variable time. */
+static int secp256k1_gej_eq_var(const secp256k1_gej *a, const secp256k1_gej *b);
+
 /** Compare the X coordinate of a group element (jacobian). */
 static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a);
 
@@ -124,6 +144,9 @@ static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge
 /** Convert a group element back from the storage type. */
 static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a);
 
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time.  Both *r and *a must be initialized.*/
+static void secp256k1_gej_cmov(secp256k1_gej *r, const secp256k1_gej *a, int flag);
+
 /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time.  Both *r and *a must be initialized.*/
 static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag);
 
diff --git a/src/secp256k1/src/group_impl.h b/src/secp256k1/src/group_impl.h
index 47aea32be18..dfe6e32c7ff 100644
--- a/src/secp256k1/src/group_impl.h
+++ b/src/secp256k1/src/group_impl.h
@@ -10,6 +10,27 @@
 #include "field.h"
 #include "group.h"
 
+#define SECP256K1_G_ORDER_13 SECP256K1_GE_CONST(\
+    0xc3459c3d, 0x35326167, 0xcd86cce8, 0x07a2417f,\
+    0x5b8bd567, 0xde8538ee, 0x0d507b0c, 0xd128f5bb,\
+    0x8e467fec, 0xcd30000a, 0x6cc1184e, 0x25d382c2,\
+    0xa2f4494e, 0x2fbe9abc, 0x8b64abac, 0xd005fb24\
+)
+#define SECP256K1_G_ORDER_199 SECP256K1_GE_CONST(\
+    0x226e653f, 0xc8df7744, 0x9bacbf12, 0x7d1dcbf9,\
+    0x87f05b2a, 0xe7edbd28, 0x1f564575, 0xc48dcf18,\
+    0xa13872c2, 0xe933bb17, 0x5d9ffd5b, 0xb5b6e10c,\
+    0x57fe3c00, 0xbaaaa15a, 0xe003ec3e, 0x9c269bae\
+)
+/** Generator for secp256k1, value 'g' defined in
+ *  "Standards for Efficient Cryptography" (SEC2) 2.7.1.
+ */
+#define SECP256K1_G SECP256K1_GE_CONST(\
+    0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,\
+    0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL,\
+    0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL,\
+    0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL\
+)
 /* These exhaustive group test orders and generators are chosen such that:
  * - The field size is equal to that of secp256k1, so field code is the same.
  * - The curve equation is of the form y^2=x^3+B for some constant B.
@@ -21,23 +42,15 @@
  */
 #if defined(EXHAUSTIVE_TEST_ORDER)
 #  if EXHAUSTIVE_TEST_ORDER == 13
-static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
-    0xc3459c3d, 0x35326167, 0xcd86cce8, 0x07a2417f,
-    0x5b8bd567, 0xde8538ee, 0x0d507b0c, 0xd128f5bb,
-    0x8e467fec, 0xcd30000a, 0x6cc1184e, 0x25d382c2,
-    0xa2f4494e, 0x2fbe9abc, 0x8b64abac, 0xd005fb24
-);
+static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G_ORDER_13;
+
 static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(
     0x3d3486b2, 0x159a9ca5, 0xc75638be, 0xb23a69bc,
     0x946a45ab, 0x24801247, 0xb4ed2b8e, 0x26b6a417
 );
 #  elif EXHAUSTIVE_TEST_ORDER == 199
-static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
-    0x226e653f, 0xc8df7744, 0x9bacbf12, 0x7d1dcbf9,
-    0x87f05b2a, 0xe7edbd28, 0x1f564575, 0xc48dcf18,
-    0xa13872c2, 0xe933bb17, 0x5d9ffd5b, 0xb5b6e10c,
-    0x57fe3c00, 0xbaaaa15a, 0xe003ec3e, 0x9c269bae
-);
+static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G_ORDER_199;
+
 static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(
     0x2cca28fa, 0xfc614b80, 0x2a3db42b, 0x00ba00b1,
     0xbea8d943, 0xdace9ab2, 0x9536daea, 0x0074defb
@@ -46,15 +59,7 @@ static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(
 #    error No known generator for the specified exhaustive test group order.
 #  endif
 #else
-/** Generator for secp256k1, value 'g' defined in
- *  "Standards for Efficient Cryptography" (SEC2) 2.7.1.
- */
-static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
-    0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,
-    0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL,
-    0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL,
-    0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
-);
+static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G;
 
 static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 7);
 #endif
@@ -62,6 +67,7 @@ static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(0, 0, 0, 0,
 static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) {
     secp256k1_fe zi2;
     secp256k1_fe zi3;
+    VERIFY_CHECK(!a->infinity);
     secp256k1_fe_sqr(&zi2, zi);
     secp256k1_fe_mul(&zi3, &zi2, zi);
     secp256k1_fe_mul(&r->x, &a->x, &zi2);
@@ -155,27 +161,26 @@ static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a
     }
 }
 
-static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr) {
+static void secp256k1_ge_table_set_globalz(size_t len, secp256k1_ge *a, const secp256k1_fe *zr) {
     size_t i = len - 1;
     secp256k1_fe zs;
 
     if (len > 0) {
-        /* The z of the final point gives us the "global Z" for the table. */
-        r[i].x = a[i].x;
-        r[i].y = a[i].y;
         /* Ensure all y values are in weak normal form for fast negation of points */
-        secp256k1_fe_normalize_weak(&r[i].y);
-        *globalz = a[i].z;
-        r[i].infinity = 0;
+        secp256k1_fe_normalize_weak(&a[i].y);
         zs = zr[i];
 
         /* Work our way backwards, using the z-ratios to scale the x/y values. */
         while (i > 0) {
+            secp256k1_gej tmpa;
             if (i != len - 1) {
                 secp256k1_fe_mul(&zs, &zs, &zr[i]);
             }
             i--;
-            secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zs);
+            tmpa.x = a[i].x;
+            tmpa.y = a[i].y;
+            tmpa.infinity = 0;
+            secp256k1_ge_set_gej_zinv(&a[i], &tmpa, &zs);
         }
     }
 }
@@ -231,6 +236,13 @@ static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a) {
    secp256k1_fe_set_int(&r->z, 1);
 }
 
+static int secp256k1_gej_eq_var(const secp256k1_gej *a, const secp256k1_gej *b) {
+    secp256k1_gej tmp;
+    secp256k1_gej_neg(&tmp, a);
+    secp256k1_gej_add_var(&tmp, &tmp, b, NULL);
+    return secp256k1_gej_is_infinity(&tmp);
+}
+
 static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a) {
     secp256k1_fe r, r2;
     VERIFY_CHECK(!a->infinity);
@@ -266,37 +278,35 @@ static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
 }
 
 static SECP256K1_INLINE void secp256k1_gej_double(secp256k1_gej *r, const secp256k1_gej *a) {
-    /* Operations: 3 mul, 4 sqr, 0 normalize, 12 mul_int/add/negate.
-     *
-     * Note that there is an implementation described at
-     *     https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
-     * which trades a multiply for a square, but in practice this is actually slower,
-     * mainly because it requires more normalizations.
-     */
-    secp256k1_fe t1,t2,t3,t4;
+    /* Operations: 3 mul, 4 sqr, 8 add/half/mul_int/negate */
+    secp256k1_fe l, s, t;
 
     r->infinity = a->infinity;
 
-    secp256k1_fe_mul(&r->z, &a->z, &a->y);
-    secp256k1_fe_mul_int(&r->z, 2);       /* Z' = 2*Y*Z (2) */
-    secp256k1_fe_sqr(&t1, &a->x);
-    secp256k1_fe_mul_int(&t1, 3);         /* T1 = 3*X^2 (3) */
-    secp256k1_fe_sqr(&t2, &t1);           /* T2 = 9*X^4 (1) */
-    secp256k1_fe_sqr(&t3, &a->y);
-    secp256k1_fe_mul_int(&t3, 2);         /* T3 = 2*Y^2 (2) */
-    secp256k1_fe_sqr(&t4, &t3);
-    secp256k1_fe_mul_int(&t4, 2);         /* T4 = 8*Y^4 (2) */
-    secp256k1_fe_mul(&t3, &t3, &a->x);    /* T3 = 2*X*Y^2 (1) */
-    r->x = t3;
-    secp256k1_fe_mul_int(&r->x, 4);       /* X' = 8*X*Y^2 (4) */
-    secp256k1_fe_negate(&r->x, &r->x, 4); /* X' = -8*X*Y^2 (5) */
-    secp256k1_fe_add(&r->x, &t2);         /* X' = 9*X^4 - 8*X*Y^2 (6) */
-    secp256k1_fe_negate(&t2, &t2, 1);     /* T2 = -9*X^4 (2) */
-    secp256k1_fe_mul_int(&t3, 6);         /* T3 = 12*X*Y^2 (6) */
-    secp256k1_fe_add(&t3, &t2);           /* T3 = 12*X*Y^2 - 9*X^4 (8) */
-    secp256k1_fe_mul(&r->y, &t1, &t3);    /* Y' = 36*X^3*Y^2 - 27*X^6 (1) */
-    secp256k1_fe_negate(&t2, &t4, 2);     /* T2 = -8*Y^4 (3) */
-    secp256k1_fe_add(&r->y, &t2);         /* Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4) */
+    /* Formula used:
+     * L = (3/2) * X1^2
+     * S = Y1^2
+     * T = -X1*S
+     * X3 = L^2 + 2*T
+     * Y3 = -(L*(X3 + T) + S^2)
+     * Z3 = Y1*Z1
+     */
+
+    secp256k1_fe_mul(&r->z, &a->z, &a->y); /* Z3 = Y1*Z1 (1) */
+    secp256k1_fe_sqr(&s, &a->y);           /* S = Y1^2 (1) */
+    secp256k1_fe_sqr(&l, &a->x);           /* L = X1^2 (1) */
+    secp256k1_fe_mul_int(&l, 3);           /* L = 3*X1^2 (3) */
+    secp256k1_fe_half(&l);                 /* L = 3/2*X1^2 (2) */
+    secp256k1_fe_negate(&t, &s, 1);        /* T = -S (2) */
+    secp256k1_fe_mul(&t, &t, &a->x);       /* T = -X1*S (1) */
+    secp256k1_fe_sqr(&r->x, &l);           /* X3 = L^2 (1) */
+    secp256k1_fe_add(&r->x, &t);           /* X3 = L^2 + T (2) */
+    secp256k1_fe_add(&r->x, &t);           /* X3 = L^2 + 2*T (3) */
+    secp256k1_fe_sqr(&s, &s);              /* S' = S^2 (1) */
+    secp256k1_fe_add(&t, &r->x);           /* T' = X3 + T (4) */
+    secp256k1_fe_mul(&r->y, &t, &l);       /* Y3 = L*(X3 + T) (1) */
+    secp256k1_fe_add(&r->y, &s);           /* Y3 = L*(X3 + T) + S^2 (2) */
+    secp256k1_fe_negate(&r->y, &r->y, 2);  /* Y3 = -(L*(X3 + T) + S^2) (3) */
 }
 
 static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
@@ -321,22 +331,20 @@ static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, s
     if (rzr != NULL) {
         *rzr = a->y;
         secp256k1_fe_normalize_weak(rzr);
-        secp256k1_fe_mul_int(rzr, 2);
     }
 
     secp256k1_gej_double(r, a);
 }
 
 static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr) {
-    /* Operations: 12 mul, 4 sqr, 2 normalize, 12 mul_int/add/negate */
-    secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+    /* 12 mul, 4 sqr, 11 add/negate/normalizes_to_zero (ignoring special cases) */
+    secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, h2, h3, t;
 
     if (a->infinity) {
         VERIFY_CHECK(rzr == NULL);
         *r = *b;
         return;
     }
-
     if (b->infinity) {
         if (rzr != NULL) {
             secp256k1_fe_set_int(rzr, 1);
@@ -345,7 +353,6 @@ static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, cons
         return;
     }
 
-    r->infinity = 0;
     secp256k1_fe_sqr(&z22, &b->z);
     secp256k1_fe_sqr(&z12, &a->z);
     secp256k1_fe_mul(&u1, &a->x, &z22);
@@ -353,7 +360,7 @@ static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, cons
     secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z);
     secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
     secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
-    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1);
     if (secp256k1_fe_normalizes_to_zero_var(&h)) {
         if (secp256k1_fe_normalizes_to_zero_var(&i)) {
             secp256k1_gej_double_var(r, a, rzr);
@@ -365,24 +372,33 @@ static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, cons
         }
         return;
     }
-    secp256k1_fe_sqr(&i2, &i);
-    secp256k1_fe_sqr(&h2, &h);
-    secp256k1_fe_mul(&h3, &h, &h2);
-    secp256k1_fe_mul(&h, &h, &b->z);
+
+    r->infinity = 0;
+    secp256k1_fe_mul(&t, &h, &b->z);
     if (rzr != NULL) {
-        *rzr = h;
+        *rzr = t;
     }
-    secp256k1_fe_mul(&r->z, &a->z, &h);
+    secp256k1_fe_mul(&r->z, &a->z, &t);
+
+    secp256k1_fe_sqr(&h2, &h);
+    secp256k1_fe_negate(&h2, &h2, 1);
+    secp256k1_fe_mul(&h3, &h2, &h);
     secp256k1_fe_mul(&t, &u1, &h2);
-    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
-    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
-    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+
+    secp256k1_fe_sqr(&r->x, &i);
+    secp256k1_fe_add(&r->x, &h3);
+    secp256k1_fe_add(&r->x, &t);
+    secp256k1_fe_add(&r->x, &t);
+
+    secp256k1_fe_add(&t, &r->x);
+    secp256k1_fe_mul(&r->y, &t, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1);
     secp256k1_fe_add(&r->y, &h3);
 }
 
 static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr) {
-    /* 8 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
-    secp256k1_fe z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+    /* 8 mul, 3 sqr, 13 add/negate/normalize_weak/normalizes_to_zero (ignoring special cases) */
+    secp256k1_fe z12, u1, u2, s1, s2, h, i, h2, h3, t;
     if (a->infinity) {
         VERIFY_CHECK(rzr == NULL);
         secp256k1_gej_set_ge(r, b);
@@ -395,7 +411,6 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, c
         *r = *a;
         return;
     }
-    r->infinity = 0;
 
     secp256k1_fe_sqr(&z12, &a->z);
     u1 = a->x; secp256k1_fe_normalize_weak(&u1);
@@ -403,7 +418,7 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, c
     s1 = a->y; secp256k1_fe_normalize_weak(&s1);
     secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
     secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
-    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1);
     if (secp256k1_fe_normalizes_to_zero_var(&h)) {
         if (secp256k1_fe_normalizes_to_zero_var(&i)) {
             secp256k1_gej_double_var(r, a, rzr);
@@ -415,28 +430,33 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, c
         }
         return;
     }
-    secp256k1_fe_sqr(&i2, &i);
-    secp256k1_fe_sqr(&h2, &h);
-    secp256k1_fe_mul(&h3, &h, &h2);
+
+    r->infinity = 0;
     if (rzr != NULL) {
         *rzr = h;
     }
     secp256k1_fe_mul(&r->z, &a->z, &h);
+
+    secp256k1_fe_sqr(&h2, &h);
+    secp256k1_fe_negate(&h2, &h2, 1);
+    secp256k1_fe_mul(&h3, &h2, &h);
     secp256k1_fe_mul(&t, &u1, &h2);
-    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
-    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
-    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+
+    secp256k1_fe_sqr(&r->x, &i);
+    secp256k1_fe_add(&r->x, &h3);
+    secp256k1_fe_add(&r->x, &t);
+    secp256k1_fe_add(&r->x, &t);
+
+    secp256k1_fe_add(&t, &r->x);
+    secp256k1_fe_mul(&r->y, &t, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1);
     secp256k1_fe_add(&r->y, &h3);
 }
 
 static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv) {
-    /* 9 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
-    secp256k1_fe az, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+    /* 9 mul, 3 sqr, 13 add/negate/normalize_weak/normalizes_to_zero (ignoring special cases) */
+    secp256k1_fe az, z12, u1, u2, s1, s2, h, i, h2, h3, t;
 
-    if (b->infinity) {
-        *r = *a;
-        return;
-    }
     if (a->infinity) {
         secp256k1_fe bzinv2, bzinv3;
         r->infinity = b->infinity;
@@ -447,7 +467,10 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,
         secp256k1_fe_set_int(&r->z, 1);
         return;
     }
-    r->infinity = 0;
+    if (b->infinity) {
+        *r = *a;
+        return;
+    }
 
     /** We need to calculate (rx,ry,rz) = (ax,ay,az) + (bx,by,1/bzinv). Due to
      *  secp256k1's isomorphism we can multiply the Z coordinates on both sides
@@ -465,7 +488,7 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,
     s1 = a->y; secp256k1_fe_normalize_weak(&s1);
     secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &az);
     secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
-    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1);
     if (secp256k1_fe_normalizes_to_zero_var(&h)) {
         if (secp256k1_fe_normalizes_to_zero_var(&i)) {
             secp256k1_gej_double_var(r, a, NULL);
@@ -474,21 +497,29 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,
         }
         return;
     }
-    secp256k1_fe_sqr(&i2, &i);
+
+    r->infinity = 0;
+    secp256k1_fe_mul(&r->z, &a->z, &h);
+
     secp256k1_fe_sqr(&h2, &h);
-    secp256k1_fe_mul(&h3, &h, &h2);
-    r->z = a->z; secp256k1_fe_mul(&r->z, &r->z, &h);
+    secp256k1_fe_negate(&h2, &h2, 1);
+    secp256k1_fe_mul(&h3, &h2, &h);
     secp256k1_fe_mul(&t, &u1, &h2);
-    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
-    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
-    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+
+    secp256k1_fe_sqr(&r->x, &i);
+    secp256k1_fe_add(&r->x, &h3);
+    secp256k1_fe_add(&r->x, &t);
+    secp256k1_fe_add(&r->x, &t);
+
+    secp256k1_fe_add(&t, &r->x);
+    secp256k1_fe_mul(&r->y, &t, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1);
     secp256k1_fe_add(&r->y, &h3);
 }
 
 
 static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b) {
-    /* Operations: 7 mul, 5 sqr, 4 normalize, 21 mul_int/add/negate/cmov */
-    static const secp256k1_fe fe_1 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+    /* Operations: 7 mul, 5 sqr, 24 add/cmov/half/mul_int/negate/normalize_weak/normalizes_to_zero */
     secp256k1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr;
     secp256k1_fe m_alt, rr_alt;
     int infinity, degenerate;
@@ -509,11 +540,11 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const
      *    Z = Z1*Z2
      *    T = U1+U2
      *    M = S1+S2
-     *    Q = T*M^2
+     *    Q = -T*M^2
      *    R = T^2-U1*U2
-     *    X3 = 4*(R^2-Q)
-     *    Y3 = 4*(R*(3*Q-2*R^2)-M^4)
-     *    Z3 = 2*M*Z
+     *    X3 = R^2+Q
+     *    Y3 = -(R*(2*X3+Q)+M^4)/2
+     *    Z3 = M*Z
      *  (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.)
      *
      *  This formula has the benefit of being the same for both addition
@@ -577,7 +608,8 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const
      * and denominator of lambda; R and M represent the explicit
      * expressions x1^2 + x2^2 + x1x2 and y1 + y2. */
     secp256k1_fe_sqr(&n, &m_alt);                       /* n = Malt^2 (1) */
-    secp256k1_fe_mul(&q, &n, &t);                       /* q = Q = T*Malt^2 (1) */
+    secp256k1_fe_negate(&q, &t, 2);                     /* q = -T (3) */
+    secp256k1_fe_mul(&q, &q, &n);                       /* q = Q = -T*Malt^2 (1) */
     /* These two lines use the observation that either M == Malt or M == 0,
      * so M^3 * Malt is either Malt^4 (which is computed by squaring), or
      * zero (which is "computed" by cmov). So the cost is one squaring
@@ -585,26 +617,21 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const
     secp256k1_fe_sqr(&n, &n);
     secp256k1_fe_cmov(&n, &m, degenerate);              /* n = M^3 * Malt (2) */
     secp256k1_fe_sqr(&t, &rr_alt);                      /* t = Ralt^2 (1) */
-    secp256k1_fe_mul(&r->z, &a->z, &m_alt);             /* r->z = Malt*Z (1) */
+    secp256k1_fe_mul(&r->z, &a->z, &m_alt);             /* r->z = Z3 = Malt*Z (1) */
     infinity = secp256k1_fe_normalizes_to_zero(&r->z) & ~a->infinity;
-    secp256k1_fe_mul_int(&r->z, 2);                     /* r->z = Z3 = 2*Malt*Z (2) */
-    secp256k1_fe_negate(&q, &q, 1);                     /* q = -Q (2) */
-    secp256k1_fe_add(&t, &q);                           /* t = Ralt^2-Q (3) */
-    secp256k1_fe_normalize_weak(&t);
-    r->x = t;                                           /* r->x = Ralt^2-Q (1) */
-    secp256k1_fe_mul_int(&t, 2);                        /* t = 2*x3 (2) */
-    secp256k1_fe_add(&t, &q);                           /* t = 2*x3 - Q: (4) */
-    secp256k1_fe_mul(&t, &t, &rr_alt);                  /* t = Ralt*(2*x3 - Q) (1) */
-    secp256k1_fe_add(&t, &n);                           /* t = Ralt*(2*x3 - Q) + M^3*Malt (3) */
-    secp256k1_fe_negate(&r->y, &t, 3);                  /* r->y = Ralt*(Q - 2x3) - M^3*Malt (4) */
-    secp256k1_fe_normalize_weak(&r->y);
-    secp256k1_fe_mul_int(&r->x, 4);                     /* r->x = X3 = 4*(Ralt^2-Q) */
-    secp256k1_fe_mul_int(&r->y, 4);                     /* r->y = Y3 = 4*Ralt*(Q - 2x3) - 4*M^3*Malt (4) */
+    secp256k1_fe_add(&t, &q);                           /* t = Ralt^2 + Q (2) */
+    r->x = t;                                           /* r->x = X3 = Ralt^2 + Q (2) */
+    secp256k1_fe_mul_int(&t, 2);                        /* t = 2*X3 (4) */
+    secp256k1_fe_add(&t, &q);                           /* t = 2*X3 + Q (5) */
+    secp256k1_fe_mul(&t, &t, &rr_alt);                  /* t = Ralt*(2*X3 + Q) (1) */
+    secp256k1_fe_add(&t, &n);                           /* t = Ralt*(2*X3 + Q) + M^3*Malt (3) */
+    secp256k1_fe_negate(&r->y, &t, 3);                  /* r->y = -(Ralt*(2*X3 + Q) + M^3*Malt) (4) */
+    secp256k1_fe_half(&r->y);                           /* r->y = Y3 = -(Ralt*(2*X3 + Q) + M^3*Malt)/2 (3) */
 
     /** In case a->infinity == 1, replace r with (b->x, b->y, 1). */
     secp256k1_fe_cmov(&r->x, &b->x, a->infinity);
     secp256k1_fe_cmov(&r->y, &b->y, a->infinity);
-    secp256k1_fe_cmov(&r->z, &fe_1, a->infinity);
+    secp256k1_fe_cmov(&r->z, &secp256k1_fe_one, a->infinity);
     r->infinity = infinity;
 }
 
@@ -636,18 +663,22 @@ static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storag
     r->infinity = 0;
 }
 
+static SECP256K1_INLINE void secp256k1_gej_cmov(secp256k1_gej *r, const secp256k1_gej *a, int flag) {
+    secp256k1_fe_cmov(&r->x, &a->x, flag);
+    secp256k1_fe_cmov(&r->y, &a->y, flag);
+    secp256k1_fe_cmov(&r->z, &a->z, flag);
+
+    r->infinity ^= (r->infinity ^ a->infinity) & flag;
+}
+
 static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag) {
     secp256k1_fe_storage_cmov(&r->x, &a->x, flag);
     secp256k1_fe_storage_cmov(&r->y, &a->y, flag);
 }
 
 static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) {
-    static const secp256k1_fe beta = SECP256K1_FE_CONST(
-        0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
-        0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
-    );
     *r = *a;
-    secp256k1_fe_mul(&r->x, &r->x, &beta);
+    secp256k1_fe_mul(&r->x, &r->x, &secp256k1_const_beta);
 }
 
 static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge) {
diff --git a/src/secp256k1/src/hash.h b/src/secp256k1/src/hash.h
index 0947a096943..4e0384cfbff 100644
--- a/src/secp256k1/src/hash.h
+++ b/src/secp256k1/src/hash.h
@@ -12,8 +12,8 @@
 
 typedef struct {
     uint32_t s[8];
-    uint32_t buf[16]; /* In big endian */
-    size_t bytes;
+    unsigned char buf[64];
+    uint64_t bytes;
 } secp256k1_sha256;
 
 static void secp256k1_sha256_initialize(secp256k1_sha256 *hash);
diff --git a/src/secp256k1/src/hash_impl.h b/src/secp256k1/src/hash_impl.h
index f8cd3a16341..0991fe78383 100644
--- a/src/secp256k1/src/hash_impl.h
+++ b/src/secp256k1/src/hash_impl.h
@@ -28,12 +28,6 @@
     (h) = t1 + t2; \
 } while(0)
 
-#if defined(SECP256K1_BIG_ENDIAN)
-#define BE32(x) (x)
-#elif defined(SECP256K1_LITTLE_ENDIAN)
-#define BE32(p) ((((p) & 0xFF) << 24) | (((p) & 0xFF00) << 8) | (((p) & 0xFF0000) >> 8) | (((p) & 0xFF000000) >> 24))
-#endif
-
 static void secp256k1_sha256_initialize(secp256k1_sha256 *hash) {
     hash->s[0] = 0x6a09e667ul;
     hash->s[1] = 0xbb67ae85ul;
@@ -47,26 +41,26 @@ static void secp256k1_sha256_initialize(secp256k1_sha256 *hash) {
 }
 
 /** Perform one SHA-256 transformation, processing 16 big endian 32-bit words. */
-static void secp256k1_sha256_transform(uint32_t* s, const uint32_t* chunk) {
+static void secp256k1_sha256_transform(uint32_t* s, const unsigned char* buf) {
     uint32_t a = s[0], b = s[1], c = s[2], d = s[3], e = s[4], f = s[5], g = s[6], h = s[7];
     uint32_t w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15;
 
-    Round(a, b, c, d, e, f, g, h, 0x428a2f98, w0 = BE32(chunk[0]));
-    Round(h, a, b, c, d, e, f, g, 0x71374491, w1 = BE32(chunk[1]));
-    Round(g, h, a, b, c, d, e, f, 0xb5c0fbcf, w2 = BE32(chunk[2]));
-    Round(f, g, h, a, b, c, d, e, 0xe9b5dba5, w3 = BE32(chunk[3]));
-    Round(e, f, g, h, a, b, c, d, 0x3956c25b, w4 = BE32(chunk[4]));
-    Round(d, e, f, g, h, a, b, c, 0x59f111f1, w5 = BE32(chunk[5]));
-    Round(c, d, e, f, g, h, a, b, 0x923f82a4, w6 = BE32(chunk[6]));
-    Round(b, c, d, e, f, g, h, a, 0xab1c5ed5, w7 = BE32(chunk[7]));
-    Round(a, b, c, d, e, f, g, h, 0xd807aa98, w8 = BE32(chunk[8]));
-    Round(h, a, b, c, d, e, f, g, 0x12835b01, w9 = BE32(chunk[9]));
-    Round(g, h, a, b, c, d, e, f, 0x243185be, w10 = BE32(chunk[10]));
-    Round(f, g, h, a, b, c, d, e, 0x550c7dc3, w11 = BE32(chunk[11]));
-    Round(e, f, g, h, a, b, c, d, 0x72be5d74, w12 = BE32(chunk[12]));
-    Round(d, e, f, g, h, a, b, c, 0x80deb1fe, w13 = BE32(chunk[13]));
-    Round(c, d, e, f, g, h, a, b, 0x9bdc06a7, w14 = BE32(chunk[14]));
-    Round(b, c, d, e, f, g, h, a, 0xc19bf174, w15 = BE32(chunk[15]));
+    Round(a, b, c, d, e, f, g, h, 0x428a2f98,  w0 = secp256k1_read_be32(&buf[0]));
+    Round(h, a, b, c, d, e, f, g, 0x71374491,  w1 = secp256k1_read_be32(&buf[4]));
+    Round(g, h, a, b, c, d, e, f, 0xb5c0fbcf,  w2 = secp256k1_read_be32(&buf[8]));
+    Round(f, g, h, a, b, c, d, e, 0xe9b5dba5,  w3 = secp256k1_read_be32(&buf[12]));
+    Round(e, f, g, h, a, b, c, d, 0x3956c25b,  w4 = secp256k1_read_be32(&buf[16]));
+    Round(d, e, f, g, h, a, b, c, 0x59f111f1,  w5 = secp256k1_read_be32(&buf[20]));
+    Round(c, d, e, f, g, h, a, b, 0x923f82a4,  w6 = secp256k1_read_be32(&buf[24]));
+    Round(b, c, d, e, f, g, h, a, 0xab1c5ed5,  w7 = secp256k1_read_be32(&buf[28]));
+    Round(a, b, c, d, e, f, g, h, 0xd807aa98,  w8 = secp256k1_read_be32(&buf[32]));
+    Round(h, a, b, c, d, e, f, g, 0x12835b01,  w9 = secp256k1_read_be32(&buf[36]));
+    Round(g, h, a, b, c, d, e, f, 0x243185be, w10 = secp256k1_read_be32(&buf[40]));
+    Round(f, g, h, a, b, c, d, e, 0x550c7dc3, w11 = secp256k1_read_be32(&buf[44]));
+    Round(e, f, g, h, a, b, c, d, 0x72be5d74, w12 = secp256k1_read_be32(&buf[48]));
+    Round(d, e, f, g, h, a, b, c, 0x80deb1fe, w13 = secp256k1_read_be32(&buf[52]));
+    Round(c, d, e, f, g, h, a, b, 0x9bdc06a7, w14 = secp256k1_read_be32(&buf[56]));
+    Round(b, c, d, e, f, g, h, a, 0xc19bf174, w15 = secp256k1_read_be32(&buf[60]));
 
     Round(a, b, c, d, e, f, g, h, 0xe49b69c1, w0 += sigma1(w14) + w9 + sigma0(w1));
     Round(h, a, b, c, d, e, f, g, 0xefbe4786, w1 += sigma1(w15) + w10 + sigma0(w2));
@@ -136,7 +130,7 @@ static void secp256k1_sha256_write(secp256k1_sha256 *hash, const unsigned char *
     while (len >= 64 - bufsize) {
         /* Fill the buffer, and process it. */
         size_t chunk_len = 64 - bufsize;
-        memcpy(((unsigned char*)hash->buf) + bufsize, data, chunk_len);
+        memcpy(hash->buf + bufsize, data, chunk_len);
         data += chunk_len;
         len -= chunk_len;
         secp256k1_sha256_transform(hash->s, hash->buf);
@@ -149,19 +143,19 @@ static void secp256k1_sha256_write(secp256k1_sha256 *hash, const unsigned char *
 }
 
 static void secp256k1_sha256_finalize(secp256k1_sha256 *hash, unsigned char *out32) {
-    static const unsigned char pad[64] = {0x80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
-    uint32_t sizedesc[2];
-    uint32_t out[8];
-    int i = 0;
-    sizedesc[0] = BE32(hash->bytes >> 29);
-    sizedesc[1] = BE32(hash->bytes << 3);
+    static const unsigned char pad[64] = {0x80};
+    unsigned char sizedesc[8];
+    int i;
+    /* The maximum message size of SHA256 is 2^64-1 bits. */
+    VERIFY_CHECK(hash->bytes < ((uint64_t)1 << 61));
+    secp256k1_write_be32(&sizedesc[0], hash->bytes >> 29);
+    secp256k1_write_be32(&sizedesc[4], hash->bytes << 3);
     secp256k1_sha256_write(hash, pad, 1 + ((119 - (hash->bytes % 64)) % 64));
-    secp256k1_sha256_write(hash, (const unsigned char*)sizedesc, 8);
+    secp256k1_sha256_write(hash, sizedesc, 8);
     for (i = 0; i < 8; i++) {
-        out[i] = BE32(hash->s[i]);
+        secp256k1_write_be32(&out32[4*i], hash->s[i]);
         hash->s[i] = 0;
     }
-    memcpy(out32, (const unsigned char*)out, 32);
 }
 
 /* Initializes a sha256 struct and writes the 64 byte string
@@ -285,7 +279,6 @@ static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256
     rng->retry = 0;
 }
 
-#undef BE32
 #undef Round
 #undef sigma1
 #undef sigma0
diff --git a/src/secp256k1/src/int128.h b/src/secp256k1/src/int128.h
new file mode 100644
index 00000000000..84d969a2367
--- /dev/null
+++ b/src/secp256k1/src/int128.h
@@ -0,0 +1,85 @@
+#ifndef SECP256K1_INT128_H
+#define SECP256K1_INT128_H
+
+#include "util.h"
+
+#if defined(SECP256K1_WIDEMUL_INT128)
+#  if defined(SECP256K1_INT128_NATIVE)
+#    include "int128_native.h"
+#  elif defined(SECP256K1_INT128_STRUCT)
+#    include "int128_struct.h"
+#  else
+#    error "Please select int128 implementation"
+#  endif
+
+/* Construct an unsigned 128-bit value from a high and a low 64-bit value. */
+static SECP256K1_INLINE void secp256k1_u128_load(secp256k1_uint128 *r, uint64_t hi, uint64_t lo);
+
+/* Multiply two unsigned 64-bit values a and b and write the result to r. */
+static SECP256K1_INLINE void secp256k1_u128_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b);
+
+/* Multiply two unsigned 64-bit values a and b and add the result to r.
+ * The final result is taken modulo 2^128.
+ */
+static SECP256K1_INLINE void secp256k1_u128_accum_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b);
+
+/* Add an unsigned 64-bit value a to r.
+ * The final result is taken modulo 2^128.
+ */
+static SECP256K1_INLINE void secp256k1_u128_accum_u64(secp256k1_uint128 *r, uint64_t a);
+
+/* Unsigned (logical) right shift.
+ * Non-constant time in n.
+ */
+static SECP256K1_INLINE void secp256k1_u128_rshift(secp256k1_uint128 *r, unsigned int n);
+
+/* Return the low 64-bits of a 128-bit value as an unsigned 64-bit value. */
+static SECP256K1_INLINE uint64_t secp256k1_u128_to_u64(const secp256k1_uint128 *a);
+
+/* Return the high 64-bits of a 128-bit value as an unsigned 64-bit value. */
+static SECP256K1_INLINE uint64_t secp256k1_u128_hi_u64(const secp256k1_uint128 *a);
+
+/* Write an unsigned 64-bit value to r. */
+static SECP256K1_INLINE void secp256k1_u128_from_u64(secp256k1_uint128 *r, uint64_t a);
+
+/* Tests if r is strictly less than to 2^n.
+ * n must be strictly less than 128.
+ */
+static SECP256K1_INLINE int secp256k1_u128_check_bits(const secp256k1_uint128 *r, unsigned int n);
+
+/* Construct an signed 128-bit value from a high and a low 64-bit value. */
+static SECP256K1_INLINE void secp256k1_i128_load(secp256k1_int128 *r, int64_t hi, uint64_t lo);
+
+/* Multiply two signed 64-bit values a and b and write the result to r. */
+static SECP256K1_INLINE void secp256k1_i128_mul(secp256k1_int128 *r, int64_t a, int64_t b);
+
+/* Multiply two signed 64-bit values a and b and add the result to r.
+ * Overflow or underflow from the addition is undefined behaviour.
+ */
+static SECP256K1_INLINE void secp256k1_i128_accum_mul(secp256k1_int128 *r, int64_t a, int64_t b);
+
+/* Compute a*d - b*c from signed 64-bit values and write the result to r. */
+static SECP256K1_INLINE void secp256k1_i128_det(secp256k1_int128 *r, int64_t a, int64_t b, int64_t c, int64_t d);
+
+/* Signed (arithmetic) right shift.
+ * Non-constant time in b.
+ */
+static SECP256K1_INLINE void secp256k1_i128_rshift(secp256k1_int128 *r, unsigned int b);
+
+/* Return the low 64-bits of a 128-bit value interpreted as an signed 64-bit value. */
+static SECP256K1_INLINE int64_t secp256k1_i128_to_i64(const secp256k1_int128 *a);
+
+/* Write a signed 64-bit value to r. */
+static SECP256K1_INLINE void secp256k1_i128_from_i64(secp256k1_int128 *r, int64_t a);
+
+/* Compare two 128-bit values for equality. */
+static SECP256K1_INLINE int secp256k1_i128_eq_var(const secp256k1_int128 *a, const secp256k1_int128 *b);
+
+/* Tests if r is equal to 2^n.
+ * n must be strictly less than 127.
+ */
+static SECP256K1_INLINE int secp256k1_i128_check_pow2(const secp256k1_int128 *r, unsigned int n);
+
+#endif
+
+#endif
diff --git a/src/secp256k1/src/int128_impl.h b/src/secp256k1/src/int128_impl.h
new file mode 100644
index 00000000000..cfc573408a0
--- /dev/null
+++ b/src/secp256k1/src/int128_impl.h
@@ -0,0 +1,18 @@
+#ifndef SECP256K1_INT128_IMPL_H
+#define SECP256K1_INT128_IMPL_H
+
+#include "util.h"
+
+#include "int128.h"
+
+#if defined(SECP256K1_WIDEMUL_INT128)
+#  if defined(SECP256K1_INT128_NATIVE)
+#    include "int128_native_impl.h"
+#  elif defined(SECP256K1_INT128_STRUCT)
+#    include "int128_struct_impl.h"
+#  else
+#    error "Please select int128 implementation"
+#  endif
+#endif
+
+#endif
diff --git a/src/secp256k1/src/int128_native.h b/src/secp256k1/src/int128_native.h
new file mode 100644
index 00000000000..7c97aafc749
--- /dev/null
+++ b/src/secp256k1/src/int128_native.h
@@ -0,0 +1,19 @@
+#ifndef SECP256K1_INT128_NATIVE_H
+#define SECP256K1_INT128_NATIVE_H
+
+#include <stdint.h>
+#include "util.h"
+
+#if !defined(UINT128_MAX) && defined(__SIZEOF_INT128__)
+SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t;
+SECP256K1_GNUC_EXT typedef __int128 int128_t;
+# define UINT128_MAX ((uint128_t)(-1))
+# define INT128_MAX ((int128_t)(UINT128_MAX >> 1))
+# define INT128_MIN (-INT128_MAX - 1)
+/* No (U)INT128_C macros because compilers providing __int128 do not support 128-bit literals.  */
+#endif
+
+typedef uint128_t secp256k1_uint128;
+typedef int128_t secp256k1_int128;
+
+#endif
diff --git a/src/secp256k1/src/int128_native_impl.h b/src/secp256k1/src/int128_native_impl.h
new file mode 100644
index 00000000000..e4b7f4106c0
--- /dev/null
+++ b/src/secp256k1/src/int128_native_impl.h
@@ -0,0 +1,87 @@
+#ifndef SECP256K1_INT128_NATIVE_IMPL_H
+#define SECP256K1_INT128_NATIVE_IMPL_H
+
+#include "int128.h"
+
+static SECP256K1_INLINE void secp256k1_u128_load(secp256k1_uint128 *r, uint64_t hi, uint64_t lo) {
+    *r = (((uint128_t)hi) << 64) + lo;
+}
+
+static SECP256K1_INLINE void secp256k1_u128_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) {
+   *r = (uint128_t)a * b;
+}
+
+static SECP256K1_INLINE void secp256k1_u128_accum_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) {
+   *r += (uint128_t)a * b;
+}
+
+static SECP256K1_INLINE void secp256k1_u128_accum_u64(secp256k1_uint128 *r, uint64_t a) {
+   *r += a;
+}
+
+static SECP256K1_INLINE void secp256k1_u128_rshift(secp256k1_uint128 *r, unsigned int n) {
+   VERIFY_CHECK(n < 128);
+   *r >>= n;
+}
+
+static SECP256K1_INLINE uint64_t secp256k1_u128_to_u64(const secp256k1_uint128 *a) {
+   return (uint64_t)(*a);
+}
+
+static SECP256K1_INLINE uint64_t secp256k1_u128_hi_u64(const secp256k1_uint128 *a) {
+   return (uint64_t)(*a >> 64);
+}
+
+static SECP256K1_INLINE void secp256k1_u128_from_u64(secp256k1_uint128 *r, uint64_t a) {
+   *r = a;
+}
+
+static SECP256K1_INLINE int secp256k1_u128_check_bits(const secp256k1_uint128 *r, unsigned int n) {
+   VERIFY_CHECK(n < 128);
+   return (*r >> n == 0);
+}
+
+static SECP256K1_INLINE void secp256k1_i128_load(secp256k1_int128 *r, int64_t hi, uint64_t lo) {
+    *r = (((uint128_t)(uint64_t)hi) << 64) + lo;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_mul(secp256k1_int128 *r, int64_t a, int64_t b) {
+   *r = (int128_t)a * b;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_accum_mul(secp256k1_int128 *r, int64_t a, int64_t b) {
+   int128_t ab = (int128_t)a * b;
+   VERIFY_CHECK(0 <= ab ? *r <= INT128_MAX - ab : INT128_MIN - ab <= *r);
+   *r += ab;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_det(secp256k1_int128 *r, int64_t a, int64_t b, int64_t c, int64_t d) {
+   int128_t ad = (int128_t)a * d;
+   int128_t bc = (int128_t)b * c;
+   VERIFY_CHECK(0 <= bc ? INT128_MIN + bc <= ad : ad <= INT128_MAX + bc);
+   *r = ad - bc;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_rshift(secp256k1_int128 *r, unsigned int n) {
+   VERIFY_CHECK(n < 128);
+   *r >>= n;
+}
+
+static SECP256K1_INLINE int64_t secp256k1_i128_to_i64(const secp256k1_int128 *a) {
+   return *a;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_from_i64(secp256k1_int128 *r, int64_t a) {
+   *r = a;
+}
+
+static SECP256K1_INLINE int secp256k1_i128_eq_var(const secp256k1_int128 *a, const secp256k1_int128 *b) {
+   return *a == *b;
+}
+
+static SECP256K1_INLINE int secp256k1_i128_check_pow2(const secp256k1_int128 *r, unsigned int n) {
+   VERIFY_CHECK(n < 127);
+   return (*r == (int128_t)1 << n);
+}
+
+#endif
diff --git a/src/secp256k1/src/int128_struct.h b/src/secp256k1/src/int128_struct.h
new file mode 100644
index 00000000000..6156f82cc2d
--- /dev/null
+++ b/src/secp256k1/src/int128_struct.h
@@ -0,0 +1,14 @@
+#ifndef SECP256K1_INT128_STRUCT_H
+#define SECP256K1_INT128_STRUCT_H
+
+#include <stdint.h>
+#include "util.h"
+
+typedef struct {
+  uint64_t lo;
+  uint64_t hi;
+} secp256k1_uint128;
+
+typedef secp256k1_uint128 secp256k1_int128;
+
+#endif
diff --git a/src/secp256k1/src/int128_struct_impl.h b/src/secp256k1/src/int128_struct_impl.h
new file mode 100644
index 00000000000..b5f8fb7b650
--- /dev/null
+++ b/src/secp256k1/src/int128_struct_impl.h
@@ -0,0 +1,192 @@
+#ifndef SECP256K1_INT128_STRUCT_IMPL_H
+#define SECP256K1_INT128_STRUCT_IMPL_H
+
+#include "int128.h"
+
+#if defined(_MSC_VER) && (defined(_M_X64) || defined(_M_ARM64)) /* MSVC */
+#    include <intrin.h>
+#    if defined(_M_ARM64) || defined(SECP256K1_MSVC_MULH_TEST_OVERRIDE)
+/* On ARM64 MSVC, use __(u)mulh for the upper half of 64x64 multiplications.
+   (Define SECP256K1_MSVC_MULH_TEST_OVERRIDE to test this code path on X64,
+   which supports both __(u)mulh and _umul128.) */
+#        if defined(SECP256K1_MSVC_MULH_TEST_OVERRIDE)
+#            pragma message(__FILE__ ": SECP256K1_MSVC_MULH_TEST_OVERRIDE is defined, forcing use of __(u)mulh.")
+#        endif
+static SECP256K1_INLINE uint64_t secp256k1_umul128(uint64_t a, uint64_t b, uint64_t* hi) {
+    *hi = __umulh(a, b);
+    return a * b;
+}
+
+static SECP256K1_INLINE int64_t secp256k1_mul128(int64_t a, int64_t b, int64_t* hi) {
+    *hi = __mulh(a, b);
+    return (uint64_t)a * (uint64_t)b;
+}
+#    else
+/* On x84_64 MSVC, use native _(u)mul128 for 64x64->128 multiplications. */
+#        define secp256k1_umul128 _umul128
+#        define secp256k1_mul128 _mul128
+#    endif
+#else
+/* On other systems, emulate 64x64->128 multiplications using 32x32->64 multiplications. */
+static SECP256K1_INLINE uint64_t secp256k1_umul128(uint64_t a, uint64_t b, uint64_t* hi) {
+    uint64_t ll = (uint64_t)(uint32_t)a * (uint32_t)b;
+    uint64_t lh = (uint32_t)a * (b >> 32);
+    uint64_t hl = (a >> 32) * (uint32_t)b;
+    uint64_t hh = (a >> 32) * (b >> 32);
+    uint64_t mid34 = (ll >> 32) + (uint32_t)lh + (uint32_t)hl;
+    *hi = hh + (lh >> 32) + (hl >> 32) + (mid34 >> 32);
+    return (mid34 << 32) + (uint32_t)ll;
+}
+
+static SECP256K1_INLINE int64_t secp256k1_mul128(int64_t a, int64_t b, int64_t* hi) {
+    uint64_t ll = (uint64_t)(uint32_t)a * (uint32_t)b;
+    int64_t lh = (uint32_t)a * (b >> 32);
+    int64_t hl = (a >> 32) * (uint32_t)b;
+    int64_t hh = (a >> 32) * (b >> 32);
+    uint64_t mid34 = (ll >> 32) + (uint32_t)lh + (uint32_t)hl;
+    *hi = hh + (lh >> 32) + (hl >> 32) + (mid34 >> 32);
+    return (mid34 << 32) + (uint32_t)ll;
+}
+#endif
+
+static SECP256K1_INLINE void secp256k1_u128_load(secp256k1_uint128 *r, uint64_t hi, uint64_t lo) {
+    r->hi = hi;
+    r->lo = lo;
+}
+
+static SECP256K1_INLINE void secp256k1_u128_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) {
+   r->lo = secp256k1_umul128(a, b, &r->hi);
+}
+
+static SECP256K1_INLINE void secp256k1_u128_accum_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) {
+   uint64_t lo, hi;
+   lo = secp256k1_umul128(a, b, &hi);
+   r->lo += lo;
+   r->hi += hi + (r->lo < lo);
+}
+
+static SECP256K1_INLINE void secp256k1_u128_accum_u64(secp256k1_uint128 *r, uint64_t a) {
+   r->lo += a;
+   r->hi += r->lo < a;
+}
+
+/* Unsigned (logical) right shift.
+ * Non-constant time in n.
+ */
+static SECP256K1_INLINE void secp256k1_u128_rshift(secp256k1_uint128 *r, unsigned int n) {
+   VERIFY_CHECK(n < 128);
+   if (n >= 64) {
+     r->lo = r->hi >> (n-64);
+     r->hi = 0;
+   } else if (n > 0) {
+     r->lo = ((1U * r->hi) << (64-n)) | r->lo >> n;
+     r->hi >>= n;
+   }
+}
+
+static SECP256K1_INLINE uint64_t secp256k1_u128_to_u64(const secp256k1_uint128 *a) {
+   return a->lo;
+}
+
+static SECP256K1_INLINE uint64_t secp256k1_u128_hi_u64(const secp256k1_uint128 *a) {
+   return a->hi;
+}
+
+static SECP256K1_INLINE void secp256k1_u128_from_u64(secp256k1_uint128 *r, uint64_t a) {
+   r->hi = 0;
+   r->lo = a;
+}
+
+static SECP256K1_INLINE int secp256k1_u128_check_bits(const secp256k1_uint128 *r, unsigned int n) {
+   VERIFY_CHECK(n < 128);
+   return n >= 64 ? r->hi >> (n - 64) == 0
+                  : r->hi == 0 && r->lo >> n == 0;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_load(secp256k1_int128 *r, int64_t hi, uint64_t lo) {
+    r->hi = hi;
+    r->lo = lo;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_mul(secp256k1_int128 *r, int64_t a, int64_t b) {
+   int64_t hi;
+   r->lo = (uint64_t)secp256k1_mul128(a, b, &hi);
+   r->hi = (uint64_t)hi;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_accum_mul(secp256k1_int128 *r, int64_t a, int64_t b) {
+   int64_t hi;
+   uint64_t lo = (uint64_t)secp256k1_mul128(a, b, &hi);
+   r->lo += lo;
+   hi += r->lo < lo;
+   /* Verify no overflow.
+    * If r represents a positive value (the sign bit is not set) and the value we are adding is a positive value (the sign bit is not set),
+    * then we require that the resulting value also be positive (the sign bit is not set).
+    * Note that (X <= Y) means (X implies Y) when X and Y are boolean values (i.e. 0 or 1).
+    */
+   VERIFY_CHECK((r->hi <= 0x7fffffffffffffffu && (uint64_t)hi <= 0x7fffffffffffffffu) <= (r->hi + (uint64_t)hi <= 0x7fffffffffffffffu));
+   /* Verify no underflow.
+    * If r represents a negative value (the sign bit is set) and the value we are adding is a negative value (the sign bit is set),
+    * then we require that the resulting value also be negative (the sign bit is set).
+    */
+   VERIFY_CHECK((r->hi > 0x7fffffffffffffffu && (uint64_t)hi > 0x7fffffffffffffffu) <= (r->hi + (uint64_t)hi > 0x7fffffffffffffffu));
+   r->hi += hi;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_dissip_mul(secp256k1_int128 *r, int64_t a, int64_t b) {
+   int64_t hi;
+   uint64_t lo = (uint64_t)secp256k1_mul128(a, b, &hi);
+   hi += r->lo < lo;
+   /* Verify no overflow.
+    * If r represents a positive value (the sign bit is not set) and the value we are subtracting is a negative value (the sign bit is set),
+    * then we require that the resulting value also be positive (the sign bit is not set).
+    */
+   VERIFY_CHECK((r->hi <= 0x7fffffffffffffffu && (uint64_t)hi > 0x7fffffffffffffffu) <= (r->hi - (uint64_t)hi <= 0x7fffffffffffffffu));
+   /* Verify no underflow.
+    * If r represents a negative value (the sign bit is set) and the value we are subtracting is a positive value (the sign sign bit is not set),
+    * then we require that the resulting value also be negative (the sign bit is set).
+    */
+   VERIFY_CHECK((r->hi > 0x7fffffffffffffffu && (uint64_t)hi <= 0x7fffffffffffffffu) <= (r->hi - (uint64_t)hi > 0x7fffffffffffffffu));
+   r->hi -= hi;
+   r->lo -= lo;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_det(secp256k1_int128 *r, int64_t a, int64_t b, int64_t c, int64_t d) {
+   secp256k1_i128_mul(r, a, d);
+   secp256k1_i128_dissip_mul(r, b, c);
+}
+
+/* Signed (arithmetic) right shift.
+ * Non-constant time in n.
+ */
+static SECP256K1_INLINE void secp256k1_i128_rshift(secp256k1_int128 *r, unsigned int n) {
+   VERIFY_CHECK(n < 128);
+   if (n >= 64) {
+     r->lo = (uint64_t)((int64_t)(r->hi) >> (n-64));
+     r->hi = (uint64_t)((int64_t)(r->hi) >> 63);
+   } else if (n > 0) {
+     r->lo = ((1U * r->hi) << (64-n)) | r->lo >> n;
+     r->hi = (uint64_t)((int64_t)(r->hi) >> n);
+   }
+}
+
+static SECP256K1_INLINE int64_t secp256k1_i128_to_i64(const secp256k1_int128 *a) {
+   return (int64_t)a->lo;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_from_i64(secp256k1_int128 *r, int64_t a) {
+   r->hi = (uint64_t)(a >> 63);
+   r->lo = (uint64_t)a;
+}
+
+static SECP256K1_INLINE int secp256k1_i128_eq_var(const secp256k1_int128 *a, const secp256k1_int128 *b) {
+   return a->hi == b->hi && a->lo == b->lo;
+}
+
+static SECP256K1_INLINE int secp256k1_i128_check_pow2(const secp256k1_int128 *r, unsigned int n) {
+   VERIFY_CHECK(n < 127);
+   return n >= 64 ? r->hi == (uint64_t)1 << (n - 64) && r->lo == 0
+                  : r->hi == 0 && r->lo == (uint64_t)1 << n;
+}
+
+#endif
diff --git a/src/secp256k1/src/modinv64_impl.h b/src/secp256k1/src/modinv64_impl.h
index 0743a9c8210..50be2e5e784 100644
--- a/src/secp256k1/src/modinv64_impl.h
+++ b/src/secp256k1/src/modinv64_impl.h
@@ -7,10 +7,9 @@
 #ifndef SECP256K1_MODINV64_IMPL_H
 #define SECP256K1_MODINV64_IMPL_H
 
+#include "int128.h"
 #include "modinv64.h"
 
-#include "util.h"
-
 /* This file implements modular inversion based on the paper "Fast constant-time gcd computation and
  * modular inversion" by Daniel J. Bernstein and Bo-Yin Yang.
  *
@@ -18,6 +17,15 @@
  * implementation for N=62, using 62-bit signed limbs represented as int64_t.
  */
 
+/* Data type for transition matrices (see section 3 of explanation).
+ *
+ * t = [ u  v ]
+ *     [ q  r ]
+ */
+typedef struct {
+    int64_t u, v, q, r;
+} secp256k1_modinv64_trans2x2;
+
 #ifdef VERIFY
 /* Helper function to compute the absolute value of an int64_t.
  * (we don't use abs/labs/llabs as it depends on the int sizes). */
@@ -32,15 +40,17 @@ static const secp256k1_modinv64_signed62 SECP256K1_SIGNED62_ONE = {{1}};
 /* Compute a*factor and put it in r. All but the top limb in r will be in range [0,2^62). */
 static void secp256k1_modinv64_mul_62(secp256k1_modinv64_signed62 *r, const secp256k1_modinv64_signed62 *a, int alen, int64_t factor) {
     const int64_t M62 = (int64_t)(UINT64_MAX >> 2);
-    int128_t c = 0;
+    secp256k1_int128 c, d;
     int i;
+    secp256k1_i128_from_i64(&c, 0);
     for (i = 0; i < 4; ++i) {
-        if (i < alen) c += (int128_t)a->v[i] * factor;
-        r->v[i] = (int64_t)c & M62; c >>= 62;
+        if (i < alen) secp256k1_i128_accum_mul(&c, a->v[i], factor);
+        r->v[i] = secp256k1_i128_to_i64(&c) & M62; secp256k1_i128_rshift(&c, 62);
     }
-    if (4 < alen) c += (int128_t)a->v[4] * factor;
-    VERIFY_CHECK(c == (int64_t)c);
-    r->v[4] = (int64_t)c;
+    if (4 < alen) secp256k1_i128_accum_mul(&c, a->v[4], factor);
+    secp256k1_i128_from_i64(&d, secp256k1_i128_to_i64(&c));
+    VERIFY_CHECK(secp256k1_i128_eq_var(&c, &d));
+    r->v[4] = secp256k1_i128_to_i64(&c);
 }
 
