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Diffstat (limited to 'src/tests.c')
| -rw-r--r-- | src/tests.c | 1080 |
1 files changed, 1080 insertions, 0 deletions
diff --git a/src/tests.c b/src/tests.c new file mode 100644 index 0000000000..5d9b8344d9 --- /dev/null +++ b/src/tests.c @@ -0,0 +1,1080 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include <stdio.h> +#include <stdlib.h> + +#include "secp256k1.c" +#include "testrand_impl.h" + +#ifdef ENABLE_OPENSSL_TESTS +#include "openssl/bn.h" +#include "openssl/ec.h" +#include "openssl/ecdsa.h" +#include "openssl/obj_mac.h" +#endif + +static int count = 64; + +/***** NUM TESTS *****/ + +void random_num_negate(secp256k1_num_t *num) { + if (secp256k1_rand32() & 1) + secp256k1_num_negate(num); +} + +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_field_element_magnitude(secp256k1_fe_t *fe) { + secp256k1_fe_normalize(fe); + int n = secp256k1_rand32() % 4; + for (int i = 0; i < n; i++) { + secp256k1_fe_negate(fe, fe, 1 + 2*i); + secp256k1_fe_negate(fe, fe, 2 + 2*i); + } +} + +void random_group_element_test(secp256k1_ge_t *ge) { + secp256k1_fe_t fe; + do { + random_field_element_test(&fe); + if (secp256k1_ge_set_xo(ge, &fe, secp256k1_rand32() & 1)) + break; + } while(1); +} + +void random_group_element_jacobian_test(secp256k1_gej_t *gej, const secp256k1_ge_t *ge) { + do { + random_field_element_test(&gej->z); + if (!secp256k1_fe_is_zero(&gej->z)) { + break; + } + } while(1); + secp256k1_fe_t z2; secp256k1_fe_sqr(&z2, &gej->z); + secp256k1_fe_t z3; secp256k1_fe_mul(&z3, &z2, &gej->z); + secp256k1_fe_mul(&gej->x, &ge->x, &z2); + secp256k1_fe_mul(&gej->y, &ge->y, &z3); + gej->infinity = ge->infinity; +} + +void random_num_order_test(secp256k1_num_t *num) { + do { + unsigned char b32[32]; + secp256k1_rand256_test(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 random_scalar_order_test(secp256k1_scalar_t *num) { + do { + unsigned char b32[32]; + secp256k1_rand256_test(b32); + int overflow = 0; + secp256k1_scalar_set_b32(num, b32, &overflow); + if (overflow || secp256k1_scalar_is_zero(num)) + continue; + 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_copy_inc_cmp(void) { + secp256k1_num_t n1,n2; + random_num_order(&n1); + secp256k1_num_copy(&n2, &n1); + CHECK(secp256k1_num_eq(&n1, &n2)); + CHECK(secp256k1_num_eq(&n2, &n1)); + secp256k1_num_inc(&n2); + CHECK(!secp256k1_num_eq(&n1, &n2)); + CHECK(!secp256k1_num_eq(&n2, &n1)); +} + + +void test_num_get_set_hex(void) { + secp256k1_num_t n1,n2; + random_num_order_test(&n1); + char c[64]; + secp256k1_num_get_hex(c, 64, &n1); + secp256k1_num_set_hex(&n2, c, 64); + CHECK(secp256k1_num_eq(&n1, &n2)); + 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; + CHECK(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); + CHECK(secp256k1_num_eq(&n1, &n2)); + } +} + +void test_num_get_set_bin(void) { + secp256k1_num_t n1,n2; + random_num_order_test(&n1); + unsigned char c[32]; + secp256k1_num_get_bin(c, 32, &n1); + secp256k1_num_set_bin(&n2, c, 