diff --git a/README.md b/README.md index 5e61741..0605bc5 100644 --- a/README.md +++ b/README.md @@ -47,6 +47,11 @@ serial output in Intel HEX format. [README](src/dump_otp/README.md) +secp256k1\_{tests,bench} +------------------------ + +Run tests and benchmarks for the secp256k1 elliptic curve cryptographic library on this RISC-V CPU. + rust/k210-console ----------------- @@ -73,7 +78,7 @@ Annotated radare2 config files for the Boot ROM and OTP can be found under [r2]( Other projects ============== -Some other interesting K210-based projects and demos: +Some interesting K210-based projects and demos by other people: - [accelerometer](https://github.com/GitJer/Some-Sipeed-MAIX-GO-k210-stuff/tree/master/src/accelerometer) - Example of using the MSA300 accelerometer on the MAIX Go board, by GitJer diff --git a/src/secp256k1_bench/bench.h b/src/secp256k1_bench/bench.h new file mode 100644 index 0000000..5b59783 --- /dev/null +++ b/src/secp256k1_bench/bench.h @@ -0,0 +1,82 @@ +/********************************************************************** + * Copyright (c) 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_BENCH_H +#define SECP256K1_BENCH_H + +#include +#include +#include +#include "sys/time.h" + +static double gettimedouble(void) { + struct timeval tv; + gettimeofday(&tv, NULL); + return tv.tv_usec * 0.000001 + tv.tv_sec; +} + +void print_number(double x) { + double y = x; + int c = 0; + if (y < 0.0) { + y = -y; + } + while (y > 0 && y < 100.0) { + y *= 10.0; + c++; + } + printf("%.*f", c, x); +} + +void run_benchmark(char *name, void (*benchmark)(void*), void (*setup)(void*), void (*teardown)(void*), void* data, int count, int iter) { + int i; + double min = HUGE_VAL; + double sum = 0.0; + double max = 0.0; + for (i = 0; i < count; i++) { + double begin, total; + if (setup != NULL) { + setup(data); + } + begin = gettimedouble(); + benchmark(data); + total = gettimedouble() - begin; + if (teardown != NULL) { + teardown(data); + } + if (total < min) { + min = total; + } + if (total > max) { + max = total; + } + sum += total; + } + printf("%s: min ", name); + print_number(min * 1000000.0 / iter); + printf("us / avg "); + print_number((sum / count) * 1000000.0 / iter); + printf("us / max "); + print_number(max * 1000000.0 / iter); + printf("us\n"); +} + +int have_flag(int argc, char** argv, char *flag) { + char** argm = argv + argc; + argv++; + if (argv == argm) { + return 1; + } + while (argv != NULL && argv != argm) { + if (strcmp(*argv, flag) == 0) { + return 1; + } + argv++; + } + return 0; +} + +#endif /* SECP256K1_BENCH_H */ diff --git a/src/secp256k1_bench/main.c b/src/secp256k1_bench/main.c new file mode 100644 index 0000000..48f1b4c --- /dev/null +++ b/src/secp256k1_bench/main.c @@ -0,0 +1,179 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ +#define HAVE_CONFIG_H +#define SECP256K1_BUILD +// Do not define VERIFY for the benchmarks: it makes things run much slower + +#if defined HAVE_CONFIG_H +#include "../secp256k1_tests/libsecp256k1-config.h" +#endif + +#include +#include + +#include "../secp256k1_tests/secp256k1_c.h" +#include "util.h" +#include "bench.h" + +#include "sysctl.h" +#include "uarths.h" +#include "sleep.h" + +#define V_RUNS (200) + +typedef struct { + secp256k1_context *ctx; + unsigned char msg[32]; + unsigned char key[32]; + unsigned char sig[72]; + size_t siglen; + unsigned char pubkey[33]; + size_t pubkeylen; +} benchmark_verify_t; + +static void benchmark_verify(void* arg) { + int i; + benchmark_verify_t* data = (benchmark_verify_t*)arg; + + for (i = 0; i < V_RUNS; i++) { + secp256k1_pubkey pubkey; + secp256k1_ecdsa_signature sig; + data->sig[data->siglen - 1] ^= (i & 0xFF); + data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF); + data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF); + CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->pubkey, data->pubkeylen) == 1); + CHECK(secp256k1_ecdsa_signature_parse_der(data->ctx, &sig, data->sig, data->siglen) == 1); + CHECK(secp256k1_ecdsa_verify(data->ctx, &sig, data->msg, &pubkey) == (i == 0)); + data->sig[data->siglen - 1] ^= (i & 0xFF); + data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF); + data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF); + } +} + +int bench_verify_main(void) { + int i; + secp256k1_pubkey pubkey; + secp256k1_ecdsa_signature sig; + benchmark_verify_t data; + + data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); + + for (i = 0; i < 32; i++) { + data.msg[i] = 1 + i; + } + for (i = 0; i < 32; i++) { + data.key[i] = 33 + i; + } + data.siglen = 72; + CHECK(secp256k1_ecdsa_sign(data.ctx, &sig, data.msg, data.key, NULL, NULL)); + CHECK(secp256k1_ecdsa_signature_serialize_der(data.ctx, data.sig, &data.siglen, &sig)); + CHECK(secp256k1_ec_pubkey_create(data.ctx, &pubkey, data.key)); + data.pubkeylen = 33; + CHECK(secp256k1_ec_pubkey_serialize(data.ctx, data.pubkey, &data.pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED) == 1); + + run_benchmark("ecdsa_verify", benchmark_verify, NULL, NULL, &data, 10, V_RUNS); + + secp256k1_context_destroy(data.ctx); + + return 0; +} + +typedef struct { + secp256k1_context* ctx; + unsigned char msg[32]; + unsigned char key[32]; +} bench_sign; + +static void bench_sign_setup(void* arg) { + int i; + bench_sign *data = (bench_sign*)arg; + + for (i = 0; i < 32; i++) { + data->msg[i] = i + 1; + } + for (i = 0; i < 32; i++) { + data->key[i] = i + 65; + } +} + +static void bench_sign_run(void* arg) { + int i; + bench_sign *data = (bench_sign*)arg; + + unsigned char sig[74]; + for (i = 0; i < V_RUNS; i++) { + size_t siglen = 74; + int j; + secp256k1_ecdsa_signature signature; + CHECK(secp256k1_ecdsa_sign(data->ctx, &signature, data->msg, data->key, NULL, NULL)); + CHECK(secp256k1_ecdsa_signature_serialize_der(data->ctx, sig, &siglen, &signature)); + for (j = 0; j < 32; j++) { + data->msg[j] = sig[j]; + data->key[j] = sig[j + 32]; + } + } +} + +int bench_sign_main(void) { + bench_sign data; + + data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN); + + run_benchmark("ecdsa_sign", bench_sign_run, bench_sign_setup, NULL, &data, 10, 20000); + + secp256k1_context_destroy(data.ctx); + + return 0; +} + +typedef struct { + secp256k1_context *ctx; + secp256k1_pubkey point; + unsigned char scalar[32]; +} bench_ecdh_data; + +static void bench_ecdh_setup(void* arg) { + int i; + bench_ecdh_data *data = (bench_ecdh_data*)arg; + const unsigned char point[] = { + 0x03, + 0x54, 0x94, 0xc1, 0x5d, 0x32, 0x09, 0x97, 0x06, + 0xc2, 0x39, 0x5f, 0x94, 0x34, 0x87, 0x45, 0xfd, + 0x75, 0x7c, 0xe3, 0x0e, 0x4e, 0x8c, 0x90, 0xfb, + 0xa2, 0xba, 0xd1, 0x84, 0xf8, 0x83, 0xc6, 0x9f + }; + + /* create a context with no capabilities */ + data->ctx = secp256k1_context_create(SECP256K1_FLAGS_TYPE_CONTEXT); + for (i = 0; i < 32; i++) { + data->scalar[i] = i + 1; + } + CHECK(secp256k1_ec_pubkey_parse(data->ctx, &data->point, point, sizeof(point)) == 1); +} + +int main(void) { + if (current_coreid() != 0) { + while (1) + asm volatile ("wfi"); + } + + sysctl_pll_set_freq(SYSCTL_PLL0, 800000000UL); + + uarths_init(); + usleep(100000); + + printf("Running secp256k1 benchamrks with CPU clock %u\n", sysctl_clock_get_freq(SYSCTL_CLOCK_CPU)); + printf("see add_compile_flags in cmake/compile-flags.cmake to tweak optimization flags\n"); + printf(" WINDOW_A is %d\n", WINDOW_A); + printf(" WINDOW_G is %d\n", WINDOW_G); + bench_verify_main(); + bench_sign_main(); + printf("[done]\n"); + + while (1) + asm volatile ("wfi"); + return 0; +} diff --git a/src/secp256k1_bench/util.h b/src/secp256k1_bench/util.h new file mode 100644 index 0000000..e1f5b76 --- /dev/null +++ b/src/secp256k1_bench/util.h @@ -0,0 +1,121 @@ +/********************************************************************** + * 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_UTIL_H +#define SECP256K1_UTIL_H + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include +#include +#include + +typedef struct { + void (*fn)(const char *text, void* data); + const void* data; +} secp256k1_callback; + +static SECP256K1_INLINE void secp256k1_callback_call(const secp256k1_callback * const cb, const char * const text) { + cb->fn(text, (void*)cb->data); +} + +#ifdef DETERMINISTIC +#define TEST_FAILURE(msg) do { \ + fprintf(stderr, "%s\n", msg); \ + abort(); \ +} while(0); +#else +#define TEST_FAILURE(msg) do { \ + fprintf(stderr, "%s:%d: %s\n", __FILE__, __LINE__, msg); \ + abort(); \ +} while(0) +#endif + +#if SECP256K1_GNUC_PREREQ(3, 0) +#define EXPECT(x,c) __builtin_expect((x),(c)) +#else +#define EXPECT(x,c) (x) +#endif + +#ifdef DETERMINISTIC +#define CHECK(cond) do { \ + if (EXPECT(!(cond), 0)) { \ + TEST_FAILURE("test condition failed"); \ + } \ +} while(0) +#else +#define CHECK(cond) do { \ + if (EXPECT(!(cond), 0)) { \ + TEST_FAILURE("test condition failed: " #cond); \ + } \ +} while(0) +#endif + +/* Like assert(), but when VERIFY is defined, and side-effect safe. */ +#if defined(COVERAGE) +#define VERIFY_CHECK(check) +#define VERIFY_SETUP(stmt) +#elif defined(VERIFY) +#define VERIFY_CHECK CHECK +#define VERIFY_SETUP(stmt) do { stmt; } while(0) +#else +#define VERIFY_CHECK(cond) do { (void)(cond); } while(0) +#define VERIFY_SETUP(stmt) +#endif + +static SECP256K1_INLINE void *checked_malloc(const secp256k1_callback* cb, size_t size) { + void *ret = malloc(size); + if (ret == NULL) { + secp256k1_callback_call(cb, "Out of memory"); + } + return ret; +} + +static SECP256K1_INLINE void *checked_realloc(const secp256k1_callback* cb, void *ptr, size_t size) { + void *ret = realloc(ptr, size); + if (ret == NULL) { + secp256k1_callback_call(cb, "Out of memory"); + } + return ret; +} + +/* Macro for restrict, when available and not in a VERIFY build. */ +#if defined(SECP256K1_BUILD) && defined(VERIFY) +# define SECP256K1_RESTRICT +#else +# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) ) +# if SECP256K1_GNUC_PREREQ(3,0) +# define SECP256K1_RESTRICT __restrict__ +# elif (defined(_MSC_VER) && _MSC_VER >= 1400) +# define SECP256K1_RESTRICT __restrict +# else +# define SECP256K1_RESTRICT +# endif +# else +# define SECP256K1_RESTRICT restrict +# endif +#endif + +#if defined(_WIN32) +# define I64FORMAT "I64d" +# define I64uFORMAT "I64u" +#else +# define I64FORMAT "lld" +# define I64uFORMAT "llu" +#endif + +#if defined(HAVE___INT128) +# if defined(__GNUC__) +# define SECP256K1_GNUC_EXT __extension__ +# else +# define SECP256K1_GNUC_EXT +# endif +SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t; +#endif + +#endif /* SECP256K1_UTIL_H */ diff --git a/src/secp256k1_tests/COPYING b/src/secp256k1_tests/COPYING new file mode 100644 index 0000000..4522a59 --- /dev/null +++ b/src/secp256k1_tests/COPYING @@ -0,0 +1,19 @@ +Copyright (c) 2013 Pieter Wuille + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. diff --git a/src/secp256k1_tests/README.md b/src/secp256k1_tests/README.md new file mode 100644 index 0000000..64ae566 --- /dev/null +++ b/src/secp256k1_tests/README.md @@ -0,0 +1,54 @@ +libsecp256k1 +============ + +Run tests and benchmarks for the secp256k1 elliptic curve cryptographic library on this RISC-V CPU. + +Description +----------- + +Optimized C library for EC operations on curve secp256k1. + +This library is a work in progress and is being used to research best practices. Use at your own risk. + +Features: +* secp256k1 ECDSA signing/verification and key generation. +* Adding/multiplying private/public keys. +* Serialization/parsing of private keys, public keys, signatures. +* Constant time, constant memory access signing and pubkey generation. +* Derandomized DSA (via RFC6979 or with a caller provided function.) +* Very efficient implementation. + +Implementation details +---------------------- + +* General + * No runtime heap allocation. + * Extensive testing infrastructure. + * Structured to facilitate review and analysis. + * Intended to be portable to any system with a C89 compiler