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diff --git a/src/secp256k1/src/bench_ecmult.c b/src/secp256k1/src/bench_ecmult.c
index 04bc82089..57b3baeea 100644
--- a/src/secp256k1/src/bench_ecmult.c
+++ b/src/secp256k1/src/bench_ecmult.c
@@ -1,199 +1,199 @@
/**********************************************************************
* Copyright (c) 2017 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#include <stdio.h>
#include "include/secp256k1.h"
#include "util.h"
#include "hash_impl.h"
#include "num_impl.h"
#include "field_impl.h"
#include "group_impl.h"
#include "scalar_impl.h"
#include "ecmult_impl.h"
#include "bench.h"
#include "secp256k1.c"
#define POINTS 32768
#define ITERS 10000
typedef struct {
/* Setup once in advance */
secp256k1_context* ctx;
secp256k1_scratch_space* scratch;
secp256k1_scalar* scalars;
secp256k1_ge* pubkeys;
secp256k1_scalar* seckeys;
secp256k1_gej* expected_output;
secp256k1_ecmult_multi_func ecmult_multi;
/* Changes per test */
size_t count;
int includes_g;
/* Changes per test iteration */
size_t offset1;
size_t offset2;
/* Test output. */
secp256k1_gej* output;
} bench_data;
static int bench_callback(secp256k1_scalar* sc, secp256k1_ge* ge, size_t idx, void* arg) {
bench_data* data = (bench_data*)arg;
if (data->includes_g) ++idx;
if (idx == 0) {
*sc = data->scalars[data->offset1];
*ge = secp256k1_ge_const_g;
} else {
*sc = data->scalars[(data->offset1 + idx) % POINTS];
*ge = data->pubkeys[(data->offset2 + idx - 1) % POINTS];
}
return 1;
}
static void bench_ecmult(void* arg) {
bench_data* data = (bench_data*)arg;
size_t count = data->count;
int includes_g = data->includes_g;
size_t iters = 1 + ITERS / count;
size_t iter;
for (iter = 0; iter < iters; ++iter) {
data->ecmult_multi(&data->ctx->ecmult_ctx, data->scratch, &data->output[iter], data->includes_g ? &data->scalars[data->offset1] : NULL, bench_callback, arg, count - includes_g);
data->offset1 = (data->offset1 + count) % POINTS;
data->offset2 = (data->offset2 + count - 1) % POINTS;
}
}
static void bench_ecmult_setup(void* arg) {
bench_data* data = (bench_data*)arg;
data->offset1 = (data->count * 0x537b7f6f + 0x8f66a481) % POINTS;
data->offset2 = (data->count * 0x7f6f537b + 0x6a1a8f49) % POINTS;
}
static void bench_ecmult_teardown(void* arg) {
bench_data* data = (bench_data*)arg;
size_t iters = 1 + ITERS / data->count;
size_t iter;
/* Verify the results in teardown, to avoid doing comparisons while benchmarking. */
for (iter = 0; iter < iters; ++iter) {
secp256k1_gej tmp;
secp256k1_gej_add_var(&tmp, &data->output[iter], &data->expected_output[iter], NULL);
CHECK(secp256k1_gej_is_infinity(&tmp));
}
}
static void generate_scalar(uint32_t num, secp256k1_scalar* scalar) {
secp256k1_sha256 sha256;
unsigned char c[11] = {'e', 'c', 'm', 'u', 'l', 't', 0, 0, 0, 0};
unsigned char buf[32];
int overflow = 0;
c[6] = num;
c[7] = num >> 8;
c[8] = num >> 16;
c[9] = num >> 24;
secp256k1_sha256_initialize(&sha256);
secp256k1_sha256_write(&sha256, c, sizeof(c));
secp256k1_sha256_finalize(&sha256, buf);
secp256k1_scalar_set_b32(scalar, buf, &overflow);
CHECK(!overflow);
}
static void run_test(bench_data* data, size_t count, int includes_g) {
char str[32];
static const secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
size_t iters = 1 + ITERS / count;
size_t iter;
data->count = count;
data->includes_g = includes_g;
/* Compute (the negation of) the expected results directly. */
data->offset1 = (data->count * 0x537b7f6f + 0x8f66a481) % POINTS;
data->offset2 = (data->count * 0x7f6f537b + 0x6a1a8f49) % POINTS;
for (iter = 0; iter < iters; ++iter) {
secp256k1_scalar tmp;
secp256k1_scalar total = data->scalars[(data->offset1++) % POINTS];
size_t i = 0;
for (i = 0; i + 1 < count; ++i) {
secp256k1_scalar_mul(&tmp, &data->seckeys[(data->offset2++) % POINTS], &data->scalars[(data->offset1++) % POINTS]);
secp256k1_scalar_add(&total, &total, &tmp);
}
secp256k1_scalar_negate(&total, &total);
secp256k1_ecmult(&data->ctx->ecmult_ctx, &data->expected_output[iter], NULL, &zero, &total);
}
/* Run the benchmark. */
sprintf(str, includes_g ? "ecmult_%ig" : "ecmult_%i", (int)count);
run_benchmark(str, bench_ecmult, bench_ecmult_setup, bench_ecmult_teardown, data, 10, count * (1 + ITERS / count));
}
int main(int argc, char **argv) {
bench_data data;
int i, p;
secp256k1_gej* pubkeys_gej;
size_t scratch_size;
data.ecmult_multi = secp256k1_ecmult_multi_var;
if (argc > 1) {
if(have_flag(argc, argv, "pippenger_wnaf")) {
printf("Using pippenger_wnaf:\n");
data.ecmult_multi = secp256k1_ecmult_pippenger_batch_single;
} else if(have_flag(argc, argv, "strauss_wnaf")) {
printf("Using strauss_wnaf:\n");
data.ecmult_multi = secp256k1_ecmult_strauss_batch_single;
} else {
fprintf(stderr, "%s: unrecognized argument '%s'.\n", argv[0], argv[1]);
fprintf(stderr, "Use 'pippenger_wnaf', 'strauss_wnaf' or no argument to benchmark a combined algorithm.\n");
return 1;
}
}
/* Allocate stuff */
data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
scratch_size = secp256k1_strauss_scratch_size(POINTS) + STRAUSS_SCRATCH_OBJECTS*16;
data.scratch = secp256k1_scratch_space_create(data.ctx, scratch_size);
data.scalars = malloc(sizeof(secp256k1_scalar) * POINTS);
data.seckeys = malloc(sizeof(secp256k1_scalar) * POINTS);
data.pubkeys = malloc(sizeof(secp256k1_ge) * POINTS);
data.expected_output = malloc(sizeof(secp256k1_gej) * (ITERS + 1));
data.output = malloc(sizeof(secp256k1_gej) * (ITERS + 1));
/* Generate a set of scalars, and private/public keypairs. */
pubkeys_gej = malloc(sizeof(secp256k1_gej) * POINTS);
secp256k1_gej_set_ge(&pubkeys_gej[0], &secp256k1_ge_const_g);
secp256k1_scalar_set_int(&data.seckeys[0], 1);
for (i = 0; i < POINTS; ++i) {
generate_scalar(i, &data.scalars[i]);
if (i) {
secp256k1_gej_double_var(&pubkeys_gej[i], &pubkeys_gej[i - 1], NULL);
secp256k1_scalar_add(&data.seckeys[i], &data.seckeys[i - 1], &data.seckeys[i - 1]);
}
}
- secp256k1_ge_set_all_gej_var(data.pubkeys, pubkeys_gej, POINTS, &data.ctx->error_callback);
+ secp256k1_ge_set_all_gej_var(data.pubkeys, pubkeys_gej, POINTS);
free(pubkeys_gej);
for (i = 1; i <= 8; ++i) {
run_test(&data, i, 1);
}
for (p = 0; p <= 11; ++p) {
for (i = 9; i <= 16; ++i) {
run_test(&data, i << p, 1);
}
}
secp256k1_context_destroy(data.ctx);
secp256k1_scratch_space_destroy(data.scratch);
free(data.scalars);
free(data.pubkeys);
free(data.seckeys);
free(data.output);
free(data.expected_output);
return(0);
}
diff --git a/src/secp256k1/src/ecmult_gen_impl.h b/src/secp256k1/src/ecmult_gen_impl.h
index 714f02e94..d64505dc0 100644
--- a/src/secp256k1/src/ecmult_gen_impl.h
+++ b/src/secp256k1/src/ecmult_gen_impl.h
@@ -1,210 +1,210 @@
/**********************************************************************
* Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef SECP256K1_ECMULT_GEN_IMPL_H
#define SECP256K1_ECMULT_GEN_IMPL_H
#include "scalar.h"
#include "group.h"
#include "ecmult_gen.h"
#include "hash_impl.h"
#ifdef USE_ECMULT_STATIC_PRECOMPUTATION
#include "ecmult_static_context.h"
#endif
static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context *ctx) {
ctx->prec = NULL;
}
static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx, const secp256k1_callback* cb) {
#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
secp256k1_ge prec[1024];
secp256k1_gej gj;
secp256k1_gej nums_gej;
int i, j;
#endif
if (ctx->prec != NULL) {
return;
}
#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
ctx->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*ctx->prec));
/* get the generator */
secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
/* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
{
static const unsigned char nums_b32[33] = "The scalar for this x is unknown";
secp256k1_fe nums_x;
secp256k1_ge nums_ge;
int r;
r = secp256k1_fe_set_b32(&nums_x, nums_b32);
(void)r;
VERIFY_CHECK(r);
r = secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0);
(void)r;
VERIFY_CHECK(r);
secp256k1_gej_set_ge(&nums_gej, &nums_ge);
/* Add G to make the bits in x uniformly distributed. */
secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g, NULL);
}
/* compute prec. */
{
secp256k1_gej precj[1024]; /* Jacobian versions of prec. */
secp256k1_gej gbase;
secp256k1_gej numsbase;
gbase = gj; /* 16^j * G */
numsbase = nums_gej; /* 2^j * nums. */
for (j = 0; j < 64; j++) {
/* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
precj[j*16] = numsbase;
for (i = 1; i < 16; i++) {
secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase, NULL);
}
/* Multiply gbase by 16. */
for (i = 0; i < 4; i++) {
secp256k1_gej_double_var(&gbase, &gbase, NULL);
}
/* Multiply numbase by 2. */
secp256k1_gej_double_var(&numsbase, &numsbase, NULL);
if (j == 62) {
/* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
secp256k1_gej_neg(&numsbase, &numsbase);
secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL);
}
}
- secp256k1_ge_set_all_gej_var(prec, precj, 1024, cb);
+ secp256k1_ge_set_all_gej_var(prec, precj, 1024);
}
for (j = 0; j < 64; j++) {
for (i = 0; i < 16; i++) {
secp256k1_ge_to_storage(&(*ctx->prec)[j][i], &prec[j*16 + i]);
}
}
#else
(void)cb;
ctx->prec = (secp256k1_ge_storage (*)[64][16])secp256k1_ecmult_static_context;
#endif
secp256k1_ecmult_gen_blind(ctx, NULL);
}
static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx) {
return ctx->prec != NULL;
}
static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context *dst,
const secp256k1_ecmult_gen_context *src, const secp256k1_callback* cb) {
if (src->prec == NULL) {
dst->prec = NULL;
} else {
#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
dst->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*dst->prec));
memcpy(dst->prec, src->prec, sizeof(*dst->prec));
#else
(void)cb;
dst->prec = src->prec;
#endif
dst->initial = src->initial;
dst->blind = src->blind;
}
}
static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context *ctx) {
#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
free(ctx->prec);
#endif
secp256k1_scalar_clear(&ctx->blind);
secp256k1_gej_clear(&ctx->initial);
ctx->prec = NULL;
}
static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp256k1_gej *r, const secp256k1_scalar *gn) {
secp256k1_ge add;
secp256k1_ge_storage adds;
secp256k1_scalar gnb;
int bits;
int i, j;
memset(&adds, 0, sizeof(adds));
*r = ctx->initial;
/* Blind scalar/point multiplication by computing (n-b)G + bG instead of nG. */
secp256k1_scalar_add(&gnb, gn, &ctx->blind);
add.infinity = 0;
for (j = 0; j < 64; j++) {
bits = secp256k1_scalar_get_bits(&gnb, j * 4, 4);
for (i = 0; i < 16; i++) {
/** This uses a conditional move to avoid any secret data in array indexes.
* _Any_ use of secret indexes has been demonstrated to result in timing
* sidechannels, even when the cache-line access patterns are uniform.
* See also:
* "A word of warning", CHES 2013 Rump Session, by Daniel J. Bernstein and Peter Schwabe
* (https://cryptojedi.org/peter/data/chesrump-20130822.pdf) and
* "Cache Attacks and Countermeasures: the Case of AES", RSA 2006,
* by Dag Arne Osvik, Adi Shamir, and Eran Tromer
* (http://www.tau.ac.il/~tromer/papers/cache.pdf)
*/
secp256k1_ge_storage_cmov(&adds, &(*ctx->prec)[j][i], i == bits);
}
secp256k1_ge_from_storage(&add, &adds);
secp256k1_gej_add_ge(r, r, &add);
}
bits = 0;
secp256k1_ge_clear(&add);
secp256k1_scalar_clear(&gnb);
}
/* Setup blinding values for secp256k1_ecmult_gen. */
static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32) {
secp256k1_scalar b;
secp256k1_gej gb;
secp256k1_fe s;
unsigned char nonce32[32];
secp256k1_rfc6979_hmac_sha256 rng;
int retry;
unsigned char keydata[64] = {0};
if (seed32 == NULL) {
/* When seed is NULL, reset the initial point and blinding value. */
secp256k1_gej_set_ge(&ctx->initial, &secp256k1_ge_const_g);
secp256k1_gej_neg(&ctx->initial, &ctx->initial);
secp256k1_scalar_set_int(&ctx->blind, 1);
}
/* The prior blinding value (if not reset) is chained forward by including it in the hash. */
secp256k1_scalar_get_b32(nonce32, &ctx->blind);
/** Using a CSPRNG allows a failure free interface, avoids needing large amounts of random data,
* and guards against weak or adversarial seeds. This is a simpler and safer interface than
* asking the caller for blinding values directly and expecting them to retry on failure.
*/
memcpy(keydata, nonce32, 32);
if (seed32 != NULL) {
memcpy(keydata + 32, seed32, 32);
}
secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, seed32 ? 64 : 32);
memset(keydata, 0, sizeof(keydata));
/* Retry for out of range results to achieve uniformity. */
do {
secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
retry = !secp256k1_fe_set_b32(&s, nonce32);
retry |= secp256k1_fe_is_zero(&s);
} while (retry); /* This branch true is cryptographically unreachable. Requires sha256_hmac output > Fp. */
/* Randomize the projection to defend against multiplier sidechannels. */
secp256k1_gej_rescale(&ctx->initial, &s);
secp256k1_fe_clear(&s);
do {
secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
secp256k1_scalar_set_b32(&b, nonce32, &retry);
/* A blinding value of 0 works, but would undermine the projection hardening. */
retry |= secp256k1_scalar_is_zero(&b);
} while (retry); /* This branch true is cryptographically unreachable. Requires sha256_hmac output > order. */
secp256k1_rfc6979_hmac_sha256_finalize(&rng);
memset(nonce32, 0, 32);
secp256k1_ecmult_gen(ctx, &gb, &b);
secp256k1_scalar_negate(&b, &b);
ctx->blind = b;
ctx->initial = gb;
secp256k1_scalar_clear(&b);
secp256k1_gej_clear(&gb);
}
#endif /* SECP256K1_ECMULT_GEN_IMPL_H */
diff --git a/src/secp256k1/src/ecmult_impl.h b/src/secp256k1/src/ecmult_impl.h
index fe87c4fe8..508bde8ab 100644
--- a/src/secp256k1/src/ecmult_impl.h
+++ b/src/secp256k1/src/ecmult_impl.h
@@ -1,1028 +1,1139 @@
/*****************************************************************************
* Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra, Jonas Nick *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php. *
*****************************************************************************/
#ifndef SECP256K1_ECMULT_IMPL_H
#define SECP256K1_ECMULT_IMPL_H
#include <string.h>
#include <stdint.h>
#include "group.h"
#include "scalar.h"
#include "ecmult.h"
#if defined(EXHAUSTIVE_TEST_ORDER)
/* We need to lower these values for exhaustive tests because
* the tables cannot have infinities in them (this breaks the
* affine-isomorphism stuff which tracks z-ratios) */
# if EXHAUSTIVE_TEST_ORDER > 128
# define WINDOW_A 5
# define WINDOW_G 8
# elif EXHAUSTIVE_TEST_ORDER > 8
# define WINDOW_A 4
# define WINDOW_G 4
# else
# define WINDOW_A 2
# define WINDOW_G 2
# endif
#else
/* optimal for 128-bit and 256-bit exponents. */
#define WINDOW_A 5
/** larger numbers may result in slightly better performance, at the cost of
exponentially larger precomputed tables. */
#ifdef USE_ENDOMORPHISM
/** Two tables for window size 15: 1.375 MiB. */
#define WINDOW_G 15
#else
/** One table for window size 16: 1.375 MiB. */
#define WINDOW_G 16
#endif
#endif
#ifdef USE_ENDOMORPHISM
#define WNAF_BITS 128
#else
#define WNAF_BITS 256
#endif
#define WNAF_SIZE_BITS(bits, w) (((bits) + (w) - 1) / (w))
#define WNAF_SIZE(w) WNAF_SIZE_BITS(WNAF_BITS, w)
/** The number of entries a table with precomputed multiples needs to have. */
#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
/* The number of objects allocated on the scratch space for ecmult_multi algorithms */
#define PIPPENGER_SCRATCH_OBJECTS 6
#define STRAUSS_SCRATCH_OBJECTS 6
#define PIPPENGER_MAX_BUCKET_WINDOW 12
/* Minimum number of points for which pippenger_wnaf is faster than strauss wnaf */
#ifdef USE_ENDOMORPHISM
#define ECMULT_PIPPENGER_THRESHOLD 88
#else
#define ECMULT_PIPPENGER_THRESHOLD 160
#endif
#ifdef USE_ENDOMORPHISM
#define ECMULT_MAX_POINTS_PER_BATCH 5000000
#else
#define ECMULT_MAX_POINTS_PER_BATCH 10000000
#endif
/** Fill a table 'prej' with precomputed odd multiples of a. Prej will contain
* the values [1*a,3*a,...,(2*n-1)*a], so it space for n values. zr[0] will
* contain prej[0].z / a.z. The other zr[i] values = prej[i].z / prej[i-1].z.
* Prej's Z values are undefined, except for the last value.
*/
static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_gej *prej, secp256k1_fe *zr, const secp256k1_gej *a) {
secp256k1_gej d;
secp256k1_ge a_ge, d_ge;
int i;
VERIFY_CHECK(!a->infinity);
secp256k1_gej_double_var(&d, a, NULL);
/*
* Perform the additions on an isomorphism where 'd' is affine: drop the z coordinate
* of 'd', and scale the 1P starting value's x/y coordinates without changing its z.
*/
d_ge.x = d.x;
d_ge.y = d.y;
d_ge.infinity = 0;
secp256k1_ge_set_gej_zinv(&a_ge, a, &d.z);
prej[0].x = a_ge.x;
prej[0].y = a_ge.y;
prej[0].z = a->z;
prej[0].infinity = 0;
zr[0] = d.z;
for (i = 1; i < n; i++) {
secp256k1_gej_add_ge_var(&prej[i], &prej[i-1], &d_ge, &zr[i]);
}
/*
* Each point in 'prej' has a z coordinate too small by a factor of 'd.z'. Only
* the final point's z coordinate is actually used though, so just update that.
*/
secp256k1_fe_mul(&prej[n-1].z, &prej[n-1].z, &d.z);
}
/** Fill a table 'pre' with precomputed odd multiples of a.
*
* There are two versions of this function:
* - secp256k1_ecmult_odd_multiples_table_globalz_windowa which brings its
* resulting point set to a single constant Z denominator, stores the X and Y
* coordinates as ge_storage points in pre, and stores the global Z in rz.
* It only operates on tables sized for WINDOW_A wnaf multiples.
* - secp256k1_ecmult_odd_multiples_table_storage_var, which converts its
* resulting point set to actually affine points, and stores those in pre.
* It operates on tables of any size, but uses heap-allocated temporaries.
*
* To compute a*P + b*G, we compute a table for P using the first function,
* and for G using the second (which requires an inverse, but it only needs to
* happen once).
*/
static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) {
secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)];
secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)];
/* Compute the odd multiples in Jacobian form. */
secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), prej, zr, a);
/* Bring them to the same Z denominator. */
secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A), pre, globalz, prej, zr);
}
-static void secp256k1_ecmult_odd_multiples_table_storage_var(int n, secp256k1_ge_storage *pre, const secp256k1_gej *a, const secp256k1_callback *cb) {
- secp256k1_gej *prej = (secp256k1_gej*)checked_malloc(cb, sizeof(secp256k1_gej) * n);
- secp256k1_ge *prea = (secp256k1_ge*)checked_malloc(cb, sizeof(secp256k1_ge) * n);
- secp256k1_fe *zr = (secp256k1_fe*)checked_malloc(cb, sizeof(secp256k1_fe) * n);
+static void secp256k1_ecmult_odd_multiples_table_storage_var(const int n, secp256k1_ge_storage *pre, const secp256k1_gej *a) {
+ secp256k1_gej d;
+ secp256k1_ge d_ge, p_ge;
+ secp256k1_gej pj;
+ secp256k1_fe zi;
+ secp256k1_fe zr;
+ secp256k1_fe dx_over_dz_squared;
int i;
- /* Compute the odd multiples in Jacobian form. */
- secp256k1_ecmult_odd_multiples_table(n, prej, zr, a);
- /* Convert them in batch to affine coordinates. */
- secp256k1_ge_set_table_gej_var(prea, prej, zr, n);
- /* Convert them to compact storage form. */
- for (i = 0; i < n; i++) {
- secp256k1_ge_to_storage(&pre[i], &prea[i]);
+ VERIFY_CHECK(!a->infinity);
+
+ secp256k1_gej_double_var(&d, a, NULL);
+
+ /* First, we perform all the additions in an isomorphic curve obtained by multiplying
+ * all `z` coordinates by 1/`d.z`. In these coordinates `d` is affine so we can use
+ * `secp256k1_gej_add_ge_var` to perform the additions. For each addition, we store
+ * the resulting y-coordinate and the z-ratio, since we only have enough memory to
+ * store two field elements. These are sufficient to efficiently undo the isomorphism
+ * and recompute all the `x`s.
+ */
+ d_ge.x = d.x;
+ d_ge.y = d.y;
+ d_ge.infinity = 0;
+
+ secp256k1_ge_set_gej_zinv(&p_ge, a, &d.z);
+ pj.x = p_ge.x;
+ pj.y = p_ge.y;
+ pj.z = a->z;
+ pj.infinity = 0;
+
+ for (i = 0; i < (n - 1); i++) {
+ secp256k1_fe_normalize_var(&pj.y);
+ secp256k1_fe_to_storage(&pre[i].y, &pj.y);
+ secp256k1_gej_add_ge_var(&pj, &pj, &d_ge, &zr);
+ secp256k1_fe_normalize_var(&zr);
+ secp256k1_fe_to_storage(&pre[i].x, &zr);
}
- free(prea);
- free(prej);
- free(zr);
+ /* Invert d.z in the same batch, preserving pj.z so we can extract 1/d.z */
+ secp256k1_fe_mul(&zi, &pj.z, &d.z);
+ secp256k1_fe_inv_var(&zi, &zi);
+
+ /* Directly set `pre[n - 1]` to `pj`, saving the inverted z-coordinate so
+ * that we can combine it with the saved z-ratios to compute the other zs
+ * without any more inversions. */
+ secp256k1_ge_set_gej_zinv(&p_ge, &pj, &zi);
+ secp256k1_ge_to_storage(&pre[n - 1], &p_ge);
+
+ /* Compute the actual x-coordinate of D, which will be needed below. */
+ secp256k1_fe_mul(&d.z, &zi, &pj.z); /* d.z = 1/d.z */
+ secp256k1_fe_sqr(&dx_over_dz_squared, &d.z);
+ secp256k1_fe_mul(&dx_over_dz_squared, &dx_over_dz_squared, &d.x);
+
+ /* Going into the second loop, we have set `pre[n-1]` to its final affine
+ * form, but still need to set `pre[i]` for `i` in 0 through `n-2`. We
+ * have `zi = (p.z * d.z)^-1`, where
+ *
+ * `p.z` is the z-coordinate of the point on the isomorphic curve
+ * which was ultimately assigned to `pre[n-1]`.
+ * `d.z` is the multiplier that must be applied to all z-coordinates
+ * to move from our isomorphic curve back to secp256k1; so the
+ * product `p.z * d.z` is the z-coordinate of the secp256k1
+ * point assigned to `pre[n-1]`.
+ *
+ * All subsequent inverse-z-coordinates can be obtained by multiplying this
+ * factor by successive z-ratios, which is much more efficient than directly
+ * computing each one.
+ *
+ * Importantly, these inverse-zs will be coordinates of points on secp256k1,
+ * while our other stored values come from computations on the isomorphic
+ * curve. So in the below loop, we will take care not to actually use `zi`
+ * or any derived values until we're back on secp256k1.
+ */
+ i = n - 1;
+ while (i > 0) {
+ secp256k1_fe zi2, zi3;
+ const secp256k1_fe *rzr;
+ i--;
+
+ secp256k1_ge_from_storage(&p_ge, &pre[i]);
+
+ /* For each remaining point, we extract the z-ratio from the stored
+ * x-coordinate, compute its z^-1 from that, and compute the full
+ * point from that. */
+ rzr = &p_ge.x;
+ secp256k1_fe_mul(&zi, &zi, rzr);
+ secp256k1_fe_sqr(&zi2, &zi);
+ secp256k1_fe_mul(&zi3, &zi2, &zi);
+ /* To compute the actual x-coordinate, we use the stored z ratio and
+ * y-coordinate, which we obtained from `secp256k1_gej_add_ge_var`
+ * in the loop above, as well as the inverse of the square of its
+ * z-coordinate. We store the latter in the `zi2` variable, which is
+ * computed iteratively starting from the overall Z inverse then
+ * multiplying by each z-ratio in turn.
+ *
+ * Denoting the z-ratio as `rzr`, we observe that it is equal to `h`
+ * from the inside of the above `gej_add_ge_var` call. This satisfies
+ *
+ * rzr = d_x * z^2 - x * d_z^2
+ *
+ * where (`d_x`, `d_z`) are Jacobian coordinates of `D` and `(x, z)`
+ * are Jacobian coordinates of our desired point -- except both are on
+ * the isomorphic curve that we were using when we called `gej_add_ge_var`.
+ * To get back to secp256k1, we must multiply both `z`s by `d_z`, or
+ * equivalently divide both `x`s by `d_z^2`. Our equation then becomes
+ *
+ * rzr = d_x * z^2 / d_z^2 - x
+ *
+ * (The left-hand-side, being a ratio of z-coordinates, is unaffected
+ * by the isomorphism.)
+ *
+ * Rearranging to solve for `x`, we have
+ *
+ * x = d_x * z^2 / d_z^2 - rzr
+ *
+ * But what we actually want is the affine coordinate `X = x/z^2`,
+ * which will satisfy
+ *
+ * X = d_x / d_z^2 - rzr / z^2
+ * = dx_over_dz_squared - rzr * zi2
+ */
+ secp256k1_fe_mul(&p_ge.x, rzr, &zi2);
+ secp256k1_fe_negate(&p_ge.x, &p_ge.x, 1);
+ secp256k1_fe_add(&p_ge.x, &dx_over_dz_squared);
+ /* y is stored_y/z^3, as we expect */
+ secp256k1_fe_mul(&p_ge.y, &p_ge.y, &zi3);
+ /* Store */
+ secp256k1_ge_to_storage(&pre[i], &p_ge);
+ }
}
/** The following two macro retrieves a particular odd multiple from a table
* of precomputed multiples. */
#define ECMULT_TABLE_GET_GE(r,pre,n,w) do { \
VERIFY_CHECK(((n) & 1) == 1); \
VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
if ((n) > 0) { \
*(r) = (pre)[((n)-1)/2]; \
} else { \
*(r) = (pre)[(-(n)-1)/2]; \
secp256k1_fe_negate(&((r)->y), &((r)->y), 1); \
} \
} while(0)
#define ECMULT_TABLE_GET_GE_STORAGE(r,pre,n,w) do { \
VERIFY_CHECK(((n) & 1) == 1); \
VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
if ((n) > 0) { \
secp256k1_ge_from_storage((r), &(pre)[((n)-1)/2]); \
} else { \
secp256k1_ge_from_storage((r), &(pre)[(-(n)-1)/2]); \
secp256k1_fe_negate(&((r)->y), &((r)->y), 1); \
} \
} while(0)
static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx) {
ctx->pre_g = NULL;
#ifdef USE_ENDOMORPHISM
ctx->pre_g_128 = NULL;
#endif
}
static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb) {
secp256k1_gej gj;
if (ctx->pre_g != NULL) {
return;
}
/* get the generator */
secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
ctx->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
/* precompute the tables with odd multiples */
- secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g, &gj, cb);
+ secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g, &gj);
#ifdef USE_ENDOMORPHISM
{
secp256k1_gej g_128j;
int i;
ctx->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
/* calculate 2^128*generator */
g_128j = gj;
for (i = 0; i < 128; i++) {
secp256k1_gej_double_var(&g_128j, &g_128j, NULL);
}
- secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g_128, &g_128j, cb);
+ secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g_128, &g_128j);
}
#endif
}
static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst,
const secp256k1_ecmult_context *src, const secp256k1_callback *cb) {
if (src->pre_g == NULL) {
dst->pre_g = NULL;
} else {
size_t size = sizeof((*dst->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
dst->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, size);
memcpy(dst->pre_g, src->pre_g, size);
}
#ifdef USE_ENDOMORPHISM
if (src->pre_g_128 == NULL) {
dst->pre_g_128 = NULL;
} else {
size_t size = sizeof((*dst->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
dst->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, size);
memcpy(dst->pre_g_128, src->pre_g_128, size);
}
#endif
}
static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx) {
return ctx->pre_g != NULL;
}
static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx) {
free(ctx->pre_g);
#ifdef USE_ENDOMORPHISM
free(ctx->pre_g_128);
#endif
secp256k1_ecmult_context_init(ctx);
}
/** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits),
* with the following guarantees:
* - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1)
* - two non-zero entries in wnaf are separated by at least w-1 zeroes.
* - the number of set values in wnaf is returned. This number is at most 256, and at most one more
* than the number of bits in the (absolute value) of the input.
*/
static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a, int w) {
secp256k1_scalar s = *a;
int last_set_bit = -1;
int bit = 0;
int sign = 1;
int carry = 0;
VERIFY_CHECK(wnaf != NULL);
VERIFY_CHECK(0 <= len && len <= 256);
VERIFY_CHECK(a != NULL);
VERIFY_CHECK(2 <= w && w <= 31);
memset(wnaf, 0, len * sizeof(wnaf[0]));
if (secp256k1_scalar_get_bits(&s, 255, 1)) {
secp256k1_scalar_negate(&s, &s);
sign = -1;
}
while (bit < len) {
int now;
int word;
if (secp256k1_scalar_get_bits(&s, bit, 1) == (unsigned int)carry) {
bit++;
continue;
}
now = w;
if (now > len - bit) {
now = len - bit;
}
word = secp256k1_scalar_get_bits_var(&s, bit, now) + carry;
carry = (word >> (w-1)) & 1;
word -= carry << w;
wnaf[bit] = sign * word;
last_set_bit = bit;
bit += now;
}
#ifdef VERIFY
CHECK(carry == 0);
while (bit < 256) {
CHECK(secp256k1_scalar_get_bits(&s, bit++, 1) == 0);
}
#endif
return last_set_bit + 1;
}
struct secp256k1_strauss_point_state {
#ifdef USE_ENDOMORPHISM
secp256k1_scalar na_1, na_lam;
int wnaf_na_1[130];
int wnaf_na_lam[130];
int bits_na_1;
int bits_na_lam;
#else
int wnaf_na[256];
int bits_na;
#endif
size_t input_pos;
};
struct secp256k1_strauss_state {
secp256k1_gej* prej;
secp256k1_fe* zr;
secp256k1_ge* pre_a;
#ifdef USE_ENDOMORPHISM
secp256k1_ge* pre_a_lam;
#endif
struct secp256k1_strauss_point_state* ps;
};
static void secp256k1_ecmult_strauss_wnaf(const secp256k1_ecmult_context *ctx, const struct secp256k1_strauss_state *state, secp256k1_gej *r, int num, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
secp256k1_ge tmpa;
secp256k1_fe Z;
#ifdef USE_ENDOMORPHISM
/* Splitted G factors. */
secp256k1_scalar ng_1, ng_128;
int wnaf_ng_1[129];
int bits_ng_1 = 0;
int wnaf_ng_128[129];
int bits_ng_128 = 0;
#else
int wnaf_ng[256];
int bits_ng = 0;
#endif
int i;
int bits = 0;
int np;
int no = 0;
for (np = 0; np < num; ++np) {
if (secp256k1_scalar_is_zero(&na[np]) || secp256k1_gej_is_infinity(&a[np])) {
continue;
}
state->ps[no].input_pos = np;
#ifdef USE_ENDOMORPHISM
/* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */
secp256k1_scalar_split_lambda(&state->ps[no].na_1, &state->ps[no].na_lam, &na[np]);
/* build wnaf representation for na_1 and na_lam. */
state->ps[no].bits_na_1 = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_1, 130, &state->ps[no].na_1, WINDOW_A);
state->ps[no].bits_na_lam = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_lam, 130, &state->ps[no].na_lam, WINDOW_A);
VERIFY_CHECK(state->ps[no].bits_na_1 <= 130);
VERIFY_CHECK(state->ps[no].bits_na_lam <= 130);
if (state->ps[no].bits_na_1 > bits) {
bits = state->ps[no].bits_na_1;
}
if (state->ps[no].bits_na_lam > bits) {
bits = state->ps[no].bits_na_lam;
}
#else
/* build wnaf representation for na. */
state->ps[no].bits_na = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na, 256, &na[np], WINDOW_A);
if (state->ps[no].bits_na > bits) {
bits = state->ps[no].bits_na;
}
#endif
++no;
}
/* Calculate odd multiples of a.
* All multiples are brought to the same Z 'denominator', which is stored
* in Z. Due to secp256k1' isomorphism we can do all operations pretending
* that the Z coordinate was 1, use affine addition formulae, and correct
* the Z coordinate of the result once at the end.
* The exception is the precomputed G table points, which are actually
* affine. Compared to the base used for other points, they have a Z ratio
* of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same
* isomorphism to efficiently add with a known Z inverse.
