From 83836a95472ab8ddf8c27cf4e9956d4eeed3bdaf Mon Sep 17 00:00:00 2001 From: Andrew Poelstra Date: Thu, 7 Jul 2016 10:11:30 +0000 Subject: [PATCH] Add exhaustive tests for group arithmetic, signing, and ecmult on a small group If you compile without ./configure --enable-exhaustive-tests=no, this will create a binary ./exhaustive_tests which will execute every function possible on a group of small order obtained by moving to a twist of our curve and locating a generator of small order. Currently defaults to order 13, though by changing some #ifdefs you can get a couple other ones. (Currently 199, which will take forever to run, and 14, which won't work because it's composite.) TODO exhaustive tests for the various modules --- Makefile.am | 3 +- src/ecmult_const_impl.h | 2 +- src/ecmult_impl.h | 13 ++-- src/group_impl.h | 43 ++++++++++- src/scalar.h | 4 +- src/scalar_impl.h | 39 +++++++++- src/scalar_low.h | 15 ++++ src/scalar_low_impl.h | 114 +++++++++++++++++++++++++++++ src/tests_exhaustive.c | 157 +++++++++++++++++++++++++++++++++++----- 9 files changed, 360 insertions(+), 30 deletions(-) create mode 100644 src/scalar_low.h create mode 100644 src/scalar_low_impl.h diff --git a/Makefile.am b/Makefile.am index df2017a..e5657f7 100644 --- a/Makefile.am +++ b/Makefile.am @@ -12,9 +12,11 @@ noinst_HEADERS = noinst_HEADERS += src/scalar.h noinst_HEADERS += src/scalar_4x64.h noinst_HEADERS += src/scalar_8x32.h +noinst_HEADERS += src/scalar_low.h noinst_HEADERS += src/scalar_impl.h noinst_HEADERS += src/scalar_4x64_impl.h noinst_HEADERS += src/scalar_8x32_impl.h +noinst_HEADERS += src/scalar_low_impl.h noinst_HEADERS += src/group.h noinst_HEADERS += src/group_impl.h noinst_HEADERS += src/num_gmp.h @@ -150,7 +152,6 @@ $(gen_context_BIN): $(gen_context_OBJECTS) $(libsecp256k1_la_OBJECTS): src/ecmult_static_context.h $(tests_OBJECTS): src/ecmult_static_context.h -$(exhaustive_tests_OBJECTS): src/ecmult_static_context.h $(bench_internal_OBJECTS): src/ecmult_static_context.h src/ecmult_static_context.h: $(gen_context_BIN) diff --git a/src/ecmult_const_impl.h b/src/ecmult_const_impl.h index 7a6a253..0db314c 100644 --- a/src/ecmult_const_impl.h +++ b/src/ecmult_const_impl.h @@ -78,7 +78,7 @@ static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w) { /* Negative numbers will be negated to keep their bit representation below the maximum width */ flip = secp256k1_scalar_is_high(&s); /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */ - bit = flip ^ (s.d[0] & 1); + bit = flip ^ !secp256k1_scalar_is_even(&s); /* We check for negative one, since adding 2 to it will cause an overflow */ secp256k1_scalar_negate(&neg_s, &s); not_neg_one = !secp256k1_scalar_is_one(&neg_s); diff --git a/src/ecmult_impl.h b/src/ecmult_impl.h index 8ed19b7..4e40104 100644 --- a/src/ecmult_impl.h +++ b/src/ecmult_impl.h @@ -13,20 +13,23 @@ #include "scalar.h" #include "ecmult.h" -#include - -/* optimal for 128-bit and 256-bit exponents. */ -#define WINDOW_A 5 - #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 diff --git a/src/group_impl.h b/src/group_impl.h index 97d5118..2e192b6 100644 --- a/src/group_impl.h +++ b/src/group_impl.h @@ -11,6 +11,31 @@ #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 const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST( @@ -19,6 +44,16 @@ const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST( 0x78AC123A, 0x5ED8AEF3, 0x8732BC91, 0x1F3A2868, 0x48DF246C, 0x808DAE72, 0xCFE52572, 0x7F0501ED ); + +const int CURVE_B = 4; +# elif EXHAUSTIVE_TEST_ORDER == 13 +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 +); +const int CURVE_B = 2; # else # error No known generator for the specified exhaustive test group