Commit message: Add blinding to an ECDSA signature

Keegan Ryan (NCC Group) has demonstrated a side channel attack on an
ECDSA signature operation. During signing the signer calculates:

s:= k^-1 * (m + r * priv_key) mod order

The addition operation above provides a sufficient signal for a
flush+reload attack to derive the private key given sufficient signature
operations.

As a mitigation (based on a suggestion from Keegan) we add blinding to
the operation so that:

s := k^-1 * blind^-1 (blind * m + blind * r * priv_key) mod order

Since this attack is a localhost side channel only no CVE is assigned.

Reviewed-by: Rich Salz <rsalz@openssl.org>
CVE: CVE-2018-0495
CWE: CWE-203
Vulnerability description: Libgcrypt before 1.7.10 and 1.8.x before 1.8.3 allows a memory-cache side-channel attack on ECDSA signatures that can be mitigated through the use of blinding during the signing process in the _gcry_ecc_ecdsa_sign function in cipher/ecc-ecdsa.c, aka the Return Of the Hidden Number Problem or ROHNP. To discover an ECDSA key, the attacker needs access to either the local machine or a different virtual machine on the same physical host.

Project: openssl

int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len,
                      const unsigned char *sigbuf, int sig_len, EC_KEY *eckey)
{
    ECDSA_SIG *s;
    const unsigned char *p = sigbuf;
    unsigned char *der = NULL;
    int derlen = -1;
    int ret = -1;

    s = ECDSA_SIG_new();
    if (s == NULL)
        return (ret);
    if (d2i_ECDSA_SIG(&s, &p, sig_len) == NULL)
        goto err;
    /* Ensure signature uses DER and doesn't have trailing garbage */
    derlen = i2d_ECDSA_SIG(s, &der);
    if (derlen != sig_len || memcmp(sigbuf, der, derlen) != 0)
        goto err;
    ret = ECDSA_do_verify(dgst, dgst_len, s, eckey);
 err:
    OPENSSL_clear_free(der, derlen);
    ECDSA_SIG_free(s);
    return (ret);
}

Project: openssl

static int ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in,
                            BIGNUM **kinvp, BIGNUM **rp,
                            const unsigned char *dgst, int dlen)
{
    BN_CTX *ctx = NULL;
    BIGNUM *k = NULL, *r = NULL, *X = NULL;
    const BIGNUM *order;
    EC_POINT *tmp_point = NULL;
    const EC_GROUP *group;
    int ret = 0;
    int order_bits;

    if (eckey == NULL || (group = EC_KEY_get0_group(eckey)) == NULL) {
        ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_PASSED_NULL_PARAMETER);
        return 0;
    }

    if (!EC_KEY_can_sign(eckey)) {
        ECerr(EC_F_ECDSA_SIGN_SETUP, EC_R_CURVE_DOES_NOT_SUPPORT_SIGNING);
        return 0;
    }

    if (ctx_in == NULL) {
        if ((ctx = BN_CTX_new()) == NULL) {
            ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_MALLOC_FAILURE);
            return 0;
        }
    } else
        ctx = ctx_in;

    k = BN_new();               /* this value is later returned in *kinvp */
    r = BN_new();               /* this value is later returned in *rp */
    X = BN_new();
    if (k == NULL || r == NULL || X == NULL) {
        ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_MALLOC_FAILURE);
        goto err;
    }
    if ((tmp_point = EC_POINT_new(group)) == NULL) {
        ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB);
        goto err;
    }
    order = EC_GROUP_get0_order(group);
    if (order == NULL) {
        ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB);
        goto err;
    }

    /* Preallocate space */
    order_bits = BN_num_bits(order);
    if (!BN_set_bit(k, order_bits)
        || !BN_set_bit(r, order_bits)
        || !BN_set_bit(X, order_bits))
        goto err;

    do {
        /* get random k */
        do
            if (dgst != NULL) {
                if (!BN_generate_dsa_nonce
                    (k, order, EC_KEY_get0_private_key(eckey), dgst, dlen,
                     ctx)) {
                    ECerr(EC_F_ECDSA_SIGN_SETUP,
                             EC_R_RANDOM_NUMBER_GENERATION_FAILED);
                    goto err;
                }
            } else {
                if (!BN_rand_range(k, order)) {
                    ECerr(EC_F_ECDSA_SIGN_SETUP,
                             EC_R_RANDOM_NUMBER_GENERATION_FAILED);
                    goto err;
                }
            }
        while (BN_is_zero(k));