*/
if (no > 0) {
/* Compute the odd multiples in Jacobian form. */
secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), state->prej, state->zr, &a[state->ps[0].input_pos]);
for (np = 1; np < no; ++np) {
secp256k1_gej tmp = a[state->ps[np].input_pos];
#ifdef VERIFY
secp256k1_fe_normalize_var(&(state->prej[(np - 1) * ECMULT_TABLE_SIZE(WINDOW_A) + ECMULT_TABLE_SIZE(WINDOW_A) - 1].z));
#endif
secp256k1_gej_rescale(&tmp, &(state->prej[(np - 1) * ECMULT_TABLE_SIZE(WINDOW_A) + ECMULT_TABLE_SIZE(WINDOW_A) - 1].z));
secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), state->prej + np * ECMULT_TABLE_SIZE(WINDOW_A), state->zr + np * ECMULT_TABLE_SIZE(WINDOW_A), &tmp);
secp256k1_fe_mul(state->zr + np * ECMULT_TABLE_SIZE(WINDOW_A), state->zr + np * ECMULT_TABLE_SIZE(WINDOW_A), &(a[state->ps[np].input_pos].z));
}
/* Bring them to the same Z denominator. */
secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A) * no, state->pre_a, &Z, state->prej, state->zr);
} else {
secp256k1_fe_set_int(&Z, 1);
}
#ifdef USE_ENDOMORPHISM
for (np = 0; np < no; ++np) {
for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
secp256k1_ge_mul_lambda(&state->pre_a_lam[np * ECMULT_TABLE_SIZE(WINDOW_A) + i], &state->pre_a[np * ECMULT_TABLE_SIZE(WINDOW_A) + i]);
}
}
if (ng) {
/* split ng into ng_1 and ng_128 (where gn = gn_1 + gn_128*2^128, and gn_1 and gn_128 are ~128 bit) */
secp256k1_scalar_split_128(&ng_1, &ng_128, ng);
/* Build wnaf representation for ng_1 and ng_128 */
bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, 129, &ng_1, WINDOW_G);
bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, 129, &ng_128, WINDOW_G);
if (bits_ng_1 > bits) {
bits = bits_ng_1;
}
if (bits_ng_128 > bits) {
bits = bits_ng_128;
}
}
#else
if (ng) {
bits_ng = secp256k1_ecmult_wnaf(wnaf_ng, 256, ng, WINDOW_G);
if (bits_ng > bits) {
bits = bits_ng;
}
}
#endif
secp256k1_gej_set_infinity(r);
for (i = bits - 1; i >= 0; i--) {
int n;
secp256k1_gej_double_var(r, r, NULL);
#ifdef USE_ENDOMORPHISM
for (np = 0; np < no; ++np) {
if (i < state->ps[np].bits_na_1 && (n = state->ps[np].wnaf_na_1[i])) {
ECMULT_TABLE_GET_GE(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A);
secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
}
if (i < state->ps[np].bits_na_lam && (n = state->ps[np].wnaf_na_lam[i])) {
ECMULT_TABLE_GET_GE(&tmpa, state->pre_a_lam + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A);
secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
}
}
if (i < bits_ng_1 && (n = wnaf_ng_1[i])) {
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
}
if (i < bits_ng_128 && (n = wnaf_ng_128[i])) {
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g_128, n, WINDOW_G);
secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
}
#else
for (np = 0; np < no; ++np) {
if (i < state->ps[np].bits_na && (n = state->ps[np].wnaf_na[i])) {
ECMULT_TABLE_GET_GE(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A);
secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
}
}
if (i < bits_ng && (n = wnaf_ng[i])) {
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
}
#endif
}
if (!r->infinity) {
secp256k1_fe_mul(&r->z, &r->z, &Z);
}
}
static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)];
secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)];
secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
struct secp256k1_strauss_point_state ps[1];
#ifdef USE_ENDOMORPHISM
secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
#endif
struct secp256k1_strauss_state state;
state.prej = prej;
state.zr = zr;
state.pre_a = pre_a;
#ifdef USE_ENDOMORPHISM
state.pre_a_lam = pre_a_lam;
#endif
state.ps = ps;
secp256k1_ecmult_strauss_wnaf(ctx, &state, r, 1, a, na, ng);
}
static size_t secp256k1_strauss_scratch_size(size_t n_points) {
#ifdef USE_ENDOMORPHISM
static const size_t point_size = (2 * sizeof(secp256k1_ge) + sizeof(secp256k1_gej) + sizeof(secp256k1_fe)) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar);
#else
static const size_t point_size = (sizeof(secp256k1_ge) + sizeof(secp256k1_gej) + sizeof(secp256k1_fe)) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar);
#endif
return n_points*point_size;
}
static int secp256k1_ecmult_strauss_batch(const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) {
secp256k1_gej* points;
secp256k1_scalar* scalars;
struct secp256k1_strauss_state state;
size_t i;
secp256k1_gej_set_infinity(r);
if (inp_g_sc == NULL && n_points == 0) {
return 1;
}
if (!secp256k1_scratch_allocate_frame(scratch, secp256k1_strauss_scratch_size(n_points), STRAUSS_SCRATCH_OBJECTS)) {
return 0;
}
points = (secp256k1_gej*)secp256k1_scratch_alloc(scratch, n_points * sizeof(secp256k1_gej));
scalars = (secp256k1_scalar*)secp256k1_scratch_alloc(scratch, n_points * sizeof(secp256k1_scalar));
state.prej = (secp256k1_gej*)secp256k1_scratch_alloc(scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_gej));
state.zr = (secp256k1_fe*)secp256k1_scratch_alloc(scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_fe));
#ifdef USE_ENDOMORPHISM
state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(scratch, n_points * 2 * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge));
state.pre_a_lam = state.pre_a + n_points * ECMULT_TABLE_SIZE(WINDOW_A);
#else
state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge));
#endif
state.ps = (struct secp256k1_strauss_point_state*)secp256k1_scratch_alloc(scratch, n_points * sizeof(struct secp256k1_strauss_point_state));
for (i = 0; i < n_points; i++) {
secp256k1_ge point;
if (!cb(&scalars[i], &point, i+cb_offset, cbdata)) {
secp256k1_scratch_deallocate_frame(scratch);
return 0;
}
secp256k1_gej_set_ge(&points[i], &point);
}
secp256k1_ecmult_strauss_wnaf(ctx, &state, r, n_points, points, scalars, inp_g_sc);
secp256k1_scratch_deallocate_frame(scratch);
return 1;
}
/* Wrapper for secp256k1_ecmult_multi_func interface */
static int secp256k1_ecmult_strauss_batch_single(const secp256k1_ecmult_context *actx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) {
return secp256k1_ecmult_strauss_batch(actx, scratch, r, inp_g_sc, cb, cbdata, n, 0);
}
static size_t secp256k1_strauss_max_points(secp256k1_scratch *scratch) {
return secp256k1_scratch_max_allocation(scratch, STRAUSS_SCRATCH_OBJECTS) / secp256k1_strauss_scratch_size(1);
}
/** Convert a number to WNAF notation.
* The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val.
* It has the following guarantees:
* - each wnaf[i] is either 0 or an odd integer between -(1 << w) and (1 << w)
* - the number of words set is always WNAF_SIZE(w)
* - the returned skew is 0 or 1
*/
static int secp256k1_wnaf_fixed(int *wnaf, const secp256k1_scalar *s, int w) {
int skew = 0;
int pos;
int max_pos;
int last_w;
const secp256k1_scalar *work = s;
if (secp256k1_scalar_is_zero(s)) {
for (pos = 0; pos < WNAF_SIZE(w); pos++) {
wnaf[pos] = 0;
}
return 0;
}
if (secp256k1_scalar_is_even(s)) {
skew = 1;
}
wnaf[0] = secp256k1_scalar_get_bits_var(work, 0, w) + skew;
/* Compute last window size. Relevant when window size doesn't divide the
* number of bits in the scalar */
last_w = WNAF_BITS - (WNAF_SIZE(w) - 1) * w;
/* Store the position of the first nonzero word in max_pos to allow
* skipping leading zeros when calculating the wnaf. */
for (pos = WNAF_SIZE(w) - 1; pos > 0; pos--) {
int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w);
if(val != 0) {
break;
}
wnaf[pos] = 0;
}
max_pos = pos;
pos = 1;
while (pos <= max_pos) {
int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w);
if ((val & 1) == 0) {
wnaf[pos - 1] -= (1 << w);
wnaf[pos] = (val + 1);
} else {
wnaf[pos] = val;
}
/* Set a coefficient to zero if it is 1 or -1 and the proceeding digit
* is strictly negative or strictly positive respectively. Only change
* coefficients at previous positions because above code assumes that
* wnaf[pos - 1] is odd.
*/
if (pos >= 2 && ((wnaf[pos - 1] == 1 && wnaf[pos - 2] < 0) || (wnaf[pos - 1] == -1 && wnaf[pos - 2] > 0))) {
if (wnaf[pos - 1] == 1) {
wnaf[pos - 2] += 1 << w;
} else {
wnaf[pos - 2] -= 1 << w;
}
wnaf[pos - 1] = 0;
}
++pos;
}
return skew;
}
struct secp256k1_pippenger_point_state {
int skew_na;
size_t input_pos;
};
struct secp256k1_pippenger_state {
int *wnaf_na;
struct secp256k1_pippenger_point_state* ps;
};
/*
* pippenger_wnaf computes the result of a multi-point multiplication as
* follows: The scalars are brought into wnaf with n_wnaf elements each. Then
* for every i < n_wnaf, first each point is added to a "bucket" corresponding
* to the point's wnaf[i]. Second, the buckets are added together such that
* r += 1*bucket[0] + 3*bucket[1] + 5*bucket[2] + ...
*/
static int secp256k1_ecmult_pippenger_wnaf(secp256k1_gej *buckets, int bucket_window, struct secp256k1_pippenger_state *state, secp256k1_gej *r, const secp256k1_scalar *sc, const secp256k1_ge *pt, size_t num) {
size_t n_wnaf = WNAF_SIZE(bucket_window+1);
size_t np;
size_t no = 0;
int i;
int j;
for (np = 0; np < num; ++np) {
if (secp256k1_scalar_is_zero(&sc[np]) || secp256k1_ge_is_infinity(&pt[np])) {
continue;
}
state->ps[no].input_pos = np;
state->ps[no].skew_na = secp256k1_wnaf_fixed(&state->wnaf_na[no*n_wnaf], &sc[np], bucket_window+1);
no++;
}
secp256k1_gej_set_infinity(r);
if (no == 0) {
return 1;
}
for (i = n_wnaf - 1; i >= 0; i--) {
secp256k1_gej running_sum;
for(j = 0; j < ECMULT_TABLE_SIZE(bucket_window+2); j++) {
secp256k1_gej_set_infinity(&buckets[j]);
}
for (np = 0; np < no; ++np) {
int n = state->wnaf_na[np*n_wnaf + i];
struct secp256k1_pippenger_point_state point_state = state->ps[np];
secp256k1_ge tmp;
int idx;
if (i == 0) {
/* correct for wnaf skew */
int skew = point_state.skew_na;
if (skew) {
secp256k1_ge_neg(&tmp, &pt[point_state.input_pos]);
secp256k1_gej_add_ge_var(&buckets[0], &buckets[0], &tmp, NULL);
}
}
if (n > 0) {
idx = (n - 1)/2;
secp256k1_gej_add_ge_var(&buckets[idx], &buckets[idx], &pt[point_state.input_pos], NULL);
} else if (n < 0) {
idx = -(n + 1)/2;
secp256k1_ge_neg(&tmp, &pt[point_state.input_pos]);
secp256k1_gej_add_ge_var(&buckets[idx], &buckets[idx], &tmp, NULL);
}
}
for(j = 0; j < bucket_window; j++) {
secp256k1_gej_double_var(r, r, NULL);
}
secp256k1_gej_set_infinity(&running_sum);
/* Accumulate the sum: bucket[0] + 3*bucket[1] + 5*bucket[2] + 7*bucket[3] + ...
* = bucket[0] + bucket[1] + bucket[2] + bucket[3] + ...
* + 2 * (bucket[1] + 2*bucket[2] + 3*bucket[3] + ...)
* using an intermediate running sum:
* running_sum = bucket[0] + bucket[1] + bucket[2] + ...
*
* The doubling is done implicitly by deferring the final window doubling (of 'r').
*/
for(j = ECMULT_TABLE_SIZE(bucket_window+2) - 1; j > 0; j--) {
secp256k1_gej_add_var(&running_sum, &running_sum, &buckets[j], NULL);
secp256k1_gej_add_var(r, r, &running_sum, NULL);
}
secp256k1_gej_add_var(&running_sum, &running_sum, &buckets[0], NULL);
secp256k1_gej_double_var(r, r, NULL);
secp256k1_gej_add_var(r, r, &running_sum, NULL);
}
return 1;
}
/**
* Returns optimal bucket_window (number of bits of a scalar represented by a
* set of buckets) for a given number of points.
*/
static int secp256k1_pippenger_bucket_window(size_t n) {
#ifdef USE_ENDOMORPHISM
if (n <= 1) {
return 1;
} else if (n <= 4) {
return 2;
} else if (n <= 20) {
return 3;
} else if (n <= 57) {
return 4;
} else if (n <= 136) {
return 5;
} else if (n <= 235) {
return 6;
} else if (n <= 1260) {
return 7;
} else if (n <= 4420) {
return 9;
} else if (n <= 7880) {
return 10;
} else if (n <= 16050) {
return 11;
} else {
return PIPPENGER_MAX_BUCKET_WINDOW;
}
#else
if (n <= 1) {
return 1;
} else if (n <= 11) {
return 2;
} else if (n <= 45) {
return 3;
} else if (n <= 100) {
return 4;
} else if (n <= 275) {
return 5;
} else if (n <= 625) {
return 6;
} else if (n <= 1850) {
return 7;
} else if (n <= 3400) {
return 8;
} else if (n <= 9630) {
return 9;
} else if (n <= 17900) {
return 10;
} else if (n <= 32800) {
return 11;
} else {
return PIPPENGER_MAX_BUCKET_WINDOW;
}
#endif
}
/**
* Returns the maximum optimal number of points for a bucket_window.
*/
static size_t secp256k1_pippenger_bucket_window_inv(int bucket_window) {
switch(bucket_window) {
#ifdef USE_ENDOMORPHISM
case 1: return 1;
case 2: return 4;
case 3: return 20;
case 4: return 57;
case 5: return 136;
case 6: return 235;
case 7: return 1260;
case 8: return 1260;
case 9: return 4420;
case 10: return 7880;
case 11: return 16050;
case PIPPENGER_MAX_BUCKET_WINDOW: return SIZE_MAX;
#else
case 1: return 1;
case 2: return 11;
case 3: return 45;
case 4: return 100;
case 5: return 275;
case 6: return 625;
case 7: return 1850;
case 8: return 3400;
case 9: return 9630;
case 10: return 17900;
case 11: return 32800;
case PIPPENGER_MAX_BUCKET_WINDOW: return SIZE_MAX;
#endif
}
return 0;
}
#ifdef USE_ENDOMORPHISM
SECP256K1_INLINE static void secp256k1_ecmult_endo_split(secp256k1_scalar *s1, secp256k1_scalar *s2, secp256k1_ge *p1, secp256k1_ge *p2) {
secp256k1_scalar tmp = *s1;
secp256k1_scalar_split_lambda(s1, s2, &tmp);
secp256k1_ge_mul_lambda(p2, p1);
if (secp256k1_scalar_is_high(s1)) {
secp256k1_scalar_negate(s1, s1);
secp256k1_ge_neg(p1, p1);
}
if (secp256k1_scalar_is_high(s2)) {
secp256k1_scalar_negate(s2, s2);
secp256k1_ge_neg(p2, p2);
}
}
#endif
/**
* Returns the scratch size required for a given number of points (excluding
* base point G) without considering alignment.
*/
static size_t secp256k1_pippenger_scratch_size(size_t n_points, int bucket_window) {
#ifdef USE_ENDOMORPHISM
size_t entries = 2*n_points + 2;
#else
size_t entries = n_points + 1;
#endif
size_t entry_size = sizeof(secp256k1_ge) + sizeof(secp256k1_scalar) + sizeof(struct secp256k1_pippenger_point_state) + (WNAF_SIZE(bucket_window+1)+1)*sizeof(int);
return ((1<<bucket_window) * sizeof(secp256k1_gej) + sizeof(struct secp256k1_pippenger_state) + entries * entry_size);
}
static int secp256k1_ecmult_pippenger_batch(const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) {
/* Use 2(n+1) with the endomorphism, n+1 without, when calculating batch
* sizes. The reason for +1 is that we add the G scalar to the list of
* other scalars. */
#ifdef USE_ENDOMORPHISM
size_t entries = 2*n_points + 2;
#else
size_t entries = n_points + 1;
#endif
secp256k1_ge *points;
secp256k1_scalar *scalars;
secp256k1_gej *buckets;
struct secp256k1_pippenger_state *state_space;
size_t idx = 0;
size_t point_idx = 0;
int i, j;
int bucket_window;
(void)ctx;
secp256k1_gej_set_infinity(r);
if (inp_g_sc == NULL && n_points == 0) {
return 1;
}
bucket_window = secp256k1_pippenger_bucket_window(n_points);
if (!secp256k1_scratch_allocate_frame(scratch, secp256k1_pippenger_scratch_size(n_points, bucket_window), PIPPENGER_SCRATCH_OBJECTS)) {
return 0;
}
points = (secp256k1_ge *) secp256k1_scratch_alloc(scratch, entries * sizeof(*points));
scalars = (secp256k1_scalar *) secp256k1_scratch_alloc(scratch, entries * sizeof(*scalars));
state_space = (struct secp256k1_pippenger_state *) secp256k1_scratch_alloc(scratch, sizeof(*state_space));
state_space->ps = (struct secp256k1_pippenger_point_state *) secp256k1_scratch_alloc(scratch, entries * sizeof(*state_space->ps));
state_space->wnaf_na = (int *) secp256k1_scratch_alloc(scratch, entries*(WNAF_SIZE(bucket_window+1)) * sizeof(int));
buckets = (secp256k1_gej *) secp256k1_scratch_alloc(scratch, (1<<bucket_window) * sizeof(*buckets));
if (inp_g_sc != NULL) {
scalars[0] = *inp_g_sc;
points[0] = secp256k1_ge_const_g;
idx++;
#ifdef USE_ENDOMORPHISM
secp256k1_ecmult_endo_split(&scalars[0], &scalars[1], &points[0], &points[1]);
idx++;
#endif
}
while (point_idx < n_points) {
if (!cb(&scalars[idx], &points[idx], point_idx + cb_offset, cbdata)) {
secp256k1_scratch_deallocate_frame(scratch);
return 0;
}
idx++;
#ifdef USE_ENDOMORPHISM
secp256k1_ecmult_endo_split(&scalars[idx - 1], &scalars[idx], &points[idx - 1], &points[idx]);
idx++;
#endif
point_idx++;
}
secp256k1_ecmult_pippenger_wnaf(buckets, bucket_window, state_space, r, scalars, points, idx);
/* Clear data */
for(i = 0; (size_t)i < idx; i++) {
secp256k1_scalar_clear(&scalars[i]);
state_space->ps[i].skew_na = 0;
for(j = 0; j < WNAF_SIZE(bucket_window+1); j++) {
state_space->wnaf_na[i * WNAF_SIZE(bucket_window+1) + j] = 0;
}
}
for(i = 0; i < 1<<bucket_window; i++) {
secp256k1_gej_clear(&buckets[i]);
}
secp256k1_scratch_deallocate_frame(scratch);
return 1;
}
/* Wrapper for secp256k1_ecmult_multi_func interface */
static int secp256k1_ecmult_pippenger_batch_single(const secp256k1_ecmult_context *actx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) {
return secp256k1_ecmult_pippenger_batch(actx, scratch, r, inp_g_sc, cb, cbdata, n, 0);
}
/**
* Returns the maximum number of points in addition to G that can be used with
* a given scratch space. The function ensures that fewer points may also be
* used.
*/
static size_t secp256k1_pippenger_max_points(secp256k1_scratch *scratch) {
size_t max_alloc = secp256k1_scratch_max_allocation(scratch, PIPPENGER_SCRATCH_OBJECTS);
int bucket_window;
size_t res = 0;
for (bucket_window = 1; bucket_window <= PIPPENGER_MAX_BUCKET_WINDOW; bucket_window++) {
size_t n_points;
size_t max_points = secp256k1_pippenger_bucket_window_inv(bucket_window);
size_t space_for_points;
size_t space_overhead;
size_t entry_size = sizeof(secp256k1_ge) + sizeof(secp256k1_scalar) + sizeof(struct secp256k1_pippenger_point_state) + (WNAF_SIZE(bucket_window+1)+1)*sizeof(int);
#ifdef USE_ENDOMORPHISM
entry_size = 2*entry_size;
#endif
space_overhead = ((1<<bucket_window) * sizeof(secp256k1_gej) + entry_size + sizeof(struct secp256k1_pippenger_state));
if (space_overhead > max_alloc) {
break;
}
space_for_points = max_alloc - space_overhead;
n_points = space_for_points/entry_size;
n_points = n_points > max_points ? max_points : n_points;
if (n_points > res) {
res = n_points;
}
if (n_points < max_points) {
/* A larger bucket_window may support even more points. But if we
* would choose that then the caller couldn't safely use any number
* smaller than what this function returns */
break;
}
}
return res;
}
typedef int (*secp256k1_ecmult_multi_func)(const secp256k1_ecmult_context*, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t);
static int secp256k1_ecmult_multi_var(const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) {
size_t i;
int (*f)(const secp256k1_ecmult_context*, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t, size_t);
size_t max_points;
size_t n_batches;
size_t n_batch_points;
secp256k1_gej_set_infinity(r);
if (inp_g_sc == NULL && n == 0) {
return 1;
} else if (n == 0) {
secp256k1_scalar szero;
secp256k1_scalar_set_int(&szero, 0);
secp256k1_ecmult(ctx, r, r, &szero, inp_g_sc);
return 1;
}
max_points = secp256k1_pippenger_max_points(scratch);
if (max_points == 0) {
return 0;
} else if (max_points > ECMULT_MAX_POINTS_PER_BATCH) {
max_points = ECMULT_MAX_POINTS_PER_BATCH;
}
n_batches = (n+max_points-1)/max_points;
n_batch_points = (n+n_batches-1)/n_batches;
if (n_batch_points >= ECMULT_PIPPENGER_THRESHOLD) {
f = secp256k1_ecmult_pippenger_batch;
} else {
max_points = secp256k1_strauss_max_points(scratch);
if (max_points == 0) {
return 0;
}
n_batches = (n+max_points-1)/max_points;
n_batch_points = (n+n_batches-1)/n_batches;
f = secp256k1_ecmult_strauss_batch;
}
for(i = 0; i < n_batches; i++) {
size_t nbp = n < n_batch_points ? n : n_batch_points;
size_t offset = n_batch_points*i;
secp256k1_gej tmp;
if (!f(ctx, scratch, &tmp, i == 0 ? inp_g_sc : NULL, cb, cbdata, nbp, offset)) {
return 0;
}
secp256k1_gej_add_var(r, r, &tmp, NULL);
n -= nbp;
}
return 1;
}
#endif /* SECP256K1_ECMULT_IMPL_H */
diff --git a/src/secp256k1/src/group.h b/src/secp256k1/src/group.h
index 3947ea2dd..8e122ab42 100644
--- a/src/secp256k1/src/group.h
+++ b/src/secp256k1/src/group.h
@@ -1,147 +1,142 @@
/**********************************************************************
* 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.*
**********************************************************************/
#ifndef SECP256K1_GROUP_H
#define SECP256K1_GROUP_H
#include "num.h"
#include "field.h"
/** A group element of the secp256k1 curve, in affine coordinates. */
typedef struct {
secp256k1_fe x;
secp256k1_fe y;
int infinity; /* whether this represents the point at infinity */
} secp256k1_ge;
#define SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0}
#define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
/** A group element of the secp256k1 curve, in jacobian coordinates. */
typedef struct {
secp256k1_fe x; /* actual X: x/z^2 */
secp256k1_fe y; /* actual Y: y/z^3 */
secp256k1_fe z;
int infinity; /* whether this represents the point at infinity */
} secp256k1_gej;
#define SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0}
#define SECP256K1_GEJ_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
typedef struct {
secp256k1_fe_storage x;
secp256k1_fe_storage y;
} secp256k1_ge_storage;
#define SECP256K1_GE_STORAGE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))}
#define SECP256K1_GE_STORAGE_CONST_GET(t) SECP256K1_FE_STORAGE_CONST_GET(t.x), SECP256K1_FE_STORAGE_CONST_GET(t.y)
/** Set a group element equal to the point with given X and Y coordinates */
static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y);
/** Set a group element (affine) equal to the point with the given X coordinate
* and a Y coordinate that is a quadratic residue modulo p. The return value
* is true iff a coordinate with the given X coordinate exists.
*/
static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x);
/** Set a group element (affine) equal to the point with the given X coordinate, and given oddness
* for Y. Return value indicates whether the result is valid. */
static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd);
/** Check whether a group element is the point at infinity. */
static int secp256k1_ge_is_infinity(const secp256k1_ge *a);
/** Check whether a group element is valid (i.e., on the curve). */
static int secp256k1_ge_is_valid_var(const secp256k1_ge *a);
static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a);
/** Set a group element equal to another which is given in jacobian coordinates */
static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a);
/** Set a batch of group elements equal to the inputs given in jacobian coordinates */
-static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len, const secp256k1_callback *cb);
-
-/** Set a batch of group elements equal to the inputs given in jacobian
- * coordinates (with known z-ratios). zr must contain the known z-ratios such
- * that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. */
-static void secp256k1_ge_set_table_gej_var(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr, size_t len);
+static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len);
/** Bring a batch inputs given in jacobian coordinates (with known z-ratios) to
* the same global z "denominator". zr must contain the known z-ratios such
* that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. The x and y
* coordinates of the result are stored in r, the common z coordinate is
* stored in globalz. */
static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr);
/** Set a group element (affine) equal to the point at infinity. */
static void secp256k1_ge_set_infinity(secp256k1_ge *r);
/** Set a group element (jacobian) equal to the point at infinity. */
static void secp256k1_gej_set_infinity(secp256k1_gej *r);
/** Set a group element (jacobian) equal to another which is given in affine coordinates. */
static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a);
/** Compare the X coordinate of a group element (jacobian). */
static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a);
/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */
static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a);
/** Check whether a group element is the point at infinity. */
static int secp256k1_gej_is_infinity(const secp256k1_gej *a);
/** Check whether a group element's y coordinate is a quadratic residue. */
static int secp256k1_gej_has_quad_y_var(const secp256k1_gej *a);
/** Set r equal to the double of a. If rzr is not-NULL, r->z = a->z * *rzr (where infinity means an implicit z = 0).
* a may not be zero. Constant time. */
static void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
/** Set r equal to the double of a. If rzr is not-NULL, r->z = a->z * *rzr (where infinity means an implicit z = 0). */
static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
/** Set r equal to the sum of a and b. If rzr is non-NULL, r->z = a->z * *rzr (a cannot be infinity in that case). */
static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr);
/** Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). */
static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b);
/** Set r equal to the sum of a and b (with b given in affine coordinates). This is more efficient
than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time
guarantee, and b is allowed to be infinity. If rzr is non-NULL, r->z = a->z * *rzr (a cannot be infinity in that case). */
static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr);
/** Set r equal to the sum of a and b (with the inverse of b's Z coordinate passed as bzinv). */
static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv);
#ifdef USE_ENDOMORPHISM
/** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */
static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a);
#endif
/** Clear a secp256k1_gej to prevent leaking sensitive information. */
static void secp256k1_gej_clear(secp256k1_gej *r);
/** Clear a secp256k1_ge to prevent leaking sensitive information. */
static void secp256k1_ge_clear(secp256k1_ge *r);
/** Convert a group element to the storage type. */
static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a);
/** Convert a group element back from the storage type. */
static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a);
/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag);
/** Rescale a jacobian point by b which must be non-zero. Constant-time. */
static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *b);
#endif /* SECP256K1_GROUP_H */
diff --git a/src/secp256k1/src/group_impl.h b/src/secp256k1/src/group_impl.h
index cb6ab7cb2..9b93c39e9 100644
--- a/src/secp256k1/src/group_impl.h
+++ b/src/secp256k1/src/group_impl.h
@@ -1,708 +1,705 @@
/**********************************************************************
* 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.*
**********************************************************************/
#ifndef SECP256K1_GROUP_IMPL_H
#define SECP256K1_GROUP_IMPL_H
#include "num.h"
#include "field.h"
#include "group.h"
/* These points can be generated in sage as follows:
*
* 0. Setup a worksheet with the following parameters.
* b = 4 # whatever CURVE_B will be set to
* F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
* C = EllipticCurve ([F (0), F (b)])
*
* 1. Determine all the small orders available to you. (If there are
* no satisfactory ones, go back and change b.)
* print C.order().factor(limit=1000)
*
* 2. Choose an order as one of the prime factors listed in the above step.
* (You can also multiply some to get a composite order, though the
* tests will crash trying to invert scalars during signing.) We take a
* random point and scale it to drop its order to the desired value.
* There is some probability this won't work; just try again.
* order = 199
* P = C.random_point()
* P = (int(P.order()) / int(order)) * P
* assert(P.order() == order)
*
* 3. Print the values. You'll need to use a vim macro or something to
* split the hex output into 4-byte chunks.
* print "%x %x" % P.xy()
*/
#if defined(EXHAUSTIVE_TEST_ORDER)
# if EXHAUSTIVE_TEST_ORDER == 199
static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
0xFA7CC9A7, 0x0737F2DB, 0xA749DD39, 0x2B4FB069,
0x3B017A7D, 0xA808C2F1, 0xFB12940C, 0x9EA66C18,
0x78AC123A, 0x5ED8AEF3, 0x8732BC91, 0x1F3A2868,
0x48DF246C, 0x808DAE72, 0xCFE52572, 0x7F0501ED
);
static const int CURVE_B = 4;
# elif EXHAUSTIVE_TEST_ORDER == 13
static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
0xedc60018, 0xa51a786b, 0x2ea91f4d, 0x4c9416c0,
0x9de54c3b, 0xa1316554, 0x6cf4345c, 0x7277ef15,
0x54cb1b6b, 0xdc8c1273, 0x087844ea, 0x43f4603e,
0x0eaf9a43, 0xf6effe55, 0x939f806d, 0x37adf8ac
);
static const int CURVE_B = 2;
# else
# error No known generator for the specified exhaustive test group order.
# endif
#else
/** Generator for secp256k1, value 'g' defined in
* "Standards for Efficient Cryptography" (SEC2) 2.7.1.
*/
static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,
0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL,
0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL,
0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
);
static const int CURVE_B = 7;
#endif
static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) {
secp256k1_fe zi2;
secp256k1_fe zi3;
secp256k1_fe_sqr(&zi2, zi);
secp256k1_fe_mul(&zi3, &zi2, zi);
secp256k1_fe_mul(&r->x, &a->x, &zi2);
secp256k1_fe_mul(&r->y, &a->y, &zi3);
r->infinity = a->infinity;
}
static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y) {
r->infinity = 0;
r->x = *x;
r->y = *y;
}
static int secp256k1_ge_is_infinity(const secp256k1_ge *a) {
return a->infinity;
}
static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a) {
*r = *a;
secp256k1_fe_normalize_weak(&r->y);
secp256k1_fe_negate(&r->y, &r->y, 1);
}
static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a) {
secp256k1_fe z2, z3;
r->infinity = a->infinity;
secp256k1_fe_inv(&a->z, &a->z);
secp256k1_fe_sqr(&z2, &a->z);
secp256k1_fe_mul(&z3, &a->z, &z2);
secp256k1_fe_mul(&a->x, &a->x, &z2);
secp256k1_fe_mul(&a->y, &a->y, &z3);
secp256k1_fe_set_int(&a->z, 1);
r->x = a->x;
r->y = a->y;
}
static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) {
secp256k1_fe z2, z3;
r->infinity = a->infinity;
if (a->infinity) {
return;
}
secp256k1_fe_inv_var(&a->z, &a->z);
secp256k1_fe_sqr(&z2, &a->z);
secp256k1_fe_mul(&z3, &a->z, &z2);
secp256k1_fe_mul(&a->x, &a->x, &z2);
secp256k1_fe_mul(&a->y, &a->y, &z3);
secp256k1_fe_set_int(&a->z, 1);
r->x = a->x;
r->y = a->y;
}
-static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len, const secp256k1_callback *cb) {
- secp256k1_fe *az;
- secp256k1_fe *azi;
+static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len) {
+ secp256k1_fe u;
size_t i;
- size_t count = 0;
- az = (secp256k1_fe *)checked_malloc(cb, sizeof(secp256k1_fe) * len);
+ size_t last_i = SIZE_MAX;
+
for (i = 0; i < len; i++) {
if (!a[i].infinity) {
- az[count++] = a[i].z;
+ /* Use destination's x coordinates as scratch space */
+ if (last_i == SIZE_MAX) {
+ r[i].x = a[i].z;
+ } else {
+ secp256k1_fe_mul(&r[i].x, &r[last_i].x, &a[i].z);
+ }
+ last_i = i;
}
}
+ if (last_i == SIZE_MAX) {
+ return;
+ }
+ secp256k1_fe_inv_var(&u, &r[last_i].x);
- azi = (secp256k1_fe *)checked_malloc(cb, sizeof(secp256k1_fe) * count);
- secp256k1_fe_inv_all_var(azi, az, count);
- free(az);
-
- count = 0;
- for (i = 0; i < len; i++) {
- r[i].infinity = a[i].infinity;
+ i = last_i;
+ while (i > 0) {
+ i--;
if (!a[i].infinity) {
- secp256k1_ge_set_gej_zinv(&r[i], &a[i], &azi[count++]);
+ secp256k1_fe_mul(&r[last_i].x, &r[i].x, &u);
+ secp256k1_fe_mul(&u, &u, &a[last_i].z);
+ last_i = i;
}
}
- free(azi);
-}
+ VERIFY_CHECK(!a[last_i].infinity);
+ r[last_i].x = u;
-static void secp256k1_ge_set_table_gej_var(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr, size_t len) {
- size_t i = len - 1;
- secp256k1_fe zi;
-
- if (len > 0) {
- /* Compute the inverse of the last z coordinate, and use it to compute the last affine output. */
- secp256k1_fe_inv(&zi, &a[i].z);
- secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zi);
-
- /* Work out way backwards, using the z-ratios to scale the x/y values. */
- while (i > 0) {
- secp256k1_fe_mul(&zi, &zi, &zr[i]);
- i--;
- secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zi);
+ for (i = 0; i < len; i++) {
+ r[i].infinity = a[i].infinity;
+ if (!a[i].infinity) {
+ secp256k1_ge_set_gej_zinv(&r[i], &a[i], &r[i].x);
}
}
}
static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr) {
size_t i = len - 1;
secp256k1_fe zs;
if (len > 0) {
/* The z of the final point gives us the "global Z" for the table. */
r[i].x = a[i].x;
r[i].y = a[i].y;
/* Ensure all y values are in weak normal form for fast negation of points */
secp256k1_fe_normalize_weak(&r[i].y);
*globalz = a[i].z;
r[i].infinity = 0;
zs = zr[i];
/* Work our way backwards, using the z-ratios to scale the x/y values. */
while (i > 0) {
if (i != len - 1) {
secp256k1_fe_mul(&zs, &zs, &zr[i]);
}
i--;
secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zs);
}
}
}
static void secp256k1_gej_set_infinity(secp256k1_gej *r) {
r->infinity = 1;
secp256k1_fe_clear(&r->x);
secp256k1_fe_clear(&r->y);
secp256k1_fe_clear(&r->z);
}
static void secp256k1_ge_set_infinity(secp256k1_ge *r) {
r->infinity = 1;
secp256k1_fe_clear(&r->x);
secp256k1_fe_clear(&r->y);
}
static void secp256k1_gej_clear(secp256k1_gej *r) {
r->infinity = 0;
secp256k1_fe_clear(&r->x);
secp256k1_fe_clear(&r->y);
secp256k1_fe_clear(&r->z);
}
static void secp256k1_ge_clear(secp256k1_ge *r) {
r->infinity = 0;
secp256k1_fe_clear(&r->x);
secp256k1_fe_clear(&r->y);
}
static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x) {
secp256k1_fe x2, x3, c;
r->x = *x;
secp256k1_fe_sqr(&x2, x);
secp256k1_fe_mul(&x3, x, &x2);
r->infinity = 0;
secp256k1_fe_set_int(&c, CURVE_B);
secp256k1_fe_add(&c, &x3);
return secp256k1_fe_sqrt(&r->y, &c);
}
static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd) {
if (!secp256k1_ge_set_xquad(r, x)) {
return 0;
}
secp256k1_fe_normalize_var(&r->y);
if (secp256k1_fe_is_odd(&r->y) != odd) {
secp256k1_fe_negate(&r->y, &r->y, 1);
}
return 1;
}
static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a) {
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
secp256k1_fe_set_int(&r->z, 1);
}
static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a) {
secp256k1_fe r, r2;
VERIFY_CHECK(!a->infinity);
secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x);
r2 = a->x; secp256k1_fe_normalize_weak(&r2);
return secp256k1_fe_equal_var(&r, &r2);
}
static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a) {
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
r->z = a->z;
secp256k1_fe_normalize_weak(&r->y);
secp256k1_fe_negate(&r->y, &r->y, 1);
}
static int secp256k1_gej_is_infinity(const secp256k1_gej *a) {
return a->infinity;
}
static int secp256k1_gej_is_valid_var(const secp256k1_gej *a) {
secp256k1_fe y2, x3, z2, z6;
if (a->infinity) {
return 0;
}
/** y^2 = x^3 + 7
* (Y/Z^3)^2 = (X/Z^2)^3 + 7
* Y^2 / Z^6 = X^3 / Z^6 + 7
* Y^2 = X^3 + 7*Z^6
*/
secp256k1_fe_sqr(&y2, &a->y);
secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
secp256k1_fe_sqr(&z2, &a->z);
secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
secp256k1_fe_mul_int(&z6, CURVE_B);
secp256k1_fe_add(&x3, &z6);
secp256k1_fe_normalize_weak(&x3);
return secp256k1_fe_equal_var(&y2, &x3);
}
static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
secp256k1_fe y2, x3, c;
if (a->infinity) {
return 0;
}
/* y^2 = x^3 + 7 */
secp256k1_fe_sqr(&y2, &a->y);
secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
secp256k1_fe_set_int(&c, CURVE_B);
secp256k1_fe_add(&x3, &c);
secp256k1_fe_normalize_weak(&x3);
return secp256k1_fe_equal_var(&y2, &x3);
}
static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
/* Operations: 3 mul, 4 sqr, 0 normalize, 12 mul_int/add/negate.