32); + CHECK(secp256k1_num_eq(&n1, &n2)); + 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]; + CHECK(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); + CHECK(secp256k1_num_eq(&n1, &n2)); + } +} + +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_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)); +} + +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)); +} + +void run_num_smalltests(void) { + for (int i=0; i<100*count; i++) { + test_num_copy_inc_cmp(); + test_num_get_set_hex(); + test_num_get_set_bin(); + test_num_negate(); + test_num_add_sub(); + } + run_num_int(); +} + +/***** SCALAR TESTS *****/ + +int secp256k1_scalar_eq(const secp256k1_scalar_t *s1, const secp256k1_scalar_t *s2) { + secp256k1_scalar_t t; + secp256k1_scalar_negate(&t, s2); + secp256k1_scalar_add(&t, &t, s1); + int ret = secp256k1_scalar_is_zero(&t); + return ret; +} + +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 run_scalar_tests(void) { + for (int i = 0; i < 128 * count; i++) { + scalar_test(); + } +} + +/***** FIELD TESTS *****/ + +void random_fe(secp256k1_fe_t *x) { + unsigned char bin[32]; + secp256k1_rand256(bin); + secp256k1_fe_set_b32(x, bin); +} + +void random_fe_non_zero(secp256k1_fe_t *nz) { + int tries = 10; + while (--tries >= 0) { + random_fe(nz); + secp256k1_fe_normalize(nz); + if (!secp256k1_fe_is_zero(nz)) + break; + } + /* Infinitesimal probability of spurious failure here */ + CHECK(tries >= 0); +} + +void random_fe_non_square(secp256k1_fe_t *ns) { + random_fe_non_zero(ns); + secp256k1_fe_t r; + if (secp256k1_fe_sqrt(&r, ns)) { + secp256k1_fe_negate(ns, ns, 1); + } +} + +int check_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe_t *b) { + secp256k1_fe_t an = *a; secp256k1_fe_normalize(&an); + secp256k1_fe_t bn = *b; secp256k1_fe_normalize(&bn); + return secp256k1_fe_equal(&an, &bn); +} + +int check_fe_inverse(const secp256k1_fe_t *a, const secp256k1_fe_t *ai) { + secp256k1_fe_t x; secp256k1_fe_mul(&x, a, ai); + secp256k1_fe_t one; secp256k1_fe_set_int(&one, 1); + return check_fe_equal(&x, &one); +} + +void run_field_inv(void) { + secp256k1_fe_t x, xi, xii; + for (int i=0; i<10*count; i++) { + random_fe_non_zero(&x); + secp256k1_fe_inv(&xi, &x); + CHECK(check_fe_inverse(&x, &xi)); + secp256k1_fe_inv(&xii, &xi); + CHECK(check_fe_equal(&x, &xii)); + } +} + +void run_field_inv_var(void) { + secp256k1_fe_t x, xi, xii; + for (int i=0; i<10*count; i++) { + random_fe_non_zero(&x); + secp256k1_fe_inv_var(&xi, &x); + CHECK(check_fe_inverse(&x, &xi)); + secp256k1_fe_inv_var(&xii, &xi); + CHECK(check_fe_equal(&x, &xii)); + } +} + +void run_field_inv_all(void) { + secp256k1_fe_t x[16], xi[16], xii[16]; + /* Check it's safe to call for 0 elements */ + secp256k1_fe_inv_all(0, xi, x); + for (int i=0; i<count; i++) { + size_t len = (secp256k1_rand32() & 15) + 1; + for (size_t j=0; j<len; j++) + random_fe_non_zero(&x[j]); + secp256k1_fe_inv_all(len, xi, x); + for (size_t j=0; j<len; j++) + CHECK(check_fe_inverse(&x[j], &xi[j])); + secp256k1_fe_inv_all(len, xii, xi); + for (size_t j=0; j<len; j++) + CHECK(check_fe_equal(&x[j], &xii[j])); + } +} + +void run_field_inv_all_var(void) { + secp256k1_fe_t x[16], xi[16], xii[16]; + /* Check it's safe to call for 0 elements */ + secp256k1_fe_inv_all_var(0, xi, x); + for (int i=0; i<count; i++) { + size_t len = (secp256k1_rand32() & 15) + 1; + for (size_t j=0; j<len; j++) + random_fe_non_zero(&x[j]); + secp256k1_fe_inv_all_var(len, xi, x); + for (size_t j=0; j<len; j++) + CHECK(check_fe_inverse(&x[j], &xi[j])); + secp256k1_fe_inv_all_var(len, xii, xi); + for (size_t j=0; j<len; j++) + CHECK(check_fe_equal(&x[j], &xii[j])); + } +} + +void run_sqr(void) { + secp256k1_fe_t x, s; + + { + secp256k1_fe_set_int(&x, 1); + secp256k1_fe_negate(&x, &x, 1); + + for (int i=1; i<=512; ++i) { + secp256k1_fe_mul_int(&x, 2); + secp256k1_fe_normalize(&x); + secp256k1_fe_sqr(&s, &x); + } + } +} + +void test_sqrt(const secp256k1_fe_t *a, const secp256k1_fe_t *k) { + secp256k1_fe_t r1, r2; + int v = secp256k1_fe_sqrt(&r1, a); + CHECK((v == 0) == (k == NULL)); + + if (k != NULL) { + /* Check that the returned root is +/- the given known answer */ + secp256k1_fe_negate(&r2, &r1, 1); + secp256k1_fe_add(&r1, k); secp256k1_fe_add(&r2, k); + secp256k1_fe_normalize(&r1); secp256k1_fe_normalize(&r2); + CHECK(secp256k1_fe_is_zero(&r1) || secp256k1_fe_is_zero(&r2)); + } +} + +void run_sqrt(void) { + secp256k1_fe_t ns, x, s, t; + + /* Check sqrt(0) is 0 */ + secp256k1_fe_set_int(&x, 0); + secp256k1_fe_sqr(&s, &x); + test_sqrt(&s, &x); + + /* Check sqrt of small squares (and their negatives) */ + for (int i=1; i<=100; i++) { + secp256k1_fe_set_int(&x, i); + secp256k1_fe_sqr(&s, &x); + test_sqrt(&s, &x); + secp256k1_fe_negate(&t, &s, 1); + test_sqrt(&t, NULL); + } + + /* Consistency checks for large random values */ + for (int i=0; i<10; i++) { + random_fe_non_square(&ns); + for (int j=0; j<count; j++) { + random_fe(&x); + secp256k1_fe_sqr(&s, &x); + test_sqrt(&s, &x); + secp256k1_fe_negate(&t, &s, 1); + test_sqrt(&t, NULL); + secp256k1_fe_mul(&t, &s, &ns); + test_sqrt(&t, NULL); + } + } +} + +/***** GROUP TESTS *****/ + +int ge_equals_ge(const secp256k1_ge_t *a, const secp256k1_ge_t *b) { + if (a->infinity && b->infinity) + return 1; + return check_fe_equal(&a->x, &b->x) && check_fe_equal(&a->y, &b->y); +} + +void ge_equals_gej(const secp256k1_ge_t *a, const secp256k1_gej_t *b) { + secp256k1_ge_t bb; + secp256k1_gej_t bj = *b; + secp256k1_ge_set_gej_var(&bb, &bj); + CHECK(ge_equals_ge(a, &bb)); +} + +void gej_equals_gej(const secp256k1_gej_t *a, const secp256k1_gej_t *b) { + secp256k1_ge_t aa, bb; + secp256k1_gej_t aj = *a, bj = *b; + secp256k1_ge_set_gej_var(&aa, &aj); + secp256k1_ge_set_gej_var(&bb, &bj); + CHECK(ge_equals_ge(&aa, &bb)); +} + +void test_ge(void) { + secp256k1_ge_t a, b, i, n; + random_group_element_test(&a); + random_group_element_test(&b); + n = a; + secp256k1_fe_normalize(&a.y); + secp256k1_fe_negate(&n.y, &a.y, 