        /*
         * We do not want timing information to leak the length of k, so we
         * compute G*k using an equivalent scalar of fixed bit-length.
         *
         * We unconditionally perform both of these additions to prevent a
         * small timing information leakage.  We then choose the sum that is
         * one bit longer than the order.  This guarantees the code
         * path used in the constant time implementations elsewhere.
         *
         * TODO: revisit the BN_copy aiming for a memory access agnostic
         * conditional copy.
         */
        if (!BN_add(r, k, order)
            || !BN_add(X, r, order)
            || !BN_copy(k, BN_num_bits(r) > order_bits ? r : X))
            goto err;

        /* compute r the x-coordinate of generator * k */
        if (!EC_POINT_mul(group, tmp_point, k, NULL, NULL, ctx)) {
            ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB);
            goto err;
        }
        if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) ==
            NID_X9_62_prime_field) {
            if (!EC_POINT_get_affine_coordinates_GFp
                (group, tmp_point, X, NULL, ctx)) {
                ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB);
                goto err;
            }
        }
#ifndef OPENSSL_NO_EC2M
        else {                  /* NID_X9_62_characteristic_two_field */

            if (!EC_POINT_get_affine_coordinates_GF2m(group,
                                                      tmp_point, X, NULL,
                                                      ctx)) {
                ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB);
                goto err;
            }
        }
#endif
        if (!BN_nnmod(r, X, order, ctx)) {
            ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB);
            goto err;
        }
    }
    while (BN_is_zero(r));

    /* compute the inverse of k */
    if (EC_GROUP_get_mont_data(group) != NULL) {
        /*
         * We want inverse in constant time, therefore we utilize the fact
         * order must be prime and use Fermats Little Theorem instead.
         */
        if (!BN_set_word(X, 2)) {
            ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB);
            goto err;
        }
        if (!BN_mod_sub(X, order, X, order, ctx)) {
            ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB);
            goto err;
        }
        BN_set_flags(X, BN_FLG_CONSTTIME);
        if (!BN_mod_exp_mont_consttime
            (k, k, X, order, ctx, EC_GROUP_get_mont_data(group))) {
            ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB);
            goto err;
        }
    } else {
        if (!BN_mod_inverse(k, k, order, ctx)) {
            ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB);
            goto err;
        }
    }

    /* clear old values if necessary */
    BN_clear_free(*rp);
    BN_clear_free(*kinvp);
    /* save the pre-computed values  */
    *rp = r;
    *kinvp = k;
    ret = 1;
 err:
    if (!ret) {
        BN_clear_free(k);
        BN_clear_free(r);
    }
    if (ctx != ctx_in)
        BN_CTX_free(ctx);
    EC_POINT_free(tmp_point);
    BN_clear_free(X);
    return (ret);
}

Project: openssl

int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len,
                          const ECDSA_SIG *sig, EC_KEY *eckey)
{
    int ret = -1, i;
    BN_CTX *ctx;
    const BIGNUM *order;
    BIGNUM *u1, *u2, *m, *X;
    EC_POINT *point = NULL;
    const EC_GROUP *group;
    const EC_POINT *pub_key;

    /* check input values */
    if (eckey == NULL || (group = EC_KEY_get0_group(eckey)) == NULL ||
        (pub_key = EC_KEY_get0_public_key(eckey)) == NULL || sig == NULL) {
        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, EC_R_MISSING_PARAMETERS);
        return -1;
    }

    if (!EC_KEY_can_sign(eckey)) {
        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, EC_R_CURVE_DOES_NOT_SUPPORT_SIGNING);
        return -1;
    }

    ctx = BN_CTX_new();
    if (ctx == NULL) {
        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_MALLOC_FAILURE);
        return -1;
    }
    BN_CTX_start(ctx);
    u1 = BN_CTX_get(ctx);
    u2 = BN_CTX_get(ctx);
    m = BN_CTX_get(ctx);
    X = BN_CTX_get(ctx);
    if (X == NULL) {
        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB);
        goto err;
    }