*
* Note that there is an implementation described at
* https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
* which trades a multiply for a square, but in practice this is actually slower,
* mainly because it requires more normalizations.
*/
secp256k1_fe t1,t2,t3,t4;
/** For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity,
* Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have
* y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p.
*
* Having said this, if this function receives a point on a sextic twist, e.g. by
* a fault attack, it is possible for y to be 0. This happens for y^2 = x^3 + 6,
* since -6 does have a cube root mod p. For this point, this function will not set
* the infinity flag even though the point doubles to infinity, and the result
* point will be gibberish (z = 0 but infinity = 0).
*/
r->infinity = a->infinity;
if (r->infinity) {
if (rzr != NULL) {
secp256k1_fe_set_int(rzr, 1);
}
return;
}
if (rzr != NULL) {
*rzr = a->y;
secp256k1_fe_normalize_weak(rzr);
secp256k1_fe_mul_int(rzr, 2);
}
secp256k1_fe_mul(&r->z, &a->z, &a->y);
secp256k1_fe_mul_int(&r->z, 2); /* Z' = 2*Y*Z (2) */
secp256k1_fe_sqr(&t1, &a->x);
secp256k1_fe_mul_int(&t1, 3); /* T1 = 3*X^2 (3) */
secp256k1_fe_sqr(&t2, &t1); /* T2 = 9*X^4 (1) */
secp256k1_fe_sqr(&t3, &a->y);
secp256k1_fe_mul_int(&t3, 2); /* T3 = 2*Y^2 (2) */
secp256k1_fe_sqr(&t4, &t3);
secp256k1_fe_mul_int(&t4, 2); /* T4 = 8*Y^4 (2) */
secp256k1_fe_mul(&t3, &t3, &a->x); /* T3 = 2*X*Y^2 (1) */
r->x = t3;
secp256k1_fe_mul_int(&r->x, 4); /* X' = 8*X*Y^2 (4) */
secp256k1_fe_negate(&r->x, &r->x, 4); /* X' = -8*X*Y^2 (5) */
secp256k1_fe_add(&r->x, &t2); /* X' = 9*X^4 - 8*X*Y^2 (6) */
secp256k1_fe_negate(&t2, &t2, 1); /* T2 = -9*X^4 (2) */
secp256k1_fe_mul_int(&t3, 6); /* T3 = 12*X*Y^2 (6) */
secp256k1_fe_add(&t3, &t2); /* T3 = 12*X*Y^2 - 9*X^4 (8) */
secp256k1_fe_mul(&r->y, &t1, &t3); /* Y' = 36*X^3*Y^2 - 27*X^6 (1) */
secp256k1_fe_negate(&t2, &t4, 2); /* T2 = -8*Y^4 (3) */
secp256k1_fe_add(&r->y, &t2); /* Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4) */
}
static SECP256K1_INLINE void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
VERIFY_CHECK(!secp256k1_gej_is_infinity(a));
secp256k1_gej_double_var(r, a, rzr);
}
static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr) {
/* Operations: 12 mul, 4 sqr, 2 normalize, 12 mul_int/add/negate */
secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
if (a->infinity) {
VERIFY_CHECK(rzr == NULL);
*r = *b;
return;
}
if (b->infinity) {
if (rzr != NULL) {
secp256k1_fe_set_int(rzr, 1);
}
*r = *a;
return;
}
r->infinity = 0;
secp256k1_fe_sqr(&z22, &b->z);
secp256k1_fe_sqr(&z12, &a->z);
secp256k1_fe_mul(&u1, &a->x, &z22);
secp256k1_fe_mul(&u2, &b->x, &z12);
secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z);
secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
if (secp256k1_fe_normalizes_to_zero_var(&h)) {
if (secp256k1_fe_normalizes_to_zero_var(&i)) {
secp256k1_gej_double_var(r, a, rzr);
} else {
if (rzr != NULL) {
secp256k1_fe_set_int(rzr, 0);
}
r->infinity = 1;
}
return;
}
secp256k1_fe_sqr(&i2, &i);
secp256k1_fe_sqr(&h2, &h);
secp256k1_fe_mul(&h3, &h, &h2);
secp256k1_fe_mul(&h, &h, &b->z);
if (rzr != NULL) {
*rzr = h;
}
secp256k1_fe_mul(&r->z, &a->z, &h);
secp256k1_fe_mul(&t, &u1, &h2);
r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
secp256k1_fe_add(&r->y, &h3);
}
static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr) {
/* 8 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
secp256k1_fe z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
if (a->infinity) {
VERIFY_CHECK(rzr == NULL);
secp256k1_gej_set_ge(r, b);
return;
}
if (b->infinity) {
if (rzr != NULL) {
secp256k1_fe_set_int(rzr, 1);
}
*r = *a;
return;
}
r->infinity = 0;
secp256k1_fe_sqr(&z12, &a->z);
u1 = a->x; secp256k1_fe_normalize_weak(&u1);
secp256k1_fe_mul(&u2, &b->x, &z12);
s1 = a->y; secp256k1_fe_normalize_weak(&s1);
secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
if (secp256k1_fe_normalizes_to_zero_var(&h)) {
if (secp256k1_fe_normalizes_to_zero_var(&i)) {
secp256k1_gej_double_var(r, a, rzr);
} else {
if (rzr != NULL) {
secp256k1_fe_set_int(rzr, 0);
}
r->infinity = 1;
}
return;
}
secp256k1_fe_sqr(&i2, &i);
secp256k1_fe_sqr(&h2, &h);
secp256k1_fe_mul(&h3, &h, &h2);
if (rzr != NULL) {
*rzr = h;
}
secp256k1_fe_mul(&r->z, &a->z, &h);
secp256k1_fe_mul(&t, &u1, &h2);
r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
secp256k1_fe_add(&r->y, &h3);
}
static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv) {
/* 9 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
secp256k1_fe az, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
if (b->infinity) {
*r = *a;
return;
}
if (a->infinity) {
secp256k1_fe bzinv2, bzinv3;
r->infinity = b->infinity;
secp256k1_fe_sqr(&bzinv2, bzinv);
secp256k1_fe_mul(&bzinv3, &bzinv2, bzinv);
secp256k1_fe_mul(&r->x, &b->x, &bzinv2);
secp256k1_fe_mul(&r->y, &b->y, &bzinv3);
secp256k1_fe_set_int(&r->z, 1);
return;
}
r->infinity = 0;
/** We need to calculate (rx,ry,rz) = (ax,ay,az) + (bx,by,1/bzinv). Due to
* secp256k1's isomorphism we can multiply the Z coordinates on both sides
* by bzinv, and get: (rx,ry,rz*bzinv) = (ax,ay,az*bzinv) + (bx,by,1).
* This means that (rx,ry,rz) can be calculated as
* (ax,ay,az*bzinv) + (bx,by,1), when not applying the bzinv factor to rz.
* The variable az below holds the modified Z coordinate for a, which is used
* for the computation of rx and ry, but not for rz.
*/
secp256k1_fe_mul(&az, &a->z, bzinv);
secp256k1_fe_sqr(&z12, &az);
u1 = a->x; secp256k1_fe_normalize_weak(&u1);
secp256k1_fe_mul(&u2, &b->x, &z12);
s1 = a->y; secp256k1_fe_normalize_weak(&s1);
secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &az);
secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
if (secp256k1_fe_normalizes_to_zero_var(&h)) {
if (secp256k1_fe_normalizes_to_zero_var(&i)) {
secp256k1_gej_double_var(r, a, NULL);
} else {
r->infinity = 1;
}
return;
}
secp256k1_fe_sqr(&i2, &i);
secp256k1_fe_sqr(&h2, &h);
secp256k1_fe_mul(&h3, &h, &h2);
r->z = a->z; secp256k1_fe_mul(&r->z, &r->z, &h);
secp256k1_fe_mul(&t, &u1, &h2);
r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
secp256k1_fe_add(&r->y, &h3);
}
static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b) {
/* Operations: 7 mul, 5 sqr, 4 normalize, 21 mul_int/add/negate/cmov */
static const secp256k1_fe fe_1 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
secp256k1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr;
secp256k1_fe m_alt, rr_alt;
int infinity, degenerate;
VERIFY_CHECK(!b->infinity);
VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
/** In:
* Eric Brier and Marc Joye, Weierstrass Elliptic Curves and Side-Channel Attacks.
* In D. Naccache and P. Paillier, Eds., Public Key Cryptography, vol. 2274 of Lecture Notes in Computer Science, pages 335-345. Springer-Verlag, 2002.
* we find as solution for a unified addition/doubling formula:
* lambda = ((x1 + x2)^2 - x1 * x2 + a) / (y1 + y2), with a = 0 for secp256k1's curve equation.
* x3 = lambda^2 - (x1 + x2)
* 2*y3 = lambda * (x1 + x2 - 2 * x3) - (y1 + y2).
*
* Substituting x_i = Xi / Zi^2 and yi = Yi / Zi^3, for i=1,2,3, gives:
* U1 = X1*Z2^2, U2 = X2*Z1^2
* S1 = Y1*Z2^3, S2 = Y2*Z1^3
* Z = Z1*Z2
* T = U1+U2
* M = S1+S2
* Q = T*M^2
* R = T^2-U1*U2
* X3 = 4*(R^2-Q)
* Y3 = 4*(R*(3*Q-2*R^2)-M^4)
* Z3 = 2*M*Z
* (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.)
*
* This formula has the benefit of being the same for both addition
* of distinct points and doubling. However, it breaks down in the
* case that either point is infinity, or that y1 = -y2. We handle
* these cases in the following ways:
*
* - If b is infinity we simply bail by means of a VERIFY_CHECK.
*
* - If a is infinity, we detect this, and at the end of the
* computation replace the result (which will be meaningless,
* but we compute to be constant-time) with b.x : b.y : 1.
*
* - If a = -b, we have y1 = -y2, which is a degenerate case.
* But here the answer is infinity, so we simply set the
* infinity flag of the result, overriding the computed values
* without even needing to cmov.
*
* - If y1 = -y2 but x1 != x2, which does occur thanks to certain
* properties of our curve (specifically, 1 has nontrivial cube
* roots in our field, and the curve equation has no x coefficient)
* then the answer is not infinity but also not given by the above
* equation. In this case, we cmov in place an alternate expression
* for lambda. Specifically (y1 - y2)/(x1 - x2). Where both these
* expressions for lambda are defined, they are equal, and can be
* obtained from each other by multiplication by (y1 + y2)/(y1 + y2)
* then substitution of x^3 + 7 for y^2 (using the curve equation).
* For all pairs of nonzero points (a, b) at least one is defined,
* so this covers everything.
*/
secp256k1_fe_sqr(&zz, &a->z); /* z = Z1^2 */
u1 = a->x; secp256k1_fe_normalize_weak(&u1); /* u1 = U1 = X1*Z2^2 (1) */
secp256k1_fe_mul(&u2, &b->x, &zz); /* u2 = U2 = X2*Z1^2 (1) */
s1 = a->y; secp256k1_fe_normalize_weak(&s1); /* s1 = S1 = Y1*Z2^3 (1) */
secp256k1_fe_mul(&s2, &b->y, &zz); /* s2 = Y2*Z1^2 (1) */
secp256k1_fe_mul(&s2, &s2, &a->z); /* s2 = S2 = Y2*Z1^3 (1) */
t = u1; secp256k1_fe_add(&t, &u2); /* t = T = U1+U2 (2) */
m = s1; secp256k1_fe_add(&m, &s2); /* m = M = S1+S2 (2) */
secp256k1_fe_sqr(&rr, &t); /* rr = T^2 (1) */
secp256k1_fe_negate(&m_alt, &u2, 1); /* Malt = -X2*Z1^2 */
secp256k1_fe_mul(&tt, &u1, &m_alt); /* tt = -U1*U2 (2) */
secp256k1_fe_add(&rr, &tt); /* rr = R = T^2-U1*U2 (3) */
/** If lambda = R/M = 0/0 we have a problem (except in the "trivial"
* case that Z = z1z2 = 0, and this is special-cased later on). */
degenerate = secp256k1_fe_normalizes_to_zero(&m) &
secp256k1_fe_normalizes_to_zero(&rr);
/* This only occurs when y1 == -y2 and x1^3 == x2^3, but x1 != x2.
* This means either x1 == beta*x2 or beta*x1 == x2, where beta is
* a nontrivial cube root of one. In either case, an alternate
* non-indeterminate expression for lambda is (y1 - y2)/(x1 - x2),
* so we set R/M equal to this. */
rr_alt = s1;
secp256k1_fe_mul_int(&rr_alt, 2); /* rr = Y1*Z2^3 - Y2*Z1^3 (2) */
secp256k1_fe_add(&m_alt, &u1); /* Malt = X1*Z2^2 - X2*Z1^2 */
secp256k1_fe_cmov(&rr_alt, &rr, !degenerate);
secp256k1_fe_cmov(&m_alt, &m, !degenerate);
/* Now Ralt / Malt = lambda and is guaranteed not to be 0/0.
* From here on out Ralt and Malt represent the numerator
* and denominator of lambda; R and M represent the explicit
* expressions x1^2 + x2^2 + x1x2 and y1 + y2. */
secp256k1_fe_sqr(&n, &m_alt); /* n = Malt^2 (1) */
secp256k1_fe_mul(&q, &n, &t); /* q = Q = T*Malt^2 (1) */
/* These two lines use the observation that either M == Malt or M == 0,
* so M^3 * Malt is either Malt^4 (which is computed by squaring), or
* zero (which is "computed" by cmov). So the cost is one squaring
* versus two multiplications. */
secp256k1_fe_sqr(&n, &n);
secp256k1_fe_cmov(&n, &m, degenerate); /* n = M^3 * Malt (2) */
secp256k1_fe_sqr(&t, &rr_alt); /* t = Ralt^2 (1) */
secp256k1_fe_mul(&r->z, &a->z, &m_alt); /* r->z = Malt*Z (1) */
infinity = secp256k1_fe_normalizes_to_zero(&r->z) * (1 - a->infinity);
secp256k1_fe_mul_int(&r->z, 2); /* r->z = Z3 = 2*Malt*Z (2) */
secp256k1_fe_negate(&q, &q, 1); /* q = -Q (2) */
secp256k1_fe_add(&t, &q); /* t = Ralt^2-Q (3) */
secp256k1_fe_normalize_weak(&t);
r->x = t; /* r->x = Ralt^2-Q (1) */
secp256k1_fe_mul_int(&t, 2); /* t = 2*x3 (2) */
secp256k1_fe_add(&t, &q); /* t = 2*x3 - Q: (4) */
secp256k1_fe_mul(&t, &t, &rr_alt); /* t = Ralt*(2*x3 - Q) (1) */
secp256k1_fe_add(&t, &n); /* t = Ralt*(2*x3 - Q) + M^3*Malt (3) */
secp256k1_fe_negate(&r->y, &t, 3); /* r->y = Ralt*(Q - 2x3) - M^3*Malt (4) */
secp256k1_fe_normalize_weak(&r->y);
secp256k1_fe_mul_int(&r->x, 4); /* r->x = X3 = 4*(Ralt^2-Q) */
secp256k1_fe_mul_int(&r->y, 4); /* r->y = Y3 = 4*Ralt*(Q - 2x3) - 4*M^3*Malt (4) */
/** In case a->infinity == 1, replace r with (b->x, b->y, 1). */
secp256k1_fe_cmov(&r->x, &b->x, a->infinity);
secp256k1_fe_cmov(&r->y, &b->y, a->infinity);
secp256k1_fe_cmov(&r->z, &fe_1, a->infinity);
r->infinity = infinity;
}
static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *s) {
/* Operations: 4 mul, 1 sqr */
secp256k1_fe zz;
VERIFY_CHECK(!secp256k1_fe_is_zero(s));
secp256k1_fe_sqr(&zz, s);
secp256k1_fe_mul(&r->x, &r->x, &zz); /* r->x *= s^2 */
secp256k1_fe_mul(&r->y, &r->y, &zz);
secp256k1_fe_mul(&r->y, &r->y, s); /* r->y *= s^3 */
secp256k1_fe_mul(&r->z, &r->z, s); /* r->z *= s */
}
static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a) {
secp256k1_fe x, y;
VERIFY_CHECK(!a->infinity);
x = a->x;
secp256k1_fe_normalize(&x);
y = a->y;
secp256k1_fe_normalize(&y);
secp256k1_fe_to_storage(&r->x, &x);
secp256k1_fe_to_storage(&r->y, &y);
}
static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a) {
secp256k1_fe_from_storage(&r->x, &a->x);
secp256k1_fe_from_storage(&r->y, &a->y);
r->infinity = 0;
}
static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag) {
secp256k1_fe_storage_cmov(&r->x, &a->x, flag);
secp256k1_fe_storage_cmov(&r->y, &a->y, flag);
}
#ifdef USE_ENDOMORPHISM
static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) {
static const secp256k1_fe beta = SECP256K1_FE_CONST(
0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
);
*r = *a;
secp256k1_fe_mul(&r->x, &r->x, &beta);
}
#endif
static int secp256k1_gej_has_quad_y_var(const secp256k1_gej *a) {
secp256k1_fe yz;
if (a->infinity) {
return 0;
}
/* We rely on the fact that the Jacobi symbol of 1 / a->z^3 is the same as
* that of a->z. Thus a->y / a->z^3 is a quadratic residue iff a->y * a->z
is */
secp256k1_fe_mul(&yz, &a->y, &a->z);
return secp256k1_fe_is_quad_var(&yz);
}
#endif /* SECP256K1_GROUP_IMPL_H */
diff --git a/src/secp256k1/src/tests.c b/src/secp256k1/src/tests.c
index 85eb5c458..1572551a3 100644
--- a/src/secp256k1/src/tests.c
+++ b/src/secp256k1/src/tests.c
@@ -1,5108 +1,5120 @@
/**********************************************************************
* Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell *
* 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 <string.h>
#include <time.h>
#include "secp256k1.c"
#include "include/secp256k1.h"
#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"
# if OPENSSL_VERSION_NUMBER < 0x10100000L
void ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **pr, const BIGNUM **ps) {*pr = sig->r; *ps = sig->s;}
# endif
#endif
#include "contrib/lax_der_parsing.c"
#include "contrib/lax_der_privatekey_parsing.c"
#if !defined(VG_CHECK)
# if defined(VALGRIND)
# include <valgrind/memcheck.h>
# define VG_UNDEF(x,y) VALGRIND_MAKE_MEM_UNDEFINED((x),(y))
# define VG_CHECK(x,y) VALGRIND_CHECK_MEM_IS_DEFINED((x),(y))
# else
# define VG_UNDEF(x,y)
# define VG_CHECK(x,y)
# endif
#endif
static int count = 64;
static secp256k1_context *ctx = NULL;
static void counting_illegal_callback_fn(const char* str, void* data) {
/* Dummy callback function that just counts. */
int32_t *p;
(void)str;
p = data;
(*p)++;
}
static void uncounting_illegal_callback_fn(const char* str, void* data) {
/* Dummy callback function that just counts (backwards). */
int32_t *p;
(void)str;
p = data;
(*p)--;
}
void random_field_element_test(secp256k1_fe *fe) {
do {
unsigned char b32[32];
secp256k1_rand256_test(b32);
if (secp256k1_fe_set_b32(fe, b32)) {
break;
}
} while(1);
}
void random_field_element_magnitude(secp256k1_fe *fe) {
secp256k1_fe zero;
int n = secp256k1_rand_int(9);
secp256k1_fe_normalize(fe);
if (n == 0) {
return;
}
secp256k1_fe_clear(&zero);
secp256k1_fe_negate(&zero, &zero, 0);
secp256k1_fe_mul_int(&zero, n - 1);
secp256k1_fe_add(fe, &zero);
VERIFY_CHECK(fe->magnitude == n);
}
void random_group_element_test(secp256k1_ge *ge) {
secp256k1_fe fe;
do {
random_field_element_test(&fe);
if (secp256k1_ge_set_xo_var(ge, &fe, secp256k1_rand_bits(1))) {
secp256k1_fe_normalize(&ge->y);
break;
}
} while(1);
}
void random_group_element_jacobian_test(secp256k1_gej *gej, const secp256k1_ge *ge) {
secp256k1_fe z2, z3;
do {
random_field_element_test(&gej->z);
if (!secp256k1_fe_is_zero(&gej->z)) {
break;
}
} while(1);
secp256k1_fe_sqr(&z2, &gej->z);
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_scalar_order_test(secp256k1_scalar *num) {
do {
unsigned char b32[32];
int overflow = 0;
secp256k1_rand256_test(b32);
secp256k1_scalar_set_b32(num, b32, &overflow);
if (overflow || secp256k1_scalar_is_zero(num)) {
continue;
}
break;
} while(1);
}
void random_scalar_order(secp256k1_scalar *num) {
do {
unsigned char b32[32];
int overflow = 0;
secp256k1_rand256(b32);
secp256k1_scalar_set_b32(num, b32, &overflow);
if (overflow || secp256k1_scalar_is_zero(num)) {
continue;
}
break;
} while(1);
}
void run_context_tests(void) {
secp256k1_pubkey pubkey;
secp256k1_pubkey zero_pubkey;
secp256k1_ecdsa_signature sig;
unsigned char ctmp[32];
int32_t ecount;
int32_t ecount2;
secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
secp256k1_context *sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
secp256k1_context *vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
secp256k1_context *both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
secp256k1_gej pubj;
secp256k1_ge pub;
secp256k1_scalar msg, key, nonce;
secp256k1_scalar sigr, sigs;
memset(&zero_pubkey, 0, sizeof(zero_pubkey));
ecount = 0;
ecount2 = 10;
secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount2);
secp256k1_context_set_error_callback(sign, counting_illegal_callback_fn, NULL);
CHECK(vrfy->error_callback.fn != sign->error_callback.fn);
/*** clone and destroy all of them to make sure cloning was complete ***/
{
secp256k1_context *ctx_tmp;
ctx_tmp = none; none = secp256k1_context_clone(none); secp256k1_context_destroy(ctx_tmp);
ctx_tmp = sign; sign = secp256k1_context_clone(sign); secp256k1_context_destroy(ctx_tmp);
ctx_tmp = vrfy; vrfy = secp256k1_context_clone(vrfy); secp256k1_context_destroy(ctx_tmp);
ctx_tmp = both; both = secp256k1_context_clone(both); secp256k1_context_destroy(ctx_tmp);
}
/* Verify that the error callback makes it across the clone. */
CHECK(vrfy->error_callback.fn != sign->error_callback.fn);
/* And that it resets back to default. */
secp256k1_context_set_error_callback(sign, NULL, NULL);
CHECK(vrfy->error_callback.fn == sign->error_callback.fn);
/*** attempt to use them ***/
random_scalar_order_test(&msg);
random_scalar_order_test(&key);
secp256k1_ecmult_gen(&both->ecmult_gen_ctx, &pubj, &key);
secp256k1_ge_set_gej(&pub, &pubj);
/* Verify context-type checking illegal-argument errors. */
memset(ctmp, 1, 32);
CHECK(secp256k1_ec_pubkey_create(vrfy, &pubkey, ctmp) == 0);
CHECK(ecount == 1);
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(sign, &pubkey, ctmp) == 1);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ecdsa_sign(vrfy, &sig, ctmp, ctmp, NULL, NULL) == 0);
CHECK(ecount == 2);
VG_UNDEF(&sig, sizeof(sig));
CHECK(secp256k1_ecdsa_sign(sign, &sig, ctmp, ctmp, NULL, NULL) == 1);
VG_CHECK(&sig, sizeof(sig));
CHECK(ecount2 == 10);
CHECK(secp256k1_ecdsa_verify(sign, &sig, ctmp, &pubkey) == 0);
CHECK(ecount2 == 11);
CHECK(secp256k1_ecdsa_verify(vrfy, &sig, ctmp, &pubkey) == 1);
CHECK(ecount == 2);
CHECK(secp256k1_ec_pubkey_tweak_add(sign, &pubkey, ctmp) == 0);
CHECK(ecount2 == 12);
CHECK(secp256k1_ec_pubkey_tweak_add(vrfy, &pubkey, ctmp) == 1);
CHECK(ecount == 2);
CHECK(secp256k1_ec_pubkey_tweak_mul(sign, &pubkey, ctmp) == 0);
CHECK(ecount2 == 13);
CHECK(secp256k1_ec_pubkey_negate(vrfy, &pubkey) == 1);
CHECK(ecount == 2);
CHECK(secp256k1_ec_pubkey_negate(sign, &pubkey) == 1);
CHECK(ecount == 2);
CHECK(secp256k1_ec_pubkey_negate(sign, NULL) == 0);
CHECK(ecount2 == 14);
CHECK(secp256k1_ec_pubkey_negate(vrfy, &zero_pubkey) == 0);
CHECK(ecount == 3);
CHECK(secp256k1_ec_pubkey_tweak_mul(vrfy, &pubkey, ctmp) == 1);
CHECK(ecount == 3);
CHECK(secp256k1_context_randomize(vrfy, ctmp) == 1);
CHECK(ecount == 3);
CHECK(secp256k1_context_randomize(vrfy, NULL) == 1);
CHECK(ecount == 3);
CHECK(secp256k1_context_randomize(sign, ctmp) == 1);
CHECK(ecount2 == 14);
CHECK(secp256k1_context_randomize(sign, NULL) == 1);
CHECK(ecount2 == 14);
secp256k1_context_set_illegal_callback(vrfy, NULL, NULL);
secp256k1_context_set_illegal_callback(sign, NULL, NULL);
/* This shouldn't leak memory, due to already-set tests. */
secp256k1_ecmult_gen_context_build(&sign->ecmult_gen_ctx, NULL);
secp256k1_ecmult_context_build(&vrfy->ecmult_ctx, NULL);
/* obtain a working nonce */
do {
random_scalar_order_test(&nonce);
} while(!secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
/* try signing */
CHECK(secp256k1_ecdsa_sig_sign(&sign->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
CHECK(secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
/* try verifying */
CHECK(secp256k1_ecdsa_sig_verify(&vrfy->ecmult_ctx, &sigr, &sigs, &pub, &msg));
CHECK(secp256k1_ecdsa_sig_verify(&both->ecmult_ctx, &sigr, &sigs, &pub, &msg));
/* cleanup */
secp256k1_context_destroy(none);
secp256k1_context_destroy(sign);
secp256k1_context_destroy(vrfy);
secp256k1_context_destroy(both);
/* Defined as no-op. */
secp256k1_context_destroy(NULL);
}
void run_scratch_tests(void) {
int32_t ecount = 0;
secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
secp256k1_scratch_space *scratch;
/* Test public API */
secp256k1_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount);
scratch = secp256k1_scratch_space_create(none, 1000);
CHECK(scratch != NULL);
CHECK(ecount == 0);
/* Test internal API */
CHECK(secp256k1_scratch_max_allocation(scratch, 0) == 1000);
CHECK(secp256k1_scratch_max_allocation(scratch, 1) < 1000);
/* Allocating 500 bytes with no frame fails */
CHECK(secp256k1_scratch_alloc(scratch, 500) == NULL);
CHECK(secp256k1_scratch_max_allocation(scratch, 0) == 1000);
/* ...but pushing a new stack frame does affect the max allocation */
CHECK(secp256k1_scratch_allocate_frame(scratch, 500, 1) == 1);
CHECK(secp256k1_scratch_max_allocation(scratch, 1) < 500); /* 500 - ALIGNMENT */
CHECK(secp256k1_scratch_alloc(scratch, 500) != NULL);
CHECK(secp256k1_scratch_alloc(scratch, 500) == NULL);
CHECK(secp256k1_scratch_allocate_frame(scratch, 500, 1) == 0);
/* ...and this effect is undone by popping the frame */
secp256k1_scratch_deallocate_frame(scratch);
CHECK(secp256k1_scratch_max_allocation(scratch, 0) == 1000);
CHECK(secp256k1_scratch_alloc(scratch, 500) == NULL);
/* cleanup */
secp256k1_scratch_space_destroy(scratch);
secp256k1_context_destroy(none);
}
/***** HASH TESTS *****/
void run_sha256_tests(void) {
static const char *inputs[8] = {
"", "abc", "message digest", "secure hash algorithm", "SHA256 is considered to be safe",
"abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq",
"For this sample, this 63-byte string will be used as input data",
"This is exactly 64 bytes long, not counting the terminating byte"
};
static const unsigned char outputs[8][32] = {
{0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55},
{0xba, 0x78, 0x16, 0xbf, 0x8f, 0x01, 0xcf, 0xea, 0x41, 0x41, 0x40, 0xde, 0x5d, 0xae, 0x22, 0x23, 0xb0, 0x03, 0x61, 0xa3, 0x96, 0x17, 0x7a, 0x9c, 0xb4, 0x10, 0xff, 0x61, 0xf2, 0x00, 0x15, 0xad},
{0xf7, 0x84, 0x6f, 0x55, 0xcf, 0x23, 0xe1, 0x4e, 0xeb, 0xea, 0xb5, 0xb4, 0xe1, 0x55, 0x0c, 0xad, 0x5b, 0x50, 0x9e, 0x33, 0x48, 0xfb, 0xc4, 0xef, 0xa3, 0xa1, 0x41, 0x3d, 0x39, 0x3c, 0xb6, 0x50},
{0xf3, 0x0c, 0xeb, 0x2b, 0xb2, 0x82, 0x9e, 0x79, 0xe4, 0xca, 0x97, 0x53, 0xd3, 0x5a, 0x8e, 0xcc, 0x00, 0x26, 0x2d, 0x16, 0x4c, 0xc0, 0x77, 0x08, 0x02, 0x95, 0x38, 0x1c, 0xbd, 0x64, 0x3f, 0x0d},
{0x68, 0x19, 0xd9, 0x15, 0xc7, 0x3f, 0x4d, 0x1e, 0x77, 0xe4, 0xe1, 0xb5, 0x2d, 0x1f, 0xa0, 0xf9, 0xcf, 0x9b, 0xea, 0xea, 0xd3, 0x93, 0x9f, 0x15, 0x87, 0x4b, 0xd9, 0x88, 0xe2, 0xa2, 0x36, 0x30},
{0x24, 0x8d, 0x6a, 0x61, 0xd2, 0x06, 0x38, 0xb8, 0xe5, 0xc0, 0x26, 0x93, 0x0c, 0x3e, 0x60, 0x39, 0xa3, 0x3c, 0xe4, 0x59, 0x64, 0xff, 0x21, 0x67, 0xf6, 0xec, 0xed, 0xd4, 0x19, 0xdb, 0x06, 0xc1},
{0xf0, 0x8a, 0x78, 0xcb, 0xba, 0xee, 0x08, 0x2b, 0x05, 0x2a, 0xe0, 0x70, 0x8f, 0x32, 0xfa, 0x1e, 0x50, 0xc5, 0xc4, 0x21, 0xaa, 0x77, 0x2b, 0xa5, 0xdb, 0xb4, 0x06, 0xa2, 0xea, 0x6b, 0xe3, 0x42},
{0xab, 0x64, 0xef, 0xf7, 0xe8, 0x8e, 0x2e, 0x46, 0x16, 0x5e, 0x29, 0xf2, 0xbc, 0xe4, 0x18, 0x26, 0xbd, 0x4c, 0x7b, 0x35, 0x52, 0xf6, 0xb3, 0x82, 0xa9, 0xe7, 0xd3, 0xaf, 0x47, 0xc2, 0x45, 0xf8}
};
int i;
for (i = 0; i < 8; i++) {
unsigned char out[32];
secp256k1_sha256 hasher;
secp256k1_sha256_initialize(&hasher);
secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
secp256k1_sha256_finalize(&hasher, out);
CHECK(memcmp(out, outputs[i], 32) == 0);
if (strlen(inputs[i]) > 0) {
int split = secp256k1_rand_int(strlen(inputs[i]));
secp256k1_sha256_initialize(&hasher);
secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
secp256k1_sha256_finalize(&hasher, out);
CHECK(memcmp(out, outputs[i], 32) == 0);
}
}
}
void run_hmac_sha256_tests(void) {
static const char *keys[6] = {
"\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b",
"\x4a\x65\x66\x65",
"\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa",
"\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19",
"\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa",
"\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa"
};
static const char *inputs[6] = {
"\x48\x69\x20\x54\x68\x65\x72\x65",
"\x77\x68\x61\x74\x20\x64\x6f\x20\x79\x61\x20\x77\x61\x6e\x74\x20\x66\x6f\x72\x20\x6e\x6f\x74\x68\x69\x6e\x67\x3f",
"\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd",
"\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd",
"\x54\x65\x73\x74\x20\x55\x73\x69\x6e\x67\x20\x4c\x61\x72\x67\x65\x72\x20\x54\x68\x61\x6e\x20\x42\x6c\x6f\x63\x6b\x2d\x53\x69\x7a\x65\x20\x4b\x65\x79\x20\x2d\x20\x48\x61\x73\x68\x20\x4b\x65\x79\x20\x46\x69\x72\x73\x74",
"\x54\x68\x69\x73\x20\x69\x73\x20\x61\x20\x74\x65\x73\x74\x20\x75\x73\x69\x6e\x67\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x6b\x65\x79\x20\x61\x6e\x64\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x64\x61\x74\x61\x2e\x20\x54\x68\x65\x20\x6b\x65\x79\x20\x6e\x65\x65\x64\x73\x20\x74\x6f\x20\x62\x65\x20\x68\x61\x73\x68\x65\x64\x20\x62\x65\x66\x6f\x72\x65\x20\x62\x65\x69\x6e\x67\x20\x75\x73\x65\x64\x20\x62\x79\x20\x74\x68\x65\x20\x48\x4d\x41\x43\x20\x61\x6c\x67\x6f\x72\x69\x74\x68\x6d\x2e"
};
static const unsigned char outputs[6][32] = {
{0xb0, 0x34, 0x4c, 0x61, 0xd8, 0xdb, 0x38, 0x53, 0x5c, 0xa8, 0xaf, 0xce, 0xaf, 0x0b, 0xf1, 0x2b, 0x88, 0x1d, 0xc2, 0x00, 0xc9, 0x83, 0x3d, 0xa7, 0x26, 0xe9, 0x37, 0x6c, 0x2e, 0x32, 0xcf, 0xf7},
