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+/***********************************************************************
+ * Copyright (c) 2016 Andrew Poelstra *
+ * 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 <time.h>
+
+#undef USE_ECMULT_STATIC_PRECOMPUTATION
+
+#ifndef EXHAUSTIVE_TEST_ORDER
+/* see group_impl.h for allowable values */
+#define EXHAUSTIVE_TEST_ORDER 13
+#define EXHAUSTIVE_TEST_LAMBDA 9 /* cube root of 1 mod 13 */
+#endif
+
+#include "include/secp256k1.h"
+#include "group.h"
+#include "secp256k1.c"
+#include "testrand_impl.h"
+
+/** stolen from tests.c */
+void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) {
+ CHECK(a->infinity == b->infinity);
+ if (a->infinity) {
+ return;
+ }
+ CHECK(secp256k1_fe_equal_var(&a->x, &b->x));
+ CHECK(secp256k1_fe_equal_var(&a->y, &b->y));
+}
+
+void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) {
+ secp256k1_fe z2s;
+ secp256k1_fe u1, u2, s1, s2;
+ CHECK(a->infinity == b->infinity);
+ if (a->infinity) {
+ return;
+ }
+ /* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */
+ secp256k1_fe_sqr(&z2s, &b->z);
+ secp256k1_fe_mul(&u1, &a->x, &z2s);
+ u2 = b->x; secp256k1_fe_normalize_weak(&u2);
+ secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z);
+ s2 = b->y; secp256k1_fe_normalize_weak(&s2);
+ CHECK(secp256k1_fe_equal_var(&u1, &u2));
+ CHECK(secp256k1_fe_equal_var(&s1, &s2));
+}
+
+void random_fe(secp256k1_fe *x) {
+ unsigned char bin[32];
+ do {
+ secp256k1_rand256(bin);
+ if (secp256k1_fe_set_b32(x, bin)) {
+ return;
+ }
+ } while(1);
+}
+/** END stolen from tests.c */
+
+int secp256k1_nonce_function_smallint(unsigned char *nonce32, const unsigned char *msg32,
+ const unsigned char *key32, const unsigned char *algo16,
+ void *data, unsigned int attempt) {
+ secp256k1_scalar s;
+ int *idata = data;
+ (void)msg32;
+ (void)key32;
+ (void)algo16;
+ /* Some nonces cannot be used because they'd cause s and/or r to be zero.
+ * The signing function has retry logic here that just re-calls the nonce
+ * function with an increased `attempt`. So if attempt > 0 this means we
+ * need to change the nonce to avoid an infinite loop. */
+ if (attempt > 0) {
+ (*idata)++;
+ }
+ secp256k1_scalar_set_int(&s, *idata);
+ secp256k1_scalar_get_b32(nonce32, &s);
+ return 1;
+}
+
+#ifdef USE_ENDOMORPHISM
+void test_exhaustive_endomorphism(const secp256k1_ge *group, int order) {
+ int i;
+ for (i = 0; i < order; i++) {
+ secp256k1_ge res;
+ secp256k1_ge_mul_lambda(&res, &group[i]);
+ ge_equals_ge(&group[i * EXHAUSTIVE_TEST_LAMBDA % EXHAUSTIVE_TEST_ORDER], &res);
+ }
+}
+#endif
+
+void test_exhaustive_addition(const secp256k1_ge *group, const secp256k1_gej *groupj, int order) {
+ int i, j;
+
+ /* Sanity-check (and check infinity functions) */
+ CHECK(secp256k1_ge_is_infinity(&group[0]));
+ CHECK(secp256k1_gej_is_infinity(&groupj[0]));
+ for (i = 1; i < order; i++) {
+ CHECK(!secp256k1_ge_is_infinity(&group[i]));
+ CHECK(!secp256k1_gej_is_infinity(&groupj[i]));
+ }
+
+ /* Check all addition formulae */