1); + secp256k1_ge_set_infinity(&i); + random_field_element_magnitude(&a.x); + random_field_element_magnitude(&a.y); + random_field_element_magnitude(&b.x); + random_field_element_magnitude(&b.y); + random_field_element_magnitude(&n.x); + random_field_element_magnitude(&n.y); + + secp256k1_gej_t aj, bj, ij, nj; + random_group_element_jacobian_test(&aj, &a); + random_group_element_jacobian_test(&bj, &b); + secp256k1_gej_set_infinity(&ij); + random_group_element_jacobian_test(&nj, &n); + random_field_element_magnitude(&aj.x); + random_field_element_magnitude(&aj.y); + random_field_element_magnitude(&aj.z); + random_field_element_magnitude(&bj.x); + random_field_element_magnitude(&bj.y); + random_field_element_magnitude(&bj.z); + random_field_element_magnitude(&nj.x); + random_field_element_magnitude(&nj.y); + random_field_element_magnitude(&nj.z); + + /* gej + gej adds */ + secp256k1_gej_t aaj; secp256k1_gej_add_var(&aaj, &aj, &aj); + secp256k1_gej_t abj; secp256k1_gej_add_var(&abj, &aj, &bj); + secp256k1_gej_t aij; secp256k1_gej_add_var(&aij, &aj, &ij); + secp256k1_gej_t anj; secp256k1_gej_add_var(&anj, &aj, &nj); + secp256k1_gej_t iaj; secp256k1_gej_add_var(&iaj, &ij, &aj); + secp256k1_gej_t iij; secp256k1_gej_add_var(&iij, &ij, &ij); + + /* gej + ge adds */ + secp256k1_gej_t aa; secp256k1_gej_add_ge_var(&aa, &aj, &a); + secp256k1_gej_t ab; secp256k1_gej_add_ge_var(&ab, &aj, &b); + secp256k1_gej_t ai; secp256k1_gej_add_ge_var(&ai, &aj, &i); + secp256k1_gej_t an; secp256k1_gej_add_ge_var(&an, &aj, &n); + secp256k1_gej_t ia; secp256k1_gej_add_ge_var(&ia, &ij, &a); + secp256k1_gej_t ii; secp256k1_gej_add_ge_var(&ii, &ij, &i); + + /* const gej + ge adds */ + secp256k1_gej_t aac; secp256k1_gej_add_ge(&aac, &aj, &a); + secp256k1_gej_t abc; secp256k1_gej_add_ge(&abc, &aj, &b); + secp256k1_gej_t anc; secp256k1_gej_add_ge(&anc, &aj, &n); + secp256k1_gej_t iac; secp256k1_gej_add_ge(&iac, &ij, &a); + + CHECK(secp256k1_gej_is_infinity(&an)); + CHECK(secp256k1_gej_is_infinity(&anj)); + CHECK(secp256k1_gej_is_infinity(&anc)); + gej_equals_gej(&aa, &aaj); + gej_equals_gej(&aa, &aac); + gej_equals_gej(&ab, &abj); + gej_equals_gej(&ab, &abc); + gej_equals_gej(&an, &anj); + gej_equals_gej(&an, &anc); + gej_equals_gej(&ia, &iaj); + gej_equals_gej(&ai, &aij); + gej_equals_gej(&ii, &iij); + ge_equals_gej(&a, &ai); + ge_equals_gej(&a, &ai); + ge_equals_gej(&a, &iaj); + ge_equals_gej(&a, &iaj); + ge_equals_gej(&a, &iac); +} + +void run_ge(void) { + for (int i = 0; i < 2000*count; i++) { + test_ge(); + } +} + +/***** ECMULT TESTS *****/ + +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); +} + +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_point_times_order(void) { + secp256k1_fe_t x; secp256k1_fe_set_hex(&x, "02", 2); + for (int i=0; i<500; i++) { + secp256k1_ge_t p; + if (secp256k1_ge_set_xo(&p, &x, 1)) { + CHECK(secp256k1_ge_is_valid(&p)); + secp256k1_gej_t j; + secp256k1_gej_set_ge(&j, &p); + CHECK(secp256k1_gej_is_valid(&j)); + test_point_times_order(&j); + } + secp256k1_fe_sqr(&x, &x); + } + char c[65]; int