{0x5b, 0xdc, 0xc1, 0x46, 0xbf, 0x60, 0x75, 0x4e, 0x6a, 0x04, 0x24, 0x26, 0x08, 0x95, 0x75, 0xc7, 0x5a, 0x00, 0x3f, 0x08, 0x9d, 0x27, 0x39, 0x83, 0x9d, 0xec, 0x58, 0xb9, 0x64, 0xec, 0x38, 0x43},
{0x77, 0x3e, 0xa9, 0x1e, 0x36, 0x80, 0x0e, 0x46, 0x85, 0x4d, 0xb8, 0xeb, 0xd0, 0x91, 0x81, 0xa7, 0x29, 0x59, 0x09, 0x8b, 0x3e, 0xf8, 0xc1, 0x22, 0xd9, 0x63, 0x55, 0x14, 0xce, 0xd5, 0x65, 0xfe},
{0x82, 0x55, 0x8a, 0x38, 0x9a, 0x44, 0x3c, 0x0e, 0xa4, 0xcc, 0x81, 0x98, 0x99, 0xf2, 0x08, 0x3a, 0x85, 0xf0, 0xfa, 0xa3, 0xe5, 0x78, 0xf8, 0x07, 0x7a, 0x2e, 0x3f, 0xf4, 0x67, 0x29, 0x66, 0x5b},
{0x60, 0xe4, 0x31, 0x59, 0x1e, 0xe0, 0xb6, 0x7f, 0x0d, 0x8a, 0x26, 0xaa, 0xcb, 0xf5, 0xb7, 0x7f, 0x8e, 0x0b, 0xc6, 0x21, 0x37, 0x28, 0xc5, 0x14, 0x05, 0x46, 0x04, 0x0f, 0x0e, 0xe3, 0x7f, 0x54},
{0x9b, 0x09, 0xff, 0xa7, 0x1b, 0x94, 0x2f, 0xcb, 0x27, 0x63, 0x5f, 0xbc, 0xd5, 0xb0, 0xe9, 0x44, 0xbf, 0xdc, 0x63, 0x64, 0x4f, 0x07, 0x13, 0x93, 0x8a, 0x7f, 0x51, 0x53, 0x5c, 0x3a, 0x35, 0xe2}
};
int i;
for (i = 0; i < 6; i++) {
secp256k1_hmac_sha256 hasher;
unsigned char out[32];
secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
secp256k1_hmac_sha256_finalize(&hasher, out);
CHECK(memcmp(out, outputs[i], 32) == 0);
if (strlen(inputs[i]) > 0) {
int split = secp256k1_rand_int(strlen(inputs[i]));
secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
secp256k1_hmac_sha256_finalize(&hasher, out);
CHECK(memcmp(out, outputs[i], 32) == 0);
}
}
}
void run_rfc6979_hmac_sha256_tests(void) {
static const unsigned char key1[65] = {0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x00, 0x4b, 0xf5, 0x12, 0x2f, 0x34, 0x45, 0x54, 0xc5, 0x3b, 0xde, 0x2e, 0xbb, 0x8c, 0xd2, 0xb7, 0xe3, 0xd1, 0x60, 0x0a, 0xd6, 0x31, 0xc3, 0x85, 0xa5, 0xd7, 0xcc, 0xe2, 0x3c, 0x77, 0x85, 0x45, 0x9a, 0};
static const unsigned char out1[3][32] = {
{0x4f, 0xe2, 0x95, 0x25, 0xb2, 0x08, 0x68, 0x09, 0x15, 0x9a, 0xcd, 0xf0, 0x50, 0x6e, 0xfb, 0x86, 0xb0, 0xec, 0x93, 0x2c, 0x7b, 0xa4, 0x42, 0x56, 0xab, 0x32, 0x1e, 0x42, 0x1e, 0x67, 0xe9, 0xfb},
{0x2b, 0xf0, 0xff, 0xf1, 0xd3, 0xc3, 0x78, 0xa2, 0x2d, 0xc5, 0xde, 0x1d, 0x85, 0x65, 0x22, 0x32, 0x5c, 0x65, 0xb5, 0x04, 0x49, 0x1a, 0x0c, 0xbd, 0x01, 0xcb, 0x8f, 0x3a, 0xa6, 0x7f, 0xfd, 0x4a},
{0xf5, 0x28, 0xb4, 0x10, 0xcb, 0x54, 0x1f, 0x77, 0x00, 0x0d, 0x7a, 0xfb, 0x6c, 0x5b, 0x53, 0xc5, 0xc4, 0x71, 0xea, 0xb4, 0x3e, 0x46, 0x6d, 0x9a, 0xc5, 0x19, 0x0c, 0x39, 0xc8, 0x2f, 0xd8, 0x2e}
};
static const unsigned char key2[64] = {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55};
static const unsigned char out2[3][32] = {
{0x9c, 0x23, 0x6c, 0x16, 0x5b, 0x82, 0xae, 0x0c, 0xd5, 0x90, 0x65, 0x9e, 0x10, 0x0b, 0x6b, 0xab, 0x30, 0x36, 0xe7, 0xba, 0x8b, 0x06, 0x74, 0x9b, 0xaf, 0x69, 0x81, 0xe1, 0x6f, 0x1a, 0x2b, 0x95},
{0xdf, 0x47, 0x10, 0x61, 0x62, 0x5b, 0xc0, 0xea, 0x14, 0xb6, 0x82, 0xfe, 0xee, 0x2c, 0x9c, 0x02, 0xf2, 0x35, 0xda, 0x04, 0x20, 0x4c, 0x1d, 0x62, 0xa1, 0x53, 0x6c, 0x6e, 0x17, 0xae, 0xd7, 0xa9},
{0x75, 0x97, 0x88, 0x7c, 0xbd, 0x76, 0x32, 0x1f, 0x32, 0xe3, 0x04, 0x40, 0x67, 0x9a, 0x22, 0xcf, 0x7f, 0x8d, 0x9d, 0x2e, 0xac, 0x39, 0x0e, 0x58, 0x1f, 0xea, 0x09, 0x1c, 0xe2, 0x02, 0xba, 0x94}
};
secp256k1_rfc6979_hmac_sha256 rng;
unsigned char out[32];
int i;
secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 64);
for (i = 0; i < 3; i++) {
secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
CHECK(memcmp(out, out1[i], 32) == 0);
}
secp256k1_rfc6979_hmac_sha256_finalize(&rng);
secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 65);
for (i = 0; i < 3; i++) {
secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
CHECK(memcmp(out, out1[i], 32) != 0);
}
secp256k1_rfc6979_hmac_sha256_finalize(&rng);
secp256k1_rfc6979_hmac_sha256_initialize(&rng, key2, 64);
for (i = 0; i < 3; i++) {
secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
CHECK(memcmp(out, out2[i], 32) == 0);
}
secp256k1_rfc6979_hmac_sha256_finalize(&rng);
}
/***** RANDOM TESTS *****/
void test_rand_bits(int rand32, int bits) {
/* (1-1/2^B)^rounds[B] < 1/10^9, so rounds is the number of iterations to
* get a false negative chance below once in a billion */
static const unsigned int rounds[7] = {1, 30, 73, 156, 322, 653, 1316};
/* We try multiplying the results with various odd numbers, which shouldn't
* influence the uniform distribution modulo a power of 2. */
static const uint32_t mults[6] = {1, 3, 21, 289, 0x9999, 0x80402011};
/* We only select up to 6 bits from the output to analyse */
unsigned int usebits = bits > 6 ? 6 : bits;
unsigned int maxshift = bits - usebits;
/* For each of the maxshift+1 usebits-bit sequences inside a bits-bit
number, track all observed outcomes, one per bit in a uint64_t. */
uint64_t x[6][27] = {{0}};
unsigned int i, shift, m;
/* Multiply the output of all rand calls with the odd number m, which
should not change the uniformity of its distribution. */
for (i = 0; i < rounds[usebits]; i++) {
uint32_t r = (rand32 ? secp256k1_rand32() : secp256k1_rand_bits(bits));
CHECK((((uint64_t)r) >> bits) == 0);
for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
uint32_t rm = r * mults[m];
for (shift = 0; shift <= maxshift; shift++) {
x[m][shift] |= (((uint64_t)1) << ((rm >> shift) & ((1 << usebits) - 1)));
}
}
}
for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
for (shift = 0; shift <= maxshift; shift++) {
/* Test that the lower usebits bits of x[shift] are 1 */
CHECK(((~x[m][shift]) << (64 - (1 << usebits))) == 0);
}
}
}
/* Subrange must be a whole divisor of range, and at most 64 */
void test_rand_int(uint32_t range, uint32_t subrange) {
/* (1-1/subrange)^rounds < 1/10^9 */
int rounds = (subrange * 2073) / 100;
int i;
uint64_t x = 0;
CHECK((range % subrange) == 0);
for (i = 0; i < rounds; i++) {
uint32_t r = secp256k1_rand_int(range);
CHECK(r < range);
r = r % subrange;
x |= (((uint64_t)1) << r);
}
/* Test that the lower subrange bits of x are 1. */
CHECK(((~x) << (64 - subrange)) == 0);
}
void run_rand_bits(void) {
size_t b;
test_rand_bits(1, 32);
for (b = 1; b <= 32; b++) {
test_rand_bits(0, b);
}
}
void run_rand_int(void) {
static const uint32_t ms[] = {1, 3, 17, 1000, 13771, 999999, 33554432};
static const uint32_t ss[] = {1, 3, 6, 9, 13, 31, 64};
unsigned int m, s;
for (m = 0; m < sizeof(ms) / sizeof(ms[0]); m++) {
for (s = 0; s < sizeof(ss) / sizeof(ss[0]); s++) {
test_rand_int(ms[m] * ss[s], ss[s]);
}
}
}
/***** NUM TESTS *****/
#ifndef USE_NUM_NONE
void random_num_negate(secp256k1_num *num) {
if (secp256k1_rand_bits(1)) {
secp256k1_num_negate(num);
}
}
void random_num_order_test(secp256k1_num *num) {
secp256k1_scalar sc;
random_scalar_order_test(&sc);
secp256k1_scalar_get_num(num, &sc);
}
void random_num_order(secp256k1_num *num) {
secp256k1_scalar sc;
random_scalar_order(&sc);
secp256k1_scalar_get_num(num, &sc);
}
void test_num_negate(void) {
secp256k1_num n1;
secp256k1_num 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 i;
secp256k1_scalar s;
secp256k1_num n1;
secp256k1_num n2;
secp256k1_num n1p2, n2p1, n1m2, n2m1;
random_num_order_test(&n1); /* n1 = R1 */
if (secp256k1_rand_bits(1)) {
random_num_negate(&n1);
}
random_num_order_test(&n2); /* n2 = R2 */
if (secp256k1_rand_bits(1)) {
random_num_negate(&n2);
}
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));
/* check is_one */
secp256k1_scalar_set_int(&s, 1);
secp256k1_scalar_get_num(&n1, &s);
CHECK(secp256k1_num_is_one(&n1));
/* check that 2^n + 1 is never 1 */
secp256k1_scalar_get_num(&n2, &s);
for (i = 0; i < 250; ++i) {
secp256k1_num_add(&n1, &n1, &n1); /* n1 *= 2 */
secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = n1 + 1 */
CHECK(!secp256k1_num_is_one(&n1p2));
}
}
void test_num_mod(void) {
int i;
secp256k1_scalar s;
secp256k1_num order, n;
/* check that 0 mod anything is 0 */
random_scalar_order_test(&s);
secp256k1_scalar_get_num(&order, &s);
secp256k1_scalar_set_int(&s, 0);
secp256k1_scalar_get_num(&n, &s);
secp256k1_num_mod(&n, &order);
CHECK(secp256k1_num_is_zero(&n));
/* check that anything mod 1 is 0 */
secp256k1_scalar_set_int(&s, 1);
secp256k1_scalar_get_num(&order, &s);
secp256k1_scalar_get_num(&n, &s);
secp256k1_num_mod(&n, &order);
CHECK(secp256k1_num_is_zero(&n));
/* check that increasing the number past 2^256 does not break this */
random_scalar_order_test(&s);
secp256k1_scalar_get_num(&n, &s);
/* multiply by 2^8, which'll test this case with high probability */
for (i = 0; i < 8; ++i) {
secp256k1_num_add(&n, &n, &n);
}
secp256k1_num_mod(&n, &order);
CHECK(secp256k1_num_is_zero(&n));
}
void test_num_jacobi(void) {
secp256k1_scalar sqr;
secp256k1_scalar small;
secp256k1_scalar five; /* five is not a quadratic residue */
secp256k1_num order, n;
int i;
/* squares mod 5 are 1, 4 */
const int jacobi5[10] = { 0, 1, -1, -1, 1, 0, 1, -1, -1, 1 };
/* check some small values with 5 as the order */
secp256k1_scalar_set_int(&five, 5);
secp256k1_scalar_get_num(&order, &five);
for (i = 0; i < 10; ++i) {
secp256k1_scalar_set_int(&small, i);
secp256k1_scalar_get_num(&n, &small);
CHECK(secp256k1_num_jacobi(&n, &order) == jacobi5[i]);
}
/** test large values with 5 as group order */
secp256k1_scalar_get_num(&order, &five);
/* we first need a scalar which is not a multiple of 5 */
do {
secp256k1_num fiven;
random_scalar_order_test(&sqr);
secp256k1_scalar_get_num(&fiven, &five);
secp256k1_scalar_get_num(&n, &sqr);
secp256k1_num_mod(&n, &fiven);
} while (secp256k1_num_is_zero(&n));
/* next force it to be a residue. 2 is a nonresidue mod 5 so we can
* just multiply by two, i.e. add the number to itself */
if (secp256k1_num_jacobi(&n, &order) == -1) {
secp256k1_num_add(&n, &n, &n);
}
/* test residue */
CHECK(secp256k1_num_jacobi(&n, &order) == 1);
/* test nonresidue */
secp256k1_num_add(&n, &n, &n);
CHECK(secp256k1_num_jacobi(&n, &order) == -1);
/** test with secp group order as order */
secp256k1_scalar_order_get_num(&order);
random_scalar_order_test(&sqr);
secp256k1_scalar_sqr(&sqr, &sqr);
/* test residue */
secp256k1_scalar_get_num(&n, &sqr);
CHECK(secp256k1_num_jacobi(&n, &order) == 1);
/* test nonresidue */
secp256k1_scalar_mul(&sqr, &sqr, &five);
secp256k1_scalar_get_num(&n, &sqr);
CHECK(secp256k1_num_jacobi(&n, &order) == -1);
/* test multiple of the order*/
CHECK(secp256k1_num_jacobi(&order, &order) == 0);
/* check one less than the order */
secp256k1_scalar_set_int(&small, 1);
secp256k1_scalar_get_num(&n, &small);
secp256k1_num_sub(&n, &order, &n);
CHECK(secp256k1_num_jacobi(&n, &order) == 1); /* sage confirms this is 1 */
}
void run_num_smalltests(void) {
int i;
for (i = 0; i < 100*count; i++) {
test_num_negate();
test_num_add_sub();
test_num_mod();
test_num_jacobi();
}
}
#endif
/***** SCALAR TESTS *****/
void scalar_test(void) {
secp256k1_scalar s;
secp256k1_scalar s1;
secp256k1_scalar s2;
#ifndef USE_NUM_NONE
secp256k1_num snum, s1num, s2num;
secp256k1_num order, half_order;
#endif
unsigned char c[32];
/* Set 's' to a random scalar, with value 'snum'. */
random_scalar_order_test(&s);
/* Set 's1' to a random scalar, with value 's1num'. */
random_scalar_order_test(&s1);
/* Set 's2' to a random scalar, with value 'snum2', and byte array representation 'c'. */
random_scalar_order_test(&s2);
secp256k1_scalar_get_b32(c, &s2);
#ifndef USE_NUM_NONE
secp256k1_scalar_get_num(&snum, &s);
secp256k1_scalar_get_num(&s1num, &s1);
secp256k1_scalar_get_num(&s2num, &s2);
secp256k1_scalar_order_get_num(&order);
half_order = order;
secp256k1_num_shift(&half_order, 1);
#endif
{
int i;
/* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */
secp256k1_scalar n;
secp256k1_scalar_set_int(&n, 0);
for (i = 0; i < 256; i += 4) {
secp256k1_scalar t;
int j;
secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits(&s, 256 - 4 - i, 4));
for (j = 0; j < 4; j++) {
secp256k1_scalar_add(&n, &n, &n);
}
secp256k1_scalar_add(&n, &n, &t);
}
CHECK(secp256k1_scalar_eq(&n, &s));
}
{
/* Test that fetching groups of randomly-sized bits from a scalar and recursing n(i)=b*n(i-1)+p(i) reconstructs it. */
secp256k1_scalar n;
int i = 0;
secp256k1_scalar_set_int(&n, 0);
while (i < 256) {
secp256k1_scalar t;
int j;
int now = secp256k1_rand_int(15) + 1;
if (now + i > 256) {
now = 256 - i;
}
secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits_var(&s, 256 - now - i, now));
for (j = 0; j < now; j++) {
secp256k1_scalar_add(&n, &n, &n);
}
secp256k1_scalar_add(&n, &n, &t);
i += now;
}
CHECK(secp256k1_scalar_eq(&n, &s));
}
#ifndef USE_NUM_NONE
{
/* Test that adding the scalars together is equal to adding their numbers together modulo the order. */
secp256k1_num rnum;
secp256k1_num r2num;
secp256k1_scalar r;
secp256k1_num_add(&rnum, &snum, &s2num);
secp256k1_num_mod(&rnum, &order);
secp256k1_scalar_add(&r, &s, &s2);
secp256k1_scalar_get_num(&r2num, &r);
CHECK(secp256k1_num_eq(&rnum, &r2num));
}
{
/* Test that multiplying the scalars is equal to multiplying their numbers modulo the order. */
secp256k1_scalar r;
secp256k1_num r2num;
secp256k1_num rnum;
secp256k1_num_mul(&rnum, &snum, &s2num);
secp256k1_num_mod(&rnum, &order);
secp256k1_scalar_mul(&r, &s, &s2);
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)));
}
{
secp256k1_scalar neg;
secp256k1_num negnum;
secp256k1_num negnum2;
/* 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, &half_order) > 0));
secp256k1_scalar_negate(&neg, &s);
secp256k1_num_sub(&negnum, &order, &snum);
secp256k1_num_mod(&negnum, &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, &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_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 secp256k1_scalar_mul_shift_var. */
secp256k1_scalar r;
secp256k1_num one;
secp256k1_num rnum;
secp256k1_num rnum2;
unsigned char cone[1] = {0x01};
unsigned int shift = 256 + secp256k1_rand_int(257);
secp256k1_scalar_mul_shift_var(&r, &s1, &s2, shift);
secp256k1_num_mul(&rnum, &s1num, &s2num);
secp256k1_num_shift(&rnum, shift - 1);
secp256k1_num_set_bin(&one, cone, 1);
secp256k1_num_add(&rnum, &rnum, &one);
secp256k1_num_shift(&rnum, 1);
secp256k1_scalar_get_num(&rnum2, &r);
CHECK(secp256k1_num_eq(&rnum, &rnum2));
}
{
/* test secp256k1_scalar_shr_int */
secp256k1_scalar r;
int i;
random_scalar_order_test(&r);
for (i = 0; i < 100; ++i) {
int low;
int shift = 1 + secp256k1_rand_int(15);
int expected = r.d[0] % (1 << shift);
low = secp256k1_scalar_shr_int(&r, shift);
CHECK(expected == low);
}
}
#endif
{
/* Test that scalar inverses are equal to the inverse of their number modulo the order. */
if (!secp256k1_scalar_is_zero(&s)) {
secp256k1_scalar inv;
#ifndef USE_NUM_NONE
secp256k1_num invnum;
secp256k1_num invnum2;
#endif
secp256k1_scalar_inverse(&inv, &s);
#ifndef USE_NUM_NONE
secp256k1_num_mod_inverse(&invnum, &snum, &order);
secp256k1_scalar_get_num(&invnum2, &inv);
CHECK(secp256k1_num_eq(&invnum, &invnum2));
#endif
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));
#ifndef USE_NUM_NONE
secp256k1_scalar_get_num(&invnum, &inv);
CHECK(secp256k1_num_is_one(&invnum));
#endif
}
}
{
/* Test commutativity of add. */
secp256k1_scalar r1, r2;
secp256k1_scalar_add(&r1, &s1, &s2);
secp256k1_scalar_add(&r2, &s2, &s1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
secp256k1_scalar r1, r2;
secp256k1_scalar b;
int i;
/* Test add_bit. */
int bit = secp256k1_rand_bits(8);
secp256k1_scalar_set_int(&b, 1);
CHECK(secp256k1_scalar_is_one(&b));
for (i = 0; i < bit; i++) {
secp256k1_scalar_add(&b, &b, &b);
}
r1 = s1;
r2 = s1;
if (!secp256k1_scalar_add(&r1, &r1, &b)) {
/* No overflow happened. */
secp256k1_scalar_cadd_bit(&r2, bit, 1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
/* cadd is a noop when flag is zero */
secp256k1_scalar_cadd_bit(&r2, bit, 0);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
}
{
/* Test commutativity of mul. */
secp256k1_scalar 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 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 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 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 r1, r2;
secp256k1_scalar_sqr(&r1, &s1);
secp256k1_scalar_mul(&r2, &s1, &s1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
/* Test multiplicative identity. */
secp256k1_scalar r1, v1;
secp256k1_scalar_set_int(&v1,1);
secp256k1_scalar_mul(&r1, &s1, &v1);
CHECK(secp256k1_scalar_eq(&r1, &s1));
}
{
/* Test additive identity. */
secp256k1_scalar r1, v0;
secp256k1_scalar_set_int(&v0,0);
secp256k1_scalar_add(&r1, &s1, &v0);
CHECK(secp256k1_scalar_eq(&r1, &s1));
}
{
/* Test zero product property. */
secp256k1_scalar r1, v0;
secp256k1_scalar_set_int(&v0,0);
secp256k1_scalar_mul(&r1, &s1, &v0);
CHECK(secp256k1_scalar_eq(&r1, &v0));
}
}
void run_scalar_tests(void) {
int i;
for (i = 0; i < 128 * count; i++) {
scalar_test();
}
{
/* (-1)+1 should be zero. */
secp256k1_scalar s, o;
secp256k1_scalar_set_int(&s, 1);
CHECK(secp256k1_scalar_is_one(&s));
secp256k1_scalar_negate(&o, &s);
secp256k1_scalar_add(&o, &o, &s);
CHECK(secp256k1_scalar_is_zero(&o));
secp256k1_scalar_negate(&o, &o);
CHECK(secp256k1_scalar_is_zero(&o));
}
#ifndef USE_NUM_NONE
{
/* A scalar with value of the curve order should be 0. */
secp256k1_num order;
secp256k1_scalar zero;
unsigned char bin[32];
int overflow = 0;
secp256k1_scalar_order_get_num(&order);
secp256k1_num_get_bin(bin, 32, &order);
secp256k1_scalar_set_b32(&zero, bin, &overflow);
CHECK(overflow == 1);
CHECK(secp256k1_scalar_is_zero(&zero));
}
#endif
{
/* Does check_overflow check catch all ones? */
static const secp256k1_scalar overflowed = SECP256K1_SCALAR_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL
);
CHECK(secp256k1_scalar_check_overflow(&overflowed));
}
{
/* Static test vectors.
* These were reduced from ~10^12 random vectors based on comparison-decision
* and edge-case coverage on 32-bit and 64-bit implementations.
* The responses were generated with Sage 5.9.
*/
secp256k1_scalar x;
secp256k1_scalar y;
secp256k1_scalar z;
secp256k1_scalar zz;
secp256k1_scalar one;
secp256k1_scalar r1;
secp256k1_scalar r2;
#if defined(USE_SCALAR_INV_NUM)
secp256k1_scalar zzv;
#endif
int overflow;
unsigned char chal[33][2][32] = {
{{0xff, 0xff, 0x03, 0x07, 0x00, 0x00, 0x00, 0x00,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03,
0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff,
0xff, 0xff, 0x03, 0x00, 0xc0, 0xff, 0xff, 0xff},
{0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff}},
{{0xef, 0xff, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x00,
0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0,
0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x80, 0xff}},
{{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x06, 0x00, 0x00,
0x80, 0x00, 0x00, 0x80, 0xff, 0x3f, 0x00, 0x00,
0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0x00},
{0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0x80,
0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0xe0,
0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x7f, 0xff, 0xff, 0xff}},
{{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x00, 0x1e, 0xf8, 0xff, 0xff, 0xff, 0xfd, 0xff},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f,
0x00, 0x00, 0x00, 0xf8, 0xff, 0x03, 0x00, 0xe0,
0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0xf0, 0xff,
0xf3, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00}},
{{0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00,
0x00, 0x1c, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff, 0x00,
0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00,
0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0x1f, 0x00, 0x00, 0x80, 0xff, 0xff, 0x3f,
0x00, 0xfe, 0xff, 0xff, 0xff, 0xdf, 0xff, 0xff}},
{{0xff, 0xff, 0xff, 0xff, 0x00, 0x0f, 0xfc, 0x9f,
0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80,
0xff, 0x0f, 0xfc, 0xff, 0x7f, 0x00, 0x00, 0x00,
0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
{0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
0x00, 0x00, 0xf8, 0xff, 0x0f, 0xc0, 0xff, 0xff,
0xff, 0x1f, 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff,
0xff, 0xff, 0xff, 0x07, 0x80, 0xff, 0xff, 0xff}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00,
0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
0xf7, 0xff, 0xff, 0xef, 0xff, 0xff, 0xff, 0x00,
0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0xf0},
{0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00,
0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
{{0x00, 0xf8, 0xff, 0x03, 0xff, 0xff, 0xff, 0x00,
0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0x03, 0xc0, 0xff, 0x0f, 0xfc, 0xff},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xe0, 0xff, 0xff,
0xff, 0x01, 0x00, 0x00, 0x00, 0x3f, 0x00, 0xc0,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
{{0x8f, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0x7f, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
{{0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0x03, 0x00, 0x80, 0x00, 0x00, 0x80,
0xff, 0xff, 0xff, 0x00, 0x00, 0x80, 0xff, 0x7f},
{0xff, 0xcf, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00,
0x00, 0xc0, 0xff, 0xcf, 0xff, 0xff, 0xff, 0xff,
0xbf, 0xff, 0x0e, 0x00, 0x00, 0x00, 0x00, 0x00,
0x80, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00}},
{{0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff,
0xff, 0xff, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80,
0xff, 0x01, 0xfc, 0xff, 0x01, 0x00, 0xfe, 0xff},
{0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xc0,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00}},
{{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0x7f, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0xf8, 0xff, 0x01, 0x00, 0xf0, 0xff, 0xff,
0xe0, 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0x00},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00,
0xfc, 0xff, 0xff, 0x3f, 0xf0, 0xff, 0xff, 0x3f,
0x00, 0x00, 0xf8, 0x07, 0x00, 0x00, 0x00, 0xff,
0xff, 0xff, 0xff, 0xff, 0x0f, 0x7e, 0x00, 0x00}},
{{0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0x1f, 0x00, 0x00, 0xfe, 0x07, 0x00},
{0x00, 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xfb, 0xff, 0x07, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x60}},
{{0xff, 0x01, 0x00, 0xff, 0xff, 0xff, 0x0f, 0x00,
0x80, 0x7f, 0xfe, 0xff, 0xff, 0xff, 0xff, 0x03,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
{0xff, 0xff, 0x1f, 0x00, 0xf0, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x00, 0x00}},
{{0x80, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf1, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03,
0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x7e, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0xc0, 0xff, 0xff, 0xcf, 0xff, 0x1f, 0x00, 0x00,
0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x7e,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00},
{0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
0xff, 0xff, 0x7f, 0x00, 0x80, 0x00, 0x00, 0x00,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
{0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x80,
0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff,
0xff, 0x7f, 0xf8, 0xff, 0xff, 0x1f, 0x00, 0xfe}},
{{0xff, 0xff, 0xff, 0x3f, 0xf8, 0xff, 0xff, 0xff,
0xff, 0x03, 0xfe, 0x01, 0x00, 0x00, 0x00, 0x00,
0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
0xff, 0xff, 0xff, 0xff, 0x01, 0x80, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}},
{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40}},
{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
{{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0xc0,
0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, 0x00,
0xf0, 0xff, 0xff, 0xff, 0xff, 0x07, 0x00, 0x00,
0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0x01, 0xff, 0xff, 0xff}},
{{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0x7e, 0x00, 0x00, 0xc0, 0xff, 0xff, 0x07, 0x00,
0x80, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x00,
0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
{0xff, 0x01, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80,
0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
{{0xff, 0xff, 0xf0, 0xff, 0xff, 0xff, 0xff, 0x00,
0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01,
0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff},
{0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
0xff, 0xff, 0x3f, 0x00, 0xf8, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0x3f, 0x00, 0x00, 0xc0, 0xf1, 0x7f, 0x00}},
{{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00},
{0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff,
0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0x80, 0x1f,
0x00, 0x00, 0xfc, 0xff, 0xff, 0x01, 0xff, 0xff}},
{{0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x80, 0x00, 0x00, 0x80, 0xff, 0x03, 0xe0, 0x01,
0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0xfc, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
{0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00,
0xfe, 0xff, 0xff, 0xf0, 0x07, 0x00, 0x3c, 0x80,
0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff,
0xff, 0xff, 0x07, 0xe0, 0xff, 0x00, 0x00, 0x00}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07, 0xf8,
0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0x0c, 0x80, 0x00,
0x00, 0x00, 0x00, 0xc0, 0x7f, 0xfe, 0xff, 0x1f,
0x00, 0xfe, 0xff, 0x03, 0x00, 0x00, 0xfe, 0xff}},
{{0xff, 0xff, 0x81, 0xff, 0xff, 0xff, 0xff, 0x00,
0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x83,
0xff, 0xff, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
0xff, 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0xf0},
{0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x00,
0xf8, 0x07, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
0xff, 0xc7, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff}},
{{0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb,
0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03},
{0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb,
0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03}}
};
unsigned char res[33][2][32] = {
{{0x0c, 0x3b, 0x0a, 0xca, 0x8d, 0x1a, 0x2f, 0xb9,
0x8a, 0x7b, 0x53, 0x5a, 0x1f, 0xc5, 0x22, 0xa1,
0x07, 0x2a, 0x48, 0xea, 0x02, 0xeb, 0xb3, 0xd6,
0x20, 0x1e, 0x86, 0xd0, 0x95, 0xf6, 0x92, 0x35},
{0xdc, 0x90, 0x7a, 0x07, 0x2e, 0x1e, 0x44, 0x6d,
0xf8, 0x15, 0x24, 0x5b, 0x5a, 0x96, 0x37, 0x9c,
0x37, 0x7b, 0x0d, 0xac, 0x1b, 0x65, 0x58, 0x49,