 /* Return -1 for a<b*factor, 0 for a==b*factor, 1 for a>b*factor. A has alen limbs; b has 5. */
@@ -60,6 +70,13 @@ static int secp256k1_modinv64_mul_cmp_62(const secp256k1_modinv64_signed62 *a, i
     }
     return 0;
 }
+
+/* Check if the determinant of t is equal to 1 << n. */
+static int secp256k1_modinv64_det_check_pow2(const secp256k1_modinv64_trans2x2 *t, unsigned int n) {
+    secp256k1_int128 a;
+    secp256k1_i128_det(&a, t->u, t->v, t->q, t->r);
+    return secp256k1_i128_check_pow2(&a, n);
+}
 #endif
 
 /* Take as input a signed62 number in range (-2*modulus,modulus), and add a multiple of the modulus
@@ -136,15 +153,6 @@ static void secp256k1_modinv64_normalize_62(secp256k1_modinv64_signed62 *r, int6
 #endif
 }
 
-/* Data type for transition matrices (see section 3 of explanation).
- *
- * t = [ u  v ]
- *     [ q  r ]
- */
-typedef struct {
-    int64_t u, v, q, r;
-} secp256k1_modinv64_trans2x2;
-
 /* Compute the transition matrix and eta for 59 divsteps (where zeta=-(delta+1/2)).
  * Note that the transformation matrix is scaled by 2^62 and not 2^59.
  *
@@ -203,13 +211,15 @@ static int64_t secp256k1_modinv64_divsteps_59(int64_t zeta, uint64_t f0, uint64_
     t->v = (int64_t)v;
     t->q = (int64_t)q;
     t->r = (int64_t)r;
+#ifdef VERIFY
     /* The determinant of t must be a power of two. This guarantees that multiplication with t
      * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which
      * will be divided out again). As each divstep's individual matrix has determinant 2, the
      * aggregate of 59 of them will have determinant 2^59. Multiplying with the initial
      * 8*identity (which has determinant 2^6) means the overall outputs has determinant
      * 2^65. */
-    VERIFY_CHECK((int128_t)t->u * t->r - (int128_t)t->v * t->q == ((int128_t)1) << 65);
+    VERIFY_CHECK(secp256k1_modinv64_det_check_pow2(t, 65));
+#endif
     return zeta;
 }
 
@@ -286,11 +296,13 @@ static int64_t secp256k1_modinv64_divsteps_62_var(int64_t eta, uint64_t f0, uint
     t->v = (int64_t)v;
     t->q = (int64_t)q;
     t->r = (int64_t)r;
+#ifdef VERIFY
     /* The determinant of t must be a power of two. This guarantees that multiplication with t
      * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which
      * will be divided out again). As each divstep's individual matrix has determinant 2, the
      * aggregate of 62 of them will have determinant 2^62. */
-    VERIFY_CHECK((int128_t)t->u * t->r - (int128_t)t->v * t->q == ((int128_t)1) << 62);
+    VERIFY_CHECK(secp256k1_modinv64_det_check_pow2(t, 62));
+#endif
     return eta;
 }
 
@@ -307,7 +319,7 @@ static void secp256k1_modinv64_update_de_62(secp256k1_modinv64_signed62 *d, secp
     const int64_t e0 = e->v[0], e1 = e->v[1], e2 = e->v[2], e3 = e->v[3], e4 = e->v[4];
     const int64_t u = t->u, v = t->v, q = t->q, r = t->r;
     int64_t md, me, sd, se;
-    int128_t cd, ce;
+    secp256k1_int128 cd, ce;
 #ifdef VERIFY
     VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, -2) > 0); /* d > -2*modulus */
     VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, 1) < 0);  /* d <    modulus */
@@ -324,54 +336,64 @@ static void secp256k1_modinv64_update_de_62(secp256k1_modinv64_signed62 *d, secp
     md = (u & sd) + (v & se);
     me = (q & sd) + (r & se);
     /* Begin computing t*[d,e]. */
-    cd = (int128_t)u * d0 + (int128_t)v * e0;
-    ce = (int128_t)q * d0 + (int128_t)r * e0;
+    secp256k1_i128_mul(&cd, u, d0);
+    secp256k1_i128_accum_mul(&cd, v, e0);
+    secp256k1_i128_mul(&ce, q, d0);
+    secp256k1_i128_accum_mul(&ce, r, e0);
     /* Correct md,me so that t*[d,e]+modulus*[md,me] has 62 zero bottom bits. */
-    md -= (modinfo->modulus_inv62 * (uint64_t)cd + md) & M62;
-    me -= (modinfo->modulus_inv62 * (uint64_t)ce + me) & M62;
+    md -= (modinfo->modulus_inv62 * (uint64_t)secp256k1_i128_to_i64(&cd) + md) & M62;
+    me -= (modinfo->modulus_inv62 * (uint64_t)secp256k1_i128_to_i64(&ce) + me) & M62;
     /* Update the beginning of computation for t*[d,e]+modulus*[md,me] now md,me are known. */
-    cd += (int128_t)modinfo->modulus.v[0] * md;
-    ce += (int128_t)modinfo->modulus.v[0] * me;
+    secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[0], md);
+    secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[0], me);
     /* Verify that the low 62 bits of the computation are indeed zero, and then throw them away. */
-    VERIFY_CHECK(((int64_t)cd & M62) == 0); cd >>= 62;
-    VERIFY_CHECK(((int64_t)ce & M62) == 0); ce >>= 62;
+    VERIFY_CHECK((secp256k1_i128_to_i64(&cd) & M62) == 0); secp256k1_i128_rshift(&cd, 62);
+    VERIFY_CHECK((secp256k1_i128_to_i64(&ce) & M62) == 0); secp256k1_i128_rshift(&ce, 62);
     /* Compute limb 1 of t*[d,e]+modulus*[md,me], and store it as output limb 0 (= down shift). */
-    cd += (int128_t)u * d1 + (int128_t)v * e1;
-    ce += (int128_t)q * d1 + (int128_t)r * e1;
+    secp256k1_i128_accum_mul(&cd, u, d1);
+    secp256k1_i128_accum_mul(&cd, v, e1);
+    secp256k1_i128_accum_mul(&ce, q, d1);
+    secp256k1_i128_accum_mul(&ce, r, e1);
     if (modinfo->modulus.v[1]) { /* Optimize for the case where limb of modulus is zero. */
-        cd += (int128_t)modinfo->modulus.v[1] * md;
-        ce += (int128_t)modinfo->modulus.v[1] * me;
+        secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[1], md);
+        secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[1], me);
     }
-    d->v[0] = (int64_t)cd & M62; cd >>= 62;
-    e->v[0] = (int64_t)ce & M62; ce >>= 62;
+    d->v[0] = secp256k1_i128_to_i64(&cd) & M62; secp256k1_i128_rshift(&cd, 62);
+    e->v[0] = secp256k1_i128_to_i64(&ce) & M62; secp256k1_i128_rshift(&ce, 62);
     /* Compute limb 2 of t*[d,e]+modulus*[md,me], and store it as output limb 1. */
-    cd += (int128_t)u * d2 + (int128_t)v * e2;
-    ce += (int128_t)q * d2 + (int128_t)r * e2;
+    secp256k1_i128_accum_mul(&cd, u, d2);
+    secp256k1_i128_accum_mul(&cd, v, e2);
+    secp256k1_i128_accum_mul(&ce, q, d2);
+    secp256k1_i128_accum_mul(&ce, r, e2);
     if (modinfo->modulus.v[2]) { /* Optimize for the case where limb of modulus is zero. */
-        cd += (int128_t)modinfo->modulus.v[2] * md;
-        ce += (int128_t)modinfo->modulus.v[2] * me;
+        secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[2], md);
+        secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[2], me);
     }
-    d->v[1] = (int64_t)cd & M62; cd >>= 62;
-    e->v[1] = (int64_t)ce & M62; ce >>= 62;
+    d->v[1] = secp256k1_i128_to_i64(&cd) & M62; secp256k1_i128_rshift(&cd, 62);
+    e->v[1] = secp256k1_i128_to_i64(&ce) & M62; secp256k1_i128_rshift(&ce, 62);
     /* Compute limb 3 of t*[d,e]+modulus*[md,me], and store it as output limb 2. */
-    cd += (int128_t)u * d3 + (int128_t)v * e3;
-    ce += (int128_t)q * d3 + (int128_t)r * e3;
+    secp256k1_i128_accum_mul(&cd, u, d3);
+    secp256k1_i128_accum_mul(&cd, v, e3);
+    secp256k1_i128_accum_mul(&ce, q, d3);
+    secp256k1_i128_accum_mul(&ce, r, e3);
     if (modinfo->modulus.v[3]) { /* Optimize for the case where limb of modulus is zero. */
-        cd += (int128_t)modinfo->modulus.v[3] * md;
-        ce += (int128_t)modinfo->modulus.v[3] * me;
+        secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[3], md);
+        secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[3], me);
     }
-    d->v[2] = (int64_t)cd & M62; cd >>= 62;
-    e->v[2] = (int64_t)ce & M62; ce >>= 62;
+    d->v[2] = secp256k1_i128_to_i64(&cd) & M62; secp256k1_i128_rshift(&cd, 62);
+    e->v[2] = secp256k1_i128_to_i64(&ce) & M62; secp256k1_i128_rshift(&ce, 62);
     /* Compute limb 4 of t*[d,e]+modulus*[md,me], and store it as output limb 3. */
-    cd += (int128_t)u * d4 + (int128_t)v * e4;
-    ce += (int128_t)q * d4 + (int128_t)r * e4;
-    cd += (int128_t)modinfo->modulus.v[4] * md;
-    ce += (int128_t)modinfo->modulus.v[4] * me;
-    d->v[3] = (int64_t)cd & M62; cd >>= 62;
-    e->v[3] = (int64_t)ce & M62; ce >>= 62;
+    secp256k1_i128_accum_mul(&cd, u, d4);
+    secp256k1_i128_accum_mul(&cd, v, e4);
+    secp256k1_i128_accum_mul(&ce, q, d4);
+    secp256k1_i128_accum_mul(&ce, r, e4);
+    secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[4], md);
+    secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[4], me);
+    d->v[3] = secp256k1_i128_to_i64(&cd) & M62; secp256k1_i128_rshift(&cd, 62);
+    e->v[3] = secp256k1_i128_to_i64(&ce) & M62; secp256k1_i128_rshift(&ce, 62);
     /* What remains is limb 5 of t*[d,e]+modulus*[md,me]; store it as output limb 4. */
-    d->v[4] = (int64_t)cd;
-    e->v[4] = (int64_t)ce;
+    d->v[4] = secp256k1_i128_to_i64(&cd);
+    e->v[4] = secp256k1_i128_to_i64(&ce);
 #ifdef VERIFY
     VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, -2) > 0); /* d > -2*modulus */
     VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, 1) < 0);  /* d <    modulus */
@@ -389,36 +411,46 @@ static void secp256k1_modinv64_update_fg_62(secp256k1_modinv64_signed62 *f, secp
     const int64_t f0 = f->v[0], f1 = f->v[1], f2 = f->v[2], f3 = f->v[3], f4 = f->v[4];
     const int64_t g0 = g->v[0], g1 = g->v[1], g2 = g->v[2], g3 = g->v[3], g4 = g->v[4];
     const int64_t u = t->u, v = t->v, q = t->q, r = t->r;
-    int128_t cf, cg;
+    secp256k1_int128 cf, cg;
     /* Start computing t*[f,g]. */
-    cf = (int128_t)u * f0 + (int128_t)v * g0;
-    cg = (int128_t)q * f0 + (int128_t)r * g0;
+    secp256k1_i128_mul(&cf, u, f0);
+    secp256k1_i128_accum_mul(&cf, v, g0);
+    secp256k1_i128_mul(&cg, q, f0);
+    secp256k1_i128_accum_mul(&cg, r, g0);
     /* Verify that the bottom 62 bits of the result are zero, and then throw them away. */
-    VERIFY_CHECK(((int64_t)cf & M62) == 0); cf >>= 62;
-    VERIFY_CHECK(((int64_t)cg & M62) == 0); cg >>= 62;
+    VERIFY_CHECK((secp256k1_i128_to_i64(&cf) & M62) == 0); secp256k1_i128_rshift(&cf, 62);
+    VERIFY_CHECK((secp256k1_i128_to_i64(&cg) & M62) == 0); secp256k1_i128_rshift(&cg, 62);
     /* Compute limb 1 of t*[f,g], and store it as output limb 0 (= down shift). */
-    cf += (int128_t)u * f1 + (int128_t)v * g1;
-    cg += (int128_t)q * f1 + (int128_t)r * g1;
-    f->v[0] = (int64_t)cf & M62; cf >>= 62;
-    g->v[0] = (int64_t)cg & M62; cg >>= 62;
+    secp256k1_i128_accum_mul(&cf, u, f1);
+    secp256k1_i128_accum_mul(&cf, v, g1);
+    secp256k1_i128_accum_mul(&cg, q, f1);
+    secp256k1_i128_accum_mul(&cg, r, g1);
+    f->v[0] = secp256k1_i128_to_i64(&cf) & M62; secp256k1_i128_rshift(&cf, 62);
+    g->v[0] = secp256k1_i128_to_i64(&cg) & M62; secp256k1_i128_rshift(&cg, 62);
     /* Compute limb 2 of t*[f,g], and store it as output limb 1. */
-    cf += (int128_t)u * f2 + (int128_t)v * g2;
-    cg += (int128_t)q * f2 + (int128_t)r * g2;
-    f->v[1] = (int64_t)cf & M62; cf >>= 62;
-    g->v[1] = (int64_t)cg & M62; cg >>= 62;
+    secp256k1_i128_accum_mul(&cf, u, f2);
+    secp256k1_i128_accum_mul(&cf, v, g2);
+    secp256k1_i128_accum_mul(&cg, q, f2);
+    secp256k1_i128_accum_mul(&cg, r, g2);
+    f->v[1] = secp256k1_i128_to_i64(&cf) & M62; secp256k1_i128_rshift(&cf, 62);
+    g->v[1] = secp256k1_i128_to_i64(&cg) & M62; secp256k1_i128_rshift(&cg, 62);
     /* Compute limb 3 of t*[f,g], and store it as output limb 2. */
-    cf += (int128_t)u * f3 + (int128_t)v * g3;
-    cg += (int128_t)q * f3 + (int128_t)r * g3;
-    f->v[2] = (int64_t)cf & M62; cf >>= 62;
-    g->v[2] = (int64_t)cg & M62; cg >>= 62;
+    secp256k1_i128_accum_mul(&cf, u, f3);
+    secp256k1_i128_accum_mul(&cf, v, g3);
+    secp256k1_i128_accum_mul(&cg, q, f3);
+    secp256k1_i128_accum_mul(&cg, r, g3);
+    f->v[2] = secp256k1_i128_to_i64(&cf) & M62; secp256k1_i128_rshift(&cf, 62);
+    g->v[2] = secp256k1_i128_to_i64(&cg) & M62; secp256k1_i128_rshift(&cg, 62);
     /* Compute limb 4 of t*[f,g], and store it as output limb 3. */
-    cf += (int128_t)u * f4 + (int128_t)v * g4;
-    cg += (int128_t)q * f4 + (int128_t)r * g4;
-    f->v[3] = (int64_t)cf & M62; cf >>= 62;
-    g->v[3] = (int64_t)cg & M62; cg >>= 62;
+    secp256k1_i128_accum_mul(&cf, u, f4);
+    secp256k1_i128_accum_mul(&cf, v, g4);
+    secp256k1_i128_accum_mul(&cg, q, f4);
+    secp256k1_i128_accum_mul(&cg, r, g4);
+    f->v[3] = secp256k1_i128_to_i64(&cf) & M62; secp256k1_i128_rshift(&cf, 62);
+    g->v[3] = secp256k1_i128_to_i64(&cg) & M62; secp256k1_i128_rshift(&cg, 62);
     /* What remains is limb 5 of t*[f,g]; store it as output limb 4. */
-    f->v[4] = (int64_t)cf;
-    g->v[4] = (int64_t)cg;
+    f->v[4] = secp256k1_i128_to_i64(&cf);
+    g->v[4] = secp256k1_i128_to_i64(&cg);
 }
 
 /* Compute (t/2^62) * [f, g], where t is a transition matrix for 62 divsteps.
@@ -431,30 +463,34 @@ static void secp256k1_modinv64_update_fg_62_var(int len, secp256k1_modinv64_sign
     const int64_t M62 = (int64_t)(UINT64_MAX >> 2);
     const int64_t u = t->u, v = t->v, q = t->q, r = t->r;
     int64_t fi, gi;
-    int128_t cf, cg;
+    secp256k1_int128 cf, cg;
     int i;
     VERIFY_CHECK(len > 0);
     /* Start computing t*[f,g]. */
     fi = f->v[0];
     gi = g->v[0];
-    cf = (int128_t)u * fi + (int128_t)v * gi;
-    cg = (int128_t)q * fi + (int128_t)r * gi;
+    secp256k1_i128_mul(&cf, u, fi);
+    secp256k1_i128_accum_mul(&cf, v, gi);
+    secp256k1_i128_mul(&cg, q, fi);
+    secp256k1_i128_accum_mul(&cg, r, gi);
     /* Verify that the bottom 62 bits of the result are zero, and then throw them away. */
-    VERIFY_CHECK(((int64_t)cf & M62) == 0); cf >>= 62;
-    VERIFY_CHECK(((int64_t)cg & M62) == 0); cg >>= 62;
+    VERIFY_CHECK((secp256k1_i128_to_i64(&cf) & M62) == 0); secp256k1_i128_rshift(&cf, 62);
+    VERIFY_CHECK((secp256k1_i128_to_i64(&cg) & M62) == 0); secp256k1_i128_rshift(&cg, 62);
     /* Now iteratively compute limb i=1..len of t*[f,g], and store them in output limb i-1 (shifting
      * down by 62 bits). */
     for (i = 1; i < len; ++i) {
         fi = f->v[i];
         gi = g->v[i];
-        cf += (int128_t)u * fi + (int128_t)v * gi;
-        cg += (int128_t)q * fi + (int128_t)r * gi;
-        f->v[i - 1] = (int64_t)cf & M62; cf >>= 62;
-        g->v[i - 1] = (int64_t)cg & M62; cg >>= 62;
+        secp256k1_i128_accum_mul(&cf, u, fi);
+        secp256k1_i128_accum_mul(&cf, v, gi);
+        secp256k1_i128_accum_mul(&cg, q, fi);
+        secp256k1_i128_accum_mul(&cg, r, gi);
+        f->v[i - 1] = secp256k1_i128_to_i64(&cf) & M62; secp256k1_i128_rshift(&cf, 62);
+        g->v[i - 1] = secp256k1_i128_to_i64(&cg) & M62; secp256k1_i128_rshift(&cg, 62);
     }
     /* What remains is limb (len) of t*[f,g]; store it as output limb (len-1). */
-    f->v[len - 1] = (int64_t)cf;
-    g->v[len - 1] = (int64_t)cg;
+    f->v[len - 1] = secp256k1_i128_to_i64(&cf);
+    g->v[len - 1] = secp256k1_i128_to_i64(&cg);
 }
 
 /* Compute the inverse of x modulo modinfo->modulus, and replace x with it (constant time in x). */
diff --git a/src/secp256k1/src/modules/ecdh/Makefile.am.include b/src/secp256k1/src/modules/ecdh/Makefile.am.include
index e3088b46979..7f7f95f1fd6 100644
--- a/src/secp256k1/src/modules/ecdh/Makefile.am.include
+++ b/src/secp256k1/src/modules/ecdh/Makefile.am.include
@@ -1,8 +1,4 @@
 include_HEADERS += include/secp256k1_ecdh.h
 noinst_HEADERS += src/modules/ecdh/main_impl.h
 noinst_HEADERS += src/modules/ecdh/tests_impl.h
-if USE_BENCHMARK
-noinst_PROGRAMS += bench_ecdh
-bench_ecdh_SOURCES = src/bench_ecdh.c
-bench_ecdh_LDADD = libsecp256k1.la $(SECP_LIBS) $(COMMON_LIB)
-endif
+noinst_HEADERS += src/modules/ecdh/bench_impl.h
diff --git a/src/secp256k1/src/bench_ecdh.c b/src/secp256k1/src/modules/ecdh/bench_impl.h
similarity index 80%
rename from src/secp256k1/src/bench_ecdh.c
rename to src/secp256k1/src/modules/ecdh/bench_impl.h
index cb020d26b4d..8df15bcf43c 100644
--- a/src/secp256k1/src/bench_ecdh.c
+++ b/src/secp256k1/src/modules/ecdh/bench_impl.h
@@ -4,12 +4,10 @@
  * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
  ***********************************************************************/
 
-#include <string.h>
+#ifndef SECP256K1_MODULE_ECDH_BENCH_H
+#define SECP256K1_MODULE_ECDH_BENCH_H
 
-#include "../include/secp256k1.h"
-#include "../include/secp256k1_ecdh.h"
-#include "util.h"
-#include "bench.h"
+#include "../../../include/secp256k1_ecdh.h"
 
 typedef struct {
     secp256k1_context *ctx;
@@ -44,16 +42,16 @@ static void bench_ecdh(void* arg, int iters) {
     }
 }
 
-int main(void) {
+void run_ecdh_bench(int iters, int argc, char** argv) {
     bench_ecdh_data data;
-
-    int iters = get_iters(20000);
+    int d = argc == 1;
 
     /* create a context with no capabilities */
     data.ctx = secp256k1_context_create(SECP256K1_FLAGS_TYPE_CONTEXT);
 
-    run_benchmark("ecdh", bench_ecdh, bench_ecdh_setup, NULL, &data, 10, iters);
+    if (d || have_flag(argc, argv, "ecdh")) run_benchmark("ecdh", bench_ecdh, bench_ecdh_setup, NULL, &data, 10, iters);
 
     secp256k1_context_destroy(data.ctx);
-    return 0;
 }
+
+#endif /* SECP256K1_MODULE_ECDH_BENCH_H */
diff --git a/src/secp256k1/src/modules/extrakeys/main_impl.h b/src/secp256k1/src/modules/extrakeys/main_impl.h
index 8607bbede73..e1003052f4c 100644
--- a/src/secp256k1/src/modules/extrakeys/main_impl.h
+++ b/src/secp256k1/src/modules/extrakeys/main_impl.h
@@ -120,12 +120,11 @@ int secp256k1_xonly_pubkey_tweak_add(const secp256k1_context* ctx, secp256k1_pub
     VERIFY_CHECK(ctx != NULL);
     ARG_CHECK(output_pubkey != NULL);
     memset(output_pubkey, 0, sizeof(*output_pubkey));
-    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
     ARG_CHECK(internal_pubkey != NULL);
     ARG_CHECK(tweak32 != NULL);
 
     if (!secp256k1_xonly_pubkey_load(ctx, &pk, internal_pubkey)
-        || !secp256k1_ec_pubkey_tweak_add_helper(&ctx->ecmult_ctx, &pk, tweak32)) {
+        || !secp256k1_ec_pubkey_tweak_add_helper(&pk, tweak32)) {
         return 0;
     }
     secp256k1_pubkey_save(output_pubkey, &pk);
@@ -137,13 +136,12 @@ int secp256k1_xonly_pubkey_tweak_add_check(const secp256k1_context* ctx, const u
     unsigned char pk_expected32[32];
 
     VERIFY_CHECK(ctx != NULL);
-    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
     ARG_CHECK(internal_pubkey != NULL);
     ARG_CHECK(tweaked_pubkey32 != NULL);
     ARG_CHECK(tweak32 != NULL);
 
     if (!secp256k1_xonly_pubkey_load(ctx, &pk, internal_pubkey)
-        || !secp256k1_ec_pubkey_tweak_add_helper(&ctx->ecmult_ctx, &pk, tweak32)) {
+        || !secp256k1_ec_pubkey_tweak_add_helper(&pk, tweak32)) {
         return 0;
     }
     secp256k1_fe_normalize_var(&pk.x);
@@ -260,7 +258,6 @@ int secp256k1_keypair_xonly_tweak_add(const secp256k1_context* ctx, secp256k1_ke
     int ret;
 
     VERIFY_CHECK(ctx != NULL);
-    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
     ARG_CHECK(keypair != NULL);
     ARG_CHECK(tweak32 != NULL);
 
@@ -273,7 +270,7 @@ int secp256k1_keypair_xonly_tweak_add(const secp256k1_context* ctx, secp256k1_ke
     }
 
     ret &= secp256k1_ec_seckey_tweak_add_helper(&sk, tweak32);
-    ret &= secp256k1_ec_pubkey_tweak_add_helper(&ctx->ecmult_ctx, &pk, tweak32);
+    ret &= secp256k1_ec_pubkey_tweak_add_helper(&pk, tweak32);
 
     secp256k1_declassify(ctx, &ret, sizeof(ret));
     if (ret) {
diff --git a/src/secp256k1/src/modules/recovery/Makefile.am.include b/src/secp256k1/src/modules/recovery/Makefile.am.include
index e2d3f1248d2..156ea690fad 100644
--- a/src/secp256k1/src/modules/recovery/Makefile.am.include
+++ b/src/secp256k1/src/modules/recovery/Makefile.am.include
@@ -2,8 +2,4 @@ include_HEADERS += include/secp256k1_recovery.h
 noinst_HEADERS += src/modules/recovery/main_impl.h
 noinst_HEADERS += src/modules/recovery/tests_impl.h
 noinst_HEADERS += src/modules/recovery/tests_exhaustive_impl.h
-if USE_BENCHMARK
-noinst_PROGRAMS += bench_recover
-bench_recover_SOURCES = src/bench_recover.c
-bench_recover_LDADD = libsecp256k1.la $(SECP_LIBS) $(COMMON_LIB)
-endif
+noinst_HEADERS += src/modules/recovery/bench_impl.h
diff --git a/src/secp256k1/src/bench_recover.c b/src/secp256k1/src/modules/recovery/bench_impl.h
similarity index 76%
rename from src/secp256k1/src/bench_recover.c
rename to src/secp256k1/src/modules/recovery/bench_impl.h
index 4bcac19dc0a..ffa00df4790 100644
--- a/src/secp256k1/src/bench_recover.c
+++ b/src/secp256k1/src/modules/recovery/bench_impl.h
@@ -4,10 +4,10 @@
  * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
  ***********************************************************************/
 
-#include "../include/secp256k1.h"
-#include "../include/secp256k1_recovery.h"
-#include "util.h"
-#include "bench.h"
+#ifndef SECP256K1_MODULE_RECOVERY_BENCH_H
+#define SECP256K1_MODULE_RECOVERY_BENCH_H
+
+#include "../../../include/secp256k1_recovery.h"
 
 typedef struct {
     secp256k1_context *ctx;
@@ -48,15 +48,15 @@ void bench_recover_setup(void* arg) {
     }
 }
 
-int main(void) {
+void run_recovery_bench(int iters, int argc, char** argv) {
     bench_recover_data data;
+    int d = argc == 1;
 
-    int iters = get_iters(20000);
-
-    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
 
-    run_benchmark("ecdsa_recover", bench_recover, bench_recover_setup, NULL, &data, 10, iters);
+    if (d || have_flag(argc, argv, "ecdsa") || have_flag(argc, argv, "recover") || have_flag(argc, argv, "ecdsa_recover")) run_benchmark("ecdsa_recover", bench_recover, bench_recover_setup, NULL, &data, 10, iters);
 
     secp256k1_context_destroy(data.ctx);
-    return 0;
 }
+
+#endif /* SECP256K1_MODULE_RECOVERY_BENCH_H */
diff --git a/src/secp256k1/src/modules/recovery/main_impl.h b/src/secp256k1/src/modules/recovery/main_impl.h
index 9e19f2a2dc9..e7906eb62e0 100644
--- a/src/secp256k1/src/modules/recovery/main_impl.h
+++ b/src/secp256k1/src/modules/recovery/main_impl.h
@@ -40,7 +40,7 @@ int secp256k1_ecdsa_recoverable_signature_parse_compact(const secp256k1_context*
     int ret = 1;
     int overflow = 0;
 
-    (void)ctx;
+    VERIFY_CHECK(ctx != NULL);
     ARG_CHECK(sig != NULL);
     ARG_CHECK(input64 != NULL);
     ARG_CHECK(recid >= 0 && recid <= 3);
@@ -60,7 +60,7 @@ int secp256k1_ecdsa_recoverable_signature_parse_compact(const secp256k1_context*
 int secp256k1_ecdsa_recoverable_signature_serialize_compact(const secp256k1_context* ctx, unsigned char *output64, int *recid, const secp256k1_ecdsa_recoverable_signature* sig) {
     secp256k1_scalar r, s;
 
-    (void)ctx;
+    VERIFY_CHECK(ctx != NULL);
     ARG_CHECK(output64 != NULL);
     ARG_CHECK(sig != NULL);
     ARG_CHECK(recid != NULL);
@@ -75,7 +75,7 @@ int secp256k1_ecdsa_recoverable_signature_convert(const secp256k1_context* ctx,
     secp256k1_scalar r, s;
     int recid;
 
-    (void)ctx;
+    VERIFY_CHECK(ctx != NULL);
     ARG_CHECK(sig != NULL);
     ARG_CHECK(sigin != NULL);
 
@@ -84,7 +84,7 @@ int secp256k1_ecdsa_recoverable_signature_convert(const secp256k1_context* ctx,
     return 1;
 }
 
-static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar* sigs, secp256k1_ge *pubkey, const secp256k1_scalar *message, int recid) {
+static int secp256k1_ecdsa_sig_recover(const secp256k1_scalar *sigr, const secp256k1_scalar* sigs, secp256k1_ge *pubkey, const secp256k1_scalar *message, int recid) {
     unsigned char brx[32];
     secp256k1_fe fx;
     secp256k1_ge x;
@@ -115,7 +115,7 @@ static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context *ctx, cons
     secp256k1_scalar_mul(&u1, &rn, message);
     secp256k1_scalar_negate(&u1, &u1);
     secp256k1_scalar_mul(&u2, &rn, sigs);
-    secp256k1_ecmult(ctx, &qj, &xj, &u2, &u1);
+    secp256k1_ecmult(&qj, &xj, &u2, &u1);
     secp256k1_ge_set_gej_var(pubkey, &qj);
     return !secp256k1_gej_is_infinity(&qj);
 }
@@ -140,7 +140,6 @@ int secp256k1_ecdsa_recover(const secp256k1_context* ctx, secp256k1_pubkey *pubk
     secp256k1_scalar m;
     int recid;
     VERIFY_CHECK(ctx != NULL);
-    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
     ARG_CHECK(msghash32 != NULL);
     ARG_CHECK(signature != NULL);
     ARG_CHECK(pubkey != NULL);
@@ -148,7 +147,7 @@ int secp256k1_ecdsa_recover(const secp256k1_context* ctx, secp256k1_pubkey *pubk
     secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, signature);
     VERIFY_CHECK(recid >= 0 && recid < 4);  /* should have been caught in parse_compact */
     secp256k1_scalar_set_b32(&m, msghash32, NULL);
-    if (secp256k1_ecdsa_sig_recover(&ctx->ecmult_ctx, &r, &s, &q, &m, recid)) {
+    if (secp256k1_ecdsa_sig_recover(&r, &s, &q, &m, recid)) {
         secp256k1_pubkey_save(pubkey, &q);
         return 1;
     } else {
diff --git a/src/secp256k1/src/modules/schnorrsig/Makefile.am.include b/src/secp256k1/src/modules/schnorrsig/Makefile.am.include
index 568bcc35232..654fa2e5ae5 100644
--- a/src/secp256k1/src/modules/schnorrsig/Makefile.am.include
+++ b/src/secp256k1/src/modules/schnorrsig/Makefile.am.include
@@ -2,8 +2,4 @@ include_HEADERS += include/secp256k1_schnorrsig.h
 noinst_HEADERS += src/modules/schnorrsig/main_impl.h
 noinst_HEADERS += src/modules/schnorrsig/tests_impl.h
 noinst_HEADERS += src/modules/schnorrsig/tests_exhaustive_impl.h
-if USE_BENCHMARK
-noinst_PROGRAMS += bench_schnorrsig
-bench_schnorrsig_SOURCES = src/bench_schnorrsig.c
-bench_schnorrsig_LDADD = libsecp256k1.la $(SECP_LIBS) $(COMMON_LIB)
-endif
+noinst_HEADERS += src/modules/schnorrsig/bench_impl.h
diff --git a/src/secp256k1/src/bench_schnorrsig.c b/src/secp256k1/src/modules/schnorrsig/bench_impl.h
similarity index 65%
rename from src/secp256k1/src/bench_schnorrsig.c
rename to src/secp256k1/src/modules/schnorrsig/bench_impl.h
index dfea1441484..f0b0d3de757 100644
--- a/src/secp256k1/src/bench_schnorrsig.c
+++ b/src/secp256k1/src/modules/schnorrsig/bench_impl.h
@@ -4,14 +4,12 @@
  * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
  ***********************************************************************/
 
-#include <string.h>
-#include <stdlib.h>
+#ifndef SECP256K1_MODULE_SCHNORRSIG_BENCH_H
+#define SECP256K1_MODULE_SCHNORRSIG_BENCH_H
 
+#include "../../../include/secp256k1_schnorrsig.h"
 
-#include "../include/secp256k1.h"
-#include "../include/secp256k1_schnorrsig.h"
-#include "util.h"
-#include "bench.h"
+#define MSGLEN 32
 
 typedef struct {
     secp256k1_context *ctx;
@@ -26,13 +24,13 @@ typedef struct {
 void bench_schnorrsig_sign(void* arg, int iters) {
     bench_schnorrsig_data *data = (bench_schnorrsig_data *)arg;
     int i;
-    unsigned char msg[32] = "benchmarkexamplemessagetemplate";
+    unsigned char msg[MSGLEN] = {0};
     unsigned char sig[64];
 
     for (i = 0; i < iters; i++) {
         msg[0] = i;
         msg[1] = i >> 8;
-        CHECK(secp256k1_schnorrsig_sign(data->ctx, sig, msg, data->keypairs[i], NULL, NULL));
+        CHECK(secp256k1_schnorrsig_sign_custom(data->ctx, sig, msg, MSGLEN, data->keypairs[i], NULL));
     }
 }
 
@@ -43,24 +41,25 @@ void bench_schnorrsig_verify(void* arg, int iters) {
     for (i = 0; i < iters; i++) {
         secp256k1_xonly_pubkey pk;
         CHECK(secp256k1_xonly_pubkey_parse(data->ctx, &pk, data->pk[i]) == 1);
-        CHECK(secp256k1_schnorrsig_verify(data->ctx, data->sigs[i], data->msgs[i], &pk));
+        CHECK(secp256k1_schnorrsig_verify(data->ctx, data->sigs[i], data->msgs[i], MSGLEN, &pk));
     }
 }
 
-int main(void) {
+void run_schnorrsig_bench(int iters, int argc, char** argv) {
     int i;
     bench_schnorrsig_data data;
-    int iters = get_iters(10000);
+    int d = argc == 1;
 
-    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY | SECP256K1_CONTEXT_SIGN);
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
     data.keypairs = (const secp256k1_keypair **)malloc(iters * sizeof(secp256k1_keypair *));
     data.pk = (const unsigned char **)malloc(iters * sizeof(unsigned char *));
     data.msgs = (const unsigned char **)malloc(iters * sizeof(unsigned char *));
     data.sigs = (const unsigned char **)malloc(iters * sizeof(unsigned char *));
 
+    CHECK(MSGLEN >= 4);
     for (i = 0; i < iters; i++) {
         unsigned char sk[32];
-        unsigned char *msg = (unsigned char *)malloc(32);
+        unsigned char *msg = (unsigned char *)malloc(MSGLEN);
         unsigned char *sig = (unsigned char *)malloc(64);
         secp256k1_keypair *keypair = (secp256k1_keypair *)malloc(sizeof(*keypair));
         unsigned char *pk_char = (unsigned char *)malloc(32);
@@ -69,7 +68,7 @@ int main(void) {
         msg[1] = sk[1] = i >> 8;
         msg[2] = sk[2] = i >> 16;
         msg[3] = sk[3] = i >> 24;
-        memset(&msg[4], 'm', 28);
+        memset(&msg[4], 'm', MSGLEN - 4);
         memset(&sk[4], 's', 28);
 
         data.keypairs[i] = keypair;
@@ -78,13 +77,13 @@ int main(void) {
         data.sigs[i] = sig;
 
         CHECK(secp256k1_keypair_create(data.ctx, keypair, sk));
-        CHECK(secp256k1_schnorrsig_sign(data.ctx, sig, msg, keypair, NULL, NULL));
+        CHECK(secp256k1_schnorrsig_sign_custom(data.ctx, sig, msg, MSGLEN, keypair, NULL));
         CHECK(secp256k1_keypair_xonly_pub(data.ctx, &pk, NULL, keypair));
         CHECK(secp256k1_xonly_pubkey_serialize(data.ctx, pk_char, &pk) == 1);
     }
 
-    run_benchmark("schnorrsig_sign", bench_schnorrsig_sign, NULL, NULL, (void *) &data, 10, iters);
-    run_benchmark("schnorrsig_verify", bench_schnorrsig_verify, NULL, NULL, (void *) &data, 10, iters);
+    if (d || have_flag(argc, argv, "schnorrsig") || have_flag(argc, argv, "sign") || have_flag(argc, argv, "schnorrsig_sign")) run_benchmark("schnorrsig_sign", bench_schnorrsig_sign, NULL, NULL, (void *) &data, 10, iters);
+    if (d || have_flag(argc, argv, "schnorrsig") || have_flag(argc, argv, "verify") || have_flag(argc, argv, "schnorrsig_verify")) run_benchmark("schnorrsig_verify", bench_schnorrsig_verify, NULL, NULL, (void *) &data, 10, iters);
 
     for (i = 0; i < iters; i++) {
         free((void *)data.keypairs[i]);
@@ -92,11 +91,14 @@ int main(void) {
         free((void *)data.msgs[i]);
         free((void *)data.sigs[i]);
     }
-    free(data.keypairs);
-    free(data.pk);
-    free(data.msgs);
-    free(data.sigs);
+
+    /* Casting to (void *) avoids a stupid warning in MSVC. */
+    free((void *)data.keypairs);
+    free((void *)data.pk);
+    free((void *)data.msgs);
+    free((void *)data.sigs);
 
     secp256k1_context_destroy(data.ctx);
-    return 0;
 }
+
+#endif
diff --git a/src/secp256k1/src/modules/schnorrsig/main_impl.h b/src/secp256k1/src/modules/schnorrsig/main_impl.h
index af503bf5ebe..cd651591c4e 100644
--- a/src/secp256k1/src/modules/schnorrsig/main_impl.h
+++ b/src/secp256k1/src/modules/schnorrsig/main_impl.h
@@ -43,16 +43,18 @@ static void secp256k1_nonce_function_bip340_sha256_tagged_aux(secp256k1_sha256 *
     sha->bytes = 64;
 }
 
-/* algo16 argument for nonce_function_bip340 to derive the nonce exactly as stated in BIP-340
+/* algo argument for nonce_function_bip340 to derive the nonce exactly as stated in BIP-340
  * by using the correct tagged hash function. */
-static const unsigned char bip340_algo16[16] = "BIP0340/nonce\0\0\0";
+static const unsigned char bip340_algo[13] = "BIP0340/nonce";
 
-static int nonce_function_bip340(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo16, void *data) {
+static const unsigned char schnorrsig_extraparams_magic[4] = SECP256K1_SCHNORRSIG_EXTRAPARAMS_MAGIC;
+
+static int nonce_function_bip340(unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) {
     secp256k1_sha256 sha;
     unsigned char masked_key[32];
     int i;
 
-    if (algo16 == NULL) {
+    if (algo == NULL) {
         return 0;
     }
 
@@ -63,30 +65,33 @@ static int nonce_function_bip340(unsigned char *nonce32, const unsigned char *ms
         for (i = 0; i < 32; i++) {
             masked_key[i] ^= key32[i];
         }
+    } else {
+        /* Precomputed TaggedHash("BIP0340/aux", 0x0000...00); */
+        static const unsigned char ZERO_MASK[32] = {
+              84, 241, 105, 207, 201, 226, 229, 114,
+             116, 128,  68,  31, 144, 186,  37, 196,
+             136, 244,  97, 199,  11,  94, 165, 220,
+             170, 247, 175, 105, 39,  10, 165,  20
+        };
+        for (i = 0; i < 32; i++) {
+            masked_key[i] = key32[i] ^ ZERO_MASK[i];
+        }
     }
 
-    /* Tag the hash with algo16 which is important to avoid nonce reuse across
+    /* Tag the hash with algo which is important to avoid nonce reuse across
      * algorithms. If this nonce function is used in BIP-340 signing as defined
      * in the spec, an optimized tagging implementation is used. */
-    if (secp256k1_memcmp_var(algo16, bip340_algo16, 16) == 0) {
+    if (algolen == sizeof(bip340_algo)
+            && secp256k1_memcmp_var(algo, bip340_algo, algolen) == 0) {
         secp256k1_nonce_function_bip340_sha256_tagged(&sha);
     } else {
-        int algo16_len = 16;
-        /* Remove terminating null bytes */
-        while (algo16_len > 0 && !algo16[algo16_len - 1]) {
-            algo16_len--;
-        }
-        secp256k1_sha256_initialize_tagged(&sha, algo16, algo16_len);
+        secp256k1_sha256_initialize_tagged(&sha, algo, algolen);
     }
 
-    /* Hash (masked-)key||pk||msg using the tagged hash as per the spec */
-    if (data != NULL) {
-        secp256k1_sha256_write(&sha, masked_key, 32);
-    } else {
-        secp256k1_sha256_write(&sha, key32, 32);
-    }
+    /* Hash masked-key||pk||msg using the tagged hash as per the spec */
+    secp256k1_sha256_write(&sha, masked_key, 32);
     secp256k1_sha256_write(&sha, xonly_pk32, 32);
-    secp256k1_sha256_write(&sha, msg32, 32);
+    secp256k1_sha256_write(&sha, msg, msglen);
     secp256k1_sha256_finalize(&sha, nonce32);
     return 1;
 }
@@ -108,23 +113,23 @@ static void secp256k1_schnorrsig_sha256_tagged(secp256k1_sha256 *sha) {
     sha->bytes = 64;
 }
 
-static void secp256k1_schnorrsig_challenge(secp256k1_scalar* e, const unsigned char *r32, const unsigned char *msg32, const unsigned char *pubkey32)
+static void secp256k1_schnorrsig_challenge(secp256k1_scalar* e, const unsigned char *r32, const unsigned char *msg, size_t msglen, const unsigned char *pubkey32)
 {
     unsigned char buf[32];
     secp256k1_sha256 sha;
 
-    /* tagged hash(r.x, pk.x, msg32) */
+    /* tagged hash(r.x, pk.x, msg) */
     secp256k1_schnorrsig_sha256_tagged(&sha);
     secp256k1_sha256_write(&sha, r32, 32);
     secp256k1_sha256_write(&sha, pubkey32, 32);
-    secp256k1_sha256_write(&sha, msg32, 32);
+    secp256k1_sha256_write(&sha, msg, msglen);
     secp256k1_sha256_finalize(&sha, buf);
     /* Set scalar e to the challenge hash modulo the curve order as per
      * BIP340. */
     secp256k1_scalar_set_b32(e, buf, NULL);
 }
 
-int secp256k1_schnorrsig_sign(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const secp256k1_keypair *keypair, secp256k1_nonce_function_hardened noncefp, void *ndata) {
+static int secp256k1_schnorrsig_sign_internal(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg, size_t msglen, const secp256k1_keypair *keypair, secp256k1_nonce_function_hardened noncefp, void *ndata) {
     secp256k1_scalar sk;
     secp256k1_scalar e;
     secp256k1_scalar k;
@@ -139,7 +144,7 @@ int secp256k1_schnorrsig_sign(const secp256k1_context* ctx, unsigned char *sig64
     VERIFY_CHECK(ctx != NULL);
     ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
     ARG_CHECK(sig64 != NULL);
-    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(msg != NULL || msglen == 0);
     ARG_CHECK(keypair != NULL);
 
     if (noncefp == NULL) {
@@ -156,7 +161,7 @@ int secp256k1_schnorrsig_sign(const secp256k1_context* ctx, unsigned char *sig64
 
     secp256k1_scalar_get_b32(seckey, &sk);
     secp256k1_fe_get_b32(pk_buf, &pk.x);
-    ret &= !!noncefp(buf, msg32, seckey, pk_buf, bip340_algo16, ndata);
+    ret &= !!noncefp(buf, msg, msglen, seckey, pk_buf, bip340_algo, sizeof(bip340_algo), ndata);
     secp256k1_scalar_set_b32(&k, buf, NULL);
     ret &= !secp256k1_scalar_is_zero(&k);
     secp256k1_scalar_cmov(&k, &secp256k1_scalar_one, !ret);
@@ -174,7 +179,7 @@ int secp256k1_schnorrsig_sign(const secp256k1_context* ctx, unsigned char *sig64
     secp256k1_fe_normalize_var(&r.x);
     secp256k1_fe_get_b32(&sig64[0], &r.x);
 
-    secp256k1_schnorrsig_challenge(&e, &sig64[0], msg32, pk_buf);
+    secp256k1_schnorrsig_challenge(&e, &sig64[0], msg, msglen, pk_buf);
     secp256k1_scalar_mul(&e, &e, &sk);
     secp256k1_scalar_add(&e, &e, &k);
     secp256k1_scalar_get_b32(&sig64[32], &e);
@@ -187,7 +192,31 @@ int secp256k1_schnorrsig_sign(const secp256k1_context* ctx, unsigned char *sig64
     return ret;
 }
 
-int secp256k1_schnorrsig_verify(const secp256k1_context* ctx, const unsigned char *sig64, const unsigned char *msg32, const secp256k1_xonly_pubkey *pubkey) {
+int secp256k1_schnorrsig_sign32(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const secp256k1_keypair *keypair, const unsigned char *aux_rand32) {
+    /* We cast away const from the passed aux_rand32 argument since we know the default nonce function does not modify it. */
+    return secp256k1_schnorrsig_sign_internal(ctx, sig64, msg32, 32, keypair, secp256k1_nonce_function_bip340, (unsigned char*)aux_rand32);
+}
+
+int secp256k1_schnorrsig_sign(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const secp256k1_keypair *keypair, const unsigned char *aux_rand32) {
+    return secp256k1_schnorrsig_sign32(ctx, sig64, msg32, keypair, aux_rand32);
+}
+
+int secp256k1_schnorrsig_sign_custom(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg, size_t msglen, const secp256k1_keypair *keypair, secp256k1_schnorrsig_extraparams *extraparams) {
+    secp256k1_nonce_function_hardened noncefp = NULL;
+    void *ndata = NULL;
+    VERIFY_CHECK(ctx != NULL);
+
+    if (extraparams != NULL) {
+        ARG_CHECK(secp256k1_memcmp_var(extraparams->magic,
+                                       schnorrsig_extraparams_magic,
+                                       sizeof(extraparams->magic)) == 0);
+        noncefp = extraparams->noncefp;
+        ndata = extraparams->ndata;
+    }
+    return secp256k1_schnorrsig_sign_internal(ctx, sig64, msg, msglen, keypair, noncefp, ndata);
+}
+
+int secp256k1_schnorrsig_verify(const secp256k1_context* ctx, const unsigned char *sig64, const unsigned char *msg, size_t msglen, const secp256k1_xonly_pubkey *pubkey) {
     secp256k1_scalar s;
     secp256k1_scalar e;
     secp256k1_gej rj;
@@ -199,9 +228,8 @@ int secp256k1_schnorrsig_verify(const secp256k1_context* ctx, const unsigned cha
     int overflow;
 
     VERIFY_CHECK(ctx != NULL);
-    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
     ARG_CHECK(sig64 != NULL);
-    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(msg != NULL || msglen == 0);
     ARG_CHECK(pubkey != NULL);
 
     if (!secp256k1_fe_set_b32(&rx, &sig64[0])) {
@@ -219,12 +247,12 @@ int secp256k1_schnorrsig_verify(const secp256k1_context* ctx, const unsigned cha
 
     /* Compute e. */
     secp256k1_fe_get_b32(buf, &pk.x);
-    secp256k1_schnorrsig_challenge(&e, &sig64[0], msg32, buf);
+    secp256k1_schnorrsig_challenge(&e, &sig64[0], msg, msglen, buf);
 
