1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
|
/***********************************************************************
* Copyright (c) 2016 Andrew Poelstra *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or https://www.opensource.org/licenses/mit-license.php.*
***********************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#ifndef EXHAUSTIVE_TEST_ORDER
/* see group_impl.h for allowable values */
#define EXHAUSTIVE_TEST_ORDER 13
#endif
/* These values of B are all values in [1, 8] that result in a curve with even order. */
#define EXHAUSTIVE_TEST_CURVE_HAS_EVEN_ORDER (SECP256K1_B == 1 || SECP256K1_B == 6 || SECP256K1_B == 8)
#ifdef USE_EXTERNAL_DEFAULT_CALLBACKS
#pragma message("Ignoring USE_EXTERNAL_CALLBACKS in exhaustive_tests.")
#undef USE_EXTERNAL_DEFAULT_CALLBACKS
#endif
#include "secp256k1.c"
#include "../include/secp256k1.h"
#include "assumptions.h"
#include "group.h"
#include "testrand_impl.h"
#include "ecmult_compute_table_impl.h"
#include "ecmult_gen_compute_table_impl.h"
#include "testutil.h"
#include "util.h"
static int count = 2;
static uint32_t num_cores = 1;
static uint32_t this_core = 0;
SECP256K1_INLINE static int skip_section(uint64_t* iter) {
if (num_cores == 1) return 0;
*iter += 0xe7037ed1a0b428dbULL;
return ((((uint32_t)*iter ^ (*iter >> 32)) * num_cores) >> 32) != this_core;
}
static 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 = (*idata + 1) % EXHAUSTIVE_TEST_ORDER;
}
secp256k1_scalar_set_int(&s, *idata);
secp256k1_scalar_get_b32(nonce32, &s);
return 1;
}
static void test_exhaustive_endomorphism(const secp256k1_ge *group) {
int i;
for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) {
secp256k1_ge res;
secp256k1_ge_mul_lambda(&res, &group[i]);
CHECK(secp256k1_ge_eq_var(&group[i * EXHAUSTIVE_TEST_LAMBDA % EXHAUSTIVE_TEST_ORDER], &res));
}
}
static void test_exhaustive_addition(const secp256k1_ge *group, const secp256k1_gej *groupj) {
int i, j;
uint64_t iter = 0;
/* Sanity-check (and check infinity functions) */
CHECK(secp256k1_ge_is_infinity(&group[0]));
CHECK(secp256k1_gej_is_infinity(&groupj[0]));
for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) {
CHECK(!secp256k1_ge_is_infinity(&group[i]));
CHECK(!secp256k1_gej_is_infinity(&groupj[i]));
}
/* Check all addition formulae */
for (j = 0; j < EXHAUSTIVE_TEST_ORDER; j++) {
secp256k1_fe fe_inv;
if (skip_section(&iter)) continue;
secp256k1_fe_inv(&fe_inv, &groupj[j].z);
for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) {
secp256k1_ge zless_gej;
secp256k1_gej tmp;
/* add_var */
secp256k1_gej_add_var(&tmp, &groupj[i], &groupj[j], NULL);
CHECK(secp256k1_gej_eq_ge_var(&tmp, &group[(i + j) % EXHAUSTIVE_TEST_ORDER]));
/* add_ge */
if (j > 0) {
secp256k1_gej_add_ge(&tmp, &groupj[i], &group[j]);
CHECK(secp256k1_gej_eq_ge_var(&tmp, &group[(i + j) % EXHAUSTIVE_TEST_ORDER]));
}
/* add_ge_var */
secp256k1_gej_add_ge_var(&tmp, &groupj[i], &group[j], NULL);
CHECK(secp256k1_gej_eq_ge_var(&tmp, &group[(i + j) % EXHAUSTIVE_TEST_ORDER]));
/* 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);
CHECK(secp256k1_gej_eq_ge_var(&tmp, &group[(i + j) % EXHAUSTIVE_TEST_ORDER]));
}
}
/* Check doubling */
for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) {
secp256k1_gej tmp;
secp256k1_gej_double(&tmp, &groupj[i]);
CHECK(secp256k1_gej_eq_ge_var(&tmp, &group[(2 * i) % EXHAUSTIVE_TEST_ORDER]));
secp256k1_gej_double_var(&tmp, &groupj[i], NULL);
CHECK(secp256k1_gej_eq_ge_var(&tmp, &group[(2 * i) % EXHAUSTIVE_TEST_ORDER]));
}
/* Check negation */
for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) {
secp256k1_ge tmp;
secp256k1_gej tmpj;
secp256k1_ge_neg(&tmp, &group[i]);
CHECK(secp256k1_ge_eq_var(&tmp, &group[EXHAUSTIVE_TEST_ORDER - i]));
secp256k1_gej_neg(&tmpj, &groupj[i]);
CHECK(secp256k1_gej_eq_ge_var(&tmpj, &group[EXHAUSTIVE_TEST_ORDER - i]));
}
}
static void test_exhaustive_ecmult(const secp256k1_ge *group, const secp256k1_gej *groupj) {
int i, j, r_log;