0x43, 0xb7, 0x31, 0xbb, 0xa7, 0xf4, 0x97, 0x15}},
{{0xf1, 0xf7, 0x3a, 0x50, 0xe6, 0x10, 0xba, 0x22,
0x43, 0x4d, 0x1f, 0x1f, 0x7c, 0x27, 0xca, 0x9c,
0xb8, 0xb6, 0xa0, 0xfc, 0xd8, 0xc0, 0x05, 0x2f,
0xf7, 0x08, 0xe1, 0x76, 0xdd, 0xd0, 0x80, 0xc8},
{0xe3, 0x80, 0x80, 0xb8, 0xdb, 0xe3, 0xa9, 0x77,
0x00, 0xb0, 0xf5, 0x2e, 0x27, 0xe2, 0x68, 0xc4,
0x88, 0xe8, 0x04, 0xc1, 0x12, 0xbf, 0x78, 0x59,
0xe6, 0xa9, 0x7c, 0xe1, 0x81, 0xdd, 0xb9, 0xd5}},
{{0x96, 0xe2, 0xee, 0x01, 0xa6, 0x80, 0x31, 0xef,
0x5c, 0xd0, 0x19, 0xb4, 0x7d, 0x5f, 0x79, 0xab,
0xa1, 0x97, 0xd3, 0x7e, 0x33, 0xbb, 0x86, 0x55,
0x60, 0x20, 0x10, 0x0d, 0x94, 0x2d, 0x11, 0x7c},
{0xcc, 0xab, 0xe0, 0xe8, 0x98, 0x65, 0x12, 0x96,
0x38, 0x5a, 0x1a, 0xf2, 0x85, 0x23, 0x59, 0x5f,
0xf9, 0xf3, 0xc2, 0x81, 0x70, 0x92, 0x65, 0x12,
0x9c, 0x65, 0x1e, 0x96, 0x00, 0xef, 0xe7, 0x63}},
{{0xac, 0x1e, 0x62, 0xc2, 0x59, 0xfc, 0x4e, 0x5c,
0x83, 0xb0, 0xd0, 0x6f, 0xce, 0x19, 0xf6, 0xbf,
0xa4, 0xb0, 0xe0, 0x53, 0x66, 0x1f, 0xbf, 0xc9,
0x33, 0x47, 0x37, 0xa9, 0x3d, 0x5d, 0xb0, 0x48},
{0x86, 0xb9, 0x2a, 0x7f, 0x8e, 0xa8, 0x60, 0x42,
0x26, 0x6d, 0x6e, 0x1c, 0xa2, 0xec, 0xe0, 0xe5,
0x3e, 0x0a, 0x33, 0xbb, 0x61, 0x4c, 0x9f, 0x3c,
0xd1, 0xdf, 0x49, 0x33, 0xcd, 0x72, 0x78, 0x18}},
{{0xf7, 0xd3, 0xcd, 0x49, 0x5c, 0x13, 0x22, 0xfb,
0x2e, 0xb2, 0x2f, 0x27, 0xf5, 0x8a, 0x5d, 0x74,
0xc1, 0x58, 0xc5, 0xc2, 0x2d, 0x9f, 0x52, 0xc6,
0x63, 0x9f, 0xba, 0x05, 0x76, 0x45, 0x7a, 0x63},
{0x8a, 0xfa, 0x55, 0x4d, 0xdd, 0xa3, 0xb2, 0xc3,
0x44, 0xfd, 0xec, 0x72, 0xde, 0xef, 0xc0, 0x99,
0xf5, 0x9f, 0xe2, 0x52, 0xb4, 0x05, 0x32, 0x58,
0x57, 0xc1, 0x8f, 0xea, 0xc3, 0x24, 0x5b, 0x94}},
{{0x05, 0x83, 0xee, 0xdd, 0x64, 0xf0, 0x14, 0x3b,
0xa0, 0x14, 0x4a, 0x3a, 0x41, 0x82, 0x7c, 0xa7,
0x2c, 0xaa, 0xb1, 0x76, 0xbb, 0x59, 0x64, 0x5f,
0x52, 0xad, 0x25, 0x29, 0x9d, 0x8f, 0x0b, 0xb0},
{0x7e, 0xe3, 0x7c, 0xca, 0xcd, 0x4f, 0xb0, 0x6d,
0x7a, 0xb2, 0x3e, 0xa0, 0x08, 0xb9, 0xa8, 0x2d,
0xc2, 0xf4, 0x99, 0x66, 0xcc, 0xac, 0xd8, 0xb9,
0x72, 0x2a, 0x4a, 0x3e, 0x0f, 0x7b, 0xbf, 0xf4}},
{{0x8c, 0x9c, 0x78, 0x2b, 0x39, 0x61, 0x7e, 0xf7,
0x65, 0x37, 0x66, 0x09, 0x38, 0xb9, 0x6f, 0x70,
0x78, 0x87, 0xff, 0xcf, 0x93, 0xca, 0x85, 0x06,
0x44, 0x84, 0xa7, 0xfe, 0xd3, 0xa4, 0xe3, 0x7e},
{0xa2, 0x56, 0x49, 0x23, 0x54, 0xa5, 0x50, 0xe9,
0x5f, 0xf0, 0x4d, 0xe7, 0xdc, 0x38, 0x32, 0x79,
0x4f, 0x1c, 0xb7, 0xe4, 0xbb, 0xf8, 0xbb, 0x2e,
0x40, 0x41, 0x4b, 0xcc, 0xe3, 0x1e, 0x16, 0x36}},
{{0x0c, 0x1e, 0xd7, 0x09, 0x25, 0x40, 0x97, 0xcb,
0x5c, 0x46, 0xa8, 0xda, 0xef, 0x25, 0xd5, 0xe5,
0x92, 0x4d, 0xcf, 0xa3, 0xc4, 0x5d, 0x35, 0x4a,
0xe4, 0x61, 0x92, 0xf3, 0xbf, 0x0e, 0xcd, 0xbe},
{0xe4, 0xaf, 0x0a, 0xb3, 0x30, 0x8b, 0x9b, 0x48,
0x49, 0x43, 0xc7, 0x64, 0x60, 0x4a, 0x2b, 0x9e,
0x95, 0x5f, 0x56, 0xe8, 0x35, 0xdc, 0xeb, 0xdc,
0xc7, 0xc4, 0xfe, 0x30, 0x40, 0xc7, 0xbf, 0xa4}},
{{0xd4, 0xa0, 0xf5, 0x81, 0x49, 0x6b, 0xb6, 0x8b,
0x0a, 0x69, 0xf9, 0xfe, 0xa8, 0x32, 0xe5, 0xe0,
0xa5, 0xcd, 0x02, 0x53, 0xf9, 0x2c, 0xe3, 0x53,
0x83, 0x36, 0xc6, 0x02, 0xb5, 0xeb, 0x64, 0xb8},
{0x1d, 0x42, 0xb9, 0xf9, 0xe9, 0xe3, 0x93, 0x2c,
0x4c, 0xee, 0x6c, 0x5a, 0x47, 0x9e, 0x62, 0x01,
0x6b, 0x04, 0xfe, 0xa4, 0x30, 0x2b, 0x0d, 0x4f,
0x71, 0x10, 0xd3, 0x55, 0xca, 0xf3, 0x5e, 0x80}},
{{0x77, 0x05, 0xf6, 0x0c, 0x15, 0x9b, 0x45, 0xe7,
0xb9, 0x11, 0xb8, 0xf5, 0xd6, 0xda, 0x73, 0x0c,
0xda, 0x92, 0xea, 0xd0, 0x9d, 0xd0, 0x18, 0x92,
0xce, 0x9a, 0xaa, 0xee, 0x0f, 0xef, 0xde, 0x30},
{0xf1, 0xf1, 0xd6, 0x9b, 0x51, 0xd7, 0x77, 0x62,
0x52, 0x10, 0xb8, 0x7a, 0x84, 0x9d, 0x15, 0x4e,
0x07, 0xdc, 0x1e, 0x75, 0x0d, 0x0c, 0x3b, 0xdb,
0x74, 0x58, 0x62, 0x02, 0x90, 0x54, 0x8b, 0x43}},
{{0xa6, 0xfe, 0x0b, 0x87, 0x80, 0x43, 0x67, 0x25,
0x57, 0x5d, 0xec, 0x40, 0x50, 0x08, 0xd5, 0x5d,
0x43, 0xd7, 0xe0, 0xaa, 0xe0, 0x13, 0xb6, 0xb0,
0xc0, 0xd4, 0xe5, 0x0d, 0x45, 0x83, 0xd6, 0x13},
{0x40, 0x45, 0x0a, 0x92, 0x31, 0xea, 0x8c, 0x60,
0x8c, 0x1f, 0xd8, 0x76, 0x45, 0xb9, 0x29, 0x00,
0x26, 0x32, 0xd8, 0xa6, 0x96, 0x88, 0xe2, 0xc4,
0x8b, 0xdb, 0x7f, 0x17, 0x87, 0xcc, 0xc8, 0xf2}},
{{0xc2, 0x56, 0xe2, 0xb6, 0x1a, 0x81, 0xe7, 0x31,
0x63, 0x2e, 0xbb, 0x0d, 0x2f, 0x81, 0x67, 0xd4,
0x22, 0xe2, 0x38, 0x02, 0x25, 0x97, 0xc7, 0x88,
0x6e, 0xdf, 0xbe, 0x2a, 0xa5, 0x73, 0x63, 0xaa},
{0x50, 0x45, 0xe2, 0xc3, 0xbd, 0x89, 0xfc, 0x57,
0xbd, 0x3c, 0xa3, 0x98, 0x7e, 0x7f, 0x36, 0x38,
0x92, 0x39, 0x1f, 0x0f, 0x81, 0x1a, 0x06, 0x51,
0x1f, 0x8d, 0x6a, 0xff, 0x47, 0x16, 0x06, 0x9c}},
{{0x33, 0x95, 0xa2, 0x6f, 0x27, 0x5f, 0x9c, 0x9c,
0x64, 0x45, 0xcb, 0xd1, 0x3c, 0xee, 0x5e, 0x5f,
0x48, 0xa6, 0xaf, 0xe3, 0x79, 0xcf, 0xb1, 0xe2,
0xbf, 0x55, 0x0e, 0xa2, 0x3b, 0x62, 0xf0, 0xe4},
{0x14, 0xe8, 0x06, 0xe3, 0xbe, 0x7e, 0x67, 0x01,
0xc5, 0x21, 0x67, 0xd8, 0x54, 0xb5, 0x7f, 0xa4,
0xf9, 0x75, 0x70, 0x1c, 0xfd, 0x79, 0xdb, 0x86,
0xad, 0x37, 0x85, 0x83, 0x56, 0x4e, 0xf0, 0xbf}},
{{0xbc, 0xa6, 0xe0, 0x56, 0x4e, 0xef, 0xfa, 0xf5,
0x1d, 0x5d, 0x3f, 0x2a, 0x5b, 0x19, 0xab, 0x51,
0xc5, 0x8b, 0xdd, 0x98, 0x28, 0x35, 0x2f, 0xc3,
0x81, 0x4f, 0x5c, 0xe5, 0x70, 0xb9, 0xeb, 0x62},
{0xc4, 0x6d, 0x26, 0xb0, 0x17, 0x6b, 0xfe, 0x6c,
0x12, 0xf8, 0xe7, 0xc1, 0xf5, 0x2f, 0xfa, 0x91,
0x13, 0x27, 0xbd, 0x73, 0xcc, 0x33, 0x31, 0x1c,
0x39, 0xe3, 0x27, 0x6a, 0x95, 0xcf, 0xc5, 0xfb}},
{{0x30, 0xb2, 0x99, 0x84, 0xf0, 0x18, 0x2a, 0x6e,
0x1e, 0x27, 0xed, 0xa2, 0x29, 0x99, 0x41, 0x56,
0xe8, 0xd4, 0x0d, 0xef, 0x99, 0x9c, 0xf3, 0x58,
0x29, 0x55, 0x1a, 0xc0, 0x68, 0xd6, 0x74, 0xa4},
{0x07, 0x9c, 0xe7, 0xec, 0xf5, 0x36, 0x73, 0x41,
0xa3, 0x1c, 0xe5, 0x93, 0x97, 0x6a, 0xfd, 0xf7,
0x53, 0x18, 0xab, 0xaf, 0xeb, 0x85, 0xbd, 0x92,
0x90, 0xab, 0x3c, 0xbf, 0x30, 0x82, 0xad, 0xf6}},
{{0xc6, 0x87, 0x8a, 0x2a, 0xea, 0xc0, 0xa9, 0xec,
0x6d, 0xd3, 0xdc, 0x32, 0x23, 0xce, 0x62, 0x19,
0xa4, 0x7e, 0xa8, 0xdd, 0x1c, 0x33, 0xae, 0xd3,
0x4f, 0x62, 0x9f, 0x52, 0xe7, 0x65, 0x46, 0xf4},
{0x97, 0x51, 0x27, 0x67, 0x2d, 0xa2, 0x82, 0x87,
0x98, 0xd3, 0xb6, 0x14, 0x7f, 0x51, 0xd3, 0x9a,
0x0b, 0xd0, 0x76, 0x81, 0xb2, 0x4f, 0x58, 0x92,
0xa4, 0x86, 0xa1, 0xa7, 0x09, 0x1d, 0xef, 0x9b}},
{{0xb3, 0x0f, 0x2b, 0x69, 0x0d, 0x06, 0x90, 0x64,
0xbd, 0x43, 0x4c, 0x10, 0xe8, 0x98, 0x1c, 0xa3,
0xe1, 0x68, 0xe9, 0x79, 0x6c, 0x29, 0x51, 0x3f,
0x41, 0xdc, 0xdf, 0x1f, 0xf3, 0x60, 0xbe, 0x33},
{0xa1, 0x5f, 0xf7, 0x1d, 0xb4, 0x3e, 0x9b, 0x3c,
0xe7, 0xbd, 0xb6, 0x06, 0xd5, 0x60, 0x06, 0x6d,
0x50, 0xd2, 0xf4, 0x1a, 0x31, 0x08, 0xf2, 0xea,
0x8e, 0xef, 0x5f, 0x7d, 0xb6, 0xd0, 0xc0, 0x27}},
{{0x62, 0x9a, 0xd9, 0xbb, 0x38, 0x36, 0xce, 0xf7,
0x5d, 0x2f, 0x13, 0xec, 0xc8, 0x2d, 0x02, 0x8a,
0x2e, 0x72, 0xf0, 0xe5, 0x15, 0x9d, 0x72, 0xae,
0xfc, 0xb3, 0x4f, 0x02, 0xea, 0xe1, 0x09, 0xfe},
{0x00, 0x00, 0x00, 0x00, 0xfa, 0x0a, 0x3d, 0xbc,
0xad, 0x16, 0x0c, 0xb6, 0xe7, 0x7c, 0x8b, 0x39,
0x9a, 0x43, 0xbb, 0xe3, 0xc2, 0x55, 0x15, 0x14,
0x75, 0xac, 0x90, 0x9b, 0x7f, 0x9a, 0x92, 0x00}},
{{0x8b, 0xac, 0x70, 0x86, 0x29, 0x8f, 0x00, 0x23,
0x7b, 0x45, 0x30, 0xaa, 0xb8, 0x4c, 0xc7, 0x8d,
0x4e, 0x47, 0x85, 0xc6, 0x19, 0xe3, 0x96, 0xc2,
0x9a, 0xa0, 0x12, 0xed, 0x6f, 0xd7, 0x76, 0x16},
{0x45, 0xaf, 0x7e, 0x33, 0xc7, 0x7f, 0x10, 0x6c,
0x7c, 0x9f, 0x29, 0xc1, 0xa8, 0x7e, 0x15, 0x84,
0xe7, 0x7d, 0xc0, 0x6d, 0xab, 0x71, 0x5d, 0xd0,
0x6b, 0x9f, 0x97, 0xab, 0xcb, 0x51, 0x0c, 0x9f}},
{{0x9e, 0xc3, 0x92, 0xb4, 0x04, 0x9f, 0xc8, 0xbb,
0xdd, 0x9e, 0xc6, 0x05, 0xfd, 0x65, 0xec, 0x94,
0x7f, 0x2c, 0x16, 0xc4, 0x40, 0xac, 0x63, 0x7b,
0x7d, 0xb8, 0x0c, 0xe4, 0x5b, 0xe3, 0xa7, 0x0e},
{0x43, 0xf4, 0x44, 0xe8, 0xcc, 0xc8, 0xd4, 0x54,
0x33, 0x37, 0x50, 0xf2, 0x87, 0x42, 0x2e, 0x00,
0x49, 0x60, 0x62, 0x02, 0xfd, 0x1a, 0x7c, 0xdb,
0x29, 0x6c, 0x6d, 0x54, 0x53, 0x08, 0xd1, 0xc8}},
{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
{{0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92},
{0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}},
{{0x28, 0x56, 0xac, 0x0e, 0x4f, 0x98, 0x09, 0xf0,
0x49, 0xfa, 0x7f, 0x84, 0xac, 0x7e, 0x50, 0x5b,
0x17, 0x43, 0x14, 0x89, 0x9c, 0x53, 0xa8, 0x94,
0x30, 0xf2, 0x11, 0x4d, 0x92, 0x14, 0x27, 0xe8},
{0x39, 0x7a, 0x84, 0x56, 0x79, 0x9d, 0xec, 0x26,
0x2c, 0x53, 0xc1, 0x94, 0xc9, 0x8d, 0x9e, 0x9d,
0x32, 0x1f, 0xdd, 0x84, 0x04, 0xe8, 0xe2, 0x0a,
0x6b, 0xbe, 0xbb, 0x42, 0x40, 0x67, 0x30, 0x6c}},
{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
0x40, 0x2d, 0xa1, 0x73, 0x2f, 0xc9, 0xbe, 0xbd},
{0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
{{0x1c, 0xc4, 0xf7, 0xda, 0x0f, 0x65, 0xca, 0x39,
0x70, 0x52, 0x92, 0x8e, 0xc3, 0xc8, 0x15, 0xea,
0x7f, 0x10, 0x9e, 0x77, 0x4b, 0x6e, 0x2d, 0xdf,
0xe8, 0x30, 0x9d, 0xda, 0xe8, 0x9a, 0x65, 0xae},
{0x02, 0xb0, 0x16, 0xb1, 0x1d, 0xc8, 0x57, 0x7b,
0xa2, 0x3a, 0xa2, 0xa3, 0x38, 0x5c, 0x8f, 0xeb,
0x66, 0x37, 0x91, 0xa8, 0x5f, 0xef, 0x04, 0xf6,
0x59, 0x75, 0xe1, 0xee, 0x92, 0xf6, 0x0e, 0x30}},
{{0x8d, 0x76, 0x14, 0xa4, 0x14, 0x06, 0x9f, 0x9a,
0xdf, 0x4a, 0x85, 0xa7, 0x6b, 0xbf, 0x29, 0x6f,
0xbc, 0x34, 0x87, 0x5d, 0xeb, 0xbb, 0x2e, 0xa9,
0xc9, 0x1f, 0x58, 0xd6, 0x9a, 0x82, 0xa0, 0x56},
{0xd4, 0xb9, 0xdb, 0x88, 0x1d, 0x04, 0xe9, 0x93,
0x8d, 0x3f, 0x20, 0xd5, 0x86, 0xa8, 0x83, 0x07,
0xdb, 0x09, 0xd8, 0x22, 0x1f, 0x7f, 0xf1, 0x71,
0xc8, 0xe7, 0x5d, 0x47, 0xaf, 0x8b, 0x72, 0xe9}},
{{0x83, 0xb9, 0x39, 0xb2, 0xa4, 0xdf, 0x46, 0x87,
0xc2, 0xb8, 0xf1, 0xe6, 0x4c, 0xd1, 0xe2, 0xa9,
0xe4, 0x70, 0x30, 0x34, 0xbc, 0x52, 0x7c, 0x55,
0xa6, 0xec, 0x80, 0xa4, 0xe5, 0xd2, 0xdc, 0x73},
{0x08, 0xf1, 0x03, 0xcf, 0x16, 0x73, 0xe8, 0x7d,
0xb6, 0x7e, 0x9b, 0xc0, 0xb4, 0xc2, 0xa5, 0x86,
0x02, 0x77, 0xd5, 0x27, 0x86, 0xa5, 0x15, 0xfb,
0xae, 0x9b, 0x8c, 0xa9, 0xf9, 0xf8, 0xa8, 0x4a}},
{{0x8b, 0x00, 0x49, 0xdb, 0xfa, 0xf0, 0x1b, 0xa2,
0xed, 0x8a, 0x9a, 0x7a, 0x36, 0x78, 0x4a, 0xc7,
0xf7, 0xad, 0x39, 0xd0, 0x6c, 0x65, 0x7a, 0x41,
0xce, 0xd6, 0xd6, 0x4c, 0x20, 0x21, 0x6b, 0xc7},
{0xc6, 0xca, 0x78, 0x1d, 0x32, 0x6c, 0x6c, 0x06,
0x91, 0xf2, 0x1a, 0xe8, 0x43, 0x16, 0xea, 0x04,
0x3c, 0x1f, 0x07, 0x85, 0xf7, 0x09, 0x22, 0x08,
0xba, 0x13, 0xfd, 0x78, 0x1e, 0x3f, 0x6f, 0x62}},
{{0x25, 0x9b, 0x7c, 0xb0, 0xac, 0x72, 0x6f, 0xb2,
0xe3, 0x53, 0x84, 0x7a, 0x1a, 0x9a, 0x98, 0x9b,
0x44, 0xd3, 0x59, 0xd0, 0x8e, 0x57, 0x41, 0x40,
0x78, 0xa7, 0x30, 0x2f, 0x4c, 0x9c, 0xb9, 0x68},
{0xb7, 0x75, 0x03, 0x63, 0x61, 0xc2, 0x48, 0x6e,
0x12, 0x3d, 0xbf, 0x4b, 0x27, 0xdf, 0xb1, 0x7a,
0xff, 0x4e, 0x31, 0x07, 0x83, 0xf4, 0x62, 0x5b,
0x19, 0xa5, 0xac, 0xa0, 0x32, 0x58, 0x0d, 0xa7}},
{{0x43, 0x4f, 0x10, 0xa4, 0xca, 0xdb, 0x38, 0x67,
0xfa, 0xae, 0x96, 0xb5, 0x6d, 0x97, 0xff, 0x1f,
0xb6, 0x83, 0x43, 0xd3, 0xa0, 0x2d, 0x70, 0x7a,
0x64, 0x05, 0x4c, 0xa7, 0xc1, 0xa5, 0x21, 0x51},
{0xe4, 0xf1, 0x23, 0x84, 0xe1, 0xb5, 0x9d, 0xf2,
0xb8, 0x73, 0x8b, 0x45, 0x2b, 0x35, 0x46, 0x38,
0x10, 0x2b, 0x50, 0xf8, 0x8b, 0x35, 0xcd, 0x34,
0xc8, 0x0e, 0xf6, 0xdb, 0x09, 0x35, 0xf0, 0xda}},
{{0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34,
0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13,
0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46,
0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5},
{0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34,
0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13,
0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46,
0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5}}
};
secp256k1_scalar_set_int(&one, 1);
for (i = 0; i < 33; i++) {
secp256k1_scalar_set_b32(&x, chal[i][0], &overflow);
CHECK(!overflow);
secp256k1_scalar_set_b32(&y, chal[i][1], &overflow);
CHECK(!overflow);
secp256k1_scalar_set_b32(&r1, res[i][0], &overflow);
CHECK(!overflow);
secp256k1_scalar_set_b32(&r2, res[i][1], &overflow);
CHECK(!overflow);
secp256k1_scalar_mul(&z, &x, &y);
CHECK(!secp256k1_scalar_check_overflow(&z));
CHECK(secp256k1_scalar_eq(&r1, &z));
if (!secp256k1_scalar_is_zero(&y)) {
secp256k1_scalar_inverse(&zz, &y);
CHECK(!secp256k1_scalar_check_overflow(&zz));
#if defined(USE_SCALAR_INV_NUM)
secp256k1_scalar_inverse_var(&zzv, &y);
CHECK(secp256k1_scalar_eq(&zzv, &zz));
#endif
secp256k1_scalar_mul(&z, &z, &zz);
CHECK(!secp256k1_scalar_check_overflow(&z));
CHECK(secp256k1_scalar_eq(&x, &z));
secp256k1_scalar_mul(&zz, &zz, &y);
CHECK(!secp256k1_scalar_check_overflow(&zz));
CHECK(secp256k1_scalar_eq(&one, &zz));
}
secp256k1_scalar_mul(&z, &x, &x);
CHECK(!secp256k1_scalar_check_overflow(&z));
secp256k1_scalar_sqr(&zz, &x);
CHECK(!secp256k1_scalar_check_overflow(&zz));
CHECK(secp256k1_scalar_eq(&zz, &z));
CHECK(secp256k1_scalar_eq(&r2, &zz));
}
}
}
/***** FIELD TESTS *****/
void random_fe(secp256k1_fe *x) {
unsigned char bin[32];
do {
secp256k1_rand256(bin);
if (secp256k1_fe_set_b32(x, bin)) {
return;
}
} while(1);
}
void random_fe_test(secp256k1_fe *x) {
unsigned char bin[32];
do {
secp256k1_rand256_test(bin);
if (secp256k1_fe_set_b32(x, bin)) {
return;
}
} while(1);
}
void random_fe_non_zero(secp256k1_fe *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 *ns) {
secp256k1_fe r;
random_fe_non_zero(ns);
if (secp256k1_fe_sqrt(&r, ns)) {
secp256k1_fe_negate(ns, ns, 1);
}
}
int check_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
secp256k1_fe an = *a;
secp256k1_fe bn = *b;
secp256k1_fe_normalize_weak(&an);
secp256k1_fe_normalize_var(&bn);
return secp256k1_fe_equal_var(&an, &bn);
}
int check_fe_inverse(const secp256k1_fe *a, const secp256k1_fe *ai) {
secp256k1_fe x;
secp256k1_fe one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
secp256k1_fe_mul(&x, a, ai);
return check_fe_equal(&x, &one);
}
void run_field_convert(void) {
static const unsigned char b32[32] = {
0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18,
0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29,
0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x40
};
static const secp256k1_fe_storage fes = SECP256K1_FE_STORAGE_CONST(
0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL,
0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL
);
static const secp256k1_fe fe = SECP256K1_FE_CONST(
0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL,
0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL
);
secp256k1_fe fe2;
unsigned char b322[32];
secp256k1_fe_storage fes2;
/* Check conversions to fe. */
CHECK(secp256k1_fe_set_b32(&fe2, b32));
CHECK(secp256k1_fe_equal_var(&fe, &fe2));
secp256k1_fe_from_storage(&fe2, &fes);
CHECK(secp256k1_fe_equal_var(&fe, &fe2));
/* Check conversion from fe. */
secp256k1_fe_get_b32(b322, &fe);
CHECK(memcmp(b322, b32, 32) == 0);
secp256k1_fe_to_storage(&fes2, &fe);
CHECK(memcmp(&fes2, &fes, sizeof(fes)) == 0);
}
int fe_memcmp(const secp256k1_fe *a, const secp256k1_fe *b) {
secp256k1_fe t = *b;
#ifdef VERIFY
t.magnitude = a->magnitude;
t.normalized = a->normalized;
#endif
return memcmp(a, &t, sizeof(secp256k1_fe));
}
void run_field_misc(void) {
secp256k1_fe x;
secp256k1_fe y;
secp256k1_fe z;
secp256k1_fe q;
secp256k1_fe fe5 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 5);
int i, j;
for (i = 0; i < 5*count; i++) {
secp256k1_fe_storage xs, ys, zs;
random_fe(&x);
random_fe_non_zero(&y);
/* Test the fe equality and comparison operations. */
CHECK(secp256k1_fe_cmp_var(&x, &x) == 0);
CHECK(secp256k1_fe_equal_var(&x, &x));
z = x;
secp256k1_fe_add(&z,&y);
/* Test fe conditional move; z is not normalized here. */
q = x;
secp256k1_fe_cmov(&x, &z, 0);
VERIFY_CHECK(!x.normalized && x.magnitude == z.magnitude);
secp256k1_fe_cmov(&x, &x, 1);
CHECK(fe_memcmp(&x, &z) != 0);
CHECK(fe_memcmp(&x, &q) == 0);
secp256k1_fe_cmov(&q, &z, 1);
VERIFY_CHECK(!q.normalized && q.magnitude == z.magnitude);
CHECK(fe_memcmp(&q, &z) == 0);
secp256k1_fe_normalize_var(&x);
secp256k1_fe_normalize_var(&z);
CHECK(!secp256k1_fe_equal_var(&x, &z));
secp256k1_fe_normalize_var(&q);
secp256k1_fe_cmov(&q, &z, (i&1));
VERIFY_CHECK(q.normalized && q.magnitude == 1);
for (j = 0; j < 6; j++) {
secp256k1_fe_negate(&z, &z, j+1);
secp256k1_fe_normalize_var(&q);
secp256k1_fe_cmov(&q, &z, (j&1));
VERIFY_CHECK(!q.normalized && q.magnitude == (j+2));
}
secp256k1_fe_normalize_var(&z);
/* Test storage conversion and conditional moves. */
secp256k1_fe_to_storage(&xs, &x);
secp256k1_fe_to_storage(&ys, &y);
secp256k1_fe_to_storage(&zs, &z);
secp256k1_fe_storage_cmov(&zs, &xs, 0);
secp256k1_fe_storage_cmov(&zs, &zs, 1);
CHECK(memcmp(&xs, &zs, sizeof(xs)) != 0);
secp256k1_fe_storage_cmov(&ys, &xs, 1);
CHECK(memcmp(&xs, &ys, sizeof(xs)) == 0);
secp256k1_fe_from_storage(&x, &xs);
secp256k1_fe_from_storage(&y, &ys);
secp256k1_fe_from_storage(&z, &zs);
/* Test that mul_int, mul, and add agree. */
secp256k1_fe_add(&y, &x);
secp256k1_fe_add(&y, &x);
z = x;
secp256k1_fe_mul_int(&z, 3);
CHECK(check_fe_equal(&y, &z));
secp256k1_fe_add(&y, &x);
secp256k1_fe_add(&z, &x);
CHECK(check_fe_equal(&z, &y));
z = x;
secp256k1_fe_mul_int(&z, 5);
secp256k1_fe_mul(&q, &x, &fe5);
CHECK(check_fe_equal(&z, &q));
secp256k1_fe_negate(&x, &x, 1);
secp256k1_fe_add(&z, &x);
secp256k1_fe_add(&q, &x);
CHECK(check_fe_equal(&y, &z));
CHECK(check_fe_equal(&q, &y));
}
}
void run_field_inv(void) {
secp256k1_fe x, xi, xii;
int i;
for (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 x, xi, xii;
int i;
for (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_var(void) {
secp256k1_fe x[16], xi[16], xii[16];
int i;
/* Check it's safe to call for 0 elements */
secp256k1_fe_inv_all_var(xi, x, 0);
for (i = 0; i < count; i++) {
size_t j;
size_t len = secp256k1_rand_int(15) + 1;
for (j = 0; j < len; j++) {
random_fe_non_zero(&x[j]);
}
secp256k1_fe_inv_all_var(xi, x, len);
for (j = 0; j < len; j++) {
CHECK(check_fe_inverse(&x[j], &xi[j]));
}
secp256k1_fe_inv_all_var(xii, xi, len);
for (j = 0; j < len; j++) {
CHECK(check_fe_equal(&x[j], &xii[j]));
}
}
}
void run_sqr(void) {
secp256k1_fe x, s;
{
int i;
secp256k1_fe_set_int(&x, 1);
secp256k1_fe_negate(&x, &x, 1);
for (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 *a, const secp256k1_fe *k) {
secp256k1_fe 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 ns, x, s, t;
int i;
/* 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 (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 (i = 0; i < 10; i++) {
int j;
random_fe_non_square(&ns);
for (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 *****/
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));
}
/* This compares jacobian points including their Z, not just their geometric meaning. */
int gej_xyz_equals_gej(const secp256k1_gej *a, const secp256k1_gej *b) {
secp256k1_gej a2;
secp256k1_gej b2;
int ret = 1;
ret &= a->infinity == b->infinity;
if (ret && !a->infinity) {
a2 = *a;
b2 = *b;
secp256k1_fe_normalize(&a2.x);
secp256k1_fe_normalize(&a2.y);
secp256k1_fe_normalize(&a2.z);
secp256k1_fe_normalize(&b2.x);
secp256k1_fe_normalize(&b2.y);
secp256k1_fe_normalize(&b2.z);
ret &= secp256k1_fe_cmp_var(&a2.x, &b2.x) == 0;
ret &= secp256k1_fe_cmp_var(&a2.y, &b2.y) == 0;
ret &= secp256k1_fe_cmp_var(&a2.z, &b2.z) == 0;
}
return ret;
}
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 test_ge(void) {
int i, i1;
#ifdef USE_ENDOMORPHISM
int runs = 6;
#else
int runs = 4;
#endif
/* Points: (infinity, p1, p1, -p1, -p1, p2, p2, -p2, -p2, p3, p3, -p3, -p3, p4, p4, -p4, -p4).
* The second in each pair of identical points uses a random Z coordinate in the Jacobian form.
* All magnitudes are randomized.
* All 17*17 combinations of points are added to each other, using all applicable methods.
*
* When the endomorphism code is compiled in, p5 = lambda*p1 and p6 = lambda^2*p1 are added as well.
*/
secp256k1_ge *ge = (secp256k1_ge *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_ge) * (1 + 4 * runs));
secp256k1_gej *gej = (secp256k1_gej *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_gej) * (1 + 4 * runs));
secp256k1_fe *zinv = (secp256k1_fe *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_fe) * (1 + 4 * runs));
secp256k1_fe zf;
secp256k1_fe zfi2, zfi3;
secp256k1_gej_set_infinity(&gej[0]);
secp256k1_ge_clear(&ge[0]);
secp256k1_ge_set_gej_var(&ge[0], &gej[0]);
for (i = 0; i < runs; i++) {
int j;
secp256k1_ge g;
random_group_element_test(&g);
#ifdef USE_ENDOMORPHISM
if (i >= runs - 2) {
secp256k1_ge_mul_lambda(&g, &ge[1]);
}
if (i >= runs - 1) {
secp256k1_ge_mul_lambda(&g, &g);
}
#endif
ge[1 + 4 * i] = g;
ge[2 + 4 * i] = g;
secp256k1_ge_neg(&ge[3 + 4 * i], &g);
secp256k1_ge_neg(&ge[4 + 4 * i], &g);
secp256k1_gej_set_ge(&gej[1 + 4 * i], &ge[1 + 4 * i]);
random_group_element_jacobian_test(&gej[2 + 4 * i], &ge[2 + 4 * i]);
secp256k1_gej_set_ge(&gej[3 + 4 * i], &ge[3 + 4 * i]);
random_group_element_jacobian_test(&gej[4 + 4 * i], &ge[4 + 4 * i]);
for (j = 0; j < 4; j++) {
random_field_element_magnitude(&ge[1 + j + 4 * i].x);
random_field_element_magnitude(&ge[1 + j + 4 * i].y);
random_field_element_magnitude(&gej[1 + j + 4 * i].x);
random_field_element_magnitude(&gej[1 + j + 4 * i].y);
random_field_element_magnitude(&gej[1 + j + 4 * i].z);
}
}
/* Compute z inverses. */
{
secp256k1_fe *zs = checked_malloc(&ctx->error_callback, sizeof(secp256k1_fe) * (1 + 4 * runs));
for (i = 0; i < 4 * runs + 1; i++) {
if (i == 0) {
/* The point at infinity does not have a meaningful z inverse. Any should do. */
do {
random_field_element_test(&zs[i]);
} while(secp256k1_fe_is_zero(&zs[i]));
} else {
zs[i] = gej[i].z;
}
}
secp256k1_fe_inv_all_var(zinv, zs, 4 * runs + 1);
free(zs);
}
/* Generate random zf, and zfi2 = 1/zf^2, zfi3 = 1/zf^3 */
do {
random_field_element_test(&zf);
} while(secp256k1_fe_is_zero(&zf));
random_field_element_magnitude(&zf);
secp256k1_fe_inv_var(&zfi3, &zf);
secp256k1_fe_sqr(&zfi2, &zfi3);
secp256k1_fe_mul(&zfi3, &zfi3, &zfi2);
for (i1 = 0; i1 < 1 + 4 * runs; i1++) {
int i2;
for (i2 = 0; i2 < 1 + 4 * runs; i2++) {
/* Compute reference result using gej + gej (var). */
secp256k1_gej refj, resj;
secp256k1_ge ref;
secp256k1_fe zr;
secp256k1_gej_add_var(&refj, &gej[i1], &gej[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr);
/* Check Z ratio. */
if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&refj)) {
secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z);
CHECK(secp256k1_fe_equal_var(&zrz, &refj.z));
}
secp256k1_ge_set_gej_var(&ref, &refj);
/* Test gej + ge with Z ratio result (var). */
secp256k1_gej_add_ge_var(&resj, &gej[i1], &ge[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr);
ge_equals_gej(&ref, &resj);
if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&resj)) {
secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z);
CHECK(secp256k1_fe_equal_var(&zrz, &resj.z));
}
/* Test gej + ge (var, with additional Z factor). */
{
secp256k1_ge ge2_zfi = ge[i2]; /* the second term with x and y rescaled for z = 1/zf */
secp256k1_fe_mul(&ge2_zfi.x, &ge2_zfi.x, &zfi2);
secp256k1_fe_mul(&ge2_zfi.y, &ge2_zfi.y, &zfi3);
random_field_element_magnitude(&ge2_zfi.x);
random_field_element_magnitude(&ge2_zfi.y);
secp256k1_gej_add_zinv_var(&resj, &gej[i1], &ge2_zfi, &zf);
ge_equals_gej(&ref, &resj);
}
/* Test gej + ge (const). */
if (i2 != 0) {
/* secp256k1_gej_add_ge does not support its second argument being infinity. */
secp256k1_gej_add_ge(&resj, &gej[i1], &ge[i2]);
ge_equals_gej(&ref, &resj);
}
/* Test doubling (var). */
if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 == ((i2 + 3)%4)/2)) {
secp256k1_fe zr2;
/* Normal doubling with Z ratio result. */
secp256k1_gej_double_var(&resj, &gej[i1], &zr2);
ge_equals_gej(&ref, &resj);
/* Check Z ratio. */
secp256k1_fe_mul(&zr2, &zr2, &gej[i1].z);
CHECK(secp256k1_fe_equal_var(&zr2, &resj.z));
/* Normal doubling. */
secp256k1_gej_double_var(&resj, &gej[i2], NULL);
ge_equals_gej(&ref, &resj);
}
/* Test adding opposites. */
if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 != ((i2 + 3)%4)/2)) {
CHECK(secp256k1_ge_is_infinity(&ref));
}
/* Test adding infinity. */
if (i1 == 0) {
CHECK(secp256k1_ge_is_infinity(&ge[i1]));
CHECK(secp256k1_gej_is_infinity(&gej[i1]));
ge_equals_gej(&ref, &gej[i2]);
}
if (i2 == 0) {
CHECK(secp256k1_ge_is_infinity(&ge[i2]));
CHECK(secp256k1_gej_is_infinity(&gej[i2]));
ge_equals_gej(&ref, &gej[i1]);
}
}
}
/* Test adding all points together in random order equals infinity. */
{
secp256k1_gej sum = SECP256K1_GEJ_CONST_INFINITY;
secp256k1_gej *gej_shuffled = (secp256k1_gej *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_gej));
for (i = 0; i < 4 * runs + 1; i++) {
gej_shuffled[i] = gej[i];
}
for (i = 0; i < 4 * runs + 1; i++) {
int swap = i + secp256k1_rand_int(4 * runs + 1 - i);
if (swap != i) {
secp256k1_gej t = gej_shuffled[i];
gej_shuffled[i] = gej_shuffled[swap];
gej_shuffled[swap] = t;
}
}
for (i = 0; i < 4 * runs + 1; i++) {
secp256k1_gej_add_var(&sum, &sum, &gej_shuffled[i], NULL);
}
CHECK(secp256k1_gej_is_infinity(&sum));
free(gej_shuffled);
}
/* Test batch gej -> ge conversion with and without known z ratios. */
{
secp256k1_fe *zr = (secp256k1_fe *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_fe));
- secp256k1_ge *ge_set_table = (secp256k1_ge *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_ge));
secp256k1_ge *ge_set_all = (secp256k1_ge *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_ge));
for (i = 0; i < 4 * runs + 1; i++) {
/* Compute gej[i + 1].z / gez[i].z (with gej[n].z taken to be 1). */
if (i < 4 * runs) {
secp256k1_fe_mul(&zr[i + 1], &zinv[i], &gej[i + 1].z);
}
}
- secp256k1_ge_set_table_gej_var(ge_set_table, gej, zr, 4 * runs + 1);
- secp256k1_ge_set_all_gej_var(ge_set_all, gej, 4 * runs + 1, &ctx->error_callback);
+ secp256k1_ge_set_all_gej_var(ge_set_all, gej, 4 * runs + 1);
for (i = 0; i < 4 * runs + 1; i++) {
secp256k1_fe s;
random_fe_non_zero(&s);
secp256k1_gej_rescale(&gej[i], &s);
- ge_equals_gej(&ge_set_table[i], &gej[i]);
ge_equals_gej(&ge_set_all[i], &gej[i]);
}
- free(ge_set_table);
free(ge_set_all);
free(zr);
}
+ /* Test batch gej -> ge conversion with many infinities. */
+ for (i = 0; i < 4 * runs + 1; i++) {
+ random_group_element_test(&ge[i]);
+ /* randomly set half the points to infinitiy */
+ if(secp256k1_fe_is_odd(&ge[i].x)) {
+ secp256k1_ge_set_infinity(&ge[i]);
+ }
+ secp256k1_gej_set_ge(&gej[i], &ge[i]);
+ }
+ /* batch invert */
+ secp256k1_ge_set_all_gej_var(ge, gej, 4 * runs + 1);
+ /* check result */
+ for (i = 0; i < 4 * runs + 1; i++) {
+ ge_equals_gej(&ge[i], &gej[i]);
+ }
+
free(ge);
free(gej);
free(zinv);
}
void test_add_neg_y_diff_x(void) {
/* The point of this test is to check that we can add two points
* whose y-coordinates are negatives of each other but whose x
* coordinates differ. If the x-coordinates were the same, these
* points would be negatives of each other and their sum is
* infinity. This is cool because it "covers up" any degeneracy
* in the addition algorithm that would cause the xy coordinates
* of the sum to be wrong (since infinity has no xy coordinates).