     /* Compute rj =  s*G + (-e)*pkj */
     secp256k1_scalar_negate(&e, &e);
     secp256k1_gej_set_ge(&pkj, &pk);
-    secp256k1_ecmult(&ctx->ecmult_ctx, &rj, &pkj, &e, &s);
+    secp256k1_ecmult(&rj, &pkj, &e, &s);
 
     secp256k1_ge_set_gej_var(&r, &rj);
     if (secp256k1_ge_is_infinity(&r)) {
diff --git a/src/secp256k1/src/precompute_ecmult.c b/src/secp256k1/src/precompute_ecmult.c
new file mode 100644
index 00000000000..2aa37b8fe38
--- /dev/null
+++ b/src/secp256k1/src/precompute_ecmult.c
@@ -0,0 +1,99 @@
+/*****************************************************************************************************
+ * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor *
+ * Distributed under the MIT software license, see the accompanying                                  *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.                              *
+ *****************************************************************************************************/
+
+#include <inttypes.h>
+#include <stdio.h>
+
+/* Autotools creates libsecp256k1-config.h, of which ECMULT_WINDOW_SIZE is needed.
+   ifndef guard so downstream users can define their own if they do not use autotools. */
+#if !defined(ECMULT_WINDOW_SIZE)
+#include "libsecp256k1-config.h"
+#endif
+
+#include "../include/secp256k1.h"
+
+#include "assumptions.h"
+#include "util.h"
+
+#include "field_impl.h"
+#include "group_impl.h"
+#include "int128_impl.h"
+#include "ecmult.h"
+#include "ecmult_compute_table_impl.h"
+
+static void print_table(FILE *fp, const char *name, int window_g, const secp256k1_ge_storage* table) {
+    int j;
+    int i;
+
+    fprintf(fp, "const secp256k1_ge_storage %s[ECMULT_TABLE_SIZE(WINDOW_G)] = {\n", name);
+    fprintf(fp, " S(%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32
+                  ",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32")\n",
+                SECP256K1_GE_STORAGE_CONST_GET(table[0]));
+
+    j = 1;
+    for(i = 3; i <= window_g; ++i) {
+        fprintf(fp, "#if WINDOW_G > %d\n", i-1);
+        for(;j < ECMULT_TABLE_SIZE(i); ++j) {
+            fprintf(fp, ",S(%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32
+                          ",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32")\n",
+                        SECP256K1_GE_STORAGE_CONST_GET(table[j]));
+        }
+        fprintf(fp, "#endif\n");
+    }
+    fprintf(fp, "};\n");
+}
+
+static void print_two_tables(FILE *fp, int window_g) {
+    secp256k1_ge_storage* table = malloc(ECMULT_TABLE_SIZE(window_g) * sizeof(secp256k1_ge_storage));
+    secp256k1_ge_storage* table_128 = malloc(ECMULT_TABLE_SIZE(window_g) * sizeof(secp256k1_ge_storage));
+
+    secp256k1_ecmult_compute_two_tables(table, table_128, window_g, &secp256k1_ge_const_g);
+
+    print_table(fp, "secp256k1_pre_g", window_g, table);
+    print_table(fp, "secp256k1_pre_g_128", window_g, table_128);
+
+    free(table);
+    free(table_128);
+}
+
+int main(void) {
+    /* Always compute all tables for window sizes up to 15. */
+    int window_g = (ECMULT_WINDOW_SIZE < 15) ? 15 : ECMULT_WINDOW_SIZE;
+    FILE* fp;
+
+    fp = fopen("src/precomputed_ecmult.c","w");
+    if (fp == NULL) {
+        fprintf(stderr, "Could not open src/precomputed_ecmult.h for writing!\n");
+        return -1;
+    }
+
+    fprintf(fp, "/* This file was automatically generated by precompute_ecmult. */\n");
+    fprintf(fp, "/* This file contains an array secp256k1_pre_g with odd multiples of the base point G and\n");
+    fprintf(fp, " * an array secp256k1_pre_g_128 with odd multiples of 2^128*G for accelerating the computation of a*P + b*G.\n");
+    fprintf(fp, " */\n");
+    fprintf(fp, "#if defined HAVE_CONFIG_H\n");
+    fprintf(fp, "#    include \"libsecp256k1-config.h\"\n");
+    fprintf(fp, "#endif\n");
+    fprintf(fp, "#include \"../include/secp256k1.h\"\n");
+    fprintf(fp, "#include \"group.h\"\n");
+    fprintf(fp, "#include \"ecmult.h\"\n");
+    fprintf(fp, "#include \"precomputed_ecmult.h\"\n");
+    fprintf(fp, "#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u)\n");
+    fprintf(fp, "#if ECMULT_WINDOW_SIZE > %d\n", window_g);
+    fprintf(fp, "   #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. Try deleting precomputed_ecmult.c before the build.\n");
+    fprintf(fp, "#endif\n");
+    fprintf(fp, "#ifdef EXHAUSTIVE_TEST_ORDER\n");
+    fprintf(fp, "#    error Cannot compile precomputed_ecmult.c in exhaustive test mode\n");
+    fprintf(fp, "#endif /* EXHAUSTIVE_TEST_ORDER */\n");
+    fprintf(fp, "#define WINDOW_G ECMULT_WINDOW_SIZE\n");
+
+    print_two_tables(fp, window_g);
+
+    fprintf(fp, "#undef S\n");
+    fclose(fp);
+
+    return 0;
+}
diff --git a/src/secp256k1/src/precompute_ecmult_gen.c b/src/secp256k1/src/precompute_ecmult_gen.c
new file mode 100644
index 00000000000..a4ec8e0dc6e
--- /dev/null
+++ b/src/secp256k1/src/precompute_ecmult_gen.c
@@ -0,0 +1,83 @@
+/*********************************************************************************
+ * Copyright (c) 2013, 2014, 2015, 2021 Thomas Daede, Cory Fields, Pieter Wuille *
+ * Distributed under the MIT software license, see the accompanying              *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.          *
+ *********************************************************************************/
+
+#include <inttypes.h>
+#include <stdio.h>
+
+#include "../include/secp256k1.h"
+
+#include "assumptions.h"
+#include "util.h"
+
+#include "group.h"
+#include "int128_impl.h"
+#include "ecmult_gen.h"
+#include "ecmult_gen_compute_table_impl.h"
+
+int main(int argc, char **argv) {
+    const char outfile[] = "src/precomputed_ecmult_gen.c";
+    FILE* fp;
+    int bits;
+
+    (void)argc;
+    (void)argv;
+
+    fp = fopen(outfile, "w");
+    if (fp == NULL) {
+        fprintf(stderr, "Could not open %s for writing!\n", outfile);
+        return -1;
+    }
+
+    fprintf(fp, "/* This file was automatically generated by precompute_ecmult_gen. */\n");
+    fprintf(fp, "/* See ecmult_gen_impl.h for details about the contents of this file. */\n");
+    fprintf(fp, "#if defined HAVE_CONFIG_H\n");
+    fprintf(fp, "#    include \"libsecp256k1-config.h\"\n");
+    fprintf(fp, "#endif\n");
+    fprintf(fp, "#include \"../include/secp256k1.h\"\n");
+    fprintf(fp, "#include \"group.h\"\n");
+    fprintf(fp, "#include \"ecmult_gen.h\"\n");
+    fprintf(fp, "#include \"precomputed_ecmult_gen.h\"\n");
+    fprintf(fp, "#ifdef EXHAUSTIVE_TEST_ORDER\n");
+    fprintf(fp, "#    error Cannot compile precomputed_ecmult_gen.c in exhaustive test mode\n");
+    fprintf(fp, "#endif /* EXHAUSTIVE_TEST_ORDER */\n");
+    fprintf(fp, "#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u)\n");
+    fprintf(fp, "const secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)] = {\n");
+
+    for (bits = 2; bits <= 8; bits *= 2) {
+        int g = ECMULT_GEN_PREC_G(bits);
+        int n = ECMULT_GEN_PREC_N(bits);
+        int inner, outer;
+
+        secp256k1_ge_storage* table = checked_malloc(&default_error_callback, n * g * sizeof(secp256k1_ge_storage));
+        secp256k1_ecmult_gen_compute_table(table, &secp256k1_ge_const_g, bits);
+
+        fprintf(fp, "#if ECMULT_GEN_PREC_BITS == %d\n", bits);
+        for(outer = 0; outer != n; outer++) {
+            fprintf(fp,"{");
+            for(inner = 0; inner != g; inner++) {
+                fprintf(fp, "S(%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32
+                            ",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32")",
+                        SECP256K1_GE_STORAGE_CONST_GET(table[outer * g + inner]));
+                if (inner != g - 1) {
+                    fprintf(fp,",\n");
+                } 
+            }
+            if (outer != n - 1) {
+                fprintf(fp,"},\n");
+            } else {
+                fprintf(fp,"}\n");
+            }
+        }
+        fprintf(fp, "#endif\n");
+        free(table);
+    }
+
+    fprintf(fp, "};\n");
+    fprintf(fp, "#undef S\n");
+    fclose(fp);
+
+    return 0;
+}
diff --git a/src/secp256k1/src/precomputed_ecmult.c b/src/secp256k1/src/precomputed_ecmult.c
new file mode 100644
index 00000000000..3e67f37b747
--- /dev/null
+++ b/src/secp256k1/src/precomputed_ecmult.c
@@ -0,0 +1,16460 @@
+/* This file was automatically generated by precompute_ecmult. */
+/* This file contains an array secp256k1_pre_g with odd multiples of the base point G and
+ * an array secp256k1_pre_g_128 with odd multiples of 2^128*G for accelerating the computation of a*P + b*G.
+ */
+#if defined HAVE_CONFIG_H
+#    include "libsecp256k1-config.h"
+#endif
+#include "../include/secp256k1.h"
+#include "group.h"
+#include "ecmult.h"
+#include "precomputed_ecmult.h"
+#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u)
+#if ECMULT_WINDOW_SIZE > 15
+   #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. Try deleting precomputed_ecmult.c before the build.
+#endif
+#ifdef EXHAUSTIVE_TEST_ORDER
+#    error Cannot compile precomputed_ecmult.c in exhaustive test mode
+#endif /* EXHAUSTIVE_TEST_ORDER */
+#define WINDOW_G ECMULT_WINDOW_SIZE
+const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = {
+ S(79be667e,f9dcbbac,55a06295,ce870b07,29bfcdb,2dce28d9,59f2815b,16f81798,483ada77,26a3c465,5da4fbfc,e1108a8,fd17b448,a6855419,9c47d08f,fb10d4b8)
+#if WINDOW_G > 2
+,S(f9308a01,9258c310,49344f85,f89d5229,b531c845,836f99b0,8601f113,bce036f9,388f7b0f,632de814,fe337e6,2a37f356,6500a999,34c2231b,6cb9fd75,84b8e672)
+#endif
+#if WINDOW_G > 3
+,S(2f8bde4d,1a072093,55b4a725,a5c5128,e88b84bd,dc619ab7,cba8d569,b240efe4,d8ac2226,36e5e3d6,d4dba9dd,a6c9c426,f788271b,ab0d6840,dca87d3a,a6ac62d6)
+,S(5cbdf064,6e5db4ea,a398f365,f2ea7a0e,3d419b7e,330e39c,e92bdded,cac4f9bc,6aebca40,ba255960,a3178d6d,861a54db,a813d0b8,13fde7b5,a5082628,87264da)
+#endif
+#if WINDOW_G > 4
+,S(acd484e2,f0c7f653,9ad178a,9f559abd,e0979697,4c57e714,c35f110d,fc27ccbe,cc338921,b0a7d9fd,64380971,763b61e9,add888a4,375f8e0f,5cc262a,c64f9c37)
+,S(774ae7f8,58a9411e,5ef4246b,70c65aac,5649980b,e5c17891,bbec1789,5da008cb,d984a032,eb6b5e19,243dd56,d7b7b365,372db1e2,dff9d6a8,301d74c9,c953c61b)
+,S(f28773c2,d975288b,c7d1d205,c3748651,b075fbc6,610e58cd,deeddf8f,19405aa8,ab0902e,8d880a89,758212eb,65cdaf47,3a1a06da,521fa91f,29b5cb52,db03ed81)
+,S(d7924d4f,7d43ea96,5a465ae3,95ff411,31e5946f,3c85f79e,44adbcf8,e27e080e,581e2872,a86c72a6,83842ec2,28cc6def,ea40af2b,d896d3a5,c504dc9f,f6a26b58)
+#endif
+#if WINDOW_G > 5
+,S(defdea4c,db677750,a420fee8,7eacf21,eb9898ae,79b97687,66e4faa0,4a2d4a34,4211ab06,94635168,e997b0ea,d2a93dae,ced1f4a0,4a95c0f6,cfb199f6,9e56eb77)
+,S(2b4ea0a7,97a443d2,93ef5cff,444f4979,f06acfeb,d7e86d27,74756561,38385b6c,85e89bc0,37945d93,b343083b,5a1c8613,1a01f60c,50269763,b570c854,e5c09b7a)
+,S(352bbf4a,4cdd1256,4f93fa33,2ce33330,1d9ad402,71f81071,81340aef,25be59d5,321eb407,5348f534,d59c1825,9dda3e1f,4a1b3b2e,71b1039c,67bd3d8b,cf81998c)
+,S(2fa2104d,6b38d11b,2300105,59879124,e42ab8df,eff5ff29,dc9cdadd,4ecacc3f,2de1068,295dd865,b6456933,5bd5dd80,181d70ec,fc882648,423ba76b,532b7d67)
+,S(9248279b,9b4d68d,ab21a9b0,66edda83,263c3d84,e09572e2,69ca0cd7,f5453714,73016f7b,f234aade,5d1aa71b,dea2b1ff,3fc0de2a,887912ff,e54a32ce,97cb3402)
+,S(daed4f2b,e3a8bf27,8e70132f,b0beb752,2f570e14,4bf615c0,7e996d44,3dee8729,a69dce4a,7d6c98e8,d4a1aca8,7ef8d700,3f83c230,f3afa726,ab40e522,90be1c55)
+,S(c44d12c7,65d812e,8acf28d7,cbb19f90,11ecd9e9,fdf281b0,e6a3b5e8,7d22e7db,2119a460,ce326cdc,76c45926,c982fdac,e106e86,1edf61c5,a039063f,e0e6482)
+,S(6a245bf6,dc698504,c89a20cf,ded60853,152b6953,36c28063,b61c65cb,d269e6b4,e022cf42,c2bd4a70,8b3f5126,f16a24ad,8b33ba48,d0423b6e,fd5e6348,100d8a82)
+#endif
+#if WINDOW_G > 6
+,S(1697ffa6,fd9de627,c077e3d2,fe541084,ce13300b,bec1146,f95ae57f,d0bd6a5,b9c398f1,86806f5d,27561506,e4557433,a2cf1500,9e498ae7,adee9d63,d01b2396)
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+,S(62d14dab,4150bf49,7402fdc4,5a215e10,dcb01c35,4959b10c,fe31c7e9,d87ff33d,80fc06bd,8cc5b010,98088a19,50eed0db,1aa1329,67ab4722,35f56424,83b25eaf)
+,S(80c60ad0,40f27da,de5b4b06,c408e56b,2c50e9f5,6b9b8b42,5e555c2f,86308b6f,1c38303f,1cc5c30f,26e66bad,7fe72f70,a65eed4c,be7024eb,1aa01f56,430bd57a)
+,S(7a9375ad,6167ad54,aa74c634,8cc54d34,4cc5dc94,87d84704,9d5eabb0,fa03c8fb,d0e3fa9,eca87269,9559e0d,79269046,bdc59ea1,c70ce2b,2d499ec,224dc7f7)
+,S(d528ecd9,b696b54c,907a9ed0,45447a79,bb408ec3,9b68df50,4bb51f45,9bc3ffc9,eecf4125,3136e5f9,9966f218,81fd656e,bc434540,5c520dbc,63465b5,21409933)
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+,S(77f23093,6ee88cbb,d73df930,d64702ef,881d811e,e1498e2,f1c13eb1,fc345d74,958ef42a,7886b640,a08266e,9ba1b378,96c95330,d97077cb,be8eb3c7,671c60d6)
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+,S(463b3d9f,662621fb,1b4be8fb,be252012,5a216cdf,c9dae3de,bcba4850,c690d45b,5ed430d7,8c296c35,43114306,dd8622d7,c622e27c,970a1de3,1cb377b0,1af7307e)
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+,S(2600ca4b,282cb986,f85d0f17,9979d8b,44a09c07,cb86d7c1,24497bc8,6f082120,4119b887,53c15bd6,a693b03f,cddbb45d,5ac6be74,ab5f0ef4,4b0be947,5a7e4b40)
+,S(7635ca72,d7e8432c,338ec53c,d12220bc,1c48685,e24f7dc8,c602a774,6998e435,91b6496,9489d61,3d1d5e59,f78e6d7,4ecfc061,d57048ba,d9e76f30,2c5b9c61)
+,S(754e3239,f325570c,dbbf4a87,deee8a66,b7f2b334,79d468fb,c1a50743,bf56cc18,673fb86,e5bda30f,b3cd0ed3,4ea49a0,23ee33d0,197a695d,c5d9809,3c536683)
+,S(e3e6bd10,71a1e96a,ff57859c,82d570f0,33080066,1d1c952f,9fe26946,91d9b9e8,59c9e0bb,a394e76f,40c0aa58,379a3cb6,a5a22839,93e90c41,67002af4,920e37f5)
+#endif
+#if WINDOW_G > 7
+,S(186b483d,56a0338,26ae73d8,8f732985,c4ccb1f3,2ba35f4b,4cc47fdc,f04aa6eb,3b952d32,c67cf77e,2e17446e,204180ab,21fb8090,895138b4,a4a797f8,6e80888b)
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+,S(5edd5cc2,3c51e87a,497ca815,d5dce0f8,ab52554f,849ed899,5de64c5f,34ce7143,efae9c8d,bc141306,61e8cec0,30c89ad0,c13c66c0,d17a2905,cdc706ab,7399a868)
+,S(290798c2,b6476830,da12fe02,287e9e77,7aa3fba1,c355b17a,722d362f,84614fba,e38da76d,cd440621,988d00bc,f79af25d,5b29c094,db2a2314,6d003afd,41943e7a)
+,S(af3c423a,95d9f5b3,54754ef,a150ac39,cd29552f,e3602573,62dfdece,f4053b45,f98a3fd8,31eb2b74,9a93b0e6,f35cfb40,c8cd5aa6,67a15581,bc2feded,498fd9c6)
+,S(766dbb24,d134e745,cccaa28c,99bf2749,6bb66b2,6dcf98df,8d2fed50,d884249a,744b1152,eacbe5e3,8dcc8879,80da38b8,97584a65,fa06cedd,2c924f97,cbac5996)
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+,S(d3cc30ad,6b483e4b,c79ce2c9,dd8bc549,93e947eb,8df787b4,42943d3f,7b527eaf,8b378a22,d827278d,89c5e9be,8f9508ae,3c2ad462,90358630,afb34db0,4eede0a4)
+,S(1624d847,80732860,ce1c78fc,bfefe08b,2b29823d,b913f649,3975ba0f,f4847610,68651cf9,b6da903e,914448c,6cd9d4ca,896878f5,282be4c8,cc06e2a4,4078575)
+,S(733ce80d,a955a8a2,6902c956,33e62a98,5192474b,5af207da,6df7b4fd,5fc61cd4,f5435a2b,d2badf7d,485a4d8b,8db9fcce,3e1ef8e0,201e4578,c54673bc,1dc5ea1d)
+,S(15d94412,54945064,cf1a1c33,bbd3b49f,8966c509,2171e699,ef258dfa,b81c045c,d56eb30b,69463e72,34f5137b,73b84177,434800ba,cebfc685,fc37bbe9,efe4070d)
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+,S(e22fbe15,c0af8ccc,5780c073,5f84dbe9,a790bade,e8245c06,c7ca3733,1cb36980,a855bab,ad5cd60c,88b430a6,9f53a1a7,a3828915,4964799b,e43d06d7,7d31da06)
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+,S(494f4be2,19a1a770,16dcd838,431aea00,1cdc8ae,7a6fc688,726578d9,702857a5,42242a96,9283a5f3,39ba7f07,5e36ba2a,f925ce30,d767ed6e,55f4b031,880d562c)
+,S(a598a803,da6d86c,6bc7f2f5,144ea549,d28211ea,58faa70e,bf4c1e66,5c1fe9b5,204b5d6f,84822c30,7e4b4a71,40737aec,23fc63b6,5b35f86a,10026dbd,2d864e6b)
+,S(c4191636,5abb2b5d,9192f5f,2dbeafec,208f020f,12570a18,4dbadc3e,58595997,4f14351,d0087efa,49d245b3,28984989,d5caf945,f34bfc0,ed16e96b,58fa9913)
+,S(841d6063,a586fa47,5a724604,da03bc5b,92a2e0d2,e0a36acf,e4c73a55,14742881,73867f5,9c0659e8,1904f9a1,c7543698,e62562d6,744c169c,e7a36de0,1a8d6154)
+#endif
+#if WINDOW_G > 8
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+,S(1e33f1a7,46c9c577,8133344d,9299fcaa,20b0938e,8acff254,4bb40284,b8c5fb94,6066025,7dd11b3a,a9c8ed61,8d24edff,2306d320,f1d03010,e33a7d20,57f3b3b6)
+,S(85b7c1dc,b3cec1b7,ee7f30de,d79dd20a,ed1f4cc,18cbcfcf,a410361f,d8f08f31,3d98a9cd,d026dd43,f39048f2,5a8847f4,fcafad18,95d7a633,c6fed3c3,5e999511)
+,S(29df9fbd,8d9e4650,9275f4b1,25d6d45d,7fbe9a3b,878a7af8,72a28006,61ac5f51,b4c4fe9,9c775a60,6e2d8862,179139ff,da61dc86,1c019e55,cd2876eb,2a27d84b)
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+#endif
+#if WINDOW_G > 9
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+#endif
+#if WINDOW_G > 10
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+#endif
+#if WINDOW_G > 11
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+#endif
+#if WINDOW_G > 12
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+#endif
+#if WINDOW_G > 13
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+#endif
+#if WINDOW_G > 14
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+,S(20990660,f1055420,b885fb0a,38824740,3b141c37,5aa20dce,8a29191a,e77bbb16,7d434476,9e302e38,9e14c02e,f5fd8a5c,64cfcf3d,e9813f1c,f53bc6d3,4da93559)
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+#endif
+};
+const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)] = {
+ S(8f68b9d2,f63b5f33,9239c1ad,981f162e,e88c5678,723ea335,1b7b444c,9ec4c0da,662a9f2d,ba063986,de1d90c2,b6be215d,bbea2cfe,95510bfd,f23cbf79,501fff82)
+#if WINDOW_G > 2
+,S(38381dbe,2e509f22,8ba93363,f2451f08,fd845cb3,51d954be,18e2b8ed,d23809fa,e4a32d0a,fb917dc,b09405a5,520eb1cc,3681fccb,32d8f24d,bd707518,331fed52)
+#endif
+#if WINDOW_G > 3
+,S(49262724,e4372ae6,f6921b82,aa4699a1,f186aea5,40122630,3ea42648,97c2a310,1337e773,bca7abf9,5a2cfa56,9714303b,6d163612,a75ff8ce,c41b681,5e27ded0)
+,S(e306568c,1a240c90,d5e253b3,e477e2f8,4dcc1a56,ff06db8d,1384b079,cebd2d31,eac6fe3,78934260,888f2b10,7f7d0db6,ffbc8042,be373826,692b4083,92546e44)
+#endif
+#if WINDOW_G > 4
+,S(3b9e100e,2428cefc,271b0e76,23fbd633,74ebf8d9,aab41dd9,c530c39e,363136b0,fafb9815,2d16bb71,df1533eb,8f475b26,a2ae28a3,3ad31f81,953ec16f,6cdbbc8a)
+,S(bb0aad49,712ac9a9,2b76ca80,f5dedef7,17ca0768,8107beee,9608f047,2f485d3f,ea699c53,c5835479,8ecd201f,7297da34,895a5afa,31670bff,e7939250,3ca2f975)
+,S(79090ac8,e4eefcc0,d4e8eb19,7afe0113,e1e58b4d,b01123de,4aeed33a,36718dc9,eaab722b,91905b8f,13d816cb,cd9aaa56,dd36afb7,ba9008b,963322b1,1cfae7c5)
+,S(e77c81ad,e9f97b55,1c03dbbc,e549ba66,8dd71de7,cd775ad2,a269694c,7f60c7d1,3acf1478,eef81321,c5fc3b32,3ea81543,631470f7,1c2986d3,4ec581f2,82d72449)
+#endif
+#if WINDOW_G > 5
+,S(de2b5ce9,dbce511c,f2d8878e,3ded87cc,3d633dae,a2d45341,501fb3a4,55ccf6b0,f10576f3,d3c3e0e1,bbf717e9,8b1a3744,65b8c45a,c66318bb,34829eb7,11100666)
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+,S(d0803b78,39ab48a3,8475bdcc,f9a9f219,5759c343,dbbf8e93,23e1f882,5be6a5d9,2cc3b180,ff29c97e,a12ec15f,b38bafa4,4ecf06c,e51d1d24,2894a926,64582f0b)
+,S(1f56f096,b18a7499,a153a5ae,acf8be05,8496dd23,da8e6c19,215628fb,c0567ed0,fef22b8a,3b52f490,83004436,b65cd69,c94189f4,1a93c0d5,1fc13cb4,379dff58)
+,S(1d9f69b1,a4a47432,e386f525,234aa30,79e947cf,cf203297,4e0fc05b,638e213b,d898ec17,949c0761,b38500c3,a2b1da24,5438d5b3,d3f6f720,41f15d6e,e4d4ccbb)
+#endif
+#if WINDOW_G > 6
+,S(128c913,4d9dcb78,12fc4361,5c67ad0,55213354,dc8008b1,aeb5a9dc,fb629efd,fee3e54a,dd152610,d9725936,99d662,c160c8e4,ec6f76e4,5ff41818,be67c96)
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+,S(688f5202,fb9d8bc0,9e480e89,4c7cfc74,761c3be7,7dafb11c,58422836,3e331cc5,96ba7d59,63b541a7,2ec7cabd,92403434,1a393eaf,89eebd94,62d9c218,c7302cd3)
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+#endif
+#if WINDOW_G > 7
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+#endif
+#if WINDOW_G > 8
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+#endif
+#if WINDOW_G > 10
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+#endif
+#if WINDOW_G > 12
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+#endif
+#if WINDOW_G > 13
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+#endif
+#if WINDOW_G > 14
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+,S(858b019c,8a93524f,6c86738d,cb10b534,d8caaf86,5c0ce75c,fc9b83b0,7c661a0a,7c59d30,1ffc8ce1,b0767ed7,91f84bc5,60bb8ca,ed3464ba,698a53c,160ec570)
+,S(e1e217b8,69da0c77,599dcc38,40fa1d8c,a8d08b1a,4ac9a882,da1476cc,cc76fa56,83f0ef77,905f0801,4bd86e17,63b8c2cf,ab2018a8,9586620a,b49a15,9fc314ca)
+,S(15a1ae40,b4fc51dc,554b75d4,db0c2bfd,62dfbbfc,dede18e1,4edbb689,91525cff,4f0453b7,e4e0e99d,9663e5c6,bb018007,b52c8e14,d78a28d,c4a888e4,8c4326c2)
+,S(1b9a142f,fc4d03ea,4b079f2d,b05fad98,8ddb2d32,b359967f,c173801f,63320825,59bda7ed,5b691c20,4fc8f8ac,f53be298,ae628954,a8134d0f,dd097e67,be9ff9b6)
+#endif
+};
+#undef S
diff --git a/src/secp256k1/src/precomputed_ecmult.h b/src/secp256k1/src/precomputed_ecmult.h
new file mode 100644
index 00000000000..949b62c874b
--- /dev/null
+++ b/src/secp256k1/src/precomputed_ecmult.h
@@ -0,0 +1,35 @@
+/*****************************************************************************************************
+ * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor *
+ * Distributed under the MIT software license, see the accompanying                                  *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.                              *
+ *****************************************************************************************************/
+
+#ifndef SECP256K1_PRECOMPUTED_ECMULT_H
+#define SECP256K1_PRECOMPUTED_ECMULT_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include "group.h"
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#if EXHAUSTIVE_TEST_ORDER == 13
+#        define WINDOW_G 4
+#    elif EXHAUSTIVE_TEST_ORDER == 199
+#        define WINDOW_G 8
+#    else
+#        error No known generator for the specified exhaustive test group order.
+#    endif
+static secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)];
+static secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)];
+#else /* !defined(EXHAUSTIVE_TEST_ORDER) */
+#    define WINDOW_G ECMULT_WINDOW_SIZE
+extern const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)];
+extern const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)];
+#endif /* defined(EXHAUSTIVE_TEST_ORDER) */
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_PRECOMPUTED_ECMULT_H */
diff --git a/src/secp256k1/src/precomputed_ecmult_gen.c b/src/secp256k1/src/precomputed_ecmult_gen.c
new file mode 100644
index 00000000000..d67291fcf50
--- /dev/null
+++ b/src/secp256k1/src/precomputed_ecmult_gen.c
@@ -0,0 +1,9750 @@
+/* This file was automatically generated by precompute_ecmult_gen. */
+/* See ecmult_gen_impl.h for details about the contents of this file. */
+#if defined HAVE_CONFIG_H
+#    include "libsecp256k1-config.h"
+#endif
+#include "../include/secp256k1.h"
+#include "group.h"
+#include "ecmult_gen.h"
+#include "precomputed_ecmult_gen.h"
+#ifdef EXHAUSTIVE_TEST_ORDER
+#    error Cannot compile precomputed_ecmult_gen.c in exhaustive test mode
+#endif /* EXHAUSTIVE_TEST_ORDER */
+#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u)
+const secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)] = {
+#if ECMULT_GEN_PREC_BITS == 2
+{S(3a9ed373,6eed3eec,9aeb5ac0,21b54652,56817b1f,8de6cd0,fbcee548,ba044bb5,7bcc5928,bdc9c023,dfc663b8,9e4f6969,ab751798,8e600ec1,d242010c,45c7974a),
+S(e44d7675,c3cb2857,4e133c01,a74f4afc,5ce684f8,4a789711,603f7c4f,50abef58,25bcb62f,fe2e2ce2,196ad86c,a006e20,8c64d21b,b25320a3,b5574b9c,1e1bfb4b),
+S(6ada98a4,8118166f,e7082591,d6cda51e,914b60b1,49696270,3350249b,ee8d4770,c234dfad,f3847877,a0a7bcda,112dba85,1cdddf00,84d0c07,df1d1a,a3ec3aeb),
+S(a94ae8,63264dfb,b910ea95,4ce9ca7e,4f86f92d,9f3a95d1,ed61552a,7a3f5743,7f53f7f1,6ad2d08f,15e73314,6d80467,41557acf,19556c0f,ed7117ce,37040823)},
+{S(1b8462eb,1ccdf7b2,b8372f2f,cec1f479,ab07c09f,cb26d6c3,965ec73,4d654f81,62f6755,b4a7891d,55de6427,fbc37d33,e4eea418,a2c04392,a3d11807,ccc9025),
+S(c3b55f99,9cd9113c,fcb4f29,be00c785,cc70d1c1,f1cfd0ed,593abe8d,260bd2bb,8945790b,5696225a,1c6a1f45,1d6b085e,cde2f332,df068271,f6279877,6d1015aa),
+S(a4b41b41,1a255142,ee62144d,96ccfdc,a3cdf5a6,af32bdd8,d1c3d26b,d6aab0b9,3ade7f6a,299ee56c,299fcaad,72a146d2,62db1dcd,2ea1a355,d6e00294,ee34c3),
+S(d4af67c6,75f97f30,4a621fe5,343dfa5b,e432d9f1,43758d4d,62df1e09,b79abfe8,d0fea700,2a851a85,33929e5f,1f41d4a9,68b9e520,6c19f3b0,35ce96a5,12b61921)},
+{S(6ae991de,18418b49,160194f,a735eb72,c299b987,1981a4f9,aa717ad2,bcdcf13,7ee8011a,40f384f2,e50add2d,97005173,2787cc7c,89dafb66,301bc94d,24b913f),
+S(c28203a6,e0f93259,778bddca,10f994be,67cec8a3,109d0001,d830a8e7,b452794b,18df3a42,ec24b713,2ac4b6ec,dd7605e4,169aa07a,41d7559e,bde808d9,bbfbcb14),
+S(4848adb6,b0350cd7,b745b603,cff69deb,8be10519,cc02881c,4b980157,5635aa37,7a814076,187ed7b9,84d0be65,b2f83b90,325441cf,54325183,beb01136,d626ca5c),
+S(515d497f,f274da3d,9bb9e4f7,e1b77e8a,af859d52,be7c7e93,f197267,d73ce5ae,da648754,a5ed476,3fad55e1,e93f9687,2d1fe961,b448b9bf,2c42c885,b44678f0)},
+{S(64850a04,76870a44,2cfa57e0,4e4707f7,eccc5e99,12dbcb07,3b457317,717f5686,7c5facd2,91a6defb,a1837cb9,3bcbd0f5,bc37572e,68ccb2a0,c062a155,46656fcc),
+S(c3ae412c,a3e5f22b,44863ab1,b5e64719,99078ac0,d5844d9,6a37899f,3e064475,e491d89e,b38b0443,50d96e01,7baceb35,fa0e247,8c982d25,5a2a332c,239e0a54),
+S(e72c3804,a774f3db,42348883,297b5035,c9dd3970,7e3bc60d,1e51e41,d7d8e395,e3cb5abb,c3c259ab,2c9e5,fa059c10,fe6f633b,4f99da29,61b9117e,61fbb457),
+S(6a7b9de1,8d16a0e2,1b30cb61,3586ebc6,78b60618,e2b45e2d,8c94ad09,36227f74,ac1fb735,266d34,eb995f8f,91cbc339,f63b6e6,bd4c89f0,d7607908,75a4918f)},
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+S(6ff70715,17bdc2a4,c0267caa,38ca96ad,8a235744,2a24db87,a07cdec6,c3b022fa,2f16b295,a2db7a6d,321280c3,a53dfcf4,674dc215,38e2a556,75cd37e5,d3ee7362),
+S(b5619c5e,edbc92f0,c88a9cad,9955a08b,764dd683,361bb7f2,8c611857,d473c45b,11f6864b,36116181,d2af3f6c,fe738c84,7820ebe1,53f0c82b,14e5c67a,b3a2213e)},
+{S(c7452697,d7691662,ae3b754c,7be11df8,ac70cc8c,e2e80a9b,9638b0f2,a323ecd5,fe84e963,3231caac,63a5c7cc,90cef693,a69ea140,c846e1b3,b96a6fc6,68b43c68),
+S(c797ca59,95cda70a,a33093bc,4f7f83c6,1a31ab1e,dbd6f10d,31e0da05,64f41407,ce4a64f9,ae7eef1b,7abfad94,f4a6a7f1,c746268e,9006995e,8f7d311,1b81f85e),
+S(288a2e26,8fb8fb28,29bd9d21,4ec5860b,fc1ed577,f40c6184,79a0b921,c2f4b67a,8343d03d,556bfee4,b66ca598,f4fecbcb,aa2723c2,f3c35203,ee12710d,d9ff0b52),
+S(7aa02a72,adefd779,fd994c77,697ee142,dd25d168,38c8b8a0,5178b7e7,37f33032,a060f7d4,8e0c2929,864208a7,1668129b,3b3908c3,7e89ba0,e7e55aa6,5e3ed98e)},
+{S(34925d1a,b1c7c081,e945d66d,60ed394e,f474e38a,423562b3,95bc51d4,c4f55321,8ef8dd58,ae1661b5,a7c327ba,ac4105e6,d02d6a30,2263c5f8,62b712fa,b064e562),
+S(2bbf19eb,9a6211a,7881c7e0,5483a318,c9d91280,d09e0634,2a54a9f2,b5654be8,3cf7b41,bfab218d,e182cf34,32450abf,88da1e16,fdb79699,ecfeb962,39d422d3),
+S(97f1b30a,6ce2dd8e,1d0358fb,45b432fe,be6d9916,34ecc7a4,b7cb4f3c,f1663fb8,c7cba22b,88a5f5c4,498f0f22,cea6830e,1bb44e1c,7f9d9833,60139c2e,97dab7da),
+S(b5d0e718,621a0a40,c2adf34a,3e1e64d6,bbad3598,e6944436,f8f87450,575d61ef,2e43eb70,8fb8e2a0,f24a1a12,7a890c07,d79b51d,60e3a281,649afa3c,182d5b77)},
+{S(463080f9,19ecd42f,593dc20a,2d3160cc,74d9592e,446f299d,be5446f4,236a5b17,2a65200d,e1b16975,9d5c75d6,fa6c666,ba45728d,343d6339,48233391,60c14a16),
+S(547eef23,516851a2,2f160ec0,781a49f1,1480d07d,2607ab5a,89656c94,2f774b5a,eb6f249d,ee624cae,cbc59f02,63da0fcc,e33a515c,843c3632,661f13e4,39c4f0e4),
+S(77f0c9a2,51d48b39,62f92e2a,679fd9cc,f458f17a,edf588be,d4bd6448,47f9306f,355f4827,b10e614b,4590242b,da546e53,dbd419de,1d1a7fa3,208d9350,3496db0c),
+S(81e606c1,19b6ef80,418aa008,7ebaf9d3,7adff1ff,a81f739a,172a580b,27c7545c,ddb0404c,e56113c5,93920382,6d2adab2,6590b509,45865406,ce1fd256,6565209a)},
+{S(92d469ed,e0969dd6,7e9d7b31,f0f703e3,97cad53b,e6101b2e,eeb8714d,645eaa9c,24a0a786,916297f4,6a53c7c2,29a3c95,80eec521,355b823,f0488460,39595dd2),
+S(e5035341,5c49c24d,f672a74e,4eb2d108,57fa987a,afc50178,ffba8797,5503006f,38522661,fe682984,7b6dda61,9dbbe47b,35c0c9eb,b79b5d2f,2c6ba882,26cb95d4),
+S(d0777020,cf6dc469,cf020ce5,e64bc2e4,1e2bf116,4f4e814f,18bbbc4f,f468b0b8,997b2163,c4670401,281ad84b,a914cbe4,e76a5cb1,cb90c1bd,ecdac585,621cb0a6),
+S(881abd9c,717f0a2,360de50d,66a9b655,b9459e62,80a985da,e811f2b2,154e307a,beec571,1375031f,354dda5c,b9d8377d,1cb49816,1f4c738d,f6b9d323,f9acacd)},
+{S(ab7d18ba,955fdaaa,b1a0bb25,25844e2a,9d2e204d,ff224588,ae96c41,e690e010,4e0090b1,dcd619c3,10ff5027,9c534612,84ec2467,77b63179,c80724c4,42d00204),
+S(1a5982e3,37e3eb50,e679f24e,c3473b4d,1af3dcbe,ac3c7a96,a95f51f9,a9875266,dca6c614,85d55985,1fdc229,56ee59cd,fac74069,6276299b,a199f39c,869e5c9c),
+S(bcdf870f,8d5394b4,f1f3446c,a25ec6d,5b4c939,b598e596,814a6dda,a054bb2f,71cfbdd,d1aa7722,892f83e4,ea2dec50,81c4d14e,548a16c4,2818b76d,5721fb7c),
+S(cb28eeda,338a5088,db505da,949cddf2,741e071e,378f92f1,dbba270e,9c322c57,d98cba61,cceca53f,7d84d71f,f892b962,6f26e156,841d2dfb,7aaab839,3f515903)}
+#endif
+#if ECMULT_GEN_PREC_BITS == 4
+{S(3a9ed373,6eed3eec,9aeb5ac0,21b54652,56817b1f,8de6cd0,fbcee548,ba044bb5,7bcc5928,bdc9c023,dfc663b8,9e4f6969,ab751798,8e600ec1,d242010c,45c7974a),
+S(e44d7675,c3cb2857,4e133c01,a74f4afc,5ce684f8,4a789711,603f7c4f,50abef58,25bcb62f,fe2e2ce2,196ad86c,a006e20,8c64d21b,b25320a3,b5574b9c,1e1bfb4b),
+S(6ada98a4,8118166f,e7082591,d6cda51e,914b60b1,49696270,3350249b,ee8d4770,c234dfad,f3847877,a0a7bcda,112dba85,1cdddf00,84d0c07,df1d1a,a3ec3aeb),
+S(a94ae8,63264dfb,b910ea95,4ce9ca7e,4f86f92d,9f3a95d1,ed61552a,7a3f5743,7f53f7f1,6ad2d08f,15e73314,6d80467,41557acf,19556c0f,ed7117ce,37040823),
+S(b692c750,d23d3674,c351e3b7,e1a8a87b,14a5df81,852eaf35,209d0ec5,6e22a2cf,b18c4f17,252db89f,838de32f,b3340ea2,bb961a39,54b38c47,f9a8219c,4820a0cb),
+S(691fc741,80e75b55,47b375f1,1bf60abe,451d27de,1743a436,5f8e4bac,ad421c09,8eb5fd9d,f3c03240,6cebf370,8125955f,bf2ef703,475d3fd6,1a0291b6,69b52d9d),
+S(703b5f14,a7d82473,1196b52f,ae9ca8cb,b245b004,7a9928d7,d0c42f33,391411dc,5ed74eaa,49f276c0,4d61f31b,6da4137c,bde5673d,8e3f815d,efea7951,f88585c),
+S(29b8ec47,d241eda1,e51bbb1e,3928444c,3747b4fe,7cecb365,2bbc4587,2f504875,88693238,8562f8bf,f7d72324,62ebc54,6b93a95f,77936b02,eb1cd6a7,d4199bcb),
+S(444a07ad,e81916c9,32bdeec2,21c556c4,6b7f6491,e99b479,2cfec82f,4ec17910,2e084c2f,eead5200,77c151b6,eff9375a,713b9d15,5306708d,b3f538e1,8eb18cf),
+S(e0dd618b,226ceddc,f560527e,20b4fe58,e5fcf28,39911ea6,c3e8a4a7,e15f9121,a063a157,3377bbbf,1b9a5ebe,afbe11aa,660c1e65,df1392b8,97205858,3c86a3fc),
+S(9b99461a,2e8360f2,f2ba0bb8,bcaeb699,159e0652,69d9042a,fa0c4e30,a7b6f30d,3fe7fe04,3cb45303,3d4f5560,7d41cd76,9036a49b,82912350,6d8b9995,254154fd),
+S(504da3a9,d9d9c81b,c2065398,4ed28cb1,b5beec9b,6ce5dfb6,cea94e54,fdff044b,cbd40d1e,858133c9,cd20b9e4,ff9fe94,f7cc9579,39e6df49,7a6bd702,797f96cf),
+S(ddec0aac,1ebce6aa,ad6300d5,60f0e503,829f0bc6,479641f9,b19d9f6,484376fb,332ff5b1,fc83085e,736736bf,3c265e4c,8f80925e,6f38479d,6563bc34,e5faea1),
+S(dc530ceb,b82c246e,41c522f1,d2571d31,4b14edf3,91577a2b,64e42172,b23562c1,563ddd93,857d6529,8b81de24,19e5cede,7a4c5b7,a2fe98f6,9efb8906,6f32a98a),
+S(7604d60f,418dd132,78058942,fb2d2153,c0a2bfeb,e83c5011,a451bcb1,58db0773,38be14ae,d9e1c404,63ef92bd,d62c599a,b37625a8,182a3763,4fa2de90,535d50a9),
+S(cb896744,77b20829,f5e2bd42,8852c70b,91cbd0af,cadf219,a69727b4,cbec8d7a,5710d17a,20ea0dff,980d3f06,38d8b910,b8940d00,dd4a323f,d777d942,213e1093)},
+{S(1b8462eb,1ccdf7b2,b8372f2f,cec1f479,ab07c09f,cb26d6c3,965ec73,4d654f81,62f6755,b4a7891d,55de6427,fbc37d33,e4eea418,a2c04392,a3d11807,ccc9025),
+S(f6fa4c02,1b697e93,ae34145b,481a3ac7,462343dc,6022040f,834dd9d2,c69b5d,5de5e04b,351f9928,b84abaed,d3319e61,ea91fc59,8d6fcac3,401d1ae7,c08943e),
+S(cf805a58,d8f9b414,aa73cd0c,e545c9af,3f7d6543,8ae57688,81d30866,e81242d4,f455c617,99a2ca5c,fac3eb6f,23282774,7c9e914e,fce447ad,8fd71ffc,4fc3306b),
+S(48dbd9a5,88d1f02d,6eacc5a6,36c0fb4f,de87eb44,11329442,1265b0ff,a72e473,9a206d25,5dc1d916,e3b1e301,cab1bd91,ea29eb7e,979c0b84,608ed770,4af325d0),
+S(ceb3637b,28997733,ad6ef0dd,5004e32,9c87981b,e6d811a3,88804884,652780d4,6aed5e97,c0e836b2,73a309fc,5d389779,1f6f0bc9,246921ef,5fa9767f,dacac3f5),
+S(8940dca2,52ebefad,61db720b,e709c749,7302b5e1,a4174893,9626910c,43708a18,e1b0d7be,1e36c585,8bc6125f,7fd5c423,5e643f7f,11668026,c1536e9d,f6305efd),
+S(aa33c3cb,bb97ccee,5b8f452f,6a615900,392d78f5,b8c1f022,5266b8c,cb3449e0,e9ba50b4,7d3e3279,2253e925,5261f2f8,263c30dc,e613ea9e,737c3b92,8c8e3eef),
+S(39f3965d,b455a466,930e5e82,ef214452,ef5c9019,bd805fe9,67fd362d,193a1b2a,8f69a32b,35bd6f1b,c5ada308,f61550b1,534c07b0,1a3465f0,564ed6d,a8f443c1),
+S(6725d4a6,a827fef7,a0fb0214,900f526c,e23cc0b4,a6e291d0,ccb96ad9,e77393cd,69f91bac,b09facdd,b55fb70e,68164028,a8cf1bbc,207653c2,d898992f,89244f35),
+S(3b71b2f,84d355f4,d246a57e,b235e396,ee236c57,d6ab3a46,f89b5d3c,1a911c1a,7616be06,59e5b42,9f105499,38d17654,c605f81a,e4bdf2b7,b9c1817b,c8db03b3),
+S(a346e9c5,d8cc2ce1,1a733026,3136d92c,925f1b22,b27d3037,d9c4b109,9a06ecb6,4a3fd930,54f0cfa,6799e236,add0f928,6e45b77d,cef57797,7dcdac63,485c4f00),
+S(8e3c768a,ee07f0aa,3eaa43e3,f6986805,b7829c50,d67861c0,c75ab390,5a6fb794,33d3c292,7a9e9c54,a671788a,fc0ec58d,cc2a0574,a172665e,347690d7,50de0acd),
+S(b231176e,d39a928f,76a60397,79643e94,d5e75d17,238487be,f9b38b60,748711c3,3ae1ccae,204fb13d,74705b0b,8a0689eb,aea16e8e,c2f3d5db,177609ec,64027f0d),
+S(8afbe02e,161ed971,44075da2,cea389b2,f53562d2,dc771d3f,9405259c,fe4232da,e2c16621,f38a0831,d2839585,9cbceb53,254398ef,b58308cc,bcf3d79,ee0af228),
+S(1a263c8,c2c9080b,b0d4d61a,bb5d6b55,e6a7f520,80ef3f36,706e685d,7a527957,3925a458,779c3c25,7b546b99,7399a56c,b3c0b9ca,f6c77f9,c41b708d,f831253e),
+S(35d88ae9,b1d3ee59,fe79c24e,de6cad1f,6d822f57,708ee54c,26e7495b,357e92c6,de74f353,d8115188,724c2a32,39b18661,6b8f7951,34aefc75,8e724a30,8be7f31e)},
+{S(6ae991de,18418b49,160194f,a735eb72,c299b987,1981a4f9,aa717ad2,bcdcf13,7ee8011a,40f384f2,e50add2d,97005173,2787cc7c,89dafb66,301bc94d,24b913f),
+S(22165bce,e76e1594,5b9041e5,ccdee553,eba60e4f,1ece2d9f,e0ad7440,565f2665,fe8f383b,bae7e284,d1d890bd,569ab7b3,ebe5f1bb,b60ee19e,8e8de65f,88f3ab96),
+S(a2600e0e,9265b7d8,fcc46a5,51872122,66ad5334,4ddedbf3,ac8cdf2a,b86f2b8e,d00f90a0,97fe3863,b4854dce,fa5a36e7,3f94015e,f892303f,2e5cb2c7,aefbf15),
+S(38758ff9,5cefa7c1,b7a2443a,ba29b65b,aee1fa81,5ed49595,a4ec760f,b995df1d,43bc94bf,dfff3c59,7a6e41c0,52194d41,c1601b91,792f42a,6872ded2,a5e8f4cf),
+S(57122897,d98019ae,a6dcbe99,49682895,c95471e8,d53680ac,49927e23,16abfd27,c30cb105,d9edc36c,9e237e93,2edd6bef,3d553d67,fec3a37b,fbe0ef56,a3cb6c),
+S(7b7247c7,73470f13,2477c974,7820ce4d,51dde95b,dd14923d,e31dfb13,5a8aacdf,2e7054f4,a33361a7,a4282bb2,7e738884,3a91b211,3f71e160,60fb2235,6b40ffc1),
+S(1d3f0661,13c271db,374adce9,ef0c444d,4ffbc1b2,a34b9c91,55986371,52376f68,1a4c07f3,e3752c71,f772c55b,d269f3ae,a9cb40a1,ac8a96b3,7387cd1c,bf22e864),
+S(456ada98,2bcfa52a,55018711,6926b843,82754297,9af5c113,8af21e1e,3b625071,a7141c4c,673e441e,f67ccf99,53a7a6a6,3a77432,76261717,21f581b,2893243c),
+S(b898efae,8582d8de,b315220c,dc79d2bc,1a221072,300e0971,c4a610f4,7f6b70dc,8da8b020,8d674418,5620db55,fa3cd928,be672c5c,22897030,bb5a5957,37758a8),
+S(b732f7e6,9280227d,c1f56e84,7e72989,b834be6b,f04e2e3d,ca8553b5,ded18493,9157298a,5ff6e6e4,d705efcf,7601f33f,76cd2a64,6118103d,98fa000b,8ff9ad99),
+S(9601ce19,964403b6,a58d1d51,be876199,d63755ef,91bd657a,fbfac3ef,c85c78d0,df06aeb0,517ae1da,ff3a48bd,7ecceaf5,b10ac9d9,67e7ef4,520593cf,d7502058),
+S(a95814ec,11446773,36258a94,56670207,d068d8ae,19ada794,52210f2d,bd67bc5,29d7e4b3,5e5a4300,6297f9c1,f71a6a26,118693ce,fc738fea,ccf1b873,339617b3),
+S(d3533330,c6afe33b,ae921c0f,558fe47d,b97e7711,ce98c884,3abe894,320e8926,e1be0b16,72f8ea16,b59a6b9a,20c27621,e63854cb,4efde5d8,d1da8929,4f777383),
+S(4f05f649,e8ec9fe9,f675957f,7454a89e,c020feea,217782bb,43bbed43,b0a62881,dde64c2b,255d8518,da7461c6,b160286c,5222baa5,483fd5cf,dade9ae4,96432904),
+S(1a06ead0,5ef3dcc1,a9080234,b6158fe5,681cc5ca,acebbbf2,c336ecdf,3505768b,63661e6e,816bad91,1c7bd073,a15b185,c4c7b7b0,ae440dd7,40a54286,3a86721f),
+S(e2b163f9,f1b6ad48,e8bea9d3,b199cfe,378fbd2c,8f005cdc,e5959154,b2eca0e7,30759d6c,f55f7f15,a156a705,1f702294,72b9544,ba73fa40,27839cd5,67147083)},
+{S(64850a04,76870a44,2cfa57e0,4e4707f7,eccc5e99,12dbcb07,3b457317,717f5686,7c5facd2,91a6defb,a1837cb9,3bcbd0f5,bc37572e,68ccb2a0,c062a155,46656fcc),
+S(4afd2a50,f79b1403,844523a7,e88e0156,f77f7856,8668ac7c,79d2160f,cac27acd,40346549,fb5b8450,165c2a4,c47665be,b1d31f73,1cd758ce,6c8f2b17,37a832d1),
+S(f4132840,9cd5ac7d,7a0c92f2,5e39eb57,b8fcfbd5,d535ec00,a281d3d5,1275199b,6b66ce56,99a92cf1,8f635a0,7441f0c1,3561c8d4,cb0075f8,8a1596da,b6da6d29),
+S(1a6c66d3,1a54ae12,59b709b4,c70fb434,f3347d11,7921ce06,fd4f0dbe,d211e4f4,b6438fae,74524dbe,2d03e27c,8af409ad,67af8eb6,84760c85,1e81c6af,a4cb004e),
+S(3afe6f2e,8b5f1cf4,20ba1dc9,f527c662,a3af94c3,9d0e726e,b7942a2f,c9c1a91d,892cde5,f1420590,ff801f3f,8ec2ace,69f0dd74,31ca7e7,aed14c37,c2c12492),
+S(28afcf30,a1f5079d,e6f340bc,9e616ce0,7a89b67d,4e7f0dc0,6f54fe9e,d17f1519,b7cc26ec,9a25b585,33a43369,40b6bdc0,c2462e39,2246a863,e67bdefe,1ae51be1),
+S(13980996,af67f2e4,6dc5f389,d0269d1f,39a9341d,5e941e6,b4ff7bdb,ea54cb65,37a37717,d206b584,9eb79193,96ff5af0,449f3164,4c9eb31c,f27d8a,be66c741),
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+S(93899e6f,fc291a4b,e986f938,b8b378be,bf4c3d35,f9a1bdd3,ecea5f04,d8f4bada,a19a2983,55cb62fc,43334649,1c89f26d,fbb67bc3,872f7512,9229cb73,d126293e),
+S(8fe07488,b5b173c,d530d796,a18eac08,80164c2a,ed787b05,90ac8dce,3bb120d8,829abce1,43ea8009,e4f5f481,125ca6d4,ecff3f32,577cdbf1,c054a23e,67f18b0b),
+S(10c3b093,5461407c,369494a7,631eb4a2,365b122e,ce0a6b95,7c1bdbee,387394a4,f09d69ec,925c9a43,57648509,f7db85a9,22f609cd,32b400ce,3a80567,88a74627),
+S(cfe48dfc,f5566fbd,7562ed68,576a7911,baef64f0,dc63e158,1a29bf23,3e1a058e,440c6051,19f2a948,b4b6c3a2,7e711cea,c7983d7,f4a2db9,537536db,fdebab76)},
+{S(53d772b6,b18211f7,1478e9d3,3a0c061e,2d232358,44177867,af91508d,e014f22d,b2e85a07,8160d31c,3ca32d9c,ba025904,1bea0368,d9eb13de,8af8f505,73142ed8),
+S(b9d6067c,fc26ba4a,1f5bab8e,d5f28ffc,bb6bd6,b61990c4,1b091ec8,2cba973f,532d0ab,7731c02d,91cc7e51,71b625b3,af5a605,d92d02a5,fc4cee4f,afa09ebb),
+S(e8a93ceb,3db0a4a3,9a3b768c,700fb504,652161e0,4a1d4d92,df52cd4b,83e65e38,791b967f,22543fea,9ec38e5e,a14a94cc,9d11ea8a,73ca0c13,e022d53b,f8bf1148),
+S(ac6130f7,41e1601f,5a92bb75,90a799a8,3e8ad9c,c911ed7b,7dee1bcf,da14f332,97ea5d16,d5c7e368,c7b97c2d,7283cb03,f215f79c,d1d80276,6f9923e0,ce80ce44),
+S(ac34d4c1,1d2d4ade,2f044e88,6b57cd45,c1b23550,538059c4,e9855077,4132643c,7191e155,aeb3b578,6b55db41,652e8af2,bac1f933,d6f62723,808c6172,bf0eb0aa),
+S(a7c4bafb,f1988992,1ce15754,187d41b9,eb653dd,bc97cf05,ddf449d8,c9ff734c,ccf20733,da4aab6d,81db8d5a,d3f12d1d,9cbc943,8b92165c,e83c5afa,5ee108e3),
+S(c04ba857,e758fdb0,29c02712,1671fe33,9b7184b3,50ad952e,9d234681,43f7568d,9ce5d9ca,65f96b76,b4b06f57,f34de7e3,c64a1d21,f07fd6fd,eb7d47e7,bbf4e6c8),
+S(8230e7e7,81259e58,e9b74a49,340733dc,252bef7b,5b7dc82,a4e99f0b,2998ba67,9c71921,3b3254d1,f53b4f30,d0a8e665,186e272c,d0e5d316,a7451eb3,2ac8bb3f),
+S(720c2f5f,6465d38d,3916939f,8d095657,e547cc5f,849f4a41,30485b1,2d94b5c7,8635961f,5f74d176,e4ae0ec6,e4b3b394,6d5b1766,fcb902fd,9f9bd982,2ad4e4c4),
+S(263b45ca,b3547cf1,5eca4381,3d1c402e,5c209d3e,34a288cf,182aa4a3,f04304f,3516b1f3,524bbdcc,fddd94bc,fb86a43a,27a7a78a,fcbbefdd,6692fc21,87364438),
+S(4edb7d61,a45ebb51,1fb0c220,6f16fe60,5a202976,9007c3e7,11b94889,a983d0c8,b482fee3,fe824b1a,3251cd2c,3f38ab4f,adad1fee,d398be92,58d2c81d,79b0eb36),
+S(f44c286a,b8196e25,87c225f7,2091db05,e47f18b,5b9a0b9,79d2cd3b,15441767,b7aa2018,5925845e,661ad980,a6c215d5,fd7072cb,46010930,ae64089,4c8a0af8),
+S(593f9bdd,b246bd1e,19eeaafa,17e348e,5199decc,8e63ef68,ed8bff89,bdffad48,5201d11f,a4ac67db,dd66fbaf,5c2ba20f,8bb1a6b3,18cdfbac,6b257aa8,d30dd316),
+S(823b4c96,8be9e125,262d52d9,4aaff240,55def10d,6353a347,e4248de0,7889ecb2,adfafa7a,fb1c60e,e7fb3e2e,73c66063,5a9e97e0,4a38a120,b7a81f17,7d1a6c41),
+S(8daef78b,c46e0f5f,858fd74c,68be31bd,3b474d9,6bd74deb,eeba69af,5ef3056a,15db0684,bb6d4e7f,b135a4ab,f4b81d4a,a9fc7e93,c26e3616,b7b938da,25d44a06),
+S(2b7616ca,eb608427,5a14eb53,b67a2ee3,b831fb55,6f63e0b2,e01650f6,e6900a0d,915e7dbc,62f8e349,8ffdf22d,d3604d77,bb701137,b6c36543,84cce993,c4613ca4)}
+#endif
+#if ECMULT_GEN_PREC_BITS == 8
+{S(3a9ed373,6eed3eec,9aeb5ac0,21b54652,56817b1f,8de6cd0,fbcee548,ba044bb5,7bcc5928,bdc9c023,dfc663b8,9e4f6969,ab751798,8e600ec1,d242010c,45c7974a),
+S(e44d7675,c3cb2857,4e133c01,a74f4afc,5ce684f8,4a789711,603f7c4f,50abef58,25bcb62f,fe2e2ce2,196ad86c,a006e20,8c64d21b,b25320a3,b5574b9c,1e1bfb4b),
+S(6ada98a4,8118166f,e7082591,d6cda51e,914b60b1,49696270,3350249b,ee8d4770,c234dfad,f3847877,a0a7bcda,112dba85,1cdddf00,84d0c07,df1d1a,a3ec3aeb),
+S(a94ae8,63264dfb,b910ea95,4ce9ca7e,4f86f92d,9f3a95d1,ed61552a,7a3f5743,7f53f7f1,6ad2d08f,15e73314,6d80467,41557acf,19556c0f,ed7117ce,37040823),
+S(b692c750,d23d3674,c351e3b7,e1a8a87b,14a5df81,852eaf35,209d0ec5,6e22a2cf,b18c4f17,252db89f,838de32f,b3340ea2,bb961a39,54b38c47,f9a8219c,4820a0cb),
+S(691fc741,80e75b55,47b375f1,1bf60abe,451d27de,1743a436,5f8e4bac,ad421c09,8eb5fd9d,f3c03240,6cebf370,8125955f,bf2ef703,475d3fd6,1a0291b6,69b52d9d),
+S(703b5f14,a7d82473,1196b52f,ae9ca8cb,b245b004,7a9928d7,d0c42f33,391411dc,5ed74eaa,49f276c0,4d61f31b,6da4137c,bde5673d,8e3f815d,efea7951,f88585c),
+S(29b8ec47,d241eda1,e51bbb1e,3928444c,3747b4fe,7cecb365,2bbc4587,2f504875,88693238,8562f8bf,f7d72324,62ebc54,6b93a95f,77936b02,eb1cd6a7,d4199bcb),
+S(444a07ad,e81916c9,32bdeec2,21c556c4,6b7f6491,e99b479,2cfec82f,4ec17910,2e084c2f,eead5200,77c151b6,eff9375a,713b9d15,5306708d,b3f538e1,8eb18cf),
+S(e0dd618b,226ceddc,f560527e,20b4fe58,e5fcf28,39911ea6,c3e8a4a7,e15f9121,a063a157,3377bbbf,1b9a5ebe,afbe11aa,660c1e65,df1392b8,97205858,3c86a3fc),
+S(9b99461a,2e8360f2,f2ba0bb8,bcaeb699,159e0652,69d9042a,fa0c4e30,a7b6f30d,3fe7fe04,3cb45303,3d4f5560,7d41cd76,9036a49b,82912350,6d8b9995,254154fd),
+S(504da3a9,d9d9c81b,c2065398,4ed28cb1,b5beec9b,6ce5dfb6,cea94e54,fdff044b,cbd40d1e,858133c9,cd20b9e4,ff9fe94,f7cc9579,39e6df49,7a6bd702,797f96cf),
+S(ddec0aac,1ebce6aa,ad6300d5,60f0e503,829f0bc6,479641f9,b19d9f6,484376fb,332ff5b1,fc83085e,736736bf,3c265e4c,8f80925e,6f38479d,6563bc34,e5faea1),
+S(dc530ceb,b82c246e,41c522f1,d2571d31,4b14edf3,91577a2b,64e42172,b23562c1,563ddd93,857d6529,8b81de24,19e5cede,7a4c5b7,a2fe98f6,9efb8906,6f32a98a),
+S(7604d60f,418dd132,78058942,fb2d2153,c0a2bfeb,e83c5011,a451bcb1,58db0773,38be14ae,d9e1c404,63ef92bd,d62c599a,b37625a8,182a3763,4fa2de90,535d50a9),
+S(cb896744,77b20829,f5e2bd42,8852c70b,91cbd0af,cadf219,a69727b4,cbec8d7a,5710d17a,20ea0dff,980d3f06,38d8b910,b8940d00,dd4a323f,d777d942,213e1093),
+S(501915b1,391e083d,e88c795f,8464c846,f699a79e,edb1b963,3e29f71a,9ce4d022,9e1dcc94,17ceb0e,15762f8f,7d0db85f,3bce3ad6,fecbe2c3,567853ef,ccd6d0f9),
+S(a63c0b8a,4eb2cb10,1e556904,a7246356,9909055,f45aa4c0,e89c2237,cbffafca,9650b428,12374811,738f4ac3,a2ac0505,396339be,4eeeda8b,c35e6fdd,c51a1e56),
+S(a16760e5,c3643d19,da15c034,5feced27,488ccafa,ad5298fa,6ee1070d,a258a761,736a7c7e,69db053,6f541079,158d671d,598efb1c,d75ec804,c7b2b49b,1ad7638a),
+S(840693fe,73b96819,bb1b24a9,35d5dc83,f361273c,d0989e76,1edc35ef,50faf90b,4294e19b,49558667,bc6237c6,86c30aba,a2660580,563d465a,fde9875d,74c9a57f),
+S(97273c3e,26e12369,1d0ade3,3aa261cd,a45b2d2c,d749af71,a60c0d15,85e18e03,2700c565,dbb08439,fb74317e,60776fca,d0efc1a5,5d0ad87c,18f82f2d,a97caf19),
+S(978d68a0,5ce30528,e4db2dae,99f6a245,f69cbd04,3c7171ce,ce2bee57,60e68b9,ffef379c,1515b068,df562f3f,bdadacfb,8aabe5aa,466105d1,97a8febc,1596915b),
+S(dfaea7bc,c78d275d,9f6a74fd,21fdec14,bcabfa45,e44070c1,9c44d449,c5d52231,927b810b,c2994b8d,2ed5124d,98e2f5cc,58410607,82b1ed80,d0fae288,8c42d538),
+S(ca0b766b,8b8d76fd,ce471a88,18e043d2,604d1ad2,b689cbce,70ceae78,fddf5a27,ddf9e3bc,935ea0bc,22f977ab,98a92414,643140ae,be0448a3,35d6d44a,1bedfc48),
+S(11dcc001,3be8d4b7,85e87153,e060d13,57cabb5,34a2c1de,2a4a70cb,9803a031,5b5d46b0,6a96c30c,b1901c12,eaa1c656,3a2f35b1,e9026954,36e087aa,3deb777e),
+S(a828121a,18d23262,bce26648,ab44c45d,c5027ae3,f74786b9,598f22b3,c408bf08,37893209,80d7d2de,6074778b,2e8916f0,4043a616,982a9b61,d4089623,31375cab),
+S(291ec5eb,e010daff,3ac00825,3452b065,d9f7fcb3,66e125af,22f11358,6263fbaf,4647cba2,45d190d8,2337f217,c278c98c,370120b3,d4e04110,e6df2c54,92d63bb7),
+S(44735d48,4c584d70,6afc573e,8ece7670,c79c7b99,99eb0141,4a73905d,34a1cf01,30a27c9f,67b47348,583f1e84,5e7af221,438d4c9f,a1e0cc19,7312ec6b,908d613b),
+S(fce8958f,507d5d59,bf0fb944,7be40c23,db2741e6,f89351a7,f29fc642,a60c7d4a,69de744b,9d2ef778,a7280325,bc699cb8,29874d33,bacc1fe7,6264eff,600c815b),
+S(171a3251,bc6e72cd,630f8130,d4695e48,e0e649c6,82bdd5b1,b87c7b7c,968cf664,3492ac7,faf2ab56,cfdd5278,9831ea1d,e90ddaa6,b4d6e6e6,fa960bab,2b55a55c),
+S(adc566cc,6c9afbe1,41a011fe,e121f0b9,a5dded68,fa9cdf63,45a00fdd,d38d69b3,38db9e85,26ab355b,5ed12b5e,84e795e7,7e2d2c57,24cec516,9cca1946,1d8d9c04),
+S(9694e1df,8067defc,de9dd34b,4a4bc91b,653ede57,3139b9f9,4df55858,74f04,f002d8b4,3940cd6b,7cba586e,18f1616e,db907010,230445d1,a96b9eee,b43778fa),
+S(8a90adbb,a8c32e,a9149e02,57bd9d24,7da8b0f6,5cd6332c,5803f83e,26a1bdc5,f7f24ef2,aae5a954,db200e45,ae75bdfd,5f4ec6d7,b203459a,7360a9b1,5ae2a9d7),
+S(234b3911,f965ef93,5ab16aa2,392d2198,f5df9022,962ceae3,5e73f05e,d7d8f817,a66aa264,a24e1a5c,e9bd5ce6,164cde8,4083c7b9,c354ebbc,caac78c3,f5da2aad),
+S(7d22623c,84ed234,5194c248,eb984ad1,28d2d4b,638b687f,730a3693,10f1c4ed,f97e515b,618719be,ea3603ad,7c40e827,59bff425,a8633365,c28c755e,b06769c1),
+S(e210b4e3,cf3a2e24,951b0623,a83a8793,11cb942,8d679cbb,16a15718,2e6655eb,f4bfb50,43768438,592e7b75,41bee9c5,f263dc15,59be620,c0dc128b,d5e29339),
+S(878c0097,ddb0f977,d75d579e,ca8d0bf1,a887fe50,e33b0c8b,bbaf2874,8875b321,a3401763,39f99298,9335879c,dd43a46e,d21d1387,55be87c9,2f486629,49918020),
+S(9a6dee6,4c79975d,2adcccf2,8cbd8bcd,c8bbff9b,2811039d,5a6fc051,9a212503,9c0f3d81,5d56afc8,31de81f2,750cb54,9fd5fc63,b63e2c66,ae88dffa,cd072236),
+S(3fa53681,f50925b2,710b66ca,1efa5e8f,b819c5e4,206a591f,d1492a1e,d13279f5,82a5c753,367d57d4,fdad7e9e,8b7ba625,7c50c07,10f93c8,5cb180e1,a459698a),
+S(7ce51172,8f94ef7,7924a1fb,fa8b7d1d,411d0e21,65c4a1ec,e105d4a0,909081cb,dbd596d1,bda2f32e,12cdc910,2762f3cd,627cf29b,1b145ca9,dd2037f1,7daa6a86),
+S(afbee9e6,d5b0bd25,1dd70bc9,e3b3a013,40116e09,905bb29b,797ba66c,16db5135,8a315473,84275d82,3c5296ed,b56ef5d9,7af96617,dc2e507,c009be9c,f3d3da4),
+S(14d13a78,96bd0978,d4a4d4d5,2266afd2,e0f21ea,5c1a693a,9ed4990,81e43974,dc84f2d1,86d91fca,62ef088d,1794715c,c8dcd9fe,efb4aa5c,46800240,886c41dc),
+S(7bc1045c,4960054a,fc979961,5cd7faee,5dec92bb,98b4c3d0,9620a488,fd32c35a,b8f420ec,cb5dd9ae,3f075e28,811ec9ca,bd770836,ad40371,66073db5,c1166735),
+S(fa24d112,4cf21fd1,bfb06c10,9fa49f10,c3ab248e,3d08f620,4529612b,f7a5328e,c0745547,b64a0068,25ae8f90,82f8565f,ed94865a,d185a364,602e6468,277b3cb9),
+S(8758ade8,745d4d18,c8f7ad6a,32fa05e1,c7a08bcf,c7cad42f,7aef474b,de02cff3,7864edbd,2efcbdc3,946dd250,6fdc2ea5,2f1626e0,b7300f8,9ef16420,12ae4853),
+S(d2783741,6944bdaa,d212dbd9,40cdc7fc,2847fe5c,a6eabd45,dd6daa9b,9e122693,c7139931,989b4f6d,3acf854d,5aec897,52c69105,2c6d2586,27ef13b7,66e91875),
+S(624120d8,420a5afb,64673e4e,b272f7a9,3b7f1f7b,59f4b145,10115691,70a597a2,3e055b16,ce482c12,88bcb9f7,40128b71,e5a441b,4c45056c,dca1466c,6491cad2),
+S(96a21be9,a6e8b94c,7ebd4782,809830ac,f2a373fc,6781405f,a320025a,e7bcb4de,772ce6fb,711c2898,dc8446,aaa8cc7b,41608392,6212908b,705ca412,1e2c5e1b),
+S(a9e2a4b6,4032f43,46ee1148,46ba487d,9a82f80d,3408b8ea,8434c521,33135ce8,c8537b6e,51846fc3,18898604,192d86a6,36ba3c36,f7ec9aa9,6185e7be,f160b5d3),
+S(b43b42e9,381358ce,b8a595c4,77a9caf4,afc6e0db,1f58af55,6dc5bbdf,2cb4449a,556e4e70,cf7d1a16,9249e954,b749619c,dd87aa7c,723176b1,7361966d,2d2b6fa),
+S(224cd0fc,393fb763,bfbc3c44,b829f61a,22ae6b98,22622367,2d0890c3,eb9ce9e5,97273eeb,eb71bdb6,5ac5c677,807a533a,f190cd12,e01ccb9a,d617af76,c3bef1ae),
+S(6c997b99,b7349b8b,6f399b78,34bcf510,56f070d4,b501f8a3,28ef3a39,7f6019ea,370796ed,ee708852,6ae9ba78,2aac403e,5b57dd21,cc77d0e,1674d6f4,e4ec60e),
+S(9c8970cd,125f1c6,1b845a19,a153ef53,594bc62a,3121d43c,e9890888,9c5a7adf,2157717c,55747f64,b8b51feb,9a6c8483,6dc4de7f,40908ff4,4e37d7e9,ef1354b3),
+S(eaf2ac12,6894bce4,8862c0de,165c03d6,4c561cb9,d338cb84,17d8811d,55af309d,f9e8f0f3,eeedcb85,67232a8e,cdbcbbfa,1a3b1a67,7a67c129,f07e091d,bb82ca78),
+S(8b69c681,7de28f6d,c539687d,28dd6a0,7cf16302,f0cc0f41,a340f6b,2a5669a5,576e108d,b9ae716c,91859b28,25de886,2de16591,eac5cf3d,5a802785,4551f778),
+S(aec8ab4d,f8c21840,c3d449f1,cf1100ff,baa91729,a35efbd2,53ad4ca,92af4d19,2350038d,bed217b6,353c31dd,bee52f96,e1706e8b,45350e96,6c55a522,b536ab3d),
+S(32b75afb,9fc485f1,744c18ce,8987deb9,51cfd485,26aa491,3dcff45,6b5e394e,c5edbb3e,4b95fb5f,55d24017,86fe65e7,9b8c20f,4e927e2a,caeb2b0a,1aa34ae),
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+S(64919bfc,50072a00,8769f559,3ad0e5b7,72ed6575,81ecf37c,8c759a3d,51149fc4,5759727c,20ae86e,b38aa3f,5e53b848,8ecd2b,477dca0a,ffb83903,65e70900),
+S(d392e5cf,3c2d4a0a,20779b28,f4957800,ec7148aa,63b2bcb2,348afe9b,d28ad57d,54062719,a0ee0869,b1a99d9a,e4716487,70386747,9ead4774,66df29e1,78c87c6b),
+S(6b9fe223,333b0802,34fb49d4,85218d11,9123c430,94e4ffba,38f33bb2,dbe7d9e2,5ea16bea,b5101109,4d34ec62,e6a63a71,c78de1f1,fcb7ce23,4ba2f51e,e4eb2ef1),
+S(b1a505c,eb85f130,ef6e4a49,e429b0c5,51a87831,f850ed83,6bc8649d,6097ce12,a887e16a,805c0708,45589bff,2b22fc6f,4187cc06,cecef137,9130becb,5d5d149f),
+S(8bd25993,c653b1e3,6f477988,61743aba,a5ffdaf,fd0890c3,caeb2963,736cbb44,341aef51,13b0d08d,90e90ffa,56570d57,5777260f,e85a15c2,2b5b3139,4f0a8c20),
+S(2da121de,147507bd,b8836321,40394006,afc65465,7c6d4399,97cf6c88,ce0c4016,3ec87a24,eb19c502,848ff433,7ac3f48b,9a56ca56,3d0bffe8,eaa98e97,49f04aaa),
+S(147541,9e9e9ff8,5b93f56,2832e74f,6c8c311a,676a759e,7dc62c63,5faa0b07,40fb95e4,810607ce,7ed10d9d,61404078,10ddbc55,261badc0,5e07bd1a,579ca271),
+S(7c48371b,7eb5655f,b9d95bc3,5660d783,b1884573,d2934346,c5a5342b,a0949cb0,8b8cfb2,4cab96fa,1ee1e5d7,7dade5bd,23fa7868,445d9ad4,723529db,38110dae),
+S(6ac2912f,d959d41c,19ff8ac4,bc136e85,91944b79,470d633f,b9fe65f0,f72541f4,63351f35,d4a7787a,31ef0bd6,f28aedd7,864ec5ab,7d841f11,9163e351,e070fcba),
+S(db08e4fd,63e16bf6,abc05d78,be6bccc7,c9b8e15e,334ad697,9205a2e9,c2100e15,eeb0ba62,e1a5ee98,c2e2cc5a,8d9cbf11,d265019c,9eea8f50,4aa1e50,a422d4e),
+S(4160dad,5255da89,12f69754,77b445a7,26fb7b8f,6ae8e2bb,d6276ae7,2a31afb8,ab0817bc,7a9b6907,9f6db9f3,c9a77718,23a1d79d,9f2739b2,cbeca18f,e5b8fbf8),
+S(3794fc72,f432c983,2f9ba8dd,b46b1c64,d979e899,78b3c14f,2f903ec4,75af091e,a898cdf,7cdaf6c0,3715e38a,4bea1081,fda150b3,7faa4a11,ddbdc350,c7e0bb05),
+S(244b87a4,fcecef37,76c16c5c,24c7785,be3b3c13,46595363,b8c066ec,45bfe561,9642f5fd,e0ec25ed,bd2129ca,6c023ec1,a2eadac7,f6ec5b7d,2b7fe894,41e5aa11),
+S(9de52b81,157165cc,aef44485,4c2b3535,a599a79,80d024de,5334b385,ecbb2e91,74fca165,26fe2f87,a41ce510,4dd5634,5cf98c11,803c0392,3eb4b8b7,60240c02)}
+#endif
+};
+#undef S
diff --git a/src/secp256k1/src/precomputed_ecmult_gen.h b/src/secp256k1/src/precomputed_ecmult_gen.h
new file mode 100644
index 00000000000..7256ad2e304
--- /dev/null
+++ b/src/secp256k1/src/precomputed_ecmult_gen.h
@@ -0,0 +1,26 @@
+/*********************************************************************************
+ * Copyright (c) 2013, 2014, 2015, 2021 Thomas Daede, Cory Fields, Pieter Wuille *
+ * Distributed under the MIT software license, see the accompanying              *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.          *
+ *********************************************************************************/
+
+#ifndef SECP256K1_PRECOMPUTED_ECMULT_GEN_H
+#define SECP256K1_PRECOMPUTED_ECMULT_GEN_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include "group.h"
+#include "ecmult_gen.h"
+#ifdef EXHAUSTIVE_TEST_ORDER
+static secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)];
+#else
+extern const secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)];
+#endif /* defined(EXHAUSTIVE_TEST_ORDER) */
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_PRECOMPUTED_ECMULT_GEN_H */
diff --git a/src/secp256k1/src/scalar_4x64_impl.h b/src/secp256k1/src/scalar_4x64_impl.h
index 232bba661a8..d8a68e66dc5 100644
--- a/src/secp256k1/src/scalar_4x64_impl.h
+++ b/src/secp256k1/src/scalar_4x64_impl.h
@@ -7,6 +7,7 @@
 #ifndef SECP256K1_SCALAR_REPR_IMPL_H
 #define SECP256K1_SCALAR_REPR_IMPL_H
 
