Пример #1
0
void test_num_add_sub() {
    secp256k1_num_t n1;
    secp256k1_num_t n2;
    secp256k1_num_init(&n1);
    secp256k1_num_init(&n2);
    random_num_order_test(&n1); // n1 = R1
    random_num_negate(&n1);
    random_num_order_test(&n2); // n2 = R2
    random_num_negate(&n2);
    secp256k1_num_t n1p2, n2p1, n1m2, n2m1;
    secp256k1_num_init(&n1p2);
    secp256k1_num_init(&n2p1);
    secp256k1_num_init(&n1m2);
    secp256k1_num_init(&n2m1);
    secp256k1_num_add(&n1p2, &n1, &n2); // n1p2 = R1 + R2
    secp256k1_num_add(&n2p1, &n2, &n1); // n2p1 = R2 + R1
    secp256k1_num_sub(&n1m2, &n1, &n2); // n1m2 = R1 - R2
    secp256k1_num_sub(&n2m1, &n2, &n1); // n2m1 = R2 - R1
    assert(secp256k1_num_cmp(&n1p2, &n2p1) == 0);
    assert(secp256k1_num_cmp(&n1p2, &n1m2) != 0);
    secp256k1_num_negate(&n2m1); // n2m1 = -R2 + R1
    assert(secp256k1_num_cmp(&n2m1, &n1m2) == 0);
    assert(secp256k1_num_cmp(&n2m1, &n1) != 0);
    secp256k1_num_add(&n2m1, &n2m1, &n2); // n2m1 = -R2 + R1 + R2 = R1
    assert(secp256k1_num_cmp(&n2m1, &n1) == 0);
    assert(secp256k1_num_cmp(&n2p1, &n1) != 0);
    secp256k1_num_sub(&n2p1, &n2p1, &n2); // n2p1 = R2 + R1 - R2 = R1
    assert(secp256k1_num_cmp(&n2p1, &n1) == 0);
    secp256k1_num_free(&n2m1);
    secp256k1_num_free(&n1m2);
    secp256k1_num_free(&n2p1);
    secp256k1_num_free(&n1p2);
    secp256k1_num_free(&n2);
    secp256k1_num_free(&n1);
}
Пример #2
0
void test_num_add_sub(void) {
    int r = secp256k1_rand32();
    secp256k1_num_t n1;
    secp256k1_num_t n2;
    random_num_order_test(&n1); /* n1 = R1 */
    if (r & 1) {
        random_num_negate(&n1);
    }
    random_num_order_test(&n2); /* n2 = R2 */
    if (r & 2) {
        random_num_negate(&n2);
    }
    secp256k1_num_t n1p2, n2p1, n1m2, n2m1;
    secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = R1 + R2 */
    secp256k1_num_add(&n2p1, &n2, &n1); /* n2p1 = R2 + R1 */
    secp256k1_num_sub(&n1m2, &n1, &n2); /* n1m2 = R1 - R2 */
    secp256k1_num_sub(&n2m1, &n2, &n1); /* n2m1 = R2 - R1 */
    CHECK(secp256k1_num_eq(&n1p2, &n2p1));
    CHECK(!secp256k1_num_eq(&n1p2, &n1m2));
    secp256k1_num_negate(&n2m1); /* n2m1 = -R2 + R1 */
    CHECK(secp256k1_num_eq(&n2m1, &n1m2));
    CHECK(!secp256k1_num_eq(&n2m1, &n1));
    secp256k1_num_add(&n2m1, &n2m1, &n2); /* n2m1 = -R2 + R1 + R2 = R1 */
    CHECK(secp256k1_num_eq(&n2m1, &n1));
    CHECK(!secp256k1_num_eq(&n2p1, &n1));
    secp256k1_num_sub(&n2p1, &n2p1, &n2); /* n2p1 = R2 + R1 - R2 = R1 */
    CHECK(secp256k1_num_eq(&n2p1, &n1));
}
Пример #3
0
int secp256k1_ecdsa_privkey_tweak_add(unsigned char *seckey, const unsigned char *tweak) {
    DEBUG_CHECK(seckey != NULL);
    DEBUG_CHECK(tweak != NULL);

    int ret = 1;
    secp256k1_num_t term;
    secp256k1_num_init(&term);
    secp256k1_num_set_bin(&term, tweak, 32);
    if (secp256k1_num_cmp(&term, &secp256k1_ge_consts->order) >= 0)
        ret = 0;
    secp256k1_num_t sec;
    secp256k1_num_init(&sec);
    if (ret) {
        secp256k1_num_set_bin(&sec, seckey, 32);
        secp256k1_num_add(&sec, &sec, &term);
        secp256k1_num_mod(&sec, &secp256k1_ge_consts->order);
        if (secp256k1_num_is_zero(&sec))
            ret = 0;
    }
    if (ret)
        secp256k1_num_get_bin(seckey, 32, &sec);
    secp256k1_num_clear(&sec);
