示例#1
0
void test_exhaustive_recovery_verify(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
    /* This is essentially a copy of test_exhaustive_verify, with recovery added */
    int s, r, msg, key;
    for (s = 1; s < order; s++) {
        for (r = 1; r < order; r++) {
            for (msg = 1; msg < order; msg++) {
                for (key = 1; key < order; key++) {
                    secp256k1_ge nonconst_ge;
                    secp256k1_ecdsa_recoverable_signature rsig;
                    secp256k1_ecdsa_signature sig;
                    secp256k1_pubkey pk;
                    secp256k1_scalar sk_s, msg_s, r_s, s_s;
                    secp256k1_scalar s_times_k_s, msg_plus_r_times_sk_s;
                    int recid = 0;
                    int k, should_verify;
                    unsigned char msg32[32];

                    secp256k1_scalar_set_int(&s_s, s);
                    secp256k1_scalar_set_int(&r_s, r);
                    secp256k1_scalar_set_int(&msg_s, msg);
                    secp256k1_scalar_set_int(&sk_s, key);
                    secp256k1_scalar_get_b32(msg32, &msg_s);

                    /* Verify by hand */
                    /* Run through every k value that gives us this r and check that *one* works.
                     * Note there could be none, there could be multiple, ECDSA is weird. */
                    should_verify = 0;
                    for (k = 0; k < order; k++) {
                        secp256k1_scalar check_x_s;
                        r_from_k(&check_x_s, group, k);
                        if (r_s == check_x_s) {
                            secp256k1_scalar_set_int(&s_times_k_s, k);
                            secp256k1_scalar_mul(&s_times_k_s, &s_times_k_s, &s_s);
                            secp256k1_scalar_mul(&msg_plus_r_times_sk_s, &r_s, &sk_s);
                            secp256k1_scalar_add(&msg_plus_r_times_sk_s, &msg_plus_r_times_sk_s, &msg_s);
                            should_verify |= secp256k1_scalar_eq(&s_times_k_s, &msg_plus_r_times_sk_s);
                        }
                    }
                    /* nb we have a "high s" rule */
                    should_verify &= !secp256k1_scalar_is_high(&s_s);

                    /* We would like to try recovering the pubkey and checking that it matches,
                     * but pubkey recovery is impossible in the exhaustive tests (the reason
                     * being that there are 12 nonzero r values, 12 nonzero points, and no
                     * overlap between the sets, so there are no valid signatures). */

                    /* Verify by converting to a standard signature and calling verify */
                    secp256k1_ecdsa_recoverable_signature_save(&rsig, &r_s, &s_s, recid);
                    secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig);
                    memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge));
                    secp256k1_pubkey_save(&pk, &nonconst_ge);
                    CHECK(should_verify ==
                          secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk));
                }
            }
        }
    }
}
示例#2
0
void test_exhaustive_verify(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
    int s, r, msg, key;
    for (s = 1; s < order; s++) {
        for (r = 1; r < order; r++) {
            for (msg = 1; msg < order; msg++) {
                for (key = 1; key < order; key++) {
                    secp256k1_ge nonconst_ge;
                    secp256k1_ecdsa_signature sig;
                    secp256k1_pubkey pk;
                    secp256k1_scalar sk_s, msg_s, r_s, s_s;
                    secp256k1_scalar s_times_k_s, msg_plus_r_times_sk_s;
                    int k, should_verify;
                    unsigned char msg32[32];

                    secp256k1_scalar_set_int(&s_s, s);
                    secp256k1_scalar_set_int(&r_s, r);
                    secp256k1_scalar_set_int(&msg_s, msg);
                    secp256k1_scalar_set_int(&sk_s, key);

                    /* Verify by hand */
                    /* Run through every k value that gives us this r and check that *one* works.
                     * Note there could be none, there could be multiple, ECDSA is weird. */
                    should_verify = 0;
                    for (k = 0; k < order; k++) {
                        secp256k1_scalar check_x_s;
                        r_from_k(&check_x_s, group, k);
                        if (r_s == check_x_s) {
                            secp256k1_scalar_set_int(&s_times_k_s, k);
                            secp256k1_scalar_mul(&s_times_k_s, &s_times_k_s, &s_s);
                            secp256k1_scalar_mul(&msg_plus_r_times_sk_s, &r_s, &sk_s);
                            secp256k1_scalar_add(&msg_plus_r_times_sk_s, &msg_plus_r_times_sk_s, &msg_s);
                            should_verify |= secp256k1_scalar_eq(&s_times_k_s, &msg_plus_r_times_sk_s);
                        }
                    }
                    /* nb we have a "high s" rule */
                    should_verify &= !secp256k1_scalar_is_high(&s_s);

