text: /**********************************************************************
   * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell      *
   * Distributed under the MIT software license, see the accompanying   *
   * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
   **********************************************************************/
  
  #ifndef _SECP256K1_ECMULT_GEN_IMPL_H_
  #define _SECP256K1_ECMULT_GEN_IMPL_H_
  
  #include "scalar.h"
  #include "group.h"
  #include "ecmult_gen.h"
  #include "hash_impl.h"
  #ifdef USE_ECMULT_STATIC_PRECOMPUTATION
  #include "ecmult_static_context.h"
  #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, const secp256k1_callback* cb) {
  #ifndef USE_ECMULT_STATIC_PRECOMPUTATION
      secp256k1_ge prec[1024];
      secp256k1_gej gj;
      secp256k1_gej nums_gej;
      int i, j;
  #endif
  
      if (ctx->prec != NULL) {
          return;
      }
  #ifndef USE_ECMULT_STATIC_PRECOMPUTATION
      ctx->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*ctx->prec));
  
      /* 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[1024]; /* Jacobian versions of prec. */
          secp256k1_gej gbase;
          secp256k1_gej numsbase;
          gbase = gj; /* 16^j * G */
          numsbase = nums_gej; /* 2^j * nums. */
          for (j = 0; j < 64; j++) {
              /* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
              precj[j*16] = numsbase;
              for (i = 1; i < 16; i++) {
                  secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase, NULL);
              }
              /* Multiply gbase by 16. */
              for (i = 0; i < 4; i++) {
                  secp256k1_gej_double_var(&gbase, &gbase, NULL);
              }
              /* Multiply numbase by 2. */
              secp256k1_gej_double_var(&numsbase, &numsbase, NULL);
              if (j == 62) {
                  /* 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, 1024, cb);
      }
      for (j = 0; j < 64; j++) {
          for (i = 0; i < 16; i++) {
              secp256k1_ge_to_storage(&(*ctx->prec)[j][i], &prec[j*16 + i]);
          }
      }
  #else
      (void)cb;
      ctx->prec = (secp256k1_ge_storage (*)[64][16])secp256k1_ecmult_static_context;
  #endif
      secp256k1_ecmult_gen_blind(ctx, NULL);
  }
  
  static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx) {
      return ctx->prec != NULL;
  }
  
  static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context *dst,
                                                 const secp256k1_ecmult_gen_context *src, const secp256k1_callback* cb) {
      if (src->prec == NULL) {
          dst->prec = NULL;
      } else {
  #ifndef USE_ECMULT_STATIC_PRECOMPUTATION
          dst->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*dst->prec));
          memcpy(dst->prec, src->prec, sizeof(*dst->prec));
  #else
          (void)cb;
          dst->prec = src->prec;
  #endif
          dst->initial = src->initial;
          dst->blind = src->blind;
      }
  }
  
  static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context *ctx) {
  #ifndef USE_ECMULT_STATIC_PRECOMPUTATION
      free(ctx->prec);
  #endif
      secp256k1_scalar_clear(&ctx->blind);
      secp256k1_gej_clear(&ctx->initial);
      ctx->prec = NULL;
  }
  
  static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp256k1_gej *r, const secp256k1_scalar *gn) {
      secp256k1_ge add;
      secp256k1_ge_storage adds;
      secp256k1_scalar gnb;
      int bits;
      int i, j;
      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 < 64; j++) {
          bits = secp256k1_scalar_get_bits(&gnb, j * 4, 4);
          for (i = 0; i < 16; i++) {
              /** 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.
               *  See also:
               *   "A word of warning", CHES 2013 Rump Session, by Daniel J. Bernstein and Peter Schwabe
               *    (https://cryptojedi.org/peter/data/chesrump-20130822.pdf) and
               *   "Cache Attacks and Countermeasures: the Case of AES", RSA 2006,
               *    by Dag Arne Osvik, Adi Shamir, and Eran Tromer
               *    (http://www.tau.ac.il/~tromer/papers/cache.pdf)
               */
              secp256k1_ge_storage_cmov(&adds, &(*ctx->prec)[j][i], i == bits);
          }
          secp256k1_ge_from_storage(&add, &adds);
          secp256k1_gej_add_ge(r, r, &add);
      }
      bits = 0;
      secp256k1_ge_clear(&add);
      secp256k1_scalar_clear(&gnb);
  }
  
  /* Setup blinding values for secp256k1_ecmult_gen. */
  static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32) {
      secp256k1_scalar b;
      secp256k1_gej gb;
      secp256k1_fe s;
      unsigned char nonce32[32];
      secp256k1_rfc6979_hmac_sha256_t rng;
      int retry;
      unsigned char keydata[64] = {0};
      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);
      }
      /* The prior blinding value (if not reset) is chained forward by including it in the hash. */
      secp256k1_scalar_get_b32(nonce32, &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);
      memset(keydata, 0, sizeof(keydata));
      /* Retry for out of range results to achieve uniformity. */
      do {
          secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
          retry = !secp256k1_fe_set_b32(&s, nonce32);
          retry |= secp256k1_fe_is_zero(&s);
      } while (retry); /* This branch true is cryptographically unreachable. Requires sha256_hmac output > Fp. */
      /* Randomize the projection to defend against multiplier sidechannels. */
      secp256k1_gej_rescale(&ctx->initial, &s);
      secp256k1_fe_clear(&s);
      do {
          secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
          secp256k1_scalar_set_b32(&b, nonce32, &retry);
          /* A blinding value of 0 works, but would undermine the projection hardening. */
          retry |= secp256k1_scalar_is_zero(&b);
      } while (retry); /* This branch true is cryptographically unreachable. Requires sha256_hmac output > order. */
      secp256k1_rfc6979_hmac_sha256_finalize(&rng);
      memset(nonce32, 0, 32);
      secp256k1_ecmult_gen(ctx, &gb, &b);
      secp256k1_scalar_negate(&b, &b);
      ctx->blind = b;
      ctx->initial = gb;
      secp256k1_scalar_clear(&b);
      secp256k1_gej_clear(&gb);
  }
  
  #endif
  