and uint64_t support. + * Expose only higher level interfaces to minimize the API surface and improve application security. ("Be difficult to use insecurely.") +* Field operations + * Optimized implementation of arithmetic modulo the curve's field size (2^256 - 0x1000003D1). + * Using 5 52-bit limbs (including hand-optimized assembly for x86_64, by Diederik Huys). + * Using 10 26-bit limbs. + * Field inverses and square roots using a sliding window over blocks of 1s (by Peter Dettman). +* Scalar operations + * Optimized implementation without data-dependent branches of arithmetic modulo the curve's order. + * Using 4 64-bit limbs (relying on __int128 support in the compiler). + * Using 8 32-bit limbs. +* Group operations + * Point addition formula specifically simplified for the curve equation (y^2 = x^3 + 7). + * Use addition between points in Jacobian and affine coordinates where possible. + * Use a unified addition/doubling formula where necessary to avoid data-dependent branches. + * Point/x comparison without a field inversion by comparison in the Jacobian coordinate space. +* Point multiplication for verification (a*P + b*G). + * Use wNAF notation for point multiplicands. + * Use a much larger window for multiples of G, using precomputed multiples. + * Use Shamir's trick to do the multiplication with the public key and the generator simultaneously. + * Optionally (off by default) use secp256k1's efficiently-computable endomorphism to split the P multiplicand into 2 half-sized ones. +* Point multiplication for signing + * Use a precomputed table of multiples of powers of 16 multiplied with the generator, so general multiplication becomes a series of additions. + * Access the table with branch-free conditional moves so memory access is uniform. + * No data-dependent branches + * The precomputed tables add and eventually subtract points for which no known scalar (private key) is known, preventing even an attacker with control over the private key used to control the data internally. + diff --git a/src/secp256k1_tests/contrib/lax_der_parsing.c.h b/src/secp256k1_tests/contrib/lax_der_parsing.c.h new file mode 100644 index 0000000..3fedefa --- /dev/null +++ b/src/secp256k1_tests/contrib/lax_der_parsing.c.h @@ -0,0 +1,150 @@ +/********************************************************************** + * Copyright (c) 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#include +#include + +#include "lax_der_parsing.h" + +int ecdsa_signature_parse_der_lax(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) { + size_t rpos, rlen, spos, slen; + size_t pos = 0; + size_t lenbyte; + unsigned char tmpsig[64] = {0}; + int overflow = 0; + + /* Hack to initialize sig with a correctly-parsed but invalid signature. */ + secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig); + + /* Sequence tag byte */ + if (pos == inputlen || input[pos] != 0x30) { + return 0; + } + pos++; + + /* Sequence length bytes */ + if (pos == inputlen) { + return 0; + } + lenbyte = input[pos++]; + if (lenbyte & 0x80) { + lenbyte -= 0x80; + if (pos + lenbyte > inputlen) { + return 0; + } + pos += lenbyte; + } + + /* Integer tag byte for R */ + if (pos == inputlen || input[pos] != 0x02) { + return 0; + } + pos++; + + /* Integer length for R */ + if (pos == inputlen) { + return 0; + } + lenbyte = input[pos++]; + if (lenbyte & 0x80) { + lenbyte -= 0x80; + if (pos + lenbyte > inputlen) { + return 0; + } + while (lenbyte > 0 && input[pos] == 0) { + pos++; + lenbyte--; + } + if (lenbyte >= sizeof(size_t)) { + return 0; + } + rlen = 0; + while (lenbyte > 0) { + rlen = (rlen << 8) + input[pos]; + pos++; + lenbyte--; + } + } else { + rlen = lenbyte; + } + if (rlen > inputlen - pos) { + return 0; + } + rpos = pos; + pos += rlen; + + /* Integer tag byte for S */ + if (pos == inputlen || input[pos] != 0x02) { + return 0; + } + pos++; + + /* Integer length for S */ + if (pos == inputlen) { + return 0; + } + lenbyte = input[pos++]; + if (lenbyte & 0x80) { + lenbyte -= 0x80; + if (pos + lenbyte > inputlen) { + return 0; + } + while (lenbyte > 0 && input[pos] == 0) { + pos++; + lenbyte--; + } + if (lenbyte >= sizeof(size_t)) { + return 0; + } + slen = 0; + while (lenbyte > 0) { + slen = (slen << 8) + input[pos]; + pos++; + lenbyte--; + } + } else { + slen = lenbyte; + } + if (slen > inputlen - pos) { + return 0; + } + spos = pos; + pos += slen; + + /* Ignore leading zeroes in R */ + while (rlen > 0 && input[rpos] == 0) { + rlen--; + rpos++; + } + /* Copy R value */ + if (rlen > 32) { + overflow = 1; + } else { + memcpy(tmpsig + 32 - rlen, input + rpos, rlen); + } + + /* Ignore leading zeroes in S */ + while (slen > 0 && input[spos] == 0) { + slen--; + spos++; + } + /* Copy S value */ + if (slen > 32) { + overflow = 1; + } else { + memcpy(tmpsig + 64 - slen, input + spos, slen); + } + + if (!overflow) { + overflow = !secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig); + } + if (overflow) { + memset(tmpsig, 0, 64); + secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig); + } + return 1; +} + diff --git a/src/secp256k1_tests/contrib/lax_der_parsing.h b/src/secp256k1_tests/contrib/lax_der_parsing.h new file mode 100644 index 0000000..7c9a504 --- /dev/null +++ b/src/secp256k1_tests/contrib/lax_der_parsing.h @@ -0,0 +1,91 @@ +/********************************************************************** + * Copyright (c) 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +/**** + * Please do not link this file directly. It is not part of the libsecp256k1 + * project and does not promise any stability in its API, functionality or + * presence. Projects which use this code should instead copy this header + * and its accompanying .c file directly into their codebase. + ****/ + +/* This file defines a function that parses DER with various errors and + * violations. This is not a part of the library itself, because the allowed + * violations are chosen arbitrarily and do not follow or establish any + * standard. + * + * In many places it matters that different implementations do not only accept + * the same set of valid signatures, but also reject the same set of signatures. + * The only means to accomplish that is by strictly obeying a standard, and not + * accepting anything else. + * + * Nonetheless, sometimes there is a need for compatibility with systems that + * use signatures which do not strictly obey DER. The snippet below shows how + * certain violations are easily supported. You may need to adapt it. + * + * Do not use this for new systems. Use well-defined DER or compact signatures + * instead if you have the choice (see secp256k1_ecdsa_signature_parse_der and + * secp256k1_ecdsa_signature_parse_compact). + * + * The supported violations are: + * - All numbers are parsed as nonnegative integers, even though X.609-0207 + * section 8.3.3 specifies that integers are always encoded as two's + * complement. + * - Integers can have length 0, even though section 8.3.1 says they can't. + * - Integers with overly long padding are accepted, violation section + * 8.3.2. + * - 127-byte long length descriptors are accepted, even though section + * 8.1.3.5.c says that they are not. + * - Trailing garbage data inside or after the signature is ignored. + * - The length descriptor of the sequence is ignored. + * + * Compared to for example OpenSSL, many violations are NOT supported: + * - Using overly long tag descriptors for the sequence or integers inside, + * violating section 8.1.2.2. + * - Encoding primitive integers as constructed values, violating section + * 8.3.1. + */ + +#ifndef SECP256K1_CONTRIB_LAX_DER_PARSING_H +#define SECP256K1_CONTRIB_LAX_DER_PARSING_H + +#include + +#ifdef __cplusplus +extern "C" { +#endif + +/** Parse a signature in "lax DER" format + * + * Returns: 1 when the signature could be parsed, 0 otherwise. + * Args: ctx: a secp256k1 context object + * Out: sig: a pointer to a signature object + * In: input: a pointer to the signature to be parsed + * inputlen: the length of the array pointed to be input + * + * This function will accept any valid DER encoded signature, even if the + * encoded numbers are out of range. In addition, it will accept signatures + * which violate the DER spec in various ways. Its purpose is to allow + * validation of the Bitcoin blockchain, which includes non-DER signatures + * from before the network rules were updated to enforce DER. Note that + * the set of supported violations is a strict subset of what OpenSSL will + * accept. + * + * After the call, sig will always be initialized. If parsing failed or the + * encoded numbers are out of range, signature validation with it is + * guaranteed to fail for every message and public key. + */ +int ecdsa_signature_parse_der_lax( + const secp256k1_context* ctx, + secp256k1_ecdsa_signature* sig, + const unsigned char *input, + size_t inputlen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_CONTRIB_LAX_DER_PARSING_H */ diff --git a/src/secp256k1_tests/contrib/lax_der_privatekey_parsing.c.h b/src/secp256k1_tests/contrib/lax_der_privatekey_parsing.c.h new file mode 100644 index 0000000..3ff5bc5 --- /dev/null +++ b/src/secp256k1_tests/contrib/lax_der_privatekey_parsing.c.h @@ -0,0 +1,113 @@ +/********************************************************************** + * Copyright (c) 2014, 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#include +#include + +#include "lax_der_privatekey_parsing.h" + +int ec_privkey_import_der(const secp256k1_context* ctx, unsigned char *out32, const unsigned char *privkey, size_t privkeylen) { + const unsigned char *end = privkey + privkeylen; + int lenb = 0; + int len = 0; + memset(out32, 0, 32); + /* sequence header */ + if (end < privkey+1 || *privkey != 0x30) { + return 0; + } + privkey++; + /* sequence length constructor */ + if (end < privkey+1 || !(*privkey & 0x80)) { + return 0; + } + lenb = *privkey & ~0x80; privkey++; + if (lenb < 1 || lenb > 2) { + return 0; + } + if (end < privkey+lenb) { + return 0; + } + /* sequence length */ + len = privkey[lenb-1] | (lenb > 1 ? privkey[lenb-2] << 8 : 0); + privkey += lenb; + if (end < privkey+len) { + return 0; + } + /* sequence element 0: version number (=1) */ + if (end < privkey+3 || privkey[0] != 0x02 || privkey[1] != 0x01 || privkey[2] != 0x01) { + return 0; + } + privkey += 3; + /* sequence element 1: octet string, up to 32 bytes */ + if (end < privkey+2 || privkey[0] != 0x04 || privkey[1] > 0x20 || end < privkey+2+privkey[1]) { + return 0; + } + memcpy(out32 + 32 - privkey[1], privkey + 2, privkey[1]); + if (!secp256k1_ec_seckey_verify(ctx, out32)) { + memset(out32, 0, 32); + return 0; + } + return 1; +} + +int ec_privkey_export_der(const secp256k1_context *ctx, unsigned char *privkey, size_t *privkeylen, const unsigned char *key32, int compressed) { + secp256k1_pubkey pubkey; + size_t pubkeylen = 0; + if (!secp256k1_ec_pubkey_create(ctx, &pubkey, key32)) { + *privkeylen = 0; + return 0; + } + if (compressed) { + static const unsigned char begin[] = { + 0x30,0x81,0xD3,0x02,0x01,0x01,0x04,0x20 + }; + static const unsigned char middle[] = { + 0xA0,0x81,0x85,0x30,0x81,0x82,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48, + 0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,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,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04, + 0x21,0x02,0x79,0xBE,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, + 0x17,0x98,0x02,0x21,0x00,0xFF,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,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x24,0x03,0x22,0x00 + }; + unsigned char *ptr = privkey; + memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin); + memcpy(ptr, key32, 32); ptr += 32; + memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle); + pubkeylen = 33; + secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED); + ptr += pubkeylen; + *privkeylen = ptr - privkey; + } else { + static const unsigned char begin[] = { + 0x30,0x82,0x01,0x13,0x02,0x01,0x01,0x04,0x20 + }; + static const unsigned char middle[] = { + 0xA0,0x81,0xA5,0x30,0x81,0xA2,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48, + 0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,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,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04, + 0x41,0x04,0x79,0xBE,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, + 0xD4,0xB8,0x02,0x21,0x00,0xFF,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,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x44,0x03,0x42,0x00 + }; + unsigned char *ptr = privkey; + memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin); + memcpy(ptr, key32, 32); ptr += 32; + memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle); + pubkeylen = 65; + secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_UNCOMPRESSED); + ptr += pubkeylen; + *privkeylen = ptr - privkey; + } + return 1; +} diff --git a/src/secp256k1_tests/contrib/lax_der_privatekey_parsing.h b/src/secp256k1_tests/contrib/lax_der_privatekey_parsing.h new file mode 100644 index 0000000..00a26c7 --- /dev/null +++ b/src/secp256k1_tests/contrib/lax_der_privatekey_parsing.h @@ -0,0 +1,90 @@ +/********************************************************************** + * Copyright (c) 2014, 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +/**** + * Please do not link this file directly. It is not part of the libsecp256k1 + * project and does not promise any stability in its API, functionality or + * presence. Projects which use this code should instead copy this header + * and its accompanying .c file directly into their codebase. + ****/ + +/* This file contains code snippets that parse DER private keys with + * various errors and violations. This is not a part of the library + * itself, because the allowed violations are chosen arbitrarily and + * do not follow or establish any standard. + * + * It also contains code to serialize private keys in a compatible + * manner. + * + * These functions are meant for compatibility with applications + * that require BER encoded keys. When working with secp256k1-specific + * code, the simple 32-byte private keys normally used by the + * library are sufficient. + */ + +#ifndef SECP256K1_CONTRIB_BER_PRIVATEKEY_H +#define SECP256K1_CONTRIB_BER_PRIVATEKEY_H + +#include + +#ifdef __cplusplus +extern "C" { +#endif + +/** Export a private key in DER format. + * + * Returns: 1 if the private key was valid. + * Args: ctx: pointer to a context object, initialized for signing (cannot + * be NULL) + * Out: privkey: pointer to an array for storing the private key in BER. + * Should have space for 279 bytes, and cannot be NULL. + * privkeylen: Pointer to an int where the length of the private key in + * privkey will be stored. + * In: seckey: pointer to a 32-byte secret key to export. + * compressed: 1 if the key should be exported in + * compressed format, 0 otherwise + * + * This function is purely meant for compatibility with applications that + * require BER encoded keys. When working with secp256k1-specific code, the + * simple 32-byte private keys are sufficient. + * + * Note that this function does not guarantee correct DER output. It is + * guaranteed to be parsable by secp256k1_ec_privkey_import_der + */ +SECP256K1_WARN_UNUSED_RESULT int ec_privkey_export_der( + const secp256k1_context* ctx, + unsigned char *privkey, + size_t *privkeylen, + const unsigned char *seckey, + int compressed +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Import a private key in DER format. + * Returns: 1 if a private key was extracted. + * Args: ctx: pointer to a context object (cannot be NULL). + * Out: seckey: pointer to a 32-byte array for storing the private key. + * (cannot be NULL). + * In: privkey: pointer to a private key in DER format (cannot be NULL). + * privkeylen: length of the DER private key pointed to be privkey. + * + * This function will accept more than just strict DER, and even allow some BER + * violations. The public key stored inside the DER-encoded private key is not + * verified for correctness, nor are the curve parameters. Use this function + * only if you know in advance it is supposed to contain a secp256k1 private + * key. + */ +SECP256K1_WARN_UNUSED_RESULT int ec_privkey_import_der( + const secp256k1_context* ctx, + unsigned char *seckey, + const unsigned char *privkey, + size_t privkeylen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_CONTRIB_BER_PRIVATEKEY_H */ diff --git a/src/secp256k1_tests/ecdsa.h b/src/secp256k1_tests/ecdsa.h new file mode 100644 index 0000000..80590c7 --- /dev/null +++ b/src/secp256k1_tests/ecdsa.h @@ -0,0 +1,21 @@ +/********************************************************************** + * 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_ECDSA_H +#define SECP256K1_ECDSA_H + +#include + +#include "scalar.h" +#include "group.h" +#include "ecmult.h" + +static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *r, secp256k1_scalar *s, const unsigned char *sig, size_t size); +static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar *r, const secp256k1_scalar *s); +static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar* r, const secp256k1_scalar* s, const secp256k1_ge *pubkey, const secp256k1_scalar *message); +static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid); + +#endif /* SECP256K1_ECDSA_H */ diff --git a/src/secp256k1_tests/ecdsa_impl.h b/src/secp256k1_tests/ecdsa_impl.h new file mode 100644 index 0000000..c340004 --- /dev/null +++ b/src/secp256k1_tests/ecdsa_impl.h @@ -0,0 +1,313 @@ +/********************************************************************** + * Copyright (c) 2013-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + + +#ifndef SECP256K1_ECDSA_IMPL_H +#define SECP256K1_ECDSA_IMPL_H + +#include "scalar.h" +#include "field.h" +#include "group.h" +#include "ecmult.h" +#include "ecmult_gen.h" +#include "ecdsa.h" + +/** Group order for secp256k1 defined as 'n' in "Standards for Efficient Cryptography" (SEC2) 2.7.1 + * sage: for t in xrange(1023, -1, -1): + * .. p = 2**256 - 2**32 - t + * .. if p.is_prime(): + * .. print '%x'%p + * .. break + * 'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f' + * sage: a = 0 + * sage: b = 7 + * sage: F = FiniteField (p) + * sage: '%x' % (EllipticCurve ([F (a), F (b)]).order()) + * 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141' + */ +static const secp256k1_fe secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, + 0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL +); + +/** Difference between field and order, values 'p' and 'n' values defined in + * "Standards for Efficient Cryptography" (SEC2) 2.7.1. + * sage: p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F + * sage: a = 0 + * sage: b = 7 + * sage: F = FiniteField (p) + * sage: '%x' % (p - EllipticCurve ([F (a), F (b)]).order()) + * '14551231950b75fc4402da1722fc9baee' + */ +static const secp256k1_fe secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST( + 0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL +); + +static int secp256k1_der_read_len(const unsigned char **sigp, const unsigned char *sigend) { + int lenleft, b1; + size_t ret = 0; + if (*sigp >= sigend) { + return -1; + } + b1 = *((*sigp)++); + if (b1 == 0xFF) { + /* X.690-0207 8.1.3.5.c the value 0xFF shall not be used. */ + return -1; + } + if ((b1 & 0x80) == 0) { + /* X.690-0207 8.1.3.4 short form length octets */ + return b1; + } + if (b1 == 0x80) { + /* Indefinite length is not allowed in DER. */ + return -1; + } + /* X.690-207 8.1.3.5 long form length octets */ + lenleft = b1 & 0x7F; + if (lenleft > sigend - *sigp) { + return -1; + } + if (**sigp == 0) { + /* Not the shortest possible length encoding. */ + return -1; + } + if ((size_t)lenleft > sizeof(size_t)) { + /* The resulting length would exceed the range of a size_t, so + * certainly longer than the passed array size. + */ + return -1; + } + while (lenleft > 0) { + ret = (ret << 8) | **sigp; + if (ret + lenleft > (size_t)(sigend - *sigp)) { + /* Result exceeds the length of the passed array. */ + return -1; + } + (*sigp)++; + lenleft--; + } + if (ret < 128) { + /* Not the shortest possible length encoding. */ + return -1; + } + return ret; +} + +static int secp256k1_der_parse_integer(secp256k1_scalar *r, const unsigned char **sig, const unsigned char *sigend) { + int overflow = 0; + unsigned char ra[32] = {0}; + int rlen; + + if (*sig == sigend || **sig != 0x02) { + /* Not a primitive integer (X.690-0207 8.3.1). */ + return 0; + } + (*sig)++; + rlen = secp256k1_der_read_len(sig, sigend); + if (rlen <= 0 || (*sig) + rlen > sigend) { + /* Exceeds bounds or not at least length 1 (X.690-0207 8.3.1). */ + return 0; + } + if (**sig == 0x00 && rlen > 1 && (((*sig)[1]) & 0x80) == 0x00) { + /* Excessive 0x00 padding. */ + return 0; + } + if (**sig == 0xFF && rlen > 1 && (((*sig)[1]) & 0x80) == 0x80) { + /* Excessive 0xFF padding. */ + return 0; + } + if ((**sig & 0x80) == 0x80) { + /* Negative. */ + overflow = 1; + } + while (rlen > 0 && **sig == 0) { + /* Skip leading zero bytes */ + rlen--; + (*sig)++; + } + if (rlen > 32) { + overflow = 1; + } + if (!overflow) { + memcpy(ra + 32 - rlen, *sig, rlen); + secp256k1_scalar_set_b32(r, ra, &overflow); + } + if (overflow) { + secp256k1_scalar_set_int(r, 0); + } + (*sig) += rlen; + return 1; +} + +static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *rr, secp256k1_scalar *rs, const unsigned char *sig, size_t size) { + const unsigned char *sigend = sig + size; + int rlen; + if (sig == sigend || *(sig++) != 0x30) { + /* The encoding doesn't start with a constructed sequence (X.690-0207 8.9.1). */ + return 0; + } + rlen = secp256k1_der_read_len(&sig, sigend); + if (rlen < 0 || sig + rlen > sigend) { + /* Tuple exceeds bounds */ + return 0; + } + if (sig + rlen != sigend) { + /* Garbage after tuple. */ + return 0; + } + + if (!secp256k1_der_parse_integer(rr, &sig, sigend)) { + return 0; + } + if (!secp256k1_der_parse_integer(rs, &sig, sigend)) { + return 0; + } + + if (sig != sigend) { + /* Trailing garbage inside tuple. */ + return 0; + } + + return 1; +} + +static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar* ar, const secp256k1_scalar* as) { + unsigned char r[33] = {0}, s[33] = {0}; + unsigned char *rp = r, *sp = s; + size_t lenR = 33, lenS = 33; + secp256k1_scalar_get_b32(&r[1], ar); + secp256k1_scalar_get_b32(&s[1], as); + while (lenR > 1 && rp[0] == 0 && rp[1] < 0x80) { lenR--; rp++; } + while (lenS > 1 && sp[0] == 0 && sp[1] < 0x80) { lenS--; sp++; } + if (*size < 6+lenS+lenR) { + *size = 6 + lenS + lenR; + return 0; + } + *size = 6 + lenS + lenR; + sig[0] = 0x30; + sig[1] = 4 + lenS + lenR; + sig[2] = 0x02; + sig[3] = lenR; + memcpy(sig+4, rp, lenR); + sig[4+lenR] = 0x02; + sig[5+lenR] = lenS; + memcpy(sig+lenR+6, sp, lenS); + return 1; +} + +static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar *sigs, const secp256k1_ge *pubkey, const secp256k1_scalar *message) { + unsigned char c[32]; + secp256k1_scalar sn, u1, u2; +#if !defined(EXHAUSTIVE_TEST_ORDER) + secp256k1_fe xr; +#endif + secp256k1_gej pubkeyj; + secp256k1_gej pr; + + if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) { + return 0; + } + + secp256k1_scalar_inverse_var(&sn, sigs); + secp256k1_scalar_mul(&u1, &sn, message); + secp256k1_scalar_mul(&u2, &sn, sigr); + secp256k1_gej_set_ge(&pubkeyj, pubkey); + secp256k1_ecmult(ctx, &pr, &pubkeyj, &u2, &u1); + if (secp256k1_gej_is_infinity(&pr)) { + return 0; + } + +#if defined(EXHAUSTIVE_TEST_ORDER) +{ + secp256k1_scalar computed_r; + secp256k1_ge pr_ge; + secp256k1_ge_set_gej(&pr_ge, &pr); + secp256k1_fe_normalize(&pr_ge.x); + + secp256k1_fe_get_b32(c, &pr_ge.x); + secp256k1_scalar_set_b32(&computed_r, c, NULL); + return secp256k1_scalar_eq(sigr, &computed_r); +} +#else + secp256k1_scalar_get_b32(c, sigr); + secp256k1_fe_set_b32(&xr, c); + + /** We now have the recomputed R point in pr, and its claimed x coordinate (modulo n) + * in xr. Naively, we would extract the x coordinate from pr (requiring a inversion modulo p), + * compute the remainder modulo n, and compare it to xr. However: + * + * xr == X(pr) mod n + * <=> exists h. (xr + h * n < p && xr + h * n == X(pr)) + * [Since 2 * n > p, h can only be 0 or 1] + * <=> (xr == X(pr)) || (xr + n < p && xr + n == X(pr)) + * [In Jacobian coordinates, X(pr) is pr.x / pr.z^2 mod p] + * <=> (xr == pr.x / pr.z^2 mod p) || (xr + n < p && xr + n == pr.x / pr.z^2 mod p) + * [Multiplying both sides of the equations by pr.z^2 mod p] + * <=> (xr * pr.z^2 mod p == pr.x) || (xr + n < p && (xr + n) * pr.z^2 mod p == pr.x) + * + * Thus, we can avoid the inversion, but we have to check both cases separately. + * secp256k1_gej_eq_x implements the (xr * pr.z^2 mod p == pr.x) test. + */ + if (secp256k1_gej_eq_x_var(&xr, &pr)) { + /* xr * pr.z^2 mod p == pr.x, so the signature is valid. */ + return 1; + } + if (secp256k1_fe_cmp_var(&xr, &secp256k1_ecdsa_const_p_minus_order) >= 0) { + /* xr + n >= p, so we can skip testing the second case. */ + return 0; + } + secp256k1_fe_add(&xr, &secp256k1_ecdsa_const_order_as_fe); + if (secp256k1_gej_eq_x_var(&xr, &pr)) { + /* (xr + n) * pr.z^2 mod p == pr.x, so the signature is valid. */ + return 1; + } + return 0; +#endif +} + +static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid) { + unsigned char b[32]; + secp256k1_gej rp; + secp256k1_ge r; + secp256k1_scalar n; + int overflow = 0; + + secp256k1_ecmult_gen(ctx, &rp, nonce); + secp256k1_ge_set_gej(&r, &rp); + secp256k1_fe_normalize(&r.x); + secp256k1_fe_normalize(&r.y); + secp256k1_fe_get_b32(b, &r.x); + secp256k1_scalar_set_b32(sigr, b, &overflow); + /* These two conditions should be checked before calling */ + VERIFY_CHECK(!secp256k1_scalar_is_zero(sigr)); + VERIFY_CHECK(overflow == 0); + + if (recid) { + /* The overflow condition is cryptographically unreachable as hitting it requires finding the discrete log + * of some P where P.x >= order, and only 1 in about 2^127 points meet this criteria. + */ + *recid = (overflow ? 2 : 0) | (secp256k1_fe_is_odd(&r.y) ? 1 : 0); + } + secp256k1_scalar_mul(&n, sigr, seckey); + secp256k1_scalar_add(&n, &n, message); + secp256k1_scalar_inverse(sigs, nonce); + secp256k1_scalar_mul(sigs, sigs, &n); + secp256k1_scalar_clear(&n); + secp256k1_gej_clear(&rp); + secp256k1_ge_clear(&r); + if (secp256k1_scalar_is_zero(sigs)) { + return 0; + } + if (secp256k1_scalar_is_high(sigs)) { + secp256k1_scalar_negate(sigs, sigs); + if (recid) { + *recid ^= 1; + } + } + return 1; +} + +#endif /* SECP256K1_ECDSA_IMPL_H */ diff --git a/src/secp256k1_tests/eckey.h b/src/secp256k1_tests/eckey.h new file mode 100644 index 0000000..b621f1e --- /dev/null +++ b/src/secp256k1_tests/eckey.h @@ -0,0 +1,25 @@ +/********************************************************************** + * 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_ECKEY_H +#define SECP256K1_ECKEY_H + +#include + +#include "group.h" +#include "scalar.h" +#include "ecmult.h" +#include "ecmult_gen.h" + +static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size); +static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed); + +static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak); +static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak); +static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak); +static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak); + +#endif /* SECP256K1_ECKEY_H */ diff --git a/src/secp256k1_tests/eckey_impl.h b/src/secp256k1_tests/eckey_impl.h new file mode 100644 index 0000000..7c5b789 --- /dev/null +++ b/src/secp256k1_tests/eckey_impl.h @@ -0,0 +1,100 @@ +/********************************************************************** + * 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_ECKEY_IMPL_H +#define SECP256K1_ECKEY_IMPL_H + +#include "eckey.h" + +#include "scalar.h" +#include "field.h" +#include "group.h" +#include "ecmult_gen.h" + +static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size) { + if (size == 33 && (pub[0] == SECP256K1_TAG_PUBKEY_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_ODD)) { + secp256k1_fe x; + return secp256k1_fe_set_b32(&x, pub+1) && secp256k1_ge_set_xo_var(elem, &x, pub[0] == SECP256K1_TAG_PUBKEY_ODD); + } else if (size == 65 && (pub[0] == SECP256K1_TAG_PUBKEY_UNCOMPRESSED || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD)) { + secp256k1_fe x, y; + if (!secp256k1_fe_set_b32(&x, pub+1) || !secp256k1_fe_set_b32(&y, pub+33)) { + return 0; + } + secp256k1_ge_set_xy(elem, &x, &y); + if ((pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD) && + secp256k1_fe_is_odd(&y) != (pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD)) { + return 0; + } + return secp256k1_ge_is_valid_var(elem); + } else { + return 0; + } +} + +static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed) { + if (secp256k1_ge_is_infinity(elem)) { + return 0; + } + secp256k1_fe_normalize_var(&elem->x); + secp256k1_fe_normalize_var(&elem->y); + secp256k1_fe_get_b32(&pub[1], &elem->x); + if (compressed) { + *size = 33; + pub[0] = secp256k1_fe_is_odd(&elem->y) ? SECP256K1_TAG_PUBKEY_ODD : SECP256K1_TAG_PUBKEY_EVEN; + } else { + *size = 65; + pub[0] = SECP256K1_TAG_PUBKEY_UNCOMPRESSED; + secp256k1_fe_get_b32(&pub[33], &elem->y); + } + return 1; +} + +static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak) { + secp256k1_scalar_add(key, key, tweak); + if (secp256k1_scalar_is_zero(key)) { + return 0; + } + return 1; +} + +static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) { + secp256k1_gej pt; + secp256k1_scalar one; + secp256k1_gej_set_ge(&pt, key); + secp256k1_scalar_set_int(&one, 1); + secp256k1_ecmult(ctx, &pt, &pt, &one, tweak); + + if (secp256k1_gej_is_infinity(&pt)) { + return 0; + } + secp256k1_ge_set_gej(key, &pt); + return 1; +} + +static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak) { + if (secp256k1_scalar_is_zero(tweak)) { + return 0; + } + + secp256k1_scalar_mul(key, key, tweak); + return 1; +} + +static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) { + secp256k1_scalar zero; + secp256k1_gej pt; + if (secp256k1_scalar_is_zero(tweak)) { + return 0; + } + + secp256k1_scalar_set_int(&zero, 0); + secp256k1_gej_set_ge(&pt, key); + secp256k1_ecmult(ctx, &pt, &pt, tweak, &zero); + secp256k1_ge_set_gej(key, &pt); + return 1; +} + +#endif /* SECP256K1_ECKEY_IMPL_H */ diff --git a/src/secp256k1_tests/ecmult.h b/src/secp256k1_tests/ecmult.h new file mode 100644 index 0000000..3d75a96 --- /dev/null +++ b/src/secp256k1_tests/ecmult.h @@ -0,0 +1,48 @@ +/********************************************************************** + * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_ECMULT_H +#define SECP256K1_ECMULT_H + +#include "num.h" +#include "group.h" +#include "scalar.h" +#include "scratch.h" + +typedef struct { + /* For accelerating the computation of a*P + b*G: */ + secp256k1_ge_storage (*pre_g)[]; /* odd multiples of the generator */ +#ifdef USE_ENDOMORPHISM + secp256k1_ge_storage (*pre_g_128)[]; /* odd multiples of 2^128*generator */ +#endif +} secp256k1_ecmult_context; + +static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx); +static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb); +static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst, + const secp256k1_ecmult_context *src, const secp256k1_callback *cb); +static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx); +static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx); + +/** Double multiply: R = na*A + ng*G */ +static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng); + +typedef int (secp256k1_ecmult_multi_callback)(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *data); + +/** + * Multi-multiply: R = inp_g_sc * G + sum_i ni * Ai. + * Chooses the right algorithm for a given number of points and scratch space + * size. Resets and overwrites the given scratch space. If the points do not + * fit in the scratch space the algorithm is repeatedly run with batches of + * points. If no scratch space is given then a simple algorithm is used that + * simply multiplies the points with the corresponding scalars and adds them up. + * Returns: 1 on success (including when inp_g_sc is NULL and n is 0) + * 0 if there is not enough scratch space for a single point or + * callback returns 0 + */ +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); + +#endif /* SECP256K1_ECMULT_H */ diff --git a/src/secp256k1_tests/ecmult_const.h b/src/secp256k1_tests/ecmult_const.h new file mode 100644 index 0000000..d4804b8 --- /dev/null +++ b/src/secp256k1_tests/ecmult_const.h @@ -0,0 +1,17 @@ +/********************************************************************** + * 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_ECMULT_CONST_H +#define SECP256K1_ECMULT_CONST_H + +#include "scalar.h" +#include "group.h" + +/* Here `bits` should be set to the maximum bitlength of the _absolute value_ of `q`, plus + * one because we internally sometimes add 2 to the number during the WNAF conversion. */ +static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q, int bits); + +#endif /* SECP256K1_ECMULT_CONST_H */ diff --git a/src/secp256k1_tests/ecmult_const_impl.h b/src/secp256k1_tests/ecmult_const_impl.h new file mode 100644 index 0000000..8411752 --- /dev/null +++ b/src/secp256k1_tests/ecmult_const_impl.h @@ -0,0 +1,257 @@ +/********************************************************************** + * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_ECMULT_CONST_IMPL_H +#define SECP256K1_ECMULT_CONST_IMPL_H + +#include "scalar.h" +#include "group.h" +#include "ecmult_const.h" +#include "ecmult_impl.h" + +/* This is like `ECMULT_TABLE_GET_GE` but is constant time */ +#define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \ + int m; \ + int abs_n = (n) * (((n) > 0) * 2 - 1); \ + int idx_n = abs_n / 2; \ + secp256k1_fe neg_y; \ + VERIFY_CHECK(((n) & 1) == 1); \ + VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \ + VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \ + VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \ + VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \ + for (m = 0; m < ECMULT_TABLE_SIZE(w); m++) { \ + /* This loop is used to avoid secret data in array indices. See + * the comment in ecmult_gen_impl.h for rationale. */ \ + secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \ + secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \ + } \ + (r)->infinity = 0; \ + secp256k1_fe_negate(&neg_y, &(r)->y, 1); \ + secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \ +} while(0) + + +/** 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] an odd integer between -(1 << w) and (1 << w) + * - each wnaf[i] is nonzero + * - the number of words set is always WNAF_SIZE(w) + 1 + * + * Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar + * Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.) + * CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlagy Berlin Heidelberg 2003 + * + * Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335 + */ +static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w, int size) { + int global_sign; + int skew = 0; + int word = 0; + + /* 1 2 3 */ + int u_last; + int u; + + int flip; + int bit; + secp256k1_scalar neg_s; + int not_neg_one; + /* Note that we cannot handle even numbers by negating them to be odd, as is + * done in other implementations, since if our scalars were specified to have + * width < 256 for performance reasons, their negations would have width 256 + * and we'd lose any performance benefit. Instead, we use a technique from + * Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even) + * or 2 (for odd) to the number we are encoding, returning a skew value indicating + * this, and