order. # endif @@ -32,6 +67,8 @@ static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST( 0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL, 0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL ); + +const int CURVE_B = 7; #endif static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) { @@ -188,7 +225,7 @@ static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x) { secp256k1_fe_sqr(&x2, x); secp256k1_fe_mul(&x3, x, &x2); r->infinity = 0; - secp256k1_fe_set_int(&c, 7); + secp256k1_fe_set_int(&c, CURVE_B); secp256k1_fe_add(&c, &x3); return secp256k1_fe_sqrt(&r->y, &c); } @@ -247,7 +284,7 @@ static int secp256k1_gej_is_valid_var(const secp256k1_gej *a) { 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, 7); + secp256k1_fe_mul_int(&z6, CURVE_B); secp256k1_fe_add(&x3, &z6); secp256k1_fe_normalize_weak(&x3); return secp256k1_fe_equal_var(&y2, &x3); @@ -261,7 +298,7 @@ static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) { /* 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, 7); + secp256k1_fe_set_int(&c, CURVE_B); secp256k1_fe_add(&x3, &c); secp256k1_fe_normalize_weak(&x3); return secp256k1_fe_equal_var(&y2, &x3); diff --git a/src/scalar.h b/src/scalar.h index b590ccd..27e9d83 100644 --- a/src/scalar.h +++ b/src/scalar.h @@ -13,7 +13,9 @@ #include "libsecp256k1-config.h" #endif -#if defined(USE_SCALAR_4X64) +#if defined(EXHAUSTIVE_TEST_ORDER) +#include "scalar_low.h" +#elif defined(USE_SCALAR_4X64) #include "scalar_4x64.h" #elif defined(USE_SCALAR_8X32) #include "scalar_8x32.h" diff --git a/src/scalar_impl.h b/src/scalar_impl.h index c5baf4d..f5b2376 100644 --- a/src/scalar_impl.h +++ b/src/scalar_impl.h @@ -14,7 +14,9 @@ #include "libsecp256k1-config.h" #endif -#if defined(USE_SCALAR_4X64) +#if defined(EXHAUSTIVE_TEST_ORDER) +#include "scalar_low_impl.h" +#elif defined(USE_SCALAR_4X64) #include "scalar_4x64_impl.h" #elif defined(USE_SCALAR_8X32) #include "scalar_8x32_impl.h" @@ -31,17 +33,37 @@ static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a /** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */ static void secp256k1_scalar_order_get_num(secp256k1_num *r) { +#if defined(EXHAUSTIVE_TEST_ORDER) + static const unsigned char order[32] = { + 0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,EXHAUSTIVE_TEST_ORDER + }; +#else static const unsigned char order[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 }; +#endif secp256k1_num_set_bin(r, order, 32); } #endif static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) { +#if defined(EXHAUSTIVE_TEST_ORDER) + int i; + *r = 0; + for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) + if ((i * *x) % EXHAUSTIVE_TEST_ORDER == 1) + *r = i; + /* If this VERIFY_CHECK triggers we were given a noninvertible scalar (and thus + * have a composite group order; fix it in exhaustive_tests.c). */ + VERIFY_CHECK(*r != 0); +} +#else secp256k1_scalar *t; int i; /* First compute x ^ (2^N - 1) for some values of N. */ @@ -233,9 +255,9 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar } SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) { - /* d[0] is present and is the lowest word for all representations */ return !