* HOWEVER, if the x-coordinates are different, infinity is the
* wrong answer, and such degeneracies are exposed. This is the
* root of https://github.com/bitcoin-core/secp256k1/issues/257
* which this test is a regression test for.
*
* These points were generated in sage as
* # secp256k1 params
* F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
* C = EllipticCurve ([F (0), F (7)])
* G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
* N = FiniteField(G.order())
*
* # endomorphism values (lambda is 1^{1/3} in N, beta is 1^{1/3} in F)
* x = polygen(N)
* lam = (1 - x^3).roots()[1][0]
*
* # random "bad pair"
* P = C.random_element()
* Q = -int(lam) * P
* print " P: %x %x" % P.xy()
* print " Q: %x %x" % Q.xy()
* print "P + Q: %x %x" % (P + Q).xy()
*/
secp256k1_gej aj = SECP256K1_GEJ_CONST(
0x8d24cd95, 0x0a355af1, 0x3c543505, 0x44238d30,
0x0643d79f, 0x05a59614, 0x2f8ec030, 0xd58977cb,
0x001e337a, 0x38093dcd, 0x6c0f386d, 0x0b1293a8,
0x4d72c879, 0xd7681924, 0x44e6d2f3, 0x9190117d
);
secp256k1_gej bj = SECP256K1_GEJ_CONST(
0xc7b74206, 0x1f788cd9, 0xabd0937d, 0x164a0d86,
0x95f6ff75, 0xf19a4ce9, 0xd013bd7b, 0xbf92d2a7,
0xffe1cc85, 0xc7f6c232, 0x93f0c792, 0xf4ed6c57,
0xb28d3786, 0x2897e6db, 0xbb192d0b, 0x6e6feab2
);
secp256k1_gej sumj = SECP256K1_GEJ_CONST(
0x671a63c0, 0x3efdad4c, 0x389a7798, 0x24356027,
0xb3d69010, 0x278625c3, 0x5c86d390, 0x184a8f7a,
0x5f6409c2, 0x2ce01f2b, 0x511fd375, 0x25071d08,
0xda651801, 0x70e95caf, 0x8f0d893c, 0xbed8fbbe
);
secp256k1_ge b;
secp256k1_gej resj;
secp256k1_ge res;
secp256k1_ge_set_gej(&b, &bj);
secp256k1_gej_add_var(&resj, &aj, &bj, NULL);
secp256k1_ge_set_gej(&res, &resj);
ge_equals_gej(&res, &sumj);
secp256k1_gej_add_ge(&resj, &aj, &b);
secp256k1_ge_set_gej(&res, &resj);
ge_equals_gej(&res, &sumj);
secp256k1_gej_add_ge_var(&resj, &aj, &b, NULL);
secp256k1_ge_set_gej(&res, &resj);
ge_equals_gej(&res, &sumj);
}
void run_ge(void) {
int i;
for (i = 0; i < count * 32; i++) {
test_ge();
}
test_add_neg_y_diff_x();
}
void test_ec_combine(void) {
secp256k1_scalar sum = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
secp256k1_pubkey data[6];
const secp256k1_pubkey* d[6];
secp256k1_pubkey sd;
secp256k1_pubkey sd2;
secp256k1_gej Qj;
secp256k1_ge Q;
int i;
for (i = 1; i <= 6; i++) {
secp256k1_scalar s;
random_scalar_order_test(&s);
secp256k1_scalar_add(&sum, &sum, &s);
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &s);
secp256k1_ge_set_gej(&Q, &Qj);
secp256k1_pubkey_save(&data[i - 1], &Q);
d[i - 1] = &data[i - 1];
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &sum);
secp256k1_ge_set_gej(&Q, &Qj);
secp256k1_pubkey_save(&sd, &Q);
CHECK(secp256k1_ec_pubkey_combine(ctx, &sd2, d, i) == 1);
CHECK(memcmp(&sd, &sd2, sizeof(sd)) == 0);
}
}
void run_ec_combine(void) {
int i;
for (i = 0; i < count * 8; i++) {
test_ec_combine();
}
}
void test_group_decompress(const secp256k1_fe* x) {
/* The input itself, normalized. */
secp256k1_fe fex = *x;
secp256k1_fe fez;
/* Results of set_xquad_var, set_xo_var(..., 0), set_xo_var(..., 1). */
secp256k1_ge ge_quad, ge_even, ge_odd;
secp256k1_gej gej_quad;
/* Return values of the above calls. */
int res_quad, res_even, res_odd;
secp256k1_fe_normalize_var(&fex);
res_quad = secp256k1_ge_set_xquad(&ge_quad, &fex);
res_even = secp256k1_ge_set_xo_var(&ge_even, &fex, 0);
res_odd = secp256k1_ge_set_xo_var(&ge_odd, &fex, 1);
CHECK(res_quad == res_even);
CHECK(res_quad == res_odd);
if (res_quad) {
secp256k1_fe_normalize_var(&ge_quad.x);
secp256k1_fe_normalize_var(&ge_odd.x);
secp256k1_fe_normalize_var(&ge_even.x);
secp256k1_fe_normalize_var(&ge_quad.y);
secp256k1_fe_normalize_var(&ge_odd.y);
secp256k1_fe_normalize_var(&ge_even.y);
/* No infinity allowed. */
CHECK(!ge_quad.infinity);
CHECK(!ge_even.infinity);
CHECK(!ge_odd.infinity);
/* Check that the x coordinates check out. */
CHECK(secp256k1_fe_equal_var(&ge_quad.x, x));
CHECK(secp256k1_fe_equal_var(&ge_even.x, x));
CHECK(secp256k1_fe_equal_var(&ge_odd.x, x));
/* Check that the Y coordinate result in ge_quad is a square. */
CHECK(secp256k1_fe_is_quad_var(&ge_quad.y));
/* Check odd/even Y in ge_odd, ge_even. */
CHECK(secp256k1_fe_is_odd(&ge_odd.y));
CHECK(!secp256k1_fe_is_odd(&ge_even.y));
/* Check secp256k1_gej_has_quad_y_var. */
secp256k1_gej_set_ge(&gej_quad, &ge_quad);
CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
do {
random_fe_test(&fez);
} while (secp256k1_fe_is_zero(&fez));
secp256k1_gej_rescale(&gej_quad, &fez);
CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
secp256k1_gej_neg(&gej_quad, &gej_quad);
CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad));
do {
random_fe_test(&fez);
} while (secp256k1_fe_is_zero(&fez));
secp256k1_gej_rescale(&gej_quad, &fez);
CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad));
secp256k1_gej_neg(&gej_quad, &gej_quad);
CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
}
}
void run_group_decompress(void) {
int i;
for (i = 0; i < count * 4; i++) {
secp256k1_fe fe;
random_fe_test(&fe);
test_group_decompress(&fe);
}
}
/***** ECMULT TESTS *****/
void run_ecmult_chain(void) {
/* random starting point A (on the curve) */
secp256k1_gej a = SECP256K1_GEJ_CONST(
0x8b30bbe9, 0xae2a9906, 0x96b22f67, 0x0709dff3,
0x727fd8bc, 0x04d3362c, 0x6c7bf458, 0xe2846004,
0xa357ae91, 0x5c4a6528, 0x1309edf2, 0x0504740f,
0x0eb33439, 0x90216b4f, 0x81063cb6, 0x5f2f7e0f
);
/* two random initial factors xn and gn */
secp256k1_scalar xn = SECP256K1_SCALAR_CONST(
0x84cc5452, 0xf7fde1ed, 0xb4d38a8c, 0xe9b1b84c,
0xcef31f14, 0x6e569be9, 0x705d357a, 0x42985407
);
secp256k1_scalar gn = SECP256K1_SCALAR_CONST(
0xa1e58d22, 0x553dcd42, 0xb2398062, 0x5d4c57a9,
0x6e9323d4, 0x2b3152e5, 0xca2c3990, 0xedc7c9de
);
/* two small multipliers to be applied to xn and gn in every iteration: */
static const secp256k1_scalar xf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x1337);
static const secp256k1_scalar gf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x7113);
/* accumulators with the resulting coefficients to A and G */
secp256k1_scalar ae = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
secp256k1_scalar ge = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
/* actual points */
secp256k1_gej x;
secp256k1_gej x2;
int i;
/* the point being computed */
x = a;
for (i = 0; i < 200*count; i++) {
/* in each iteration, compute X = xn*X + gn*G; */
secp256k1_ecmult(&ctx->ecmult_ctx, &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_scalar_mul(&ae, &ae, &xn);
secp256k1_scalar_mul(&ge, &ge, &xn);
secp256k1_scalar_add(&ge, &ge, &gn);
/* modify xn and gn */
secp256k1_scalar_mul(&xn, &xn, &xf);
secp256k1_scalar_mul(&gn, &gn, &gf);
/* verify */
if (i == 19999) {
/* expected result after 19999 iterations */
secp256k1_gej rp = SECP256K1_GEJ_CONST(
0xD6E96687, 0xF9B10D09, 0x2A6F3543, 0x9D86CEBE,
0xA4535D0D, 0x409F5358, 0x6440BD74, 0xB933E830,
0xB95CBCA2, 0xC77DA786, 0x539BE8FD, 0x53354D2D,
0x3B4F566A, 0xE6580454, 0x07ED6015, 0xEE1B2A88
);
secp256k1_gej_neg(&rp, &rp);
secp256k1_gej_add_var(&rp, &rp, &x, NULL);
CHECK(secp256k1_gej_is_infinity(&rp));
}
}
/* redo the computation, but directly with the resulting ae and ge coefficients: */
secp256k1_ecmult(&ctx->ecmult_ctx, &x2, &a, &ae, &ge);
secp256k1_gej_neg(&x2, &x2);
secp256k1_gej_add_var(&x2, &x2, &x, NULL);
CHECK(secp256k1_gej_is_infinity(&x2));
}
void test_point_times_order(const secp256k1_gej *point) {
/* X * (point + G) + (order-X) * (pointer + G) = 0 */
secp256k1_scalar x;
secp256k1_scalar nx;
secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
secp256k1_gej res1, res2;
secp256k1_ge res3;
unsigned char pub[65];
size_t psize = 65;
random_scalar_order_test(&x);
secp256k1_scalar_negate(&nx, &x);
secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &x, &x); /* calc res1 = x * point + x * G; */
secp256k1_ecmult(&ctx->ecmult_ctx, &res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */
secp256k1_gej_add_var(&res1, &res1, &res2, NULL);
CHECK(secp256k1_gej_is_infinity(&res1));
CHECK(secp256k1_gej_is_valid_var(&res1) == 0);
secp256k1_ge_set_gej(&res3, &res1);
CHECK(secp256k1_ge_is_infinity(&res3));
CHECK(secp256k1_ge_is_valid_var(&res3) == 0);
CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 0) == 0);
psize = 65;
CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 1) == 0);
/* check zero/one edge cases */
secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &zero);
secp256k1_ge_set_gej(&res3, &res1);
CHECK(secp256k1_ge_is_infinity(&res3));
secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &one, &zero);
secp256k1_ge_set_gej(&res3, &res1);
ge_equals_gej(&res3, point);
secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &one);
secp256k1_ge_set_gej(&res3, &res1);
ge_equals_ge(&res3, &secp256k1_ge_const_g);
}
void run_point_times_order(void) {
int i;
secp256k1_fe x = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2);
static const secp256k1_fe xr = SECP256K1_FE_CONST(
0x7603CB59, 0xB0EF6C63, 0xFE608479, 0x2A0C378C,
0xDB3233A8, 0x0F8A9A09, 0xA877DEAD, 0x31B38C45
);
for (i = 0; i < 500; i++) {
secp256k1_ge p;
if (secp256k1_ge_set_xo_var(&p, &x, 1)) {
secp256k1_gej j;
CHECK(secp256k1_ge_is_valid_var(&p));
secp256k1_gej_set_ge(&j, &p);
CHECK(secp256k1_gej_is_valid_var(&j));
test_point_times_order(&j);
}
secp256k1_fe_sqr(&x, &x);
}
secp256k1_fe_normalize_var(&x);
CHECK(secp256k1_fe_equal_var(&x, &xr));
}
void ecmult_const_random_mult(void) {
/* random starting point A (on the curve) */
secp256k1_ge a = SECP256K1_GE_CONST(
0x6d986544, 0x57ff52b8, 0xcf1b8126, 0x5b802a5b,
0xa97f9263, 0xb1e88044, 0x93351325, 0x91bc450a,
0x535c59f7, 0x325e5d2b, 0xc391fbe8, 0x3c12787c,
0x337e4a98, 0xe82a9011, 0x0123ba37, 0xdd769c7d
);
/* random initial factor xn */
secp256k1_scalar xn = SECP256K1_SCALAR_CONST(
0x649d4f77, 0xc4242df7, 0x7f2079c9, 0x14530327,
0xa31b876a, 0xd2d8ce2a, 0x2236d5c6, 0xd7b2029b
);
/* expected xn * A (from sage) */
secp256k1_ge expected_b = SECP256K1_GE_CONST(
0x23773684, 0x4d209dc7, 0x098a786f, 0x20d06fcd,
0x070a38bf, 0xc11ac651, 0x03004319, 0x1e2a8786,
0xed8c3b8e, 0xc06dd57b, 0xd06ea66e, 0x45492b0f,
0xb84e4e1b, 0xfb77e21f, 0x96baae2a, 0x63dec956
);
secp256k1_gej b;
secp256k1_ecmult_const(&b, &a, &xn, 256);
CHECK(secp256k1_ge_is_valid_var(&a));
ge_equals_gej(&expected_b, &b);
}
void ecmult_const_commutativity(void) {
secp256k1_scalar a;
secp256k1_scalar b;
secp256k1_gej res1;
secp256k1_gej res2;
secp256k1_ge mid1;
secp256k1_ge mid2;
random_scalar_order_test(&a);
random_scalar_order_test(&b);
secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a, 256);
secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b, 256);
secp256k1_ge_set_gej(&mid1, &res1);
secp256k1_ge_set_gej(&mid2, &res2);
secp256k1_ecmult_const(&res1, &mid1, &b, 256);
secp256k1_ecmult_const(&res2, &mid2, &a, 256);
secp256k1_ge_set_gej(&mid1, &res1);
secp256k1_ge_set_gej(&mid2, &res2);
ge_equals_ge(&mid1, &mid2);
}
void ecmult_const_mult_zero_one(void) {
secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
secp256k1_scalar negone;
secp256k1_gej res1;
secp256k1_ge res2;
secp256k1_ge point;
secp256k1_scalar_negate(&negone, &one);
random_group_element_test(&point);
secp256k1_ecmult_const(&res1, &point, &zero, 3);
secp256k1_ge_set_gej(&res2, &res1);
CHECK(secp256k1_ge_is_infinity(&res2));
secp256k1_ecmult_const(&res1, &point, &one, 2);
secp256k1_ge_set_gej(&res2, &res1);
ge_equals_ge(&res2, &point);
secp256k1_ecmult_const(&res1, &point, &negone, 256);
secp256k1_gej_neg(&res1, &res1);
secp256k1_ge_set_gej(&res2, &res1);
ge_equals_ge(&res2, &point);
}
void ecmult_const_chain_multiply(void) {
/* Check known result (randomly generated test problem from sage) */
const secp256k1_scalar scalar = SECP256K1_SCALAR_CONST(
0x4968d524, 0x2abf9b7a, 0x466abbcf, 0x34b11b6d,
0xcd83d307, 0x827bed62, 0x05fad0ce, 0x18fae63b
);
const secp256k1_gej expected_point = SECP256K1_GEJ_CONST(
0x5494c15d, 0x32099706, 0xc2395f94, 0x348745fd,
0x757ce30e, 0x4e8c90fb, 0xa2bad184, 0xf883c69f,
0x5d195d20, 0xe191bf7f, 0x1be3e55f, 0x56a80196,
0x6071ad01, 0xf1462f66, 0xc997fa94, 0xdb858435
);
secp256k1_gej point;
secp256k1_ge res;
int i;
secp256k1_gej_set_ge(&point, &secp256k1_ge_const_g);
for (i = 0; i < 100; ++i) {
secp256k1_ge tmp;
secp256k1_ge_set_gej(&tmp, &point);
secp256k1_ecmult_const(&point, &tmp, &scalar, 256);
}
secp256k1_ge_set_gej(&res, &point);
ge_equals_gej(&res, &expected_point);
}
void run_ecmult_const_tests(void) {
ecmult_const_mult_zero_one();
ecmult_const_random_mult();
ecmult_const_commutativity();
ecmult_const_chain_multiply();
}
typedef struct {
secp256k1_scalar *sc;
secp256k1_ge *pt;
} 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 int ecmult_multi_false_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) {
(void)sc;
(void)pt;
(void)idx;
(void)cbdata;
return 0;
}
void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func ecmult_multi) {
int ncount;
secp256k1_scalar szero;
secp256k1_scalar sc[32];
secp256k1_ge pt[32];
secp256k1_gej r;
secp256k1_gej r2;
ecmult_multi_data data;
secp256k1_scratch *scratch_empty;
data.sc = sc;
data.pt = pt;
secp256k1_scalar_set_int(&szero, 0);
/* No points to multiply */
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, NULL, ecmult_multi_callback, &data, 0));
/* Check 1- and 2-point multiplies against ecmult */
for (ncount = 0; ncount < count; ncount++) {
secp256k1_ge ptg;
secp256k1_gej ptgj;
random_scalar_order(&sc[0]);
random_scalar_order(&sc[1]);
random_group_element_test(&ptg);
secp256k1_gej_set_ge(&ptgj, &ptg);
pt[0] = ptg;
pt[1] = secp256k1_ge_const_g;
/* only G scalar */
secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &szero, &sc[0]);
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &sc[0], ecmult_multi_callback, &data, 0));
secp256k1_gej_neg(&r2, &r2);
secp256k1_gej_add_var(&r, &r, &r2, NULL);
CHECK(secp256k1_gej_is_infinity(&r));
/* 1-point */
secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &szero);
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 1));
secp256k1_gej_neg(&r2, &r2);
secp256k1_gej_add_var(&r, &r, &r2, NULL);
CHECK(secp256k1_gej_is_infinity(&r));
/* Try to multiply 1 point, but scratch space is empty */
scratch_empty = secp256k1_scratch_create(&ctx->error_callback, 0);
CHECK(!ecmult_multi(&ctx->ecmult_ctx, scratch_empty, &r, &szero, ecmult_multi_callback, &data, 1));
secp256k1_scratch_destroy(scratch_empty);
/* Try to multiply 1 point, but callback returns false */
CHECK(!ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_false_callback, &data, 1));
/* 2-point */
secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &sc[1]);
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 2));
secp256k1_gej_neg(&r2, &r2);
secp256k1_gej_add_var(&r, &r, &r2, NULL);
CHECK(secp256k1_gej_is_infinity(&r));
/* 2-point with G scalar */
secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &sc[1]);
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &sc[1], ecmult_multi_callback, &data, 1));
secp256k1_gej_neg(&r2, &r2);
secp256k1_gej_add_var(&r, &r, &r2, NULL);
CHECK(secp256k1_gej_is_infinity(&r));
}
/* Check infinite outputs of various forms */
for (ncount = 0; ncount < count; ncount++) {
secp256k1_ge ptg;
size_t i, j;
size_t sizes[] = { 2, 10, 32 };
for (j = 0; j < 3; j++) {
for (i = 0; i < 32; i++) {
random_scalar_order(&sc[i]);
secp256k1_ge_set_infinity(&pt[i]);
}
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
CHECK(secp256k1_gej_is_infinity(&r));
}
for (j = 0; j < 3; j++) {
for (i = 0; i < 32; i++) {
random_group_element_test(&ptg);
pt[i] = ptg;
secp256k1_scalar_set_int(&sc[i], 0);
}
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
CHECK(secp256k1_gej_is_infinity(&r));
}
for (j = 0; j < 3; j++) {
random_group_element_test(&ptg);
for (i = 0; i < 16; i++) {
random_scalar_order(&sc[2*i]);
secp256k1_scalar_negate(&sc[2*i + 1], &sc[2*i]);
pt[2 * i] = ptg;
pt[2 * i + 1] = ptg;
}
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
CHECK(secp256k1_gej_is_infinity(&r));
random_scalar_order(&sc[0]);
for (i = 0; i < 16; i++) {
random_group_element_test(&ptg);
sc[2*i] = sc[0];
sc[2*i+1] = sc[0];
pt[2 * i] = ptg;
secp256k1_ge_neg(&pt[2*i+1], &pt[2*i]);
}
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
CHECK(secp256k1_gej_is_infinity(&r));
}
random_group_element_test(&ptg);
secp256k1_scalar_set_int(&sc[0], 0);
pt[0] = ptg;
for (i = 1; i < 32; i++) {
pt[i] = ptg;
random_scalar_order(&sc[i]);
secp256k1_scalar_add(&sc[0], &sc[0], &sc[i]);
secp256k1_scalar_negate(&sc[i], &sc[i]);
}
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 32));
CHECK(secp256k1_gej_is_infinity(&r));
}
/* Check random points, constant scalar */
for (ncount = 0; ncount < count; ncount++) {
size_t i;
secp256k1_gej_set_infinity(&r);
random_scalar_order(&sc[0]);
for (i = 0; i < 20; i++) {
secp256k1_ge ptg;
sc[i] = sc[0];
random_group_element_test(&ptg);
pt[i] = ptg;
secp256k1_gej_add_ge_var(&r, &r, &pt[i], NULL);
}
secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &r, &sc[0], &szero);
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
secp256k1_gej_neg(&r2, &r2);
secp256k1_gej_add_var(&r, &r, &r2, NULL);
CHECK(secp256k1_gej_is_infinity(&r));
}
/* Check random scalars, constant point */
for (ncount = 0; ncount < count; ncount++) {
size_t i;
secp256k1_ge ptg;
secp256k1_gej p0j;
secp256k1_scalar rs;
secp256k1_scalar_set_int(&rs, 0);
random_group_element_test(&ptg);
for (i = 0; i < 20; i++) {
random_scalar_order(&sc[i]);
pt[i] = ptg;
secp256k1_scalar_add(&rs, &rs, &sc[i]);
}
secp256k1_gej_set_ge(&p0j, &pt[0]);
secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &p0j, &rs, &szero);
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
secp256k1_gej_neg(&r2, &r2);
secp256k1_gej_add_var(&r, &r, &r2, NULL);
CHECK(secp256k1_gej_is_infinity(&r));
}
/* Sanity check that zero scalars don't cause problems */
for (ncount = 0; ncount < 20; ncount++) {
random_scalar_order(&sc[ncount]);
random_group_element_test(&pt[ncount]);
}
secp256k1_scalar_clear(&sc[0]);
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
secp256k1_scalar_clear(&sc[1]);
secp256k1_scalar_clear(&sc[2]);
secp256k1_scalar_clear(&sc[3]);
secp256k1_scalar_clear(&sc[4]);
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 6));
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 5));
CHECK(secp256k1_gej_is_infinity(&r));
/* Run through s0*(t0*P) + s1*(t1*P) exhaustively for many small values of s0, s1, t0, t1 */
{
const size_t TOP = 8;
size_t s0i, s1i;
size_t t0i, t1i;
secp256k1_ge ptg;
secp256k1_gej ptgj;
random_group_element_test(&ptg);
secp256k1_gej_set_ge(&ptgj, &ptg);
for(t0i = 0; t0i < TOP; t0i++) {
for(t1i = 0; t1i < TOP; t1i++) {
secp256k1_gej t0p, t1p;
secp256k1_scalar t0, t1;
secp256k1_scalar_set_int(&t0, (t0i + 1) / 2);
secp256k1_scalar_cond_negate(&t0, t0i & 1);
secp256k1_scalar_set_int(&t1, (t1i + 1) / 2);
secp256k1_scalar_cond_negate(&t1, t1i & 1);
secp256k1_ecmult(&ctx->ecmult_ctx, &t0p, &ptgj, &t0, &szero);
secp256k1_ecmult(&ctx->ecmult_ctx, &t1p, &ptgj, &t1, &szero);
for(s0i = 0; s0i < TOP; s0i++) {
for(s1i = 0; s1i < TOP; s1i++) {
secp256k1_scalar tmp1, tmp2;
secp256k1_gej expected, actual;
secp256k1_ge_set_gej(&pt[0], &t0p);
secp256k1_ge_set_gej(&pt[1], &t1p);
secp256k1_scalar_set_int(&sc[0], (s0i + 1) / 2);
secp256k1_scalar_cond_negate(&sc[0], s0i & 1);
secp256k1_scalar_set_int(&sc[1], (s1i + 1) / 2);
secp256k1_scalar_cond_negate(&sc[1], s1i & 1);
secp256k1_scalar_mul(&tmp1, &t0, &sc[0]);
secp256k1_scalar_mul(&tmp2, &t1, &sc[1]);
secp256k1_scalar_add(&tmp1, &tmp1, &tmp2);
secp256k1_ecmult(&ctx->ecmult_ctx, &expected, &ptgj, &tmp1, &szero);
CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &actual, &szero, ecmult_multi_callback, &data, 2));
secp256k1_gej_neg(&expected, &expected);
secp256k1_gej_add_var(&actual, &actual, &expected, NULL);
CHECK(secp256k1_gej_is_infinity(&actual));
}
}
}
}
}
}
void test_secp256k1_pippenger_bucket_window_inv(void) {
int i;
CHECK(secp256k1_pippenger_bucket_window_inv(0) == 0);
for(i = 1; i <= PIPPENGER_MAX_BUCKET_WINDOW; i++) {
#ifdef USE_ENDOMORPHISM
/* Bucket_window of 8 is not used with endo */
if (i == 8) {
continue;
}
#endif
CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)) == i);
if (i != PIPPENGER_MAX_BUCKET_WINDOW) {
CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)+1) > i);
}
}
}
/**
* Probabilistically test the function returning the maximum number of possible points
* for a given scratch space.
*/
void test_ecmult_multi_pippenger_max_points(void) {
size_t scratch_size = secp256k1_rand_int(256);
size_t max_size = secp256k1_pippenger_scratch_size(secp256k1_pippenger_bucket_window_inv(PIPPENGER_MAX_BUCKET_WINDOW-1)+512, 12);
secp256k1_scratch *scratch;
size_t n_points_supported;
int bucket_window = 0;
for(; scratch_size < max_size; scratch_size+=256) {
scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size);
CHECK(scratch != NULL);
n_points_supported = secp256k1_pippenger_max_points(scratch);
if (n_points_supported == 0) {
secp256k1_scratch_destroy(scratch);
continue;
}
bucket_window = secp256k1_pippenger_bucket_window(n_points_supported);
CHECK(secp256k1_scratch_allocate_frame(scratch, secp256k1_pippenger_scratch_size(n_points_supported, bucket_window), PIPPENGER_SCRATCH_OBJECTS));
secp256k1_scratch_deallocate_frame(scratch);
secp256k1_scratch_destroy(scratch);
}
CHECK(bucket_window == PIPPENGER_MAX_BUCKET_WINDOW);
}
/**
* Run secp256k1_ecmult_multi_var with num points and a scratch space restricted to
* 1 <= i <= num points.