                    /* Verify by calling verify */
                    secp256k1_ecdsa_signature_save(&sig, &r_s, &s_s);
                    memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge));
                    secp256k1_pubkey_save(&pk, &nonconst_ge);
                    secp256k1_scalar_get_b32(msg32, &msg_s);
                    CHECK(should_verify ==
                          secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk));
                }
            }
        }
    }
}
示例#3
0
int secp256k1_ecdsa_verify(const secp256k1_context* ctx, const secp256k1_ecdsa_signature *sig, const unsigned char *msg32, const secp256k1_pubkey *pubkey) {
    secp256k1_ge q;
    secp256k1_scalar r, s;
    secp256k1_scalar m;
    VERIFY_CHECK(ctx != NULL);
    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
    ARG_CHECK(msg32 != NULL);
    ARG_CHECK(sig != NULL);
    ARG_CHECK(pubkey != NULL);

    secp256k1_scalar_set_b32(&m, msg32, NULL);
    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));
}
示例#4
0
int secp256k1_ecdsa_signature_normalize(const secp256k1_context* ctx, secp256k1_ecdsa_signature *sigout, const secp256k1_ecdsa_signature *sigin) {
    secp256k1_scalar r, s;
    int ret = 0;

    VERIFY_CHECK(ctx != NULL);
    ARG_CHECK(sigin != NULL);

    secp256k1_ecdsa_signature_load(ctx, &r, &s, sigin);
    ret = secp256k1_scalar_is_high(&s);
    if (sigout != NULL) {
        if (ret) {
            secp256k1_scalar_negate(&s, &s);
        }
        secp256k1_ecdsa_signature_save(sigout, &r, &s);
    }

    return ret;
}
示例#5
0
文件: tests.c 项目: 13XeNuS37/bitcoin
void scalar_test(void) {
    unsigned char c[32];

    /* Set 's' to a random scalar, with value 'snum'. */
    secp256k1_scalar_t s;
    random_scalar_order_test(&s);

    /* Set 's1' to a random scalar, with value 's1num'. */
    secp256k1_scalar_t s1;
    random_scalar_order_test(&s1);

    /* Set 's2' to a random scalar, with value 'snum2', and byte array representation 'c'. */
    secp256k1_scalar_t s2;
    random_scalar_order_test(&s2);
    secp256k1_scalar_get_b32(c, &s2);

#ifndef USE_NUM_NONE
    secp256k1_num_t snum, s1num, s2num;
    secp256k1_scalar_get_num(&snum, &s);
    secp256k1_scalar_get_num(&s1num, &s1);
    secp256k1_scalar_get_num(&s2num, &s2);

    secp256k1_num_t order;
    secp256k1_scalar_order_get_num(&order);
    secp256k1_num_t half_order = order;
    secp256k1_num_shift(&half_order, 1);
#endif

    {
        /* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */
        secp256k1_scalar_t n;
        secp256k1_scalar_set_int(&n, 0);
        for (int i = 0; i < 256; i += 4) {
            secp256k1_scalar_t t;
            secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits(&s, 256 - 4 - i, 4));
            for (int j = 0; j < 4; j++) {
                secp256k1_scalar_add(&n, &n, &n);
            }
            secp256k1_scalar_add(&n, &n, &t);
        }
        CHECK(secp256k1_scalar_eq(&n, &s));
    }