    secp256k1_num_clear(&term);
    secp256k1_num_free(&sec);
    secp256k1_num_free(&term);
    return ret;
}
Пример #4
0
void test_wnaf(const secp256k1_num_t *number, int w) {
    secp256k1_num_t x, two, t;
    secp256k1_num_set_int(&x, 0);
    secp256k1_num_set_int(&two, 2);
    int wnaf[257];
    int bits = secp256k1_ecmult_wnaf(wnaf, number, w);
    int zeroes = -1;
    for (int i=bits-1; i>=0; i--) {
        secp256k1_num_mul(&x, &x, &two);
        int v = wnaf[i];
        if (v) {
            CHECK(zeroes == -1 || zeroes >= w-1); /* check that distance between non-zero elements is at least w-1 */
            zeroes=0;
            CHECK((v & 1) == 1); /* check non-zero elements are odd */
            CHECK(v <= (1 << (w-1)) - 1); /* check range below */
            CHECK(v >= -(1 << (w-1)) - 1); /* check range above */
        } else {
            CHECK(zeroes != -1); /* check that no unnecessary zero padding exists */
            zeroes++;
        }
        secp256k1_num_set_int(&t, v);
        secp256k1_num_add(&x, &x, &t);
    }
    CHECK(secp256k1_num_eq(&x, number)); /* check that wnaf represents number */
}
Пример #5
0
void test_wnaf(const secp256k1_num_t *number, int w) {
    secp256k1_num_t x, two, t;
    secp256k1_num_init(&x);
    secp256k1_num_init(&two);
    secp256k1_num_init(&t);
    secp256k1_num_set_int(&x, 0);
    secp256k1_num_set_int(&two, 2);
    int wnaf[257];
    int bits = secp256k1_ecmult_wnaf(wnaf, number, w);
    int zeroes = -1;
    for (int i=bits-1; i>=0; i--) {
        secp256k1_num_mul(&x, &x, &two);
        int v = wnaf[i];
        if (v) {
            assert(zeroes == -1 || zeroes >= w-1); // check that distance between non-zero elements is at least w-1
            zeroes=0;
            assert((v & 1) == 1); // check non-zero elements are odd
            assert(v <= (1 << (w-1)) - 1); // check range below
            assert(v >= -(1 << (w-1)) - 1); // check range above
        } else {
            assert(zeroes != -1); // check that no unnecessary zero padding exists
            zeroes++;
        }
        secp256k1_num_set_int(&t, v);
        secp256k1_num_add(&x, &x, &t);
    }
    assert(secp256k1_num_cmp(&x, number) == 0); // check that wnaf represents number
    secp256k1_num_free(&x);
    secp256k1_num_free(&two);
    secp256k1_num_free(&t);
}
Пример #6
0
void run_ecmult_chain(void) {
    /* random starting point A (on the curve) */
    secp256k1_fe_t ax; secp256k1_fe_set_hex(&ax, "8b30bbe9ae2a990696b22f670709dff3727fd8bc04d3362c6c7bf458e2846004", 64);
    secp256k1_fe_t ay; secp256k1_fe_set_hex(&ay, "a357ae915c4a65281309edf20504740f0eb3343990216b4f81063cb65f2f7e0f", 64);
    secp256k1_gej_t a; secp256k1_gej_set_xy(&a, &ax, &ay);
    /* two random initial factors xn and gn */
    secp256k1_num_t xn;
    secp256k1_num_set_hex(&xn, "84cc5452f7fde1edb4d38a8ce9b1b84ccef31f146e569be9705d357a42985407", 64);
    secp256k1_num_t gn;
    secp256k1_num_set_hex(&gn, "a1e58d22553dcd42b23980625d4c57a96e9323d42b3152e5ca2c3990edc7c9de", 64);
    /* two small multipliers to be applied to xn and gn in every iteration: */
    secp256k1_num_t xf;
    secp256k1_num_set_hex(&xf, "1337", 4);
    secp256k1_num_t gf;
    secp256k1_num_set_hex(&gf, "7113", 4);
    /* accumulators with the resulting coefficients to A and G */