    order = EC_GROUP_get0_order(group);
    if (order == NULL) {
        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_EC_LIB);
        goto err;
    }

    if (BN_is_zero(sig->r) || BN_is_negative(sig->r) ||
        BN_ucmp(sig->r, order) >= 0 || BN_is_zero(sig->s) ||
        BN_is_negative(sig->s) || BN_ucmp(sig->s, order) >= 0) {
        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, EC_R_BAD_SIGNATURE);
        ret = 0;                /* signature is invalid */
        goto err;
    }
    /* calculate tmp1 = inv(S) mod order */
    if (!BN_mod_inverse(u2, sig->s, order, ctx)) {
        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB);
        goto err;
    }
    /* digest -> m */
    i = BN_num_bits(order);
    /*
     * Need to truncate digest if it is too long: first truncate whole bytes.
     */
    if (8 * dgst_len > i)
        dgst_len = (i + 7) / 8;
    if (!BN_bin2bn(dgst, dgst_len, m)) {
        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB);
        goto err;
    }
    /* If still too long truncate remaining bits with a shift */
    if ((8 * dgst_len > i) && !BN_rshift(m, m, 8 - (i & 0x7))) {
        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB);
        goto err;
    }
    /* u1 = m * tmp mod order */
    if (!BN_mod_mul(u1, m, u2, order, ctx)) {
        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB);
        goto err;
    }
    /* u2 = r * w mod q */
    if (!BN_mod_mul(u2, sig->r, u2, order, ctx)) {
        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB);
        goto err;
    }

    if ((point = EC_POINT_new(group)) == NULL) {
        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_MALLOC_FAILURE);
        goto err;
    }
    if (!EC_POINT_mul(group, point, u1, pub_key, u2, ctx)) {
        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_EC_LIB);
        goto err;
    }
    if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) ==
        NID_X9_62_prime_field) {
        if (!EC_POINT_get_affine_coordinates_GFp(group, point, X, NULL, ctx)) {
            ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_EC_LIB);
            goto err;
        }
    }
#ifndef OPENSSL_NO_EC2M
    else {                      /* NID_X9_62_characteristic_two_field */

        if (!EC_POINT_get_affine_coordinates_GF2m(group, point, X, NULL, ctx)) {
            ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_EC_LIB);
            goto err;
        }
    }
#endif
    if (!BN_nnmod(u1, X, order, ctx)) {
        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB);
        goto err;
    }
    /*  if the signature is correct u1 is equal to sig->r */
    ret = (BN_ucmp(u1, sig->r) == 0);
 err:
    BN_CTX_end(ctx);
    BN_CTX_free(ctx);
    EC_POINT_free(point);
    return ret;
}

Project: openssl

int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen,
                    unsigned char *sig, unsigned int *siglen,
                    const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey)
{
    ECDSA_SIG *s;
    RAND_seed(dgst, dlen);
    s = ECDSA_do_sign_ex(dgst, dlen, kinv, r, eckey);
    if (s == NULL) {
        *siglen = 0;
        return 0;
    }
    *siglen = i2d_ECDSA_SIG(s, &sig);
    ECDSA_SIG_free(s);
    return 1;
}

Project: openssl

ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
                               const BIGNUM *in_kinv, const BIGNUM *in_r,
                               EC_KEY *eckey)
{
    int ok = 0, i;
    BIGNUM *kinv = NULL, *s, *m = NULL, *tmp = NULL, *blind = NULL;
    BIGNUM *blindm = NULL;
    const BIGNUM *order, *ckinv;
    BN_CTX *ctx = NULL;
    const EC_GROUP *group;
    ECDSA_SIG *ret;
    const BIGNUM *priv_key;

    group = EC_KEY_get0_group(eckey);
    priv_key = EC_KEY_get0_private_key(eckey);

    if (group == NULL || priv_key == NULL) {
        ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_PASSED_NULL_PARAMETER);
        return NULL;
    }

    if (!EC_KEY_can_sign(eckey)) {
        ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, EC_R_CURVE_DOES_NOT_SUPPORT_SIGNING);
        return NULL;
    }

    ret = ECDSA_SIG_new();
    if (ret == NULL) {
        ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE);
        return NULL;
    }
    ret->r = BN_new();
    ret->s = BN_new();
    if (ret->r == NULL || ret->s == NULL) {
        ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE);
        goto err;
    }
    s = ret->s;

    ctx = BN_CTX_secure_new();
    if (ctx == NULL) {
        ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE);
        goto err;
    }