    {
        /* Test that fetching groups of randomly-sized bits from a scalar and recursing n(i)=b*n(i-1)+p(i) reconstructs it. */
        secp256k1_scalar_t n;
        secp256k1_scalar_set_int(&n, 0);
        int i = 0;
        while (i < 256) {
            int now = (secp256k1_rand32() % 15) + 1;
            if (now + i > 256) {
                now = 256 - i;
            }
            secp256k1_scalar_t t;
            secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits_var(&s, 256 - now - i, now));
            for (int j = 0; j < now; j++) {
                secp256k1_scalar_add(&n, &n, &n);
            }
            secp256k1_scalar_add(&n, &n, &t);
            i += now;
        }
        CHECK(secp256k1_scalar_eq(&n, &s));
    }

#ifndef USE_NUM_NONE
    {
        /* Test that adding the scalars together is equal to adding their numbers together modulo the order. */
        secp256k1_num_t rnum;
        secp256k1_num_add(&rnum, &snum, &s2num);
        secp256k1_num_mod(&rnum, &order);
        secp256k1_scalar_t r;
        secp256k1_scalar_add(&r, &s, &s2);
        secp256k1_num_t r2num;
        secp256k1_scalar_get_num(&r2num, &r);
        CHECK(secp256k1_num_eq(&rnum, &r2num));
    }

    {
        /* Test that multipying the scalars is equal to multiplying their numbers modulo the order. */
        secp256k1_num_t rnum;
        secp256k1_num_mul(&rnum, &snum, &s2num);
        secp256k1_num_mod(&rnum, &order);
        secp256k1_scalar_t r;
        secp256k1_scalar_mul(&r, &s, &s2);
        secp256k1_num_t r2num;
        secp256k1_scalar_get_num(&r2num, &r);
        CHECK(secp256k1_num_eq(&rnum, &r2num));
        /* The result can only be zero if at least one of the factors was zero. */
        CHECK(secp256k1_scalar_is_zero(&r) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_zero(&s2)));
        /* The results can only be equal to one of the factors if that factor was zero, or the other factor was one. */
        CHECK(secp256k1_num_eq(&rnum, &snum) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_one(&s2)));
        CHECK(secp256k1_num_eq(&rnum, &s2num) == (secp256k1_scalar_is_zero(&s2) || secp256k1_scalar_is_one(&s)));
    }

    {
        /* Check that comparison with zero matches comparison with zero on the number. */
        CHECK(secp256k1_num_is_zero(&snum) == secp256k1_scalar_is_zero(&s));
        /* Check that comparison with the half order is equal to testing for high scalar. */
        CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &half_order) > 0));
        secp256k1_scalar_t neg;
        secp256k1_scalar_negate(&neg, &s);
        secp256k1_num_t negnum;
        secp256k1_num_sub(&negnum, &order, &snum);
        secp256k1_num_mod(&negnum, &order);
        /* Check that comparison with the half order is equal to testing for high scalar after negation. */
        CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &half_order) > 0));
        /* Negating should change the high property, unless the value was already zero. */
        CHECK((secp256k1_scalar_is_high(&s) == secp256k1_scalar_is_high(&neg)) == secp256k1_scalar_is_zero(&s));
        secp256k1_num_t negnum2;
        secp256k1_scalar_get_num(&negnum2, &neg);
        /* Negating a scalar should be equal to (order - n) mod order on the number. */
        CHECK(secp256k1_num_eq(&negnum, &negnum2));
        secp256k1_scalar_add(&neg, &neg, &s);
        /* Adding a number to its negation should result in zero. */
        CHECK(secp256k1_scalar_is_zero(&neg));
        secp256k1_scalar_negate(&neg, &neg);
        /* Negating zero should still result in zero. */
        CHECK(secp256k1_scalar_is_zero(&neg));
    }

    {
        /* Test secp256k1_scalar_mul_shift_var. */
        secp256k1_scalar_t r;
        unsigned int shift = 256 + (secp256k1_rand32() % 257);
        secp256k1_scalar_mul_shift_var(&r, &s1, &s2, shift);
        secp256k1_num_t rnum;
        secp256k1_num_mul(&rnum, &s1num, &s2num);
        secp256k1_num_shift(&rnum, shift - 1);
        secp256k1_num_t one;
        unsigned char cone[1] = {0x01};
        secp256k1_num_set_bin(&one, cone, 1);
        secp256k1_num_add(&rnum, &rnum, &one);
        secp256k1_num_shift(&rnum, 1);
        secp256k1_num_t rnum2;
        secp256k1_scalar_get_num(&rnum2, &r);
        CHECK(secp256k1_num_eq(&rnum, &rnum2));
    }
#endif