having the caller compensate after doing the multiplication. + * + * In fact, we _do_ want to negate numbers to minimize their bit-lengths (and in + * particular, to ensure that the outputs from the endomorphism-split fit into + * 128 bits). If we negate, the parity of our number flips, inverting which of + * {1, 2} we want to add to the scalar when ensuring that it's odd. Further + * complicating things, -1 interacts badly with `secp256k1_scalar_cadd_bit` and + * we need to special-case it in this logic. */ + flip = secp256k1_scalar_is_high(&s); + /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */ + 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); + secp256k1_scalar_cadd_bit(&s, bit, not_neg_one); + /* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects + * that we added two to it and flipped it. In fact for -1 these operations are + * identical. We only flipped, but since skewing is required (in the sense that + * the skew must be 1 or 2, never zero) and flipping is not, we need to change + * our flags to claim that we only skewed. */ + global_sign = secp256k1_scalar_cond_negate(&s, flip); + global_sign *= not_neg_one * 2 - 1; + skew = 1 << bit; + + /* 4 */ + u_last = secp256k1_scalar_shr_int(&s, w); + while (word * w < size) { + int sign; + int even; + + /* 4.1 4.4 */ + u = secp256k1_scalar_shr_int(&s, w); + /* 4.2 */ + even = ((u & 1) == 0); + sign = 2 * (u_last > 0) - 1; + u += sign * even; + u_last -= sign * even * (1 << w); + + /* 4.3, adapted for global sign change */ + wnaf[word++] = u_last * global_sign; + + u_last = u; + } + wnaf[word] = u * global_sign; + + VERIFY_CHECK(secp256k1_scalar_is_zero(&s)); + VERIFY_CHECK(word == WNAF_SIZE_BITS(size, w)); + return skew; +} + +static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar, int size) { + secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)]; + secp256k1_ge tmpa; + secp256k1_fe Z; + + int skew_1; +#ifdef USE_ENDOMORPHISM + secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)]; + int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)]; + int skew_lam; + secp256k1_scalar q_1, q_lam; +#endif + int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)]; + + int i; + secp256k1_scalar sc = *scalar; + + /* build wnaf representation for q. */ + int rsize = size; +#ifdef USE_ENDOMORPHISM + if (size > 128) { + rsize = 128; + /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */ + secp256k1_scalar_split_lambda(&q_1, &q_lam, &sc); + skew_1 = secp256k1_wnaf_const(wnaf_1, q_1, WINDOW_A - 1, 128); + skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A - 1, 128); + } else +#endif + { + skew_1 = secp256k1_wnaf_const(wnaf_1, sc, WINDOW_A - 1, size); +#ifdef USE_ENDOMORPHISM + skew_lam = 0; +#endif + } + + /* 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. + */ + secp256k1_gej_set_ge(r, a); + secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r); + for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { + secp256k1_fe_normalize_weak(&pre_a[i].y); + } +#ifdef USE_ENDOMORPHISM + if (size > 128) { + for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { + secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]); + } + } +#endif + + /* first loop iteration (separated out so we can directly set r, rather + * than having it start at infinity, get doubled several times, then have + * its new value added to it) */ + i = wnaf_1[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)]; + VERIFY_CHECK(i != 0); + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A); + secp256k1_gej_set_ge(r, &tmpa); +#ifdef USE_ENDOMORPHISM + if (size > 128) { + i = wnaf_lam[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)]; + VERIFY_CHECK(i != 0); + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A); + secp256k1_gej_add_ge(r, r, &tmpa); + } +#endif + /* remaining loop iterations */ + for (i = WNAF_SIZE_BITS(rsize, WINDOW_A - 1) - 1; i >= 0; i--) { + int n; + int j; + for (j = 0; j < WINDOW_A - 1; ++j) { + secp256k1_gej_double_nonzero(r, r, NULL); + } + + n = wnaf_1[i]; + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A); + VERIFY_CHECK(n != 0); + secp256k1_gej_add_ge(r, r, &tmpa); +#ifdef USE_ENDOMORPHISM + if (size > 128) { + n = wnaf_lam[i]; + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A); + VERIFY_CHECK(n != 0); + secp256k1_gej_add_ge(r, r, &tmpa); + } +#endif + } + + secp256k1_fe_mul(&r->z, &r->z, &Z); + + { + /* Correct for wNAF skew */ + secp256k1_ge correction = *a; + secp256k1_ge_storage correction_1_stor; +#ifdef USE_ENDOMORPHISM + secp256k1_ge_storage correction_lam_stor; +#endif + secp256k1_ge_storage a2_stor; + secp256k1_gej tmpj; + secp256k1_gej_set_ge(&tmpj, &correction); + secp256k1_gej_double_var(&tmpj, &tmpj, NULL); + secp256k1_ge_set_gej(&correction, &tmpj); + secp256k1_ge_to_storage(&correction_1_stor, a); +#ifdef USE_ENDOMORPHISM + if (size > 128) { + secp256k1_ge_to_storage(&correction_lam_stor, a); + } +#endif + secp256k1_ge_to_storage(&a2_stor, &correction); + + /* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */ + secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2); +#ifdef USE_ENDOMORPHISM + if (size > 128) { + secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2); + } +#endif + + /* Apply the correction */ + secp256k1_ge_from_storage(&correction, &correction_1_stor); + secp256k1_ge_neg(&correction, &correction); + secp256k1_gej_add_ge(r, r, &correction); + +#ifdef USE_ENDOMORPHISM + if (size > 128) { + secp256k1_ge_from_storage(&correction, &correction_lam_stor); + secp256k1_ge_neg(&correction, &correction); + secp256k1_ge_mul_lambda(&correction, &correction); + secp256k1_gej_add_ge(r, r, &correction); + } +#endif + } +} + +#endif /* SECP256K1_ECMULT_CONST_IMPL_H */ diff --git a/src/secp256k1_tests/ecmult_gen.h b/src/secp256k1_tests/ecmult_gen.h new file mode 100644 index 0000000..7564b70 --- /dev/null +++ b/src/secp256k1_tests/ecmult_gen.h @@ -0,0 +1,43 @@ +/********************************************************************** + * 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_ECMULT_GEN_H +#define SECP256K1_ECMULT_GEN_H + +#include "scalar.h" +#include "group.h" + +typedef struct { + /* For accelerating the computation of a*G: + * To harden against timing attacks, use the following mechanism: + * * Break up the multiplicand into groups of 4 bits, called n_0, n_1, n_2, ..., n_63. + * * Compute sum(n_i * 16^i * G + U_i, i=0..63), where: + * * U_i = U * 2^i (for i=0..62) + * * U_i = U * (1-2^63) (for i=63) + * where U is a point with no known corresponding scalar. Note that sum(U_i, i=0..63) = 0. + * For each i, and each of the 16 possible values of n_i, (n_i * 16^i * G + U_i) is + * precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0..63). + * None of the resulting prec group elements have a known scalar, and neither do any of + * the intermediate sums while computing a*G. + */ + secp256k1_ge_storage (*prec)[64][16]; /* prec[j][i] = 16^j * i * G + U_i */ + secp256k1_scalar blind; + secp256k1_gej initial; +} secp256k1_ecmult_gen_context; + +static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context* ctx); +static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx, const secp256k1_callback* cb); +static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context *dst, + const secp256k1_ecmult_gen_context* src, const secp256k1_callback* cb); +static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context* ctx); +static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx); + +/** Multiply with the generator: R = a*G */ +static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context* ctx, secp256k1_gej *r, const secp256k1_scalar *a); + +static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32); + +#endif /* SECP256K1_ECMULT_GEN_H */ diff --git a/src/secp256k1_tests/ecmult_gen_impl.h b/src/secp256k1_tests/ecmult_gen_impl.h new file mode 100644 index 0000000..d64505d --- /dev/null +++ b/src/secp256k1_tests/ecmult_gen_impl.h @@ -0,0 +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); + } + 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_tests/ecmult_impl.h b/src/secp256k1_tests/ecmult_impl.h new file mode 100644 index 0000000..1986914 --- /dev/null +++ b/src/secp256k1_tests/ecmult_impl.h @@ -0,0 +1,1181 @@ +/***************************************************************************** + * 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 +#include + +#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(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; + + 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); + } + + /* 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); + +#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); + } +#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 (sizeof(secp256k1_gej) << bucket_window) + 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, sizeof(*buckets) << bucket_window); + + 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< 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; +} + +/* Computes ecmult_multi by simply multiplying and adding each point. Does not + * require a scratch space */ +static int secp256k1_ecmult_multi_simple_var(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points) { + size_t point_idx; + secp256k1_scalar szero; + secp256k1_gej tmpj; + + secp256k1_scalar_set_int(&szero, 0); + secp256k1_gej_set_infinity(r); + secp256k1_gej_set_infinity(&tmpj); + /* r = inp_g_sc*G */ + secp256k1_ecmult(ctx, r, &tmpj, &szero, inp_g_sc); + for (point_idx = 0; point_idx < n_points; point_idx++) { + secp256k1_ge point; + secp256k1_gej pointj; + secp256k1_scalar scalar; + if (!cb(&scalar, &point, point_idx, cbdata)) { + return 0; + } + /* r += scalar*point */ + secp256k1_gej_set_ge(&pointj, &point); + secp256k1_ecmult(ctx, &tmpj, &pointj, &scalar, NULL); + secp256k1_gej_add_var(r, r, &tmpj, NULL); + } + return 1; +} + +/* Compute the number of batches and the batch size given the maximum batch size and the + * total number of points */ +static int secp256k1_ecmult_multi_batch_size_helper(size_t *n_batches, size_t *n_batch_points, size_t max_n_batch_points, size_t n) { + if (max_n_batch_points == 0) { + return 0; + } + if (max_n_batch_points > ECMULT_MAX_POINTS_PER_BATCH) { + max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH; + } + if (n == 0) { + *n_batches = 0; + *n_batch_points = 0; + return 1; + } + /* Compute ceil(n/max_n_batch_points) and ceil(n/n_batches) */ + *n_batches = 1 + (n - 1) / max_n_batch_points; + *n_batch_points = 1 + (n - 1) / *n_batches; + return 1; +} + +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 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; + } + if (scratch == NULL) { + return secp256k1_ecmult_multi_simple_var(ctx, r, inp_g_sc, cb, cbdata, n); + } + + /* Compute the batch sizes for pippenger given a scratch space. If it's greater than a threshold + * use pippenger. Otherwise use strauss */ + if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_pippenger_max_points(scratch), n)) { + return 0; + } + if (n_batch_points >= ECMULT_PIPPENGER_THRESHOLD) { + f = secp256k1_ecmult_pippenger_batch; + } else { + if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_strauss_max_points(scratch), n)) { + return 0; + } + 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_tests/ecmult_static_context.h b/src/secp256k1_tests/ecmult_static_context.h new file mode 100644 index 0000000..61d9373 --- /dev/null +++ b/src/secp256k1_tests/ecmult_static_context.h @@ -0,0 +1,1160 @@ +#ifndef _SECP256K1_ECMULT_STATIC_CONTEXT_ +#define _SECP256K1_ECMULT_STATIC_CONTEXT_ +#include "group.h" +#define SC SECP256K1_GE_STORAGE_CONST +static const secp256k1_ge_storage secp256k1_ecmult_static_context[64][16] = { +{ + SC(983487347u, 1861041900u, 2599115456u, 565528146u, 1451326239u, 148794576u, 4224640328u, 3120843701u, 2076989736u, 3184115747u, 3754320824u, 2656004457u, 2876577688u, 2388659905u, 