(a->d[0] & 1); } +#endif static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) { #if defined(USE_SCALAR_INV_BUILTIN) @@ -259,6 +281,18 @@ static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_sc } #ifdef USE_ENDOMORPHISM +#if defined(EXHAUSTIVE_TEST_ORDER) +/** + * Find k1 and k2 given k, such that k1 + k2 * lambda == k mod n; unlike in the + * full case we don't bother making k1 and k2 be small, we just want them to be + * nontrivial to get full test coverage for the exhaustive tests. We therefore + * (arbitrarily) set k2 = k + 5 and k1 = k - k2 * lambda. + */ +static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) { + *r2 = (*a + 5) % EXHAUSTIVE_TEST_ORDER; + *r1 = (*a + (EXHAUSTIVE_TEST_ORDER - *r2) * EXHAUSTIVE_TEST_LAMBDA) % EXHAUSTIVE_TEST_ORDER; +} +#else /** * The Secp256k1 curve has an endomorphism, where lambda * (x, y) = (beta * x, y), where * lambda is {0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a, @@ -331,5 +365,6 @@ static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar secp256k1_scalar_add(r1, r1, a); } #endif +#endif #endif diff --git a/src/scalar_low.h b/src/scalar_low.h new file mode 100644 index 0000000..5574c44 --- /dev/null +++ b/src/scalar_low.h @@ -0,0 +1,15 @@ +/********************************************************************** + * Copyright (c) 2015 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef _SECP256K1_SCALAR_REPR_ +#define _SECP256K1_SCALAR_REPR_ + +#include + +/** A scalar modulo the group order of the secp256k1 curve. */ +typedef uint32_t secp256k1_scalar; + +#endif diff --git a/src/scalar_low_impl.h b/src/scalar_low_impl.h new file mode 100644 index 0000000..4f94441 --- /dev/null +++ b/src/scalar_low_impl.h @@ -0,0 +1,114 @@ +/********************************************************************** + * Copyright (c) 2015 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef _SECP256K1_SCALAR_REPR_IMPL_H_ +#define _SECP256K1_SCALAR_REPR_IMPL_H_ + +#include "scalar.h" + +#include + +SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) { + return !(*a & 1); +} + +SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) { *r = 0; } +SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) { *r = v; } + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + if (offset < 32) + return ((*a >> offset) & ((((uint32_t)1) << count) - 1)); + else + return 0; +} + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + return secp256k1_scalar_get_bits(a, offset, count); +} + +SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) { return *a >= EXHAUSTIVE_TEST_ORDER; } + +static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + *r = (*a + *b) % EXHAUSTIVE_TEST_ORDER; + return *r < *b; +} + +static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) { + if (flag && bit < 32) + *r += (1 << bit); +#ifdef VERIFY + VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0); +#endif +} + +static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) { + const int base = 0x100 % EXHAUSTIVE_TEST_ORDER; + int i; + *r = 0; + for (i = 0; i < 32; i++) { + *r = ((*r * base) + b32[i]) % EXHAUSTIVE_TEST_ORDER; + } + /* just deny overflow, it basically always happens */ + if (overflow) *overflow = 0; +} + +static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) { + memset(bin, 0, 32); + bin[28] = *a >> 24; bin[29] = *a >> 16; bin[30] = *a >> 8; bin[31] = *a; +} + +SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) { + return *a == 0; +} + +static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) { + if (*a == 0) { + *r = 0; + } else { + *r = EXHAUSTIVE_TEST_ORDER - *a; + } +} + +SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) { + return *a == 1; +} + +static int secp256k1_scalar_is_high(const secp256k1_scalar *a) { + return *a > EXHAUSTIVE_TEST_ORDER / 2; +} + +static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) { + if (flag) secp256k1_scalar_negate(r, r); + return flag ? -1 : 1; +} + +static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + *r = (*a * *b) % EXHAUSTIVE_TEST_ORDER; +} + +static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) { + int ret; + VERIFY_CHECK(n > 0); + VERIFY_CHECK(n < 16); + ret = *r & ((1 << n) - 1); + *r >>= n; + return