    {
        /* Test that scalar inverses are equal to the inverse of their number modulo the order. */
        if (!secp256k1_scalar_is_zero(&s)) {
            secp256k1_scalar_t inv;
            secp256k1_scalar_inverse(&inv, &s);
#ifndef USE_NUM_NONE
            secp256k1_num_t invnum;
            secp256k1_num_mod_inverse(&invnum, &snum, &order);
            secp256k1_num_t invnum2;
            secp256k1_scalar_get_num(&invnum2, &inv);
            CHECK(secp256k1_num_eq(&invnum, &invnum2));
#endif
            secp256k1_scalar_mul(&inv, &inv, &s);
            /* Multiplying a scalar with its inverse must result in one. */
            CHECK(secp256k1_scalar_is_one(&inv));
            secp256k1_scalar_inverse(&inv, &inv);
            /* Inverting one must result in one. */
            CHECK(secp256k1_scalar_is_one(&inv));
        }
    }

    {
        /* Test commutativity of add. */
        secp256k1_scalar_t r1, r2;
        secp256k1_scalar_add(&r1, &s1, &s2);
        secp256k1_scalar_add(&r2, &s2, &s1);
        CHECK(secp256k1_scalar_eq(&r1, &r2));
    }

    {
        /* Test add_bit. */
        int bit = secp256k1_rand32() % 256;
        secp256k1_scalar_t b;
        secp256k1_scalar_set_int(&b, 1);
        CHECK(secp256k1_scalar_is_one(&b));
        for (int i = 0; i < bit; i++) {
            secp256k1_scalar_add(&b, &b, &b);
        }
        secp256k1_scalar_t r1 = s1, r2 = s1;
        if (!secp256k1_scalar_add(&r1, &r1, &b)) {
            /* No overflow happened. */
            secp256k1_scalar_add_bit(&r2, bit);
            CHECK(secp256k1_scalar_eq(&r1, &r2));
        }
    }

    {
        /* Test commutativity of mul. */
        secp256k1_scalar_t r1, r2;
        secp256k1_scalar_mul(&r1, &s1, &s2);
        secp256k1_scalar_mul(&r2, &s2, &s1);
        CHECK(secp256k1_scalar_eq(&r1, &r2));
    }

    {
        /* Test associativity of add. */
        secp256k1_scalar_t r1, r2;
        secp256k1_scalar_add(&r1, &s1, &s2);
        secp256k1_scalar_add(&r1, &r1, &s);
        secp256k1_scalar_add(&r2, &s2, &s);
        secp256k1_scalar_add(&r2, &s1, &r2);
        CHECK(secp256k1_scalar_eq(&r1, &r2));
    }

    {
        /* Test associativity of mul. */
        secp256k1_scalar_t r1, r2;
        secp256k1_scalar_mul(&r1, &s1, &s2);
        secp256k1_scalar_mul(&r1, &r1, &s);
        secp256k1_scalar_mul(&r2, &s2, &s);
        secp256k1_scalar_mul(&r2, &s1, &r2);
        CHECK(secp256k1_scalar_eq(&r1, &r2));
    }

    {
        /* Test distributitivity of mul over add. */
        secp256k1_scalar_t r1, r2, t;
        secp256k1_scalar_add(&r1, &s1, &s2);
        secp256k1_scalar_mul(&r1, &r1, &s);
        secp256k1_scalar_mul(&r2, &s1, &s);
        secp256k1_scalar_mul(&t, &s2, &s);
        secp256k1_scalar_add(&r2, &r2, &t);
        CHECK(secp256k1_scalar_eq(&r1, &r2));
    }

    {
        /* Test square. */
        secp256k1_scalar_t r1, r2;
        secp256k1_scalar_sqr(&r1, &s1);
        secp256k1_scalar_mul(&r2, &s1, &s1);
        CHECK(secp256k1_scalar_eq(&r1, &r2));
    }

}
示例#6
0
void scalar_test(void) {
    unsigned char c[32];