+ for (j = 0; j < order; j++) {
+ secp256k1_fe fe_inv;
+ secp256k1_fe_inv(&fe_inv, &groupj[j].z);
+ for (i = 0; i < order; i++) {
+ secp256k1_ge zless_gej;
+ secp256k1_gej tmp;
+ /* add_var */
+ secp256k1_gej_add_var(&tmp, &groupj[i], &groupj[j], NULL);
+ ge_equals_gej(&group[(i + j) % order], &tmp);
+ /* add_ge */
+ if (j > 0) {
+ secp256k1_gej_add_ge(&tmp, &groupj[i], &group[j]);
+ ge_equals_gej(&group[(i + j) % order], &tmp);
+ }
+ /* add_ge_var */
+ secp256k1_gej_add_ge_var(&tmp, &groupj[i], &group[j], NULL);
+ ge_equals_gej(&group[(i + j) % order], &tmp);
+ /* add_zinv_var */
+ zless_gej.infinity = groupj[j].infinity;
+ zless_gej.x = groupj[j].x;
+ zless_gej.y = groupj[j].y;
+ secp256k1_gej_add_zinv_var(&tmp, &groupj[i], &zless_gej, &fe_inv);
+ ge_equals_gej(&group[(i + j) % order], &tmp);
+ }
+ }
+
+ /* Check doubling */
+ for (i = 0; i < order; i++) {
+ secp256k1_gej tmp;
+ if (i > 0) {
+ secp256k1_gej_double_nonzero(&tmp, &groupj[i], NULL);
+ ge_equals_gej(&group[(2 * i) % order], &tmp);
+ }
+ secp256k1_gej_double_var(&tmp, &groupj[i], NULL);
+ ge_equals_gej(&group[(2 * i) % order], &tmp);
+ }
+
+ /* Check negation */
+ for (i = 1; i < order; i++) {
+ secp256k1_ge tmp;
+ secp256k1_gej tmpj;
+ secp256k1_ge_neg(&tmp, &group[i]);
+ ge_equals_ge(&group[order - i], &tmp);
+ secp256k1_gej_neg(&tmpj, &groupj[i]);
+ ge_equals_gej(&group[order - i], &tmpj);
+ }
+}
+
+void test_exhaustive_ecmult(const secp256k1_context *ctx, const secp256k1_ge *group, const secp256k1_gej *groupj, int order) {
+ int i, j, r_log;
+ for (r_log = 1; r_log < order; r_log++) {
+ for (j = 0; j < order; j++) {
+ for (i = 0; i < order; i++) {
+ secp256k1_gej tmp;
+ secp256k1_scalar na, ng;
+ secp256k1_scalar_set_int(&na, i);
+ secp256k1_scalar_set_int(&ng, j);
+
+ secp256k1_ecmult(&ctx->ecmult_ctx, &tmp, &groupj[r_log], &na, &ng);
+ ge_equals_gej(&group[(i * r_log + j) % order], &tmp);
+
+ if (i > 0) {
+ secp256k1_ecmult_const(&tmp, &group[i], &ng);
+ ge_equals_gej(&group[(i * j) % order], &tmp);
+ }
+ }
+ }
+ }
+}
+
+void r_from_k(secp256k1_scalar *r, const secp256k1_ge *group, int k) {
+ secp256k1_fe x;
+ unsigned char x_bin[32];
+ k %= EXHAUSTIVE_TEST_ORDER;
+ x = group[k].x;
+ secp256k1_fe_normalize(&x);
+ secp256k1_fe_get_b32(x_bin, &x);
+ secp256k1_scalar_set_b32(r, x_bin, NULL);
+}
+
+void test_exhaustive_verify(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
+ int s, r, msg, key;
+ for (s = 1; s < order; s++) {
+ for (r = 1; r < order; r++) {
+ for (msg = 1; msg < order; msg++) {
+ for (key = 1; key < order; key++) {
+ secp256k1_ge nonconst_ge;
+ secp256k1_ecdsa_signature sig;
+ secp256k1_pubkey pk;
+ secp256k1_scalar sk_s, msg_s, r_s, s_s;
+ secp256k1_scalar s_times_k_s, msg_plus_r_times_sk_s;
+ int k, should_verify;
+ unsigned char msg32[32];
+
+ secp256k1_scalar_set_int(&s_s, s);
+ secp256k1_scalar_set_int(&r_s, r);
+ secp256k1_scalar_set_int(&msg_s, msg);
+ secp256k1_scalar_set_int(&sk_s, key);
+
+ /* Verify by hand */
+ /* Run through every k value that gives us this r and check that *one* works.
