512 lines
20 KiB
C
512 lines
20 KiB
C
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/***********************************************************************
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* Copyright (c) 2016 Andrew Poelstra *
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* Distributed under the MIT software license, see the accompanying *
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* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
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**********************************************************************/
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#if defined HAVE_CONFIG_H
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#include "libsecp256k1-config.h"
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#endif
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#include <stdio.h>
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#include <stdlib.h>
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#include <time.h>
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#undef USE_ECMULT_STATIC_PRECOMPUTATION
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#ifndef EXHAUSTIVE_TEST_ORDER
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/* see group_impl.h for allowable values */
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#define EXHAUSTIVE_TEST_ORDER 13
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#define EXHAUSTIVE_TEST_LAMBDA 9 /* cube root of 1 mod 13 */
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#endif
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#include "include/secp256k1.h"
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#include "group.h"
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#include "secp256k1.c"
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#include "testrand_impl.h"
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#ifdef ENABLE_MODULE_RECOVERY
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#include "src/modules/recovery/main_impl.h"
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#include "include/secp256k1_recovery.h"
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#endif
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/** stolen from tests.c */
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void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) {
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CHECK(a->infinity == b->infinity);
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if (a->infinity) {
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return;
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}
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CHECK(secp256k1_fe_equal_var(&a->x, &b->x));
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CHECK(secp256k1_fe_equal_var(&a->y, &b->y));
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}
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void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) {
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secp256k1_fe z2s;
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secp256k1_fe u1, u2, s1, s2;
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CHECK(a->infinity == b->infinity);
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if (a->infinity) {
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return;
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}
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/* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */
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secp256k1_fe_sqr(&z2s, &b->z);
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secp256k1_fe_mul(&u1, &a->x, &z2s);
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u2 = b->x; secp256k1_fe_normalize_weak(&u2);
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secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z);
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s2 = b->y; secp256k1_fe_normalize_weak(&s2);
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CHECK(secp256k1_fe_equal_var(&u1, &u2));
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CHECK(secp256k1_fe_equal_var(&s1, &s2));
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}
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void random_fe(secp256k1_fe *x) {
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unsigned char bin[32];
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do {
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secp256k1_rand256(bin);
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if (secp256k1_fe_set_b32(x, bin)) {
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return;
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}
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} while(1);
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}
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/** END stolen from tests.c */
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int secp256k1_nonce_function_smallint(unsigned char *nonce32, const unsigned char *msg32,
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const unsigned char *key32, const unsigned char *algo16,
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void *data, unsigned int attempt) {
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secp256k1_scalar s;
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int *idata = data;
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(void)msg32;
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(void)key32;
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(void)algo16;
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/* Some nonces cannot be used because they'd cause s and/or r to be zero.
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* The signing function has retry logic here that just re-calls the nonce
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* function with an increased `attempt`. So if attempt > 0 this means we
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* need to change the nonce to avoid an infinite loop. */
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if (attempt > 0) {
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*idata = (*idata + 1) % EXHAUSTIVE_TEST_ORDER;
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}
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secp256k1_scalar_set_int(&s, *idata);
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secp256k1_scalar_get_b32(nonce32, &s);
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return 1;
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}
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#ifdef USE_ENDOMORPHISM
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void test_exhaustive_endomorphism(const secp256k1_ge *group, int order) {
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int i;
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for (i = 0; i < order; i++) {
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secp256k1_ge res;
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secp256k1_ge_mul_lambda(&res, &group[i]);
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ge_equals_ge(&group[i * EXHAUSTIVE_TEST_LAMBDA % EXHAUSTIVE_TEST_ORDER], &res);
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}
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}
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#endif
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void test_exhaustive_addition(const secp256k1_ge *group, const secp256k1_gej *groupj, int order) {
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int i, j;
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/* Sanity-check (and check infinity functions) */
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CHECK(secp256k1_ge_is_infinity(&group[0]));
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CHECK(secp256k1_gej_is_infinity(&groupj[0]));