cl=65; + secp256k1_fe_get_hex(c, &cl, &x); + CHECK(strcmp(c, "7603CB59B0EF6C63FE6084792A0C378CDB3233A80F8A9A09A877DEAD31B38C45") == 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 */ +} + +void run_wnaf(void) { + secp256k1_num_t n; + for (int i=0; i<count; i++) { + random_num_order(&n); + if (i % 1) + secp256k1_num_negate(&n); + test_wnaf(&n, 4+(i%10)); + } +} + +void random_sign(secp256k1_ecdsa_sig_t *sig, const secp256k1_scalar_t *key, const secp256k1_scalar_t *msg, int *recid) { + secp256k1_scalar_t nonce; + do { + random_scalar_order_test(&nonce); + } while(!secp256k1_ecdsa_sig_sign(sig, key, msg, &nonce, recid)); +} + +void test_ecdsa_sign_verify(void) { + secp256k1_scalar_t msg, key; + random_scalar_order_test(&msg); + random_scalar_order_test(&key); + secp256k1_gej_t pubj; secp256k1_ecmult_gen(&pubj, &key); + secp256k1_ge_t pub; secp256k1_ge_set_gej(&pub, &pubj); + secp256k1_ecdsa_sig_t sig; + random_sign(&sig, &key, &msg, NULL); + secp256k1_num_t msg_num; + secp256k1_scalar_get_num(&msg_num, &msg); + CHECK(secp256k1_ecdsa_sig_verify(&sig, &pub, &msg_num)); + secp256k1_num_inc(&msg_num); + CHECK(!secp256k1_ecdsa_sig_verify(&sig, &pub, &msg_num)); +} + +void run_ecdsa_sign_verify(void) { + for (int i=0; i<10*count; i++) { + test_ecdsa_sign_verify(); + } +} + +void test_ecdsa_end_to_end(void) { + unsigned char privkey[32]; + unsigned char message[32]; + + /* Generate a random key and message. */ + { + secp256k1_num_t msg, key; + random_num_order_test(&msg); + random_num_order_test(&key); + secp256k1_num_get_bin(privkey, 32, &key); + secp256k1_num_get_bin(message, 32, &msg); + } + + /* Construct and verify corresponding public key. */ + CHECK(secp256k1_ec_seckey_verify(privkey) == 1); + unsigned char pubkey[65]; int pubkeylen = 65; + CHECK(secp256k1_ec_pubkey_create(pubkey, &pubkeylen, privkey, secp256k1_rand32() % 2) == 1); + CHECK(secp256k1_ec_pubkey_verify(pubkey, pubkeylen)); + + /* Verify private key import and export. */ + unsigned char seckey[300]; int seckeylen = 300; + CHECK(secp256k1_ec_privkey_export(privkey, seckey, &seckeylen, secp256k1_rand32() % 2) == 1); + unsigned char privkey2[32]; + CHECK(secp256k1_ec_privkey_import(privkey2, seckey, seckeylen) == 1); + CHECK(memcmp(privkey, privkey2, 32) == 0); + + /* Optionally tweak the keys using addition. */ + if (secp256k1_rand32() % 3 == 0) { + unsigned char rnd[32]; + secp256k1_rand256_test(rnd); + int ret1 = secp256k1_ec_privkey_tweak_add(privkey, rnd); + int ret2 = secp256k1_ec_pubkey_tweak_add(pubkey, pubkeylen, rnd); + CHECK(ret1 == ret2); + if (ret1 == 0) return; + unsigned char pubkey2[65]; int pubkeylen2 = 65; + CHECK(secp256k1_ec_pubkey_create(pubkey2, &pubkeylen2, privkey, pubkeylen == 33) == 1); + CHECK(memcmp(pubkey, pubkey2, pubkeylen) == 0); + } + + /* Optionally tweak the keys using multiplication. */ + if (secp256k1_rand32() % 3 == 0) { + unsigned char rnd[32]; + secp256k1_rand256_test(rnd); + int ret1 = secp256k1_ec_privkey_tweak_mul(privkey, rnd); + int ret2 = secp256k1_ec_pubkey_tweak_mul(pubkey, pubkeylen, rnd); + CHECK(ret1 == ret2); + if (ret1 == 0) return; + unsigned char pubkey2[65]; int pubkeylen2 = 65; + CHECK(secp256k1_ec_pubkey_create(pubkey2, &pubkeylen2, privkey, pubkeylen == 33) == 1); + CHECK(memcmp(pubkey, pubkey2, pubkeylen) == 0); + } + + /* Sign. */ + unsigned char signature[72]; int signaturelen = 72; + while(1) { + unsigned char rnd[32]; + secp256k1_rand256_test(rnd); + if (secp256k1_ecdsa_sign(message, 32, signature, &signaturelen, privkey, rnd) == 1) { + break; + } + } + /* Verify. */ + CHECK(secp256k1_ecdsa_verify(message, 32, signature, signaturelen, pubkey, pubkeylen) == 1); + /* Destroy signature and verify again. */ + signature[signaturelen - 1 - secp256k1_rand32() % 20] += 1 + (secp256k1_rand32() % 255); + CHECK(secp256k1_ecdsa_verify(message, 32, signature, signaturelen, pubkey, pubkeylen) != 1); + + /* Compact sign. */ + unsigned char csignature[64]; int recid = 0; + while(1) { + unsigned char rnd[32]; + secp256k1_rand256_test(rnd); + if (secp256k1_ecdsa_sign_compact(message, 32, csignature, privkey, rnd, &recid) == 1) { + break; + } + } + /* Recover. */ + unsigned char recpubkey[65]; int recpubkeylen = 0; + CHECK(secp256k1_ecdsa_recover_compact(message, 32, csignature, recpubkey, &recpubkeylen, pubkeylen == 33, recid) == 1); + CHECK(recpubkeylen == pubkeylen); + CHECK(memcmp(pubkey, recpubkey, pubkeylen) == 0); + /* Destroy signature and verify again. */ + csignature[secp256k1_rand32() % 64] += 1 + (secp256k1_rand32() % 255); + CHECK(secp256k1_ecdsa_recover_compact(message, 32, csignature, recpubkey, &recpubkeylen, pubkeylen == 33, recid) != 1 || + memcmp(pubkey, recpubkey, pubkeylen) != 0); + CHECK(recpubkeylen == pubkeylen); + +} + +void run_ecdsa_end_to_end(void) { + for (int i=0; i<64*count; i++) { + test_ecdsa_end_to_end(); + } +} + +void test_ecdsa_infinity(void) { + const unsigned char msg32[32] = { + 'T', 'h', 'i', 's', ' ', 'i', 's', ' ', + 'a', ' ', 'v', 'e', 'r', 'y', ' ', 's', + 'e', 'c', 'r', 'e', 't', ' ', 'm', 'e', + 's', 's', 'a', 'g', 'e', '.', '.', '.' + }; + const unsigned char sig64[64] = { + // Generated by signing the above message with nonce 'This is the nonce we will use...' + // and secret key 0 (which is not valid), resulting in recid 0. + 0x67, 0xCB, 0x28, 0x5F, 0x9C, 0xD1, 0x94, 0xE8, + 0x40, 0xD6, 0x29, 0x39, 0x7A, 0xF5, 0x56, 0x96, + 0x62, 0xFD, 0xE4, 0x46, 0x49, 0x99, 0x59, 0x63, + 0x17, 0x9A, 0x7D, 0xD1, 0x7B, 0xD2, 0x35, 0x32, + 0x4B, 0x1B, 0x7D, 0xF3, 0x4C, 0xE1, 0xF6, 0x8E, + 0x69, 0x4F, 0xF6, 0xF1, 0x1A, 0xC7, 0x51, 0xDD, + 0x7D, 0xD7, 0x3E, 0x38, 0x7E, 0xE4, 0xFC, 0x86, + 0x6E, 0x1B, 0xE8, 0xEC, 0xC7, 0xDD, 0x95, 0x57 + }; + unsigned char pubkey[65]; + int pubkeylen = 65; + CHECK(!secp256k1_ecdsa_recover_compact(msg32, 32, sig64, pubkey, &pubkeylen, 0, 0)); + CHECK(secp256k1_ecdsa_recover_compact(msg32, 32, sig64, pubkey, &pubkeylen, 0, 1)); + CHECK(!secp256k1_ecdsa_recover_compact(msg32, 32, sig64, pubkey, &pubkeylen, 0, 2)); + CHECK(!secp256k1_ecdsa_recover_compact(msg32, 32, sig64, pubkey, &pubkeylen, 0, 