uint64_t iter = 0;
for (r_log = 1; r_log < EXHAUSTIVE_TEST_ORDER; r_log++) {
for (j = 0; j < EXHAUSTIVE_TEST_ORDER; j++) {
if (skip_section(&iter)) continue;
for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) {
secp256k1_gej tmp;
secp256k1_scalar na, ng;
secp256k1_scalar_set_int(&na, i);
secp256k1_scalar_set_int(&ng, j);
secp256k1_ecmult(&tmp, &groupj[r_log], &na, &ng);
CHECK(secp256k1_gej_eq_ge_var(&tmp, &group[(i * r_log + j) % EXHAUSTIVE_TEST_ORDER]));
}
}
}
for (j = 0; j < EXHAUSTIVE_TEST_ORDER; j++) {
for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) {
int ret;
secp256k1_gej tmp;
secp256k1_fe xn, xd, tmpf;
secp256k1_scalar ng;
if (skip_section(&iter)) continue;
secp256k1_scalar_set_int(&ng, j);
/* Test secp256k1_ecmult_const. */
secp256k1_ecmult_const(&tmp, &group[i], &ng);
CHECK(secp256k1_gej_eq_ge_var(&tmp, &group[(i * j) % EXHAUSTIVE_TEST_ORDER]));
if (i != 0 && j != 0) {
/* Test secp256k1_ecmult_const_xonly with all curve X coordinates, and xd=NULL. */
ret = secp256k1_ecmult_const_xonly(&tmpf, &group[i].x, NULL, &ng, 0);
CHECK(ret);
CHECK(secp256k1_fe_equal(&tmpf, &group[(i * j) % EXHAUSTIVE_TEST_ORDER].x));
/* Test secp256k1_ecmult_const_xonly with all curve X coordinates, with random xd. */
random_fe_non_zero(&xd);
secp256k1_fe_mul(&xn, &xd, &group[i].x);
ret = secp256k1_ecmult_const_xonly(&tmpf, &xn, &xd, &ng, 0);
CHECK(ret);
CHECK(secp256k1_fe_equal(&tmpf, &group[(i * j) % EXHAUSTIVE_TEST_ORDER].x));
}
}
}
}
typedef struct {
secp256k1_scalar sc[2];
secp256k1_ge pt[2];
} ecmult_multi_data;
static int ecmult_multi_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) {
ecmult_multi_data *data = (ecmult_multi_data*) cbdata;
*sc = data->sc[idx];
*pt = data->pt[idx];
return 1;
}
static void test_exhaustive_ecmult_multi(const secp256k1_context *ctx, const secp256k1_ge *group) {
int i, j, k, x, y;
uint64_t iter = 0;
secp256k1_scratch *scratch = secp256k1_scratch_create(&ctx->error_callback, 4096);
for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) {
for (j = 0; j < EXHAUSTIVE_TEST_ORDER; j++) {
for (k = 0; k < EXHAUSTIVE_TEST_ORDER; k++) {
for (x = 0; x < EXHAUSTIVE_TEST_ORDER; x++) {
if (skip_section(&iter)) continue;
for (y = 0; y < EXHAUSTIVE_TEST_ORDER; y++) {
secp256k1_gej tmp;
secp256k1_scalar g_sc;
ecmult_multi_data data;
secp256k1_scalar_set_int(&data.sc[0], i);
secp256k1_scalar_set_int(&data.sc[1], j);
secp256k1_scalar_set_int(&g_sc, k);
data.pt[0] = group[x];
data.pt[1] = group[y];
secp256k1_ecmult_multi_var(&ctx->error_callback, scratch, &tmp, &g_sc, ecmult_multi_callback, &data, 2);
CHECK(secp256k1_gej_eq_ge_var(&tmp, &group[(i * x + j * y + k) % EXHAUSTIVE_TEST_ORDER]));
}
}
}
}
}
secp256k1_scratch_destroy(&ctx->error_callback, scratch);
}
static void r_from_k(secp256k1_scalar *r, const secp256k1_ge *group, int k, int* overflow) {
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, overflow);
}
static void test_exhaustive_verify(const secp256k1_context *ctx, const secp256k1_ge *group) {
int s, r, msg, key;
uint64_t iter = 0;
for (s = 1; s < EXHAUSTIVE_TEST_ORDER; s++) {
for (r = 1; r < EXHAUSTIVE_TEST_ORDER; r++) {
for (msg = 1; msg < EXHAUSTIVE_TEST_ORDER; msg++) {
for (key = 1; key < EXHAUSTIVE_TEST_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];
if (skip_section(&iter)) continue;
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 < EXHAUSTIVE_TEST_ORDER; k++) {
secp256k1_scalar check_x_s;
r_from_k(&check_x_s, group, k, NULL);
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));
}
}
}
}
}
static void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *group) {
int i, j, k;
uint64_t iter = 0;
/* Loop */
for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) { /* message */
for (j = 1; j < EXHAUSTIVE_TEST_ORDER; j++) { /* key */
if (skip_section(&iter)) continue;
for (k = 1; k < EXHAUSTIVE_TEST_ORDER; k++) { /* nonce */
const int starting_k = k;
int ret;
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);