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for (i = 1; i < order; i++) {
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CHECK(!secp256k1_ge_is_infinity(&group[i]));
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CHECK(!secp256k1_gej_is_infinity(&groupj[i]));
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}
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/* Check all addition formulae */
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for (j = 0; j < order; j++) {
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secp256k1_fe fe_inv;
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secp256k1_fe_inv(&fe_inv, &groupj[j].z);
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for (i = 0; i < order; i++) {
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secp256k1_ge zless_gej;
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secp256k1_gej tmp;
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/* add_var */
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secp256k1_gej_add_var(&tmp, &groupj[i], &groupj[j], NULL);
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ge_equals_gej(&group[(i + j) % order], &tmp);
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/* add_ge */
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if (j > 0) {
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secp256k1_gej_add_ge(&tmp, &groupj[i], &group[j]);
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ge_equals_gej(&group[(i + j) % order], &tmp);
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}
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/* add_ge_var */
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secp256k1_gej_add_ge_var(&tmp, &groupj[i], &group[j], NULL);
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ge_equals_gej(&group[(i + j) % order], &tmp);
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/* add_zinv_var */
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zless_gej.infinity = groupj[j].infinity;
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zless_gej.x = groupj[j].x;
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zless_gej.y = groupj[j].y;
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secp256k1_gej_add_zinv_var(&tmp, &groupj[i], &zless_gej, &fe_inv);
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ge_equals_gej(&group[(i + j) % order], &tmp);
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}
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}
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/* Check doubling */
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for (i = 0; i < order; i++) {
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secp256k1_gej tmp;
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if (i > 0) {
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secp256k1_gej_double_nonzero(&tmp, &groupj[i], NULL);
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ge_equals_gej(&group[(2 * i) % order], &tmp);
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}
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secp256k1_gej_double_var(&tmp, &groupj[i], NULL);
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ge_equals_gej(&group[(2 * i) % order], &tmp);
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}
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/* Check negation */
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for (i = 1; i < order; i++) {
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secp256k1_ge tmp;
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secp256k1_gej tmpj;
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secp256k1_ge_neg(&tmp, &group[i]);
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ge_equals_ge(&group[order - i], &tmp);
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secp256k1_gej_neg(&tmpj, &groupj[i]);
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ge_equals_gej(&group[order - i], &tmpj);
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}
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}
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void test_exhaustive_ecmult(const secp256k1_context *ctx, const secp256k1_ge *group, const secp256k1_gej *groupj, int order) {
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int i, j, r_log;
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for (r_log = 1; r_log < order; r_log++) {
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for (j = 0; j < order; j++) {
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for (i = 0; i < order; i++) {
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secp256k1_gej tmp;
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secp256k1_scalar na, ng;
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secp256k1_scalar_set_int(&na, i);
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secp256k1_scalar_set_int(&ng, j);
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secp256k1_ecmult(&ctx->ecmult_ctx, &tmp, &groupj[r_log], &na, &ng);
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ge_equals_gej(&group[(i * r_log + j) % order], &tmp);
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if (i > 0) {
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secp256k1_ecmult_const(&tmp, &group[i], &ng, 256);
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ge_equals_gej(&group[(i * j) % order], &tmp);
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}
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}
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}
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}
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}
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typedef struct {
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secp256k1_scalar sc[2];
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secp256k1_ge pt[2];
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} ecmult_multi_data;
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static int ecmult_multi_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) {
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ecmult_multi_data *data = (ecmult_multi_data*) cbdata;
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*sc = data->sc[idx];
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*pt = data->pt[idx];
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return 1;
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}
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void test_exhaustive_ecmult_multi(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
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int i, j, k, x, y;
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secp256k1_scratch *scratch = secp256k1_scratch_create(&ctx->error_callback, 4096);
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for (i = 0; i < order; i++) {
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for (j = 0; j < order; j++) {
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for (k = 0; k < order; k++) {
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for (x = 0; x < order; x++) {
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for (y = 0; y < order; y++) {
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secp256k1_gej tmp;
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secp256k1_scalar g_sc;
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ecmult_multi_data data;
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secp256k1_scalar_set_int(&data.sc[0], i);
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secp256k1_scalar_set_int(&data.sc[1], j);
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secp256k1_scalar_set_int(&g_sc, k);
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data.pt[0] = group[x];
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data.pt[1] = group[y];
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secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &tmp, &g_sc, ecmult_multi_callback, &data, 2);
