void run_scalar_tests(void) { for (int i = 0; i < 128 * count; i++) { scalar_test(); } { /* (-1)+1 should be zero. */ secp256k1_scalar_t s, o; secp256k1_scalar_set_int(&s, 1); secp256k1_scalar_negate(&o, &s); secp256k1_scalar_add(&o, &o, &s); CHECK(secp256k1_scalar_is_zero(&o)); } #ifndef USE_NUM_NONE { /* A scalar with value of the curve order should be 0. */ secp256k1_num_t order; secp256k1_scalar_order_get_num(&order); unsigned char bin[32]; secp256k1_num_get_bin(bin, 32, &order); secp256k1_scalar_t zero; int overflow = 0; secp256k1_scalar_set_b32(&zero, bin, &overflow); CHECK(overflow == 1); CHECK(secp256k1_scalar_is_zero(&zero)); } #endif }
void bench_num_jacobi(void* arg) { int i; bench_inv *data = (bench_inv*)arg; secp256k1_num nx, norder; secp256k1_scalar_get_num(&nx, &data->scalar_x); secp256k1_scalar_order_get_num(&norder); secp256k1_scalar_get_num(&norder, &data->scalar_y); for (i = 0; i < 200000; i++) { secp256k1_num_jacobi(&nx, &norder); } }
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)); } }