    /* Set 's' to a random scalar, with value 'snum'. */
    secp256k1_rand256_test(c);
    secp256k1_scalar_t s;
    secp256k1_scalar_set_b32(&s, c, NULL);
    secp256k1_num_t snum;
    secp256k1_num_set_bin(&snum, c, 32);
    secp256k1_num_mod(&snum, &secp256k1_ge_consts->order);

    /* Set 's1' to a random scalar, with value 's1num'. */
    secp256k1_rand256_test(c);
    secp256k1_scalar_t s1;
    secp256k1_scalar_set_b32(&s1, c, NULL);
    secp256k1_num_t s1num;
    secp256k1_num_set_bin(&s1num, c, 32);
    secp256k1_num_mod(&s1num, &secp256k1_ge_consts->order);

    /* Set 's2' to a random scalar, with value 'snum2', and byte array representation 'c'. */
    secp256k1_rand256_test(c);
    secp256k1_scalar_t s2;
    int overflow = 0;
    secp256k1_scalar_set_b32(&s2, c, &overflow);
    secp256k1_num_t s2num;
    secp256k1_num_set_bin(&s2num, c, 32);
    secp256k1_num_mod(&s2num, &secp256k1_ge_consts->order);

    {
        /* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */
        secp256k1_num_t n, t, m;
        secp256k1_num_set_int(&n, 0);
        secp256k1_num_set_int(&m, 16);
        for (int i = 0; i < 256; i += 4) {
            secp256k1_num_set_int(&t, secp256k1_scalar_get_bits(&s, 256 - 4 - i, 4));
            secp256k1_num_mul(&n, &n, &m);
            secp256k1_num_add(&n, &n, &t);
        }
        CHECK(secp256k1_num_eq(&n, &snum));
    }

    {
        /* Test that get_b32 returns the same as get_bin on the number. */
        unsigned char r1[32];
        secp256k1_scalar_get_b32(r1, &s2);
        unsigned char r2[32];
        secp256k1_num_get_bin(r2, 32, &s2num);
        CHECK(memcmp(r1, r2, 32) == 0);
        /* If no overflow occurred when assigning, it should also be equal to the original byte array. */
        CHECK((memcmp(r1, c, 32) == 0) == (overflow == 0));
    }

    {
        /* Test that adding the scalars together is equal to adding their numbers together modulo the order. */
        secp256k1_num_t rnum;
        secp256k1_num_add(&rnum, &snum, &s2num);
        secp256k1_num_mod(&rnum, &secp256k1_ge_consts->order);
        secp256k1_scalar_t r;
        secp256k1_scalar_add(&r, &s, &s2);
        secp256k1_num_t r2num;
        secp256k1_scalar_get_num(&r2num, &r);
        CHECK(secp256k1_num_eq(&rnum, &r2num));
    }

    {
        /* Test that multipying the scalars is equal to multiplying their numbers modulo the order. */
        secp256k1_num_t rnum;
        secp256k1_num_mul(&rnum, &snum, &s2num);
        secp256k1_num_mod(&rnum, &secp256k1_ge_consts->order);
        secp256k1_scalar_t r;
        secp256k1_scalar_mul(&r, &s, &s2);
        secp256k1_num_t r2num;
        secp256k1_scalar_get_num(&r2num, &r);
        CHECK(secp256k1_num_eq(&rnum, &r2num));
        /* The result can only be zero if at least one of the factors was zero. */
        CHECK(secp256k1_scalar_is_zero(&r) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_zero(&s2)));
        /* The results can only be equal to one of the factors if that factor was zero, or the other factor was one. */
        CHECK(secp256k1_num_eq(&rnum, &snum) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_one(&s2)));
        CHECK(secp256k1_num_eq(&rnum, &s2num) == (secp256k1_scalar_is_zero(&s2) || secp256k1_scalar_is_one(&s)));
    }