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ge_equals_gej(&group[(i * x + j * y + k) % order], &tmp);
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}
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}
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}
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}
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}
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secp256k1_scratch_destroy(scratch);
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}
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void r_from_k(secp256k1_scalar *r, const secp256k1_ge *group, int k) {
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secp256k1_fe x;
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unsigned char x_bin[32];
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k %= EXHAUSTIVE_TEST_ORDER;
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x = group[k].x;
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secp256k1_fe_normalize(&x);
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secp256k1_fe_get_b32(x_bin, &x);
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secp256k1_scalar_set_b32(r, x_bin, NULL);
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}
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void test_exhaustive_verify(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
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int s, r, msg, key;
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for (s = 1; s < order; s++) {
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for (r = 1; r < order; r++) {
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for (msg = 1; msg < order; msg++) {
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for (key = 1; key < order; key++) {
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secp256k1_ge nonconst_ge;
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secp256k1_ecdsa_signature sig;
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secp256k1_pubkey pk;
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secp256k1_scalar sk_s, msg_s, r_s, s_s;
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secp256k1_scalar s_times_k_s, msg_plus_r_times_sk_s;
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int k, should_verify;
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unsigned char msg32[32];
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secp256k1_scalar_set_int(&s_s, s);
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secp256k1_scalar_set_int(&r_s, r);
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secp256k1_scalar_set_int(&msg_s, msg);
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secp256k1_scalar_set_int(&sk_s, key);
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/* Verify by hand */
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/* Run through every k value that gives us this r and check that *one* works.
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* Note there could be none, there could be multiple, ECDSA is weird. */
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should_verify = 0;
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for (k = 0; k < order; k++) {
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secp256k1_scalar check_x_s;
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r_from_k(&check_x_s, group, k);
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if (r_s == check_x_s) {
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secp256k1_scalar_set_int(&s_times_k_s, k);
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secp256k1_scalar_mul(&s_times_k_s, &s_times_k_s, &s_s);
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secp256k1_scalar_mul(&msg_plus_r_times_sk_s, &r_s, &sk_s);
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secp256k1_scalar_add(&msg_plus_r_times_sk_s, &msg_plus_r_times_sk_s, &msg_s);
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should_verify |= secp256k1_scalar_eq(&s_times_k_s, &msg_plus_r_times_sk_s);
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}
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}
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/* nb we have a "high s" rule */
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should_verify &= !secp256k1_scalar_is_high(&s_s);
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/* Verify by calling verify */
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secp256k1_ecdsa_signature_save(&sig, &r_s, &s_s);
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memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge));
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secp256k1_pubkey_save(&pk, &nonconst_ge);
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secp256k1_scalar_get_b32(msg32, &msg_s);
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CHECK(should_verify ==
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secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk));
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}
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}
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}
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}
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}
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void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
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int i, j, k;
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/* Loop */
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for (i = 1; i < order; i++) { /* message */
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for (j = 1; j < order; j++) { /* key */
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for (k = 1; k < order; k++) { /* nonce */
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const int starting_k = k;
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secp256k1_ecdsa_signature sig;
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secp256k1_scalar sk, msg, r, s, expected_r;
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unsigned char sk32[32], msg32[32];
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secp256k1_scalar_set_int(&msg, i);
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secp256k1_scalar_set_int(&sk, j);
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secp256k1_scalar_get_b32(sk32, &sk);
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secp256k1_scalar_get_b32(msg32, &msg);
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secp256k1_ecdsa_sign(ctx, &sig, msg32, sk32, secp256k1_nonce_function_smallint, &k);
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secp256k1_ecdsa_signature_load(ctx, &r, &s, &sig);
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/* Note that we compute expected_r *after* signing -- this is important
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* because our nonce-computing function function might change k during
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* signing. */
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r_from_k(&expected_r, group, k);
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CHECK(r == expected_r);
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CHECK((k * s) % order == (i + r * j) % order ||
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(k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order);
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/* Overflow means we've tried every possible nonce */
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if (k < starting_k) {
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break;
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}
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}
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}
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}
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/* 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.)