    BN_CTX_start(ctx);
    tmp = BN_CTX_get(ctx);
    m = BN_CTX_get(ctx);
    blind = BN_CTX_get(ctx);
    blindm = BN_CTX_get(ctx);
    if (blindm == NULL) {
        ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE);
        goto err;
    }

    order = EC_GROUP_get0_order(group);
    if (order == NULL) {
        ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_EC_LIB);
        goto err;
    }
    i = BN_num_bits(order);
    /*
     * Need to truncate digest if it is too long: first truncate whole bytes.
     */
    if (8 * dgst_len > i)
        dgst_len = (i + 7) / 8;
    if (!BN_bin2bn(dgst, dgst_len, m)) {
        ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
        goto err;
    }
    /* If still too long truncate remaining bits with a shift */
    if ((8 * dgst_len > i) && !BN_rshift(m, m, 8 - (i & 0x7))) {
        ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
        goto err;
    }
    do {
        if (in_kinv == NULL || in_r == NULL) {
            if (!ecdsa_sign_setup(eckey, ctx, &kinv, &ret->r, dgst, dgst_len)) {
                ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_ECDSA_LIB);
                goto err;
            }
            ckinv = kinv;
        } else {
            ckinv = in_kinv;
            if (BN_copy(ret->r, in_r) == NULL) {
                ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE);
                goto err;
            }
        }

        /*
         * The normal signature calculation is:
         *
         *   s := k^-1 * (m + r * priv_key) mod order
         *
         * We will blind this to protect against side channel attacks
         *
         *   s := k^-1 * blind^-1 * (blind * m + blind * r * priv_key) mod order
         */

        /* Generate a blinding value */
        do {
            if (!BN_rand(blind, BN_num_bits(order) - 1, BN_RAND_TOP_ANY,
                         BN_RAND_BOTTOM_ANY))
                goto err;
        } while (BN_is_zero(blind));
        BN_set_flags(blind, BN_FLG_CONSTTIME);
        BN_set_flags(blindm, BN_FLG_CONSTTIME);
        BN_set_flags(tmp, BN_FLG_CONSTTIME);

        /* tmp := blind * priv_key * r mod order */
        if (!BN_mod_mul(tmp, blind, priv_key, order, ctx)) {
            ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
            goto err;
        }
        if (!BN_mod_mul(tmp, tmp, ret->r, order, ctx)) {
            ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
            goto err;
        }

        /* blindm := blind * m mod order */
        if (!BN_mod_mul(blindm, blind, m, order, ctx)) {
            ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
            goto err;
        }

        /* s : = (blind * priv_key * r) + (blind * m) mod order */
        if (!BN_mod_add_quick(s, tmp, blindm, order)) {
            ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
            goto err;
        }

        /* s:= s * blind^-1 mod order */
        if (BN_mod_inverse(blind, blind, order, ctx) == NULL) {
            ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
            goto err;
        }
        if (!BN_mod_mul(s, s, blind, order, ctx)) {
            ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
            goto err;
        }

        /* s := s * k^-1 mod order */
        if (!BN_mod_mul(s, s, ckinv, order, ctx)) {
            ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
            goto err;
        }

        if (BN_is_zero(s)) {
            /*
             * if kinv and r have been supplied by the caller don't to
             * generate new kinv and r values
             */
            if (in_kinv != NULL && in_r != NULL) {
                ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, EC_R_NEED_NEW_SETUP_VALUES);
                goto err;
            }
        } else
            /* s != 0 => we have a valid signature */
            break;
    }
    while (1);

    ok = 1;
 err:
    if (!ok) {
        ECDSA_SIG_free(ret);
        ret = NULL;
    }
    BN_CTX_end(ctx);
    BN_CTX_free(ctx);
    BN_clear_free(kinv);
    return ret;
}

Project: openssl

int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
                          BIGNUM **rp)
{
    return ecdsa_sign_setup(eckey, ctx_in, kinvp, rp, NULL, 0);
}