3527541004u, 1170708298u), + SC(3830281845u, 3284871255u, 1309883393u, 2806991612u, 1558611192u, 1249416977u, 1614773327u, 1353445208u, 633124399u, 4264439010u, 426432620u, 167800352u, 2355417627u, 2991792291u, 3042397084u, 505150283u), + SC(1792710820u, 2165839471u, 3876070801u, 3603801374u, 2437636273u, 1231643248u, 860890267u, 4002236272u, 3258245037u, 4085545079u, 2695347418u, 288209541u, 484302592u, 139267079u, 14621978u, 2750167787u), + SC(11094760u, 1663454715u, 3104893589u, 1290390142u, 1334245677u, 2671416785u, 3982578986u, 2050971459u, 2136209393u, 1792200847u, 367473428u, 114820199u, 1096121039u, 425028623u, 3983611854u, 923011107u), + SC(3063072592u, 3527226996u, 3276923831u, 3785926779u, 346414977u, 2234429237u, 547163845u, 1847763663u, 2978762519u, 623753375u, 2207114031u, 3006533282u, 3147176505u, 1421052999u, 4188545436u, 1210097867u), + SC(1763690305u, 2162645845u, 1202943473u, 469109438u, 1159538654u, 390308918u, 1603161004u, 2906790921u, 2394291613u, 4089459264u, 1827402608u, 2166723935u, 3207526147u, 1197293526u, 436375990u, 1773481373u), + SC(1882939156u, 2815960179u, 295089455u, 2929502411u, 2990911492u, 2056857815u, 3502518067u, 957616604u, 1591168682u, 1240626880u, 1298264859u, 1839469436u, 3185927997u, 2386526557u, 4025121105u, 260593756u), + SC(699984967u, 3527536033u, 3843799838u, 958940236u, 927446270u, 2095887205u, 733758855u, 793790581u, 2288595512u, 2237855935u, 4158071588u, 103726164u, 1804839263u, 2006149890u, 3944535719u, 3558448075u), + SC(1145702317u, 3893958345u, 851308226u, 566580932u, 1803510929u, 244954233u, 754894895u, 1321302288u, 772295727u, 4004336128u, 2009158070u, 4026087258u, 1899732245u, 1392930957u, 3019192545u, 149625039u), + SC(3772604811u, 577564124u, 4116730494u, 548732504u, 241159976u, 965811878u, 3286803623u, 3781136673u, 2690883927u, 863484863u, 463101630u, 2948469162u, 1712070245u, 3742601912u, 2535479384u, 1015456764u), + SC(2610513434u, 780361970u, 4072278968u, 3165566617u, 362677842u, 1775830058u, 4195110448u, 2813784845u, 1072168452u, 1018450691u, 1028609376u, 2101464438u, 2419500187u, 2190549840u, 1837865365u, 625038589u), + SC(1347265449u, 3654928411u, 3255194520u, 1322421425u, 3049188507u, 1827004342u, 3467202132u, 4261348427u, 3419671838u, 2239837129u, 3441474020u, 268041876u, 4157379961u, 971431753u, 2053887746u, 2038404815u), + SC(3723233964u, 515696298u, 2908946645u, 1626400003u, 2191461318u, 1201029625u, 186243574u, 1212380923u, 858781105u, 4236445790u, 1936144063u, 1009147468u, 2407567966u, 1865959325u, 1701035060u, 241151649u), + SC(3696430315u, 3089900654u, 1103438577u, 3528924465u, 1259662835u, 2438429227u, 1692672370u, 2989843137u, 1446894995u, 2239587625u, 2340544036u, 434491102u, 128239031u, 2734594294u, 2667284742u, 1865591178u), + SC(1980028431u, 1099813170u, 2013628738u, 4214038867u, 3231891435u, 3896266769u, 2756820145u, 1490749299u, 951981230u, 3655451652u, 1676645053u, 3593230746u, 3010864552u, 405419875u, 1336073872u, 1398624425u), + SC(3414779716u, 2008156201u, 4125277506u, 2287126283u, 2446053551u, 212726297u, 2794923956u, 3421277562u, 1460719994u, 552209919u, 2551004934u, 953727248u, 3096710400u, 3712627263u, 3614955842u, 557715603u) +}, +{ + SC(461660907u, 483260338u, 3090624303u, 3468817529u, 2869411999u, 3408320195u, 157674611u, 1298485121u, 103769941u, 3030878493u, 1440637991u, 4223892787u, 3840844824u, 2730509202u, 2748389383u, 214732837u), + SC(4143598594u, 459898515u, 2922648667u, 1209678535u, 1176716252u, 1612841999u, 2202917330u, 13015901u, 1575346251u, 891263272u, 3091905261u, 3543244385u, 3935435865u, 2372913859u, 1075649255u, 201888830u), + SC(3481295448u, 3640243220u, 2859715852u, 3846556079u, 1065182531u, 2330293896u, 2178091110u, 3893510868u, 4099261975u, 2577582684u, 4207143791u, 589834100u, 2090766670u, 4242818989u, 2413240316u, 1338191979u), + SC(1222367653u, 2295459885u, 1856816550u, 918616911u, 3733449540u, 288527426u, 308654335u, 175301747u, 2585816357u, 1572985110u, 3820086017u, 3400646033u, 3928615806u, 2543586180u, 1619974000u, 1257448912u), + SC(3467862907u, 681146163u, 2909728989u, 83906098u, 2626131995u, 3872919971u, 2290108548u, 1697087700u, 1793941143u, 3236443826u, 1940064764u, 1563989881u, 527371209u, 610869743u, 1604941439u, 3670721525u), + SC(2302729378u, 1391194029u, 1641771531u, 3876177737u, 1929557473u, 2752989331u, 2519109900u, 1131448856u, 3786463166u, 506905989u, 2345013855u, 2144715811u, 1583628159u, 291930150u, 3243470493u, 4130365181u), + SC(2855519179u, 3147287790u, 1536116015u, 1784764672u, 959281397u, 3099717666u, 86403980u, 3409201632u, 3921301684u, 2101228153u, 575924517u, 1382150904u, 641478876u, 3860064926u, 1937521554u, 2358132463u), + SC(972265053u, 3025511526u, 2467192450u, 4011934802u, 4015820825u, 3179306985u, 1744647725u, 423238442u, 2406064939u, 901607195u, 3316491016u, 4128592049u, 1397491632u, 439641584u, 90500461u, 2834580417u), + SC(1730532518u, 2821193463u, 2700804628u, 2416923244u, 3795632308u, 2799866320u, 3434703577u, 3883111373u, 1777933228u, 2963254493u, 3042948878u, 1746288680u, 2832145340u, 544625602u, 3633879343u, 2300858165u), + SC(62331695u, 2228442612u, 3527845246u, 2989876118u, 3995298903u, 3601545798u, 4170931516u, 445717530u, 1981201926u, 94264130u, 2668647577u, 953251412u, 3322279962u, 3837653687u, 3116466555u, 3369796531u), + SC(2739333573u, 3637259489u, 443756582u, 825678124u, 2455706402u, 2994548791u, 3653546249u, 2584145078u, 1245698352u, 89066746u, 1738138166u, 2916153640u, 1850062717u, 3472193431u, 2110631011u, 1214009088u), + SC(2386327178u, 3993497770u, 1051345891u, 4137183237u, 3078790224u, 3598213568u, 3344610192u, 1517270932u, 869515922u, 2057215060u, 2792454282u, 4228826509u, 3425305972u, 2708629086u, 880185559u, 1356729037u), + SC(2989561710u, 3550122639u, 1990591383u, 2036612756u, 3588709655u, 595888062u, 4189293408u, 1955008963u, 987876526u, 542093629u, 1953520395u, 2315684331u, 2929815182u, 3270759899u, 393611756u, 1677885197u), + SC(2331762734u, 371120497u, 1141333410u, 3466824114u, 4113916626u, 3698793791u, 2483365276u, 4265751258u, 3804325409u, 4085909553u, 3531838853u, 2629626707u, 625187055u, 3045263564u, 198131065u, 3993694760u), + SC(27419592u, 3267954699u, 2966738458u, 3143461717u, 3869766944u, 2163162934u, 1886283869u, 2052225367u, 958768216u, 2006727717u, 2069130137u, 1939449196u, 3015752138u, 258766841u, 3290132621u, 4163970366u), + SC(903383785u, 2983456345u, 4269392462u, 3731664159u, 1837248343u, 1888413004u, 652691803u, 897487558u, 3732206419u, 3625013640u, 1917594162u, 967935585u, 1804564817u, 883883125u, 2389854768u, 2347234078u) +}, +{ + SC(1793692126u, 406948681u, 23075151u, 2805328754u, 3264854407u, 427926777u, 2859563730u, 198037267u, 2129133850u, 1089701106u, 3842694445u, 2533380467u, 663211132u, 2312829798u, 807127373u, 38506815u), + SC(571890638u, 3882751380u, 1536180709u, 3437159763u, 3953528399u, 516828575u, 3769463872u, 1449076325u, 4270798907u, 3135758980u, 3520630973u, 1452980147u, 3957715387u, 3054428574u, 2391664223u, 2297670550u), + SC(2724204046u, 2456139736u, 265045669u, 1367810338u, 1722635060u, 1306450931u, 2894913322u, 3094293390u, 3490680992u, 2550020195u, 3028635086u, 4200216295u, 1066664286u, 4170330175u, 777827015u, 183484181u), + SC(947228665u, 1559209921u, 3080864826u, 3123295835u, 2934045313u, 1590990229u, 2766960143u, 3113606941u, 1136432319u, 3758046297u, 2054046144u, 1377389889u, 3244301201u, 127071274u, 1752358610u, 2783507663u), + SC(1460807831u, 3649051054u, 2799484569u, 1231562901u, 3377754600u, 3577118892u, 1234337315u, 380370215u, 3272388869u, 3656237932u, 2653126291u, 786263023u, 1028996455u, 4274234235u, 4225822550u, 10734444u), + SC(2071087047u, 1934036755u, 611830132u, 2015415885u, 1373497691u, 3709112893u, 3810392851u, 1519037663u, 779113716u, 2738053543u, 2754096050u, 2121500804u, 982626833u, 1064427872u, 1627071029u, 1799421889u), + SC(490669665u, 331510235u, 927653097u, 4010558541u, 1341899186u, 2739641489u, 1436050289u, 1379364712u, 441190387u, 3816107121u, 4151493979u, 3530159022u, 2848669857u, 2894763699u, 1938279708u, 3206735972u), + SC(1164630680u, 735028522u, 1426163473u, 1764145219u, 2188722839u, 2599797011u, 2331123230u, 996298865u, 2803113036u, 1732133918u, 4135374745u, 1403496102u, 61305906u, 1982207767u, 35608603u, 680731708u), + SC(3097030574u, 2239944926u, 3004506636u, 3698971324u, 438440050u, 806226289u, 3299217652u, 2137747676u, 2376642592u, 2372355096u, 1444993877u, 4198291752u, 3194432604u, 579432496u, 3143260503u, 58153128u), + SC(3073570790u, 2457870973u, 3254087300u, 132589961u, 3090464363u, 4031655485u, 3397735349u, 3738272915u, 2438408586u, 1610016484u, 3607490511u, 1979839295u, 1993157220u, 1628966973u, 2566520843u, 2415504793u), + SC(2516700697u, 2521039798u, 2777488721u, 3196543385u, 3593950703u, 2445108602u, 4227515375u, 3361503440u, 3741757104u, 1367007706u, 4282009789u, 2127358709u, 2970274265u, 108953332u, 1376097231u, 3612352600u), + SC(2841122028u, 289695603u, 908429972u, 1449591303u, 3496532142u, 430811028u, 1377898285u, 198605765u, 702014643u, 1582973696u, 1654127041u, 4145703462u, 294032334u, 4235431914u, 3438393459u, 865474483u), + SC(3545445168u, 3333415739u, 2928811023u, 1435493501u, 3112072977u, 3466119300u, 61597844u, 839813414u, 3787328278u, 1928915478u, 3046796186u, 549615137u, 3862451403u, 1325262296u, 3520760105u, 1333228419u), + SC(1325790793u, 3907821545u, 4134901119u, 1951705246u, 3223387882u, 561480379u, 1136389443u, 2963679361u, 3722857515u, 626885912u, 3665060294u, 2975869036u, 1378007717u, 1212143055u, 3672021732u, 2520983812u), + SC(436660944u, 1593040065u, 2835874356u, 3054866405u, 1746716106u, 2901130226u, 3275156703u, 889550475u, 1667636846u, 2171317649u, 477876339u, 169193861u, 3301423024u, 2923695575u, 1084572294u, 981889567u), + SC(3803276281u, 4055280968u, 3904809427u, 186227966u, 932166956u, 2399165660u, 3851784532u, 3001852135u, 813014380u, 4116676373u, 2706810629u, 527442580u, 120296772u, 3128162880u, 662936789u, 1729392771u) +}, +{ + SC(1686440452u, 1988561476u, 754604000u, 1313277943u, 3972816537u, 316394247u, 994407191u, 1904170630u, 2086644946u, 2443632379u, 2709748921u, 1003213045u, 3157743406u, 1758245536u, 3227689301u, 1181052876u), + SC(1258105424u, 4154135555u, 2219123623u, 3901620566u, 4152326230u, 2255006844u, 2043811343u, 3401743053u, 1077175625u, 4217078864u, 23446180u, 3296093630u, 2983403379u, 483875022u, 1821322007u, 933769937u), + SC(4094896192u, 2631249021u, 2047644402u, 1580854103u, 3103587285u, 3577080832u, 2726417365u, 309664155u, 1801899606u, 2578001137u, 150353312u, 1950478529u, 895600852u, 3405805048u, 2316670682u, 3067768105u), + SC(443311827u, 441757202u, 1505167796u, 3339695156u, 4080303377u, 2032258566u, 4249816510u, 3524388084u, 3057881006u, 1951550910u, 755229308u, 2331249069u, 1739558582u, 2222328965u, 511821487u, 2764767310u), + SC(989753134u, 2338266356u, 549068233u, 4113024610u, 2746193091u, 2634969710u, 3079940655u, 3384912157u, 143838693u, 4047635856u, 4286586687u, 149695182u, 1777393012u, 52209639u, 2932952119u, 3267437714u), + SC(682610480u, 2717190045u, 3874701500u, 2657184992u, 2055845501u, 1316949440u, 1867841182u, 3514766617u, 3083609836u, 2586162565u, 866399081u, 1085717952u, 3259379257u, 575055971u, 3866877694u, 451222497u), + SC(328731030u, 2942825188u, 1841689481u, 3492191519u, 967390237u, 99172838u, 3036642267u, 3931425637u, 933459735u, 3523655044u, 2662830483u, 2533317360u, 1151283556u, 1285468956u, 15891850u, 3194406721u), + SC(3082245252u, 2305218459u, 2853219703u, 1279555698u, 3695999195u, 2225441691u, 2702374346u, 2002979755u, 3394310641u, 1438568303u, 441738339u, 2319547123u, 745721770u, 3663132780u, 3613740038u, 3163545587u), + SC(3109530474u, 209548946u, 1705898345u, 1227555051u, 1300903197u, 521706788u, 1046889791u, 392785355u, 1195852439u, 1128202903u, 589172095u, 3844020294u, 989062243u, 3765536158u, 3601935109u, 563198009u), + SC(1408383323u, 2941773350u, 4185382573u, 3662857379u, 4172908289u, 4118722458u, 1935569844u, 1296819381u, 