*/
void test_ecmult_multi_batching(void) {
static const int n_points = 2*ECMULT_PIPPENGER_THRESHOLD;
secp256k1_scalar scG;
secp256k1_scalar szero;
secp256k1_scalar *sc = (secp256k1_scalar *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_scalar) * n_points);
secp256k1_ge *pt = (secp256k1_ge *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_ge) * n_points);
secp256k1_gej r;
secp256k1_gej r2;
ecmult_multi_data data;
int i;
secp256k1_scratch *scratch;
secp256k1_gej_set_infinity(&r2);
secp256k1_scalar_set_int(&szero, 0);
/* Get random scalars and group elements and compute result */
random_scalar_order(&scG);
secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &r2, &szero, &scG);
for(i = 0; i < n_points; i++) {
secp256k1_ge ptg;
secp256k1_gej ptgj;
random_group_element_test(&ptg);
secp256k1_gej_set_ge(&ptgj, &ptg);
pt[i] = ptg;
random_scalar_order(&sc[i]);
secp256k1_ecmult(&ctx->ecmult_ctx, &ptgj, &ptgj, &sc[i], NULL);
secp256k1_gej_add_var(&r2, &r2, &ptgj, NULL);
}
data.sc = sc;
data.pt = pt;
/* Test with empty scratch space */
scratch = secp256k1_scratch_create(&ctx->error_callback, 0);
CHECK(!secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, 1));
secp256k1_scratch_destroy(scratch);
/* Test with space for 1 point in pippenger. That's not enough because
* ecmult_multi selects strauss which requires more memory. */
scratch = secp256k1_scratch_create(&ctx->error_callback, secp256k1_pippenger_scratch_size(1, 1) + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT);
CHECK(!secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, 1));
secp256k1_scratch_destroy(scratch);
secp256k1_gej_neg(&r2, &r2);
for(i = 1; i <= n_points; i++) {
if (i > ECMULT_PIPPENGER_THRESHOLD) {
int bucket_window = secp256k1_pippenger_bucket_window(i);
size_t scratch_size = secp256k1_pippenger_scratch_size(i, bucket_window);
scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT);
} else {
size_t scratch_size = secp256k1_strauss_scratch_size(i);
scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT);
}
CHECK(secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, n_points));
secp256k1_gej_add_var(&r, &r, &r2, NULL);
CHECK(secp256k1_gej_is_infinity(&r));
secp256k1_scratch_destroy(scratch);
}
free(sc);
free(pt);
}
void run_ecmult_multi_tests(void) {
secp256k1_scratch *scratch;
test_secp256k1_pippenger_bucket_window_inv();
test_ecmult_multi_pippenger_max_points();
scratch = secp256k1_scratch_create(&ctx->error_callback, 819200);
test_ecmult_multi(scratch, secp256k1_ecmult_multi_var);
test_ecmult_multi(scratch, secp256k1_ecmult_pippenger_batch_single);
test_ecmult_multi(scratch, secp256k1_ecmult_strauss_batch_single);
secp256k1_scratch_destroy(scratch);
/* Run test_ecmult_multi with space for exactly one point */
scratch = secp256k1_scratch_create(&ctx->error_callback, secp256k1_strauss_scratch_size(1) + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT);
test_ecmult_multi(scratch, secp256k1_ecmult_multi_var);
secp256k1_scratch_destroy(scratch);
test_ecmult_multi_batching();
}
void test_wnaf(const secp256k1_scalar *number, int w) {
secp256k1_scalar x, two, t;
int wnaf[256];
int zeroes = -1;
int i;
int bits;
secp256k1_scalar_set_int(&x, 0);
secp256k1_scalar_set_int(&two, 2);
bits = secp256k1_ecmult_wnaf(wnaf, 256, number, w);
CHECK(bits <= 256);
for (i = bits-1; i >= 0; i--) {
int v = wnaf[i];
secp256k1_scalar_mul(&x, &x, &two);
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++;
}
if (v >= 0) {
secp256k1_scalar_set_int(&t, v);
} else {
secp256k1_scalar_set_int(&t, -v);
secp256k1_scalar_negate(&t, &t);
}
secp256k1_scalar_add(&x, &x, &t);
}
CHECK(secp256k1_scalar_eq(&x, number)); /* check that wnaf represents number */
}
void test_constant_wnaf_negate(const secp256k1_scalar *number) {
secp256k1_scalar neg1 = *number;
secp256k1_scalar neg2 = *number;
int sign1 = 1;
int sign2 = 1;
if (!secp256k1_scalar_get_bits(&neg1, 0, 1)) {
secp256k1_scalar_negate(&neg1, &neg1);
sign1 = -1;
}
sign2 = secp256k1_scalar_cond_negate(&neg2, secp256k1_scalar_is_even(&neg2));
CHECK(sign1 == sign2);
CHECK(secp256k1_scalar_eq(&neg1, &neg2));
}
void test_constant_wnaf(const secp256k1_scalar *number, int w) {
secp256k1_scalar x, shift;
int wnaf[256] = {0};
int i;
int skew;
int bits = 256;
secp256k1_scalar num = *number;
secp256k1_scalar_set_int(&x, 0);
secp256k1_scalar_set_int(&shift, 1 << w);
/* With USE_ENDOMORPHISM on we only consider 128-bit numbers */
#ifdef USE_ENDOMORPHISM
for (i = 0; i < 16; ++i) {
secp256k1_scalar_shr_int(&num, 8);
}
bits = 128;
#endif
skew = secp256k1_wnaf_const(wnaf, num, w, bits);
for (i = WNAF_SIZE_BITS(bits, w); i >= 0; --i) {
secp256k1_scalar t;
int v = wnaf[i];
CHECK(v != 0); /* check nonzero */
CHECK(v & 1); /* check parity */
CHECK(v > -(1 << w)); /* check range above */
CHECK(v < (1 << w)); /* check range below */
secp256k1_scalar_mul(&x, &x, &shift);
if (v >= 0) {
secp256k1_scalar_set_int(&t, v);
} else {
secp256k1_scalar_set_int(&t, -v);
secp256k1_scalar_negate(&t, &t);
}
secp256k1_scalar_add(&x, &x, &t);
}
/* Skew num because when encoding numbers as odd we use an offset */
secp256k1_scalar_cadd_bit(&num, skew == 2, 1);
CHECK(secp256k1_scalar_eq(&x, &num));
}
void test_fixed_wnaf(const secp256k1_scalar *number, int w) {
secp256k1_scalar x, shift;
int wnaf[256] = {0};
int i;
int skew;
secp256k1_scalar num = *number;
secp256k1_scalar_set_int(&x, 0);
secp256k1_scalar_set_int(&shift, 1 << w);
/* With USE_ENDOMORPHISM on we only consider 128-bit numbers */
#ifdef USE_ENDOMORPHISM
for (i = 0; i < 16; ++i) {
secp256k1_scalar_shr_int(&num, 8);
}
#endif
skew = secp256k1_wnaf_fixed(wnaf, &num, w);
for (i = WNAF_SIZE(w)-1; i >= 0; --i) {
secp256k1_scalar t;
int v = wnaf[i];
CHECK(v == 0 || v & 1); /* check parity */
CHECK(v > -(1 << w)); /* check range above */
CHECK(v < (1 << w)); /* check range below */
secp256k1_scalar_mul(&x, &x, &shift);
if (v >= 0) {
secp256k1_scalar_set_int(&t, v);
} else {
secp256k1_scalar_set_int(&t, -v);
secp256k1_scalar_negate(&t, &t);
}
secp256k1_scalar_add(&x, &x, &t);
}
/* If skew is 1 then add 1 to num */
secp256k1_scalar_cadd_bit(&num, 0, skew == 1);
CHECK(secp256k1_scalar_eq(&x, &num));
}
/* Checks that the first 8 elements of wnaf are equal to wnaf_expected and the
* rest is 0.*/
void test_fixed_wnaf_small_helper(int *wnaf, int *wnaf_expected, int w) {
int i;
for (i = WNAF_SIZE(w)-1; i >= 8; --i) {
CHECK(wnaf[i] == 0);
}
for (i = 7; i >= 0; --i) {
CHECK(wnaf[i] == wnaf_expected[i]);
}
}
void test_fixed_wnaf_small(void) {
int w = 4;
int wnaf[256] = {0};
int i;
int skew;
secp256k1_scalar num;
secp256k1_scalar_set_int(&num, 0);
skew = secp256k1_wnaf_fixed(wnaf, &num, w);
for (i = WNAF_SIZE(w)-1; i >= 0; --i) {
int v = wnaf[i];
CHECK(v == 0);
}
CHECK(skew == 0);
secp256k1_scalar_set_int(&num, 1);
skew = secp256k1_wnaf_fixed(wnaf, &num, w);
for (i = WNAF_SIZE(w)-1; i >= 1; --i) {
int v = wnaf[i];
CHECK(v == 0);
}
CHECK(wnaf[0] == 1);
CHECK(skew == 0);
{
int wnaf_expected[8] = { 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf };
secp256k1_scalar_set_int(&num, 0xffffffff);
skew = secp256k1_wnaf_fixed(wnaf, &num, w);
test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
CHECK(skew == 0);
}
{
int wnaf_expected[8] = { -1, -1, -1, -1, -1, -1, -1, 0xf };
secp256k1_scalar_set_int(&num, 0xeeeeeeee);
skew = secp256k1_wnaf_fixed(wnaf, &num, w);
test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
CHECK(skew == 1);
}
{
int wnaf_expected[8] = { 1, 0, 1, 0, 1, 0, 1, 0 };
secp256k1_scalar_set_int(&num, 0x01010101);
skew = secp256k1_wnaf_fixed(wnaf, &num, w);
test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
CHECK(skew == 0);
}
{
int wnaf_expected[8] = { -0xf, 0, 0xf, -0xf, 0, 0xf, 1, 0 };
secp256k1_scalar_set_int(&num, 0x01ef1ef1);
skew = secp256k1_wnaf_fixed(wnaf, &num, w);
test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
CHECK(skew == 0);
}
}
void run_wnaf(void) {
int i;
secp256k1_scalar n = {{0}};
/* Sanity check: 1 and 2 are the smallest odd and even numbers and should
* have easier-to-diagnose failure modes */
n.d[0] = 1;
test_constant_wnaf(&n, 4);
n.d[0] = 2;
test_constant_wnaf(&n, 4);
/* Test 0 */
test_fixed_wnaf_small();
/* Random tests */
for (i = 0; i < count; i++) {
random_scalar_order(&n);
test_wnaf(&n, 4+(i%10));
test_constant_wnaf_negate(&n);
test_constant_wnaf(&n, 4 + (i % 10));
test_fixed_wnaf(&n, 4 + (i % 10));
}
secp256k1_scalar_set_int(&n, 0);
CHECK(secp256k1_scalar_cond_negate(&n, 1) == -1);
CHECK(secp256k1_scalar_is_zero(&n));
CHECK(secp256k1_scalar_cond_negate(&n, 0) == 1);
CHECK(secp256k1_scalar_is_zero(&n));
}
void test_ecmult_constants(void) {
/* Test ecmult_gen() for [0..36) and [order-36..0). */
secp256k1_scalar x;
secp256k1_gej r;
secp256k1_ge ng;
int i;
int j;
secp256k1_ge_neg(&ng, &secp256k1_ge_const_g);
for (i = 0; i < 36; i++ ) {
secp256k1_scalar_set_int(&x, i);
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x);
for (j = 0; j < i; j++) {
if (j == i - 1) {
ge_equals_gej(&secp256k1_ge_const_g, &r);
}
secp256k1_gej_add_ge(&r, &r, &ng);
}
CHECK(secp256k1_gej_is_infinity(&r));
}
for (i = 1; i <= 36; i++ ) {
secp256k1_scalar_set_int(&x, i);
secp256k1_scalar_negate(&x, &x);
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x);
for (j = 0; j < i; j++) {
if (j == i - 1) {
ge_equals_gej(&ng, &r);
}
secp256k1_gej_add_ge(&r, &r, &secp256k1_ge_const_g);
}
CHECK(secp256k1_gej_is_infinity(&r));
}
}
void run_ecmult_constants(void) {
test_ecmult_constants();
}
void test_ecmult_gen_blind(void) {
/* Test ecmult_gen() blinding and confirm that the blinding changes, the affine points match, and the z's don't match. */
secp256k1_scalar key;
secp256k1_scalar b;
unsigned char seed32[32];
secp256k1_gej pgej;
secp256k1_gej pgej2;
secp256k1_gej i;
secp256k1_ge pge;
random_scalar_order_test(&key);
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej, &key);
secp256k1_rand256(seed32);
b = ctx->ecmult_gen_ctx.blind;
i = ctx->ecmult_gen_ctx.initial;
secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32);
CHECK(!secp256k1_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind));
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej2, &key);
CHECK(!gej_xyz_equals_gej(&pgej, &pgej2));
CHECK(!gej_xyz_equals_gej(&i, &ctx->ecmult_gen_ctx.initial));
secp256k1_ge_set_gej(&pge, &pgej);
ge_equals_gej(&pge, &pgej2);
}
void test_ecmult_gen_blind_reset(void) {
/* Test ecmult_gen() blinding reset and confirm that the blinding is consistent. */
secp256k1_scalar b;
secp256k1_gej initial;
secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0);
b = ctx->ecmult_gen_ctx.blind;
initial = ctx->ecmult_gen_ctx.initial;
secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0);
CHECK(secp256k1_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind));
CHECK(gej_xyz_equals_gej(&initial, &ctx->ecmult_gen_ctx.initial));
}
void run_ecmult_gen_blind(void) {
int i;
test_ecmult_gen_blind_reset();
for (i = 0; i < 10; i++) {
test_ecmult_gen_blind();
}
}
#ifdef USE_ENDOMORPHISM
/***** ENDOMORPHISH TESTS *****/
void test_scalar_split(void) {
secp256k1_scalar full;
secp256k1_scalar s1, slam;
const unsigned char zero[32] = {0};
unsigned char tmp[32];
random_scalar_order_test(&full);
secp256k1_scalar_split_lambda(&s1, &slam, &full);
/* check that both are <= 128 bits in size */
if (secp256k1_scalar_is_high(&s1)) {
secp256k1_scalar_negate(&s1, &s1);
}
if (secp256k1_scalar_is_high(&slam)) {
secp256k1_scalar_negate(&slam, &slam);
}
secp256k1_scalar_get_b32(tmp, &s1);
CHECK(memcmp(zero, tmp, 16) == 0);
secp256k1_scalar_get_b32(tmp, &slam);
CHECK(memcmp(zero, tmp, 16) == 0);
}
void run_endomorphism_tests(void) {
test_scalar_split();
}
#endif
void ec_pubkey_parse_pointtest(const unsigned char *input, int xvalid, int yvalid) {
unsigned char pubkeyc[65];
secp256k1_pubkey pubkey;
secp256k1_ge ge;
size_t pubkeyclen;
int32_t ecount;
ecount = 0;
secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
for (pubkeyclen = 3; pubkeyclen <= 65; pubkeyclen++) {
/* Smaller sizes are tested exhaustively elsewhere. */
int32_t i;
memcpy(&pubkeyc[1], input, 64);
VG_UNDEF(&pubkeyc[pubkeyclen], 65 - pubkeyclen);
for (i = 0; i < 256; i++) {
/* Try all type bytes. */
int xpass;
int ypass;
int ysign;
pubkeyc[0] = i;
/* What sign does this point have? */
ysign = (input[63] & 1) + 2;
/* For the current type (i) do we expect parsing to work? Handled all of compressed/uncompressed/hybrid. */
xpass = xvalid && (pubkeyclen == 33) && ((i & 254) == 2);
/* Do we expect a parse and re-serialize as uncompressed to give a matching y? */
ypass = xvalid && yvalid && ((i & 4) == ((pubkeyclen == 65) << 2)) &&
((i == 4) || ((i & 251) == ysign)) && ((pubkeyclen == 33) || (pubkeyclen == 65));
if (xpass || ypass) {
/* These cases must parse. */
unsigned char pubkeyo[65];
size_t outl;
memset(&pubkey, 0, sizeof(pubkey));
VG_UNDEF(&pubkey, sizeof(pubkey));
ecount = 0;
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
VG_CHECK(&pubkey, sizeof(pubkey));
outl = 65;
VG_UNDEF(pubkeyo, 65);
CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
VG_CHECK(pubkeyo, outl);
CHECK(outl == 33);
CHECK(memcmp(&pubkeyo[1], &pubkeyc[1], 32) == 0);
CHECK((pubkeyclen != 33) || (pubkeyo[0] == pubkeyc[0]));
if (ypass) {
/* This test isn't always done because we decode with alternative signs, so the y won't match. */
CHECK(pubkeyo[0] == ysign);
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1);
memset(&pubkey, 0, sizeof(pubkey));
VG_UNDEF(&pubkey, sizeof(pubkey));
secp256k1_pubkey_save(&pubkey, &ge);
VG_CHECK(&pubkey, sizeof(pubkey));
outl = 65;
VG_UNDEF(pubkeyo, 65);
CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1);
VG_CHECK(pubkeyo, outl);
CHECK(outl == 65);
CHECK(pubkeyo[0] == 4);
CHECK(memcmp(&pubkeyo[1], input, 64) == 0);
}
CHECK(ecount == 0);
} else {
/* These cases must fail to parse. */
memset(&pubkey, 0xfe, sizeof(pubkey));
ecount = 0;
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(ecount == 0);
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
CHECK(ecount == 1);
}
}
}
secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
}
void run_ec_pubkey_parse_test(void) {
#define SECP256K1_EC_PARSE_TEST_NVALID (12)
const unsigned char valid[SECP256K1_EC_PARSE_TEST_NVALID][64] = {
{
/* Point with leading and trailing zeros in x and y serialization. */
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x42, 0x52,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x64, 0xef, 0xa1, 0x7b, 0x77, 0x61, 0xe1, 0xe4, 0x27, 0x06, 0x98, 0x9f, 0xb4, 0x83,
0xb8, 0xd2, 0xd4, 0x9b, 0xf7, 0x8f, 0xae, 0x98, 0x03, 0xf0, 0x99, 0xb8, 0x34, 0xed, 0xeb, 0x00
},
{
/* Point with x equal to a 3rd root of unity.*/
0x7a, 0xe9, 0x6a, 0x2b, 0x65, 0x7c, 0x07, 0x10, 0x6e, 0x64, 0x47, 0x9e, 0xac, 0x34, 0x34, 0xe9,
0x9c, 0xf0, 0x49, 0x75, 0x12, 0xf5, 0x89, 0x95, 0xc1, 0x39, 0x6c, 0x28, 0x71, 0x95, 0x01, 0xee,
0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
},
{
/* Point with largest x. (1/2) */
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c,
0x0e, 0x99, 0x4b, 0x14, 0xea, 0x72, 0xf8, 0xc3, 0xeb, 0x95, 0xc7, 0x1e, 0xf6, 0x92, 0x57, 0x5e,
0x77, 0x50, 0x58, 0x33, 0x2d, 0x7e, 0x52, 0xd0, 0x99, 0x5c, 0xf8, 0x03, 0x88, 0x71, 0xb6, 0x7d,
},
{
/* Point with largest x. (2/2) */
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c,
0xf1, 0x66, 0xb4, 0xeb, 0x15, 0x8d, 0x07, 0x3c, 0x14, 0x6a, 0x38, 0xe1, 0x09, 0x6d, 0xa8, 0xa1,
0x88, 0xaf, 0xa7, 0xcc, 0xd2, 0x81, 0xad, 0x2f, 0x66, 0xa3, 0x07, 0xfb, 0x77, 0x8e, 0x45, 0xb2,
},
{
/* Point with smallest x. (1/2) */
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
},
{
/* Point with smallest x. (2/2) */
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb,
0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41,
},
{
/* Point with largest y. (1/3) */
0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
},
{
/* Point with largest y. (2/3) */
0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
},
{
/* Point with largest y. (3/3) */
0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
},
{
/* Point with smallest y. (1/3) */
0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
},
{
/* Point with smallest y. (2/3) */
0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
},
{
/* Point with smallest y. (3/3) */
0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01
}
};
#define SECP256K1_EC_PARSE_TEST_NXVALID (4)
const unsigned char onlyxvalid[SECP256K1_EC_PARSE_TEST_NXVALID][64] = {
{
/* Valid if y overflow ignored (y = 1 mod p). (1/3) */
0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
},
{
/* Valid if y overflow ignored (y = 1 mod p). (2/3) */
0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
},
{
/* Valid if y overflow ignored (y = 1 mod p). (3/3)*/
0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
},
{
/* x on curve, y is from y^2 = x^3 + 8. */
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03
}
};
#define SECP256K1_EC_PARSE_TEST_NINVALID (7)
const unsigned char invalid[SECP256K1_EC_PARSE_TEST_NINVALID][64] = {
{
/* x is third root of -8, y is -1 * (x^3+7); also on the curve for y^2 = x^3 + 9. */
0x0a, 0x2d, 0x2b, 0xa9, 0x35, 0x07, 0xf1, 0xdf, 0x23, 0x37, 0x70, 0xc2, 0xa7, 0x97, 0x96, 0x2c,
0xc6, 0x1f, 0x6d, 0x15, 0xda, 0x14, 0xec, 0xd4, 0x7d, 0x8d, 0x27, 0xae, 0x1c, 0xd5, 0xf8, 0x53,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
},
{
/* Valid if x overflow ignored (x = 1 mod p). */
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
},
{
/* Valid if x overflow ignored (x = 1 mod p). */
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb,
0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41,
},
{
/* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
0xf4, 0x84, 0x14, 0x5c, 0xb0, 0x14, 0x9b, 0x82, 0x5d, 0xff, 0x41, 0x2f, 0xa0, 0x52, 0xa8, 0x3f,
0xcb, 0x72, 0xdb, 0x61, 0xd5, 0x6f, 0x37, 0x70, 0xce, 0x06, 0x6b, 0x73, 0x49, 0xa2, 0xaa, 0x28,
},
{
/* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
0x0b, 0x7b, 0xeb, 0xa3, 0x4f, 0xeb, 0x64, 0x7d, 0xa2, 0x00, 0xbe, 0xd0, 0x5f, 0xad, 0x57, 0xc0,
0x34, 0x8d, 0x24, 0x9e, 0x2a, 0x90, 0xc8, 0x8f, 0x31, 0xf9, 0x94, 0x8b, 0xb6, 0x5d, 0x52, 0x07,
},
{
/* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x8f, 0x53, 0x7e, 0xef, 0xdf, 0xc1, 0x60, 0x6a, 0x07, 0x27, 0xcd, 0x69, 0xb4, 0xa7, 0x33, 0x3d,
0x38, 0xed, 0x44, 0xe3, 0x93, 0x2a, 0x71, 0x79, 0xee, 0xcb, 0x4b, 0x6f, 0xba, 0x93, 0x60, 0xdc,
},
{
/* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x70, 0xac, 0x81, 0x10, 0x20, 0x3e, 0x9f, 0x95, 0xf8, 0xd8, 0x32, 0x96, 0x4b, 0x58, 0xcc, 0xc2,
0xc7, 0x12, 0xbb, 0x1c, 0x6c, 0xd5, 0x8e, 0x86, 0x11, 0x34, 0xb4, 0x8f, 0x45, 0x6c, 0x9b, 0x53
}
};
const unsigned char pubkeyc[66] = {
/* Serialization of G. */
0x04, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B,
0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17,
0x98, 0x48, 0x3A, 0xDA, 0x77, 0x26, 0xA3, 0xC4, 0x65, 0x5D, 0xA4, 0xFB, 0xFC, 0x0E, 0x11, 0x08,
0xA8, 0xFD, 0x17, 0xB4, 0x48, 0xA6, 0x85, 0x54, 0x19, 0x9C, 0x47, 0xD0, 0x8F, 0xFB, 0x10, 0xD4,
0xB8, 0x00
};
unsigned char sout[65];
unsigned char shortkey[2];
secp256k1_ge ge;
secp256k1_pubkey pubkey;
size_t len;
int32_t i;
int32_t ecount;
int32_t ecount2;
ecount = 0;
/* Nothing should be reading this far into pubkeyc. */
VG_UNDEF(&pubkeyc[65], 1);
secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
/* Zero length claimed, fail, zeroize, no illegal arg error. */
memset(&pubkey, 0xfe, sizeof(pubkey));
ecount = 0;
VG_UNDEF(shortkey, 2);
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 0) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(ecount == 0);
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
CHECK(ecount == 1);
/* Length one claimed, fail, zeroize, no illegal arg error. */
for (i = 0; i < 256 ; i++) {
memset(&pubkey, 0xfe, sizeof(pubkey));
ecount = 0;
shortkey[0] = i;
VG_UNDEF(&shortkey[1], 1);
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 1) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(ecount == 0);
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
CHECK(ecount == 1);
}
/* Length two claimed, fail, zeroize, no illegal arg error. */
for (i = 0; i < 65536 ; i++) {
memset(&pubkey, 0xfe, sizeof(pubkey));
ecount = 0;
shortkey[0] = i & 255;
shortkey[1] = i >> 8;
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 2) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(ecount == 0);
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
CHECK(ecount == 1);
}
memset(&pubkey, 0xfe, sizeof(pubkey));
ecount = 0;
VG_UNDEF(&pubkey, sizeof(pubkey));
/* 33 bytes claimed on otherwise valid input starting with 0x04, fail, zeroize output, no illegal arg error. */
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 33) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(ecount == 0);
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
CHECK(ecount == 1);
/* NULL pubkey, illegal arg error. Pubkey isn't rewritten before this step, since it's NULL into the parser. */
CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, pubkeyc, 65) == 0);
CHECK(ecount == 2);
/* NULL input string. Illegal arg and zeroize output. */
memset(&pubkey, 0xfe, sizeof(pubkey));
ecount = 0;
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, NULL, 65) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(ecount == 1);
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
CHECK(ecount == 2);
/* 64 bytes claimed on input starting with 0x04, fail, zeroize output, no illegal arg error. */
memset(&pubkey, 0xfe, sizeof(pubkey));
ecount = 0;
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 64) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(ecount == 0);
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
CHECK(ecount == 1);
/* 66 bytes claimed, fail, zeroize output, no illegal arg error. */
memset(&pubkey, 0xfe, sizeof(pubkey));
ecount = 0;
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 66) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(ecount == 0);
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
CHECK(ecount == 1);
/* Valid parse. */
memset(&pubkey, 0, sizeof(pubkey));
ecount = 0;
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 65) == 1);
CHECK(secp256k1_ec_pubkey_parse(secp256k1_context_no_precomp, &pubkey, pubkeyc, 65) == 1);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(ecount == 0);
VG_UNDEF(&ge, sizeof(ge));
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1);
VG_CHECK(&ge.x, sizeof(ge.x));
VG_CHECK(&ge.y, sizeof(ge.y));
VG_CHECK(&ge.infinity, sizeof(ge.infinity));
ge_equals_ge(&secp256k1_ge_const_g, &ge);
CHECK(ecount == 0);
/* secp256k1_ec_pubkey_serialize illegal args. */
ecount = 0;
len = 65;
CHECK(secp256k1_ec_pubkey_serialize(ctx, NULL, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0);
CHECK(ecount == 1);
CHECK(len == 0);
CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, NULL, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0);
CHECK(ecount == 2);
len = 65;
VG_UNDEF(sout, 65);
CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, NULL, SECP256K1_EC_UNCOMPRESSED) == 0);
VG_CHECK(sout, 65);
CHECK(ecount == 3);
CHECK(len == 0);
len = 65;
CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, ~0) == 0);
CHECK(ecount == 4);
CHECK(len == 0);
len = 65;
VG_UNDEF(sout, 65);
CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1);
VG_CHECK(sout, 65);
CHECK(ecount == 4);
CHECK(len == 65);
/* Multiple illegal args. Should still set arg error only once. */
ecount = 0;
ecount2 = 11;
CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0);
CHECK(ecount == 1);
/* Does the illegal arg callback actually change the behavior? */
secp256k1_context_set_illegal_callback(ctx, uncounting_illegal_callback_fn, &ecount2);
CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0);
CHECK(ecount == 1);
CHECK(ecount2 == 10);
secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
/* Try a bunch of prefabbed points with all possible encodings. */
for (i = 0; i < SECP256K1_EC_PARSE_TEST_NVALID; i++) {
ec_pubkey_parse_pointtest(valid[i], 1, 1);
}
for (i = 0; i < SECP256K1_EC_PARSE_TEST_NXVALID; i++) {
ec_pubkey_parse_pointtest(onlyxvalid[i], 1, 0);
}
for (i = 0; i < SECP256K1_EC_PARSE_TEST_NINVALID; i++) {
ec_pubkey_parse_pointtest(invalid[i], 0, 0);
}
}
void run_eckey_edge_case_test(void) {
const unsigned char orderc[32] = {
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41
};
const unsigned char zeros[sizeof(secp256k1_pubkey)] = {0x00};
unsigned char ctmp[33];
unsigned char ctmp2[33];
secp256k1_pubkey pubkey;
secp256k1_pubkey pubkey2;
secp256k1_pubkey pubkey_one;
secp256k1_pubkey pubkey_negone;
const secp256k1_pubkey *pubkeys[3];
size_t len;
int32_t ecount;
/* Group order is too large, reject. */
CHECK(secp256k1_ec_seckey_verify(ctx, orderc) == 0);
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, orderc) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
/* Maximum value is too large, reject. */
memset(ctmp, 255, 32);
CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
memset(&pubkey, 1, sizeof(pubkey));
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
/* Zero is too small, reject. */
memset(ctmp, 0, 32);
CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
memset(&pubkey, 1, sizeof(pubkey));
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
/* One must be accepted. */
ctmp[31] = 0x01;
CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
memset(&pubkey, 0, sizeof(pubkey));
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
pubkey_one = pubkey;
/* Group order + 1 is too large, reject. */
memcpy(ctmp, orderc, 32);
ctmp[31] = 0x42;
CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
memset(&pubkey, 1, sizeof(pubkey));
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
/* -1 must be accepted. */
ctmp[31] = 0x40;
CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
memset(&pubkey, 0, sizeof(pubkey));
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
pubkey_negone = pubkey;
/* Tweak of zero leaves the value unchanged. */
memset(ctmp2, 0, 32);
CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, ctmp2) == 1);
CHECK(memcmp(orderc, ctmp, 31) == 0 && ctmp[31] == 0x40);
memcpy(&pubkey2, &pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
/* Multiply tweak of zero zeroizes the output. */
CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, ctmp2) == 0);
CHECK(memcmp(zeros, ctmp, 32) == 0);
CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, ctmp2) == 0);
CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
memcpy(&pubkey, &pubkey2, sizeof(pubkey));
/* Overflowing key tweak zeroizes. */
memcpy(ctmp, orderc, 32);
ctmp[31] = 0x40;
CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, orderc) == 0);
CHECK(memcmp(zeros, ctmp, 32) == 0);
memcpy(ctmp, orderc, 32);
ctmp[31] = 0x40;
CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, orderc) == 0);
CHECK(memcmp(zeros, ctmp, 32) == 0);
memcpy(ctmp, orderc, 32);
ctmp[31] = 0x40;
CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, orderc) == 0);
CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
memcpy(&pubkey, &pubkey2, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, orderc) == 0);
CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
memcpy(&pubkey, &pubkey2, sizeof(pubkey));
/* Private key tweaks results in a key of zero. */
ctmp2[31] = 1;
CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp2, ctmp) == 0);
CHECK(memcmp(zeros, ctmp2, 32) == 0);
ctmp2[31] = 1;
CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0);
CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
memcpy(&pubkey, &pubkey2, sizeof(pubkey));
/* Tweak computation wraps and results in a key of 1. */
ctmp2[31] = 2;
CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp2, ctmp) == 1);
CHECK(memcmp(ctmp2, zeros, 31) == 0 && ctmp2[31] == 1);
ctmp2[31] = 2;
CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
ctmp2[31] = 1;
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, ctmp2) == 1);
CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
/* Tweak mul * 2 = 1+1. */
CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
ctmp2[31] = 2;
CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 1);
CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
/* Test argument errors. */
ecount = 0;
secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
CHECK(ecount == 0);
/* Zeroize pubkey on parse error. */
memset(&pubkey, 0, 32);
CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0);
CHECK(ecount == 1);
CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
memcpy(&pubkey, &pubkey2, sizeof(pubkey));
memset(&pubkey2, 0, 32);
CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 0);
CHECK(ecount == 2);
CHECK(memcmp(&pubkey2, zeros, sizeof(pubkey2)) == 0);
/* Plain argument errors. */
ecount = 0;
CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
CHECK(ecount == 0);
CHECK(secp256k1_ec_seckey_verify(ctx, NULL) == 0);
CHECK(ecount == 1);
ecount = 0;
memset(ctmp2, 0, 32);
ctmp2[31] = 4;
CHECK(secp256k1_ec_pubkey_tweak_add(ctx, NULL, ctmp2) == 0);
CHECK(ecount == 1);
CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, NULL) == 0);
CHECK(ecount == 2);
ecount = 0;
memset(ctmp2, 0, 32);
ctmp2[31] = 4;
CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, NULL, ctmp2) == 0);
CHECK(ecount == 1);
CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, NULL) == 0);
CHECK(ecount == 2);
ecount = 0;
memset(ctmp2, 0, 32);
CHECK(secp256k1_ec_privkey_tweak_add(ctx, NULL, ctmp2) == 0);
CHECK(ecount == 1);
CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, NULL) == 0);
CHECK(ecount == 2);
ecount = 0;
memset(ctmp2, 0, 32);
ctmp2[31] = 1;
CHECK(secp256k1_ec_privkey_tweak_mul(ctx, NULL, ctmp2) == 0);
CHECK(ecount == 1);
CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, NULL) == 0);
CHECK(ecount == 2);
ecount = 0;
CHECK(secp256k1_ec_pubkey_create(ctx, NULL, ctmp) == 0);
CHECK(ecount == 1);
memset(&pubkey, 1, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0);
CHECK(ecount == 2);
CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
/* secp256k1_ec_pubkey_combine tests. */
ecount = 0;
pubkeys[0] = &pubkey_one;
VG_UNDEF(&pubkeys[0], sizeof(secp256k1_pubkey *));
VG_UNDEF(&pubkeys[1], sizeof(secp256k1_pubkey *));
VG_UNDEF(&pubkeys[2], sizeof(secp256k1_pubkey *));
memset(&pubkey, 255, sizeof(secp256k1_pubkey));
VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 0) == 0);
VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
CHECK(ecount == 1);
CHECK(secp256k1_ec_pubkey_combine(ctx, NULL, pubkeys, 1) == 0);
CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
CHECK(ecount == 2);
memset(&pubkey, 255, sizeof(secp256k1_pubkey));
VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, NULL, 1) == 0);
VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
CHECK(ecount == 3);
pubkeys[0] = &pubkey_negone;
memset(&pubkey, 255, sizeof(secp256k1_pubkey));
VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 1) == 1);
VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
CHECK(ecount == 3);
len = 33;
CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_negone, SECP256K1_EC_COMPRESSED) == 1);
CHECK(memcmp(ctmp, ctmp2, 33) == 0);
/* Result is infinity. */
pubkeys[0] = &pubkey_one;
pubkeys[1] = &pubkey_negone;
memset(&pubkey, 255, sizeof(secp256k1_pubkey));
VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 0);
VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
CHECK(ecount == 3);
/* Passes through infinity but comes out one. */
pubkeys[2] = &pubkey_one;
memset(&pubkey, 255, sizeof(secp256k1_pubkey));
VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 3) == 1);
VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
CHECK(ecount == 3);
len = 33;
CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_one, SECP256K1_EC_COMPRESSED) == 1);
CHECK(memcmp(ctmp, ctmp2, 33) == 0);
/* Adds to two. */
pubkeys[1] = &pubkey_one;
memset(&pubkey, 255, sizeof(secp256k1_pubkey));
VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 1);
VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
CHECK(ecount == 3);
secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
}
void random_sign(secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *key, const secp256k1_scalar *msg, int *recid) {
secp256k1_scalar nonce;
do {
random_scalar_order_test(&nonce);
} while(!secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, sigr, sigs, key, msg, &nonce, recid));
}
void test_ecdsa_sign_verify(void) {
secp256k1_gej pubj;
secp256k1_ge pub;
secp256k1_scalar one;
secp256k1_scalar msg, key;
secp256k1_scalar sigr, sigs;
int recid;
int getrec;
random_scalar_order_test(&msg);
random_scalar_order_test(&key);
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubj, &key);
secp256k1_ge_set_gej(&pub, &pubj);
getrec = secp256k1_rand_bits(1);
random_sign(&sigr, &sigs, &key, &msg, getrec?&recid:NULL);
if (getrec) {
CHECK(recid >= 0 && recid < 4);
}
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg));
secp256k1_scalar_set_int(&one, 1);
secp256k1_scalar_add(&msg, &msg, &one);
CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg));
}
void run_ecdsa_sign_verify(void) {
int i;
for (i = 0; i < 10*count; i++) {
test_ecdsa_sign_verify();
}
}
/** Dummy nonce generation function that just uses a precomputed nonce, and fails if it is not accepted. Use only for testing. */
static int precomputed_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
(void)msg32;
(void)key32;
(void)algo16;
memcpy(nonce32, data, 32);
return (counter == 0);
}
static int nonce_function_test_fail(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
/* Dummy nonce generator that has a fatal error on the first counter value. */
if (counter == 0) {
return 0;
}
return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 1);
}
static int nonce_function_test_retry(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
/* Dummy nonce generator that produces unacceptable nonces for the first several counter values. */
if (counter < 3) {