+#include "int128.h"
 #include "modinv64_impl.h"
 
 /* Limbs of the secp256k1 order. */
@@ -69,50 +70,61 @@ SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scal
 }
 
 SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, unsigned int overflow) {
-    uint128_t t;
+    secp256k1_uint128 t;
     VERIFY_CHECK(overflow <= 1);
-    t = (uint128_t)r->d[0] + overflow * SECP256K1_N_C_0;
-    r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
-    t += (uint128_t)r->d[1] + overflow * SECP256K1_N_C_1;
-    r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
-    t += (uint128_t)r->d[2] + overflow * SECP256K1_N_C_2;
-    r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
-    t += (uint64_t)r->d[3];
-    r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL;
+    secp256k1_u128_from_u64(&t, r->d[0]);
+    secp256k1_u128_accum_u64(&t, overflow * SECP256K1_N_C_0);
+    r->d[0] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, r->d[1]);
+    secp256k1_u128_accum_u64(&t, overflow * SECP256K1_N_C_1);
+    r->d[1] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, r->d[2]);
+    secp256k1_u128_accum_u64(&t, overflow * SECP256K1_N_C_2);
+    r->d[2] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, r->d[3]);
+    r->d[3] = secp256k1_u128_to_u64(&t);
     return overflow;
 }
 
 static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
     int overflow;
-    uint128_t t = (uint128_t)a->d[0] + b->d[0];
-    r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
-    t += (uint128_t)a->d[1] + b->d[1];
-    r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
-    t += (uint128_t)a->d[2] + b->d[2];
-    r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
-    t += (uint128_t)a->d[3] + b->d[3];
-    r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
-    overflow = t + secp256k1_scalar_check_overflow(r);
+    secp256k1_uint128 t;
+    secp256k1_u128_from_u64(&t, a->d[0]);
+    secp256k1_u128_accum_u64(&t, b->d[0]);
+    r->d[0] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, a->d[1]);
+    secp256k1_u128_accum_u64(&t, b->d[1]);
+    r->d[1] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, a->d[2]);
+    secp256k1_u128_accum_u64(&t, b->d[2]);
+    r->d[2] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, a->d[3]);
+    secp256k1_u128_accum_u64(&t, b->d[3]);
+    r->d[3] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64);
+    overflow = secp256k1_u128_to_u64(&t) + secp256k1_scalar_check_overflow(r);
     VERIFY_CHECK(overflow == 0 || overflow == 1);
     secp256k1_scalar_reduce(r, overflow);
     return overflow;
 }
 
 static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
-    uint128_t t;
+    secp256k1_uint128 t;
     VERIFY_CHECK(bit < 256);
     bit += ((uint32_t) flag - 1) & 0x100;  /* forcing (bit >> 6) > 3 makes this a noop */
-    t = (uint128_t)r->d[0] + (((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F));
-    r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
-    t += (uint128_t)r->d[1] + (((uint64_t)((bit >> 6) == 1)) << (bit & 0x3F));
-    r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
-    t += (uint128_t)r->d[2] + (((uint64_t)((bit >> 6) == 2)) << (bit & 0x3F));
-    r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
-    t += (uint128_t)r->d[3] + (((uint64_t)((bit >> 6) == 3)) << (bit & 0x3F));
-    r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL;
+    secp256k1_u128_from_u64(&t, r->d[0]);
+    secp256k1_u128_accum_u64(&t, ((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F));
+    r->d[0] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, r->d[1]);
+    secp256k1_u128_accum_u64(&t, ((uint64_t)((bit >> 6) == 1)) << (bit & 0x3F));
+    r->d[1] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, r->d[2]);
+    secp256k1_u128_accum_u64(&t, ((uint64_t)((bit >> 6) == 2)) << (bit & 0x3F));
+    r->d[2] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, r->d[3]);
+    secp256k1_u128_accum_u64(&t, ((uint64_t)((bit >> 6) == 3)) << (bit & 0x3F));
+    r->d[3] = secp256k1_u128_to_u64(&t);
 #ifdef VERIFY
-    VERIFY_CHECK((t >> 64) == 0);
-    VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
+    VERIFY_CHECK(secp256k1_u128_hi_u64(&t) == 0);
 #endif
 }
 
@@ -169,14 +181,19 @@ SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a)
 
 static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
     uint64_t nonzero = 0xFFFFFFFFFFFFFFFFULL * (secp256k1_scalar_is_zero(a) == 0);
-    uint128_t t = (uint128_t)(~a->d[0]) + SECP256K1_N_0 + 1;
-    r->d[0] = t & nonzero; t >>= 64;
-    t += (uint128_t)(~a->d[1]) + SECP256K1_N_1;
-    r->d[1] = t & nonzero; t >>= 64;
-    t += (uint128_t)(~a->d[2]) + SECP256K1_N_2;
-    r->d[2] = t & nonzero; t >>= 64;
-    t += (uint128_t)(~a->d[3]) + SECP256K1_N_3;
-    r->d[3] = t & nonzero;
+    secp256k1_uint128 t;
+    secp256k1_u128_from_u64(&t, ~a->d[0]);
+    secp256k1_u128_accum_u64(&t, SECP256K1_N_0 + 1);
+    r->d[0] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, ~a->d[1]);
+    secp256k1_u128_accum_u64(&t, SECP256K1_N_1);
+    r->d[1] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, ~a->d[2]);
+    secp256k1_u128_accum_u64(&t, SECP256K1_N_2);
+    r->d[2] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, ~a->d[3]);
+    secp256k1_u128_accum_u64(&t, SECP256K1_N_3);
+    r->d[3] = secp256k1_u128_to_u64(&t) & nonzero;
 }
 
 SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
@@ -200,14 +217,19 @@ static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
      * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
     uint64_t mask = !flag - 1;
     uint64_t nonzero = (secp256k1_scalar_is_zero(r) != 0) - 1;
-    uint128_t t = (uint128_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
-    r->d[0] = t & nonzero; t >>= 64;
-    t += (uint128_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
-    r->d[1] = t & nonzero; t >>= 64;
-    t += (uint128_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
-    r->d[2] = t & nonzero; t >>= 64;
-    t += (uint128_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
-    r->d[3] = t & nonzero;
+    secp256k1_uint128 t;
+    secp256k1_u128_from_u64(&t, r->d[0] ^ mask);
+    secp256k1_u128_accum_u64(&t, (SECP256K1_N_0 + 1) & mask);
+    r->d[0] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, r->d[1] ^ mask);
+    secp256k1_u128_accum_u64(&t, SECP256K1_N_1 & mask);
+    r->d[1] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, r->d[2] ^ mask);
+    secp256k1_u128_accum_u64(&t, SECP256K1_N_2 & mask);
+    r->d[2] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64);
+    secp256k1_u128_accum_u64(&t, r->d[3] ^ mask);
+    secp256k1_u128_accum_u64(&t, SECP256K1_N_3 & mask);
+    r->d[3] = secp256k1_u128_to_u64(&t) & nonzero;
     return 2 * (mask == 0) - 1;
 }
 
@@ -217,9 +239,10 @@ static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
 #define muladd(a,b) { \
     uint64_t tl, th; \
     { \
-        uint128_t t = (uint128_t)a * b; \
-        th = t >> 64;         /* at most 0xFFFFFFFFFFFFFFFE */ \
-        tl = t; \
+        secp256k1_uint128 t; \
+        secp256k1_u128_mul(&t, a, b); \
+        th = secp256k1_u128_hi_u64(&t);  /* at most 0xFFFFFFFFFFFFFFFE */ \
+        tl = secp256k1_u128_to_u64(&t); \
     } \
     c0 += tl;                 /* overflow is handled on the next line */ \
     th += (c0 < tl);          /* at most 0xFFFFFFFFFFFFFFFF */ \
@@ -232,9 +255,10 @@ static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
 #define muladd_fast(a,b) { \
     uint64_t tl, th; \
     { \
-        uint128_t t = (uint128_t)a * b; \
-        th = t >> 64;         /* at most 0xFFFFFFFFFFFFFFFE */ \
-        tl = t; \
+        secp256k1_uint128 t; \
+        secp256k1_u128_mul(&t, a, b); \
+        th = secp256k1_u128_hi_u64(&t);  /* at most 0xFFFFFFFFFFFFFFFE */ \
+        tl = secp256k1_u128_to_u64(&t); \
     } \
     c0 += tl;                 /* overflow is handled on the next line */ \
     th += (c0 < tl);          /* at most 0xFFFFFFFFFFFFFFFF */ \
@@ -512,8 +536,8 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     : "g"(p0), "g"(p1), "g"(p2), "g"(p3), "g"(p4), "D"(r), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1)
     : "rax", "rdx", "r8", "r9", "r10", "cc", "memory");
 #else
-    uint128_t c;
-    uint64_t c0, c1, c2;
+    secp256k1_uint128 c128;
+    uint64_t c, c0, c1, c2;
     uint64_t n0 = l[4], n1 = l[5], n2 = l[6], n3 = l[7];
     uint64_t m0, m1, m2, m3, m4, m5;
     uint32_t m6;
@@ -570,14 +594,18 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
 
     /* Reduce 258 bits into 256. */
     /* r[0..3] = p[0..3] + p[4] * SECP256K1_N_C. */
-    c = p0 + (uint128_t)SECP256K1_N_C_0 * p4;
-    r->d[0] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
-    c += p1 + (uint128_t)SECP256K1_N_C_1 * p4;
-    r->d[1] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
-    c += p2 + (uint128_t)p4;
-    r->d[2] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
-    c += p3;
-    r->d[3] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
+    secp256k1_u128_from_u64(&c128, p0);
+    secp256k1_u128_accum_mul(&c128, SECP256K1_N_C_0, p4);
+    r->d[0] = secp256k1_u128_to_u64(&c128); secp256k1_u128_rshift(&c128, 64);
+    secp256k1_u128_accum_u64(&c128, p1);
+    secp256k1_u128_accum_mul(&c128, SECP256K1_N_C_1, p4);
+    r->d[1] = secp256k1_u128_to_u64(&c128); secp256k1_u128_rshift(&c128, 64);
+    secp256k1_u128_accum_u64(&c128, p2);
+    secp256k1_u128_accum_u64(&c128, p4);
+    r->d[2] = secp256k1_u128_to_u64(&c128); secp256k1_u128_rshift(&c128, 64);
+    secp256k1_u128_accum_u64(&c128, p3);
+    r->d[3] = secp256k1_u128_to_u64(&c128);
+    c = secp256k1_u128_hi_u64(&c128);
 #endif
 
     /* Final reduction of r. */
diff --git a/src/secp256k1/src/scalar_impl.h b/src/secp256k1/src/scalar_impl.h
index e124474773c..1b690e39444 100644
--- a/src/secp256k1/src/scalar_impl.h
+++ b/src/secp256k1/src/scalar_impl.h
@@ -74,7 +74,7 @@ static void secp256k1_scalar_split_lambda_verify(const secp256k1_scalar *r1, con
  * Both lambda and beta are primitive cube roots of unity.  That is lamba^3 == 1 mod n and
  * beta^3 == 1 mod p, where n is the curve order and p is the field order.
  *
- * Futhermore, because (X^3 - 1) = (X - 1)(X^2 + X + 1), the primitive cube roots of unity are
+ * Furthermore, because (X^3 - 1) = (X - 1)(X^2 + X + 1), the primitive cube roots of unity are
  * roots of X^2 + X + 1.  Therefore lambda^2 + lamba == -1 mod n and beta^2 + beta == -1 mod p.
  * (The other primitive cube roots of unity are lambda^2 and beta^2 respectively.)
  *
diff --git a/src/secp256k1/src/scratch_impl.h b/src/secp256k1/src/scratch_impl.h
index 688e18eb662..f71a20b9637 100644
--- a/src/secp256k1/src/scratch_impl.h
+++ b/src/secp256k1/src/scratch_impl.h
@@ -25,11 +25,11 @@ static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* err
 
 static void secp256k1_scratch_destroy(const secp256k1_callback* error_callback, secp256k1_scratch* scratch) {
     if (scratch != NULL) {
-        VERIFY_CHECK(scratch->alloc_size == 0); /* all checkpoints should be applied */
         if (secp256k1_memcmp_var(scratch->magic, "scratch", 8) != 0) {
             secp256k1_callback_call(error_callback, "invalid scratch space");
             return;
         }
+        VERIFY_CHECK(scratch->alloc_size == 0); /* all checkpoints should be applied */
         memset(scratch->magic, 0, sizeof(scratch->magic));
         free(scratch);
     }
diff --git a/src/secp256k1/src/secp256k1.c b/src/secp256k1/src/secp256k1.c
index 81b1d6eb249..5ed38241610 100644
--- a/src/secp256k1/src/secp256k1.c
+++ b/src/secp256k1/src/secp256k1.c
@@ -4,6 +4,17 @@
  * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
  ***********************************************************************/
 
+/* This is a C project. It should not be compiled with a C++ compiler,
+ * and we error out if we detect one.
+ *
+ * We still want to be able to test the project with a C++ compiler
+ * because it is still good to know if this will lead to real trouble, so
+ * there is a possibility to override the check. But be warned that
+ * compiling with a C++ compiler is not supported. */
+#if defined(__cplusplus) && !defined(SECP256K1_CPLUSPLUS_TEST_OVERRIDE)
+#error Trying to compile a C project with a C++ compiler.
+#endif
+
 #define SECP256K1_BUILD
 
 #include "../include/secp256k1.h"
@@ -11,6 +22,7 @@
 
 #include "assumptions.h"
 #include "util.h"
+
 #include "field_impl.h"
 #include "scalar_impl.h"
 #include "group_impl.h"
@@ -20,6 +32,7 @@
 #include "ecdsa_impl.h"
 #include "eckey_impl.h"
 #include "hash_impl.h"
+#include "int128_impl.h"
 #include "scratch_impl.h"
 #include "selftest.h"
 
@@ -44,53 +57,32 @@
     } \
 } while(0)
 
-#ifndef USE_EXTERNAL_DEFAULT_CALLBACKS
-#include <stdlib.h>
-#include <stdio.h>
-static void secp256k1_default_illegal_callback_fn(const char* str, void* data) {
-    (void)data;
-    fprintf(stderr, "[libsecp256k1] illegal argument: %s\n", str);
-    abort();
-}
-static void secp256k1_default_error_callback_fn(const char* str, void* data) {
-    (void)data;
-    fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str);
-    abort();
-}
-#else
-void secp256k1_default_illegal_callback_fn(const char* str, void* data);
-void secp256k1_default_error_callback_fn(const char* str, void* data);
-#endif
-
-static const secp256k1_callback default_illegal_callback = {
-    secp256k1_default_illegal_callback_fn,
-    NULL
-};
-
-static const secp256k1_callback default_error_callback = {
-    secp256k1_default_error_callback_fn,
-    NULL
-};
-
+/* Note that whenever you change the context struct, you must also change the
+ * context_eq function. */
 struct secp256k1_context_struct {
-    secp256k1_ecmult_context ecmult_ctx;
     secp256k1_ecmult_gen_context ecmult_gen_ctx;
     secp256k1_callback illegal_callback;
     secp256k1_callback error_callback;
     int declassify;
 };
 
-static const secp256k1_context secp256k1_context_no_precomp_ = {
-    { 0 },
+static const secp256k1_context secp256k1_context_static_ = {
     { 0 },
     { secp256k1_default_illegal_callback_fn, 0 },
     { secp256k1_default_error_callback_fn, 0 },
     0
 };
-const secp256k1_context *secp256k1_context_no_precomp = &secp256k1_context_no_precomp_;
+const secp256k1_context *secp256k1_context_static = &secp256k1_context_static_;
+const secp256k1_context *secp256k1_context_no_precomp = &secp256k1_context_static_;
+
+void secp256k1_selftest(void) {
+    if (!secp256k1_selftest_passes()) {
+        secp256k1_callback_call(&default_error_callback, "self test failed");
+    }
+}
 
 size_t secp256k1_context_preallocated_size(unsigned int flags) {
-    size_t ret = ROUND_TO_ALIGN(sizeof(secp256k1_context));
+    size_t ret = sizeof(secp256k1_context);
     /* A return value of 0 is reserved as an indicator for errors when we call this function internally. */
     VERIFY_CHECK(ret != 0);
 
@@ -100,59 +92,36 @@ size_t secp256k1_context_preallocated_size(unsigned int flags) {
             return 0;
     }
 
-    if (flags & SECP256K1_FLAGS_BIT_CONTEXT_SIGN) {
-        ret += SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE;
-    }
-    if (flags & SECP256K1_FLAGS_BIT_CONTEXT_VERIFY) {
-        ret += SECP256K1_ECMULT_CONTEXT_PREALLOCATED_SIZE;
-    }
     return ret;
 }
 
 size_t secp256k1_context_preallocated_clone_size(const secp256k1_context* ctx) {
-    size_t ret = ROUND_TO_ALIGN(sizeof(secp256k1_context));
+    size_t ret = sizeof(secp256k1_context);
     VERIFY_CHECK(ctx != NULL);
-    if (secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)) {
-        ret += SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE;
-    }
-    if (secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx)) {
-        ret += SECP256K1_ECMULT_CONTEXT_PREALLOCATED_SIZE;
-    }
     return ret;
 }
 
 secp256k1_context* secp256k1_context_preallocated_create(void* prealloc, unsigned int flags) {
-    void* const base = prealloc;
     size_t prealloc_size;
     secp256k1_context* ret;
 
-    if (!secp256k1_selftest()) {
-        secp256k1_callback_call(&default_error_callback, "self test failed");
-    }
+    secp256k1_selftest();
 
     prealloc_size = secp256k1_context_preallocated_size(flags);
     if (prealloc_size == 0) {
         return NULL;
     }
     VERIFY_CHECK(prealloc != NULL);
-    ret = (secp256k1_context*)manual_alloc(&prealloc, sizeof(secp256k1_context), base, prealloc_size);
+    ret = (secp256k1_context*)prealloc;
     ret->illegal_callback = default_illegal_callback;
     ret->error_callback = default_error_callback;
 
-    secp256k1_ecmult_context_init(&ret->ecmult_ctx);
-    secp256k1_ecmult_gen_context_init(&ret->ecmult_gen_ctx);
-
     /* Flags have been checked by secp256k1_context_preallocated_size. */
     VERIFY_CHECK((flags & SECP256K1_FLAGS_TYPE_MASK) == SECP256K1_FLAGS_TYPE_CONTEXT);
-    if (flags & SECP256K1_FLAGS_BIT_CONTEXT_SIGN) {
-        secp256k1_ecmult_gen_context_build(&ret->ecmult_gen_ctx, &prealloc);
-    }
-    if (flags & SECP256K1_FLAGS_BIT_CONTEXT_VERIFY) {
-        secp256k1_ecmult_context_build(&ret->ecmult_ctx, &prealloc);
-    }
+    secp256k1_ecmult_gen_context_build(&ret->ecmult_gen_ctx);
     ret->declassify = !!(flags & SECP256K1_FLAGS_BIT_CONTEXT_DECLASSIFY);
 
-    return (secp256k1_context*) ret;
+    return ret;
 }
 
 secp256k1_context* secp256k1_context_create(unsigned int flags) {
@@ -167,16 +136,12 @@ secp256k1_context* secp256k1_context_create(unsigned int flags) {
 }
 
 secp256k1_context* secp256k1_context_preallocated_clone(const secp256k1_context* ctx, void* prealloc) {
-    size_t prealloc_size;
     secp256k1_context* ret;
     VERIFY_CHECK(ctx != NULL);
     ARG_CHECK(prealloc != NULL);
 
-    prealloc_size = secp256k1_context_preallocated_clone_size(ctx);
     ret = (secp256k1_context*)prealloc;
-    memcpy(ret, ctx, prealloc_size);
-    secp256k1_ecmult_gen_context_finalize_memcpy(&ret->ecmult_gen_ctx, &ctx->ecmult_gen_ctx);
-    secp256k1_ecmult_context_finalize_memcpy(&ret->ecmult_ctx, &ctx->ecmult_ctx);
+    *ret = *ctx;
     return ret;
 }
 
@@ -192,9 +157,8 @@ secp256k1_context* secp256k1_context_clone(const secp256k1_context* ctx) {
 }
 
 void secp256k1_context_preallocated_destroy(secp256k1_context* ctx) {
-    ARG_CHECK_NO_RETURN(ctx != secp256k1_context_no_precomp);
+    ARG_CHECK_NO_RETURN(ctx != secp256k1_context_static);
     if (ctx != NULL) {
-        secp256k1_ecmult_context_clear(&ctx->ecmult_ctx);
         secp256k1_ecmult_gen_context_clear(&ctx->ecmult_gen_ctx);
     }
 }
@@ -207,7 +171,7 @@ void secp256k1_context_destroy(secp256k1_context* ctx) {
 }
 
 void secp256k1_context_set_illegal_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) {
-    ARG_CHECK_NO_RETURN(ctx != secp256k1_context_no_precomp);
+    ARG_CHECK_NO_RETURN(ctx != secp256k1_context_static);
     if (fun == NULL) {
         fun = secp256k1_default_illegal_callback_fn;
     }
@@ -216,7 +180,7 @@ void secp256k1_context_set_illegal_callback(secp256k1_context* ctx, void (*fun)(
 }
 
 void secp256k1_context_set_error_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) {
-    ARG_CHECK_NO_RETURN(ctx != secp256k1_context_no_precomp);
+    ARG_CHECK_NO_RETURN(ctx != secp256k1_context_static);
     if (fun == NULL) {
         fun = secp256k1_default_error_callback_fn;
     }
@@ -458,7 +422,6 @@ int secp256k1_ecdsa_verify(const secp256k1_context* ctx, const secp256k1_ecdsa_s
     secp256k1_scalar r, s;
     secp256k1_scalar m;
     VERIFY_CHECK(ctx != NULL);
-    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
     ARG_CHECK(msghash32 != NULL);
     ARG_CHECK(sig != NULL);
     ARG_CHECK(pubkey != NULL);
@@ -467,7 +430,7 @@ int secp256k1_ecdsa_verify(const secp256k1_context* ctx, const secp256k1_ecdsa_s
     secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
     return (!secp256k1_scalar_is_high(&s) &&
             secp256k1_pubkey_load(ctx, &q, pubkey) &&
-            secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &r, &s, &q, &m));
+            secp256k1_ecdsa_sig_verify(&r, &s, &q, &m));
 }
 
 static SECP256K1_INLINE void buffer_append(unsigned char *buf, unsigned int *offset, const void *data, unsigned int len) {
@@ -480,8 +443,12 @@ static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *m
    unsigned int offset = 0;
    secp256k1_rfc6979_hmac_sha256 rng;
    unsigned int i;
+   secp256k1_scalar msg;
+   unsigned char msgmod32[32];
+   secp256k1_scalar_set_b32(&msg, msg32, NULL);
+   secp256k1_scalar_get_b32(msgmod32, &msg);
    /* We feed a byte array to the PRNG as input, consisting of:
-    * - the private key (32 bytes) and message (32 bytes), see RFC 6979 3.2d.
+    * - the private key (32 bytes) and reduced message (32 bytes), see RFC 6979 3.2d.
     * - optionally 32 extra bytes of data, see RFC 6979 3.6 Additional Data.
     * - optionally 16 extra bytes with the algorithm name.
     * Because the arguments have distinct fixed lengths it is not possible for
@@ -489,7 +456,7 @@ static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *m
     *  nonces.
     */
    buffer_append(keydata, &offset, key32, 32);
-   buffer_append(keydata, &offset, msg32, 32);
+   buffer_append(keydata, &offset, msgmod32, 32);
    if (data != NULL) {
        buffer_append(keydata, &offset, data, 32);
    }
@@ -685,24 +652,23 @@ int secp256k1_ec_privkey_tweak_add(const secp256k1_context* ctx, unsigned char *
     return secp256k1_ec_seckey_tweak_add(ctx, seckey, tweak32);
 }
 
-static int secp256k1_ec_pubkey_tweak_add_helper(const secp256k1_ecmult_context* ecmult_ctx, secp256k1_ge *p, const unsigned char *tweak32) {
+static int secp256k1_ec_pubkey_tweak_add_helper(secp256k1_ge *p, const unsigned char *tweak32) {
     secp256k1_scalar term;
     int overflow = 0;
     secp256k1_scalar_set_b32(&term, tweak32, &overflow);
-    return !overflow && secp256k1_eckey_pubkey_tweak_add(ecmult_ctx, p, &term);
+    return !overflow && secp256k1_eckey_pubkey_tweak_add(p, &term);
 }
 
 int secp256k1_ec_pubkey_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak32) {
     secp256k1_ge p;
     int ret = 0;
     VERIFY_CHECK(ctx != NULL);
-    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
     ARG_CHECK(pubkey != NULL);
     ARG_CHECK(tweak32 != NULL);
 
     ret = secp256k1_pubkey_load(ctx, &p, pubkey);
     memset(pubkey, 0, sizeof(*pubkey));
-    ret = ret && secp256k1_ec_pubkey_tweak_add_helper(&ctx->ecmult_ctx, &p, tweak32);
+    ret = ret && secp256k1_ec_pubkey_tweak_add_helper(&p, tweak32);
     if (ret) {
         secp256k1_pubkey_save(pubkey, &p);
     }
@@ -740,7 +706,6 @@ int secp256k1_ec_pubkey_tweak_mul(const secp256k1_context* ctx, secp256k1_pubkey
     int ret = 0;
     int overflow = 0;
     VERIFY_CHECK(ctx != NULL);
-    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
     ARG_CHECK(pubkey != NULL);
     ARG_CHECK(tweak32 != NULL);
 
@@ -748,7 +713,7 @@ int secp256k1_ec_pubkey_tweak_mul(const secp256k1_context* ctx, secp256k1_pubkey
     ret = !overflow && secp256k1_pubkey_load(ctx, &p, pubkey);
     memset(pubkey, 0, sizeof(*pubkey));
     if (ret) {
-        if (secp256k1_eckey_pubkey_tweak_mul(&ctx->ecmult_ctx, &p, &factor)) {
+        if (secp256k1_eckey_pubkey_tweak_mul(&p, &factor)) {
             secp256k1_pubkey_save(pubkey, &p);
         } else {
             ret = 0;
@@ -771,6 +736,7 @@ int secp256k1_ec_pubkey_combine(const secp256k1_context* ctx, secp256k1_pubkey *
     secp256k1_gej Qj;
     secp256k1_ge Q;
 
+    VERIFY_CHECK(ctx != NULL);
     ARG_CHECK(pubnonce != NULL);
     memset(pubnonce, 0, sizeof(*pubnonce));
     ARG_CHECK(n >= 1);
@@ -779,6 +745,7 @@ int secp256k1_ec_pubkey_combine(const secp256k1_context* ctx, secp256k1_pubkey *
     secp256k1_gej_set_infinity(&Qj);
 
     for (i = 0; i < n; i++) {
+        ARG_CHECK(pubnonces[i] != NULL);
         secp256k1_pubkey_load(ctx, &Q, pubnonces[i]);
         secp256k1_gej_add_ge(&Qj, &Qj, &Q);
     }
@@ -790,6 +757,19 @@ int secp256k1_ec_pubkey_combine(const secp256k1_context* ctx, secp256k1_pubkey *
     return 1;
 }
 
+int secp256k1_tagged_sha256(const secp256k1_context* ctx, unsigned char *hash32, const unsigned char *tag, size_t taglen, const unsigned char *msg, size_t msglen) {
+    secp256k1_sha256 sha;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(hash32 != NULL);
+    ARG_CHECK(tag != NULL);
+    ARG_CHECK(msg != NULL);
+
+    secp256k1_sha256_initialize_tagged(&sha, tag, taglen);
+    secp256k1_sha256_write(&sha, msg, msglen);
+    secp256k1_sha256_finalize(&sha, hash32);
+    return 1;
+}
+
 #ifdef ENABLE_MODULE_ECDH
 # include "modules/ecdh/main_impl.h"
 #endif
diff --git a/src/secp256k1/src/util.h b/src/secp256k1/src/util.h
index f78846836cf..864baaee4dd 100644
--- a/src/secp256k1/src/util.h
+++ b/src/secp256k1/src/util.h
@@ -16,6 +16,11 @@
 #include <stdio.h>
 #include <limits.h>
 
+#define STR_(x) #x
+#define STR(x) STR_(x)
+#define DEBUG_CONFIG_MSG(x) "DEBUG_CONFIG: " x
+#define DEBUG_CONFIG_DEF(x) DEBUG_CONFIG_MSG(#x "=" STR(x))
+
 typedef struct {
     void (*fn)(const char *text, void* data);
     const void* data;
@@ -25,6 +30,33 @@ static SECP256K1_INLINE void secp256k1_callback_call(const secp256k1_callback *
     cb->fn(text, (void*)cb->data);
 }
 
+#ifndef USE_EXTERNAL_DEFAULT_CALLBACKS
+static void secp256k1_default_illegal_callback_fn(const char* str, void* data) {
+    (void)data;
+    fprintf(stderr, "[libsecp256k1] illegal argument: %s\n", str);
+    abort();
+}
+static void secp256k1_default_error_callback_fn(const char* str, void* data) {
+    (void)data;
+    fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str);
+    abort();
+}
+#else
+void secp256k1_default_illegal_callback_fn(const char* str, void* data);
+void secp256k1_default_error_callback_fn(const char* str, void* data);
+#endif
+
+static const secp256k1_callback default_illegal_callback = {
+    secp256k1_default_illegal_callback_fn,
+    NULL
+};
+
+static const secp256k1_callback default_error_callback = {
+    secp256k1_default_error_callback_fn,
+    NULL
+};
+
+
 #ifdef DETERMINISTIC
 #define TEST_FAILURE(msg) do { \
     fprintf(stderr, "%s\n", msg); \
@@ -115,36 +147,6 @@ static SECP256K1_INLINE void *checked_realloc(const secp256k1_callback* cb, void
 
 #define ROUND_TO_ALIGN(size) ((((size) + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT)
 
-/* Assume there is a contiguous memory object with bounds [base, base + max_size)
- * of which the memory range [base, *prealloc_ptr) is already allocated for usage,
- * where *prealloc_ptr is an aligned pointer. In that setting, this functions
- * reserves the subobject [*prealloc_ptr, *prealloc_ptr + alloc_size) of
- * alloc_size bytes by increasing *prealloc_ptr accordingly, taking into account
- * alignment requirements.
- *
- * The function returns an aligned pointer to the newly allocated subobject.
- *
- * This is useful for manual memory management: if we're simply given a block
- * [base, base + max_size), the caller can use this function to allocate memory
- * in this block and keep track of the current allocation state with *prealloc_ptr.
- *
- * It is VERIFY_CHECKed that there is enough space left in the memory object and
- * *prealloc_ptr is aligned relative to base.
- */
-static SECP256K1_INLINE void *manual_alloc(void** prealloc_ptr, size_t alloc_size, void* base, size_t max_size) {
-    size_t aligned_alloc_size = ROUND_TO_ALIGN(alloc_size);
-    void* ret;
-    VERIFY_CHECK(prealloc_ptr != NULL);
-    VERIFY_CHECK(*prealloc_ptr != NULL);
-    VERIFY_CHECK(base != NULL);
-    VERIFY_CHECK((unsigned char*)*prealloc_ptr >= (unsigned char*)base);
-    VERIFY_CHECK(((unsigned char*)*prealloc_ptr - (unsigned char*)base) % ALIGNMENT == 0);
-    VERIFY_CHECK((unsigned char*)*prealloc_ptr - (unsigned char*)base + aligned_alloc_size <= max_size);
-    ret = *prealloc_ptr;
-    *prealloc_ptr = (unsigned char*)*prealloc_ptr + aligned_alloc_size;
-    return ret;
-}
-
 /* Macro for restrict, when available and not in a VERIFY build. */
 #if defined(SECP256K1_BUILD) && defined(VERIFY)
 # define SECP256K1_RESTRICT
@@ -176,31 +178,6 @@ static SECP256K1_INLINE void *manual_alloc(void** prealloc_ptr, size_t alloc_siz
 # define SECP256K1_GNUC_EXT
 #endif
 
-/* If SECP256K1_{LITTLE,BIG}_ENDIAN is not explicitly provided, infer from various other system macros. */
-#if !defined(SECP256K1_LITTLE_ENDIAN) && !defined(SECP256K1_BIG_ENDIAN)
-/* Inspired by https://github.com/rofl0r/endianness.h/blob/9853923246b065a3b52d2c43835f3819a62c7199/endianness.h#L52L73 */
-# if (defined(__BYTE_ORDER__) && defined(__ORDER_LITTLE_ENDIAN__) && __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__) || \
-     defined(_X86_) || defined(__x86_64__) || defined(__i386__) || \
-     defined(__i486__) || defined(__i586__) || defined(__i686__) || \
-     defined(__MIPSEL) || defined(_MIPSEL) || defined(MIPSEL) || \
-     defined(__ARMEL__) || defined(__AARCH64EL__) || \
-     (defined(__LITTLE_ENDIAN__) && __LITTLE_ENDIAN__ == 1) || \
-     (defined(_LITTLE_ENDIAN) && _LITTLE_ENDIAN == 1) || \
-     defined(_M_IX86) || defined(_M_AMD64) || defined(_M_ARM) /* MSVC */
-#  define SECP256K1_LITTLE_ENDIAN
-# endif
-# if (defined(__BYTE_ORDER__) && defined(__ORDER_BIG_ENDIAN__) && __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__) || \
-     defined(__MIPSEB) || defined(_MIPSEB) || defined(MIPSEB) || \
-     defined(__MICROBLAZEEB__) || defined(__ARMEB__) || defined(__AARCH64EB__) || \
-     (defined(__BIG_ENDIAN__) && __BIG_ENDIAN__ == 1) || \
-     (defined(_BIG_ENDIAN) && _BIG_ENDIAN == 1)
-#  define SECP256K1_BIG_ENDIAN
-# endif
-#endif
-#if defined(SECP256K1_LITTLE_ENDIAN) == defined(SECP256K1_BIG_ENDIAN)
-# error Please make sure that either SECP256K1_LITTLE_ENDIAN or SECP256K1_BIG_ENDIAN is set, see src/util.h.
-#endif
-
 /* Zero memory if flag == 1. Flag must be 0 or 1. Constant time. */
 static SECP256K1_INLINE void secp256k1_memczero(void *s, size_t len, int flag) {
     unsigned char *p = (unsigned char *)s;
@@ -253,28 +230,36 @@ static SECP256K1_INLINE void secp256k1_int_cmov(int *r, const int *a, int flag)
     *r = (int)(r_masked | a_masked);
 }
 
-/* If USE_FORCE_WIDEMUL_{INT128,INT64} is set, use that wide multiplication implementation.
- * Otherwise use the presence of __SIZEOF_INT128__ to decide.
- */
-#if defined(USE_FORCE_WIDEMUL_INT128)
+#if defined(USE_FORCE_WIDEMUL_INT128_STRUCT)
+/* If USE_FORCE_WIDEMUL_INT128_STRUCT is set, use int128_struct. */
 # define SECP256K1_WIDEMUL_INT128 1
+# define SECP256K1_INT128_STRUCT 1
+#elif defined(USE_FORCE_WIDEMUL_INT128)
+/* If USE_FORCE_WIDEMUL_INT128 is set, use int128. */
+# define SECP256K1_WIDEMUL_INT128 1
+# define SECP256K1_INT128_NATIVE 1
 #elif defined(USE_FORCE_WIDEMUL_INT64)
+/* If USE_FORCE_WIDEMUL_INT64 is set, use int64. */
 # define SECP256K1_WIDEMUL_INT64 1
 #elif defined(UINT128_MAX) || defined(__SIZEOF_INT128__)
+/* If a native 128-bit integer type exists, use int128. */
+# define SECP256K1_WIDEMUL_INT128 1
+# define SECP256K1_INT128_NATIVE 1
+#elif defined(_MSC_VER) && (defined(_M_X64) || defined(_M_ARM64))
+/* On 64-bit MSVC targets (x86_64 and arm64), use int128_struct
+ * (which has special logic to implement using intrinsics on those systems). */
 # define SECP256K1_WIDEMUL_INT128 1
+# define SECP256K1_INT128_STRUCT 1
+#elif SIZE_MAX > 0xffffffff
+/* Systems with 64-bit pointers (and thus registers) very likely benefit from
+ * using 64-bit based arithmetic (even if we need to fall back to 32x32->64 based
+ * multiplication logic). */
+# define SECP256K1_WIDEMUL_INT128 1
+# define SECP256K1_INT128_STRUCT 1
 #else
+/* Lastly, fall back to int64 based arithmetic. */
 # define SECP256K1_WIDEMUL_INT64 1
 #endif
-#if defined(SECP256K1_WIDEMUL_INT128)
-# if !defined(UINT128_MAX) && defined(__SIZEOF_INT128__)
-SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t;
-SECP256K1_GNUC_EXT typedef __int128 int128_t;
-#define UINT128_MAX ((uint128_t)(-1))
-#define INT128_MAX ((int128_t)(UINT128_MAX >> 1))
-#define INT128_MIN (-INT128_MAX - 1)
-/* No (U)INT128_C macros because compilers providing __int128 do not support 128-bit literals.  */
-# endif
-#endif
 
 #ifndef __has_builtin
 #define __has_builtin(x) 0
@@ -341,4 +326,20 @@ static SECP256K1_INLINE int secp256k1_ctz64_var(uint64_t x) {
 #endif
 }
 
+/* Read a uint32_t in big endian */
+SECP256K1_INLINE static uint32_t secp256k1_read_be32(const unsigned char* p) {
+    return (uint32_t)p[0] << 24 |
+           (uint32_t)p[1] << 16 |
+           (uint32_t)p[2] << 8  |
+           (uint32_t)p[3];
+}
+
+/* Write a uint32_t in big endian */
+SECP256K1_INLINE static void secp256k1_write_be32(unsigned char* p, uint32_t x) {
+    p[3] = x;
+    p[2] = x >>  8;
+    p[1] = x >> 16;
+    p[0] = x >> 24;
+}
+
 #endif /* SECP256K1_UTIL_H */


Test patch:
diff --git a/src/gtest/main.cpp b/src/gtest/main.cpp
index 83c4ed6543f..b2e62a247e5 100644
--- a/src/gtest/main.cpp
+++ b/src/gtest/main.cpp
@@ -20,13 +20,6 @@ const std::function<std::string(const char*)> G_TRANSLATION_FUN = nullptr;
 uint256 insecure_rand_seed = GetRandHash();
 FastRandomContext insecure_rand_ctx(insecure_rand_seed);
 
-struct ECCryptoClosure
-{
-    ECCVerifyHandle handle;
-};
-
-ECCryptoClosure instance_of_eccryptoclosure;
-
 class LogGrabber : public ::testing::EmptyTestEventListener {
     fs::path logPath;
 
diff --git a/src/secp256k1/src/modules/ecdh/tests_impl.h b/src/secp256k1/src/modules/ecdh/tests_impl.h
index be07447a4b9..ce644d572a5 100644
--- a/src/secp256k1/src/modules/ecdh/tests_impl.h
+++ b/src/secp256k1/src/modules/ecdh/tests_impl.h
@@ -26,7 +26,7 @@ int ecdh_hash_function_custom(unsigned char *output, const unsigned char *x, con
 
 void test_ecdh_api(void) {
     /* Setup context that just counts errors */
-    secp256k1_context *tctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
+    secp256k1_context *tctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
     secp256k1_pubkey point;
     unsigned char res[32];
     unsigned char s_one[32] = { 0 };
@@ -60,7 +60,7 @@ void test_ecdh_generator_basepoint(void) {
 
     s_one[31] = 1;
     /* Check against pubkey creation when the basepoint is the generator */
-    for (i = 0; i < 100; ++i) {
+    for (i = 0; i < 2 * count; ++i) {
         secp256k1_sha256 sha;
         unsigned char s_b32[32];
         unsigned char output_ecdh[65];
@@ -123,10 +123,43 @@ void test_bad_scalar(void) {
     CHECK(secp256k1_ecdh(ctx, output, &point, s_overflow, ecdh_hash_function_test_fail, NULL) == 0);
 }
 