439467796u, 917888253u, 1573015538u, 2875181025u, 22626495u, 313409715u, 121133518u, 1579603291u), + SC(838355261u, 2323744266u, 929233883u, 1533162328u, 2939669145u, 1021427197u, 2448693967u, 1568998094u, 455286333u, 2516902543u, 1708158744u, 278073872u, 978123683u, 2512836694u, 3972232382u, 1433020779u), + SC(2010810703u, 4018381427u, 571706262u, 1692351234u, 4256546562u, 1231266051u, 268479287u, 2820752911u, 2261632188u, 845795375u, 3555293251u, 4247559674u, 3383569817u, 4149228066u, 180667610u, 1402241180u), + SC(3525485702u, 3451430050u, 2349871300u, 60510511u, 4165534527u, 3431222792u, 4244473672u, 526926602u, 763199050u, 672899723u, 1978849638u, 489006191u, 1575850086u, 1948428588u, 201110001u, 2038136322u), + SC(3829603224u, 567257667u, 2324557421u, 3080821304u, 1922441927u, 1741539649u, 2023385976u, 3349327437u, 1997432110u, 3734074051u, 1330703636u, 3180299184u, 1913578229u, 141656008u, 2692604045u, 1602929664u), + SC(29051889u, 27392875u, 2013870801u, 1608859787u, 4192290684u, 944038467u, 2706126772u, 4086572363u, 3654238115u, 631287070u, 4277765317u, 2361271762u, 4170133585u, 2022489410u, 2834765713u, 1378478404u), + SC(2835113470u, 3839837803u, 3596950757u, 2129670392u, 1881028173u, 4057879348u, 2459142230u, 3736551989u, 3032996358u, 1333513239u, 3006303259u, 3885122327u, 4228039994u, 134788219u, 3631677646u, 450886807u) +}, +{ + SC(2450731413u, 2768047193u, 2114778718u, 2363611449u, 3811833768u, 1142236074u, 836975073u, 719658637u, 89564040u, 2055034782u, 2279505737u, 2354364196u, 748992674u, 2341838369u, 3471590741u, 3103440079u), + SC(464369172u, 1784969737u, 2303680721u, 1699015058u, 1839678160u, 53342253u, 3929309179u, 3713202491u, 1764215120u, 2190365769u, 3137266333u, 3919018972u, 3446276485u, 1027535494u, 3649392538u, 1979045036u), + SC(3689697965u, 1535268856u, 4095087266u, 1879342666u, 1901613989u, 4062220771u, 1231692686u, 3479254943u, 517178359u, 3704348661u, 3200159500u, 592930780u, 3995209641u, 2367381241u, 1790597847u, 2276745810u), + SC(1563410665u, 2779883331u, 320555798u, 143478861u, 1984047202u, 2486036480u, 1819096593u, 876845470u, 4160262809u, 1685665332u, 1096211683u, 3396846267u, 1079209808u, 1622135728u, 2746449213u, 2258485533u), + SC(1981422448u, 2212169687u, 873443773u, 3576733408u, 3923794933u, 1875069523u, 3053667173u, 4292418240u, 2192702144u, 1027092432u, 278807989u, 2315740043u, 485097259u, 4099751129u, 1350843241u, 1137138810u), + SC(3929635582u, 2647315129u, 1255145681u, 2059161179u, 1939751218u, 2574940312u, 1013734441u, 3958841903u, 615021475u, 1092396560u, 1516857705u, 4167743313u, 744612233u, 1609870616u, 1905505775u, 2106400820u), + SC(1036005687u, 2272703162u, 2208830030u, 2182996589u, 441615709u, 3591433922u, 3586649797u, 164179585u, 3077875769u, 1792522157u, 2657252843u, 657567108u, 656390324u, 1816007391u, 3075467586u, 3873231707u), + SC(1236896749u, 2895887291u, 1978987518u, 822801819u, 516389325u, 1102535042u, 1787993035u, 3557481093u, 3231661433u, 991180576u, 3686912074u, 1297456949u, 3327185778u, 308709174u, 495078044u, 2969592590u), + SC(2019907021u, 744703189u, 2139199843u, 518542186u, 3124680574u, 142934434u, 551498542u, 3021773546u, 4091561632u, 1051317147u, 825719313u, 3707224763u, 335483791u, 4028731434u, 1335000639u, 4102709448u), + SC(1093818871u, 985937516u, 327542691u, 2046117782u, 1264752065u, 697293694u, 1615263505u, 1156460629u, 2812684388u, 1192736815u, 3019618111u, 4209127823u, 2556369187u, 2112950523u, 637809851u, 2176824541u), + SC(1687299893u, 3728297084u, 490922479u, 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1662956706u, 911938094u, 3456789397u, 2082200558u, 947098788u, 4036848108u, 2455542339u, 1466205449u, 4158358953u, 586549709u, 850657486u, 61343079u, 2292663847u), + SC(3487862268u, 4116082621u, 1969417576u, 1466595601u, 3136251120u, 3697533272u, 438943523u, 1041892750u, 1141661777u, 435333448u, 3031876514u, 2121342186u, 209290199u, 256519609u, 1400190683u, 4260080502u) +}, +{ + SC(1406628534u, 2978091511u, 343468499u, 973866526u, 757277528u, 1142388839u, 2945536141u, 3759469101u, 3001571847u, 2170606364u, 1017327004u, 3120716036u, 468321128u, 3656061918u, 2331571461u, 1930702552u), + SC(3117811324u, 4230396490u, 526101390u, 3589443580u, 12282838u, 3055128772u, 453582536u, 750425919u, 87216299u, 1999749165u, 2446098001u, 1907762611u, 183870981u, 3643605669u, 4232900175u, 2946539195u), + SC(3903405291u, 1034986659u, 2587588236u, 1880077572u, 1696686560u, 1243434386u, 3746745675u, 2212912696u, 2031851135u, 575946730u, 2663616094u, 2706019532u, 2635197066u, 1942621203u, 3760379195u, 4173271368u), + SC(2892050679u, 1105289247u, 1519565685u, 2426902952u, 65580444u, 3373395323u, 2112756687u, 3658806066u, 2548718870u, 3586646888u, 3350821933u, 1921239811u, 4061525916u, 3520594550u, 1872307168u, 3464547908u), + SC(2889143489u, 489507550u, 788811400u, 1800916293u, 3249681744u, 1400920516u, 3917828215u, 1093821500u, 1905385813u, 2931012984u, 1800788801u, 1697549042u, 3133274419u, 3606456099u, 2156683634u, 3205410986u), + SC(2814687995u, 4053305746u, 484530004u, 410862009u, 246830045u, 3164065541u, 3723774424u, 3388961612u, 3438413619u, 3662326637u, 2178649434u, 3555798301u, 164350275u, 2341607004u, 3896269562u, 1591806179u), + SC(3226183767u, 3881369008u, 700458770u, 376569395u, 2607908019u, 1353553198u, 2636334721u, 1140283021u, 2632309194u, 1710844790u, 3031461719u, 4081969123u, 3326745889u, 4034909949u, 3950856167u, 3153389256u), + SC(2184243175u, 2166726232u, 3921103433u, 872887260u, 623636347u, 95935618u, 2766774027u, 697875047u, 164043041u, 993154257u, 4114304816u, 3500729957u, 409872172u, 3504722710u, 2806324915u, 717798207u), + SC(1913401183u, 1684394893u, 957780895u, 2366199383u, 3846687839u, 2225031745u, 50628017u, 764720583u, 2251658783u, 1601491318u, 3836612294u, 3836982164u, 1834686310u, 4239983357u, 2677791106u, 718595268u), + SC(641418698u, 3008658673u, 1590313857u, 1025261614u, 1545641278u, 883067087u, 405447843u, 251932751u, 890679795u, 1380695500u, 4259157180u, 4219905082u, 665298826u, 4240175069u, 1720908833u, 2268480568u), + SC(1323007329u, 2757671761u, 531677728u, 1863777888u, 1512057206u, 2416428007u, 297355401u, 2843988168u, 3028483811u, 4269951770u, 844221740u, 1060678479u, 2913804270u, 3550002834u, 1490208797u, 2041637686u), + SC(4098631786u, 3088674341u, 2277647863u, 546429701u, 239595915u, 96051385u, 2043858235u, 356783975u, 3081379864u, 1495630942u, 1713035648u, 2797737429u, 4252005067u, 1174473008u, 182861961u, 1284115192u), + SC(1497340893u, 2990980382u, 435071738u, 25048206u, 1369038540u, 2388914024u, 3985375113u, 3187649864u, 1375850783u, 2762762203u, 3714513839u, 1546363407u, 2343675571u, 416152492u, 1797618344u, 3540898582u), + SC(2184924310u, 2347360549u, 640504537u, 1253044800u, 1440674061u, 1666425671u, 3827600864u, 2022304946u, 2918906490u, 263308814u, 3892002350u, 1942380643u, 1520343008u, 1245225248u, 3081248535u, 2098883649u), + SC(2377054091u, 3295547231u, 2240796492u, 1757295037u, 62158041u, 1809272299u, 4005194159u, 1592984938u, 366675588u, 3144502911u, 2973082795u, 4105706826u, 2851896979u, 3262002710u, 3082369242u, 634669574u), + SC(729159370u, 3948971047u, 1511320403u, 3061460707u, 3090283349u, 1868816562u, 3759558902u, 3868199437u, 2438888892u, 1660478281u, 2415784493u, 3546303863u, 3144683831u, 3066258755u, 2228021651u, 3294706852u) +} +}; +#undef SC +#endif diff --git a/src/secp256k1_tests/field.h b/src/secp256k1_tests/field.h new file mode 100644 index 0000000..bb6692a --- /dev/null +++ b/src/secp256k1_tests/field.h @@ -0,0 +1,132 @@ +/********************************************************************** + * 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_FIELD_H +#define SECP256K1_FIELD_H + +/** Field element module. + * + * Field elements can be represented in several ways, but code accessing + * it (and implementations) need to take certain properties into account: + * - Each field element can be normalized or not. + * - Each field element has a magnitude, which represents how far away + * its representation is away from normalization. Normalized elements + * always have a magnitude of 1, but a magnitude of 1 doesn't imply + * normality. + */ + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#if defined(USE_FIELD_10X26) +#include "field_10x26.h" +#elif defined(USE_FIELD_5X52) +#include "field_5x52.h" +#else +#error "Please select field implementation" +#endif + +#include "util.h" + +/** Normalize a field element. */ +static void secp256k1_fe_normalize(secp256k1_fe *r); + +/** Weakly normalize a field element: reduce it magnitude to 1, but don't fully normalize. */ +static void secp256k1_fe_normalize_weak(secp256k1_fe *r); + +/** Normalize a field element, without constant-time guarantee. */ +static void secp256k1_fe_normalize_var(secp256k1_fe *r); + +/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field + * implementation may optionally normalize the input, but this should not be relied upon. */ +static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r); + +/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field + * implementation may optionally normalize the input, but this should not be relied upon. */ +static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r); + +/** Set a field element equal to a small integer. Resulting field element is normalized. */ +static void secp256k1_fe_set_int(secp256k1_fe *r, int a); + +/** Sets a field element equal to zero, initializing all fields. */ +static void secp256k1_fe_clear(secp256k1_fe *a); + +/** Verify whether a field element is zero. Requires the input to be normalized. */ +static int secp256k1_fe_is_zero(const secp256k1_fe *a); + +/** Check the "oddness" of a field element. Requires the input to be normalized. */ +static int secp256k1_fe_is_odd(const secp256k1_fe *a); + +/** Compare two field elements. Requires magnitude-1 inputs. */ +static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b); + +/** Same as secp256k1_fe_equal, but may be variable time. */ +static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b); + +/** Compare two field elements. Requires both inputs to be normalized */ +static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b); + +/** Set a field element equal to 32-byte big endian value. If successful, the resulting field element is normalized. */ +static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a); + +/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */ +static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a); + +/** Set a field element equal to the additive inverse of another. Takes a maximum magnitude of the input + * as an argument. The magnitude of the output is one higher. */ +static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m); + +/** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that + * small integer. */ +static void secp256k1_fe_mul_int(secp256k1_fe *r, int a); + +/** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */ +static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a); + +/** Sets a field element to be the product of two others. Requires the inputs' magnitudes to be at most 8. + * The output magnitude is 1 (but not guaranteed to be normalized). */ +static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b); + +/** Sets a field element to be the square of another. Requires the input's magnitude to be at most 8. + * The output magnitude is 1 (but not guaranteed to be normalized). */ +static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a); + +/** If a has a square root, it is computed in r and 1 is returned. If a does not + * have a square root, the root of its negation is computed and 0 is returned. + * The input's magnitude can be at most 8. The output magnitude is 1 (but not + * guaranteed to be normalized). The result in r will always be a square + * itself. */ +static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a); + +/** Checks whether a field element is a quadratic