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);
}
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 */
}
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);
}
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_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;
}
void test_point_times_order(const secp256k1_gej_t *point) {
/* multiplying a point by the order results in O */
const secp256k1_num_t *order = &secp256k1_ge_consts->order;
secp256k1_num_t zero;
secp256k1_num_set_int(&zero, 0);
secp256k1_gej_t res;
secp256k1_ecmult(&res, point, order, order); /* calc res = order * point + order * G; */
CHECK(secp256k1_gej_is_infinity(&res));
}
void run_num_int(void) {
secp256k1_num_t n1;
for (int i=-255; i<256; i++) {
unsigned char c1[3] = {};
c1[2] = abs(i);
unsigned char c2[3] = {0x11,0x22,0x33};
secp256k1_num_set_int(&n1, i);
secp256k1_num_get_bin(c2, 3, &n1);
CHECK(memcmp(c1, c2, 3) == 0);
}
}
void test_point_times_order(const secp256k1_gej_t *point) {
// multiplying a point by the order results in O
const secp256k1_num_t *order = &secp256k1_ge_consts->order;
secp256k1_num_t zero;
secp256k1_num_init(&zero);
secp256k1_num_set_int(&zero, 0);
secp256k1_gej_t res;
secp256k1_ecmult(&res, point, order, order); // calc res = order * point + order * G;
assert(secp256k1_gej_is_infinity(&res));
secp256k1_num_free(&zero);
}
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));
}
}