+/** Test that ECDH(sG, 1/s) == ECDH((1/s)G, s) == ECDH(G, 1) for a few random s. */
+void test_result_basepoint(void) {
+    secp256k1_pubkey point;
+    secp256k1_scalar rand;
+    unsigned char s[32];
+    unsigned char s_inv[32];
+    unsigned char out[32];
+    unsigned char out_inv[32];
+    unsigned char out_base[32];
+    int i;
+
+    unsigned char s_one[32] = { 0 };
+    s_one[31] = 1;
+    CHECK(secp256k1_ec_pubkey_create(ctx, &point, s_one) == 1);
+    CHECK(secp256k1_ecdh(ctx, out_base, &point, s_one, NULL, NULL) == 1);
+
+    for (i = 0; i < 2 * count; i++) {
+        random_scalar_order(&rand);
+        secp256k1_scalar_get_b32(s, &rand);
+        secp256k1_scalar_inverse(&rand, &rand);
+        secp256k1_scalar_get_b32(s_inv, &rand);
+
+        CHECK(secp256k1_ec_pubkey_create(ctx, &point, s) == 1);
+        CHECK(secp256k1_ecdh(ctx, out, &point, s_inv, NULL, NULL) == 1);
+        CHECK(secp256k1_memcmp_var(out, out_base, 32) == 0);
+
+        CHECK(secp256k1_ec_pubkey_create(ctx, &point, s_inv) == 1);
+        CHECK(secp256k1_ecdh(ctx, out_inv, &point, s, NULL, NULL) == 1);
+        CHECK(secp256k1_memcmp_var(out_inv, out_base, 32) == 0);
+    }
+}
+
 void run_ecdh_tests(void) {
     test_ecdh_api();
     test_ecdh_generator_basepoint();
     test_bad_scalar();
+    test_result_basepoint();
 }
 
 #endif /* SECP256K1_MODULE_ECDH_TESTS_H */
diff --git a/src/secp256k1/src/modules/extrakeys/tests_exhaustive_impl.h b/src/secp256k1/src/modules/extrakeys/tests_exhaustive_impl.h
index d4a2f5bdf40..5ecc90d50fc 100644
--- a/src/secp256k1/src/modules/extrakeys/tests_exhaustive_impl.h
+++ b/src/secp256k1/src/modules/extrakeys/tests_exhaustive_impl.h
@@ -7,8 +7,8 @@
 #ifndef SECP256K1_MODULE_EXTRAKEYS_TESTS_EXHAUSTIVE_H
 #define SECP256K1_MODULE_EXTRAKEYS_TESTS_EXHAUSTIVE_H
 
-#include "src/modules/extrakeys/main_impl.h"
 #include "../../../include/secp256k1_extrakeys.h"
+#include "main_impl.h"
 
 static void test_exhaustive_extrakeys(const secp256k1_context *ctx, const secp256k1_ge* group) {
     secp256k1_keypair keypair[EXHAUSTIVE_TEST_ORDER - 1];
diff --git a/src/secp256k1/src/modules/extrakeys/tests_impl.h b/src/secp256k1/src/modules/extrakeys/tests_impl.h
index 4a5952714c4..8030aedad63 100644
--- a/src/secp256k1/src/modules/extrakeys/tests_impl.h
+++ b/src/secp256k1/src/modules/extrakeys/tests_impl.h
@@ -9,11 +9,9 @@
 
 #include "../../../include/secp256k1_extrakeys.h"
 
-static secp256k1_context* api_test_context(int flags, int *ecount) {
-    secp256k1_context *ctx0 = secp256k1_context_create(flags);
+static void set_counting_callbacks(secp256k1_context *ctx0, int *ecount) {
     secp256k1_context_set_error_callback(ctx0, counting_illegal_callback_fn, ecount);
     secp256k1_context_set_illegal_callback(ctx0, counting_illegal_callback_fn, ecount);
-    return ctx0;
 }
 
 void test_xonly_pubkey(void) {
@@ -31,28 +29,25 @@ void test_xonly_pubkey(void) {
     int i;
 
     int ecount;
-    secp256k1_context *none = api_test_context(SECP256K1_CONTEXT_NONE, &ecount);
-    secp256k1_context *sign = api_test_context(SECP256K1_CONTEXT_SIGN, &ecount);
-    secp256k1_context *verify = api_test_context(SECP256K1_CONTEXT_VERIFY, &ecount);
+
+    set_counting_callbacks(ctx, &ecount);
 
     secp256k1_testrand256(sk);
     memset(ones32, 0xFF, 32);
     secp256k1_testrand256(xy_sk);
-    CHECK(secp256k1_ec_pubkey_create(sign, &pk, sk) == 1);
-    CHECK(secp256k1_xonly_pubkey_from_pubkey(none, &xonly_pk, &pk_parity, &pk) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pk, sk) == 1);
+    CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &xonly_pk, &pk_parity, &pk) == 1);
 
     /* Test xonly_pubkey_from_pubkey */
     ecount = 0;
-    CHECK(secp256k1_xonly_pubkey_from_pubkey(none, &xonly_pk, &pk_parity, &pk) == 1);
-    CHECK(secp256k1_xonly_pubkey_from_pubkey(sign, &xonly_pk, &pk_parity, &pk) == 1);
-    CHECK(secp256k1_xonly_pubkey_from_pubkey(verify, &xonly_pk, &pk_parity, &pk) == 1);
-    CHECK(secp256k1_xonly_pubkey_from_pubkey(none, NULL, &pk_parity, &pk) == 0);
+    CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &xonly_pk, &pk_parity, &pk) == 1);
+    CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, NULL, &pk_parity, &pk) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_xonly_pubkey_from_pubkey(none, &xonly_pk, NULL, &pk) == 1);
-    CHECK(secp256k1_xonly_pubkey_from_pubkey(none, &xonly_pk, &pk_parity, NULL) == 0);
+    CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &xonly_pk, NULL, &pk) == 1);
+    CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &xonly_pk, &pk_parity, NULL) == 0);
     CHECK(ecount == 2);
     memset(&pk, 0, sizeof(pk));
-    CHECK(secp256k1_xonly_pubkey_from_pubkey(none, &xonly_pk, &pk_parity, &pk) == 0);
+    CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &xonly_pk, &pk_parity, &pk) == 0);
     CHECK(ecount == 3);
 
     /* Choose a secret key such that the resulting pubkey and xonly_pubkey match. */
@@ -78,9 +73,9 @@ void test_xonly_pubkey(void) {
 
     /* Test xonly_pubkey_serialize and xonly_pubkey_parse */
     ecount = 0;
-    CHECK(secp256k1_xonly_pubkey_serialize(none, NULL, &xonly_pk) == 0);
+    CHECK(secp256k1_xonly_pubkey_serialize(ctx, NULL, &xonly_pk) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_xonly_pubkey_serialize(none, buf32, NULL) == 0);
+    CHECK(secp256k1_xonly_pubkey_serialize(ctx, buf32, NULL) == 0);
     CHECK(secp256k1_memcmp_var(buf32, zeros64, 32) == 0);
     CHECK(ecount == 2);
     {
@@ -88,20 +83,20 @@ void test_xonly_pubkey(void) {
          * special casing. */
         secp256k1_xonly_pubkey pk_tmp;
         memset(&pk_tmp, 0, sizeof(pk_tmp));
-        CHECK(secp256k1_xonly_pubkey_serialize(none, buf32, &pk_tmp) == 0);
+        CHECK(secp256k1_xonly_pubkey_serialize(ctx, buf32, &pk_tmp) == 0);
     }
     /* pubkey_load called illegal callback */
     CHECK(ecount == 3);
 
-    CHECK(secp256k1_xonly_pubkey_serialize(none, buf32, &xonly_pk) == 1);
+    CHECK(secp256k1_xonly_pubkey_serialize(ctx, buf32, &xonly_pk) == 1);
     ecount = 0;
-    CHECK(secp256k1_xonly_pubkey_parse(none, NULL, buf32) == 0);
+    CHECK(secp256k1_xonly_pubkey_parse(ctx, NULL, buf32) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_xonly_pubkey_parse(none, &xonly_pk, NULL) == 0);
+    CHECK(secp256k1_xonly_pubkey_parse(ctx, &xonly_pk, NULL) == 0);
     CHECK(ecount == 2);
 
     /* Serialization and parse roundtrip */
-    CHECK(secp256k1_xonly_pubkey_from_pubkey(none, &xonly_pk, NULL, &pk) == 1);
+    CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &xonly_pk, NULL, &pk) == 1);
     CHECK(secp256k1_xonly_pubkey_serialize(ctx, buf32, &xonly_pk) == 1);
     CHECK(secp256k1_xonly_pubkey_parse(ctx, &xonly_pk_tmp, buf32) == 1);
     CHECK(secp256k1_memcmp_var(&xonly_pk, &xonly_pk_tmp, sizeof(xonly_pk)) == 0);
@@ -109,11 +104,11 @@ void test_xonly_pubkey(void) {
     /* Test parsing invalid field elements */
     memset(&xonly_pk, 1, sizeof(xonly_pk));
     /* Overflowing field element */
-    CHECK(secp256k1_xonly_pubkey_parse(none, &xonly_pk, ones32) == 0);
+    CHECK(secp256k1_xonly_pubkey_parse(ctx, &xonly_pk, ones32) == 0);
     CHECK(secp256k1_memcmp_var(&xonly_pk, zeros64, sizeof(xonly_pk)) == 0);
     memset(&xonly_pk, 1, sizeof(xonly_pk));
     /* There's no point with x-coordinate 0 on secp256k1 */
-    CHECK(secp256k1_xonly_pubkey_parse(none, &xonly_pk, zeros64) == 0);
+    CHECK(secp256k1_xonly_pubkey_parse(ctx, &xonly_pk, zeros64) == 0);
     CHECK(secp256k1_memcmp_var(&xonly_pk, zeros64, sizeof(xonly_pk)) == 0);
     /* If a random 32-byte string can not be parsed with ec_pubkey_parse
      * (because interpreted as X coordinate it does not correspond to a point on
@@ -131,10 +126,6 @@ void test_xonly_pubkey(void) {
         }
     }
     CHECK(ecount == 2);
-
-    secp256k1_context_destroy(none);
-    secp256k1_context_destroy(sign);
-    secp256k1_context_destroy(verify);
 }
 
 void test_xonly_pubkey_comparison(void) {
@@ -149,29 +140,28 @@ void test_xonly_pubkey_comparison(void) {
     secp256k1_xonly_pubkey pk1;
     secp256k1_xonly_pubkey pk2;
     int ecount = 0;
-    secp256k1_context *none = api_test_context(SECP256K1_CONTEXT_NONE, &ecount);
 
-    CHECK(secp256k1_xonly_pubkey_parse(none, &pk1, pk1_ser) == 1);
-    CHECK(secp256k1_xonly_pubkey_parse(none, &pk2, pk2_ser) == 1);
+    set_counting_callbacks(ctx, &ecount);
 
-    CHECK(secp256k1_xonly_pubkey_cmp(none, NULL, &pk2) < 0);
+    CHECK(secp256k1_xonly_pubkey_parse(ctx, &pk1, pk1_ser) == 1);
+    CHECK(secp256k1_xonly_pubkey_parse(ctx, &pk2, pk2_ser) == 1);
+
+    CHECK(secp256k1_xonly_pubkey_cmp(ctx, NULL, &pk2) < 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk1, NULL) > 0);
+    CHECK(secp256k1_xonly_pubkey_cmp(ctx, &pk1, NULL) > 0);
     CHECK(ecount == 2);
-    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk1, &pk2) < 0);
-    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk2, &pk1) > 0);
-    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk1, &pk1) == 0);
-    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk2, &pk2) == 0);
+    CHECK(secp256k1_xonly_pubkey_cmp(ctx, &pk1, &pk2) < 0);
+    CHECK(secp256k1_xonly_pubkey_cmp(ctx, &pk2, &pk1) > 0);
+    CHECK(secp256k1_xonly_pubkey_cmp(ctx, &pk1, &pk1) == 0);
+    CHECK(secp256k1_xonly_pubkey_cmp(ctx, &pk2, &pk2) == 0);
     CHECK(ecount == 2);
     memset(&pk1, 0, sizeof(pk1)); /* illegal pubkey */
-    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk1, &pk2) < 0);
+    CHECK(secp256k1_xonly_pubkey_cmp(ctx, &pk1, &pk2) < 0);
     CHECK(ecount == 3);
-    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk1, &pk1) == 0);
+    CHECK(secp256k1_xonly_pubkey_cmp(ctx, &pk1, &pk1) == 0);
     CHECK(ecount == 5);
-    CHECK(secp256k1_xonly_pubkey_cmp(none, &pk2, &pk1) > 0);
+    CHECK(secp256k1_xonly_pubkey_cmp(ctx, &pk2, &pk1) > 0);
     CHECK(ecount == 6);
-
-    secp256k1_context_destroy(none);
 }
 
 void test_xonly_pubkey_tweak(void) {
@@ -186,39 +176,38 @@ void test_xonly_pubkey_tweak(void) {
     int i;
 
     int ecount;
-    secp256k1_context *none = api_test_context(SECP256K1_CONTEXT_NONE, &ecount);
-    secp256k1_context *sign = api_test_context(SECP256K1_CONTEXT_SIGN, &ecount);
-    secp256k1_context *verify = api_test_context(SECP256K1_CONTEXT_VERIFY, &ecount);
+
+    set_counting_callbacks(ctx, &ecount);
 
     memset(overflows, 0xff, sizeof(overflows));
     secp256k1_testrand256(tweak);
     secp256k1_testrand256(sk);
     CHECK(secp256k1_ec_pubkey_create(ctx, &internal_pk, sk) == 1);
-    CHECK(secp256k1_xonly_pubkey_from_pubkey(none, &internal_xonly_pk, &pk_parity, &internal_pk) == 1);
+    CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &internal_xonly_pk, &pk_parity, &internal_pk) == 1);
 
     ecount = 0;
-    CHECK(secp256k1_xonly_pubkey_tweak_add(none, &output_pk, &internal_xonly_pk, tweak) == 0);
+    CHECK(secp256k1_xonly_pubkey_tweak_add(ctx, &output_pk, &internal_xonly_pk, tweak) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_xonly_pubkey_tweak_add(ctx, &output_pk, &internal_xonly_pk, tweak) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_xonly_pubkey_tweak_add(ctx, &output_pk, &internal_xonly_pk, tweak) == 1);
+    CHECK(secp256k1_xonly_pubkey_tweak_add(ctx, NULL, &internal_xonly_pk, tweak) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_xonly_pubkey_tweak_add(sign, &output_pk, &internal_xonly_pk, tweak) == 0);
+    CHECK(secp256k1_xonly_pubkey_tweak_add(ctx, &output_pk, NULL, tweak) == 0);
     CHECK(ecount == 2);
-    CHECK(secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, &internal_xonly_pk, tweak) == 1);
-    CHECK(secp256k1_xonly_pubkey_tweak_add(verify, NULL, &internal_xonly_pk, tweak) == 0);
-    CHECK(ecount == 3);
-    CHECK(secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, NULL, tweak) == 0);
-    CHECK(ecount == 4);
     /* NULL internal_xonly_pk zeroes the output_pk */
     CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0);
-    CHECK(secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, &internal_xonly_pk, NULL) == 0);
-    CHECK(ecount == 5);
+    CHECK(secp256k1_xonly_pubkey_tweak_add(ctx, &output_pk, &internal_xonly_pk, NULL) == 0);
+    CHECK(ecount == 3);
     /* NULL tweak zeroes the output_pk */
     CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0);
 
     /* Invalid tweak zeroes the output_pk */
-    CHECK(secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, &internal_xonly_pk, overflows) == 0);
+    CHECK(secp256k1_xonly_pubkey_tweak_add(ctx, &output_pk, &internal_xonly_pk, overflows) == 0);
     CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk))  == 0);
 
     /* A zero tweak is fine */
-    CHECK(secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, &internal_xonly_pk, zeros64) == 1);
+    CHECK(secp256k1_xonly_pubkey_tweak_add(ctx, &output_pk, &internal_xonly_pk, zeros64) == 1);
 
     /* Fails if the resulting key was infinity */
     for (i = 0; i < count; i++) {
@@ -228,8 +217,8 @@ void test_xonly_pubkey_tweak(void) {
         secp256k1_scalar_set_b32(&scalar_tweak, sk, NULL);
         secp256k1_scalar_negate(&scalar_tweak, &scalar_tweak);
         secp256k1_scalar_get_b32(tweak, &scalar_tweak);
-        CHECK((secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, &internal_xonly_pk, sk) == 0)
-              || (secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, &internal_xonly_pk, tweak) == 0));
+        CHECK((secp256k1_xonly_pubkey_tweak_add(ctx, &output_pk, &internal_xonly_pk, sk) == 0)
+              || (secp256k1_xonly_pubkey_tweak_add(ctx, &output_pk, &internal_xonly_pk, tweak) == 0));
         CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0);
     }
 
@@ -237,13 +226,9 @@ void test_xonly_pubkey_tweak(void) {
     memset(&internal_xonly_pk, 0, sizeof(internal_xonly_pk));
     secp256k1_testrand256(tweak);
     ecount = 0;
-    CHECK(secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, &internal_xonly_pk, tweak) == 0);
+    CHECK(secp256k1_xonly_pubkey_tweak_add(ctx, &output_pk, &internal_xonly_pk, tweak) == 0);
     CHECK(ecount == 1);
     CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk))  == 0);
-
-    secp256k1_context_destroy(none);
-    secp256k1_context_destroy(sign);
-    secp256k1_context_destroy(verify);
 }
 
 void test_xonly_pubkey_tweak_check(void) {
@@ -260,34 +245,33 @@ void test_xonly_pubkey_tweak_check(void) {
     unsigned char tweak[32];
 
     int ecount;
-    secp256k1_context *none = api_test_context(SECP256K1_CONTEXT_NONE, &ecount);
-    secp256k1_context *sign = api_test_context(SECP256K1_CONTEXT_SIGN, &ecount);
-    secp256k1_context *verify = api_test_context(SECP256K1_CONTEXT_VERIFY, &ecount);
+
+    set_counting_callbacks(ctx, &ecount);
 
     memset(overflows, 0xff, sizeof(overflows));
     secp256k1_testrand256(tweak);
     secp256k1_testrand256(sk);
     CHECK(secp256k1_ec_pubkey_create(ctx, &internal_pk, sk) == 1);
-    CHECK(secp256k1_xonly_pubkey_from_pubkey(none, &internal_xonly_pk, &pk_parity, &internal_pk) == 1);
+    CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &internal_xonly_pk, &pk_parity, &internal_pk) == 1);
 
     ecount = 0;
-    CHECK(secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, &internal_xonly_pk, tweak) == 1);
-    CHECK(secp256k1_xonly_pubkey_from_pubkey(verify, &output_xonly_pk, &pk_parity, &output_pk) == 1);
+    CHECK(secp256k1_xonly_pubkey_tweak_add(ctx, &output_pk, &internal_xonly_pk, tweak) == 1);
+    CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &output_xonly_pk, &pk_parity, &output_pk) == 1);
     CHECK(secp256k1_xonly_pubkey_serialize(ctx, buf32, &output_xonly_pk) == 1);
-    CHECK(secp256k1_xonly_pubkey_tweak_add_check(none, buf32, pk_parity, &internal_xonly_pk, tweak) == 0);
+    CHECK(secp256k1_xonly_pubkey_tweak_add_check(ctx, buf32, pk_parity, &internal_xonly_pk, tweak) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_xonly_pubkey_tweak_add_check(ctx, buf32, pk_parity, &internal_xonly_pk, tweak) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_xonly_pubkey_tweak_add_check(ctx, buf32, pk_parity, &internal_xonly_pk, tweak) == 1);
+    CHECK(secp256k1_xonly_pubkey_tweak_add_check(ctx, NULL, pk_parity, &internal_xonly_pk, tweak) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_xonly_pubkey_tweak_add_check(sign, buf32, pk_parity, &internal_xonly_pk, tweak) == 0);
-    CHECK(ecount == 2);
-    CHECK(secp256k1_xonly_pubkey_tweak_add_check(verify, buf32, pk_parity, &internal_xonly_pk, tweak) == 1);
-    CHECK(secp256k1_xonly_pubkey_tweak_add_check(verify, NULL, pk_parity, &internal_xonly_pk, tweak) == 0);
-    CHECK(ecount == 3);
     /* invalid pk_parity value */
-    CHECK(secp256k1_xonly_pubkey_tweak_add_check(verify, buf32, 2, &internal_xonly_pk, tweak) == 0);
+    CHECK(secp256k1_xonly_pubkey_tweak_add_check(ctx, buf32, 2, &internal_xonly_pk, tweak) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_xonly_pubkey_tweak_add_check(ctx, buf32, pk_parity, NULL, tweak) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_xonly_pubkey_tweak_add_check(ctx, buf32, pk_parity, &internal_xonly_pk, NULL) == 0);
     CHECK(ecount == 3);
-    CHECK(secp256k1_xonly_pubkey_tweak_add_check(verify, buf32, pk_parity, NULL, tweak) == 0);
-    CHECK(ecount == 4);
-    CHECK(secp256k1_xonly_pubkey_tweak_add_check(verify, buf32, pk_parity, &internal_xonly_pk, NULL) == 0);
-    CHECK(ecount == 5);
 
     memset(tweak, 1, sizeof(tweak));
     CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &internal_xonly_pk, NULL, &internal_pk) == 1);
@@ -306,11 +290,7 @@ void test_xonly_pubkey_tweak_check(void) {
     CHECK(secp256k1_xonly_pubkey_tweak_add_check(ctx, output_pk32, pk_parity, &internal_xonly_pk, overflows) == 0);
     CHECK(secp256k1_xonly_pubkey_tweak_add(ctx, &output_pk, &internal_xonly_pk, overflows) == 0);
     CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0);
-    CHECK(ecount == 5);
-
-    secp256k1_context_destroy(none);
-    secp256k1_context_destroy(sign);
-    secp256k1_context_destroy(verify);
+    CHECK(ecount == 3);
 }
 
 /* Starts with an initial pubkey and recursively creates N_PUBKEYS - 1
@@ -356,9 +336,10 @@ void test_keypair(void) {
     secp256k1_xonly_pubkey xonly_pk, xonly_pk_tmp;
     int pk_parity, pk_parity_tmp;
     int ecount;
-    secp256k1_context *none = api_test_context(SECP256K1_CONTEXT_NONE, &ecount);
-    secp256k1_context *sign = api_test_context(SECP256K1_CONTEXT_SIGN, &ecount);
-    secp256k1_context *verify = api_test_context(SECP256K1_CONTEXT_VERIFY, &ecount);
+    secp256k1_context *sttc = secp256k1_context_clone(secp256k1_context_static);
+
+    set_counting_callbacks(ctx, &ecount);
+    set_counting_callbacks(sttc, &ecount);
 
     CHECK(sizeof(zeros96) == sizeof(keypair));
     memset(overflows, 0xFF, sizeof(overflows));
@@ -366,71 +347,75 @@ void test_keypair(void) {
     /* Test keypair_create */
     ecount = 0;
     secp256k1_testrand256(sk);
-    CHECK(secp256k1_keypair_create(none, &keypair, sk) == 0);
-    CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0);
+    CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
+    CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) != 0);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
+    CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) != 0);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_keypair_create(ctx, NULL, sk) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_keypair_create(verify, &keypair, sk) == 0);
+    CHECK(secp256k1_keypair_create(ctx, &keypair, NULL) == 0);
     CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0);
     CHECK(ecount == 2);
-    CHECK(secp256k1_keypair_create(sign, &keypair, sk) == 1);
-    CHECK(secp256k1_keypair_create(sign, NULL, sk) == 0);
-    CHECK(ecount == 3);
-    CHECK(secp256k1_keypair_create(sign, &keypair, NULL) == 0);
+    CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_keypair_create(sttc, &keypair, sk) == 0);
     CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0);
-    CHECK(ecount == 4);
+    CHECK(ecount == 3);
 
     /* Invalid secret key */
-    CHECK(secp256k1_keypair_create(sign, &keypair, zeros96) == 0);
+    CHECK(secp256k1_keypair_create(ctx, &keypair, zeros96) == 0);
     CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0);
-    CHECK(secp256k1_keypair_create(sign, &keypair, overflows) == 0);
+    CHECK(secp256k1_keypair_create(ctx, &keypair, overflows) == 0);
     CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0);
 
     /* Test keypair_pub */
     ecount = 0;
     secp256k1_testrand256(sk);
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
-    CHECK(secp256k1_keypair_pub(none, &pk, &keypair) == 1);
-    CHECK(secp256k1_keypair_pub(none, NULL, &keypair) == 0);
+    CHECK(secp256k1_keypair_pub(ctx, &pk, &keypair) == 1);
+    CHECK(secp256k1_keypair_pub(ctx, NULL, &keypair) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_keypair_pub(none, &pk, NULL) == 0);
+    CHECK(secp256k1_keypair_pub(ctx, &pk, NULL) == 0);
     CHECK(ecount == 2);
     CHECK(secp256k1_memcmp_var(zeros96, &pk, sizeof(pk)) == 0);
 
     /* Using an invalid keypair is fine for keypair_pub */
     memset(&keypair, 0, sizeof(keypair));
-    CHECK(secp256k1_keypair_pub(none, &pk, &keypair) == 1);
+    CHECK(secp256k1_keypair_pub(ctx, &pk, &keypair) == 1);
     CHECK(secp256k1_memcmp_var(zeros96, &pk, sizeof(pk)) == 0);
 
     /* keypair holds the same pubkey as pubkey_create */
-    CHECK(secp256k1_ec_pubkey_create(sign, &pk, sk) == 1);
-    CHECK(secp256k1_keypair_create(sign, &keypair, sk) == 1);
-    CHECK(secp256k1_keypair_pub(none, &pk_tmp, &keypair) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pk, sk) == 1);
+    CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
+    CHECK(secp256k1_keypair_pub(ctx, &pk_tmp, &keypair) == 1);
     CHECK(secp256k1_memcmp_var(&pk, &pk_tmp, sizeof(pk)) == 0);
 
     /** Test keypair_xonly_pub **/
     ecount = 0;
     secp256k1_testrand256(sk);
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
-    CHECK(secp256k1_keypair_xonly_pub(none, &xonly_pk, &pk_parity, &keypair) == 1);
-    CHECK(secp256k1_keypair_xonly_pub(none, NULL, &pk_parity, &keypair) == 0);
+    CHECK(secp256k1_keypair_xonly_pub(ctx, &xonly_pk, &pk_parity, &keypair) == 1);
+    CHECK(secp256k1_keypair_xonly_pub(ctx, NULL, &pk_parity, &keypair) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_keypair_xonly_pub(none, &xonly_pk, NULL, &keypair) == 1);
-    CHECK(secp256k1_keypair_xonly_pub(none, &xonly_pk, &pk_parity, NULL) == 0);
+    CHECK(secp256k1_keypair_xonly_pub(ctx, &xonly_pk, NULL, &keypair) == 1);
+    CHECK(secp256k1_keypair_xonly_pub(ctx, &xonly_pk, &pk_parity, NULL) == 0);
     CHECK(ecount == 2);
     CHECK(secp256k1_memcmp_var(zeros96, &xonly_pk, sizeof(xonly_pk)) == 0);
     /* Using an invalid keypair will set the xonly_pk to 0 (first reset
      * xonly_pk). */
-    CHECK(secp256k1_keypair_xonly_pub(none, &xonly_pk, &pk_parity, &keypair) == 1);
+    CHECK(secp256k1_keypair_xonly_pub(ctx, &xonly_pk, &pk_parity, &keypair) == 1);
     memset(&keypair, 0, sizeof(keypair));
-    CHECK(secp256k1_keypair_xonly_pub(none, &xonly_pk, &pk_parity, &keypair) == 0);
+    CHECK(secp256k1_keypair_xonly_pub(ctx, &xonly_pk, &pk_parity, &keypair) == 0);
     CHECK(secp256k1_memcmp_var(zeros96, &xonly_pk, sizeof(xonly_pk)) == 0);
     CHECK(ecount == 3);
 
     /** keypair holds the same xonly pubkey as pubkey_create **/
-    CHECK(secp256k1_ec_pubkey_create(sign, &pk, sk) == 1);
-    CHECK(secp256k1_xonly_pubkey_from_pubkey(none, &xonly_pk, &pk_parity, &pk) == 1);
-    CHECK(secp256k1_keypair_create(sign, &keypair, sk) == 1);
-    CHECK(secp256k1_keypair_xonly_pub(none, &xonly_pk_tmp, &pk_parity_tmp, &keypair) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pk, sk) == 1);
+    CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &xonly_pk, &pk_parity, &pk) == 1);
+    CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
+    CHECK(secp256k1_keypair_xonly_pub(ctx, &xonly_pk_tmp, &pk_parity_tmp, &keypair) == 1);
     CHECK(secp256k1_memcmp_var(&xonly_pk, &xonly_pk_tmp, sizeof(pk)) == 0);
     CHECK(pk_parity == pk_parity_tmp);
 
@@ -438,27 +423,24 @@ void test_keypair(void) {
     ecount = 0;
     secp256k1_testrand256(sk);
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
-    CHECK(secp256k1_keypair_sec(none, sk_tmp, &keypair) == 1);
-    CHECK(secp256k1_keypair_sec(none, NULL, &keypair) == 0);
+    CHECK(secp256k1_keypair_sec(ctx, sk_tmp, &keypair) == 1);
+    CHECK(secp256k1_keypair_sec(ctx, NULL, &keypair) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_keypair_sec(none, sk_tmp, NULL) == 0);
+    CHECK(secp256k1_keypair_sec(ctx, sk_tmp, NULL) == 0);
     CHECK(ecount == 2);
     CHECK(secp256k1_memcmp_var(zeros96, sk_tmp, sizeof(sk_tmp)) == 0);
 
     /* keypair returns the same seckey it got */
-    CHECK(secp256k1_keypair_create(sign, &keypair, sk) == 1);
-    CHECK(secp256k1_keypair_sec(none, sk_tmp, &keypair) == 1);
+    CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
+    CHECK(secp256k1_keypair_sec(ctx, sk_tmp, &keypair) == 1);
     CHECK(secp256k1_memcmp_var(sk, sk_tmp, sizeof(sk_tmp)) == 0);
 
 
     /* Using an invalid keypair is fine for keypair_seckey */
     memset(&keypair, 0, sizeof(keypair));
-    CHECK(secp256k1_keypair_sec(none, sk_tmp, &keypair) == 1);
+    CHECK(secp256k1_keypair_sec(ctx, sk_tmp, &keypair) == 1);
     CHECK(secp256k1_memcmp_var(zeros96, sk_tmp, sizeof(sk_tmp)) == 0);
-
-    secp256k1_context_destroy(none);
-    secp256k1_context_destroy(sign);
-    secp256k1_context_destroy(verify);
+    secp256k1_context_destroy(sttc);
 }
 
 void test_keypair_add(void) {
@@ -469,9 +451,8 @@ void test_keypair_add(void) {
     unsigned char tweak[32];
     int i;
     int ecount = 0;
-    secp256k1_context *none = api_test_context(SECP256K1_CONTEXT_NONE, &ecount);
-    secp256k1_context *sign = api_test_context(SECP256K1_CONTEXT_SIGN, &ecount);
-    secp256k1_context *verify = api_test_context(SECP256K1_CONTEXT_VERIFY, &ecount);
+
+    set_counting_callbacks(ctx, &ecount);
 
     CHECK(sizeof(zeros96) == sizeof(keypair));
     secp256k1_testrand256(sk);
@@ -479,15 +460,15 @@ void test_keypair_add(void) {
     memset(overflows, 0xFF, 32);
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
 
-    CHECK(secp256k1_keypair_xonly_tweak_add(none, &keypair, tweak) == 0);
+    CHECK(secp256k1_keypair_xonly_tweak_add(ctx, &keypair, tweak) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_keypair_xonly_tweak_add(ctx, &keypair, tweak) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_keypair_xonly_tweak_add(ctx, &keypair, tweak) == 1);
+    CHECK(secp256k1_keypair_xonly_tweak_add(ctx, NULL, tweak) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_keypair_xonly_tweak_add(sign, &keypair, tweak) == 0);
+    CHECK(secp256k1_keypair_xonly_tweak_add(ctx, &keypair, NULL) == 0);
     CHECK(ecount == 2);
-    CHECK(secp256k1_keypair_xonly_tweak_add(verify, &keypair, tweak) == 1);
-    CHECK(secp256k1_keypair_xonly_tweak_add(verify, NULL, tweak) == 0);
-    CHECK(ecount == 3);
-    CHECK(secp256k1_keypair_xonly_tweak_add(verify, &keypair, NULL) == 0);
-    CHECK(ecount == 4);
     /* This does not set the keypair to zeroes */
     CHECK(secp256k1_memcmp_var(&keypair, zeros96, sizeof(keypair)) != 0);
 
@@ -522,18 +503,18 @@ void test_keypair_add(void) {
     memset(&keypair, 0, sizeof(keypair));
     secp256k1_testrand256(tweak);
     ecount = 0;
-    CHECK(secp256k1_keypair_xonly_tweak_add(verify, &keypair, tweak) == 0);
+    CHECK(secp256k1_keypair_xonly_tweak_add(ctx, &keypair, tweak) == 0);
     CHECK(ecount == 1);
     CHECK(secp256k1_memcmp_var(&keypair, zeros96, sizeof(keypair))  == 0);
     /* Only seckey part of keypair invalid */
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
     memset(&keypair, 0, 32);
-    CHECK(secp256k1_keypair_xonly_tweak_add(verify, &keypair, tweak) == 0);
+    CHECK(secp256k1_keypair_xonly_tweak_add(ctx, &keypair, tweak) == 0);
     CHECK(ecount == 2);
     /* Only pubkey part of keypair invalid */
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
     memset(&keypair.data[32], 0, 64);
-    CHECK(secp256k1_keypair_xonly_tweak_add(verify, &keypair, tweak) == 0);
+    CHECK(secp256k1_keypair_xonly_tweak_add(ctx, &keypair, tweak) == 0);
     CHECK(ecount == 3);
 
     /* Check that the keypair_tweak_add implementation is correct */
@@ -562,13 +543,10 @@ void test_keypair_add(void) {
         CHECK(secp256k1_memcmp_var(&output_pk_xy, &output_pk_expected, sizeof(output_pk_xy)) == 0);
 
         /* Check that the secret key in the keypair is tweaked correctly */
-        CHECK(secp256k1_keypair_sec(none, sk32, &keypair) == 1);
+        CHECK(secp256k1_keypair_sec(ctx, sk32, &keypair) == 1);
         CHECK(secp256k1_ec_pubkey_create(ctx, &output_pk_expected, sk32) == 1);
         CHECK(secp256k1_memcmp_var(&output_pk_xy, &output_pk_expected, sizeof(output_pk_xy)) == 0);
     }
-    secp256k1_context_destroy(none);
-    secp256k1_context_destroy(sign);
-    secp256k1_context_destroy(verify);
 }
 
 void run_extrakeys_tests(void) {
diff --git a/src/secp256k1/src/modules/recovery/tests_exhaustive_impl.h b/src/secp256k1/src/modules/recovery/tests_exhaustive_impl.h
index 590a972ed3f..ed9386b6f8a 100644
--- a/src/secp256k1/src/modules/recovery/tests_exhaustive_impl.h
+++ b/src/secp256k1/src/modules/recovery/tests_exhaustive_impl.h
@@ -7,7 +7,7 @@
 #ifndef SECP256K1_MODULE_RECOVERY_EXHAUSTIVE_TESTS_H
 #define SECP256K1_MODULE_RECOVERY_EXHAUSTIVE_TESTS_H
 
-#include "src/modules/recovery/main_impl.h"
+#include "main_impl.h"
 #include "../../../include/secp256k1_recovery.h"
 
 void test_exhaustive_recovery_sign(const secp256k1_context *ctx, const secp256k1_ge *group) {
diff --git a/src/secp256k1/src/modules/recovery/tests_impl.h b/src/secp256k1/src/modules/recovery/tests_impl.h
index 40dba87ce39..0ff9294e38a 100644
--- a/src/secp256k1/src/modules/recovery/tests_impl.h
+++ b/src/secp256k1/src/modules/recovery/tests_impl.h
@@ -30,10 +30,7 @@ static int recovery_test_nonce_function(unsigned char *nonce32, const unsigned c
 
 void test_ecdsa_recovery_api(void) {
     /* Setup contexts that just count errors */
-    secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
-    secp256k1_context *sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
-    secp256k1_context *vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
-    secp256k1_context *both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+    secp256k1_context *sttc = secp256k1_context_clone(secp256k1_context_static);
     secp256k1_pubkey pubkey;
     secp256k1_pubkey recpubkey;
     secp256k1_ecdsa_signature normal_sig;
@@ -49,14 +46,10 @@ void test_ecdsa_recovery_api(void) {
                                        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                                        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff };
 
-    secp256k1_context_set_error_callback(none, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_error_callback(sign, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_error_callback(vrfy, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_error_callback(both, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_illegal_callback(both, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(ctx, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(sttc, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(sttc, counting_illegal_callback_fn, &ecount);
 
     /* Construct and verify corresponding public key. */
     CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
@@ -64,87 +57,74 @@ void test_ecdsa_recovery_api(void) {
 
     /* Check bad contexts and NULLs for signing */
     ecount = 0;
-    CHECK(secp256k1_ecdsa_sign_recoverable(none, &recsig, message, privkey, NULL, NULL) == 0);
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &recsig, message, privkey, NULL, NULL) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, NULL, message, privkey, NULL, NULL) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_ecdsa_sign_recoverable(sign, &recsig, message, privkey, NULL, NULL) == 1);
-    CHECK(ecount == 1);
-    CHECK(secp256k1_ecdsa_sign_recoverable(vrfy, &recsig, message, privkey, NULL, NULL) == 0);
-    CHECK(ecount == 2);
-    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &recsig, NULL, privkey, NULL, NULL) == 0);
     CHECK(ecount == 2);
-    CHECK(secp256k1_ecdsa_sign_recoverable(both, NULL, message, privkey, NULL, NULL) == 0);
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &recsig, message, NULL, NULL, NULL) == 0);
     CHECK(ecount == 3);
-    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, NULL, privkey, NULL, NULL) == 0);
+    CHECK(secp256k1_ecdsa_sign_recoverable(sttc, &recsig, message, privkey, NULL, NULL) == 0);
     CHECK(ecount == 4);
-    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, NULL, NULL, NULL) == 0);
-    CHECK(ecount == 5);
     /* This will fail or succeed randomly, and in either case will not ARG_CHECK failure */
-    secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, recovery_test_nonce_function, NULL);
-    CHECK(ecount == 5);
+    secp256k1_ecdsa_sign_recoverable(ctx, &recsig, message, privkey, recovery_test_nonce_function, NULL);
+    CHECK(ecount == 4);
     /* These will all fail, but not in ARG_CHECK way */
-    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, zero_privkey, NULL, NULL) == 0);
-    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, over_privkey, NULL, NULL) == 0);
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &recsig, message, zero_privkey, NULL, NULL) == 0);
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &recsig, message, over_privkey, NULL, NULL) == 0);
     /* This one will succeed. */
-    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, NULL, NULL) == 1);
-    CHECK(ecount == 5);
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &recsig, message, privkey, NULL, NULL) == 1);
+    CHECK(ecount == 4);
 
     /* Check signing with a goofy nonce function */
 
     /* Check bad contexts and NULLs for recovery */
     ecount = 0;
-    CHECK(secp256k1_ecdsa_recover(none, &recpubkey, &recsig, message) == 0);
+    CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, &recsig, message) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_ecdsa_recover(ctx, NULL, &recsig, message) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_ecdsa_recover(sign, &recpubkey, &recsig, message) == 0);
-    CHECK(ecount == 2);
-    CHECK(secp256k1_ecdsa_recover(vrfy, &recpubkey, &recsig, message) == 1);
-    CHECK(ecount == 2);
-    CHECK(secp256k1_ecdsa_recover(both, &recpubkey, &recsig, message) == 1);
+    CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, NULL, message) == 0);
     CHECK(ecount == 2);
-    CHECK(secp256k1_ecdsa_recover(both, NULL, &recsig, message) == 0);
+    CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, &recsig, NULL) == 0);
     CHECK(ecount == 3);
-    CHECK(secp256k1_ecdsa_recover(both, &recpubkey, NULL, message) == 0);
-    CHECK(ecount == 4);
-    CHECK(secp256k1_ecdsa_recover(both, &recpubkey, &recsig, NULL) == 0);
-    CHECK(ecount == 5);
 
     /* Check NULLs for conversion */
-    CHECK(secp256k1_ecdsa_sign(both, &normal_sig, message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign(ctx, &normal_sig, message, privkey, NULL, NULL) == 1);
     ecount = 0;
-    CHECK(secp256k1_ecdsa_recoverable_signature_convert(both, NULL, &recsig) == 0);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, NULL, &recsig) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_ecdsa_recoverable_signature_convert(both, &normal_sig, NULL) == 0);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &normal_sig, NULL) == 0);
     CHECK(ecount == 2);
-    CHECK(secp256k1_ecdsa_recoverable_signature_convert(both, &normal_sig, &recsig) == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &normal_sig, &recsig) == 1);
 
     /* Check NULLs for de/serialization */
-    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &recsig, message, privkey, NULL, NULL) == 1);
     ecount = 0;
-    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, NULL, &recid, &recsig) == 0);
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, NULL, &recid, &recsig) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, sig, NULL, &recsig) == 0);
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, NULL, &recsig) == 0);
     CHECK(ecount == 2);
-    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, sig, &recid, NULL) == 0);
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, NULL) == 0);
     CHECK(ecount == 3);
-    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, sig, &recid, &recsig) == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, &recsig) == 1);
 
-    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, NULL, sig, recid) == 0);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, NULL, sig, recid) == 0);
     CHECK(ecount == 4);
-    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, NULL, recid) == 0);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &recsig, NULL, recid) == 0);
     CHECK(ecount == 5);
-    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, sig, -1) == 0);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &recsig, sig, -1) == 0);
     CHECK(ecount == 6);
-    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, sig, 5) == 0);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &recsig, sig, 5) == 0);
     CHECK(ecount == 7);
     /* overflow in signature will fail but not affect ecount */
     memcpy(sig, over_privkey, 32);
-    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, sig, recid) == 0);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &recsig, sig, recid) == 0);
     CHECK(ecount == 7);
 
     /* cleanup */
-    secp256k1_context_destroy(none);
-    secp256k1_context_destroy(sign);
-    secp256k1_context_destroy(vrfy);
-    secp256k1_context_destroy(both);
+    secp256k1_context_destroy(sttc);
 }
 
 void test_ecdsa_recovery_end_to_end(void) {
diff --git a/src/secp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h b/src/secp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h
index affabd23a67..55f9028a638 100644
--- a/src/secp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h
+++ b/src/secp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h
@@ -8,7 +8,7 @@
 #define SECP256K1_MODULE_SCHNORRSIG_TESTS_EXHAUSTIVE_H
 
 #include "../../../include/secp256k1_schnorrsig.h"
-#include "src/modules/schnorrsig/main_impl.h"
+#include "main_impl.h"
 
 static const unsigned char invalid_pubkey_bytes[][32] = {
     /* 0 */
@@ -58,15 +58,19 @@ static const unsigned char invalid_pubkey_bytes[][32] = {
 
 #define NUM_INVALID_KEYS (sizeof(invalid_pubkey_bytes) / sizeof(invalid_pubkey_bytes[0]))
 
-static int secp256k1_hardened_nonce_function_smallint(unsigned char *nonce32, const unsigned char *msg32,
+static int secp256k1_hardened_nonce_function_smallint(unsigned char *nonce32, const unsigned char *msg,
+                                                      size_t msglen,
                                                       const unsigned char *key32, const unsigned char *xonly_pk32,
-                                                      const unsigned char *algo16, void* data) {
+                                                      const unsigned char *algo, size_t algolen,
+                                                      void* data) {
     secp256k1_scalar s;
     int *idata = data;
-    (void)msg32;
+    (void)msg;
+    (void)msglen;
     (void)key32;
     (void)xonly_pk32;
-    (void)algo16;
+    (void)algo;
+    (void)algolen;
     secp256k1_scalar_set_int(&s, *idata);
     secp256k1_scalar_get_b32(nonce32, &s);
     return 1;
@@ -101,7 +105,7 @@ static void test_exhaustive_schnorrsig_verify(const secp256k1_context *ctx, cons
                 secp256k1_scalar e;
                 unsigned char msg32[32];
                 secp256k1_testrand256(msg32);
-                secp256k1_schnorrsig_challenge(&e, sig64, msg32, pk32);
+                secp256k1_schnorrsig_challenge(&e, sig64, msg32, sizeof(msg32), pk32);
                 /* Only do work if we hit a challenge we haven't tried before. */
                 if (!e_done[e]) {
                     /* Iterate over the possible valid last 32 bytes in the signature.
@@ -119,7 +123,7 @@ static void test_exhaustive_schnorrsig_verify(const secp256k1_context *ctx, cons
                             secp256k1_testrand256(sig64 + 32);
                             expect_valid = 0;
                         }
-                        valid = secp256k1_schnorrsig_verify(ctx, sig64, msg32, &pubkeys[d - 1]);
+                        valid = secp256k1_schnorrsig_verify(ctx, sig64, msg32, sizeof(msg32), &pubkeys[d - 1]);
                         CHECK(valid == expect_valid);
                         count_valid += valid;
                     }
@@ -137,6 +141,8 @@ static void test_exhaustive_schnorrsig_verify(const secp256k1_context *ctx, cons
 static void test_exhaustive_schnorrsig_sign(const secp256k1_context *ctx, unsigned char (*xonly_pubkey_bytes)[32], const secp256k1_keypair* keypairs, const int* parities) {
     int d, k;
     uint64_t iter = 0;
+    secp256k1_schnorrsig_extraparams extraparams = SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT;
+
     /* Loop over keys. */
     for (d = 1; d < EXHAUSTIVE_TEST_ORDER; ++d) {
         int actual_d = d;
@@ -149,19 +155,21 @@ static void test_exhaustive_schnorrsig_sign(const secp256k1_context *ctx, unsign
             unsigned char sig64[64];
             int actual_k = k;
             if (skip_section(&iter)) continue;
+            extraparams.noncefp = secp256k1_hardened_nonce_function_smallint;
+            extraparams.ndata = &k;
             if (parities[k - 1]) actual_k = EXHAUSTIVE_TEST_ORDER - k;
             /* Generate random messages until all challenges have been tried. */
             while (e_count_done < EXHAUSTIVE_TEST_ORDER) {
                 secp256k1_scalar e;
                 secp256k1_testrand256(msg32);
-                secp256k1_schnorrsig_challenge(&e, xonly_pubkey_bytes[k - 1], msg32, xonly_pubkey_bytes[d - 1]);
+                secp256k1_schnorrsig_challenge(&e, xonly_pubkey_bytes[k - 1], msg32, sizeof(msg32), xonly_pubkey_bytes[d - 1]);
                 /* Only do work if we hit a challenge we haven't tried before. */
                 if (!e_done[e]) {
                     secp256k1_scalar expected_s = (actual_k + e * actual_d) % EXHAUSTIVE_TEST_ORDER;
                     unsigned char expected_s_bytes[32];
                     secp256k1_scalar_get_b32(expected_s_bytes, &expected_s);
                     /* Invoke the real function to construct a signature. */
-                    CHECK(secp256k1_schnorrsig_sign(ctx, sig64, msg32, &keypairs[d - 1], secp256k1_hardened_nonce_function_smallint, &k));
+                    CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig64, msg32, sizeof(msg32), &keypairs[d - 1], &extraparams));
                     /* The first 32 bytes must match the xonly pubkey for the specified k. */
                     CHECK(secp256k1_memcmp_var(sig64, xonly_pubkey_bytes[k - 1], 32) == 0);
                     /* The last 32 bytes must match the expected s value. */
diff --git a/src/secp256k1/src/modules/schnorrsig/tests_impl.h b/src/secp256k1/src/modules/schnorrsig/tests_impl.h
index f4fa5b4d846..06cc097cc1b 100644
--- a/src/secp256k1/src/modules/schnorrsig/tests_impl.h
+++ b/src/secp256k1/src/modules/schnorrsig/tests_impl.h
@@ -12,11 +12,11 @@
 /* Checks that a bit flip in the n_flip-th argument (that has n_bytes many
  * bytes) changes the hash function
  */
-void nonce_function_bip340_bitflip(unsigned char **args, size_t n_flip, size_t n_bytes) {
+void nonce_function_bip340_bitflip(unsigned char **args, size_t n_flip, size_t n_bytes, size_t msglen, size_t algolen) {
     unsigned char nonces[2][32];
-    CHECK(nonce_function_bip340(nonces[0], args[0], args[1], args[2], args[3], args[4]) == 1);
+    CHECK(nonce_function_bip340(nonces[0], args[0], msglen, args[1], args[2], args[3], algolen, args[4]) == 1);
     secp256k1_testrand_flip(args[n_flip], n_bytes);
-    CHECK(nonce_function_bip340(nonces[1], args[0], args[1], args[2], args[3], args[4]) == 1);
+    CHECK(nonce_function_bip340(nonces[1], args[0], msglen, args[1], args[2], args[3], algolen, args[4]) == 1);
     CHECK(secp256k1_memcmp_var(nonces[0], nonces[1], 32) != 0);
 }
 
@@ -34,11 +34,13 @@ void test_sha256_eq(const secp256k1_sha256 *sha1, const secp256k1_sha256 *sha2)
 void run_nonce_function_bip340_tests(void) {
     unsigned char tag[13] = "BIP0340/nonce";
     unsigned char aux_tag[11] = "BIP0340/aux";
-    unsigned char algo16[16] = "BIP0340/nonce\0\0\0";
+    unsigned char algo[13] = "BIP0340/nonce";
+    size_t algolen = sizeof(algo);
     secp256k1_sha256 sha;
     secp256k1_sha256 sha_optimized;
-    unsigned char nonce[32];
+    unsigned char nonce[32], nonce_z[32];
     unsigned char msg[32];
+    size_t msglen = sizeof(msg);
     unsigned char key[32];
     unsigned char pk[32];
     unsigned char aux_rand[32];
@@ -68,33 +70,48 @@ void run_nonce_function_bip340_tests(void) {
     args[0] = msg;
     args[1] = key;
     args[2] = pk;
-    args[3] = algo16;
+    args[3] = algo;
     args[4] = aux_rand;
     for (i = 0; i < count; i++) {
-        nonce_function_bip340_bitflip(args, 0, 32);
-        nonce_function_bip340_bitflip(args, 1, 32);
-        nonce_function_bip340_bitflip(args, 2, 32);
-        /* Flip algo16 special case "BIP0340/nonce" */
-        nonce_function_bip340_bitflip(args, 3, 16);
-        /* Flip algo16 again */
-        nonce_function_bip340_bitflip(args, 3, 16);
-        nonce_function_bip340_bitflip(args, 4, 32);
+        nonce_function_bip340_bitflip(args, 0, 32, msglen, algolen);
+        nonce_function_bip340_bitflip(args, 1, 32, msglen, algolen);
+        nonce_function_bip340_bitflip(args, 2, 32, msglen, algolen);
+        /* Flip algo special case "BIP0340/nonce" */
+        nonce_function_bip340_bitflip(args, 3, algolen, msglen, algolen);
+        /* Flip algo again */
+        nonce_function_bip340_bitflip(args, 3, algolen, msglen, algolen);
+        nonce_function_bip340_bitflip(args, 4, 32, msglen, algolen);
     }
 
-    /* NULL algo16 is disallowed */
-    CHECK(nonce_function_bip340(nonce, msg, key, pk, NULL, NULL) == 0);
-    /* Empty algo16 is fine */
-    memset(algo16, 0x00, 16);
-    CHECK(nonce_function_bip340(nonce, msg, key, pk, algo16, NULL) == 1);
-    /* algo16 with terminating null bytes is fine */
-    algo16[1] = 65;
-    CHECK(nonce_function_bip340(nonce, msg, key, pk, algo16, NULL) == 1);
-    /* Other algo16 is fine */
-    memset(algo16, 0xFF, 16);
-    CHECK(nonce_function_bip340(nonce, msg, key, pk, algo16, NULL) == 1);
-
-    /* NULL aux_rand argument is allowed. */
-    CHECK(nonce_function_bip340(nonce, msg, key, pk, algo16, NULL) == 1);
+    /* NULL algo is disallowed */
+    CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, NULL, 0, NULL) == 0);
+    CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, algo, algolen, NULL) == 1);
+    /* Other algo is fine */
+    secp256k1_testrand_bytes_test(algo, algolen);
+    CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, algo, algolen, NULL) == 1);
+
+    for (i = 0; i < count; i++) {
+        unsigned char nonce2[32];
+        uint32_t offset = secp256k1_testrand_int(msglen - 1);
+        size_t msglen_tmp = (msglen + offset) % msglen;
+        size_t algolen_tmp;
+
+        /* Different msglen gives different nonce */
+        CHECK(nonce_function_bip340(nonce2, msg, msglen_tmp, key, pk, algo, algolen, NULL) == 1);
+        CHECK(secp256k1_memcmp_var(nonce, nonce2, 32) != 0);
+
+        /* Different algolen gives different nonce */
+        offset = secp256k1_testrand_int(algolen - 1);
+        algolen_tmp = (algolen + offset) % algolen;
+        CHECK(nonce_function_bip340(nonce2, msg, msglen, key, pk, algo, algolen_tmp, NULL) == 1);
+        CHECK(secp256k1_memcmp_var(nonce, nonce2, 32) != 0);
+    }
+
+    /* NULL aux_rand argument is allowed, and identical to passing all zero aux_rand. */
+    memset(aux_rand, 0, 32);
+    CHECK(nonce_function_bip340(nonce_z, msg, msglen, key, pk, algo, algolen, &aux_rand) == 1);
+    CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, algo, algolen, NULL) == 1);
+    CHECK(secp256k1_memcmp_var(nonce_z, nonce, 32) == 0);
 }
 
 void test_schnorrsig_api(void) {
@@ -107,22 +124,17 @@ void test_schnorrsig_api(void) {
     secp256k1_xonly_pubkey pk[3];
     secp256k1_xonly_pubkey zero_pk;
     unsigned char sig[64];
+    secp256k1_schnorrsig_extraparams extraparams = SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT;
+    secp256k1_schnorrsig_extraparams invalid_extraparams = {{ 0 }, NULL, NULL};
 
     /** setup **/
-    secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
-    secp256k1_context *sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
-    secp256k1_context *vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
-    secp256k1_context *both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+    secp256k1_context *sttc = secp256k1_context_clone(secp256k1_context_static);
     int ecount;
 