ret = secp256k1_ecdsa_sign(ctx, &sig, msg32, sk32, secp256k1_nonce_function_smallint, &k);
CHECK(ret == 1);
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, NULL);
CHECK(r == expected_r);
CHECK((k * s) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER ||
(k * (EXHAUSTIVE_TEST_ORDER - s)) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER);
/* Overflow means we've tried every possible nonce */
if (k < starting_k) {
break;
}
}
}
}
/* 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
#include "modules/recovery/tests_exhaustive_impl.h"
#endif
#ifdef ENABLE_MODULE_EXTRAKEYS
#include "modules/extrakeys/tests_exhaustive_impl.h"
#endif
#ifdef ENABLE_MODULE_SCHNORRSIG
#include "modules/schnorrsig/tests_exhaustive_impl.h"
#endif
#ifdef ENABLE_MODULE_ELLSWIFT
#include "modules/ellswift/tests_exhaustive_impl.h"
#endif
int main(int argc, char** argv) {
int i;
secp256k1_gej groupj[EXHAUSTIVE_TEST_ORDER];
secp256k1_ge group[EXHAUSTIVE_TEST_ORDER];
unsigned char rand32[32];
secp256k1_context *ctx;
/* Disable buffering for stdout to improve reliability of getting
* diagnostic information. Happens right at the start of main because
* setbuf must be used before any other operation on the stream. */
setbuf(stdout, NULL);
/* Also disable buffering for stderr because it's not guaranteed that it's
* unbuffered on all systems. */
setbuf(stderr, NULL);
printf("Exhaustive tests for order %lu\n", (unsigned long)EXHAUSTIVE_TEST_ORDER);
/* find iteration count */
if (argc > 1) {
count = strtol(argv[1], NULL, 0);
}
printf("test count = %i\n", count);
/* find random seed */
secp256k1_testrand_init(argc > 2 ? argv[2] : NULL);
/* set up split processing */
if (argc > 4) {
num_cores = strtol(argv[3], NULL, 0);
this_core = strtol(argv[4], NULL, 0);
if (num_cores < 1 || this_core >= num_cores) {
fprintf(stderr, "Usage: %s [count] [seed] [numcores] [thiscore]\n", argv[0]);
return 1;
}
printf("running tests for core %lu (out of [0..%lu])\n", (unsigned long)this_core, (unsigned long)num_cores - 1);
}
/* Recreate the ecmult{,_gen} tables using the right generator (as selected via EXHAUSTIVE_TEST_ORDER) */
secp256k1_ecmult_gen_compute_table(&secp256k1_ecmult_gen_prec_table[0][0], &secp256k1_ge_const_g, ECMULT_GEN_PREC_BITS);
secp256k1_ecmult_compute_two_tables(secp256k1_pre_g, secp256k1_pre_g_128, WINDOW_G, &secp256k1_ge_const_g);
while (count--) {
/* Build context */
ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
secp256k1_testrand256(rand32);
CHECK(secp256k1_context_randomize(ctx, rand32));
/* 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++) {
secp256k1_gej_add_ge(&groupj[i], &groupj[i - 1], &secp256k1_ge_const_g);
secp256k1_ge_set_gej(&group[i], &groupj[i]);
if (count != 0) {
/* Set a different random z-value for each Jacobian point, except z=1
is used in the last iteration. */
secp256k1_fe z;
random_fe(&z);
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(&generated.x, &group[i].x));
CHECK(secp256k1_fe_equal(&generated.y, &group[i].y));
}
}
/* Run the tests */
test_exhaustive_endomorphism(group);
test_exhaustive_addition(group, groupj);
test_exhaustive_ecmult(group, groupj);
test_exhaustive_ecmult_multi(ctx, group);
test_exhaustive_sign(ctx, group);
test_exhaustive_verify(ctx, group);
#ifdef ENABLE_MODULE_RECOVERY
test_exhaustive_recovery(ctx, group);
#endif
#ifdef ENABLE_MODULE_EXTRAKEYS
test_exhaustive_extrakeys(ctx, group);
#endif
#ifdef ENABLE_MODULE_SCHNORRSIG
test_exhaustive_schnorrsig(ctx);
#endif
#ifdef ENABLE_MODULE_ELLSWIFT
/* The ellswift algorithm does have additional edge cases when operating on
* curves of even order, which are not included in the code as secp256k1 is
* of odd order. Skip the ellswift tests if the used exhaustive tests curve
* is even-ordered accordingly. */
#if !EXHAUSTIVE_TEST_CURVE_HAS_EVEN_ORDER
test_exhaustive_ellswift(ctx, group);
#endif
#endif
secp256k1_context_destroy(ctx);
}
secp256k1_testrand_finish();
printf("no problems found\n");
return 0;
}
|