3)); +} + +void run_ecdsa_infinity(void) { + test_ecdsa_infinity(); +} + +#ifdef ENABLE_OPENSSL_TESTS +EC_KEY *get_openssl_key(const secp256k1_scalar_t *key) { + unsigned char privkey[300]; + int privkeylen; + int compr = secp256k1_rand32() & 1; + const unsigned char* pbegin = privkey; + EC_KEY *ec_key = EC_KEY_new_by_curve_name(NID_secp256k1); + CHECK(secp256k1_eckey_privkey_serialize(privkey, &privkeylen, key, compr)); + CHECK(d2i_ECPrivateKey(&ec_key, &pbegin, privkeylen)); + CHECK(EC_KEY_check_key(ec_key)); + return ec_key; +} + +void test_ecdsa_openssl(void) { + secp256k1_scalar_t key, msg; + unsigned char message[32]; + secp256k1_rand256_test(message); + secp256k1_scalar_set_b32(&msg, message, NULL); + random_scalar_order_test(&key); + secp256k1_gej_t qj; + secp256k1_ecmult_gen(&qj, &key); + secp256k1_ge_t q; + secp256k1_ge_set_gej(&q, &qj); + EC_KEY *ec_key = get_openssl_key(&key); + CHECK(ec_key); + unsigned char signature[80]; + unsigned int sigsize = 80; + CHECK(ECDSA_sign(0, message, sizeof(message), signature, &sigsize, ec_key)); + secp256k1_ecdsa_sig_t sig; + CHECK(secp256k1_ecdsa_sig_parse(&sig, signature, sigsize)); + secp256k1_num_t msg_num; + secp256k1_scalar_get_num(&msg_num, &msg); + CHECK(secp256k1_ecdsa_sig_verify(&sig, &q, &msg_num)); + secp256k1_num_inc(&sig.r); + CHECK(!secp256k1_ecdsa_sig_verify(&sig, &q, &msg_num)); + + random_sign(&sig, &key, &msg, NULL); + int secp_sigsize = 80; + CHECK(secp256k1_ecdsa_sig_serialize(signature, &secp_sigsize, &sig)); + CHECK(ECDSA_verify(0, message, sizeof(message), signature, secp_sigsize, ec_key) == 1); + + EC_KEY_free(ec_key); +} + +void run_ecdsa_openssl(void) { + for (int i=0; i<10*count; i++) { + test_ecdsa_openssl(); + } +} +#endif + +int main(int argc, char **argv) { + /* find iteration count */ + if (argc > 1) { + count = strtol(argv[1], NULL, 0); + } + + /* find random seed */ + uint64_t seed; + if (argc > 2) { + seed = strtoull(argv[2], NULL, 0); + } else { + FILE *frand = fopen("/dev/urandom", "r"); + if (!frand || !fread(&seed, sizeof(seed), 1, frand)) { + seed = time(NULL) * 1337; + } + fclose(frand); + } + secp256k1_rand_seed(seed); + + printf("test count = %i\n", count); + printf("random seed = %llu\n", (unsigned long long)seed); + + /* initialize */ + secp256k1_start(SECP256K1_START_SIGN | SECP256K1_START_VERIFY); + + /* num tests */ + run_num_smalltests(); + + /* scalar tests */ + run_scalar_tests(); + + /* field tests */ + run_field_inv(); + run_field_inv_var(); + run_field_inv_all(); + run_field_inv_all_var(); + run_sqr(); + run_sqrt(); + + /* group tests */ + run_ge(); + + /* ecmult tests */ + run_wnaf(); + run_point_times_order(); + run_ecmult_chain(); + + /* ecdsa tests */ + run_ecdsa_sign_verify(); + run_ecdsa_end_to_end(); + run_ecdsa_infinity(); +#ifdef ENABLE_OPENSSL_TESTS + run_ecdsa_openssl(); +#endif + + printf("random run = %llu\n", (unsigned long long)secp256k1_rand32() + ((unsigned long long)secp256k1_rand32() << 32)); + + /* shutdown */ + secp256k1_stop(); + return 0; +} |