-    secp256k1_context_set_error_callback(none, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_error_callback(sign, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_error_callback(vrfy, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_error_callback(both, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_illegal_callback(both, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(ctx, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(sttc, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(sttc, counting_illegal_callback_fn, &ecount);
 
     secp256k1_testrand256(sk1);
     secp256k1_testrand256(sk2);
@@ -138,48 +150,61 @@ void test_schnorrsig_api(void) {
 
     /** main test body **/
     ecount = 0;
-    CHECK(secp256k1_schnorrsig_sign(none, sig, msg, &keypairs[0], NULL, NULL) == 0);
+    CHECK(secp256k1_schnorrsig_sign32(ctx, sig, msg, &keypairs[0], NULL) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_schnorrsig_sign32(ctx, NULL, msg, &keypairs[0], NULL) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_schnorrsig_sign(vrfy, sig, msg, &keypairs[0], NULL, NULL) == 0);
-    CHECK(ecount == 2);
-    CHECK(secp256k1_schnorrsig_sign(sign, sig, msg, &keypairs[0], NULL, NULL) == 1);
+    CHECK(secp256k1_schnorrsig_sign32(ctx, sig, NULL, &keypairs[0], NULL) == 0);
     CHECK(ecount == 2);
-    CHECK(secp256k1_schnorrsig_sign(sign, NULL, msg, &keypairs[0], NULL, NULL) == 0);
+    CHECK(secp256k1_schnorrsig_sign32(ctx, sig, msg, NULL, NULL) == 0);
     CHECK(ecount == 3);
-    CHECK(secp256k1_schnorrsig_sign(sign, sig, NULL, &keypairs[0], NULL, NULL) == 0);
+    CHECK(secp256k1_schnorrsig_sign32(ctx, sig, msg, &invalid_keypair, NULL) == 0);
     CHECK(ecount == 4);
-    CHECK(secp256k1_schnorrsig_sign(sign, sig, msg, NULL, NULL, NULL) == 0);
+    CHECK(secp256k1_schnorrsig_sign32(sttc, sig, msg, &keypairs[0], NULL) == 0);
     CHECK(ecount == 5);
-    CHECK(secp256k1_schnorrsig_sign(sign, sig, msg, &invalid_keypair, NULL, NULL) == 0);
-    CHECK(ecount == 6);
 
     ecount = 0;
-    CHECK(secp256k1_schnorrsig_sign(sign, sig, msg, &keypairs[0], NULL, NULL) == 1);
-    CHECK(secp256k1_schnorrsig_verify(none, sig, msg, &pk[0]) == 0);
+    CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig, msg, sizeof(msg), &keypairs[0], &extraparams) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_schnorrsig_sign_custom(ctx, NULL, msg, sizeof(msg), &keypairs[0], &extraparams) == 0);
     CHECK(ecount == 1);
-    CHECK(secp256k1_schnorrsig_verify(sign, sig, msg, &pk[0]) == 0);
+    CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig, NULL, sizeof(msg), &keypairs[0], &extraparams) == 0);
     CHECK(ecount == 2);
-    CHECK(secp256k1_schnorrsig_verify(vrfy, sig, msg, &pk[0]) == 1);
+    CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig, NULL, 0, &keypairs[0], &extraparams) == 1);
     CHECK(ecount == 2);
-    CHECK(secp256k1_schnorrsig_verify(vrfy, NULL, msg, &pk[0]) == 0);
+    CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig, msg, sizeof(msg), NULL, &extraparams) == 0);
     CHECK(ecount == 3);
-    CHECK(secp256k1_schnorrsig_verify(vrfy, sig, NULL, &pk[0]) == 0);
+    CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig, msg, sizeof(msg), &invalid_keypair, &extraparams) == 0);
     CHECK(ecount == 4);
-    CHECK(secp256k1_schnorrsig_verify(vrfy, sig, msg, NULL) == 0);
+    CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig, msg, sizeof(msg), &keypairs[0], NULL) == 1);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig, msg, sizeof(msg), &keypairs[0], &invalid_extraparams) == 0);
     CHECK(ecount == 5);
-    CHECK(secp256k1_schnorrsig_verify(vrfy, sig, msg, &zero_pk) == 0);
+    CHECK(secp256k1_schnorrsig_sign_custom(sttc, sig, msg, sizeof(msg), &keypairs[0], &extraparams) == 0);
     CHECK(ecount == 6);
 
-    secp256k1_context_destroy(none);
-    secp256k1_context_destroy(sign);
-    secp256k1_context_destroy(vrfy);
-    secp256k1_context_destroy(both);
+    ecount = 0;
+    CHECK(secp256k1_schnorrsig_sign32(ctx, sig, msg, &keypairs[0], NULL) == 1);
+    CHECK(secp256k1_schnorrsig_verify(ctx, sig, msg, sizeof(msg), &pk[0]) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_schnorrsig_verify(ctx, NULL, msg, sizeof(msg), &pk[0]) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_schnorrsig_verify(ctx, sig, NULL, sizeof(msg), &pk[0]) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_schnorrsig_verify(ctx, sig, NULL, 0, &pk[0]) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_schnorrsig_verify(ctx, sig, msg, sizeof(msg), NULL) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_schnorrsig_verify(ctx, sig, msg, sizeof(msg), &zero_pk) == 0);
+    CHECK(ecount == 4);
+
+    secp256k1_context_destroy(sttc);
 }
 
 /* Checks that hash initialized by secp256k1_schnorrsig_sha256_tagged has the
  * expected state. */
 void test_schnorrsig_sha256_tagged(void) {
-    char tag[17] = "BIP0340/challenge";
+    unsigned char tag[17] = "BIP0340/challenge";
     secp256k1_sha256 sha;
     secp256k1_sha256 sha_optimized;
 
@@ -190,19 +215,19 @@ void test_schnorrsig_sha256_tagged(void) {
 
 /* Helper function for schnorrsig_bip_vectors
  * Signs the message and checks that it's the same as expected_sig. */
-void test_schnorrsig_bip_vectors_check_signing(const unsigned char *sk, const unsigned char *pk_serialized, unsigned char *aux_rand, const unsigned char *msg, const unsigned char *expected_sig) {
+void test_schnorrsig_bip_vectors_check_signing(const unsigned char *sk, const unsigned char *pk_serialized, const unsigned char *aux_rand, const unsigned char *msg32, const unsigned char *expected_sig) {
     unsigned char sig[64];
     secp256k1_keypair keypair;
     secp256k1_xonly_pubkey pk, pk_expected;
 
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk));
-    CHECK(secp256k1_schnorrsig_sign(ctx, sig, msg, &keypair, NULL, aux_rand));
+    CHECK(secp256k1_schnorrsig_sign32(ctx, sig, msg32, &keypair, aux_rand));
     CHECK(secp256k1_memcmp_var(sig, expected_sig, 64) == 0);
 
     CHECK(secp256k1_xonly_pubkey_parse(ctx, &pk_expected, pk_serialized));
     CHECK(secp256k1_keypair_xonly_pub(ctx, &pk, NULL, &keypair));
     CHECK(secp256k1_memcmp_var(&pk, &pk_expected, sizeof(pk)) == 0);
-    CHECK(secp256k1_schnorrsig_verify(ctx, sig, msg, &pk));
+    CHECK(secp256k1_schnorrsig_verify(ctx, sig, msg32, 32, &pk));
 }
 
 /* Helper function for schnorrsig_bip_vectors
@@ -211,7 +236,7 @@ void test_schnorrsig_bip_vectors_check_verify(const unsigned char *pk_serialized
     secp256k1_xonly_pubkey pk;
 
     CHECK(secp256k1_xonly_pubkey_parse(ctx, &pk, pk_serialized));
-    CHECK(expected == secp256k1_schnorrsig_verify(ctx, sig, msg32, &pk));
+    CHECK(expected == secp256k1_schnorrsig_verify(ctx, sig, msg32, 32, &pk));
 }
 
 /* Test vectors according to BIP-340 ("Schnorr Signatures for secp256k1"). See
@@ -634,22 +659,26 @@ void test_schnorrsig_bip_vectors(void) {
 }
 
 /* Nonce function that returns constant 0 */
-static int nonce_function_failing(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo16, void *data) {
-    (void) msg32;
+static int nonce_function_failing(unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) {
+    (void) msg;
+    (void) msglen;
     (void) key32;
     (void) xonly_pk32;
-    (void) algo16;
+    (void) algo;
+    (void) algolen;
     (void) data;
     (void) nonce32;
     return 0;
 }
 
 /* Nonce function that sets nonce to 0 */
-static int nonce_function_0(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo16, void *data) {
-    (void) msg32;
+static int nonce_function_0(unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) {
+    (void) msg;
+    (void) msglen;
     (void) key32;
     (void) xonly_pk32;
-    (void) algo16;
+    (void) algo;
+    (void) algolen;
     (void) data;
 
     memset(nonce32, 0, 32);
@@ -657,11 +686,13 @@ static int nonce_function_0(unsigned char *nonce32, const unsigned char *msg32,
 }
 
 /* Nonce function that sets nonce to 0xFF...0xFF */
-static int nonce_function_overflowing(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo16, void *data) {
-    (void) msg32;
+static int nonce_function_overflowing(unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) {
+    (void) msg;
+    (void) msglen;
     (void) key32;
     (void) xonly_pk32;
-    (void) algo16;
+    (void) algo;
+    (void) algolen;
     (void) data;
 
     memset(nonce32, 0xFF, 32);
@@ -670,24 +701,48 @@ static int nonce_function_overflowing(unsigned char *nonce32, const unsigned cha
 
 void test_schnorrsig_sign(void) {
     unsigned char sk[32];
+    secp256k1_xonly_pubkey pk;
     secp256k1_keypair keypair;
     const unsigned char msg[32] = "this is a msg for a schnorrsig..";
     unsigned char sig[64];
+    unsigned char sig2[64];
     unsigned char zeros64[64] = { 0 };
+    secp256k1_schnorrsig_extraparams extraparams = SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT;
+    unsigned char aux_rand[32];
 
     secp256k1_testrand256(sk);
+    secp256k1_testrand256(aux_rand);
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk));
-    CHECK(secp256k1_schnorrsig_sign(ctx, sig, msg, &keypair, NULL, NULL) == 1);
+    CHECK(secp256k1_keypair_xonly_pub(ctx, &pk, NULL, &keypair));
+    CHECK(secp256k1_schnorrsig_sign32(ctx, sig, msg, &keypair, NULL) == 1);
+    CHECK(secp256k1_schnorrsig_verify(ctx, sig, msg, sizeof(msg), &pk));
+    /* Check that deprecated alias gives the same result */
+    CHECK(secp256k1_schnorrsig_sign(ctx, sig2, msg, &keypair, NULL) == 1);
+    CHECK(secp256k1_memcmp_var(sig, sig2, sizeof(sig)) == 0);
 
     /* Test different nonce functions */
+    CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig, msg, sizeof(msg), &keypair, &extraparams) == 1);
+    CHECK(secp256k1_schnorrsig_verify(ctx, sig, msg, sizeof(msg), &pk));
     memset(sig, 1, sizeof(sig));
-    CHECK(secp256k1_schnorrsig_sign(ctx, sig, msg, &keypair, nonce_function_failing, NULL) == 0);
+    extraparams.noncefp = nonce_function_failing;
+    CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig, msg, sizeof(msg), &keypair, &extraparams) == 0);
     CHECK(secp256k1_memcmp_var(sig, zeros64, sizeof(sig)) == 0);
     memset(&sig, 1, sizeof(sig));
-    CHECK(secp256k1_schnorrsig_sign(ctx, sig, msg, &keypair, nonce_function_0, NULL) == 0);
+    extraparams.noncefp = nonce_function_0;
+    CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig, msg, sizeof(msg), &keypair, &extraparams) == 0);
     CHECK(secp256k1_memcmp_var(sig, zeros64, sizeof(sig)) == 0);
-    CHECK(secp256k1_schnorrsig_sign(ctx, sig, msg, &keypair, nonce_function_overflowing, NULL) == 1);
-    CHECK(secp256k1_memcmp_var(sig, zeros64, sizeof(sig)) != 0);
+    memset(&sig, 1, sizeof(sig));
+    extraparams.noncefp = nonce_function_overflowing;
+    CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig, msg, sizeof(msg), &keypair, &extraparams) == 1);
+    CHECK(secp256k1_schnorrsig_verify(ctx, sig, msg, sizeof(msg), &pk));
+
+    /* When using the default nonce function, schnorrsig_sign_custom produces
+     * the same result as schnorrsig_sign with aux_rand = extraparams.ndata */
+    extraparams.noncefp = NULL;
+    extraparams.ndata = aux_rand;
+    CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig, msg, sizeof(msg), &keypair, &extraparams) == 1);
+    CHECK(secp256k1_schnorrsig_sign32(ctx, sig2, msg, &keypair, extraparams.ndata) == 1);
+    CHECK(secp256k1_memcmp_var(sig, sig2, sizeof(sig)) == 0);
 }
 
 #define N_SIGS 3
@@ -709,47 +764,65 @@ void test_schnorrsig_sign_verify(void) {
 
     for (i = 0; i < N_SIGS; i++) {
         secp256k1_testrand256(msg[i]);
-        CHECK(secp256k1_schnorrsig_sign(ctx, sig[i], msg[i], &keypair, NULL, NULL));
-        CHECK(secp256k1_schnorrsig_verify(ctx, sig[i], msg[i], &pk));
+        CHECK(secp256k1_schnorrsig_sign32(ctx, sig[i], msg[i], &keypair, NULL));
+        CHECK(secp256k1_schnorrsig_verify(ctx, sig[i], msg[i], sizeof(msg[i]), &pk));
     }
 
     {
         /* Flip a few bits in the signature and in the message and check that
          * verify and verify_batch (TODO) fail */
         size_t sig_idx = secp256k1_testrand_int(N_SIGS);
-        size_t byte_idx = secp256k1_testrand_int(32);
+        size_t byte_idx = secp256k1_testrand_bits(5);
         unsigned char xorbyte = secp256k1_testrand_int(254)+1;
         sig[sig_idx][byte_idx] ^= xorbyte;
-        CHECK(!secp256k1_schnorrsig_verify(ctx, sig[sig_idx], msg[sig_idx], &pk));
+        CHECK(!secp256k1_schnorrsig_verify(ctx, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk));
         sig[sig_idx][byte_idx] ^= xorbyte;
 
-        byte_idx = secp256k1_testrand_int(32);
+        byte_idx = secp256k1_testrand_bits(5);
         sig[sig_idx][32+byte_idx] ^= xorbyte;
-        CHECK(!secp256k1_schnorrsig_verify(ctx, sig[sig_idx], msg[sig_idx], &pk));
+        CHECK(!secp256k1_schnorrsig_verify(ctx, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk));
         sig[sig_idx][32+byte_idx] ^= xorbyte;
 
-        byte_idx = secp256k1_testrand_int(32);
+        byte_idx = secp256k1_testrand_bits(5);
         msg[sig_idx][byte_idx] ^= xorbyte;
-        CHECK(!secp256k1_schnorrsig_verify(ctx, sig[sig_idx], msg[sig_idx], &pk));
+        CHECK(!secp256k1_schnorrsig_verify(ctx, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk));
         msg[sig_idx][byte_idx] ^= xorbyte;
 
         /* Check that above bitflips have been reversed correctly */
-        CHECK(secp256k1_schnorrsig_verify(ctx, sig[sig_idx], msg[sig_idx], &pk));
+        CHECK(secp256k1_schnorrsig_verify(ctx, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk));
     }
 
     /* Test overflowing s */
-    CHECK(secp256k1_schnorrsig_sign(ctx, sig[0], msg[0], &keypair, NULL, NULL));
-    CHECK(secp256k1_schnorrsig_verify(ctx, sig[0], msg[0], &pk));
+    CHECK(secp256k1_schnorrsig_sign32(ctx, sig[0], msg[0], &keypair, NULL));
+    CHECK(secp256k1_schnorrsig_verify(ctx, sig[0], msg[0], sizeof(msg[0]), &pk));
     memset(&sig[0][32], 0xFF, 32);
-    CHECK(!secp256k1_schnorrsig_verify(ctx, sig[0], msg[0], &pk));
+    CHECK(!secp256k1_schnorrsig_verify(ctx, sig[0], msg[0], sizeof(msg[0]), &pk));
 
     /* Test negative s */
-    CHECK(secp256k1_schnorrsig_sign(ctx, sig[0], msg[0], &keypair, NULL, NULL));
-    CHECK(secp256k1_schnorrsig_verify(ctx, sig[0], msg[0], &pk));
+    CHECK(secp256k1_schnorrsig_sign32(ctx, sig[0], msg[0], &keypair, NULL));
+    CHECK(secp256k1_schnorrsig_verify(ctx, sig[0], msg[0], sizeof(msg[0]), &pk));
     secp256k1_scalar_set_b32(&s, &sig[0][32], NULL);
     secp256k1_scalar_negate(&s, &s);
     secp256k1_scalar_get_b32(&sig[0][32], &s);
-    CHECK(!secp256k1_schnorrsig_verify(ctx, sig[0], msg[0], &pk));
+    CHECK(!secp256k1_schnorrsig_verify(ctx, sig[0], msg[0], sizeof(msg[0]), &pk));
+
+    /* The empty message can be signed & verified */
+    CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig[0], NULL, 0, &keypair, NULL) == 1);
+    CHECK(secp256k1_schnorrsig_verify(ctx, sig[0], NULL, 0, &pk) == 1);
+
+    {
+        /* Test varying message lengths */
+        unsigned char msg_large[32 * 8];
+        uint32_t msglen  = secp256k1_testrand_int(sizeof(msg_large));
+        for (i = 0; i < sizeof(msg_large); i += 32) {
+            secp256k1_testrand256(&msg_large[i]);
+        }
+        CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig[0], msg_large, msglen, &keypair, NULL) == 1);
+        CHECK(secp256k1_schnorrsig_verify(ctx, sig[0], msg_large, msglen, &pk) == 1);
+        /* Verification for a random wrong message length fails */
+        msglen = (msglen + (sizeof(msg_large) - 1)) % sizeof(msg_large);
+        CHECK(secp256k1_schnorrsig_verify(ctx, sig[0], msg_large, msglen, &pk) == 0);
+    }
 }
 #undef N_SIGS
 
@@ -777,10 +850,10 @@ void test_schnorrsig_taproot(void) {
 
     /* Key spend */
     secp256k1_testrand256(msg);
-    CHECK(secp256k1_schnorrsig_sign(ctx, sig, msg, &keypair, NULL, NULL) == 1);
+    CHECK(secp256k1_schnorrsig_sign32(ctx, sig, msg, &keypair, NULL) == 1);
     /* Verify key spend */
     CHECK(secp256k1_xonly_pubkey_parse(ctx, &output_pk, output_pk_bytes) == 1);
-    CHECK(secp256k1_schnorrsig_verify(ctx, sig, msg, &output_pk) == 1);
+    CHECK(secp256k1_schnorrsig_verify(ctx, sig, msg, sizeof(msg), &output_pk) == 1);
 
     /* Script spend */
     CHECK(secp256k1_xonly_pubkey_serialize(ctx, internal_pk_bytes, &internal_pk) == 1);
diff --git a/src/secp256k1/src/selftest.h b/src/secp256k1/src/selftest.h
index 52f1b8442e7..d083ac95248 100644
--- a/src/secp256k1/src/selftest.h
+++ b/src/secp256k1/src/selftest.h
@@ -25,7 +25,7 @@ static int secp256k1_selftest_sha256(void) {
     return secp256k1_memcmp_var(out, output32, 32) == 0;
 }
 
-static int secp256k1_selftest(void) {
+static int secp256k1_selftest_passes(void) {
     return secp256k1_selftest_sha256();
 }
 
diff --git a/src/secp256k1/src/testrand.h b/src/secp256k1/src/testrand.h
index 667d1867bd6..bd149bb1b48 100644
--- a/src/secp256k1/src/testrand.h
+++ b/src/secp256k1/src/testrand.h
@@ -17,11 +17,14 @@
 SECP256K1_INLINE static void secp256k1_testrand_seed(const unsigned char *seed16);
 
 /** Generate a pseudorandom number in the range [0..2**32-1]. */
-static uint32_t secp256k1_testrand32(void);
+SECP256K1_INLINE static uint32_t secp256k1_testrand32(void);
+
+/** Generate a pseudorandom number in the range [0..2**64-1]. */
+SECP256K1_INLINE static uint64_t secp256k1_testrand64(void);
 
 /** Generate a pseudorandom number in the range [0..2**bits-1]. Bits must be 1 or
  *  more. */
-static uint32_t secp256k1_testrand_bits(int bits);
+SECP256K1_INLINE static uint64_t secp256k1_testrand_bits(int bits);
 
 /** Generate a pseudorandom number in the range [0..range-1]. */
 static uint32_t secp256k1_testrand_int(uint32_t range);
diff --git a/src/secp256k1/src/testrand_impl.h b/src/secp256k1/src/testrand_impl.h
index c8d30ef6a81..e9b9d7ded44 100644
--- a/src/secp256k1/src/testrand_impl.h
+++ b/src/secp256k1/src/testrand_impl.h
@@ -14,37 +14,64 @@
 #include "testrand.h"
 #include "hash.h"
 
-static secp256k1_rfc6979_hmac_sha256 secp256k1_test_rng;
-static uint32_t secp256k1_test_rng_precomputed[8];
-static int secp256k1_test_rng_precomputed_used = 8;
+static uint64_t secp256k1_test_state[4];
 static uint64_t secp256k1_test_rng_integer;
 static int secp256k1_test_rng_integer_bits_left = 0;
 
 SECP256K1_INLINE static void secp256k1_testrand_seed(const unsigned char *seed16) {
-    secp256k1_rfc6979_hmac_sha256_initialize(&secp256k1_test_rng, seed16, 16);
+    static const unsigned char PREFIX[19] = "secp256k1 test init";
+    unsigned char out32[32];
+    secp256k1_sha256 hash;
+    int i;
+
+    /* Use SHA256(PREFIX || seed16) as initial state. */
+    secp256k1_sha256_initialize(&hash);
+    secp256k1_sha256_write(&hash, PREFIX, sizeof(PREFIX));
+    secp256k1_sha256_write(&hash, seed16, 16);
+    secp256k1_sha256_finalize(&hash, out32);
+    for (i = 0; i < 4; ++i) {
+        uint64_t s = 0;
+        int j;
+        for (j = 0; j < 8; ++j) s = (s << 8) | out32[8*i + j];
+        secp256k1_test_state[i] = s;
+    }
+    secp256k1_test_rng_integer_bits_left = 0;
 }
 
-SECP256K1_INLINE static uint32_t secp256k1_testrand32(void) {
-    if (secp256k1_test_rng_precomputed_used == 8) {
-        secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, (unsigned char*)(&secp256k1_test_rng_precomputed[0]), sizeof(secp256k1_test_rng_precomputed));
-        secp256k1_test_rng_precomputed_used = 0;
-    }
-    return secp256k1_test_rng_precomputed[secp256k1_test_rng_precomputed_used++];
+SECP256K1_INLINE static uint64_t rotl(const uint64_t x, int k) {
+    return (x << k) | (x >> (64 - k));
+}
+
+SECP256K1_INLINE static uint64_t secp256k1_testrand64(void) {
+    /* Test-only Xoshiro256++ RNG. See https://prng.di.unimi.it/ */
+    const uint64_t result = rotl(secp256k1_test_state[0] + secp256k1_test_state[3], 23) + secp256k1_test_state[0];
+    const uint64_t t = secp256k1_test_state[1] << 17;
+    secp256k1_test_state[2] ^= secp256k1_test_state[0];
+    secp256k1_test_state[3] ^= secp256k1_test_state[1];
+    secp256k1_test_state[1] ^= secp256k1_test_state[2];
+    secp256k1_test_state[0] ^= secp256k1_test_state[3];
+    secp256k1_test_state[2] ^= t;
+    secp256k1_test_state[3] = rotl(secp256k1_test_state[3], 45);
+    return result;
 }
 
-static uint32_t secp256k1_testrand_bits(int bits) {
-    uint32_t ret;
+SECP256K1_INLINE static uint64_t secp256k1_testrand_bits(int bits) {
+    uint64_t ret;
     if (secp256k1_test_rng_integer_bits_left < bits) {
-        secp256k1_test_rng_integer |= (((uint64_t)secp256k1_testrand32()) << secp256k1_test_rng_integer_bits_left);
-        secp256k1_test_rng_integer_bits_left += 32;
+        secp256k1_test_rng_integer = secp256k1_testrand64();
+        secp256k1_test_rng_integer_bits_left = 64;
     }
     ret = secp256k1_test_rng_integer;
     secp256k1_test_rng_integer >>= bits;
     secp256k1_test_rng_integer_bits_left -= bits;
-    ret &= ((~((uint32_t)0)) >> (32 - bits));
+    ret &= ((~((uint64_t)0)) >> (64 - bits));
     return ret;
 }
 
+SECP256K1_INLINE static uint32_t secp256k1_testrand32(void) {
+    return secp256k1_testrand_bits(32);
+}
+
 static uint32_t secp256k1_testrand_int(uint32_t range) {
     /* We want a uniform integer between 0 and range-1, inclusive.
      * B is the smallest number such that range <= 2**B.
@@ -85,7 +112,19 @@ static uint32_t secp256k1_testrand_int(uint32_t range) {
 }
 
 static void secp256k1_testrand256(unsigned char *b32) {
-    secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, b32, 32);
+    int i;
+    for (i = 0; i < 4; ++i) {
+        uint64_t val = secp256k1_testrand64();
+        b32[0] = val;
+        b32[1] = val >> 8;
+        b32[2] = val >> 16;
+        b32[3] = val >> 24;
+        b32[4] = val >> 32;
+        b32[5] = val >> 40;
+        b32[6] = val >> 48;
+        b32[7] = val >> 56;
+        b32 += 8;
+    }
 }
 
 static void secp256k1_testrand_bytes_test(unsigned char *bytes, size_t len) {
@@ -109,7 +148,7 @@ static void secp256k1_testrand256_test(unsigned char *b32) {
 }
 
 static void secp256k1_testrand_flip(unsigned char *b, size_t len) {
-    b[secp256k1_testrand_int(len)] ^= (1 << secp256k1_testrand_int(8));
+    b[secp256k1_testrand_int(len)] ^= (1 << secp256k1_testrand_bits(3));
 }
 
 static void secp256k1_testrand_init(const char* hexseed) {
diff --git a/src/secp256k1/src/tests.c b/src/secp256k1/src/tests.c
index 6ceaba5e311..53613f420a7 100644
--- a/src/secp256k1/src/tests.c
+++ b/src/secp256k1/src/tests.c
@@ -20,24 +20,17 @@
 #include "testrand_impl.h"
 #include "util.h"
 
-#ifdef ENABLE_OPENSSL_TESTS
-#include <openssl/bn.h>
-#include <openssl/ec.h>
-#include <openssl/ecdsa.h>
-#include <openssl/obj_mac.h>
-# if OPENSSL_VERSION_NUMBER < 0x10100000L
-void ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **pr, const BIGNUM **ps) {*pr = sig->r; *ps = sig->s;}
-# endif
-#endif
-
 #include "../contrib/lax_der_parsing.c"
 #include "../contrib/lax_der_privatekey_parsing.c"
 
 #include "modinv32_impl.h"
 #ifdef SECP256K1_WIDEMUL_INT128
 #include "modinv64_impl.h"
+#include "int128_impl.h"
 #endif
 
+#define CONDITIONAL_TEST(cnt, nam) if (count < (cnt)) { printf("Skipping %s (iteration count too low)\n", nam); } else
+
 static int count = 64;
 static secp256k1_context *ctx = NULL;
 
@@ -110,6 +103,12 @@ void random_group_element_jacobian_test(secp256k1_gej *gej, const secp256k1_ge *
     gej->infinity = ge->infinity;
 }
 
+void random_gej_test(secp256k1_gej *gej) {
+    secp256k1_ge ge;
+    random_group_element_test(&ge);
+    random_group_element_jacobian_test(gej, &ge);
+}
+
 void random_scalar_order_test(secp256k1_scalar *num) {
     do {
         unsigned char b32[32];
@@ -142,6 +141,43 @@ void random_scalar_order_b32(unsigned char *b32) {
     secp256k1_scalar_get_b32(b32, &num);
 }
 
+void run_selftest_tests(void) {
+    /* Test public API */
+    secp256k1_selftest();
+}
+
+int ecmult_gen_context_eq(const secp256k1_ecmult_gen_context *a, const secp256k1_ecmult_gen_context *b) {
+    return a->built == b->built
+            && secp256k1_scalar_eq(&a->blind, &b->blind)
+            && secp256k1_gej_eq_var(&a->initial, &b->initial);
+}
+
+int context_eq(const secp256k1_context *a, const secp256k1_context *b) {
+    return a->declassify == b->declassify
+            && ecmult_gen_context_eq(&a->ecmult_gen_ctx, &b->ecmult_gen_ctx)
+            && a->illegal_callback.fn == b->illegal_callback.fn
+            && a->illegal_callback.data == b->illegal_callback.
+data
+            && a->error_callback.fn == b->error_callback.fn
+            && a->error_callback.data == b->error_callback.data;
+}
+
+void test_deprecated_flags(void) {
+    unsigned int flags[] = { SECP256K1_CONTEXT_SIGN,
+                             SECP256K1_CONTEXT_VERIFY,
+                             SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY };
+    int i;
+    /* Check that a context created with any of the flags in the flags array is
+     * identical to the NONE context. */
+    for (i = 0; i < (int)(sizeof(flags)/sizeof(flags[0])); i++) {
+        secp256k1_context *tmp_ctx;
+        CHECK(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE) == secp256k1_context_preallocated_size(flags[i]));
+        tmp_ctx = secp256k1_context_create(flags[i]);
+        CHECK(context_eq(ctx, tmp_ctx));
+        secp256k1_context_destroy(tmp_ctx);
+    }
+}
+
 void run_context_tests(int use_prealloc) {
     secp256k1_pubkey pubkey;
     secp256k1_pubkey zero_pubkey;
@@ -149,56 +185,46 @@ void run_context_tests(int use_prealloc) {
     unsigned char ctmp[32];
     int32_t ecount;
     int32_t ecount2;
-    secp256k1_context *none;
-    secp256k1_context *sign;
-    secp256k1_context *vrfy;
-    secp256k1_context *both;
-    void *none_prealloc = NULL;
-    void *sign_prealloc = NULL;
-    void *vrfy_prealloc = NULL;
-    void *both_prealloc = NULL;
+    secp256k1_context *sttc;
+    void *ctx_prealloc = NULL;
+    void *sttc_prealloc = NULL;
 
     secp256k1_gej pubj;
     secp256k1_ge pub;
     secp256k1_scalar msg, key, nonce;
     secp256k1_scalar sigr, sigs;
 
+    /* Check that deprecated secp256k1_context_no_precomp is an alias to secp256k1_context_static. */
+    CHECK(secp256k1_context_no_precomp == secp256k1_context_static);
+
     if (use_prealloc) {
-        none_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE));
-        sign_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN));
-        vrfy_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY));
-        both_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY));
-        CHECK(none_prealloc != NULL);
-        CHECK(sign_prealloc != NULL);
-        CHECK(vrfy_prealloc != NULL);
-        CHECK(both_prealloc != NULL);
-        none = secp256k1_context_preallocated_create(none_prealloc, SECP256K1_CONTEXT_NONE);
-        sign = secp256k1_context_preallocated_create(sign_prealloc, SECP256K1_CONTEXT_SIGN);
-        vrfy = secp256k1_context_preallocated_create(vrfy_prealloc, SECP256K1_CONTEXT_VERIFY);
-        both = secp256k1_context_preallocated_create(both_prealloc, SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+        ctx_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE));
+        CHECK(ctx_prealloc != NULL);
+        ctx = secp256k1_context_preallocated_create(ctx_prealloc, SECP256K1_CONTEXT_NONE);
+        sttc_prealloc = malloc(secp256k1_context_preallocated_clone_size(secp256k1_context_static));
+        CHECK(sttc_prealloc != NULL);
+        sttc = secp256k1_context_preallocated_clone(secp256k1_context_static, sttc_prealloc);
     } else {
-        none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
-        sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
-        vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
-        both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+        sttc = secp256k1_context_clone(secp256k1_context_static);
+        ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
     }
 
+    test_deprecated_flags();
+
     memset(&zero_pubkey, 0, sizeof(zero_pubkey));
 
     ecount = 0;
     ecount2 = 10;
-    secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount2);
+    secp256k1_context_set_illegal_callback(sttc, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount2);
     /* set error callback (to a function that still aborts in case malloc() fails in secp256k1_context_clone() below) */
-    secp256k1_context_set_error_callback(sign, secp256k1_default_illegal_callback_fn, NULL);
-    CHECK(sign->error_callback.fn != vrfy->error_callback.fn);
-    CHECK(sign->error_callback.fn == secp256k1_default_illegal_callback_fn);
+    secp256k1_context_set_error_callback(ctx, secp256k1_default_illegal_callback_fn, NULL);
+    CHECK(ctx->error_callback.fn != sttc->error_callback.fn);
+    CHECK(ctx->error_callback.fn == secp256k1_default_illegal_callback_fn);
 
     /* check if sizes for cloning are consistent */
-    CHECK(secp256k1_context_preallocated_clone_size(none) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE));
-    CHECK(secp256k1_context_preallocated_clone_size(sign) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN));
-    CHECK(secp256k1_context_preallocated_clone_size(vrfy) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY));
-    CHECK(secp256k1_context_preallocated_clone_size(both) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY));
+    CHECK(secp256k1_context_preallocated_clone_size(ctx) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE));
+    CHECK(secp256k1_context_preallocated_clone_size(sttc) >= sizeof(secp256k1_context));
 
     /*** clone and destroy all of them to make sure cloning was complete ***/
     {
@@ -206,137 +232,101 @@ void run_context_tests(int use_prealloc) {
 
         if (use_prealloc) {
             /* clone into a non-preallocated context and then again into a new preallocated one. */
-            ctx_tmp = none; none = secp256k1_context_clone(none); secp256k1_context_preallocated_destroy(ctx_tmp);
-            free(none_prealloc); none_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); CHECK(none_prealloc != NULL);
-            ctx_tmp = none; none = secp256k1_context_preallocated_clone(none, none_prealloc); secp256k1_context_destroy(ctx_tmp);
-
-            ctx_tmp = sign; sign = secp256k1_context_clone(sign); secp256k1_context_preallocated_destroy(ctx_tmp);
-            free(sign_prealloc); sign_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); CHECK(sign_prealloc != NULL);
-            ctx_tmp = sign; sign = secp256k1_context_preallocated_clone(sign, sign_prealloc); secp256k1_context_destroy(ctx_tmp);
-
-            ctx_tmp = vrfy; vrfy = secp256k1_context_clone(vrfy); secp256k1_context_preallocated_destroy(ctx_tmp);
-            free(vrfy_prealloc); vrfy_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); CHECK(vrfy_prealloc != NULL);
-            ctx_tmp = vrfy; vrfy = secp256k1_context_preallocated_clone(vrfy, vrfy_prealloc); secp256k1_context_destroy(ctx_tmp);
-
-            ctx_tmp = both; both = secp256k1_context_clone(both); secp256k1_context_preallocated_destroy(ctx_tmp);
-            free(both_prealloc); both_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); CHECK(both_prealloc != NULL);
-            ctx_tmp = both; both = secp256k1_context_preallocated_clone(both, both_prealloc); secp256k1_context_destroy(ctx_tmp);
+            ctx_tmp = ctx; ctx = secp256k1_context_clone(ctx); secp256k1_context_preallocated_destroy(ctx_tmp);
+            free(ctx_prealloc); ctx_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); CHECK(ctx_prealloc != NULL);
+            ctx_tmp = ctx; ctx = secp256k1_context_preallocated_clone(ctx, ctx_prealloc); secp256k1_context_destroy(ctx_tmp);
         } else {
             /* clone into a preallocated context and then again into a new non-preallocated one. */
             void *prealloc_tmp;
 
             prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); CHECK(prealloc_tmp != NULL);
-            ctx_tmp = none; none = secp256k1_context_preallocated_clone(none, prealloc_tmp); secp256k1_context_destroy(ctx_tmp);
-            ctx_tmp = none; none = secp256k1_context_clone(none); secp256k1_context_preallocated_destroy(ctx_tmp);
-            free(prealloc_tmp);
-
-            prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); CHECK(prealloc_tmp != NULL);
-            ctx_tmp = sign; sign = secp256k1_context_preallocated_clone(sign, prealloc_tmp); secp256k1_context_destroy(ctx_tmp);
-            ctx_tmp = sign; sign = secp256k1_context_clone(sign); secp256k1_context_preallocated_destroy(ctx_tmp);
-            free(prealloc_tmp);
-
-            prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); CHECK(prealloc_tmp != NULL);
-            ctx_tmp = vrfy; vrfy = secp256k1_context_preallocated_clone(vrfy, prealloc_tmp); secp256k1_context_destroy(ctx_tmp);
-            ctx_tmp = vrfy; vrfy = secp256k1_context_clone(vrfy); secp256k1_context_preallocated_destroy(ctx_tmp);
-            free(prealloc_tmp);
-
-            prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); CHECK(prealloc_tmp != NULL);
-            ctx_tmp = both; both = secp256k1_context_preallocated_clone(both, prealloc_tmp); secp256k1_context_destroy(ctx_tmp);
-            ctx_tmp = both; both = secp256k1_context_clone(both); secp256k1_context_preallocated_destroy(ctx_tmp);
+            ctx_tmp = ctx; ctx = secp256k1_context_preallocated_clone(ctx, prealloc_tmp); secp256k1_context_destroy(ctx_tmp);
+            ctx_tmp = ctx; ctx = secp256k1_context_clone(ctx); secp256k1_context_preallocated_destroy(ctx_tmp);
             free(prealloc_tmp);
         }
     }
 
     /* Verify that the error callback makes it across the clone. */
-    CHECK(sign->error_callback.fn != vrfy->error_callback.fn);
-    CHECK(sign->error_callback.fn == secp256k1_default_illegal_callback_fn);
+    CHECK(ctx->error_callback.fn != sttc->error_callback.fn);
+    CHECK(ctx->error_callback.fn == secp256k1_default_illegal_callback_fn);
     /* And that it resets back to default. */
-    secp256k1_context_set_error_callback(sign, NULL, NULL);
-    CHECK(vrfy->error_callback.fn == sign->error_callback.fn);
+    secp256k1_context_set_error_callback(ctx, NULL, NULL);
+    CHECK(ctx->error_callback.fn == sttc->error_callback.fn);
 
     /*** attempt to use them ***/
     random_scalar_order_test(&msg);
     random_scalar_order_test(&key);
-    secp256k1_ecmult_gen(&both->ecmult_gen_ctx, &pubj, &key);
+    secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubj, &key);
     secp256k1_ge_set_gej(&pub, &pubj);
 
     /* Verify context-type checking illegal-argument errors. */
     memset(ctmp, 1, 32);
-    CHECK(secp256k1_ec_pubkey_create(vrfy, &pubkey, ctmp) == 0);
+    CHECK(secp256k1_ec_pubkey_create(sttc, &pubkey, ctmp) == 0);
     CHECK(ecount == 1);
     VG_UNDEF(&pubkey, sizeof(pubkey));
-    CHECK(secp256k1_ec_pubkey_create(sign, &pubkey, ctmp) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
     VG_CHECK(&pubkey, sizeof(pubkey));
-    CHECK(secp256k1_ecdsa_sign(vrfy, &sig, ctmp, ctmp, NULL, NULL) == 0);
+    CHECK(secp256k1_ecdsa_sign(sttc, &sig, ctmp, ctmp, NULL, NULL) == 0);
     CHECK(ecount == 2);
     VG_UNDEF(&sig, sizeof(sig));
-    CHECK(secp256k1_ecdsa_sign(sign, &sig, ctmp, ctmp, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign(ctx, &sig, ctmp, ctmp, NULL, NULL) == 1);
     VG_CHECK(&sig, sizeof(sig));
     CHECK(ecount2 == 10);
-    CHECK(secp256k1_ecdsa_verify(sign, &sig, ctmp, &pubkey) == 0);
-    CHECK(ecount2 == 11);
-    CHECK(secp256k1_ecdsa_verify(vrfy, &sig, ctmp, &pubkey) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &sig, ctmp, &pubkey) == 1);
+    CHECK(ecount2 == 10);
+    CHECK(secp256k1_ecdsa_verify(sttc, &sig, ctmp, &pubkey) == 1);
     CHECK(ecount == 2);
-    CHECK(secp256k1_ec_pubkey_tweak_add(sign, &pubkey, ctmp) == 0);
-    CHECK(ecount2 == 12);
-    CHECK(secp256k1_ec_pubkey_tweak_add(vrfy, &pubkey, ctmp) == 1);
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp) == 1);
+    CHECK(ecount2 == 10);
+    CHECK(secp256k1_ec_pubkey_tweak_add(sttc, &pubkey, ctmp) == 1);
     CHECK(ecount == 2);
-    CHECK(secp256k1_ec_pubkey_tweak_mul(sign, &pubkey, ctmp) == 0);
-    CHECK(ecount2 == 13);
-    CHECK(secp256k1_ec_pubkey_negate(vrfy, &pubkey) == 1);
+    CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, ctmp) == 1);
+    CHECK(ecount2 == 10);
+    CHECK(secp256k1_ec_pubkey_negate(sttc, &pubkey) == 1);
     CHECK(ecount == 2);
-    CHECK(secp256k1_ec_pubkey_negate(sign, &pubkey) == 1);
+    CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey) == 1);
     CHECK(ecount == 2);
-    CHECK(secp256k1_ec_pubkey_negate(sign, NULL) == 0);
-    CHECK(ecount2 == 14);
-    CHECK(secp256k1_ec_pubkey_negate(vrfy, &zero_pubkey) == 0);
+    CHECK(secp256k1_ec_pubkey_negate(ctx, NULL) == 0);
+    CHECK(ecount2 == 11);
+    CHECK(secp256k1_ec_pubkey_negate(sttc, &zero_pubkey) == 0);
     CHECK(ecount == 3);
-    CHECK(secp256k1_ec_pubkey_tweak_mul(vrfy, &pubkey, ctmp) == 1);
+    CHECK(secp256k1_ec_pubkey_tweak_mul(sttc, &pubkey, ctmp) == 1);
     CHECK(ecount == 3);
-    CHECK(secp256k1_context_randomize(vrfy, ctmp) == 1);
+    CHECK(secp256k1_context_randomize(sttc, ctmp) == 1);
     CHECK(ecount == 3);
-    CHECK(secp256k1_context_randomize(vrfy, NULL) == 1);
+    CHECK(secp256k1_context_randomize(sttc, NULL) == 1);
     CHECK(ecount == 3);
-    CHECK(secp256k1_context_randomize(sign, ctmp) == 1);
-    CHECK(ecount2 == 14);
-    CHECK(secp256k1_context_randomize(sign, NULL) == 1);
-    CHECK(ecount2 == 14);
-    secp256k1_context_set_illegal_callback(vrfy, NULL, NULL);
-    secp256k1_context_set_illegal_callback(sign, NULL, NULL);
+    CHECK(secp256k1_context_randomize(ctx, ctmp) == 1);
+    CHECK(ecount2 == 11);
+    CHECK(secp256k1_context_randomize(ctx, NULL) == 1);
+    CHECK(ecount2 == 11);
+    secp256k1_context_set_illegal_callback(sttc, NULL, NULL);
+    secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
 
     /* obtain a working nonce */
     do {
         random_scalar_order_test(&nonce);
-    } while(!secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
+    } while(!secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
 
     /* try signing */
-    CHECK(secp256k1_ecdsa_sig_sign(&sign->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
-    CHECK(secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
+    CHECK(secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
 
     /* try verifying */
-    CHECK(secp256k1_ecdsa_sig_verify(&vrfy->ecmult_ctx, &sigr, &sigs, &pub, &msg));
-    CHECK(secp256k1_ecdsa_sig_verify(&both->ecmult_ctx, &sigr, &sigs, &pub, &msg));
+    CHECK(secp256k1_ecdsa_sig_verify(&sigr, &sigs, &pub, &msg));
 
     /* cleanup */
     if (use_prealloc) {
-        secp256k1_context_preallocated_destroy(none);
-        secp256k1_context_preallocated_destroy(sign);
-        secp256k1_context_preallocated_destroy(vrfy);
-        secp256k1_context_preallocated_destroy(both);
-        free(none_prealloc);
-        free(sign_prealloc);
-        free(vrfy_prealloc);
-        free(both_prealloc);
+        secp256k1_context_preallocated_destroy(ctx);
+        secp256k1_context_preallocated_destroy(sttc);
+        free(ctx_prealloc);
+        free(sttc_prealloc);
     } else {
-        secp256k1_context_destroy(none);
-        secp256k1_context_destroy(sign);
-        secp256k1_context_destroy(vrfy);
-        secp256k1_context_destroy(both);
+        secp256k1_context_destroy(ctx);
+        secp256k1_context_destroy(sttc);
     }
     /* Defined as no-op. */
     secp256k1_context_destroy(NULL);
     secp256k1_context_preallocated_destroy(NULL);
-
 }
 
 void run_scratch_tests(void) {
@@ -345,83 +335,85 @@ void run_scratch_tests(void) {
     int32_t ecount = 0;
     size_t checkpoint;
     size_t checkpoint_2;
-    secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
     secp256k1_scratch_space *scratch;
     secp256k1_scratch_space local_scratch;
 
+    ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+
     /* Test public API */
-    secp256k1_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount);
-    secp256k1_context_set_error_callback(none, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(ctx, counting_illegal_callback_fn, &ecount);
 
-    scratch = secp256k1_scratch_space_create(none, 1000);
+    scratch = secp256k1_scratch_space_create(ctx, 1000);
     CHECK(scratch != NULL);
     CHECK(ecount == 0);
 
     /* Test internal API */
-    CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000);
-    CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 1) == 1000 - (ALIGNMENT - 1));
+    CHECK(secp256k1_scratch_max_allocation(&ctx->error_callback, scratch, 0) == 1000);
+    CHECK(secp256k1_scratch_max_allocation(&ctx->error_callback, scratch, 1) == 1000 - (ALIGNMENT - 1));
     CHECK(scratch->alloc_size == 0);
     CHECK(scratch->alloc_size % ALIGNMENT == 0);
 
     /* Allocating 500 bytes succeeds */
-    checkpoint = secp256k1_scratch_checkpoint(&none->error_callback, scratch);
-    CHECK(secp256k1_scratch_alloc(&none->error_callback, scratch, 500) != NULL);
-    CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000 - adj_alloc);
-    CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 1) == 1000 - adj_alloc - (ALIGNMENT - 1));
+    checkpoint = secp256k1_scratch_checkpoint(&ctx->error_callback, scratch);
+    CHECK(secp256k1_scratch_alloc(&ctx->error_callback, scratch, 500) != NULL);
+    CHECK(secp256k1_scratch_max_allocation(&ctx->error_callback, scratch, 0) == 1000 - adj_alloc);
+    CHECK(secp256k1_scratch_max_allocation(&ctx->error_callback, scratch, 1) == 1000 - adj_alloc - (ALIGNMENT - 1));
     CHECK(scratch->alloc_size != 0);
     CHECK(scratch->alloc_size % ALIGNMENT == 0);
 
     /* Allocating another 501 bytes fails */
-    CHECK(secp256k1_scratch_alloc(&none->error_callback, scratch, 501) == NULL);
-    CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000 - adj_alloc);
-    CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 1) == 1000 - adj_alloc - (ALIGNMENT - 1));
+    CHECK(secp256k1_scratch_alloc(&ctx->error_callback, scratch, 501) == NULL);
+    CHECK(secp256k1_scratch_max_allocation(&ctx->error_callback, scratch, 0) == 1000 - adj_alloc);
+    CHECK(secp256k1_scratch_max_allocation(&ctx->error_callback, scratch, 1) == 1000 - adj_alloc - (ALIGNMENT - 1));
     CHECK(scratch->alloc_size != 0);
     CHECK(scratch->alloc_size % ALIGNMENT == 0);
 
     /* ...but it succeeds once we apply the checkpoint to undo it */
-    secp256k1_scratch_apply_checkpoint(&none->error_callback, scratch, checkpoint);
+    secp256k1_scratch_apply_checkpoint(&ctx->error_callback, scratch, checkpoint);
     CHECK(scratch->alloc_size == 0);
-    CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000);
-    CHECK(secp256k1_scratch_alloc(&none->error_callback, scratch, 500) != NULL);
+    CHECK(secp256k1_scratch_max_allocation(&ctx->error_callback, scratch, 0) == 1000);
+    CHECK(secp256k1_scratch_alloc(&ctx->error_callback, scratch, 500) != NULL);
     CHECK(scratch->alloc_size != 0);
 
     /* try to apply a bad checkpoint */
-    checkpoint_2 = secp256k1_scratch_checkpoint(&none->error_callback, scratch);
-    secp256k1_scratch_apply_checkpoint(&none->error_callback, scratch, checkpoint);
+    checkpoint_2 = secp256k1_scratch_checkpoint(&ctx->error_callback, scratch);
+    secp256k1_scratch_apply_checkpoint(&ctx->error_callback, scratch, checkpoint);
     CHECK(ecount == 0);
-    secp256k1_scratch_apply_checkpoint(&none->error_callback, scratch, checkpoint_2); /* checkpoint_2 is after checkpoint */
+    secp256k1_scratch_apply_checkpoint(&ctx->error_callback, scratch, checkpoint_2); /* checkpoint_2 is after checkpoint */
     CHECK(ecount == 1);
-    secp256k1_scratch_apply_checkpoint(&none->error_callback, scratch, (size_t) -1); /* this is just wildly invalid */
+    secp256k1_scratch_apply_checkpoint(&ctx->error_callback, scratch, (size_t) -1); /* this is just wildly invalid */
     CHECK(ecount == 2);
 
     /* try to use badly initialized scratch space */
-    secp256k1_scratch_space_destroy(none, scratch);
+    secp256k1_scratch_space_destroy(ctx, scratch);
     memset(&local_scratch, 0, sizeof(local_scratch));
     scratch = &local_scratch;
-    CHECK(!secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0));
+    CHECK(!secp256k1_scratch_max_allocation(&ctx->error_callback, scratch, 0));
     CHECK(ecount == 3);
-    CHECK(secp256k1_scratch_alloc(&none->error_callback, scratch, 500) == NULL);
+    CHECK(secp256k1_scratch_alloc(&ctx->error_callback, scratch, 500) == NULL);
     CHECK(ecount == 4);
-    secp256k1_scratch_space_destroy(none, scratch);
+    secp256k1_scratch_space_destroy(ctx, scratch);
     CHECK(ecount == 5);
 
     /* Test that large integers do not wrap around in a bad way */
-    scratch = secp256k1_scratch_space_create(none, 1000);
+    scratch = secp256k1_scratch_space_create(ctx, 1000);
     /* Try max allocation with a large number of objects. Only makes sense if
      * ALIGNMENT is greater than 1 because otherwise the objects take no extra
      * space. */
-    CHECK(ALIGNMENT <= 1 || !secp256k1_scratch_max_allocation(&none->error_callback, scratch, (SIZE_MAX / (ALIGNMENT - 1)) + 1));
+    CHECK(ALIGNMENT <= 1 || !secp256k1_scratch_max_allocation(&ctx->error_callback, scratch, (SIZE_MAX / (ALIGNMENT - 1)) + 1));
     /* Try allocating SIZE_MAX to test wrap around which only happens if
      * ALIGNMENT > 1, otherwise it returns NULL anyway because the scratch
      * space is too small. */
-    CHECK(secp256k1_scratch_alloc(&none->error_callback, scratch, SIZE_MAX) == NULL);
-    secp256k1_scratch_space_destroy(none, scratch);
+    CHECK(secp256k1_scratch_alloc(&ctx->error_callback, scratch, SIZE_MAX) == NULL);
+    secp256k1_scratch_space_destroy(ctx, scratch);
 
     /* cleanup */
-    secp256k1_scratch_space_destroy(none, NULL); /* no-op */
-    secp256k1_context_destroy(none);
+    secp256k1_scratch_space_destroy(ctx, NULL); /* no-op */
+    secp256k1_context_destroy(ctx);
 }
 
+
 void run_ctz_tests(void) {
     static const uint32_t b32[] = {1, 0xffffffff, 0x5e56968f, 0xe0d63129};
     static const uint64_t b64[] = {1, 0xffffffffffffffff, 0xbcd02462139b3fc3, 0x98b5f80c769693ef};
@@ -443,14 +435,18 @@ void run_ctz_tests(void) {
 
 /***** HASH TESTS *****/
 
-void run_sha256_tests(void) {
-    static const char *inputs[8] = {
+void run_sha256_known_output_tests(void) {
+    static const char *inputs[] = {
         "", "abc", "message digest", "secure hash algorithm", "SHA256 is considered to be safe",
         "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq",
         "For this sample, this 63-byte string will be used as input data",
-        "This is exactly 64 bytes long, not counting the terminating byte"
+        "This is exactly 64 bytes long, not counting the terminating byte",
+        "aaaaa",
     };
-    static const unsigned char outputs[8][32] = {
+    static const unsigned int repeat[] = {
+        1, 1, 1, 1, 1, 1, 1, 1, 1000000/5
+    };
+    static const unsigned char outputs[][32] = {
         {0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55},
         {0xba, 0x78, 0x16, 0xbf, 0x8f, 0x01, 0xcf, 0xea, 0x41, 0x41, 0x40, 0xde, 0x5d, 0xae, 0x22, 0x23, 0xb0, 0x03, 0x61, 0xa3, 0x96, 0x17, 0x7a, 0x9c, 0xb4, 0x10, 0xff, 0x61, 0xf2, 0x00, 0x15, 0xad},
         {0xf7, 0x84, 0x6f, 0x55, 0xcf, 0x23, 0xe1, 0x4e, 0xeb, 0xea, 0xb5, 0xb4, 0xe1, 0x55, 0x0c, 0xad, 0x5b, 0x50, 0x9e, 0x33, 0x48, 0xfb, 0xc4, 0xef, 0xa3, 0xa1, 0x41, 0x3d, 0x39, 0x3c, 0xb6, 0x50},
@@ -458,27 +454,146 @@ void run_sha256_tests(void) {
         {0x68, 0x19, 0xd9, 0x15, 0xc7, 0x3f, 0x4d, 0x1e, 0x77, 0xe4, 0xe1, 0xb5, 0x2d, 0x1f, 0xa0, 0xf9, 0xcf, 0x9b, 0xea, 0xea, 0xd3, 0x93, 0x9f, 0x15, 0x87, 0x4b, 0xd9, 0x88, 0xe2, 0xa2, 0x36, 0x30},
         {0x24, 0x8d, 0x6a, 0x61, 0xd2, 0x06, 0x38, 0xb8, 0xe5, 0xc0, 0x26, 0x93, 0x0c, 0x3e, 0x60, 0x39, 0xa3, 0x3c, 0xe4, 0x59, 0x64, 0xff, 0x21, 0x67, 0xf6, 0xec, 0xed, 0xd4, 0x19, 0xdb, 0x06, 0xc1},
         {0xf0, 0x8a, 0x78, 0xcb, 0xba, 0xee, 0x08, 0x2b, 0x05, 0x2a, 0xe0, 0x70, 0x8f, 0x32, 0xfa, 0x1e, 0x50, 0xc5, 0xc4, 0x21, 0xaa, 0x77, 0x2b, 0xa5, 0xdb, 0xb4, 0x06, 0xa2, 0xea, 0x6b, 0xe3, 0x42},
-        {0xab, 0x64, 0xef, 0xf7, 0xe8, 0x8e, 0x2e, 0x46, 0x16, 0x5e, 0x29, 0xf2, 0xbc, 0xe4, 0x18, 0x26, 0xbd, 0x4c, 0x7b, 0x35, 0x52, 0xf6, 0xb3, 0x82, 0xa9, 0xe7, 0xd3, 0xaf, 0x47, 0xc2, 0x45, 0xf8}
+        {0xab, 0x64, 0xef, 0xf7, 0xe8, 0x8e, 0x2e, 0x46, 0x16, 0x5e, 0x29, 0xf2, 0xbc, 0xe4, 0x18, 0x26, 0xbd, 0x4c, 0x7b, 0x35, 0x52, 0xf6, 0xb3, 0x82, 0xa9, 0xe7, 0xd3, 0xaf, 0x47, 0xc2, 0x45, 0xf8},
+        {0xcd, 0xc7, 0x6e, 0x5c, 0x99, 0x14, 0xfb, 0x92, 0x81, 0xa1, 0xc7, 0xe2, 0x84, 0xd7, 0x3e, 0x67, 0xf1, 0x80, 0x9a, 0x48, 0xa4, 0x97, 0x20, 0x0e, 0x04, 0x6d, 0x39, 0xcc, 0xc7, 0x11, 0x2c, 0xd0},
     };
-    int i;
-    for (i = 0; i < 8; i++) {
+    unsigned int i, ninputs;
+
+    /* Skip last input vector for low iteration counts */
+    ninputs = sizeof(inputs)/sizeof(inputs[0]) - 1;
+    CONDITIONAL_TEST(16, "run_sha256_known_output_tests 1000000") ninputs++;
+
+    for (i = 0; i < ninputs; i++) {
         unsigned char out[32];
         secp256k1_sha256 hasher;
+        unsigned int j;
+        /* 1. Run: simply write the input bytestrings */
+        j = repeat[i];
         secp256k1_sha256_initialize(&hasher);
-        secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
+        while (j > 0) {
+            secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
+            j--;
+        }
         secp256k1_sha256_finalize(&hasher, out);
         CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
+        /* 2. Run: split the input bytestrings randomly before writing */
         if (strlen(inputs[i]) > 0) {
             int split = secp256k1_testrand_int(strlen(inputs[i]));
             secp256k1_sha256_initialize(&hasher);
-            secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
-            secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
+            j = repeat[i];
+            while (j > 0) {
+                secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
+                secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
+                j--;
+            }
             secp256k1_sha256_finalize(&hasher, out);
             CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
         }
     }
 }
 
