void test_num_copy_inc_cmp() { secp256k1_num_t n1,n2; secp256k1_num_init(&n1); secp256k1_num_init(&n2); random_num_order(&n1); secp256k1_num_copy(&n2, &n1); assert(secp256k1_num_cmp(&n1, &n2) == 0); assert(secp256k1_num_cmp(&n2, &n1) == 0); secp256k1_num_inc(&n2); assert(secp256k1_num_cmp(&n1, &n2) != 0); assert(secp256k1_num_cmp(&n2, &n1) != 0); secp256k1_num_free(&n1); secp256k1_num_free(&n2); }
int secp256k1_ecdsa_pubkey_tweak_add(unsigned char *pubkey, int pubkeylen, const unsigned char *tweak) { DEBUG_CHECK(secp256k1_ecmult_consts != NULL); DEBUG_CHECK(pubkey != 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_ge_t p; if (ret) { if (!secp256k1_ecdsa_pubkey_parse(&p, pubkey, pubkeylen)) ret = 0; } if (ret) { secp256k1_gej_t pt; secp256k1_gej_set_ge(&pt, &p); secp256k1_num_t one; secp256k1_num_init(&one); secp256k1_num_set_int(&one, 1); secp256k1_ecmult(&pt, &pt, &one, &term); secp256k1_num_free(&one); if (secp256k1_gej_is_infinity(&pt)) ret = 0; secp256k1_ge_set_gej(&p, &pt); int oldlen = pubkeylen; secp256k1_ecdsa_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33); VERIFY_CHECK(pubkeylen == oldlen); } secp256k1_num_free(&term); return ret; }
int secp256k1_ecdsa_pubkey_tweak_mul(unsigned char *pubkey, int pubkeylen, const unsigned char *tweak) { int ret = 1; secp256k1_num_t factor; secp256k1_num_init(&factor); secp256k1_num_set_bin(&factor, tweak, 32); if (secp256k1_num_is_zero(&factor)) ret = 0; if (secp256k1_num_cmp(&factor, &secp256k1_ge_consts->order) >= 0) ret = 0; secp256k1_ge_t p; if (ret) { if (!secp256k1_ecdsa_pubkey_parse(&p, pubkey, pubkeylen)) ret = 0; } if (ret) { secp256k1_num_t zero; secp256k1_num_init(&zero); secp256k1_num_set_int(&zero, 0); secp256k1_gej_t pt; secp256k1_gej_set_ge(&pt, &p); secp256k1_ecmult(&pt, &pt, &factor, &zero); secp256k1_num_free(&zero); secp256k1_ge_set_gej(&p, &pt); int oldlen = pubkeylen; secp256k1_ecdsa_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33); assert(pubkeylen == oldlen); } secp256k1_num_free(&factor); return ret; }
int secp256k1_ecdsa_sign(const unsigned char *message, int messagelen, unsigned char *signature, int *signaturelen, const unsigned char *seckey, const unsigned char *nonce) { secp256k1_num_t sec, non, msg; secp256k1_num_init(&sec); secp256k1_num_init(&non); secp256k1_num_init(&msg); secp256k1_num_set_bin(&sec, seckey, 32); secp256k1_num_set_bin(&non, nonce, 32); secp256k1_num_set_bin(&msg, message, messagelen); int ret = !secp256k1_num_is_zero(&non) && (secp256k1_num_cmp(&non, &secp256k1_ge_consts->order) < 0); secp256k1_ecdsa_sig_t sig; secp256k1_ecdsa_sig_init(&sig); if (ret) { ret = secp256k1_ecdsa_sig_sign(&sig, &sec, &msg, &non, NULL); } if (ret) { secp256k1_ecdsa_sig_serialize(signature, signaturelen, &sig); } secp256k1_ecdsa_sig_free(&sig); secp256k1_num_clear(&msg); secp256k1_num_clear(&non); secp256k1_num_clear(&sec); secp256k1_num_free(&msg); secp256k1_num_free(&non); secp256k1_num_free(&sec); return ret; }
int secp256k1_ecdsa_sign_compact(const unsigned char *message, int messagelen, unsigned char *sig64, const unsigned char *seckey, const unsigned char *nonce, int *recid) { secp256k1_num_t sec, non, msg; secp256k1_num_init(&sec); secp256k1_num_init(&non); secp256k1_num_init(&msg); secp256k1_num_set_bin(&sec, seckey, 32); secp256k1_num_set_bin(&non, nonce, 32); secp256k1_num_set_bin(&msg, message, messagelen); int ret = !secp256k1_num_is_zero(&non) && (secp256k1_num_cmp(&non, &secp256k1_ge_consts->order) < 0); secp256k1_ecdsa_sig_t sig; secp256k1_ecdsa_sig_init(&sig); if (ret) { ret = secp256k1_ecdsa_sig_sign(&sig, &sec, &msg, &non, recid); } if (ret) { secp256k1_num_get_bin(sig64, 32, &sig.r); secp256k1_num_get_bin(sig64 + 32, 32, &sig.s); } secp256k1_ecdsa_sig_free(&sig); secp256k1_num_clear(&msg); secp256k1_num_clear(&non); secp256k1_num_clear(&sec); secp256k1_num_free(&msg); secp256k1_num_free(&non); secp256k1_num_free(&sec); return ret; }