memset(nonce32, counter==0 ? 0 : 255, 32);
if (counter == 2) {
nonce32[31]--;
}
return 1;
}
if (counter < 5) {
static const unsigned char order[] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
};
memcpy(nonce32, order, 32);
if (counter == 4) {
nonce32[31]++;
}
return 1;
}
/* Retry rate of 6979 is negligible esp. as we only call this in deterministic tests. */
/* If someone does fine a case where it retries for secp256k1, we'd like to know. */
if (counter > 5) {
return 0;
}
return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 5);
}
int is_empty_signature(const secp256k1_ecdsa_signature *sig) {
static const unsigned char res[sizeof(secp256k1_ecdsa_signature)] = {0};
return memcmp(sig, res, sizeof(secp256k1_ecdsa_signature)) == 0;
}
void test_ecdsa_end_to_end(void) {
unsigned char extra[32] = {0x00};
unsigned char privkey[32];
unsigned char message[32];
unsigned char privkey2[32];
secp256k1_ecdsa_signature signature[6];
secp256k1_scalar r, s;
unsigned char sig[74];
size_t siglen = 74;
unsigned char pubkeyc[65];
size_t pubkeyclen = 65;
secp256k1_pubkey pubkey;
secp256k1_pubkey pubkey_tmp;
unsigned char seckey[300];
size_t seckeylen = 300;
/* Generate a random key and message. */
{
secp256k1_scalar msg, key;
random_scalar_order_test(&msg);
random_scalar_order_test(&key);
secp256k1_scalar_get_b32(privkey, &key);
secp256k1_scalar_get_b32(message, &msg);
}
/* Construct and verify corresponding public key. */
CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
/* Verify exporting and importing public key. */
CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyc, &pubkeyclen, &pubkey, secp256k1_rand_bits(1) == 1 ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED));
memset(&pubkey, 0, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
/* Verify negation changes the key and changes it back */
memcpy(&pubkey_tmp, &pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey_tmp) == 1);
CHECK(memcmp(&pubkey_tmp, &pubkey, sizeof(pubkey)) != 0);
CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey_tmp) == 1);
CHECK(memcmp(&pubkey_tmp, &pubkey, sizeof(pubkey)) == 0);
/* Verify private key import and export. */
CHECK(ec_privkey_export_der(ctx, seckey, &seckeylen, privkey, secp256k1_rand_bits(1) == 1));
CHECK(ec_privkey_import_der(ctx, privkey2, seckey, seckeylen) == 1);
CHECK(memcmp(privkey, privkey2, 32) == 0);
/* Optionally tweak the keys using addition. */
if (secp256k1_rand_int(3) == 0) {
int ret1;
int ret2;
unsigned char rnd[32];
secp256k1_pubkey pubkey2;
secp256k1_rand256_test(rnd);
ret1 = secp256k1_ec_privkey_tweak_add(ctx, privkey, rnd);
ret2 = secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, rnd);
CHECK(ret1 == ret2);
if (ret1 == 0) {
return;
}
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1);
CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
}
/* Optionally tweak the keys using multiplication. */
if (secp256k1_rand_int(3) == 0) {
int ret1;
int ret2;
unsigned char rnd[32];
secp256k1_pubkey pubkey2;
secp256k1_rand256_test(rnd);
ret1 = secp256k1_ec_privkey_tweak_mul(ctx, privkey, rnd);
ret2 = secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, rnd);
CHECK(ret1 == ret2);
if (ret1 == 0) {
return;
}
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1);
CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
}
/* Sign. */
CHECK(secp256k1_ecdsa_sign(ctx, &signature[0], message, privkey, NULL, NULL) == 1);
CHECK(secp256k1_ecdsa_sign(ctx, &signature[4], message, privkey, NULL, NULL) == 1);
CHECK(secp256k1_ecdsa_sign(ctx, &signature[1], message, privkey, NULL, extra) == 1);
extra[31] = 1;
CHECK(secp256k1_ecdsa_sign(ctx, &signature[2], message, privkey, NULL, extra) == 1);
extra[31] = 0;
extra[0] = 1;
CHECK(secp256k1_ecdsa_sign(ctx, &signature[3], message, privkey, NULL, extra) == 1);
CHECK(memcmp(&signature[0], &signature[4], sizeof(signature[0])) == 0);
CHECK(memcmp(&signature[0], &signature[1], sizeof(signature[0])) != 0);
CHECK(memcmp(&signature[0], &signature[2], sizeof(signature[0])) != 0);
CHECK(memcmp(&signature[0], &signature[3], sizeof(signature[0])) != 0);
CHECK(memcmp(&signature[1], &signature[2], sizeof(signature[0])) != 0);
CHECK(memcmp(&signature[1], &signature[3], sizeof(signature[0])) != 0);
CHECK(memcmp(&signature[2], &signature[3], sizeof(signature[0])) != 0);
/* Verify. */
CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &signature[1], message, &pubkey) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &signature[2], message, &pubkey) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &signature[3], message, &pubkey) == 1);
/* Test lower-S form, malleate, verify and fail, test again, malleate again */
CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[0]));
secp256k1_ecdsa_signature_load(ctx, &r, &s, &signature[0]);
secp256k1_scalar_negate(&s, &s);
secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 0);
CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
CHECK(secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5]));
CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
CHECK(!secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5]));
CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1);
secp256k1_scalar_negate(&s, &s);
secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1);
CHECK(memcmp(&signature[5], &signature[0], 64) == 0);
/* Serialize/parse DER and verify again */
CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1);
memset(&signature[0], 0, sizeof(signature[0]));
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1);
/* Serialize/destroy/parse DER and verify again. */
siglen = 74;
CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1);
sig[secp256k1_rand_int(siglen)] += 1 + secp256k1_rand_int(255);
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 0 ||
secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 0);
}
void test_random_pubkeys(void) {
secp256k1_ge elem;
secp256k1_ge elem2;
unsigned char in[65];
/* Generate some randomly sized pubkeys. */
size_t len = secp256k1_rand_bits(2) == 0 ? 65 : 33;
if (secp256k1_rand_bits(2) == 0) {
len = secp256k1_rand_bits(6);
}
if (len == 65) {
in[0] = secp256k1_rand_bits(1) ? 4 : (secp256k1_rand_bits(1) ? 6 : 7);
} else {
in[0] = secp256k1_rand_bits(1) ? 2 : 3;
}
if (secp256k1_rand_bits(3) == 0) {
in[0] = secp256k1_rand_bits(8);
}
if (len > 1) {
secp256k1_rand256(&in[1]);
}
if (len > 33) {
secp256k1_rand256(&in[33]);
}
if (secp256k1_eckey_pubkey_parse(&elem, in, len)) {
unsigned char out[65];
unsigned char firstb;
int res;
size_t size = len;
firstb = in[0];
/* If the pubkey can be parsed, it should round-trip... */
CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, len == 33));
CHECK(size == len);
CHECK(memcmp(&in[1], &out[1], len-1) == 0);
/* ... except for the type of hybrid inputs. */
if ((in[0] != 6) && (in[0] != 7)) {
CHECK(in[0] == out[0]);
}
size = 65;
CHECK(secp256k1_eckey_pubkey_serialize(&elem, in, &size, 0));
CHECK(size == 65);
CHECK(secp256k1_eckey_pubkey_parse(&elem2, in, size));
ge_equals_ge(&elem,&elem2);
/* Check that the X9.62 hybrid type is checked. */
in[0] = secp256k1_rand_bits(1) ? 6 : 7;
res = secp256k1_eckey_pubkey_parse(&elem2, in, size);
if (firstb == 2 || firstb == 3) {
if (in[0] == firstb + 4) {
CHECK(res);
} else {
CHECK(!res);
}
}
if (res) {
ge_equals_ge(&elem,&elem2);
CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, 0));
CHECK(memcmp(&in[1], &out[1], 64) == 0);
}
}
}
void run_random_pubkeys(void) {
int i;
for (i = 0; i < 10*count; i++) {
test_random_pubkeys();
}
}
void run_ecdsa_end_to_end(void) {
int i;
for (i = 0; i < 64*count; i++) {
test_ecdsa_end_to_end();
}
}
int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_der, int certainly_not_der) {
static const unsigned char zeroes[32] = {0};
#ifdef ENABLE_OPENSSL_TESTS
static const unsigned char max_scalar[32] = {
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40
};
#endif
int ret = 0;
secp256k1_ecdsa_signature sig_der;
unsigned char roundtrip_der[2048];
unsigned char compact_der[64];
size_t len_der = 2048;
int parsed_der = 0, valid_der = 0, roundtrips_der = 0;
secp256k1_ecdsa_signature sig_der_lax;
unsigned char roundtrip_der_lax[2048];
unsigned char compact_der_lax[64];
size_t len_der_lax = 2048;
int parsed_der_lax = 0, valid_der_lax = 0, roundtrips_der_lax = 0;
#ifdef ENABLE_OPENSSL_TESTS
ECDSA_SIG *sig_openssl;
const BIGNUM *r = NULL, *s = NULL;
const unsigned char *sigptr;
unsigned char roundtrip_openssl[2048];
int len_openssl = 2048;
int parsed_openssl, valid_openssl = 0, roundtrips_openssl = 0;
#endif
parsed_der = secp256k1_ecdsa_signature_parse_der(ctx, &sig_der, sig, siglen);
if (parsed_der) {
ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der, &sig_der)) << 0;
valid_der = (memcmp(compact_der, zeroes, 32) != 0) && (memcmp(compact_der + 32, zeroes, 32) != 0);
}
if (valid_der) {
ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der, &len_der, &sig_der)) << 1;
roundtrips_der = (len_der == siglen) && memcmp(roundtrip_der, sig, siglen) == 0;
}
parsed_der_lax = ecdsa_signature_parse_der_lax(ctx, &sig_der_lax, sig, siglen);
if (parsed_der_lax) {
ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der_lax, &sig_der_lax)) << 10;
valid_der_lax = (memcmp(compact_der_lax, zeroes, 32) != 0) && (memcmp(compact_der_lax + 32, zeroes, 32) != 0);
}
if (valid_der_lax) {
ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der_lax, &len_der_lax, &sig_der_lax)) << 11;
roundtrips_der_lax = (len_der_lax == siglen) && memcmp(roundtrip_der_lax, sig, siglen) == 0;
}
if (certainly_der) {
ret |= (!parsed_der) << 2;
}
if (certainly_not_der) {
ret |= (parsed_der) << 17;
}
if (valid_der) {
ret |= (!roundtrips_der) << 3;
}
if (valid_der) {
ret |= (!roundtrips_der_lax) << 12;
ret |= (len_der != len_der_lax) << 13;
ret |= (memcmp(roundtrip_der_lax, roundtrip_der, len_der) != 0) << 14;
}
ret |= (roundtrips_der != roundtrips_der_lax) << 15;
if (parsed_der) {
ret |= (!parsed_der_lax) << 16;
}
#ifdef ENABLE_OPENSSL_TESTS
sig_openssl = ECDSA_SIG_new();
sigptr = sig;
parsed_openssl = (d2i_ECDSA_SIG(&sig_openssl, &sigptr, siglen) != NULL);
if (parsed_openssl) {
ECDSA_SIG_get0(sig_openssl, &r, &s);
valid_openssl = !BN_is_negative(r) && !BN_is_negative(s) && BN_num_bits(r) > 0 && BN_num_bits(r) <= 256 && BN_num_bits(s) > 0 && BN_num_bits(s) <= 256;
if (valid_openssl) {
unsigned char tmp[32] = {0};
BN_bn2bin(r, tmp + 32 - BN_num_bytes(r));
valid_openssl = memcmp(tmp, max_scalar, 32) < 0;
}
if (valid_openssl) {
unsigned char tmp[32] = {0};
BN_bn2bin(s, tmp + 32 - BN_num_bytes(s));
valid_openssl = memcmp(tmp, max_scalar, 32) < 0;
}
}
len_openssl = i2d_ECDSA_SIG(sig_openssl, NULL);
if (len_openssl <= 2048) {
unsigned char *ptr = roundtrip_openssl;
CHECK(i2d_ECDSA_SIG(sig_openssl, &ptr) == len_openssl);
roundtrips_openssl = valid_openssl && ((size_t)len_openssl == siglen) && (memcmp(roundtrip_openssl, sig, siglen) == 0);
} else {
len_openssl = 0;
}
ECDSA_SIG_free(sig_openssl);
ret |= (parsed_der && !parsed_openssl) << 4;
ret |= (valid_der && !valid_openssl) << 5;
ret |= (roundtrips_openssl && !parsed_der) << 6;
ret |= (roundtrips_der != roundtrips_openssl) << 7;
if (roundtrips_openssl) {
ret |= (len_der != (size_t)len_openssl) << 8;
ret |= (memcmp(roundtrip_der, roundtrip_openssl, len_der) != 0) << 9;
}
#endif
return ret;
}
static void assign_big_endian(unsigned char *ptr, size_t ptrlen, uint32_t val) {
size_t i;
for (i = 0; i < ptrlen; i++) {
int shift = ptrlen - 1 - i;
if (shift >= 4) {
ptr[i] = 0;
} else {
ptr[i] = (val >> shift) & 0xFF;
}
}
}
static void damage_array(unsigned char *sig, size_t *len) {
int pos;
int action = secp256k1_rand_bits(3);
if (action < 1 && *len > 3) {
/* Delete a byte. */
pos = secp256k1_rand_int(*len);
memmove(sig + pos, sig + pos + 1, *len - pos - 1);
(*len)--;
return;
} else if (action < 2 && *len < 2048) {
/* Insert a byte. */
pos = secp256k1_rand_int(1 + *len);
memmove(sig + pos + 1, sig + pos, *len - pos);
sig[pos] = secp256k1_rand_bits(8);
(*len)++;
return;
} else if (action < 4) {
/* Modify a byte. */
sig[secp256k1_rand_int(*len)] += 1 + secp256k1_rand_int(255);
return;
} else { /* action < 8 */
/* Modify a bit. */
sig[secp256k1_rand_int(*len)] ^= 1 << secp256k1_rand_bits(3);
return;
}
}
static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly_der, int* certainly_not_der) {
int der;
int nlow[2], nlen[2], nlenlen[2], nhbit[2], nhbyte[2], nzlen[2];
size_t tlen, elen, glen;
int indet;
int n;
*len = 0;
der = secp256k1_rand_bits(2) == 0;
*certainly_der = der;
*certainly_not_der = 0;
indet = der ? 0 : secp256k1_rand_int(10) == 0;
for (n = 0; n < 2; n++) {
/* We generate two classes of numbers: nlow==1 "low" ones (up to 32 bytes), nlow==0 "high" ones (32 bytes with 129 top bits set, or larger than 32 bytes) */
nlow[n] = der ? 1 : (secp256k1_rand_bits(3) != 0);
/* The length of the number in bytes (the first byte of which will always be nonzero) */
nlen[n] = nlow[n] ? secp256k1_rand_int(33) : 32 + secp256k1_rand_int(200) * secp256k1_rand_int(8) / 8;
CHECK(nlen[n] <= 232);
/* The top bit of the number. */
nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : secp256k1_rand_bits(1));
/* The top byte of the number (after the potential hardcoded 16 0xFF characters for "high" 32 bytes numbers) */
nhbyte[n] = nlen[n] == 0 ? 0 : (nhbit[n] ? 128 + secp256k1_rand_bits(7) : 1 + secp256k1_rand_int(127));
/* The number of zero bytes in front of the number (which is 0 or 1 in case of DER, otherwise we extend up to 300 bytes) */
nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_rand_int(3) : secp256k1_rand_int(300 - nlen[n]) * secp256k1_rand_int(8) / 8);
if (nzlen[n] > ((nlen[n] == 0 || nhbit[n]) ? 1 : 0)) {
*certainly_not_der = 1;
}
CHECK(nlen[n] + nzlen[n] <= 300);
/* The length of the length descriptor for the number. 0 means short encoding, anything else is long encoding. */
nlenlen[n] = nlen[n] + nzlen[n] < 128 ? 0 : (nlen[n] + nzlen[n] < 256 ? 1 : 2);
if (!der) {
/* nlenlen[n] max 127 bytes */
int add = secp256k1_rand_int(127 - nlenlen[n]) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256;
nlenlen[n] += add;
if (add != 0) {
*certainly_not_der = 1;
}
}
CHECK(nlen[n] + nzlen[n] + nlenlen[n] <= 427);
}
/* The total length of the data to go, so far */
tlen = 2 + nlenlen[0] + nlen[0] + nzlen[0] + 2 + nlenlen[1] + nlen[1] + nzlen[1];
CHECK(tlen <= 856);
/* The length of the garbage inside the tuple. */
elen = (der || indet) ? 0 : secp256k1_rand_int(980 - tlen) * secp256k1_rand_int(8) / 8;
if (elen != 0) {
*certainly_not_der = 1;
}
tlen += elen;
CHECK(tlen <= 980);
/* The length of the garbage after the end of the tuple. */
glen = der ? 0 : secp256k1_rand_int(990 - tlen) * secp256k1_rand_int(8) / 8;
if (glen != 0) {
*certainly_not_der = 1;
}
CHECK(tlen + glen <= 990);
/* Write the tuple header. */
sig[(*len)++] = 0x30;
if (indet) {
/* Indeterminate length */
sig[(*len)++] = 0x80;
*certainly_not_der = 1;
} else {
int tlenlen = tlen < 128 ? 0 : (tlen < 256 ? 1 : 2);
if (!der) {
int add = secp256k1_rand_int(127 - tlenlen) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256;
tlenlen += add;
if (add != 0) {
*certainly_not_der = 1;
}
}
if (tlenlen == 0) {
/* Short length notation */
sig[(*len)++] = tlen;
} else {
/* Long length notation */
sig[(*len)++] = 128 + tlenlen;
assign_big_endian(sig + *len, tlenlen, tlen);
*len += tlenlen;
}
tlen += tlenlen;
}
tlen += 2;
CHECK(tlen + glen <= 1119);
for (n = 0; n < 2; n++) {
/* Write the integer header. */
sig[(*len)++] = 0x02;
if (nlenlen[n] == 0) {
/* Short length notation */
sig[(*len)++] = nlen[n] + nzlen[n];
} else {
/* Long length notation. */
sig[(*len)++] = 128 + nlenlen[n];
assign_big_endian(sig + *len, nlenlen[n], nlen[n] + nzlen[n]);
*len += nlenlen[n];
}
/* Write zero padding */
while (nzlen[n] > 0) {
sig[(*len)++] = 0x00;
nzlen[n]--;
}
if (nlen[n] == 32 && !nlow[n]) {
/* Special extra 16 0xFF bytes in "high" 32-byte numbers */
int i;
for (i = 0; i < 16; i++) {
sig[(*len)++] = 0xFF;
}
nlen[n] -= 16;
}
/* Write first byte of number */
if (nlen[n] > 0) {
sig[(*len)++] = nhbyte[n];
nlen[n]--;
}
/* Generate remaining random bytes of number */
secp256k1_rand_bytes_test(sig + *len, nlen[n]);
*len += nlen[n];
nlen[n] = 0;
}
/* Generate random garbage inside tuple. */
secp256k1_rand_bytes_test(sig + *len, elen);
*len += elen;
/* Generate end-of-contents bytes. */
if (indet) {
sig[(*len)++] = 0;
sig[(*len)++] = 0;
tlen += 2;
}
CHECK(tlen + glen <= 1121);
/* Generate random garbage outside tuple. */
secp256k1_rand_bytes_test(sig + *len, glen);
*len += glen;
tlen += glen;
CHECK(tlen <= 1121);
CHECK(tlen == *len);
}
void run_ecdsa_der_parse(void) {
int i,j;
for (i = 0; i < 200 * count; i++) {
unsigned char buffer[2048];
size_t buflen = 0;
int certainly_der = 0;
int certainly_not_der = 0;
random_ber_signature(buffer, &buflen, &certainly_der, &certainly_not_der);
CHECK(buflen <= 2048);
for (j = 0; j < 16; j++) {
int ret = 0;
if (j > 0) {
damage_array(buffer, &buflen);
/* We don't know anything anymore about the DERness of the result */
certainly_der = 0;
certainly_not_der = 0;
}
ret = test_ecdsa_der_parse(buffer, buflen, certainly_der, certainly_not_der);
if (ret != 0) {
size_t k;
fprintf(stderr, "Failure %x on ", ret);
for (k = 0; k < buflen; k++) {
fprintf(stderr, "%02x ", buffer[k]);
}
fprintf(stderr, "\n");
}
CHECK(ret == 0);
}
}
}
/* Tests several edge cases. */
void test_ecdsa_edge_cases(void) {
int t;
secp256k1_ecdsa_signature sig;
/* Test the case where ECDSA recomputes a point that is infinity. */
{
secp256k1_gej keyj;
secp256k1_ge key;
secp256k1_scalar msg;
secp256k1_scalar sr, ss;
secp256k1_scalar_set_int(&ss, 1);
secp256k1_scalar_negate(&ss, &ss);
secp256k1_scalar_inverse(&ss, &ss);
secp256k1_scalar_set_int(&sr, 1);
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &keyj, &sr);
secp256k1_ge_set_gej(&key, &keyj);
msg = ss;
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
}
/* Verify signature with r of zero fails. */
{
const unsigned char pubkey_mods_zero[33] = {
0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0,
0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41,
0x41
};
secp256k1_ge key;
secp256k1_scalar msg;
secp256k1_scalar sr, ss;
secp256k1_scalar_set_int(&ss, 1);
secp256k1_scalar_set_int(&msg, 0);
secp256k1_scalar_set_int(&sr, 0);
CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey_mods_zero, 33));
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
}
/* Verify signature with s of zero fails. */
{
const unsigned char pubkey[33] = {
0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x01
};
secp256k1_ge key;
secp256k1_scalar msg;
secp256k1_scalar sr, ss;
secp256k1_scalar_set_int(&ss, 0);
secp256k1_scalar_set_int(&msg, 0);
secp256k1_scalar_set_int(&sr, 1);
CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
}
/* Verify signature with message 0 passes. */
{
const unsigned char pubkey[33] = {
0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x02
};
const unsigned char pubkey2[33] = {
0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0,
0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41,
0x43
};
secp256k1_ge key;
secp256k1_ge key2;
secp256k1_scalar msg;
secp256k1_scalar sr, ss;
secp256k1_scalar_set_int(&ss, 2);
secp256k1_scalar_set_int(&msg, 0);
secp256k1_scalar_set_int(&sr, 2);
CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33));
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
secp256k1_scalar_negate(&ss, &ss);
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
secp256k1_scalar_set_int(&ss, 1);
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0);
}
/* Verify signature with message 1 passes. */
{
const unsigned char pubkey[33] = {
0x02, 0x14, 0x4e, 0x5a, 0x58, 0xef, 0x5b, 0x22,
0x6f, 0xd2, 0xe2, 0x07, 0x6a, 0x77, 0xcf, 0x05,
0xb4, 0x1d, 0xe7, 0x4a, 0x30, 0x98, 0x27, 0x8c,
0x93, 0xe6, 0xe6, 0x3c, 0x0b, 0xc4, 0x73, 0x76,
0x25
};
const unsigned char pubkey2[33] = {
0x02, 0x8a, 0xd5, 0x37, 0xed, 0x73, 0xd9, 0x40,
0x1d, 0xa0, 0x33, 0xd2, 0xdc, 0xf0, 0xaf, 0xae,
0x34, 0xcf, 0x5f, 0x96, 0x4c, 0x73, 0x28, 0x0f,
0x92, 0xc0, 0xf6, 0x9d, 0xd9, 0xb2, 0x09, 0x10,
0x62
};
const unsigned char csr[32] = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xeb
};
secp256k1_ge key;
secp256k1_ge key2;
secp256k1_scalar msg;
secp256k1_scalar sr, ss;
secp256k1_scalar_set_int(&ss, 1);
secp256k1_scalar_set_int(&msg, 1);
secp256k1_scalar_set_b32(&sr, csr, NULL);
CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33));
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
secp256k1_scalar_negate(&ss, &ss);
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
secp256k1_scalar_set_int(&ss, 2);
secp256k1_scalar_inverse_var(&ss, &ss);
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0);
}
/* Verify signature with message -1 passes. */
{
const unsigned char pubkey[33] = {
0x03, 0xaf, 0x97, 0xff, 0x7d, 0x3a, 0xf6, 0xa0,
0x02, 0x94, 0xbd, 0x9f, 0x4b, 0x2e, 0xd7, 0x52,
0x28, 0xdb, 0x49, 0x2a, 0x65, 0xcb, 0x1e, 0x27,
0x57, 0x9c, 0xba, 0x74, 0x20, 0xd5, 0x1d, 0x20,
0xf1
};
const unsigned char csr[32] = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xee
};
secp256k1_ge key;
secp256k1_scalar msg;
secp256k1_scalar sr, ss;
secp256k1_scalar_set_int(&ss, 1);
secp256k1_scalar_set_int(&msg, 1);
secp256k1_scalar_negate(&msg, &msg);
secp256k1_scalar_set_b32(&sr, csr, NULL);
CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
secp256k1_scalar_negate(&ss, &ss);
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
secp256k1_scalar_set_int(&ss, 3);
secp256k1_scalar_inverse_var(&ss, &ss);
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
}
/* Signature where s would be zero. */
{
secp256k1_pubkey pubkey;
size_t siglen;
int32_t ecount;
unsigned char signature[72];
static const unsigned char nonce[32] = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
};
static const unsigned char nonce2[32] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x40
};
const unsigned char key[32] = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
};
unsigned char msg[32] = {
0x86, 0x41, 0x99, 0x81, 0x06, 0x23, 0x44, 0x53,
0xaa, 0x5f, 0x9d, 0x6a, 0x31, 0x78, 0xf4, 0xf7,
0xb8, 0x12, 0xe0, 0x0b, 0x81, 0x7a, 0x77, 0x62,
0x65, 0xdf, 0xdd, 0x31, 0xb9, 0x3e, 0x29, 0xa9,
};
ecount = 0;
secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 0);
CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 0);
msg[31] = 0xaa;
CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 1);
CHECK(ecount == 0);
CHECK(secp256k1_ecdsa_sign(ctx, NULL, msg, key, precomputed_nonce_function, nonce2) == 0);
CHECK(ecount == 1);
CHECK(secp256k1_ecdsa_sign(ctx, &sig, NULL, key, precomputed_nonce_function, nonce2) == 0);
CHECK(ecount == 2);
CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, NULL, precomputed_nonce_function, nonce2) == 0);
CHECK(ecount == 3);
CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 1);
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, key) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, NULL, msg, &pubkey) == 0);
CHECK(ecount == 4);
CHECK(secp256k1_ecdsa_verify(ctx, &sig, NULL, &pubkey) == 0);
CHECK(ecount == 5);
CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, NULL) == 0);
CHECK(ecount == 6);
CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 1);
CHECK(ecount == 6);
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0);
CHECK(ecount == 7);
/* That pubkeyload fails via an ARGCHECK is a little odd but makes sense because pubkeys are an opaque data type. */
CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 0);
CHECK(ecount == 8);
siglen = 72;
CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, NULL, &siglen, &sig) == 0);
CHECK(ecount == 9);
CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, NULL, &sig) == 0);
CHECK(ecount == 10);
CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, NULL) == 0);
CHECK(ecount == 11);
CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 1);
CHECK(ecount == 11);
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, NULL, signature, siglen) == 0);
CHECK(ecount == 12);
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, NULL, siglen) == 0);
CHECK(ecount == 13);
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, signature, siglen) == 1);
CHECK(ecount == 13);
siglen = 10;
/* Too little room for a signature does not fail via ARGCHECK. */
CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 0);
CHECK(ecount == 13);
ecount = 0;
CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, NULL) == 0);
CHECK(ecount == 1);
CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, NULL, &sig) == 0);
CHECK(ecount == 2);
CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, NULL) == 0);
CHECK(ecount == 3);
CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, &sig) == 1);
CHECK(ecount == 3);
CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, NULL, signature) == 0);
CHECK(ecount == 4);
CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, NULL) == 0);
CHECK(ecount == 5);
CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 1);
CHECK(ecount == 5);
memset(signature, 255, 64);
CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 0);
CHECK(ecount == 5);
secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
}
/* Nonce function corner cases. */
for (t = 0; t < 2; t++) {
static const unsigned char zero[32] = {0x00};
int i;
unsigned char key[32];
unsigned char msg[32];
secp256k1_ecdsa_signature sig2;
secp256k1_scalar sr[512], ss;
const unsigned char *extra;
extra = t == 0 ? NULL : zero;
memset(msg, 0, 32);
msg[31] = 1;
/* High key results in signature failure. */
memset(key, 0xFF, 32);
CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0);
CHECK(is_empty_signature(&sig));
/* Zero key results in signature failure. */
memset(key, 0, 32);
CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0);
CHECK(is_empty_signature(&sig));
/* Nonce function failure results in signature failure. */
key[31] = 1;
CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_fail, extra) == 0);
CHECK(is_empty_signature(&sig));
/* The retry loop successfully makes its way to the first good value. */
CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_retry, extra) == 1);
CHECK(!is_empty_signature(&sig));
CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, nonce_function_rfc6979, extra) == 1);
CHECK(!is_empty_signature(&sig2));
CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0);
/* The default nonce function is deterministic. */
CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
CHECK(!is_empty_signature(&sig2));
CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0);
/* The default nonce function changes output with different messages. */
for(i = 0; i < 256; i++) {
int j;
msg[0] = i;
CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
CHECK(!is_empty_signature(&sig2));
secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2);
for (j = 0; j < i; j++) {
CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j]));
}
}
msg[0] = 0;
msg[31] = 2;
/* The default nonce function changes output with different keys. */
for(i = 256; i < 512; i++) {
int j;
key[0] = i - 256;
CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
CHECK(!is_empty_signature(&sig2));
secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2);
for (j = 0; j < i; j++) {
CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j]));
}
}
key[0] = 0;
}
{
/* Check that optional nonce arguments do not have equivalent effect. */
const unsigned char zeros[32] = {0};
unsigned char nonce[32];
unsigned char nonce2[32];
unsigned char nonce3[32];
unsigned char nonce4[32];
VG_UNDEF(nonce,32);
VG_UNDEF(nonce2,32);
VG_UNDEF(nonce3,32);
VG_UNDEF(nonce4,32);
CHECK(nonce_function_rfc6979(nonce, zeros, zeros, NULL, NULL, 0) == 1);
VG_CHECK(nonce,32);
CHECK(nonce_function_rfc6979(nonce2, zeros, zeros, zeros, NULL, 0) == 1);
VG_CHECK(nonce2,32);
CHECK(nonce_function_rfc6979(nonce3, zeros, zeros, NULL, (void *)zeros, 0) == 1);
VG_CHECK(nonce3,32);
CHECK(nonce_function_rfc6979(nonce4, zeros, zeros, zeros, (void *)zeros, 0) == 1);
VG_CHECK(nonce4,32);
CHECK(memcmp(nonce, nonce2, 32) != 0);
CHECK(memcmp(nonce, nonce3, 32) != 0);
CHECK(memcmp(nonce, nonce4, 32) != 0);
CHECK(memcmp(nonce2, nonce3, 32) != 0);
CHECK(memcmp(nonce2, nonce4, 32) != 0);
CHECK(memcmp(nonce3, nonce4, 32) != 0);
}
/* Privkey export where pubkey is the point at infinity. */
{
unsigned char privkey[300];
unsigned char seckey[32] = {
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41,
};
size_t outlen = 300;
CHECK(!ec_privkey_export_der(ctx, privkey, &outlen, seckey, 0));
outlen = 300;
CHECK(!ec_privkey_export_der(ctx, privkey, &outlen, seckey, 1));
}
}
void run_ecdsa_edge_cases(void) {
test_ecdsa_edge_cases();
}
#ifdef ENABLE_OPENSSL_TESTS
EC_KEY *get_openssl_key(const unsigned char *key32) {
unsigned char privkey[300];
size_t privkeylen;
const unsigned char* pbegin = privkey;
int compr = secp256k1_rand_bits(1);
EC_KEY *ec_key = EC_KEY_new_by_curve_name(NID_secp256k1);
CHECK(ec_privkey_export_der(ctx, privkey, &privkeylen, key32, compr));
CHECK(d2i_ECPrivateKey(&ec_key, &pbegin, privkeylen));
CHECK(EC_KEY_check_key(ec_key));
return ec_key;
}
void test_ecdsa_openssl(void) {
secp256k1_gej qj;
secp256k1_ge q;
secp256k1_scalar sigr, sigs;
secp256k1_scalar one;
secp256k1_scalar msg2;
secp256k1_scalar key, msg;
EC_KEY *ec_key;
unsigned int sigsize = 80;
size_t secp_sigsize = 80;
unsigned char message[32];
unsigned char signature[80];
unsigned char key32[32];
secp256k1_rand256_test(message);
secp256k1_scalar_set_b32(&msg, message, NULL);
random_scalar_order_test(&key);
secp256k1_scalar_get_b32(key32, &key);
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &qj, &key);
secp256k1_ge_set_gej(&q, &qj);
ec_key = get_openssl_key(key32);
CHECK(ec_key != NULL);
CHECK(ECDSA_sign(0, message, sizeof(message), signature, &sigsize, ec_key));
CHECK(secp256k1_ecdsa_sig_parse(&sigr, &sigs, signature, sigsize));
CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg));
secp256k1_scalar_set_int(&one, 1);
secp256k1_scalar_add(&msg2, &msg, &one);
CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg2));
random_sign(&sigr, &sigs, &key, &msg, NULL);
CHECK(secp256k1_ecdsa_sig_serialize(signature, &secp_sigsize, &sigr, &sigs));
CHECK(ECDSA_verify(0, message, sizeof(message), signature, secp_sigsize, ec_key) == 1);
EC_KEY_free(ec_key);
}
void run_ecdsa_openssl(void) {
int i;
for (i = 0; i < 10*count; i++) {
test_ecdsa_openssl();
}
}
#endif
#ifdef ENABLE_MODULE_ECDH
# include "modules/ecdh/tests_impl.h"
#endif
#ifdef ENABLE_MODULE_MULTISET
# include "modules/multiset/tests_impl.h"
#endif
#ifdef ENABLE_MODULE_RECOVERY
# include "modules/recovery/tests_impl.h"
#endif
#ifdef ENABLE_MODULE_SCHNORR
# include "modules/schnorr/tests_impl.h"
#endif
int main(int argc, char **argv) {
unsigned char seed16[16] = {0};
unsigned char run32[32] = {0};
/* find iteration count */
if (argc > 1) {
count = strtol(argv[1], NULL, 0);
}
/* find random seed */
if (argc > 2) {
int pos = 0;
const char* ch = argv[2];
while (pos < 16 && ch[0] != 0 && ch[1] != 0) {
unsigned short sh;
if (sscanf(ch, "%2hx", &sh)) {
seed16[pos] = sh;
} else {
break;
}
ch += 2;
pos++;
}
} else {
FILE *frand = fopen("/dev/urandom", "r");
if ((frand == NULL) || fread(&seed16, 1, sizeof(seed16), frand) != sizeof(seed16)) {
uint64_t t = time(NULL) * (uint64_t)1337;
fprintf(stderr, "WARNING: could not read 16 bytes from /dev/urandom; falling back to insecure PRNG\n");
seed16[0] ^= t;
seed16[1] ^= t >> 8;
seed16[2] ^= t >> 16;
seed16[3] ^= t >> 24;
seed16[4] ^= t >> 32;
seed16[5] ^= t >> 40;
seed16[6] ^= t >> 48;
seed16[7] ^= t >> 56;
}
if (frand) {
fclose(frand);
}
}
secp256k1_rand_seed(seed16);
printf("test count = %i\n", count);
printf("random seed = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", seed16[0], seed16[1], seed16[2], seed16[3], seed16[4], seed16[5], seed16[6], seed16[7], seed16[8], seed16[9], seed16[10], seed16[11], seed16[12], seed16[13], seed16[14], seed16[15]);
/* initialize */
run_context_tests();
run_scratch_tests();
ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
if (secp256k1_rand_bits(1)) {
secp256k1_rand256(run32);
CHECK(secp256k1_context_randomize(ctx, secp256k1_rand_bits(1) ? run32 : NULL));
}
run_rand_bits();
run_rand_int();
run_sha256_tests();
run_hmac_sha256_tests();
run_rfc6979_hmac_sha256_tests();
#ifndef USE_NUM_NONE
/* num tests */
run_num_smalltests();
#endif
/* scalar tests */
run_scalar_tests();
/* field tests */
run_field_inv();
run_field_inv_var();
run_field_inv_all_var();
run_field_misc();
run_field_convert();
run_sqr();
run_sqrt();
/* group tests */
run_ge();
run_group_decompress();
/* ecmult tests */
run_wnaf();
run_point_times_order();
run_ecmult_chain();
run_ecmult_constants();
run_ecmult_gen_blind();
run_ecmult_const_tests();
run_ecmult_multi_tests();
run_ec_combine();
/* endomorphism tests */
#ifdef USE_ENDOMORPHISM
run_endomorphism_tests();
#endif
/* EC point parser test */
run_ec_pubkey_parse_test();
/* EC key edge cases */
run_eckey_edge_case_test();
#ifdef ENABLE_MODULE_ECDH
/* ecdh tests */
run_ecdh_tests();
#endif
/* ecdsa tests */
run_random_pubkeys();
run_ecdsa_der_parse();
run_ecdsa_sign_verify();
run_ecdsa_end_to_end();
run_ecdsa_edge_cases();
#ifdef ENABLE_OPENSSL_TESTS
run_ecdsa_openssl();
#endif
#ifdef ENABLE_MODULE_MULTISET
run_multiset_tests();
#endif
#ifdef ENABLE_MODULE_RECOVERY
/* ECDSA pubkey recovery tests */
run_recovery_tests();
#endif
#ifdef ENABLE_MODULE_SCHNORR
/* Schnorr signature tests */
run_schnorr_tests();
#endif
secp256k1_rand256(run32);
printf("random run = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", run32[0], run32[1], run32[2], run32[3], run32[4], run32[5], run32[6], run32[7], run32[8], run32[9], run32[10], run32[11], run32[12], run32[13], run32[14], run32[15]);
/* shutdown */
secp256k1_context_destroy(ctx);
printf("no problems found\n");
return 0;
}

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