+/** SHA256 counter tests
+
+The tests verify that the SHA256 counter doesn't wrap around at message length
+2^i bytes for i = 20, ..., 33. This wide range aims at being independent of the
+implementation of the counter and it catches multiple natural 32-bit overflows
+(e.g., counting bits, counting bytes, counting blocks, ...).
+
+The test vectors have been generated using following Python script which relies
+on https://github.com/cloudtools/sha256/ (v0.3 on Python v3.10.2).
+
+```
+from sha256 import sha256
+from copy import copy
+
+def midstate_c_definition(hasher):
+    ret  = '    {{0x' + hasher.state[0].hex('_', 4).replace('_', ', 0x') + '},\n'
+    ret += '    {0x00}, ' + str(hex(hasher.state[1])) + '}'
+    return ret
+
+def output_c_literal(hasher):
+    return '{0x' + hasher.digest().hex('_').replace('_', ', 0x') + '}'
+
+MESSAGE = b'abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmno'
+assert(len(MESSAGE) == 64)
+BYTE_BOUNDARIES = [(2**b)//len(MESSAGE) - 1 for b in range(20, 34)]
+
+midstates = []
+digests = []
+hasher = sha256()
+for i in range(BYTE_BOUNDARIES[-1] + 1):
+    if i in BYTE_BOUNDARIES:
+        midstates.append(midstate_c_definition(hasher))
+        hasher_copy = copy(hasher)
+        hasher_copy.update(MESSAGE)
+        digests.append(output_c_literal(hasher_copy))
+    hasher.update(MESSAGE)
+
+for x in midstates:
+    print(x + ',')
+
+for x in digests:
+    print(x + ',')
+```
+*/
+void run_sha256_counter_tests(void) {
+    static const char *input = "abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmno";
+    static const secp256k1_sha256 midstates[] = {
+        {{0xa2b5c8bb, 0x26c88bb3, 0x2abdc3d2, 0x9def99a3, 0xdfd21a6e, 0x41fe585b, 0x7ef2c440, 0x2b79adda},
+         {0x00}, 0xfffc0},
+        {{0xa0d29445, 0x9287de66, 0x76aabd71, 0x41acd765, 0x0c7528b4, 0x84e14906, 0x942faec6, 0xcc5a7b26},
+         {0x00}, 0x1fffc0},
+        {{0x50449526, 0xb9f1d657, 0xa0fc13e9, 0x50860f10, 0xa550c431, 0x3fbc97c1, 0x7bbb2d89, 0xdb67bac1},
+         {0x00}, 0x3fffc0},
+        {{0x54a6efdc, 0x46762e7b, 0x88bfe73f, 0xbbd149c7, 0x41620c43, 0x1168da7b, 0x2c5960f9, 0xeccffda6},
+         {0x00}, 0x7fffc0},
+        {{0x2515a8f5, 0x5faa2977, 0x3a850486, 0xac858cad, 0x7b7276ee, 0x235c0385, 0xc53a157c, 0x7cb3e69c},
+         {0x00}, 0xffffc0},
+        {{0x34f39828, 0x409fedb7, 0x4bbdd0fb, 0x3b643634, 0x7806bf2e, 0xe0d1b713, 0xca3f2e1e, 0xe38722c2},
+         {0x00}, 0x1ffffc0},
+        {{0x389ef5c5, 0x38c54167, 0x8f5d56ab, 0x582a75cc, 0x8217caef, 0xf10947dd, 0x6a1998a8, 0x048f0b8c},
+         {0x00}, 0x3ffffc0},
+        {{0xd6c3f394, 0x0bee43b9, 0x6783f497, 0x29fa9e21, 0x6ce491c1, 0xa81fe45e, 0x2fc3859a, 0x269012d0},
+         {0x00}, 0x7ffffc0},
+        {{0x6dd3c526, 0x44d88aa0, 0x806a1bae, 0xfbcc0d32, 0x9d6144f3, 0x9d2bd757, 0x9851a957, 0xb50430ad},
+         {0x00}, 0xfffffc0},
+        {{0x2add4021, 0xdfe8a9e6, 0xa56317c6, 0x7a15f5bb, 0x4a48aacd, 0x5d368414, 0x4f00e6f0, 0xd9355023},
+         {0x00}, 0x1fffffc0},
+        {{0xb66666b4, 0xdbeac32b, 0x0ea351ae, 0xcba9da46, 0x6278b874, 0x8c508e23, 0xe16ca776, 0x8465bac1},
+         {0x00}, 0x3fffffc0},
+        {{0xb6744789, 0x9cce87aa, 0xc4c478b7, 0xf38404d8, 0x2e38ba62, 0xa3f7019b, 0x50458fe7, 0x3047dbec},
+         {0x00}, 0x7fffffc0},
+        {{0x8b1297ba, 0xba261a80, 0x2ba1b0dd, 0xfbc67d6d, 0x61072c4e, 0x4b5a2a0f, 0x52872760, 0x2dfeb162},
+         {0x00}, 0xffffffc0},
+        {{0x24f33cf7, 0x41ad6583, 0x41c8ff5d, 0xca7ef35f, 0x50395756, 0x021b743e, 0xd7126cd7, 0xd037473a},
+         {0x00}, 0x1ffffffc0},
+    };
+    static const unsigned char outputs[][32] = {
+        {0x0e, 0x83, 0xe2, 0xc9, 0x4f, 0xb2, 0xb8, 0x2b, 0x89, 0x06, 0x92, 0x78, 0x04, 0x03, 0x48, 0x5c, 0x48, 0x44, 0x67, 0x61, 0x77, 0xa4, 0xc7, 0x90, 0x9e, 0x92, 0x55, 0x10, 0x05, 0xfe, 0x39, 0x15},
+        {0x1d, 0x1e, 0xd7, 0xb8, 0xa3, 0xa7, 0x8a, 0x79, 0xfd, 0xa0, 0x05, 0x08, 0x9c, 0xeb, 0xf0, 0xec, 0x67, 0x07, 0x9f, 0x8e, 0x3c, 0x0d, 0x8e, 0xf9, 0x75, 0x55, 0x13, 0xc1, 0xe8, 0x77, 0xf8, 0xbb},
+        {0x66, 0x95, 0x6c, 0xc9, 0xe0, 0x39, 0x65, 0xb6, 0xb0, 0x05, 0xd1, 0xaf, 0xaf, 0xf3, 0x1d, 0xb9, 0xa4, 0xda, 0x6f, 0x20, 0xcd, 0x3a, 0xae, 0x64, 0xc2, 0xdb, 0xee, 0xf5, 0xb8, 0x8d, 0x57, 0x0e},
+        {0x3c, 0xbb, 0x1c, 0x12, 0x5e, 0x17, 0xfd, 0x54, 0x90, 0x45, 0xa7, 0x7b, 0x61, 0x6c, 0x1d, 0xfe, 0xe6, 0xcc, 0x7f, 0xee, 0xcf, 0xef, 0x33, 0x35, 0x50, 0x62, 0x16, 0x70, 0x2f, 0x87, 0xc3, 0xc9},
+        {0x53, 0x4d, 0xa8, 0xe7, 0x1e, 0x98, 0x73, 0x8d, 0xd9, 0xa3, 0x54, 0xa5, 0x0e, 0x59, 0x2c, 0x25, 0x43, 0x6f, 0xaa, 0xa2, 0xf5, 0x21, 0x06, 0x3e, 0xc9, 0x82, 0x06, 0x94, 0x98, 0x72, 0x9d, 0xa7},
+        {0xef, 0x7e, 0xe9, 0x6b, 0xd3, 0xe5, 0xb7, 0x41, 0x4c, 0xc8, 0xd3, 0x07, 0x52, 0x9a, 0x5a, 0x8b, 0x4e, 0x1e, 0x75, 0xa4, 0x17, 0x78, 0xc8, 0x36, 0xcd, 0xf8, 0x2e, 0xd9, 0x57, 0xe3, 0xd7, 0x07},
+        {0x87, 0x16, 0xfb, 0xf9, 0xa5, 0xf8, 0xc4, 0x56, 0x2b, 0x48, 0x52, 0x8e, 0x2d, 0x30, 0x85, 0xb6, 0x4c, 0x56, 0xb5, 0xd1, 0x16, 0x9c, 0xcf, 0x32, 0x95, 0xad, 0x03, 0xe8, 0x05, 0x58, 0x06, 0x76},
+        {0x75, 0x03, 0x80, 0x28, 0xf2, 0xa7, 0x63, 0x22, 0x1a, 0x26, 0x9c, 0x68, 0xe0, 0x58, 0xfc, 0x73, 0xeb, 0x42, 0xf6, 0x86, 0x16, 0x24, 0x4b, 0xbc, 0x24, 0xf7, 0x02, 0xc8, 0x3d, 0x90, 0xe2, 0xb0},
+        {0xdf, 0x49, 0x0f, 0x15, 0x7b, 0x7d, 0xbf, 0xe0, 0xd4, 0xcf, 0x47, 0xc0, 0x80, 0x93, 0x4a, 0x61, 0xaa, 0x03, 0x07, 0x66, 0xb3, 0x38, 0x5d, 0xc8, 0xc9, 0x07, 0x61, 0xfb, 0x97, 0x10, 0x2f, 0xd8},
+        {0x77, 0x19, 0x40, 0x56, 0x41, 0xad, 0xbc, 0x59, 0xda, 0x1e, 0xc5, 0x37, 0x14, 0x63, 0x7b, 0xfb, 0x79, 0xe2, 0x7a, 0xb1, 0x55, 0x42, 0x99, 0x42, 0x56, 0xfe, 0x26, 0x9d, 0x0f, 0x7e, 0x80, 0xc6},
+        {0x50, 0xe7, 0x2a, 0x0e, 0x26, 0x44, 0x2f, 0xe2, 0x55, 0x2d, 0xc3, 0x93, 0x8a, 0xc5, 0x86, 0x58, 0x22, 0x8c, 0x0c, 0xbf, 0xb1, 0xd2, 0xca, 0x87, 0x2a, 0xe4, 0x35, 0x26, 0x6f, 0xcd, 0x05, 0x5e},
+        {0xe4, 0x80, 0x6f, 0xdb, 0x3d, 0x7d, 0xba, 0xde, 0x50, 0x3f, 0xea, 0x00, 0x3d, 0x46, 0x59, 0x64, 0xfd, 0x58, 0x1c, 0xa1, 0xb8, 0x7d, 0x5f, 0xac, 0x94, 0x37, 0x9e, 0xa0, 0xc0, 0x9c, 0x93, 0x8b},
+        {0x2c, 0xf3, 0xa9, 0xf6, 0x15, 0x25, 0x80, 0x70, 0x76, 0x99, 0x7d, 0xf1, 0xc3, 0x2f, 0xa3, 0x31, 0xff, 0x92, 0x35, 0x2e, 0x8d, 0x04, 0x13, 0x33, 0xd8, 0x0d, 0xdb, 0x4a, 0xf6, 0x8c, 0x03, 0x34},
+        {0xec, 0x12, 0x24, 0x9f, 0x35, 0xa4, 0x29, 0x8b, 0x9e, 0x4a, 0x95, 0xf8, 0x61, 0xaf, 0x61, 0xc5, 0x66, 0x55, 0x3e, 0x3f, 0x2a, 0x98, 0xea, 0x71, 0x16, 0x6b, 0x1c, 0xd9, 0xe4, 0x09, 0xd2, 0x8e},
+    };
+    unsigned int i;
+    for (i = 0; i < sizeof(midstates)/sizeof(midstates[0]); i++) {
+        unsigned char out[32];
+        secp256k1_sha256 hasher = midstates[i];
+        secp256k1_sha256_write(&hasher, (const unsigned char*)input, strlen(input));
+        secp256k1_sha256_finalize(&hasher, out);
+        CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
+    }
+}
+
 void run_hmac_sha256_tests(void) {
     static const char *keys[6] = {
         "\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b",
@@ -564,6 +679,36 @@ void run_rfc6979_hmac_sha256_tests(void) {
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
 }
 
+void run_tagged_sha256_tests(void) {
+    int ecount = 0;
+    unsigned char tag[32] = { 0 };
+    unsigned char msg[32] = { 0 };
+    unsigned char hash32[32];
+    unsigned char hash_expected[32] = {
+        0x04, 0x7A, 0x5E, 0x17, 0xB5, 0x86, 0x47, 0xC1,
+        0x3C, 0xC6, 0xEB, 0xC0, 0xAA, 0x58, 0x3B, 0x62,
+        0xFB, 0x16, 0x43, 0x32, 0x68, 0x77, 0x40, 0x6C,
+        0xE2, 0x76, 0x55, 0x9A, 0x3B, 0xDE, 0x55, 0xB3
+    };
+
+    secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+
+    /* API test */
+    CHECK(secp256k1_tagged_sha256(ctx, hash32, tag, sizeof(tag), msg, sizeof(msg)) == 1);
+    CHECK(secp256k1_tagged_sha256(ctx, NULL, tag, sizeof(tag), msg, sizeof(msg)) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_tagged_sha256(ctx, hash32, NULL, 0, msg, sizeof(msg)) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_tagged_sha256(ctx, hash32, tag, sizeof(tag), NULL, 0) == 0);
+    CHECK(ecount == 3);
+
+    /* Static test vector */
+    memcpy(tag, "tag", 3);
+    memcpy(msg, "msg", 3);
+    CHECK(secp256k1_tagged_sha256(ctx, hash32, tag, 3, msg, 3) == 1);
+    CHECK(secp256k1_memcmp_var(hash32, hash_expected, sizeof(hash32)) == 0);
+}
+
 /***** RANDOM TESTS *****/
 
 void test_rand_bits(int rand32, int bits) {
@@ -651,7 +796,8 @@ uint64_t modinv2p64(uint64_t x) {
     return w;
 }
 
-/* compute out = (a*b) mod m; if b=NULL, treat b=1.
+
+/* compute out = (a*b) mod m; if b=NULL, treat b=1; if m=NULL, treat m=infinity.
  *
  * Out is a 512-bit number (represented as 32 uint16_t's in LE order). The other
  * arguments are 256-bit numbers (represented as 16 uint16_t's in LE order). */
@@ -693,46 +839,48 @@ void mulmod256(uint16_t* out, const uint16_t* a, const uint16_t* b, const uint16
         }
     }
 
-    /* Compute the highest set bit in m. */
-    for (i = 255; i >= 0; --i) {
-        if ((m[i >> 4] >> (i & 15)) & 1) {
-            m_bitlen = i;
-            break;
+    if (m) {
+        /* Compute the highest set bit in m. */
+        for (i = 255; i >= 0; --i) {
+            if ((m[i >> 4] >> (i & 15)) & 1) {
+                m_bitlen = i;
+                break;
+            }
         }
-    }
 
-    /* Try do mul -= m<<i, for i going down to 0, whenever the result is not negative */
-    for (i = mul_bitlen - m_bitlen; i >= 0; --i) {
-        uint16_t mul2[32];
-        int64_t cs;
-
-        /* Compute mul2 = mul - m<<i. */
-        cs = 0; /* accumulator */
-        for (j = 0; j < 32; ++j) { /* j loops over the output limbs in mul2. */
-            /* Compute sub: the 16 bits in m that will be subtracted from mul2[j]. */
-            uint16_t sub = 0;
-            int p;
-            for (p = 0; p < 16; ++p) { /* p loops over the bit positions in mul2[j]. */
-                int bitpos = j * 16 - i + p; /* bitpos is the correspond bit position in m. */
-                if (bitpos >= 0 && bitpos < 256) {
-                    sub |= ((m[bitpos >> 4] >> (bitpos & 15)) & 1) << p;
+        /* Try do mul -= m<<i, for i going down to 0, whenever the result is not negative */
+        for (i = mul_bitlen - m_bitlen; i >= 0; --i) {
+            uint16_t mul2[32];
+            int64_t cs;
+
+            /* Compute mul2 = mul - m<<i. */
+            cs = 0; /* accumulator */
+            for (j = 0; j < 32; ++j) { /* j loops over the output limbs in mul2. */
+                /* Compute sub: the 16 bits in m that will be subtracted from mul2[j]. */
+                uint16_t sub = 0;
+                int p;
+                for (p = 0; p < 16; ++p) { /* p loops over the bit positions in mul2[j]. */
+                    int bitpos = j * 16 - i + p; /* bitpos is the correspond bit position in m. */
+                    if (bitpos >= 0 && bitpos < 256) {
+                        sub |= ((m[bitpos >> 4] >> (bitpos & 15)) & 1) << p;
+                    }
                 }
+                /* Add mul[j]-sub to accumulator, and shift bottom 16 bits out to mul2[j]. */
+                cs += mul[j];
+                cs -= sub;
+                mul2[j] = (cs & 0xFFFF);
+                cs >>= 16;
+            }
+            /* If remainder of subtraction is 0, set mul = mul2. */
+            if (cs == 0) {
+                memcpy(mul, mul2, sizeof(mul));
             }
-            /* Add mul[j]-sub to accumulator, and shift bottom 16 bits out to mul2[j]. */
-            cs += mul[j];
-            cs -= sub;
-            mul2[j] = (cs & 0xFFFF);
-            cs >>= 16;
         }
-        /* If remainder of subtraction is 0, set mul = mul2. */
-        if (cs == 0) {
-            memcpy(mul, mul2, sizeof(mul));
+        /* Sanity check: test that all limbs higher than m's highest are zero */
+        for (i = (m_bitlen >> 4) + 1; i < 32; ++i) {
+            CHECK(mul[i] == 0);
         }
     }
-    /* Sanity check: test that all limbs higher than m's highest are zero */
-    for (i = (m_bitlen >> 4) + 1; i < 32; ++i) {
-        CHECK(mul[i] == 0);
-    }
     memcpy(out, mul, 32);
 }
 
@@ -758,7 +906,7 @@ void signed30_to_uint16(uint16_t* out, const secp256k1_modinv32_signed30* in) {
 void mutate_sign_signed30(secp256k1_modinv32_signed30* x) {
     int i;
     for (i = 0; i < 16; ++i) {
-        int pos = secp256k1_testrand_int(8);
+        int pos = secp256k1_testrand_bits(3);
         if (x->v[pos] > 0 && x->v[pos + 1] <= 0x3fffffff) {
             x->v[pos] -= 0x40000000;
             x->v[pos + 1] += 1;
@@ -830,7 +978,7 @@ void mutate_sign_signed62(secp256k1_modinv64_signed62* x) {
     static const int64_t M62 = (int64_t)(UINT64_MAX >> 2);
     int i;
     for (i = 0; i < 8; ++i) {
-        int pos = secp256k1_testrand_int(4);
+        int pos = secp256k1_testrand_bits(2);
         if (x->v[pos] > 0 && x->v[pos + 1] <= M62) {
             x->v[pos] -= (M62 + 1);
             x->v[pos + 1] += 1;
@@ -1547,8 +1695,305 @@ void run_modinv_tests(void) {
     }
 }
 
-/***** SCALAR TESTS *****/
+/***** INT128 TESTS *****/
+
+#ifdef SECP256K1_WIDEMUL_INT128
+/* Add two 256-bit numbers (represented as 16 uint16_t's in LE order) together mod 2^256. */
+void add256(uint16_t* out, const uint16_t* a, const uint16_t* b) {
+    int i;
+    uint32_t carry = 0;
+    for (i = 0; i < 16; ++i) {
+        carry += a[i];
+        carry += b[i];
+        out[i] = carry;
+        carry >>= 16;
+    }
+}
+
+/* Negate a 256-bit number (represented as 16 uint16_t's in LE order) mod 2^256. */
+void neg256(uint16_t* out, const uint16_t* a) {
+    int i;
+    uint32_t carry = 1;
+    for (i = 0; i < 16; ++i) {
+        carry += (uint16_t)~a[i];
+        out[i] = carry;
+        carry >>= 16;
+    }
+}
+
+/* Right-shift a 256-bit number (represented as 16 uint16_t's in LE order). */
+void rshift256(uint16_t* out, const uint16_t* a, int n, int sign_extend) {
+    uint16_t sign = sign_extend && (a[15] >> 15);
+    int i, j;
+    for (i = 15; i >= 0; --i) {
+        uint16_t v = 0;
+        for (j = 0; j < 16; ++j) {
+            int frompos = i*16 + j + n;
+            if (frompos >= 256) {
+                v |= sign << j;
+            } else {
+                v |= ((uint16_t)((a[frompos >> 4] >> (frompos & 15)) & 1)) << j;
+            }
+        }
+        out[i] = v;
+    }
+}
+
+/* Load a 64-bit unsigned integer into an array of 16 uint16_t's in LE order representing a 256-bit value. */
+void load256u64(uint16_t* out, uint64_t v, int is_signed) {
+    int i;
+    uint64_t sign = is_signed && (v >> 63) ? UINT64_MAX : 0;
+    for (i = 0; i < 4; ++i) {
+        out[i] = v >> (16 * i);
+    }
+    for (i = 4; i < 16; ++i) {
+        out[i] = sign;
+    }
+}
 
+/* Load a 128-bit unsigned integer into an array of 16 uint16_t's in LE order representing a 256-bit value. */
+void load256two64(uint16_t* out, uint64_t hi, uint64_t lo, int is_signed) {
+    int i;
+    uint64_t sign = is_signed && (hi >> 63) ? UINT64_MAX : 0;
+    for (i = 0; i < 4; ++i) {
+        out[i] = lo >> (16 * i);
+    }
+    for (i = 4; i < 8; ++i) {
+        out[i] = hi >> (16 * (i - 4));
+    }
+    for (i = 8; i < 16; ++i) {
+        out[i] = sign;
+    }
+}
+
+/* Check whether the 256-bit value represented by array of 16-bit values is in range -2^127 < v < 2^127. */
+int int256is127(const uint16_t* v) {
+    int all_0 = ((v[7] & 0x8000) == 0), all_1 = ((v[7] & 0x8000) == 0x8000);
+    int i;
+    for (i = 8; i < 16; ++i) {
+        if (v[i] != 0) all_0 = 0;
+        if (v[i] != 0xffff) all_1 = 0;
+    }
+    return all_0 || all_1;
+}
+
+void load256u128(uint16_t* out, const secp256k1_uint128* v) {
+    uint64_t lo = secp256k1_u128_to_u64(v), hi = secp256k1_u128_hi_u64(v);
+    load256two64(out, hi, lo, 0);
+}
+
+void load256i128(uint16_t* out, const secp256k1_int128* v) {
+    uint64_t lo;
+    int64_t hi;
+    secp256k1_int128 c = *v;
+    lo = secp256k1_i128_to_i64(&c);
+    secp256k1_i128_rshift(&c, 64);
+    hi = secp256k1_i128_to_i64(&c);
+    load256two64(out, hi, lo, 1);
+}
+
+void run_int128_test_case(void) {
+    unsigned char buf[32];
+    uint64_t v[4];
+    secp256k1_int128 swa, swz;
+    secp256k1_uint128 uwa, uwz;
+    uint64_t ub, uc;
+    int64_t sb, sc;
+    uint16_t rswa[16], rswz[32], rswr[32], ruwa[16], ruwz[32], ruwr[32];
+    uint16_t rub[16], ruc[16], rsb[16], rsc[16];
+    int i;
+
+    /* Generate 32-byte random value. */
+    secp256k1_testrand256_test(buf);
+    /* Convert into 4 64-bit integers. */
+    for (i = 0; i < 4; ++i) {
+        uint64_t vi = 0;
+        int j;
+        for (j = 0; j < 8; ++j) vi = (vi << 8) + buf[8*i + j];
+        v[i] = vi;
+    }
+    /* Convert those into a 128-bit value and two 64-bit values (signed and unsigned). */
+    secp256k1_u128_load(&uwa, v[1], v[0]);
+    secp256k1_i128_load(&swa, v[1], v[0]);
+    ub = v[2];
+    sb = v[2];
+    uc = v[3];
+    sc = v[3];
+    /* Load those also into 16-bit array representations. */
+    load256u128(ruwa, &uwa);
+    load256i128(rswa, &swa);
+    load256u64(rub, ub, 0);
+    load256u64(rsb, sb, 1);
+    load256u64(ruc, uc, 0);
+    load256u64(rsc, sc, 1);
+    /* test secp256k1_u128_mul */
+    mulmod256(ruwr, rub, ruc, NULL);
+    secp256k1_u128_mul(&uwz, ub, uc);
+    load256u128(ruwz, &uwz);
+    CHECK(secp256k1_memcmp_var(ruwr, ruwz, 16) == 0);
+    /* test secp256k1_u128_accum_mul */
+    mulmod256(ruwr, rub, ruc, NULL);
+    add256(ruwr, ruwr, ruwa);
+    uwz = uwa;
+    secp256k1_u128_accum_mul(&uwz, ub, uc);
+    load256u128(ruwz, &uwz);
+    CHECK(secp256k1_memcmp_var(ruwr, ruwz, 16) == 0);
+    /* test secp256k1_u128_accum_u64 */
+    add256(ruwr, rub, ruwa);
+    uwz = uwa;
+    secp256k1_u128_accum_u64(&uwz, ub);
+    load256u128(ruwz, &uwz);
+    CHECK(secp256k1_memcmp_var(ruwr, ruwz, 16) == 0);
+    /* test secp256k1_u128_rshift */
+    rshift256(ruwr, ruwa, uc % 128, 0);
+    uwz = uwa;
+    secp256k1_u128_rshift(&uwz, uc % 128);
+    load256u128(ruwz, &uwz);
+    CHECK(secp256k1_memcmp_var(ruwr, ruwz, 16) == 0);
+    /* test secp256k1_u128_to_u64 */
+    CHECK(secp256k1_u128_to_u64(&uwa) == v[0]);
+    /* test secp256k1_u128_hi_u64 */
+    CHECK(secp256k1_u128_hi_u64(&uwa) == v[1]);
+    /* test secp256k1_u128_from_u64 */
+    secp256k1_u128_from_u64(&uwz, ub);
+    load256u128(ruwz, &uwz);
+    CHECK(secp256k1_memcmp_var(rub, ruwz, 16) == 0);
+    /* test secp256k1_u128_check_bits */
+    {
+        int uwa_bits = 0;
+        int j;
+        for (j = 0; j < 128; ++j) {
+            if (ruwa[j / 16] >> (j % 16)) uwa_bits = 1 + j;
+        }
+        for (j = 0; j < 128; ++j) {
+            CHECK(secp256k1_u128_check_bits(&uwa, j) == (uwa_bits <= j));
+        }
+    }
+    /* test secp256k1_i128_mul */
+    mulmod256(rswr, rsb, rsc, NULL);
+    secp256k1_i128_mul(&swz, sb, sc);
+    load256i128(rswz, &swz);
+    CHECK(secp256k1_memcmp_var(rswr, rswz, 16) == 0);
+    /* test secp256k1_i128_accum_mul */
+    mulmod256(rswr, rsb, rsc, NULL);
+    add256(rswr, rswr, rswa);
+    if (int256is127(rswr)) {
+        swz = swa;
+        secp256k1_i128_accum_mul(&swz, sb, sc);
+        load256i128(rswz, &swz);
+        CHECK(secp256k1_memcmp_var(rswr, rswz, 16) == 0);
+    }
+    /* test secp256k1_i128_det */
+    {
+        uint16_t rsd[16], rse[16], rst[32];
+        int64_t sd = v[0], se = v[1];
+        load256u64(rsd, sd, 1);
+        load256u64(rse, se, 1);
+        mulmod256(rst, rsc, rsd, NULL);
+        neg256(rst, rst);
+        mulmod256(rswr, rsb, rse, NULL);
+        add256(rswr, rswr, rst);
+        secp256k1_i128_det(&swz, sb, sc, sd, se);
+        load256i128(rswz, &swz);
+        CHECK(secp256k1_memcmp_var(rswr, rswz, 16) == 0);
+    }
+    /* test secp256k1_i128_rshift */
+    rshift256(rswr, rswa, uc % 127, 1);
+    swz = swa;
+    secp256k1_i128_rshift(&swz, uc % 127);
+    load256i128(rswz, &swz);
+    CHECK(secp256k1_memcmp_var(rswr, rswz, 16) == 0);
+    /* test secp256k1_i128_to_i64 */
+    CHECK((uint64_t)secp256k1_i128_to_i64(&swa) == v[0]);
+    /* test secp256k1_i128_from_i64 */
+    secp256k1_i128_from_i64(&swz, sb);
+    load256i128(rswz, &swz);
+    CHECK(secp256k1_memcmp_var(rsb, rswz, 16) == 0);
+    /* test secp256k1_i128_eq_var */
+    {
+        int expect = (uc & 1);
+        swz = swa;
+        if (!expect) {
+            /* Make sure swz != swa */
+            uint64_t v0c = v[0], v1c = v[1];
+            if (ub & 64) {
+                v1c ^= (((uint64_t)1) << (ub & 63));
+            } else {
+                v0c ^= (((uint64_t)1) << (ub & 63));
+            }
+            secp256k1_i128_load(&swz, v1c, v0c);
+        }
+        CHECK(secp256k1_i128_eq_var(&swa, &swz) == expect);
+    }
+    /* test secp256k1_i128_check_pow2 */
+    {
+        int expect = (uc & 1);
+        int pos = ub % 127;
+        if (expect) {
+            /* If expect==1, set swz to exactly (2 << pos). */
+            uint64_t hi = 0;
+            uint64_t lo = 0;
+            if (pos & 64) {
+                hi = (((uint64_t)1) << (pos & 63));
+            } else {
+                lo = (((uint64_t)1) << (pos & 63));
+            }
+            secp256k1_i128_load(&swz, hi, lo);
+        } else {
+            /* If expect==0, set swz = swa, but update expect=1 if swa happens to equal (2 << pos). */
+            if (pos & 64) {
+                if ((v[1] == (((uint64_t)1) << (pos & 63))) && v[0] == 0) expect = 1;
+            } else {
+                if ((v[0] == (((uint64_t)1) << (pos & 63))) && v[1] == 0) expect = 1;
+            }
+            swz = swa;
+        }
+        CHECK(secp256k1_i128_check_pow2(&swz, pos) == expect);
+    }
+}
+
+void run_int128_tests(void) {
+    {   /* secp256k1_u128_accum_mul */
+        secp256k1_uint128 res;
+
+        /* Check secp256k1_u128_accum_mul overflow */
+        secp256k1_u128_mul(&res, UINT64_MAX, UINT64_MAX);
+        secp256k1_u128_accum_mul(&res, UINT64_MAX, UINT64_MAX);
+        CHECK(secp256k1_u128_to_u64(&res) == 2);
+        CHECK(secp256k1_u128_hi_u64(&res) == 18446744073709551612U);
+    }
+    {   /* secp256k1_u128_accum_mul */
+        secp256k1_int128 res;
+
+        /* Compute INT128_MAX = 2^127 - 1 with secp256k1_i128_accum_mul */
+        secp256k1_i128_mul(&res, INT64_MAX, INT64_MAX);
+        secp256k1_i128_accum_mul(&res, INT64_MAX, INT64_MAX);
+        CHECK(secp256k1_i128_to_i64(&res) == 2);
+        secp256k1_i128_accum_mul(&res, 4, 9223372036854775807);
+        secp256k1_i128_accum_mul(&res, 1, 1);
+        CHECK((uint64_t)secp256k1_i128_to_i64(&res) == UINT64_MAX);
+        secp256k1_i128_rshift(&res, 64);
+        CHECK(secp256k1_i128_to_i64(&res) == INT64_MAX);
+
+        /* Compute INT128_MIN = - 2^127 with secp256k1_i128_accum_mul */
+        secp256k1_i128_mul(&res, INT64_MAX, INT64_MIN);
+        CHECK(secp256k1_i128_to_i64(&res) == INT64_MIN);
+        secp256k1_i128_accum_mul(&res, INT64_MAX, INT64_MIN);
+        CHECK(secp256k1_i128_to_i64(&res) == 0);
+        secp256k1_i128_accum_mul(&res, 2, INT64_MIN);
+        CHECK(secp256k1_i128_to_i64(&res) == 0);
+        secp256k1_i128_rshift(&res, 64);
+        CHECK(secp256k1_i128_to_i64(&res) == INT64_MIN);
+    }
+    {
+        /* Randomized tests. */
+        int i;
+        for (i = 0; i < 256 * count; ++i) run_int128_test_case();
+    }
+}
+#endif
+
+/***** SCALAR TESTS *****/
 
 void scalar_test(void) {
     secp256k1_scalar s;
@@ -2419,13 +2864,65 @@ void run_field_convert(void) {
     CHECK(secp256k1_memcmp_var(&fes2, &fes, sizeof(fes)) == 0);
 }
 
-int fe_secp256k1_memcmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
-    secp256k1_fe t = *b;
+/* Returns true if two field elements have the same representation. */
+int fe_identical(const secp256k1_fe *a, const secp256k1_fe *b) {
+    int ret = 1;
+#ifdef VERIFY
+    ret &= (a->magnitude == b->magnitude);
+    ret &= (a->normalized == b->normalized);
+#endif
+    /* Compare the struct member that holds the limbs. */
+    ret &= (secp256k1_memcmp_var(a->n, b->n, sizeof(a->n)) == 0);
+    return ret;
+}
+
+void run_field_half(void) {
+    secp256k1_fe t, u;
+    int m;
+
+    /* Check magnitude 0 input */
+    secp256k1_fe_get_bounds(&t, 0);
+    secp256k1_fe_half(&t);
 #ifdef VERIFY
-    t.magnitude = a->magnitude;
-    t.normalized = a->normalized;
+    CHECK(t.magnitude == 1);
+    CHECK(t.normalized == 0);
 #endif
-    return secp256k1_memcmp_var(a, &t, sizeof(secp256k1_fe));
+    CHECK(secp256k1_fe_normalizes_to_zero(&t));
+
+    /* Check non-zero magnitudes in the supported range */
+    for (m = 1; m < 32; m++) {
+        /* Check max-value input */
+        secp256k1_fe_get_bounds(&t, m);
+
+        u = t;
+        secp256k1_fe_half(&u);
+#ifdef VERIFY
+        CHECK(u.magnitude == (m >> 1) + 1);
+        CHECK(u.normalized == 0);
+#endif
+        secp256k1_fe_normalize_weak(&u);
+        secp256k1_fe_add(&u, &u);
+        CHECK(check_fe_equal(&t, &u));
+
+        /* Check worst-case input: ensure the LSB is 1 so that P will be added,
+         * which will also cause all carries to be 1, since all limbs that can
+         * generate a carry are initially even and all limbs of P are odd in
+         * every existing field implementation. */
+        secp256k1_fe_get_bounds(&t, m);
+        CHECK(t.n[0] > 0);
+        CHECK((t.n[0] & 1) == 0);
+        --t.n[0];
+
+        u = t;
+        secp256k1_fe_half(&u);
+#ifdef VERIFY
+        CHECK(u.magnitude == (m >> 1) + 1);
+        CHECK(u.normalized == 0);
+#endif
+        secp256k1_fe_normalize_weak(&u);
+        secp256k1_fe_add(&u, &u);
+        CHECK(check_fe_equal(&t, &u));
+    }
 }
 
 void run_field_misc(void) {
@@ -2435,9 +2932,13 @@ void run_field_misc(void) {
     secp256k1_fe q;
     secp256k1_fe fe5 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 5);
     int i, j;
-    for (i = 0; i < 5*count; i++) {
+    for (i = 0; i < 1000 * count; i++) {
         secp256k1_fe_storage xs, ys, zs;
-        random_fe(&x);
+        if (i & 1) {
+            random_fe(&x);
+        } else {
+            random_fe_test(&x);
+        }
         random_fe_non_zero(&y);
         /* Test the fe equality and comparison operations. */
         CHECK(secp256k1_fe_cmp_var(&x, &x) == 0);
@@ -2451,13 +2952,13 @@ void run_field_misc(void) {
         CHECK(x.normalized && x.magnitude == 1);
 #endif
         secp256k1_fe_cmov(&x, &x, 1);
-        CHECK(fe_secp256k1_memcmp_var(&x, &z) != 0);
-        CHECK(fe_secp256k1_memcmp_var(&x, &q) == 0);
+        CHECK(!fe_identical(&x, &z));
+        CHECK(fe_identical(&x, &q));
         secp256k1_fe_cmov(&q, &z, 1);
 #ifdef VERIFY
         CHECK(!q.normalized && q.magnitude == z.magnitude);
 #endif
-        CHECK(fe_secp256k1_memcmp_var(&q, &z) == 0);
+        CHECK(fe_identical(&q, &z));
         secp256k1_fe_normalize_var(&x);
         secp256k1_fe_normalize_var(&z);
         CHECK(!secp256k1_fe_equal_var(&x, &z));
@@ -2505,6 +3006,78 @@ void run_field_misc(void) {
         secp256k1_fe_add(&q, &x);
         CHECK(check_fe_equal(&y, &z));
         CHECK(check_fe_equal(&q, &y));
+        /* Check secp256k1_fe_half. */
+        z = x;
+        secp256k1_fe_half(&z);
+        secp256k1_fe_add(&z, &z);
+        CHECK(check_fe_equal(&x, &z));
+        secp256k1_fe_add(&z, &z);
+        secp256k1_fe_half(&z);
+        CHECK(check_fe_equal(&x, &z));
+    }
+}
+
+void test_fe_mul(const secp256k1_fe* a, const secp256k1_fe* b, int use_sqr)
+{
+    secp256k1_fe c, an, bn;
+    /* Variables in BE 32-byte format. */
+    unsigned char a32[32], b32[32], c32[32];
+    /* Variables in LE 16x uint16_t format. */
+    uint16_t a16[16], b16[16], c16[16];
+    /* Field modulus in LE 16x uint16_t format. */
+    static const uint16_t m16[16] = {
+        0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
+        0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
+    };
+    uint16_t t16[32];
+    int i;
+
+    /* Compute C = A * B in fe format. */
+    c = *a;
+    if (use_sqr) {
+        secp256k1_fe_sqr(&c, &c);
+    } else {
+        secp256k1_fe_mul(&c, &c, b);
+    }
+
+    /* Convert A, B, C into LE 16x uint16_t format. */
+    an = *a;
+    bn = *b;
+    secp256k1_fe_normalize_var(&c);
+    secp256k1_fe_normalize_var(&an);
+    secp256k1_fe_normalize_var(&bn);
+    secp256k1_fe_get_b32(a32, &an);
+    secp256k1_fe_get_b32(b32, &bn);
+    secp256k1_fe_get_b32(c32, &c);
+    for (i = 0; i < 16; ++i) {
+        a16[i] = a32[31 - 2*i] + ((uint16_t)a32[30 - 2*i] << 8);
+        b16[i] = b32[31 - 2*i] + ((uint16_t)b32[30 - 2*i] << 8);
+        c16[i] = c32[31 - 2*i] + ((uint16_t)c32[30 - 2*i] << 8);
+    }
+    /* Compute T = A * B in LE 16x uint16_t format. */
+    mulmod256(t16, a16, b16, m16);
+    /* Compare */
+    CHECK(secp256k1_memcmp_var(t16, c16, 32) == 0);
+}
+
+void run_fe_mul(void) {
+    int i;
+    for (i = 0; i < 100 * count; ++i) {
+        secp256k1_fe a, b, c, d;
+        random_fe(&a);
+        random_field_element_magnitude(&a);
+        random_fe(&b);
+        random_field_element_magnitude(&b);
+        random_fe_test(&c);
+        random_field_element_magnitude(&c);
+        random_fe_test(&d);
+        random_field_element_magnitude(&d);
+        test_fe_mul(&a, &a, 1);
+        test_fe_mul(&c, &c, 1);
+        test_fe_mul(&a, &b, 0);
+        test_fe_mul(&a, &c, 0);
+        test_fe_mul(&c, &b, 0);
+        test_fe_mul(&c, &d, 0);
     }
 }
 
@@ -2595,7 +3168,7 @@ void test_inverse_scalar(secp256k1_scalar* out, const secp256k1_scalar* x, int v
 {
     secp256k1_scalar l, r, t;
 
-    (var ? secp256k1_scalar_inverse_var : secp256k1_scalar_inverse_var)(&l, x);  /* l = 1/x */
+    (var ? secp256k1_scalar_inverse_var : secp256k1_scalar_inverse)(&l, x);  /* l = 1/x */
     if (out) *out = l;
     if (secp256k1_scalar_is_zero(x)) {
         CHECK(secp256k1_scalar_is_zero(&l));
@@ -2605,9 +3178,9 @@ void test_inverse_scalar(secp256k1_scalar* out, const secp256k1_scalar* x, int v
     CHECK(secp256k1_scalar_is_one(&t));                                          /* x*(1/x) == 1 */
     secp256k1_scalar_add(&r, x, &scalar_minus_one);                              /* r = x-1 */
     if (secp256k1_scalar_is_zero(&r)) return;
-    (var ? secp256k1_scalar_inverse_var : secp256k1_scalar_inverse_var)(&r, &r); /* r = 1/(x-1) */
+    (var ? secp256k1_scalar_inverse_var : secp256k1_scalar_inverse)(&r, &r); /* r = 1/(x-1) */
     secp256k1_scalar_add(&l, &scalar_minus_one, &l);                             /* l = 1/x-1 */
-    (var ? secp256k1_scalar_inverse_var : secp256k1_scalar_inverse_var)(&l, &l); /* l = 1/(1/x-1) */
+    (var ? secp256k1_scalar_inverse_var : secp256k1_scalar_inverse)(&l, &l); /* l = 1/(1/x-1) */
     secp256k1_scalar_add(&l, &l, &secp256k1_scalar_one);                         /* l = 1/(1/x-1)+1 */
     secp256k1_scalar_add(&l, &r, &l);                                            /* l = 1/(1/x-1)+1 + 1/(x-1) */
     CHECK(secp256k1_scalar_is_zero(&l));                                         /* l == 0 */
@@ -3139,7 +3712,7 @@ void test_intialized_inf(void) {
     secp256k1_gej pj, npj, infj1, infj2, infj3;
     secp256k1_fe zinv;
 
-    /* Test that adding P+(-P) results in a fully initalized infinity*/
+    /* Test that adding P+(-P) results in a fully initialized infinity*/
     random_group_element_test(&p);
     secp256k1_gej_set_ge(&pj, &p);
     secp256k1_gej_neg(&npj, &pj);
@@ -3242,6 +3815,53 @@ void run_ge(void) {
     test_intialized_inf();
 }
 
+void test_gej_cmov(const secp256k1_gej *a, const secp256k1_gej *b) {
+    secp256k1_gej t = *a;
+    secp256k1_gej_cmov(&t, b, 0);
+    CHECK(gej_xyz_equals_gej(&t, a));
+    secp256k1_gej_cmov(&t, b, 1);
+    CHECK(gej_xyz_equals_gej(&t, b));
+}
+
+void run_gej(void) {
+    int i;
+    secp256k1_gej a, b;
+
+    /* Tests for secp256k1_gej_cmov */
+    for (i = 0; i < count; i++) {
+        secp256k1_gej_set_infinity(&a);
+        secp256k1_gej_set_infinity(&b);
+        test_gej_cmov(&a, &b);
+
+        random_gej_test(&a);
+        test_gej_cmov(&a, &b);
+        test_gej_cmov(&b, &a);
+
+        b = a;
+        test_gej_cmov(&a, &b);
+
+        random_gej_test(&b);
+        test_gej_cmov(&a, &b);
+        test_gej_cmov(&b, &a);
+    }
+
+    /* Tests for secp256k1_gej_eq_var */
+    for (i = 0; i < count; i++) {
+        secp256k1_fe fe;
+        random_gej_test(&a);
+        random_gej_test(&b);
+        CHECK(!secp256k1_gej_eq_var(&a, &b));
+
+        b = a;
+        random_field_element_test(&fe);
+        if (secp256k1_fe_is_zero(&fe)) {
+            continue;
+        }
+        secp256k1_gej_rescale(&a, &fe);
+        CHECK(secp256k1_gej_eq_var(&a, &b));
+    }
+}
+
 void test_ec_combine(void) {
     secp256k1_scalar sum = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
     secp256k1_pubkey data[6];
@@ -3320,6 +3940,80 @@ void run_group_decompress(void) {
 
 /***** ECMULT TESTS *****/
 
+void test_pre_g_table(const secp256k1_ge_storage * pre_g, size_t n) {
+    /* Tests the pre_g / pre_g_128 tables for consistency.
+     * For independent verification we take a "geometric" approach to verification.
+     * We check that every entry is on-curve.
+     * We check that for consecutive entries p and q, that p + gg - q = 0 by checking
+     *  (1) p, gg, and -q are colinear.
+     *  (2) p, gg, and -q are all distinct.
+     * where gg is twice the generator, where the generator is the first table entry.
+     *
+     * Checking the table's generators are correct is done in run_ecmult_pre_g.
+     */
+    secp256k1_gej g2;
+    secp256k1_ge p, q, gg;
+    secp256k1_fe dpx, dpy, dqx, dqy;
+    size_t i;
+
+    CHECK(0 < n);
+
+    secp256k1_ge_from_storage(&p, &pre_g[0]);
+    CHECK(secp256k1_ge_is_valid_var(&p));
+
+    secp256k1_gej_set_ge(&g2, &p);
+    secp256k1_gej_double_var(&g2, &g2, NULL);
+    secp256k1_ge_set_gej_var(&gg, &g2);
+    for (i = 1; i < n; ++i) {
+        secp256k1_fe_negate(&dpx, &p.x, 1); secp256k1_fe_add(&dpx, &gg.x); secp256k1_fe_normalize_weak(&dpx);
+        secp256k1_fe_negate(&dpy, &p.y, 1); secp256k1_fe_add(&dpy, &gg.y); secp256k1_fe_normalize_weak(&dpy);
+        /* Check that p is not equal to gg */
+        CHECK(!secp256k1_fe_normalizes_to_zero_var(&dpx) || !secp256k1_fe_normalizes_to_zero_var(&dpy));
+
+        secp256k1_ge_from_storage(&q, &pre_g[i]);
+        CHECK(secp256k1_ge_is_valid_var(&q));
+
+        secp256k1_fe_negate(&dqx, &q.x, 1); secp256k1_fe_add(&dqx, &gg.x); secp256k1_fe_normalize_weak(&dqx);
+        dqy = q.y; secp256k1_fe_add(&dqy, &gg.y); secp256k1_fe_normalize_weak(&dqy);
+        /* Check that -q is not equal to gg */
+        CHECK(!secp256k1_fe_normalizes_to_zero_var(&dqx) || !secp256k1_fe_normalizes_to_zero_var(&dqy));
+
+        /* Check that -q is not equal to p */
+        CHECK(!secp256k1_fe_equal_var(&dpx, &dqx) || !secp256k1_fe_equal_var(&dpy, &dqy));
+
+        /* Check that p, -q and gg are colinear */
+        secp256k1_fe_mul(&dpx, &dpx, &dqy);
+        secp256k1_fe_mul(&dpy, &dpy, &dqx);
+        CHECK(secp256k1_fe_equal_var(&dpx, &dpy));
+
+        p = q;
+    }
+}
+
+void run_ecmult_pre_g(void) {
+    secp256k1_ge_storage gs;
+    secp256k1_gej gj;
+    secp256k1_ge g;
+    size_t i;
+
+    /* Check that the pre_g and pre_g_128 tables are consistent. */
+    test_pre_g_table(secp256k1_pre_g, ECMULT_TABLE_SIZE(WINDOW_G));
+    test_pre_g_table(secp256k1_pre_g_128, ECMULT_TABLE_SIZE(WINDOW_G));
+
+    /* Check the first entry from the pre_g table. */
+    secp256k1_ge_to_storage(&gs, &secp256k1_ge_const_g);
+    CHECK(secp256k1_memcmp_var(&gs, &secp256k1_pre_g[0], sizeof(gs)) == 0);
+
+    /* Check the first entry from the pre_g_128 table. */
+    secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
+    for (i = 0; i < 128; ++i) {
+      secp256k1_gej_double_var(&gj, &gj, NULL);
+    }
+    secp256k1_ge_set_gej(&g, &gj);
+    secp256k1_ge_to_storage(&gs, &g);
+    CHECK(secp256k1_memcmp_var(&gs, &secp256k1_pre_g_128[0], sizeof(gs)) == 0);
+}
+
 void run_ecmult_chain(void) {
     /* random starting point A (on the curve) */
     secp256k1_gej a = SECP256K1_GEJ_CONST(
@@ -3352,7 +4046,7 @@ void run_ecmult_chain(void) {
     x = a;
     for (i = 0; i < 200*count; i++) {
         /* in each iteration, compute X = xn*X + gn*G; */
-        secp256k1_ecmult(&ctx->ecmult_ctx, &x, &x, &xn, &gn);
+        secp256k1_ecmult(&x, &x, &xn, &gn);
         /* also compute ae and ge: the actual accumulated factors for A and G */
         /* if X was (ae*A+ge*G), xn*X + gn*G results in (xn*ae*A + (xn*ge+gn)*G) */
         secp256k1_scalar_mul(&ae, &ae, &xn);
@@ -3371,17 +4065,12 @@ void run_ecmult_chain(void) {
                 0xB95CBCA2, 0xC77DA786, 0x539BE8FD, 0x53354D2D,
                 0x3B4F566A, 0xE6580454, 0x07ED6015, 0xEE1B2A88
             );
-
-            secp256k1_gej_neg(&rp, &rp);
-            secp256k1_gej_add_var(&rp, &rp, &x, NULL);
-            CHECK(secp256k1_gej_is_infinity(&rp));
+            CHECK(secp256k1_gej_eq_var(&rp, &x));
         }
     }
     /* redo the computation, but directly with the resulting ae and ge coefficients: */
-    secp256k1_ecmult(&ctx->ecmult_ctx, &x2, &a, &ae, &ge);
-    secp256k1_gej_neg(&x2, &x2);
-    secp256k1_gej_add_var(&x2, &x2, &x, NULL);
-    CHECK(secp256k1_gej_is_infinity(&x2));
+    secp256k1_ecmult(&x2, &a, &ae, &ge);
+    CHECK(secp256k1_gej_eq_var(&x, &x2));
 }
 
 void test_point_times_order(const secp256k1_gej *point) {
@@ -3396,8 +4085,8 @@ void test_point_times_order(const secp256k1_gej *point) {
     size_t psize = 65;
     random_scalar_order_test(&x);
     secp256k1_scalar_negate(&nx, &x);
-    secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &x, &x); /* calc res1 = x * point + x * G; */
-    secp256k1_ecmult(&ctx->ecmult_ctx, &res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */
+    secp256k1_ecmult(&res1, point, &x, &x); /* calc res1 = x * point + x * G; */
+    secp256k1_ecmult(&res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */
     secp256k1_gej_add_var(&res1, &res1, &res2, NULL);
     CHECK(secp256k1_gej_is_infinity(&res1));
     secp256k1_ge_set_gej(&res3, &res1);
@@ -3407,13 +4096,13 @@ void test_point_times_order(const secp256k1_gej *point) {
     psize = 65;
     CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 1) == 0);
     /* check zero/one edge cases */
-    secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &zero);
+    secp256k1_ecmult(&res1, point, &zero, &zero);
     secp256k1_ge_set_gej(&res3, &res1);
     CHECK(secp256k1_ge_is_infinity(&res3));
-    secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &one, &zero);
+    secp256k1_ecmult(&res1, point, &one, &zero);
     secp256k1_ge_set_gej(&res3, &res1);
     ge_equals_gej(&res3, point);
-    secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &one);
+    secp256k1_ecmult(&res1, point, &zero, &one);
     secp256k1_ge_set_gej(&res3, &res1);
     ge_equals_ge(&res3, &secp256k1_ge_const_g);
 }
@@ -3472,9 +4161,9 @@ void test_ecmult_target(const secp256k1_scalar* target, int mode) {
         secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &p2j, &n2);
         secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &ptj, target);
     } else if (mode == 1) {
-        secp256k1_ecmult(&ctx->ecmult_ctx, &p1j, &pj, &n1, &zero);
-        secp256k1_ecmult(&ctx->ecmult_ctx, &p2j, &pj, &n2, &zero);
-        secp256k1_ecmult(&ctx->ecmult_ctx, &ptj, &pj, target, &zero);
+        secp256k1_ecmult(&p1j, &pj, &n1, &zero);
+        secp256k1_ecmult(&p2j, &pj, &n2, &zero);
+        secp256k1_ecmult(&ptj, &pj, target, &zero);
     } else {
         secp256k1_ecmult_const(&p1j, &p, &n1, 256);
         secp256k1_ecmult_const(&p2j, &p, &n2, 256);
@@ -3657,7 +4346,7 @@ void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func e
     secp256k1_scalar_set_int(&szero, 0);
 
     /* No points to multiply */
-    CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, NULL, ecmult_multi_callback, &data, 0));
+    CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, NULL, ecmult_multi_callback, &data, 0));
 
     /* Check 1- and 2-point multiplies against ecmult */
     for (ncount = 0; ncount < count; ncount++) {
@@ -3672,35 +4361,27 @@ void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func e
         pt[1] = secp256k1_ge_const_g;
 