|
||
|
|
*/
|
||
|
|
}
|
||
|
|
|
||
|
|
#ifdef ENABLE_MODULE_RECOVERY
|
||
|
|
void test_exhaustive_recovery_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 */
|
||
|
|
const int starting_k = k;
|
||
|
|
secp256k1_fe r_dot_y_normalized;
|
||
|
|
secp256k1_ecdsa_recoverable_signature rsig;
|
||
|
|
secp256k1_ecdsa_signature sig;
|
||
|
|
secp256k1_scalar sk, msg, r, s, expected_r;
|
||
|
|
unsigned char sk32[32], msg32[32];
|
||
|
|
int expected_recid;
|
||
|
|
int recid;
|
||
|
|
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_recoverable(ctx, &rsig, msg32, sk32, secp256k1_nonce_function_smallint, &k);
|
||
|
|
|
||
|
|
/* Check directly */
|
||
|
|
secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, &rsig);
|
||
|
|
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);
|
||
|
|
/* In computing the recid, there is an overflow condition that is disabled in
|
||
|
|
* scalar_low_impl.h `secp256k1_scalar_set_b32` because almost every r.y value
|
||
|
|
* will exceed the group order, and our signing code always holds out for r
|
||
|
|
* values that don't overflow, so with a proper overflow check the tests would
|
||
|
|
* loop indefinitely. */
|
||
|
|
r_dot_y_normalized = group[k].y;
|
||
|
|
secp256k1_fe_normalize(&r_dot_y_normalized);
|
||
|
|
/* Also the recovery id is flipped depending if we hit the low-s branch */
|
||
|
|
if ((k * s) % order == (i + r * j) % order) {
|
||
|
|
expected_recid = secp256k1_fe_is_odd(&r_dot_y_normalized) ? 1 : 0;
|
||
|
|
} else {
|
||
|
|
expected_recid = secp256k1_fe_is_odd(&r_dot_y_normalized) ? 0 : 1;
|
||
|
|
}
|
||
|
|
CHECK(recid == expected_recid);
|
||
|
|
|
||
|
|
/* Convert to a standard sig then check */
|
||
|
|
secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig);
|
||
|
|
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);
|
||
|
|
|
||
|
|
/* Overflow means we've tried every possible nonce */
|
||
|
|
if (k < starting_k) {
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
void test_exhaustive_recovery_verify(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
|
||
|
|
/* This is essentially a copy of test_exhaustive_verify, with recovery added */
|
||
|
|
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_recoverable_signature rsig;
|
||
|
|
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 recid = 0;
|
||
|
|
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);
|
||
|
|
secp256k1_scalar_get_b32(msg32, &msg_s);
|
||
|
|
|
||
|
|
/* 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);
|
||
|
|
|
||
|
|
/* We would like to try recovering the pubkey and checking that it matches,
|
||
|
|
* but pubkey recovery is impossible in the exhaustive tests (the reason
|
||
|
|
* being that there are 12 nonzero r values, 12 nonzero points, and no
|
||
|
|
* overlap between the sets, so there are no valid signatures). */
|
||
|
|
|
||
|
|
/* Verify by converting to a standard signature and calling verify */
|
||
|
|
secp256k1_ecdsa_recoverable_signature_save(&rsig, &r_s, &s_s, recid);
|
||
|
|
secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig);
|
||
|
|
memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge));
|
||
|
|
secp256k1_pubkey_save(&pk, &nonconst_ge);
|
||
|
|
CHECK(should_verify ==
|
||
|
|
secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
|
||
|
|
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_ecmult_multi(ctx, group, EXHAUSTIVE_TEST_ORDER);
|
||
|
|
test_exhaustive_sign(ctx, group, EXHAUSTIVE_TEST_ORDER);
|
||
|
|
test_exhaustive_verify(ctx, group, EXHAUSTIVE_TEST_ORDER);
|
||
|
|
|
||
|
|
#ifdef ENABLE_MODULE_RECOVERY
|
||
|
|
test_exhaustive_recovery_sign(ctx, group, EXHAUSTIVE_TEST_ORDER);
|
||
|
|
test_exhaustive_recovery_verify(ctx, group, EXHAUSTIVE_TEST_ORDER);
|
||
|
|
#endif
|
||
|
|
|
||
|
|
secp256k1_context_destroy(ctx);
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|