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); }
int secp256k1_ecdsa_pubkey_tweak_add(unsigned char *pubkey, int pubkeylen, const unsigned char *tweak) { 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_ge_t p; if (ret) { if (!secp256k1_ecdsa_pubkey_parse(&p, pubkey, pubkeylen)) ret = 0; } if (ret) { secp256k1_gej_t pt; secp256k1_ecmult_gen(&pt, &term); secp256k1_gej_add_ge(&pt, &pt, &p); if (secp256k1_gej_is_infinity(&pt)) ret = 0; secp256k1_ge_set_gej(&p, &pt); int oldlen = pubkeylen; secp256k1_ecdsa_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33); assert(pubkeylen == oldlen); } secp256k1_num_free(&term); return ret; }
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; }
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); }
int secp256k1_ecdsa_seckey_verify(const unsigned char *seckey) { secp256k1_num_t sec; secp256k1_num_init(&sec); secp256k1_num_set_bin(&sec, seckey, 32); int ret = !secp256k1_num_is_zero(&sec) && (secp256k1_num_cmp(&sec, &secp256k1_ge_consts->order) < 0); secp256k1_num_free(&sec); return ret; }
void random_field_element_test(secp256k1_fe_t *fe) { do { unsigned char b32[32]; secp256k1_rand256_test(b32); secp256k1_num_t num; secp256k1_num_set_bin(&num, b32, 32); if (secp256k1_num_cmp(&num, &secp256k1_fe_consts->p) >= 0) continue; secp256k1_fe_set_b32(fe, b32); break; } while(1); }
void random_num_order(secp256k1_num_t *num) { do { unsigned char b32[32]; secp256k1_rand256(b32); secp256k1_num_set_bin(num, b32, 32); if (secp256k1_num_is_zero(num)) continue; if (secp256k1_num_cmp(num, &secp256k1_ge_consts->order) >= 0) continue; break; } while(1); }
void test_num_get_set_bin() { secp256k1_num_t n1,n2; secp256k1_num_init(&n1); secp256k1_num_init(&n2); random_num_order_test(&n1); unsigned char c[32]; secp256k1_num_get_bin(c, 32, &n1); secp256k1_num_set_bin(&n2, c, 32); assert(secp256k1_num_cmp(&n1, &n2) == 0); for (int i=0; i<32; i++) { // check whether the lower 8 bits correspond to the last byte int low1 = secp256k1_num_shift(&n1, 8); int low2 = c[31]; assert(low1 == low2); // shift bits off the byte representation, and compare memmove(c+1, c, 31); c[0] = 0; secp256k1_num_set_bin(&n2, c, 32); assert(secp256k1_num_cmp(&n1, &n2) == 0); } secp256k1_num_free(&n2); secp256k1_num_free(&n1); }
void test_num_get_set_hex() { secp256k1_num_t n1,n2; secp256k1_num_init(&n1); secp256k1_num_init(&n2); random_num_order_test(&n1); char c[64]; secp256k1_num_get_hex(c, 64, &n1); secp256k1_num_set_hex(&n2, c, 64); assert(secp256k1_num_cmp(&n1, &n2) == 0); for (int i=0; i<64; i++) { // check whether the lower 4 bits correspond to the last hex character int low1 = secp256k1_num_shift(&n1, 4); int lowh = c[63]; int low2 = (lowh>>6)*9+(lowh-'0')&15; assert(low1 == low2); // shift bits off the hex representation, and compare memmove(c+1, c, 63); c[0] = '0'; secp256k1_num_set_hex(&n2, c, 64); assert(secp256k1_num_cmp(&n1, &n2) == 0); } secp256k1_num_free(&n2); secp256k1_num_free(&n1); }
int secp256k1_ecdsa_privkey_tweak_mul(unsigned char *seckey, const unsigned char *tweak) { int ret = 1; secp256k1_num_t factor; secp256k1_num_init(&factor); secp256k1_num_set_bin(&factor, tweak, 32); if (secp256k1_num_is_zero(&factor)) ret = 0; if (secp256k1_num_cmp(&factor, &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_mod_mul(&sec, &sec, &factor, &secp256k1_ge_consts->order); } if (ret) secp256k1_num_get_bin(seckey, 32, &sec); secp256k1_num_free(&sec); secp256k1_num_free(&factor); return ret; }
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); }
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)); } }
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)); } }