         /* only G scalar */
-        secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &szero, &sc[0]);
-        CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &sc[0], ecmult_multi_callback, &data, 0));
-        secp256k1_gej_neg(&r2, &r2);
-        secp256k1_gej_add_var(&r, &r, &r2, NULL);
-        CHECK(secp256k1_gej_is_infinity(&r));
+        secp256k1_ecmult(&r2, &ptgj, &szero, &sc[0]);
+        CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &sc[0], ecmult_multi_callback, &data, 0));
+        CHECK(secp256k1_gej_eq_var(&r, &r2));
 
         /* 1-point */
-        secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &szero);
-        CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 1));
-        secp256k1_gej_neg(&r2, &r2);
-        secp256k1_gej_add_var(&r, &r, &r2, NULL);
-        CHECK(secp256k1_gej_is_infinity(&r));
+        secp256k1_ecmult(&r2, &ptgj, &sc[0], &szero);
+        CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 1));
+        CHECK(secp256k1_gej_eq_var(&r, &r2));
 
         /* Try to multiply 1 point, but callback returns false */
-        CHECK(!ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_false_callback, &data, 1));
+        CHECK(!ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_false_callback, &data, 1));
 
         /* 2-point */
-        secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &sc[1]);
-        CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 2));
-        secp256k1_gej_neg(&r2, &r2);
-        secp256k1_gej_add_var(&r, &r, &r2, NULL);
-        CHECK(secp256k1_gej_is_infinity(&r));
+        secp256k1_ecmult(&r2, &ptgj, &sc[0], &sc[1]);
+        CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 2));
+        CHECK(secp256k1_gej_eq_var(&r, &r2));
 
         /* 2-point with G scalar */
-        secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &sc[1]);
-        CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &sc[1], ecmult_multi_callback, &data, 1));
-        secp256k1_gej_neg(&r2, &r2);
-        secp256k1_gej_add_var(&r, &r, &r2, NULL);
-        CHECK(secp256k1_gej_is_infinity(&r));
+        secp256k1_ecmult(&r2, &ptgj, &sc[0], &sc[1]);
+        CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &sc[1], ecmult_multi_callback, &data, 1));
+        CHECK(secp256k1_gej_eq_var(&r, &r2));
     }
 
     /* Check infinite outputs of various forms */
@@ -3714,7 +4395,7 @@ void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func e
                 random_scalar_order(&sc[i]);
                 secp256k1_ge_set_infinity(&pt[i]);
             }
-            CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
+            CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
             CHECK(secp256k1_gej_is_infinity(&r));
         }
 
@@ -3724,7 +4405,7 @@ void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func e
                 pt[i] = ptg;
                 secp256k1_scalar_set_int(&sc[i], 0);
             }
-            CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
+            CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
             CHECK(secp256k1_gej_is_infinity(&r));
         }
 
@@ -3737,7 +4418,7 @@ void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func e
                 pt[2 * i + 1] = ptg;
             }
 
-            CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
+            CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
             CHECK(secp256k1_gej_is_infinity(&r));
 
             random_scalar_order(&sc[0]);
@@ -3750,7 +4431,7 @@ void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func e
                 secp256k1_ge_neg(&pt[2*i+1], &pt[2*i]);
             }
 
-            CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
+            CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
             CHECK(secp256k1_gej_is_infinity(&r));
         }
 
@@ -3765,7 +4446,7 @@ void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func e
             secp256k1_scalar_negate(&sc[i], &sc[i]);
         }
 
-        CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 32));
+        CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 32));
         CHECK(secp256k1_gej_is_infinity(&r));
     }
 
@@ -3783,11 +4464,9 @@ void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func e
             secp256k1_gej_add_ge_var(&r, &r, &pt[i], NULL);
         }
 
-        secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &r, &sc[0], &szero);
-        CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
-        secp256k1_gej_neg(&r2, &r2);
-        secp256k1_gej_add_var(&r, &r, &r2, NULL);
-        CHECK(secp256k1_gej_is_infinity(&r));
+        secp256k1_ecmult(&r2, &r, &sc[0], &szero);
+        CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
+        CHECK(secp256k1_gej_eq_var(&r, &r2));
     }
 
     /* Check random scalars, constant point */
@@ -3806,11 +4485,9 @@ void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func e
         }
 
         secp256k1_gej_set_ge(&p0j, &pt[0]);
-        secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &p0j, &rs, &szero);
-        CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
-        secp256k1_gej_neg(&r2, &r2);
-        secp256k1_gej_add_var(&r, &r, &r2, NULL);
-        CHECK(secp256k1_gej_is_infinity(&r));
+        secp256k1_ecmult(&r2, &p0j, &rs, &szero);
+        CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
+        CHECK(secp256k1_gej_eq_var(&r, &r2));
     }
 
     /* Sanity check that zero scalars don't cause problems */
@@ -3820,13 +4497,13 @@ void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func e
     }
 
     secp256k1_scalar_clear(&sc[0]);
-    CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
+    CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
     secp256k1_scalar_clear(&sc[1]);
     secp256k1_scalar_clear(&sc[2]);
     secp256k1_scalar_clear(&sc[3]);
     secp256k1_scalar_clear(&sc[4]);
-    CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 6));
-    CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 5));
+    CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 6));
+    CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 5));
     CHECK(secp256k1_gej_is_infinity(&r));
 
     /* Run through s0*(t0*P) + s1*(t1*P) exhaustively for many small values of s0, s1, t0, t1 */
@@ -3850,8 +4527,8 @@ void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func e
                 secp256k1_scalar_set_int(&t1, (t1i + 1) / 2);
                 secp256k1_scalar_cond_negate(&t1, t1i & 1);
 
-                secp256k1_ecmult(&ctx->ecmult_ctx, &t0p, &ptgj, &t0, &szero);
-                secp256k1_ecmult(&ctx->ecmult_ctx, &t1p, &ptgj, &t1, &szero);
+                secp256k1_ecmult(&t0p, &ptgj, &t0, &szero);
+                secp256k1_ecmult(&t1p, &ptgj, &t1, &szero);
 
                 for(s0i = 0; s0i < TOP; s0i++) {
                     for(s1i = 0; s1i < TOP; s1i++) {
@@ -3870,11 +4547,9 @@ void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func e
                         secp256k1_scalar_mul(&tmp2, &t1, &sc[1]);
                         secp256k1_scalar_add(&tmp1, &tmp1, &tmp2);
 
-                        secp256k1_ecmult(&ctx->ecmult_ctx, &expected, &ptgj, &tmp1, &szero);
-                        CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &actual, &szero, ecmult_multi_callback, &data, 2));
-                        secp256k1_gej_neg(&expected, &expected);
-                        secp256k1_gej_add_var(&actual, &actual, &expected, NULL);
-                        CHECK(secp256k1_gej_is_infinity(&actual));
+                        secp256k1_ecmult(&expected, &ptgj, &tmp1, &szero);
+                        CHECK(ecmult_multi(&ctx->error_callback, scratch, &actual, &szero, ecmult_multi_callback, &data, 2));
+                        CHECK(secp256k1_gej_eq_var(&actual, &expected));
                     }
                 }
             }
@@ -3882,6 +4557,172 @@ void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func e
     }
 }
 
+int test_ecmult_multi_random(secp256k1_scratch *scratch) {
+    /* Large random test for ecmult_multi_* functions which exercises:
+     * - Few or many inputs (0 up to 128, roughly exponentially distributed).
+     * - Few or many 0*P or a*INF inputs (roughly uniformly distributed).
+     * - Including or excluding an nonzero a*G term (or such a term at all).
+     * - Final expected result equal to infinity or not (roughly 50%).
+     * - ecmult_multi_var, ecmult_strauss_single_batch, ecmult_pippenger_single_batch
+     */
+
+    /* These 4 variables define the eventual input to the ecmult_multi function.
+     * g_scalar is the G scalar fed to it (or NULL, possibly, if g_scalar=0), and
+     * scalars[0..filled-1] and gejs[0..filled-1] are the scalars and points
+     * which form its normal inputs. */
+    int filled = 0;
+    secp256k1_scalar g_scalar = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+    secp256k1_scalar scalars[128];
+    secp256k1_gej gejs[128];
+    /* The expected result, and the computed result. */
+    secp256k1_gej expected, computed;
+    /* Temporaries. */
+    secp256k1_scalar sc_tmp;
+    secp256k1_ge ge_tmp;
+    /* Variables needed for the actual input to ecmult_multi. */
+    secp256k1_ge ges[128];
+    ecmult_multi_data data;
+
+    int i;
+    /* Which multiplication function to use */
+    int fn = secp256k1_testrand_int(3);
+    secp256k1_ecmult_multi_func ecmult_multi = fn == 0 ? secp256k1_ecmult_multi_var :
+                                               fn == 1 ? secp256k1_ecmult_strauss_batch_single :
+                                               secp256k1_ecmult_pippenger_batch_single;
+    /* Simulate exponentially distributed num. */
+    int num_bits = 2 + secp256k1_testrand_int(6);
+    /* Number of (scalar, point) inputs (excluding g). */
+    int num = secp256k1_testrand_int((1 << num_bits) + 1);
+    /* Number of those which are nonzero. */
+    int num_nonzero = secp256k1_testrand_int(num + 1);
+    /* Whether we're aiming to create an input with nonzero expected result. */
+    int nonzero_result = secp256k1_testrand_bits(1);
+    /* Whether we will provide nonzero g multiplicand. In some cases our hand
+     * is forced here based on num_nonzero and nonzero_result. */
+    int g_nonzero = num_nonzero == 0 ? nonzero_result :
+                    num_nonzero == 1 && !nonzero_result ? 1 :
+                    (int)secp256k1_testrand_bits(1);
+    /* Which g_scalar pointer to pass into ecmult_multi(). */
+    const secp256k1_scalar* g_scalar_ptr = (g_nonzero || secp256k1_testrand_bits(1)) ? &g_scalar : NULL;
+    /* How many EC multiplications were performed in this function. */
+    int mults = 0;
+    /* How many randomization steps to apply to the input list. */
+    int rands = (int)secp256k1_testrand_bits(3);
+    if (rands > num_nonzero) rands = num_nonzero;
+
+    secp256k1_gej_set_infinity(&expected);
+    secp256k1_gej_set_infinity(&gejs[0]);
+    secp256k1_scalar_set_int(&scalars[0], 0);
+
+    if (g_nonzero) {
+        /* If g_nonzero, set g_scalar to nonzero value r. */
+        random_scalar_order_test(&g_scalar);
+        if (!nonzero_result) {
+            /* If expected=0 is desired, add a (a*r, -(1/a)*g) term to compensate. */
+            CHECK(num_nonzero > filled);
+            random_scalar_order_test(&sc_tmp);
+            secp256k1_scalar_mul(&scalars[filled], &sc_tmp, &g_scalar);
+            secp256k1_scalar_inverse_var(&sc_tmp, &sc_tmp);
+            secp256k1_scalar_negate(&sc_tmp, &sc_tmp);
+            secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &gejs[filled], &sc_tmp);
+            ++filled;
+            ++mults;
+        }
+    }
+
+    if (nonzero_result && filled < num_nonzero) {
+        /* If a nonzero result is desired, and there is space, add a random nonzero term. */
+        random_scalar_order_test(&scalars[filled]);
+        random_group_element_test(&ge_tmp);
+        secp256k1_gej_set_ge(&gejs[filled], &ge_tmp);
+        ++filled;
+    }
+
+    if (nonzero_result) {
+        /* Compute the expected result using normal ecmult. */
+        CHECK(filled <= 1);
+        secp256k1_ecmult(&expected, &gejs[0], &scalars[0], &g_scalar);
+        mults += filled + g_nonzero;
+    }
+
+    /* At this point we have expected = scalar_g*G + sum(scalars[i]*gejs[i] for i=0..filled-1). */
+    CHECK(filled <= 1 + !nonzero_result);
+    CHECK(filled <= num_nonzero);
+
+    /* Add entries to scalars,gejs so that there are num of them. All the added entries
+     * either have scalar=0 or point=infinity, so these do not change the expected result. */
+    while (filled < num) {
+        if (secp256k1_testrand_bits(1)) {
+            secp256k1_gej_set_infinity(&gejs[filled]);
+            random_scalar_order_test(&scalars[filled]);
+        } else {
+            secp256k1_scalar_set_int(&scalars[filled], 0);
+            random_group_element_test(&ge_tmp);
+            secp256k1_gej_set_ge(&gejs[filled], &ge_tmp);
+        }
+        ++filled;
+    }
+
+    /* Now perform cheapish transformations on gejs and scalars, for indices
+     * 0..num_nonzero-1, which do not change the expected result, but may
+     * convert some of them to be both non-0-scalar and non-infinity-point. */
+    for (i = 0; i < rands; ++i) {
+        int j;
+        secp256k1_scalar v, iv;
+        /* Shuffle the entries. */
+        for (j = 0; j < num_nonzero; ++j) {
+            int k = secp256k1_testrand_int(num_nonzero - j);
+            if (k != 0) {
+                secp256k1_gej gej = gejs[j];
+                secp256k1_scalar sc = scalars[j];
+                gejs[j] = gejs[j + k];
+                scalars[j] = scalars[j + k];
+                gejs[j + k] = gej;
+                scalars[j + k] = sc;
+            }
+        }
+        /* Perturb all consecutive pairs of inputs:
+         * a*P + b*Q -> (a+b)*P + b*(Q-P). */
+        for (j = 0; j + 1 < num_nonzero; j += 2) {
+            secp256k1_gej gej;
+            secp256k1_scalar_add(&scalars[j], &scalars[j], &scalars[j+1]);
+            secp256k1_gej_neg(&gej, &gejs[j]);
+            secp256k1_gej_add_var(&gejs[j+1], &gejs[j+1], &gej, NULL);
+        }
+        /* Transform the last input: a*P -> (v*a) * ((1/v)*P). */
+        CHECK(num_nonzero >= 1);
+        random_scalar_order_test(&v);
+        secp256k1_scalar_inverse(&iv, &v);
+        secp256k1_scalar_mul(&scalars[num_nonzero - 1], &scalars[num_nonzero - 1], &v);
+        secp256k1_ecmult(&gejs[num_nonzero - 1], &gejs[num_nonzero - 1], &iv, NULL);
+        ++mults;
+    }
+
+    /* Shuffle all entries (0..num-1). */
+    for (i = 0; i < num; ++i) {
+        int j = secp256k1_testrand_int(num - i);
+        if (j != 0) {
+            secp256k1_gej gej = gejs[i];
+            secp256k1_scalar sc = scalars[i];
+            gejs[i] = gejs[i + j];
+            scalars[i] = scalars[i + j];
+            gejs[i + j] = gej;
+            scalars[i + j] = sc;
+        }
+    }
+
+    /* Compute affine versions of all inputs. */
+    secp256k1_ge_set_all_gej_var(ges, gejs, filled);
+    /* Invoke ecmult_multi code. */
+    data.sc = scalars;
+    data.pt = ges;
+    CHECK(ecmult_multi(&ctx->error_callback, scratch, &computed, g_scalar_ptr, ecmult_multi_callback, &data, filled));
+    mults += num_nonzero + g_nonzero;
+    /* Compare with expected result. */
+    CHECK(secp256k1_gej_eq_var(&computed, &expected));
+    return mults;
+}
+
 void test_ecmult_multi_batch_single(secp256k1_ecmult_multi_func ecmult_multi) {
     secp256k1_scalar szero;
     secp256k1_scalar sc;
@@ -3898,7 +4739,7 @@ void test_ecmult_multi_batch_single(secp256k1_ecmult_multi_func ecmult_multi) {
 
     /* Try to multiply 1 point, but scratch space is empty.*/
     scratch_empty = secp256k1_scratch_create(&ctx->error_callback, 0);
-    CHECK(!ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch_empty, &r, &szero, ecmult_multi_callback, &data, 1));
+    CHECK(!ecmult_multi(&ctx->error_callback, scratch_empty, &r, &szero, ecmult_multi_callback, &data, 1));
     secp256k1_scratch_destroy(&ctx->error_callback, scratch_empty);
 }
 
@@ -3923,7 +4764,7 @@ void test_secp256k1_pippenger_bucket_window_inv(void) {
  * for a given scratch space.
  */
 void test_ecmult_multi_pippenger_max_points(void) {
-    size_t scratch_size = secp256k1_testrand_int(256);
+    size_t scratch_size = secp256k1_testrand_bits(8);
     size_t max_size = secp256k1_pippenger_scratch_size(secp256k1_pippenger_bucket_window_inv(PIPPENGER_MAX_BUCKET_WINDOW-1)+512, 12);
     secp256k1_scratch *scratch;
     size_t n_points_supported;
@@ -4020,7 +4861,7 @@ void test_ecmult_multi_batching(void) {
 
     /* Get random scalars and group elements and compute result */
     random_scalar_order(&scG);
-    secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &r2, &szero, &scG);
+    secp256k1_ecmult(&r2, &r2, &szero, &scG);
     for(i = 0; i < n_points; i++) {
         secp256k1_ge ptg;
         secp256k1_gej ptgj;
@@ -4028,7 +4869,7 @@ void test_ecmult_multi_batching(void) {
         secp256k1_gej_set_ge(&ptgj, &ptg);
         pt[i] = ptg;
         random_scalar_order(&sc[i]);
-        secp256k1_ecmult(&ctx->ecmult_ctx, &ptgj, &ptgj, &sc[i], NULL);
+        secp256k1_ecmult(&ptgj, &ptgj, &sc[i], NULL);
         secp256k1_gej_add_var(&r2, &r2, &ptgj, NULL);
     }
     data.sc = sc;
@@ -4038,7 +4879,7 @@ void test_ecmult_multi_batching(void) {
     /* Test with empty scratch space. It should compute the correct result using
      * ecmult_mult_simple algorithm which doesn't require a scratch space. */
     scratch = secp256k1_scratch_create(&ctx->error_callback, 0);
-    CHECK(secp256k1_ecmult_multi_var(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, n_points));
+    CHECK(secp256k1_ecmult_multi_var(&ctx->error_callback, scratch, &r, &scG, ecmult_multi_callback, &data, n_points));
     secp256k1_gej_add_var(&r, &r, &r2, NULL);
     CHECK(secp256k1_gej_is_infinity(&r));
     secp256k1_scratch_destroy(&ctx->error_callback, scratch);
@@ -4047,7 +4888,7 @@ void test_ecmult_multi_batching(void) {
      * ecmult_multi selects strauss which requires more memory. It should
      * therefore select the simple algorithm. */
     scratch = secp256k1_scratch_create(&ctx->error_callback, secp256k1_pippenger_scratch_size(1, 1) + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT);
-    CHECK(secp256k1_ecmult_multi_var(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, n_points));
+    CHECK(secp256k1_ecmult_multi_var(&ctx->error_callback, scratch, &r, &scG, ecmult_multi_callback, &data, n_points));
     secp256k1_gej_add_var(&r, &r, &r2, NULL);
     CHECK(secp256k1_gej_is_infinity(&r));
     secp256k1_scratch_destroy(&ctx->error_callback, scratch);
@@ -4061,7 +4902,7 @@ void test_ecmult_multi_batching(void) {
             size_t scratch_size = secp256k1_strauss_scratch_size(i);
             scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT);
         }
-        CHECK(secp256k1_ecmult_multi_var(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, n_points));
+        CHECK(secp256k1_ecmult_multi_var(&ctx->error_callback, scratch, &r, &scG, ecmult_multi_callback, &data, n_points));
         secp256k1_gej_add_var(&r, &r, &r2, NULL);
         CHECK(secp256k1_gej_is_infinity(&r));
         secp256k1_scratch_destroy(&ctx->error_callback, scratch);
@@ -4072,6 +4913,7 @@ void test_ecmult_multi_batching(void) {
 
 void run_ecmult_multi_tests(void) {
     secp256k1_scratch *scratch;
+    int64_t todo = (int64_t)320 * count;
 
     test_secp256k1_pippenger_bucket_window_inv();
     test_ecmult_multi_pippenger_max_points();
@@ -4082,6 +4924,9 @@ void run_ecmult_multi_tests(void) {
     test_ecmult_multi_batch_single(secp256k1_ecmult_pippenger_batch_single);
     test_ecmult_multi(scratch, secp256k1_ecmult_strauss_batch_single);
     test_ecmult_multi_batch_single(secp256k1_ecmult_strauss_batch_single);
+    while (todo > 0) {
+        todo -= test_ecmult_multi_random(scratch);
+    }
     secp256k1_scratch_destroy(&ctx->error_callback, scratch);
 
     /* Run test_ecmult_multi with space for exactly one point */
@@ -4177,7 +5022,7 @@ void test_constant_wnaf(const secp256k1_scalar *number, int w) {
         secp256k1_scalar_add(&x, &x, &t);
     }
     /* Skew num because when encoding numbers as odd we use an offset */
-    secp256k1_scalar_set_int(&scalar_skew, 1 << (skew == 2));
+    secp256k1_scalar_set_int(&scalar_skew, skew);
     secp256k1_scalar_add(&num, &num, &scalar_skew);
     CHECK(secp256k1_scalar_eq(&x, &num));
 }
@@ -4329,41 +5174,166 @@ void run_wnaf(void) {
     CHECK(secp256k1_scalar_is_zero(&n));
 }
 
-void test_ecmult_constants(void) {
-    /* Test ecmult_gen() for [0..36) and [order-36..0). */
-    secp256k1_scalar x;
-    secp256k1_gej r;
-    secp256k1_ge ng;
-    int i;
-    int j;
-    secp256k1_ge_neg(&ng, &secp256k1_ge_const_g);
-    for (i = 0; i < 36; i++ ) {
-        secp256k1_scalar_set_int(&x, i);
-        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x);
-        for (j = 0; j < i; j++) {
-            if (j == i - 1) {
-                ge_equals_gej(&secp256k1_ge_const_g, &r);
-            }
-            secp256k1_gej_add_ge(&r, &r, &ng);
-        }
-        CHECK(secp256k1_gej_is_infinity(&r));
+static int test_ecmult_accumulate_cb(secp256k1_scalar* sc, secp256k1_ge* pt, size_t idx, void* data) {
+    const secp256k1_scalar* indata = (const secp256k1_scalar*)data;
+    *sc = *indata;
+    *pt = secp256k1_ge_const_g;
+    CHECK(idx == 0);
+    return 1;
+}
+
+void test_ecmult_accumulate(secp256k1_sha256* acc, const secp256k1_scalar* x, secp256k1_scratch* scratch) {
+    /* Compute x*G in 6 different ways, serialize it uncompressed, and feed it into acc. */
+    secp256k1_gej rj1, rj2, rj3, rj4, rj5, rj6, gj, infj;
+    secp256k1_ge r;
+    const secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+    unsigned char bytes[65];
+    size_t size = 65;
+    secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
+    secp256k1_gej_set_infinity(&infj);
+    secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &rj1, x);
+    secp256k1_ecmult(&rj2, &gj, x, &zero);
+    secp256k1_ecmult(&rj3, &infj, &zero, x);
+    secp256k1_ecmult_multi_var(NULL, scratch, &rj4, x, NULL, NULL, 0);
+    secp256k1_ecmult_multi_var(NULL, scratch, &rj5, &zero, test_ecmult_accumulate_cb, (void*)x, 1);
+    secp256k1_ecmult_const(&rj6, &secp256k1_ge_const_g, x, 256);
+    secp256k1_ge_set_gej_var(&r, &rj1);
+    ge_equals_gej(&r, &rj2);
+    ge_equals_gej(&r, &rj3);
+    ge_equals_gej(&r, &rj4);
+    ge_equals_gej(&r, &rj5);
+    ge_equals_gej(&r, &rj6);
+    if (secp256k1_ge_is_infinity(&r)) {
+        /* Store infinity as 0x00 */
+        const unsigned char zerobyte[1] = {0};
+        secp256k1_sha256_write(acc, zerobyte, 1);
+    } else {
+        /* Store other points using their uncompressed serialization. */
+        secp256k1_eckey_pubkey_serialize(&r, bytes, &size, 0);
+        CHECK(size == 65);
+        secp256k1_sha256_write(acc, bytes, size);
     }
-    for (i = 1; i <= 36; i++ ) {
+}
+
+void test_ecmult_constants_2bit(void) {
+    /* Using test_ecmult_accumulate, test ecmult for:
+     * - For i in 0..36:
+     *   - Key i
+     *   - Key -i
+     * - For i in 0..255:
+     *   - For j in 1..255 (only odd values):
+     *     - Key (j*2^i) mod order
+     */
+    secp256k1_scalar x;
+    secp256k1_sha256 acc;
+    unsigned char b32[32];
+    int i, j;
+    secp256k1_scratch_space *scratch = secp256k1_scratch_space_create(ctx, 65536);
+
+    /* Expected hash of all the computed points; created with an independent
+     * implementation. */
+    static const unsigned char expected32[32] = {
+        0xe4, 0x71, 0x1b, 0x4d, 0x14, 0x1e, 0x68, 0x48,
+        0xb7, 0xaf, 0x47, 0x2b, 0x4c, 0xd2, 0x04, 0x14,
+        0x3a, 0x75, 0x87, 0x60, 0x1a, 0xf9, 0x63, 0x60,
+        0xd0, 0xcb, 0x1f, 0xaa, 0x85, 0x9a, 0xb7, 0xb4
+    };
+    secp256k1_sha256_initialize(&acc);
+    for (i = 0; i <= 36; ++i) {
         secp256k1_scalar_set_int(&x, i);
+        test_ecmult_accumulate(&acc, &x, scratch);
         secp256k1_scalar_negate(&x, &x);
-        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x);
-        for (j = 0; j < i; j++) {
-            if (j == i - 1) {
-                ge_equals_gej(&ng, &r);
-            }
-            secp256k1_gej_add_ge(&r, &r, &secp256k1_ge_const_g);
+        test_ecmult_accumulate(&acc, &x, scratch);
+    };
+    for (i = 0; i < 256; ++i) {
+        for (j = 1; j < 256; j += 2) {
+            int k;
+            secp256k1_scalar_set_int(&x, j);
+            for (k = 0; k < i; ++k) secp256k1_scalar_add(&x, &x, &x);
+            test_ecmult_accumulate(&acc, &x, scratch);
         }
-        CHECK(secp256k1_gej_is_infinity(&r));
     }
+    secp256k1_sha256_finalize(&acc, b32);
+    CHECK(secp256k1_memcmp_var(b32, expected32, 32) == 0);
+
+    secp256k1_scratch_space_destroy(ctx, scratch);
+}
+
+void test_ecmult_constants_sha(uint32_t prefix, size_t iter, const unsigned char* expected32) {
+    /* Using test_ecmult_accumulate, test ecmult for:
+     * - Key 0
+     * - Key 1
+     * - Key -1
+     * - For i in range(iter):
+     *   - Key SHA256(LE32(prefix) || LE16(i))
+     */
+    secp256k1_scalar x;
+    secp256k1_sha256 acc;
+    unsigned char b32[32];
+    unsigned char inp[6];
+    size_t i;
+    secp256k1_scratch_space *scratch = secp256k1_scratch_space_create(ctx, 65536);
+
+    inp[0] = prefix & 0xFF;
+    inp[1] = (prefix >> 8) & 0xFF;
+    inp[2] = (prefix >> 16) & 0xFF;
+    inp[3] = (prefix >> 24) & 0xFF;
+    secp256k1_sha256_initialize(&acc);
+    secp256k1_scalar_set_int(&x, 0);
+    test_ecmult_accumulate(&acc, &x, scratch);
+    secp256k1_scalar_set_int(&x, 1);
+    test_ecmult_accumulate(&acc, &x, scratch);
+    secp256k1_scalar_negate(&x, &x);
+    test_ecmult_accumulate(&acc, &x, scratch);
+
+    for (i = 0; i < iter; ++i) {
+        secp256k1_sha256 gen;
+        inp[4] = i & 0xff;
+        inp[5] = (i >> 8) & 0xff;
+        secp256k1_sha256_initialize(&gen);
+        secp256k1_sha256_write(&gen, inp, sizeof(inp));
+        secp256k1_sha256_finalize(&gen, b32);
+        secp256k1_scalar_set_b32(&x, b32, NULL);
+        test_ecmult_accumulate(&acc, &x, scratch);
+    }
+    secp256k1_sha256_finalize(&acc, b32);
+    CHECK(secp256k1_memcmp_var(b32, expected32, 32) == 0);
+
+    secp256k1_scratch_space_destroy(ctx, scratch);
 }
 
 void run_ecmult_constants(void) {
-    test_ecmult_constants();
+    /* Expected hashes of all points in the tests below. Computed using an
+     * independent implementation. */
+    static const unsigned char expected32_6bit20[32] = {
+        0x68, 0xb6, 0xed, 0x6f, 0x28, 0xca, 0xc9, 0x7f,
+        0x8e, 0x8b, 0xd6, 0xc0, 0x61, 0x79, 0x34, 0x6e,
+        0x5a, 0x8f, 0x2b, 0xbc, 0x3e, 0x1f, 0xc5, 0x2e,
+        0x2a, 0xd0, 0x45, 0x67, 0x7f, 0x95, 0x95, 0x8e
+    };
+    static const unsigned char expected32_8bit8[32] = {
+        0x8b, 0x65, 0x8e, 0xea, 0x86, 0xae, 0x3c, 0x95,
+        0x90, 0xb6, 0x77, 0xa4, 0x8c, 0x76, 0xd9, 0xec,
+        0xf5, 0xab, 0x8a, 0x2f, 0xfd, 0xdb, 0x19, 0x12,
+        0x1a, 0xee, 0xe6, 0xb7, 0x6e, 0x05, 0x3f, 0xc6
+    };
+    /* For every combination of 6 bit positions out of 256, restricted to
+     * 20-bit windows (i.e., the first and last bit position are no more than
+     * 19 bits apart), all 64 bit patterns occur in the input scalars used in
+     * this test. */
+    CONDITIONAL_TEST(1, "test_ecmult_constants_sha 1024") {
+        test_ecmult_constants_sha(4808378u, 1024, expected32_6bit20);
+    }
+
+    /* For every combination of 8 consecutive bit positions, all 256 bit
+     * patterns occur in the input scalars used in this test. */
+    CONDITIONAL_TEST(3, "test_ecmult_constants_sha 2048") {
+        test_ecmult_constants_sha(1607366309u, 2048, expected32_8bit8);
+    }
+
+    CONDITIONAL_TEST(35, "test_ecmult_constants_2bit") {
+        test_ecmult_constants_2bit();
+    }
 }
 
 void test_ecmult_gen_blind(void) {
@@ -4804,7 +5774,7 @@ void run_ec_pubkey_parse_test(void) {
     ecount = 0;
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 65) == 1);
-    CHECK(secp256k1_ec_pubkey_parse(secp256k1_context_no_precomp, &pubkey, pubkeyc, 65) == 1);
+    CHECK(secp256k1_ec_pubkey_parse(secp256k1_context_static, &pubkey, pubkeyc, 65) == 1);
     VG_CHECK(&pubkey, sizeof(pubkey));
     CHECK(ecount == 0);
     VG_UNDEF(&ge, sizeof(ge));
@@ -5166,22 +6136,24 @@ void test_ecdsa_sign_verify(void) {
     secp256k1_scalar msg, key;
     secp256k1_scalar sigr, sigs;
     int getrec;
-    /* Initialize recid to suppress a false positive -Wconditional-uninitialized in clang.
-       VG_UNDEF ensures that valgrind will still treat the variable as uninitialized. */
-    int recid = -1; VG_UNDEF(&recid, sizeof(recid));
+    int recid;
     random_scalar_order_test(&msg);
     random_scalar_order_test(&key);
     secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubj, &key);
     secp256k1_ge_set_gej(&pub, &pubj);
     getrec = secp256k1_testrand_bits(1);
-    random_sign(&sigr, &sigs, &key, &msg, getrec?&recid:NULL);
+    /* The specific way in which this conditional is written sidesteps a potential bug in clang.
+       See the commit messages of the commit that introduced this comment for details. */
     if (getrec) {
+        random_sign(&sigr, &sigs, &key, &msg, &recid);
         CHECK(recid >= 0 && recid < 4);
+    } else {
+        random_sign(&sigr, &sigs, &key, &msg, NULL);
     }
-    CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg));
+    CHECK(secp256k1_ecdsa_sig_verify(&sigr, &sigs, &pub, &msg));
     secp256k1_scalar_set_int(&one, 1);
     secp256k1_scalar_add(&msg, &msg, &one);
-    CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg));
+    CHECK(!secp256k1_ecdsa_sig_verify(&sigr, &sigs, &pub, &msg));
 }
 
 void run_ecdsa_sign_verify(void) {
@@ -5513,14 +6485,6 @@ void run_ecdsa_end_to_end(void) {
 
 int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_der, int certainly_not_der) {
     static const unsigned char zeroes[32] = {0};
-#ifdef ENABLE_OPENSSL_TESTS
-    static const unsigned char max_scalar[32] = {
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
-        0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
-        0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40
-    };
-#endif
 
     int ret = 0;
 
@@ -5536,15 +6500,6 @@ int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_
     size_t len_der_lax = 2048;
     int parsed_der_lax = 0, valid_der_lax = 0, roundtrips_der_lax = 0;
 
-#ifdef ENABLE_OPENSSL_TESTS
-    ECDSA_SIG *sig_openssl;
-    const BIGNUM *r = NULL, *s = NULL;
-    const unsigned char *sigptr;
-    unsigned char roundtrip_openssl[2048];
-    int len_openssl = 2048;
-    int parsed_openssl, valid_openssl = 0, roundtrips_openssl = 0;
-#endif
-
     parsed_der = secp256k1_ecdsa_signature_parse_der(ctx, &sig_der, sig, siglen);
     if (parsed_der) {
         ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der, &sig_der)) << 0;
@@ -5585,43 +6540,6 @@ int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_
         ret |= (!parsed_der_lax) << 16;
     }
 
-#ifdef ENABLE_OPENSSL_TESTS
-    sig_openssl = ECDSA_SIG_new();
-    sigptr = sig;
-    parsed_openssl = (d2i_ECDSA_SIG(&sig_openssl, &sigptr, siglen) != NULL);
-    if (parsed_openssl) {
-        ECDSA_SIG_get0(sig_openssl, &r, &s);
-        valid_openssl = !BN_is_negative(r) && !BN_is_negative(s) && BN_num_bits(r) > 0 && BN_num_bits(r) <= 256 && BN_num_bits(s) > 0 && BN_num_bits(s) <= 256;
-        if (valid_openssl) {
-            unsigned char tmp[32] = {0};
-            BN_bn2bin(r, tmp + 32 - BN_num_bytes(r));
-            valid_openssl = secp256k1_memcmp_var(tmp, max_scalar, 32) < 0;
-        }
-        if (valid_openssl) {
-            unsigned char tmp[32] = {0};
-            BN_bn2bin(s, tmp + 32 - BN_num_bytes(s));
-            valid_openssl = secp256k1_memcmp_var(tmp, max_scalar, 32) < 0;
-        }
-    }
-    len_openssl = i2d_ECDSA_SIG(sig_openssl, NULL);
-    if (len_openssl <= 2048) {
-        unsigned char *ptr = roundtrip_openssl;
-        CHECK(i2d_ECDSA_SIG(sig_openssl, &ptr) == len_openssl);
-        roundtrips_openssl = valid_openssl && ((size_t)len_openssl == siglen) && (secp256k1_memcmp_var(roundtrip_openssl, sig, siglen) == 0);
-    } else {
-        len_openssl = 0;
-    }
-    ECDSA_SIG_free(sig_openssl);
-
-    ret |= (parsed_der && !parsed_openssl) << 4;
-    ret |= (valid_der && !valid_openssl) << 5;
-    ret |= (roundtrips_openssl && !parsed_der) << 6;
-    ret |= (roundtrips_der != roundtrips_openssl) << 7;
-    if (roundtrips_openssl) {
-        ret |= (len_der != (size_t)len_openssl) << 8;
-        ret |= ((len_der != (size_t)len_openssl) || (secp256k1_memcmp_var(roundtrip_der, roundtrip_openssl, len_der) != 0)) << 9;
-    }
-#endif
     return ret;
 }
 
@@ -5681,14 +6599,14 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly
         /* We generate two classes of numbers: nlow==1 "low" ones (up to 32 bytes), nlow==0 "high" ones (32 bytes with 129 top bits set, or larger than 32 bytes) */
         nlow[n] = der ? 1 : (secp256k1_testrand_bits(3) != 0);
         /* The length of the number in bytes (the first byte of which will always be nonzero) */
-        nlen[n] = nlow[n] ? secp256k1_testrand_int(33) : 32 + secp256k1_testrand_int(200) * secp256k1_testrand_int(8) / 8;
+        nlen[n] = nlow[n] ? secp256k1_testrand_int(33) : 32 + secp256k1_testrand_int(200) * secp256k1_testrand_bits(3) / 8;
         CHECK(nlen[n] <= 232);
         /* The top bit of the number. */
         nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : secp256k1_testrand_bits(1));
         /* The top byte of the number (after the potential hardcoded 16 0xFF characters for "high" 32 bytes numbers) */
         nhbyte[n] = nlen[n] == 0 ? 0 : (nhbit[n] ? 128 + secp256k1_testrand_bits(7) : 1 + secp256k1_testrand_int(127));
         /* The number of zero bytes in front of the number (which is 0 or 1 in case of DER, otherwise we extend up to 300 bytes) */
-        nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_testrand_int(3) : secp256k1_testrand_int(300 - nlen[n]) * secp256k1_testrand_int(8) / 8);
+        nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_testrand_int(3) : secp256k1_testrand_int(300 - nlen[n]) * secp256k1_testrand_bits(3) / 8);
         if (nzlen[n] > ((nlen[n] == 0 || nhbit[n]) ? 1 : 0)) {
             *certainly_not_der = 1;
         }
@@ -5697,7 +6615,7 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly
         nlenlen[n] = nlen[n] + nzlen[n] < 128 ? 0 : (nlen[n] + nzlen[n] < 256 ? 1 : 2);
         if (!der) {
             /* nlenlen[n] max 127 bytes */
-            int add = secp256k1_testrand_int(127 - nlenlen[n]) * secp256k1_testrand_int(16) * secp256k1_testrand_int(16) / 256;
+            int add = secp256k1_testrand_int(127 - nlenlen[n]) * secp256k1_testrand_bits(4) * secp256k1_testrand_bits(4) / 256;
             nlenlen[n] += add;
             if (add != 0) {
                 *certainly_not_der = 1;
@@ -5711,7 +6629,7 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly
     CHECK(tlen <= 856);
 
     /* The length of the garbage inside the tuple. */
-    elen = (der || indet) ? 0 : secp256k1_testrand_int(980 - tlen) * secp256k1_testrand_int(8) / 8;
+    elen = (der || indet) ? 0 : secp256k1_testrand_int(980 - tlen) * secp256k1_testrand_bits(3) / 8;
     if (elen != 0) {
         *certainly_not_der = 1;
     }
@@ -5719,7 +6637,7 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly
     CHECK(tlen <= 980);
 
     /* The length of the garbage after the end of the tuple. */
-    glen = der ? 0 : secp256k1_testrand_int(990 - tlen) * secp256k1_testrand_int(8) / 8;
+    glen = der ? 0 : secp256k1_testrand_int(990 - tlen) * secp256k1_testrand_bits(3) / 8;
     if (glen != 0) {
         *certainly_not_der = 1;
     }
@@ -5734,7 +6652,7 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly
     } else {
         int tlenlen = tlen < 128 ? 0 : (tlen < 256 ? 1 : 2);
         if (!der) {
-            int add = secp256k1_testrand_int(127 - tlenlen) * secp256k1_testrand_int(16) * secp256k1_testrand_int(16) / 256;
+            int add = secp256k1_testrand_int(127 - tlenlen) * secp256k1_testrand_bits(4) * secp256k1_testrand_bits(4) / 256;
             tlenlen += add;
             if (add != 0) {
                 *certainly_not_der = 1;
@@ -5859,7 +6777,7 @@ void test_ecdsa_edge_cases(void) {
         secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &keyj, &sr);
         secp256k1_ge_set_gej(&key, &keyj);
         msg = ss;
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0);
     }
 
     /* Verify signature with r of zero fails. */
@@ -5878,7 +6796,7 @@ void test_ecdsa_edge_cases(void) {
         secp256k1_scalar_set_int(&msg, 0);
         secp256k1_scalar_set_int(&sr, 0);
         CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey_mods_zero, 33));
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+        CHECK(secp256k1_ecdsa_sig_verify( &sr, &ss, &key, &msg) == 0);
     }
 
     /* Verify signature with s of zero fails. */
@@ -5897,7 +6815,7 @@ void test_ecdsa_edge_cases(void) {
         secp256k1_scalar_set_int(&msg, 0);
         secp256k1_scalar_set_int(&sr, 1);
         CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0);
     }
 
     /* Verify signature with message 0 passes. */
@@ -5925,14 +6843,14 @@ void test_ecdsa_edge_cases(void) {
         secp256k1_scalar_set_int(&sr, 2);
         CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
         CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33));
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1);
         secp256k1_scalar_negate(&ss, &ss);
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1);
         secp256k1_scalar_set_int(&ss, 1);
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 0);
     }
 
     /* Verify signature with message 1 passes. */
@@ -5966,15 +6884,15 @@ void test_ecdsa_edge_cases(void) {
         secp256k1_scalar_set_b32(&sr, csr, NULL);
         CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
         CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33));
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1);
         secp256k1_scalar_negate(&ss, &ss);
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1);
         secp256k1_scalar_set_int(&ss, 2);
         secp256k1_scalar_inverse_var(&ss, &ss);
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 0);
     }
 
     /* Verify signature with message -1 passes. */
@@ -6000,12 +6918,12 @@ void test_ecdsa_edge_cases(void) {
         secp256k1_scalar_negate(&msg, &msg);
         secp256k1_scalar_set_b32(&sr, csr, NULL);
         CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1);
         secp256k1_scalar_negate(&ss, &ss);
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1);
         secp256k1_scalar_set_int(&ss, 3);
         secp256k1_scalar_inverse_var(&ss, &ss);
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+        CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0);
     }
 
     /* Signature where s would be zero. */
@@ -6215,62 +7133,6 @@ void run_ecdsa_edge_cases(void) {
     test_ecdsa_edge_cases();
 }
 
-#ifdef ENABLE_OPENSSL_TESTS
-EC_KEY *get_openssl_key(const unsigned char *key32) {
-    unsigned char privkey[300];
-    size_t privkeylen;
-    const unsigned char* pbegin = privkey;
-    int compr = secp256k1_testrand_bits(1);
-    EC_KEY *ec_key = EC_KEY_new_by_curve_name(NID_secp256k1);
-    CHECK(ec_privkey_export_der(ctx, privkey, &privkeylen, key32, compr));
-    CHECK(d2i_ECPrivateKey(&ec_key, &pbegin, privkeylen));
-    CHECK(EC_KEY_check_key(ec_key));
-    return ec_key;
-}
-
-void test_ecdsa_openssl(void) {
-    secp256k1_gej qj;
-    secp256k1_ge q;
-    secp256k1_scalar sigr, sigs;
-    secp256k1_scalar one;
-    secp256k1_scalar msg2;
-    secp256k1_scalar key, msg;
-    EC_KEY *ec_key;
-    unsigned int sigsize = 80;
-    size_t secp_sigsize = 80;
-    unsigned char message[32];
-    unsigned char signature[80];
-    unsigned char key32[32];
-    secp256k1_testrand256_test(message);
-    secp256k1_scalar_set_b32(&msg, message, NULL);
-    random_scalar_order_test(&key);
-    secp256k1_scalar_get_b32(key32, &key);
-    secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &qj, &key);
-    secp256k1_ge_set_gej(&q, &qj);
-    ec_key = get_openssl_key(key32);
-    CHECK(ec_key != NULL);
-    CHECK(ECDSA_sign(0, message, sizeof(message), signature, &sigsize, ec_key));
-    CHECK(secp256k1_ecdsa_sig_parse(&sigr, &sigs, signature, sigsize));
-    CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg));
-    secp256k1_scalar_set_int(&one, 1);
-    secp256k1_scalar_add(&msg2, &msg, &one);
-    CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg2));
-
-    random_sign(&sigr, &sigs, &key, &msg, NULL);
-    CHECK(secp256k1_ecdsa_sig_serialize(signature, &secp_sigsize, &sigr, &sigs));
-    CHECK(ECDSA_verify(0, message, sizeof(message), signature, secp_sigsize, ec_key) == 1);
-
-    EC_KEY_free(ec_key);
-}
-
-void run_ecdsa_openssl(void) {
-    int i;
-    for (i = 0; i < 10*count; i++) {
-        test_ecdsa_openssl();
-    }
-}
-#endif
-
 #ifdef ENABLE_MODULE_ECDH
 # include "modules/ecdh/tests_impl.h"
 #endif
@@ -6302,6 +7164,19 @@ void run_secp256k1_memczero_test(void) {
     CHECK(secp256k1_memcmp_var(buf1, buf2, sizeof(buf1)) == 0);
 }
 
+void run_secp256k1_byteorder_tests(void) {
+    const uint32_t x = 0xFF03AB45;
+    const unsigned char x_be[4] = {0xFF, 0x03, 0xAB, 0x45};
+    unsigned char buf[4];
+    uint32_t x_;
+
+    secp256k1_write_be32(buf, x);
+    CHECK(secp256k1_memcmp_var(buf, x_be, sizeof(buf)) == 0);
+
+    x_ = secp256k1_read_be32(buf);
+    CHECK(x == x_);
+}
+
 void int_cmov_test(void) {
     int r = INT_MAX;
     int a = 0;
@@ -6485,41 +7360,55 @@ int main(int argc, char **argv) {
     secp256k1_testrand_init(argc > 2 ? argv[2] : NULL);
 
     /* initialize */
+    run_selftest_tests();
     run_context_tests(0);
     run_context_tests(1);
     run_scratch_tests();
-    ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
-    if (secp256k1_testrand_bits(1)) {
+
+    ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+    /* Randomize the context only with probability 15/16
+       to make sure we test without context randomization from time to time.
+       TODO Reconsider this when recalibrating the tests. */
+    if (secp256k1_testrand_bits(4)) {
         unsigned char rand32[32];
         secp256k1_testrand256(rand32);
-        CHECK(secp256k1_context_randomize(ctx, secp256k1_testrand_bits(1) ? rand32 : NULL));
+        CHECK(secp256k1_context_randomize(ctx, rand32));
     }
 
     run_rand_bits();
     run_rand_int();
 
+#ifdef SECP256K1_WIDEMUL_INT128
+    run_int128_tests();
+#endif
     run_ctz_tests();
     run_modinv_tests();
     run_inverse_tests();
 
-    run_sha256_tests();
+    run_sha256_known_output_tests();
+    run_sha256_counter_tests();
     run_hmac_sha256_tests();
     run_rfc6979_hmac_sha256_tests();
+    run_tagged_sha256_tests();
 
     /* scalar tests */
     run_scalar_tests();
 
     /* field tests */
+    run_field_half();
     run_field_misc();
     run_field_convert();
+    run_fe_mul();
     run_sqr();
     run_sqrt();
 
     /* group tests */
     run_ge();
+    run_gej();
     run_group_decompress();
 
     /* ecmult tests */
+    run_ecmult_pre_g();
     run_wnaf();
     run_point_times_order();
     run_ecmult_near_split_bound();
@@ -6554,9 +7443,6 @@ int main(int argc, char **argv) {
     run_ecdsa_sign_verify();
     run_ecdsa_end_to_end();
     run_ecdsa_edge_cases();
-#ifdef ENABLE_OPENSSL_TESTS
-    run_ecdsa_openssl();
-#endif
 
 #ifdef ENABLE_MODULE_RECOVERY
     /* ECDSA pubkey recovery tests */
@@ -6573,6 +7459,7 @@ int main(int argc, char **argv) {
 
     /* util tests */
     run_secp256k1_memczero_test();
+    run_secp256k1_byteorder_tests();
 
     run_cmov_tests();
 
diff --git a/src/secp256k1/src/tests_exhaustive.c b/src/secp256k1/src/tests_exhaustive.c
index b7c7828995f..c001dcb80ba 100644
--- a/src/secp256k1/src/tests_exhaustive.c
+++ b/src/secp256k1/src/tests_exhaustive.c
@@ -12,8 +12,6 @@
 #include <stdlib.h>
 #include <time.h>
 
-#undef USE_ECMULT_STATIC_PRECOMPUTATION
-
 #ifndef EXHAUSTIVE_TEST_ORDER
 /* see group_impl.h for allowable values */
 #define EXHAUSTIVE_TEST_ORDER 13
@@ -24,6 +22,8 @@
 #include "assumptions.h"
 #include "group.h"
 #include "testrand_impl.h"
+#include "ecmult_compute_table_impl.h"
+#include "ecmult_gen_compute_table_impl.h"
 
 static int count = 2;
 
@@ -163,7 +163,7 @@ void test_exhaustive_addition(const secp256k1_ge *group, const secp256k1_gej *gr
     }
 }
 
-void test_exhaustive_ecmult(const secp256k1_context *ctx, const secp256k1_ge *group, const secp256k1_gej *groupj) {
+void test_exhaustive_ecmult(const secp256k1_ge *group, const secp256k1_gej *groupj) {
     int i, j, r_log;
     uint64_t iter = 0;
     for (r_log = 1; r_log < EXHAUSTIVE_TEST_ORDER; r_log++) {
@@ -175,7 +175,7 @@ void test_exhaustive_ecmult(const secp256k1_context *ctx, const secp256k1_ge *gr
                 secp256k1_scalar_set_int(&na, i);
                 secp256k1_scalar_set_int(&ng, j);
 
-                secp256k1_ecmult(&ctx->ecmult_ctx, &tmp, &groupj[r_log], &na, &ng);
+                secp256k1_ecmult(&tmp, &groupj[r_log], &na, &ng);
                 ge_equals_gej(&group[(i * r_log + j) % EXHAUSTIVE_TEST_ORDER], &tmp);
 
                 if (i > 0) {
@@ -219,7 +219,7 @@ void test_exhaustive_ecmult_multi(const secp256k1_context *ctx, const secp256k1_
                         data.pt[0] = group[x];
                         data.pt[1] = group[y];
 
-                        secp256k1_ecmult_multi_var(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &tmp, &g_sc, ecmult_multi_callback, &data, 2);
+                        secp256k1_ecmult_multi_var(&ctx->error_callback, scratch, &tmp, &g_sc, ecmult_multi_callback, &data, 2);
                         ge_equals_gej(&group[(i * x + j * y + k) % EXHAUSTIVE_TEST_ORDER], &tmp);
                     }
                 }
@@ -302,6 +302,7 @@ void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *grou
             if (skip_section(&iter)) continue;
             for (k = 1; k < EXHAUSTIVE_TEST_ORDER; k++) {  /* nonce */
                 const int starting_k = k;
+                int ret;
                 secp256k1_ecdsa_signature sig;
                 secp256k1_scalar sk, msg, r, s, expected_r;
                 unsigned char sk32[32], msg32[32];
@@ -310,7 +311,8 @@ void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *grou
                 secp256k1_scalar_get_b32(sk32, &sk);
                 secp256k1_scalar_get_b32(msg32, &msg);
 
-                secp256k1_ecdsa_sign(ctx, &sig, msg32, sk32, secp256k1_nonce_function_smallint, &k);
+                ret = secp256k1_ecdsa_sign(ctx, &sig, msg32, sk32, secp256k1_nonce_function_smallint, &k);
+                CHECK(ret == 1);
 
                 secp256k1_ecdsa_signature_load(ctx, &r, &s, &sig);
                 /* Note that we compute expected_r *after* signing -- this is important
@@ -340,15 +342,15 @@ void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *grou
 }
 
 #ifdef ENABLE_MODULE_RECOVERY
-#include "src/modules/recovery/tests_exhaustive_impl.h"
+#include "modules/recovery/tests_exhaustive_impl.h"
 #endif
 
 #ifdef ENABLE_MODULE_EXTRAKEYS
-#include "src/modules/extrakeys/tests_exhaustive_impl.h"
+#include "modules/extrakeys/tests_exhaustive_impl.h"
 #endif
 
 #ifdef ENABLE_MODULE_SCHNORRSIG
-#include "src/modules/schnorrsig/tests_exhaustive_impl.h"
+#include "modules/schnorrsig/tests_exhaustive_impl.h"
 #endif
 
 int main(int argc, char** argv) {
@@ -388,9 +390,13 @@ int main(int argc, char** argv) {
         printf("running tests for core %lu (out of [0..%lu])\n", (unsigned long)this_core, (unsigned long)num_cores - 1);
     }
 
+    /* Recreate the ecmult{,_gen} tables using the right generator (as selected via EXHAUSTIVE_TEST_ORDER) */
+    secp256k1_ecmult_gen_compute_table(&secp256k1_ecmult_gen_prec_table[0][0], &secp256k1_ge_const_g, ECMULT_GEN_PREC_BITS);
+    secp256k1_ecmult_compute_two_tables(secp256k1_pre_g, secp256k1_pre_g_128, WINDOW_G, &secp256k1_ge_const_g);
+
     while (count--) {
         /* Build context */
-        ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+        ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
         secp256k1_testrand256(rand32);
         CHECK(secp256k1_context_randomize(ctx, rand32));
 
@@ -428,7 +434,7 @@ int main(int argc, char** argv) {
         /* Run the tests */
         test_exhaustive_endomorphism(group);
         test_exhaustive_addition(group, groupj);
-        test_exhaustive_ecmult(ctx, group, groupj);
+        test_exhaustive_ecmult(group, groupj);
         test_exhaustive_ecmult_multi(ctx, group);
         test_exhaustive_sign(ctx, group);
         test_exhaustive_verify(ctx, group);
diff --git a/src/secp256k1/src/valgrind_ctime_test.c b/src/secp256k1/src/valgrind_ctime_test.c
index 4ac0f011bd3..a0f888b00f9 100644
--- a/src/secp256k1/src/valgrind_ctime_test.c
+++ b/src/secp256k1/src/valgrind_ctime_test.c
@@ -39,9 +39,7 @@ int main(void) {
         fprintf(stderr, "Usage: libtool --mode=execute valgrind ./valgrind_ctime_test\n");
         return 1;
     }
-    ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN
-                                   | SECP256K1_CONTEXT_VERIFY
-                                   | SECP256K1_CONTEXT_DECLASSIFY);
+    ctx = secp256k1_context_create(SECP256K1_CONTEXT_DECLASSIFY);
     /** In theory, testing with a single secret input should be sufficient:
      *  If control flow depended on secrets the tool would generate an error.
      */
@@ -166,7 +164,7 @@ void run_tests(secp256k1_context *ctx, unsigned char *key) {
     ret = secp256k1_keypair_create(ctx, &keypair, key);
     VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret));
     CHECK(ret == 1);
-    ret = secp256k1_schnorrsig_sign(ctx, sig, msg, &keypair, NULL, NULL);
+    ret = secp256k1_schnorrsig_sign32(ctx, sig, msg, &keypair, NULL);
     VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret));
     CHECK(ret == 1);
 #endif
diff --git a/src/test/test_bitcoin.h b/src/test/test_bitcoin.h
index 9b3c1da6c71..14e3811a08b 100644
--- a/src/test/test_bitcoin.h
+++ b/src/test/test_bitcoin.h
@@ -35,8 +35,6 @@ static inline std::vector<unsigned char> InsecureRandBytes(size_t len) { return
  * This just configures logging and chain parameters.
  */
 struct BasicTestingSetup {
-    ECCVerifyHandle globalVerifyHandle;
-
     BasicTestingSetup(const std::string& chainName = CBaseChainParams::MAIN);
     ~BasicTestingSetup();
 };