ret; +} + +static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) { + *r = (*a * *a) % EXHAUSTIVE_TEST_ORDER; +} + +static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) { + *r1 = *a; + *r2 = 0; +} + +SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) { + return *a == *b; +} + +#endif diff --git a/src/tests_exhaustive.c b/src/tests_exhaustive.c index 7a916e9..3b88241 100644 --- a/src/tests_exhaustive.c +++ b/src/tests_exhaustive.c @@ -1,5 +1,5 @@ /********************************************************************** - * Copyright (c) 2015 Andrew Poelstra * + * Copyright (c) 2016 Andrew Poelstra * * Distributed under the MIT software license, see the accompanying * * file COPYING or http://www.opensource.org/licenses/mit-license.php.* **********************************************************************/ @@ -13,8 +13,12 @@ #include +#undef USE_ECMULT_STATIC_PRECOMPUTATION + #ifndef EXHAUSTIVE_TEST_ORDER -#define EXHAUSTIVE_TEST_ORDER 199 +/* see group_impl.h for allowable values */ +#define EXHAUSTIVE_TEST_ORDER 13 +#define EXHAUSTIVE_TEST_LAMBDA 9 /* cube root of 1 mod 13 */ #endif #include "include/secp256k1.h" @@ -60,6 +64,37 @@ void random_fe(secp256k1_fe *x) { } /** END stolen from tests.c */ +int secp256k1_nonce_function_smallint(unsigned char *nonce32, const unsigned char *msg32, + const unsigned char *key32, const unsigned char *algo16, + void *data, unsigned int attempt) { + secp256k1_scalar s; + int *idata = data; + (void)msg32; + (void)key32; + (void)algo16; + /* Some nonces cannot be used because they'd cause s and/or r to be zero. + * The signing function has retry logic here that just re-calls the nonce + * function with an increased `attempt`. So if attempt > 0 this means we + * need to change the nonce to avoid an infinite loop. */ + if (attempt > 0) { + (*idata)++; + } + secp256k1_scalar_set_int(&s, *idata); + secp256k1_scalar_get_b32(nonce32, &s); + return 1; +} + +#ifdef USE_ENDOMORPHISM +void test_exhaustive_endomorphism(const secp256k1_ge *group, int order) { + int i; + for (i = 0; i < order; i++) { + secp256k1_ge res; + secp256k1_ge_mul_lambda(&res, &group[i]); + ge_equals_ge(&group[i * EXHAUSTIVE_TEST_LAMBDA % EXHAUSTIVE_TEST_ORDER], &res); + } +} +#endif + void test_exhaustive_addition(const secp256k1_ge *group, const secp256k1_gej *groupj, int order) { int i, j; @@ -120,26 +155,90 @@ void test_exhaustive_addition(const secp256k1_ge *group, const secp256k1_gej *gr } } -void test_exhaustive_ecmult(secp256k1_context *ctx, secp256k1_ge *group, secp256k1_gej *groupj, int order) { - int i, j; - const int r_log = secp256k1_rand32() % order; /* TODO be less biased */ - for (j = 0; j < order; j++) { - for (i = 0; i < order; i++) { - secp256k1_gej tmp; - secp256k1_scalar na, ng; - secp256k1_scalar_set_int(&na, i); - secp256k1_scalar_set_int(&ng, j); +void test_exhaustive_ecmult(const secp256k1_context *ctx, const secp256k1_ge *group, const secp256k1_gej *groupj, int order) { + int i, j, r_log; + for (r_log = 1; r_log < order; r_log++) { + for (j = 0; j < order; j++) { + for (i = 0; i < order; i++) { + secp256k1_gej tmp; + secp256k1_scalar na, ng; + secp256k1_scalar_set_int(&na, i); + secp256k1_scalar_set_int(&ng, j); - secp256k1_ecmult(&ctx->ecmult_ctx, &tmp, &groupj[r_log], &na, &ng); - ge_equals_gej(&group[(i * r_log + j) % order], &tmp); + secp256k1_ecmult(&ctx->ecmult_ctx, &tmp, &groupj[r_log], &na, &ng); + ge_equals_gej(&group[(i * r_log + j) % order], &tmp); - /* TODO we cannot exhaustively test ecmult_const as it does a scalar - * negation for even numbers, and our code is not designed to handle - * such a small scalar modulus. */ + if (i > 0) { + secp256k1_ecmult_const(&tmp, &group[i], &ng); + ge_equals_gej(&group[(i * j) % order], &tmp); + } + } } } } +void r_from_k(secp256k1_scalar *r, const secp256k1_ge *group, int k) { + secp256k1_fe x; + unsigned char x_bin[32]; + k %= EXHAUSTIVE_TEST_ORDER; + x = group[k].x; + secp256k1_fe_normalize(&x); + secp256k1_fe_get_b32(x_bin, &x); + secp256k1_scalar_set_b32(r, x_bin, NULL); +} + +/* hee hee hee */ +int solve_discrete_log(const secp256k1_scalar *x_coord, const secp256k1_ge *group, int order) { + int i; + for (i = 0; i < order; i++) { + secp256k1_scalar check_x; + r_from_k(&check_x, group, i); + if (*x_coord == check_x) { + return i; + } + } + return -1; +} + +void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *group, int order) { + int i, j, k; + + /* Loop */ + for (i = 1; i < order; i++) { /* message */ + for (j = 1; j < order; j++) { /* key */ + for (k = 1; k < order; k++) { /* nonce */ + secp256k1_ecdsa_signature sig; + secp256k1_scalar sk, msg, r, s, expected_r; + unsigned char sk32[32], msg32[32]; + secp256k1_scalar_set_int(&msg, i); + secp256k1_scalar_set_int(&sk, j); + secp256k1_scalar_get_b32(sk32, &sk); + secp256k1_scalar_get_b32(msg32, &msg); + + secp256k1_ecdsa_sign(ctx, &sig, msg32, sk32, secp256k1_nonce_function_smallint, &k); + + secp256k1_ecdsa_signature_load(ctx, &r, &s, &sig); + /* Note that we compute expected_r *after* signing -- this is important + * because our nonce-computing function function might change k during + * signing. */ + r_from_k(&expected_r, group, k); + CHECK(r == expected_r); + CHECK((k * s) % order == (i + r * j) % order || + (k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order); + } + } + } + + /* We would like to verify zero-knowledge here by counting how often every + * possible (s, r) tuple appears, but because the group order is larger + * than the field order, when coercing the x-values to scalar values, some + * appear more often than others, so we are actually not zero-knowledge. + * (This effect also appears in the real code, but the difference is on the + * order of 1/2^128th the field order, so the deviation is not useful to a + * computationally bounded attacker.) + */ +} + int main(void) { int i; secp256k1_gej groupj[EXHAUSTIVE_TEST_ORDER]; @@ -151,18 +250,42 @@ int main(void) { /* TODO set z = 1, then do num_tests runs with random z values */ /* Generate the entire group */ - secp256k1_ge_set_infinity(&group[0]); secp256k1_gej_set_infinity(&groupj[0]); + secp256k1_ge_set_gej(&group[0], &groupj[0]); for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) { + /* Set a different random z-value for each Jacobian point */ secp256k1_fe z; random_fe(&z); secp256k1_gej_add_ge(&groupj[i], &groupj[i - 1], &secp256k1_ge_const_g); secp256k1_ge_set_gej(&group[i], &groupj[i]); secp256k1_gej_rescale(&groupj[i], &z); + + /* Verify against ecmult_gen */ + { + secp256k1_scalar scalar_i; + secp256k1_gej generatedj; + secp256k1_ge generated; + + secp256k1_scalar_set_int(&scalar_i, i); + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &generatedj, &scalar_i); + secp256k1_ge_set_gej(&generated, &generatedj); + + CHECK(group[i].infinity == 0); + CHECK(generated.infinity == 0); + CHECK(secp256k1_fe_equal_var(&generated.x, &group[i].x)); + CHECK(secp256k1_fe_equal_var(&generated.y, &group[i].y)); + } } /* Run the tests */ + test_exhaustive_sign(ctx, group, EXHAUSTIVE_TEST_ORDER); + /* cannot exhaustively test verify, since our verify code + * depends on the field order being less than twice the + * group order */ +#ifdef USE_ENDOMORPHISM + test_exhaustive_endomorphism(group, EXHAUSTIVE_TEST_ORDER); +#endif test_exhaustive_addition(group, groupj, EXHAUSTIVE_TEST_ORDER); test_exhaustive_ecmult(ctx, group, groupj, EXHAUSTIVE_TEST_ORDER);