+ * Note there could be none, there could be multiple, ECDSA is weird. */
+ should_verify = 0;
+ for (k = 0; k < order; k++) {
+ secp256k1_scalar check_x_s;
+ r_from_k(&check_x_s, group, k);
+ if (r_s == check_x_s) {
+ secp256k1_scalar_set_int(&s_times_k_s, k);
+ secp256k1_scalar_mul(&s_times_k_s, &s_times_k_s, &s_s);
+ secp256k1_scalar_mul(&msg_plus_r_times_sk_s, &r_s, &sk_s);
+ secp256k1_scalar_add(&msg_plus_r_times_sk_s, &msg_plus_r_times_sk_s, &msg_s);
+ should_verify |= secp256k1_scalar_eq(&s_times_k_s, &msg_plus_r_times_sk_s);
+ }
+ }
+ /* nb we have a "high s" rule */
+ should_verify &= !secp256k1_scalar_is_high(&s_s);
+
+ /* Verify by calling verify */
+ secp256k1_ecdsa_signature_save(&sig, &r_s, &s_s);
+ memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge));
+ secp256k1_pubkey_save(&pk, &nonconst_ge);
+ secp256k1_scalar_get_b32(msg32, &msg_s);
+ CHECK(should_verify ==
+ secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk));
+ }
+ }
+ }
+ }
+}
+
+void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
+ int i, j, k;
+
+ /* Loop */
+ for (i = 1; i < order; i++) { /* message */
+ for (j = 1; j < order; j++) { /* key */
+ for (k = 1; k < order; k++) { /* nonce */
+ secp256k1_ecdsa_signature sig;
+ secp256k1_scalar sk, msg, r, s, expected_r;
+ unsigned char sk32[32], msg32[32];
+ secp256k1_scalar_set_int(&msg, i);
+ secp256k1_scalar_set_int(&sk, j);
+ secp256k1_scalar_get_b32(sk32, &sk);
+ secp256k1_scalar_get_b32(msg32, &msg);
+
+ secp256k1_ecdsa_sign(ctx, &sig, msg32, sk32, secp256k1_nonce_function_smallint, &k);
+
+ secp256k1_ecdsa_signature_load(ctx, &r, &s, &sig);
+ /* Note that we compute expected_r *after* signing -- this is important
+ * because our nonce-computing function function might change k during
+ * signing. */
+ r_from_k(&expected_r, group, k);
+ CHECK(r == expected_r);
+ CHECK((k * s) % order == (i + r * j) % order ||
+ (k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order);
+ }
+ }
+ }
+
+ /* We would like to verify zero-knowledge here by counting how often every
+ * possible (s, r) tuple appears, but because the group order is larger
+ * than the field order, when coercing the x-values to scalar values, some
+ * appear more often than others, so we are actually not zero-knowledge.
+ * (This effect also appears in the real code, but the difference is on the
+ * order of 1/2^128th the field order, so the deviation is not useful to a
+ * computationally bounded attacker.)
+ */
+}
+
+int main(void) {
+ int i;
+ secp256k1_gej groupj[EXHAUSTIVE_TEST_ORDER];
+ secp256k1_ge group[EXHAUSTIVE_TEST_ORDER];
+
+ /* Build context */
+ secp256k1_context *ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+
+ /* TODO set z = 1, then do num_tests runs with random z values */
+
+ /* Generate the entire group */
+ secp256k1_gej_set_infinity(&groupj[0]);
+ secp256k1_ge_set_gej(&group[0], &groupj[0]);
+ for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) {
+ /* Set a different random z-value for each Jacobian point */
+ secp256k1_fe z;
+ random_fe(&z);
+
+ secp256k1_gej_add_ge(&groupj[i], &groupj[i - 1], &secp256k1_ge_const_g);
+ secp256k1_ge_set_gej(&group[i], &groupj[i]);
+ secp256k1_gej_rescale(&groupj[i], &z);
+
+ /* Verify against ecmult_gen */
+ {
+ secp256k1_scalar scalar_i;
+ secp256k1_gej generatedj;
+ secp256k1_ge generated;
+
+ secp256k1_scalar_set_int(&scalar_i, i);
+ secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &generatedj, &scalar_i);
+ secp256k1_ge_set_gej(&generated, &generatedj);
+
+ CHECK(group[i].infinity == 0);
+ CHECK(generated.infinity == 0);
+ CHECK(secp256k1_fe_equal_var(&generated.x, &group[i].x));
+ CHECK(secp256k1_fe_equal_var(&generated.y, &group[i].y));
+ }
+ }
+
+ /* Run the tests */
+#ifdef USE_ENDOMORPHISM
+ test_exhaustive_endomorphism(group, EXHAUSTIVE_TEST_ORDER);
+#endif
+ test_exhaustive_addition(group, groupj, EXHAUSTIVE_TEST_ORDER);
+ test_exhaustive_ecmult(ctx, group, groupj, EXHAUSTIVE_TEST_ORDER);
+ test_exhaustive_sign(ctx, group, EXHAUSTIVE_TEST_ORDER);
+ test_exhaustive_verify(ctx, group, EXHAUSTIVE_TEST_ORDER);
+
+ return 0;
+}
+
generated by cgit v1.2.3 (git 2.26.2) at 2024-11-14 03:15:12 +0000