    {
        /* Check that comparison with zero matches comparison with zero on the number. */
        CHECK(secp256k1_num_is_zero(&snum) == secp256k1_scalar_is_zero(&s));
        /* Check that comparison with the half order is equal to testing for high scalar. */
        CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &secp256k1_ge_consts->half_order) > 0));
        secp256k1_scalar_t neg;
        secp256k1_scalar_negate(&neg, &s);
        secp256k1_num_t negnum;
        secp256k1_num_sub(&negnum, &secp256k1_ge_consts->order, &snum);
        secp256k1_num_mod(&negnum, &secp256k1_ge_consts->order);
        /* Check that comparison with the half order is equal to testing for high scalar after negation. */
        CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &secp256k1_ge_consts->half_order) > 0));
        /* Negating should change the high property, unless the value was already zero. */
        CHECK((secp256k1_scalar_is_high(&s) == secp256k1_scalar_is_high(&neg)) == secp256k1_scalar_is_zero(&s));
        secp256k1_num_t negnum2;
        secp256k1_scalar_get_num(&negnum2, &neg);
        /* Negating a scalar should be equal to (order - n) mod order on the number. */
        CHECK(secp256k1_num_eq(&negnum, &negnum2));
        secp256k1_scalar_add(&neg, &neg, &s);
        /* Adding a number to its negation should result in zero. */
        CHECK(secp256k1_scalar_is_zero(&neg));
        secp256k1_scalar_negate(&neg, &neg);
        /* Negating zero should still result in zero. */
        CHECK(secp256k1_scalar_is_zero(&neg));
    }

    {
        /* Test that scalar inverses are equal to the inverse of their number modulo the order. */
        if (!secp256k1_scalar_is_zero(&s)) {
            secp256k1_scalar_t inv;
            secp256k1_scalar_inverse(&inv, &s);
            secp256k1_num_t invnum;
            secp256k1_num_mod_inverse(&invnum, &snum, &secp256k1_ge_consts->order);
            secp256k1_num_t invnum2;
            secp256k1_scalar_get_num(&invnum2, &inv);
            CHECK(secp256k1_num_eq(&invnum, &invnum2));
            secp256k1_scalar_mul(&inv, &inv, &s);
            /* Multiplying a scalar with its inverse must result in one. */
            CHECK(secp256k1_scalar_is_one(&inv));
            secp256k1_scalar_inverse(&inv, &inv);
            /* Inverting one must result in one. */
            CHECK(secp256k1_scalar_is_one(&inv));
        }
    }

    {
        /* Test commutativity of add. */
        secp256k1_scalar_t r1, r2;
        secp256k1_scalar_add(&r1, &s1, &s2);
        secp256k1_scalar_add(&r2, &s2, &s1);
        CHECK(secp256k1_scalar_eq(&r1, &r2));
    }

    {
        /* Test commutativity of mul. */
        secp256k1_scalar_t r1, r2;
        secp256k1_scalar_mul(&r1, &s1, &s2);
        secp256k1_scalar_mul(&r2, &s2, &s1);
        CHECK(secp256k1_scalar_eq(&r1, &r2));
    }

    {
        /* Test associativity of add. */
        secp256k1_scalar_t r1, r2;
        secp256k1_scalar_add(&r1, &s1, &s2);
        secp256k1_scalar_add(&r1, &r1, &s);
        secp256k1_scalar_add(&r2, &s2, &s);
        secp256k1_scalar_add(&r2, &s1, &r2);
        CHECK(secp256k1_scalar_eq(&r1, &r2));
    }

    {
        /* Test associativity of mul. */
        secp256k1_scalar_t r1, r2;
        secp256k1_scalar_mul(&r1, &s1, &s2);
        secp256k1_scalar_mul(&r1, &r1, &s);
        secp256k1_scalar_mul(&r2, &s2, &s);
        secp256k1_scalar_mul(&r2, &s1, &r2);
        CHECK(secp256k1_scalar_eq(&r1, &r2));
    }

    {
        /* Test distributitivity of mul over add. */
        secp256k1_scalar_t r1, r2, t;
        secp256k1_scalar_add(&r1, &s1, &s2);
        secp256k1_scalar_mul(&r1, &r1, &s);
        secp256k1_scalar_mul(&r2, &s1, &s);
        secp256k1_scalar_mul(&t, &s2, &s);
        secp256k1_scalar_add(&r2, &r2, &t);
        CHECK(secp256k1_scalar_eq(&r1, &r2));
    }

    {
        /* Test square. */
        secp256k1_scalar_t r1, r2;
        secp256k1_scalar_sqr(&r1, &s1);
        secp256k1_scalar_mul(&r2, &s1, &s1);
        CHECK(secp256k1_scalar_eq(&r1, &r2));
    }
}