    secp256k1_num_t ae;
    secp256k1_num_set_int(&ae, 1);
    secp256k1_num_t ge;
    secp256k1_num_set_int(&ge, 0);
    /* the point being computed */
    secp256k1_gej_t x = a;
    const secp256k1_num_t *order = &secp256k1_ge_consts->order;
    for (int i=0; i<200*count; i++) {
        /* in each iteration, compute X = xn*X + gn*G; */
        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_num_mod_mul(&ae, &ae, &xn, order);
        secp256k1_num_mod_mul(&ge, &ge, &xn, order);
        secp256k1_num_add(&ge, &ge, &gn);
        secp256k1_num_mod(&ge, order);
        /* modify xn and gn */
        secp256k1_num_mod_mul(&xn, &xn, &xf, order);
        secp256k1_num_mod_mul(&gn, &gn, &gf, order);

        /* verify */
        if (i == 19999) {
            char res[132]; int resl = 132;
            secp256k1_gej_get_hex(res, &resl, &x);
            CHECK(strcmp(res, "(D6E96687F9B10D092A6F35439D86CEBEA4535D0D409F53586440BD74B933E830,B95CBCA2C77DA786539BE8FD53354D2D3B4F566AE658045407ED6015EE1B2A88)") == 0);
        }
    }
    /* redo the computation, but directly with the resulting ae and ge coefficients: */
    secp256k1_gej_t x2; secp256k1_ecmult(&x2, &a, &ae, &ge);
    char res[132]; int resl = 132;
    char res2[132]; int resl2 = 132;
    secp256k1_gej_get_hex(res, &resl, &x);
    secp256k1_gej_get_hex(res2, &resl2, &x2);
    CHECK(strcmp(res, res2) == 0);
    CHECK(strlen(res) == 131);
}
Пример #7
0
void test_num_negate(void) {
    secp256k1_num_t n1;
    secp256k1_num_t n2;
    random_num_order_test(&n1); /* n1 = R */
    random_num_negate(&n1);
    secp256k1_num_copy(&n2, &n1); /* n2 = R */
    secp256k1_num_sub(&n1, &n2, &n1); /* n1 = n2-n1 = 0 */
    CHECK(secp256k1_num_is_zero(&n1));
    secp256k1_num_copy(&n1, &n2); /* n1 = R */
    secp256k1_num_negate(&n1); /* n1 = -R */
    CHECK(!secp256k1_num_is_zero(&n1));
    secp256k1_num_add(&n1, &n2, &n1); /* n1 = n2+n1 = 0 */
    CHECK(secp256k1_num_is_zero(&n1));
    secp256k1_num_copy(&n1, &n2); /* n1 = R */
    secp256k1_num_negate(&n1); /* n1 = -R */
    CHECK(secp256k1_num_is_neg(&n1) != secp256k1_num_is_neg(&n2));
    secp256k1_num_negate(&n1); /* n1 = R */
    CHECK(secp256k1_num_eq(&n1, &n2));
}
Пример #8
0
void test_num_negate() {
    secp256k1_num_t n1;
    secp256k1_num_t n2;
    secp256k1_num_init(&n1);
    secp256k1_num_init(&n2);
    random_num_order_test(&n1); // n1 = R
    random_num_negate(&n1);
    secp256k1_num_copy(&n2, &n1); // n2 = R
    secp256k1_num_sub(&n1, &n2, &n1); // n1 = n2-n1 = 0
    assert(secp256k1_num_is_zero(&n1));
    secp256k1_num_copy(&n1, &n2); // n1 = R
    secp256k1_num_negate(&n1); // n1 = -R
    assert(!secp256k1_num_is_zero(&n1));
    secp256k1_num_add(&n1, &n2, &n1); // n1 = n2+n1 = 0
    assert(secp256k1_num_is_zero(&n1));
    secp256k1_num_copy(&n1, &n2); // n1 = R
    secp256k1_num_negate(&n1); // n1 = -R
    assert(secp256k1_num_is_neg(&n1) != secp256k1_num_is_neg(&n2));
    secp256k1_num_negate(&n1); // n1 = R
    assert(secp256k1_num_cmp(&n1, &n2) == 0);
    assert(secp256k1_num_is_neg(&n1) == secp256k1_num_is_neg(&n2));
    secp256k1_num_free(&n2);
    secp256k1_num_free(&n1);
}
Пример #9
0
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));
    }

}
Пример #10
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));
    }
}