residue. */ +static int secp256k1_fe_is_quad_var(const secp256k1_fe *a); + +/** Sets a field element to be the (modular) inverse of another. Requires the input's magnitude to be + * at most 8. The output magnitude is 1 (but not guaranteed to be normalized). */ +static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a); + +/** Potentially faster version of secp256k1_fe_inv, without constant-time guarantee. */ +static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a); + +/** Calculate the (modular) inverses of a batch of field elements. Requires the inputs' magnitudes to be + * at most 8. The output magnitudes are 1 (but not guaranteed to be normalized). The inputs and + * outputs must not overlap in memory. */ +static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len); + +/** Convert a field element to the storage type. */ +static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a); + +/** Convert a field element back from the storage type. */ +static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a); + +/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */ +static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag); + +/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */ +static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag); + +#endif /* SECP256K1_FIELD_H */ diff --git a/src/secp256k1_tests/field_5x52.h b/src/secp256k1_tests/field_5x52.h new file mode 100644 index 0000000..fc5bfe3 --- /dev/null +++ b/src/secp256k1_tests/field_5x52.h @@ -0,0 +1,49 @@ +/********************************************************************** + * 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_FIELD_REPR_H +#define SECP256K1_FIELD_REPR_H + +#include + +typedef struct { + /* X = sum(i=0..4, n[i]*2^(i*52)) mod p + * where p = 2^256 - 0x1000003D1 + */ + uint64_t n[5]; +#ifdef VERIFY + int magnitude; + int normalized; +#endif +} secp256k1_fe; + +/* Unpacks a constant into a overlapping multi-limbed FE element. */ +#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \ + (d0) | (((uint64_t)(d1) & 0xFFFFFUL) << 32), \ + ((uint64_t)(d1) >> 20) | (((uint64_t)(d2)) << 12) | (((uint64_t)(d3) & 0xFFUL) << 44), \ + ((uint64_t)(d3) >> 8) | (((uint64_t)(d4) & 0xFFFFFFFUL) << 24), \ + ((uint64_t)(d4) >> 28) | (((uint64_t)(d5)) << 4) | (((uint64_t)(d6) & 0xFFFFUL) << 36), \ + ((uint64_t)(d6) >> 16) | (((uint64_t)(d7)) << 16) \ +} + +#ifdef VERIFY +#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1} +#else +#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))} +#endif + +typedef struct { + uint64_t n[4]; +} secp256k1_fe_storage; + +#define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ \ + (d0) | (((uint64_t)(d1)) << 32), \ + (d2) | (((uint64_t)(d3)) << 32), \ + (d4) | (((uint64_t)(d5)) << 32), \ + (d6) | (((uint64_t)(d7)) << 32) \ +}} + +#endif /* SECP256K1_FIELD_REPR_H */ diff --git a/src/secp256k1_tests/field_5x52_impl.h b/src/secp256k1_tests/field_5x52_impl.h new file mode 100644 index 0000000..f426332 --- /dev/null +++ b/src/secp256k1_tests/field_5x52_impl.h @@ -0,0 +1,496 @@ +/********************************************************************** + * 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_FIELD_REPR_IMPL_H +#define SECP256K1_FIELD_REPR_IMPL_H + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include "util.h" +#include "field.h" + +#if defined(USE_ASM_X86_64) +#include "field_5x52_asm_impl.h" +#else +#include "field_5x52_int128_impl.h" +#endif + +/** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F, + * represented as 5 uint64_t's in base 2^52. The values are allowed to contain >52 each. In particular, + * each FieldElem has a 'magnitude' associated with it. Internally, a magnitude M means each element + * is at most M*(2^53-1), except the most significant one, which is limited to M*(2^49-1). All operations + * accept any input with magnitude at most M, and have different rules for propagating magnitude to their + * output. + */ + +#ifdef VERIFY +static void secp256k1_fe_verify(const secp256k1_fe *a) { + const uint64_t *d = a->n; + int m = a->normalized ? 1 : 2 * a->magnitude, r = 1; + /* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */ + r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m); + r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m); + r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m); + r &= (d[3] <= 0xFFFFFFFFFFFFFULL * m); + r &= (d[4] <= 0x0FFFFFFFFFFFFULL * m); + r &= (a->magnitude >= 0); + r &= (a->magnitude <= 2048); + if (a->normalized) { + r &= (a->magnitude <= 1); + if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) { + r &= (d[0] < 0xFFFFEFFFFFC2FULL); + } + } + VERIFY_CHECK(r == 1); +} +#endif + +static void secp256k1_fe_normalize(secp256k1_fe *r) { + uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + uint64_t m; + uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + /* At most a single final reduction is needed; check if the value is >= the field characteristic */ + x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL) + & (t0 >= 0xFFFFEFFFFFC2FULL)); + + /* Apply the final reduction (for constant-time behaviour, we do it always) */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; + + /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */ + VERIFY_CHECK(t4 >> 48 == x); + + /* Mask off the possible multiple of 2^256 from the final reduction */ + t4 &= 0x0FFFFFFFFFFFFULL; + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_normalize_weak(secp256k1_fe *r) { + uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + +#ifdef VERIFY + r->magnitude = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_normalize_var(secp256k1_fe *r) { + uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + uint64_t m; + uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + /* At most a single final reduction is needed; check if the value is >= the field characteristic */ + x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL) + & (t0 >= 0xFFFFEFFFFFC2FULL)); + + if (x) { + t0 += 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; + + /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */ + VERIFY_CHECK(t4 >> 48 == x); + + /* Mask off the possible multiple of 2^256 from the final reduction */ + t4 &= 0x0FFFFFFFFFFFFULL; + } + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) { + uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; + + /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ + uint64_t z0, z1; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; z0 = t0; z1 = t0 ^ 0x1000003D0ULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3; + z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL); +} + +static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) { + uint64_t t0, t1, t2, t3, t4; + uint64_t z0, z1; + uint64_t x; + + t0 = r->n[0]; + t4 = r->n[4]; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + x = t4 >> 48; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + + /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ + z0 = t0 & 0xFFFFFFFFFFFFFULL; + z1 = z0 ^ 0x1000003D0ULL; + + /* Fast return path should catch the majority of cases */ + if ((z0 != 0ULL) & (z1 != 0xFFFFFFFFFFFFFULL)) { + return 0; + } + + t1 = r->n[1]; + t2 = r->n[2]; + t3 = r->n[3]; + + t4 &= 0x0FFFFFFFFFFFFULL; + + t1 += (t0 >> 52); + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3; + z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL); +} + +SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) { + r->n[0] = a; + r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0; +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) { + const uint64_t *t = a->n; +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0; +} + +SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + return a->n[0] & 1; +} + +SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) { + int i; +#ifdef VERIFY + a->magnitude = 0; + a->normalized = 1; +#endif + for (i=0; i<5; i++) { + a->n[i] = 0; + } +} + +static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) { + int i; +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + VERIFY_CHECK(b->normalized); + secp256k1_fe_verify(a); + secp256k1_fe_verify(b); +#endif + for (i = 4; i >= 0; i--) { + if (a->n[i] > b->n[i]) { + return 1; + } + if (a->n[i] < b->n[i]) { + return -1; + } + } + return 0; +} + +static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) { + r->n[0] = (uint64_t)a[31] + | ((uint64_t)a[30] << 8) + | ((uint64_t)a[29] << 16) + | ((uint64_t)a[28] << 24) + | ((uint64_t)a[27] << 32) + | ((uint64_t)a[26] << 40) + | ((uint64_t)(a[25] & 0xF) << 48); + r->n[1] = (uint64_t)((a[25] >> 4) & 0xF) + | ((uint64_t)a[24] << 4) + | ((uint64_t)a[23] << 12) + | ((uint64_t)a[22] << 20) + | ((uint64_t)a[21] << 28) + | ((uint64_t)a[20] << 36) + | ((uint64_t)a[19] << 44); + r->n[2] = (uint64_t)a[18] + | ((uint64_t)a[17] << 8) + | ((uint64_t)a[16] << 16) + | ((uint64_t)a[15] << 24) + | ((uint64_t)a[14] << 32) + | ((uint64_t)a[13] << 40) + | ((uint64_t)(a[12] & 0xF) << 48); + r->n[3] = (uint64_t)((a[12] >> 4) & 0xF) + | ((uint64_t)a[11] << 4) + | ((uint64_t)a[10] << 12) + | ((uint64_t)a[9] << 20) + | ((uint64_t)a[8] << 28) + | ((uint64_t)a[7] << 36) + | ((uint64_t)a[6] << 44); + r->n[4] = (uint64_t)a[5] + | ((uint64_t)a[4] << 8) + | ((uint64_t)a[3] << 16) + | ((uint64_t)a[2] << 24) + | ((uint64_t)a[1] << 32) + | ((uint64_t)a[0] << 40); + if (r->n[4] == 0x0FFFFFFFFFFFFULL && (r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL && r->n[0] >= 0xFFFFEFFFFFC2FULL) { + return 0; + } +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif + return 1; +} + +/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */ +static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + r[0] = (a->n[4] >> 40) & 0xFF; + r[1] = (a->n[4] >> 32) & 0xFF; + r[2] = (a->n[4] >> 24) & 0xFF; + r[3] = (a->n[4] >> 16) & 0xFF; + r[4] = (a->n[4] >> 8) & 0xFF; + r[5] = a->n[4] & 0xFF; + r[6] = (a->n[3] >> 44) & 0xFF; + r[7] = (a->n[3] >> 36) & 0xFF; + r[8] = (a->n[3] >> 28) & 0xFF; + r[9] = (a->n[3] >> 20) & 0xFF; + r[10] = (a->n[3] >> 12) & 0xFF; + r[11] = (a->n[3] >> 4) & 0xFF; + r[12] = ((a->n[2] >> 48) & 0xF) | ((a->n[3] & 0xF) << 4); + r[13] = (a->n[2] >> 40) & 0xFF; + r[14] = (a->n[2] >> 32) & 0xFF; + r[15] = (a->n[2] >> 24) & 0xFF; + r[16] = (a->n[2] >> 16) & 0xFF; + r[17] = (a->n[2] >> 8) & 0xFF; + r[18] = a->n[2] & 0xFF; + r[19] = (a->n[1] >> 44) & 0xFF; + r[20] = (a->n[1] >> 36) & 0xFF; + r[21] = (a->n[1] >> 28) & 0xFF; + r[22] = (a->n[1] >> 20) & 0xFF; + r[23] = (a->n[1] >> 12) & 0xFF; + r[24] = (a->n[1] >> 4) & 0xFF; + r[25] = ((a->n[0] >> 48) & 0xF) | ((a->n[1] & 0xF) << 4); + r[26] = (a->n[0] >> 40) & 0xFF; + r[27] = (a->n[0] >> 32) & 0xFF; + r[28] = (a->n[0] >> 24) & 0xFF; + r[29] = (a->n[0] >> 16) & 0xFF; + r[30] = (a->n[0] >> 8) & 0xFF; + r[31] = a->n[0] & 0xFF; +} + +SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= m); + secp256k1_fe_verify(a); +#endif + r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0]; + r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1]; + r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[2]; + r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[3]; + r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4]; +#ifdef VERIFY + r->magnitude = m + 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) { + r->n[0] *= a; + r->n[1] *= a; + r->n[2] *= a; + r->n[3] *= a; + r->n[4] *= a; +#ifdef VERIFY + r->magnitude *= a; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) { +#ifdef VERIFY + secp256k1_fe_verify(a); +#endif + r->n[0] += a->n[0]; + r->n[1] += a->n[1]; + r->n[2] += a->n[2]; + r->n[3] += a->n[3]; + r->n[4] += a->n[4]; +#ifdef VERIFY + r->magnitude += a->magnitude; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= 8); + VERIFY_CHECK(b->magnitude <= 8); + secp256k1_fe_verify(a); + secp256k1_fe_verify(b); + VERIFY_CHECK(r != b); + VERIFY_CHECK(a != b); +#endif + secp256k1_fe_mul_inner(r->n, a->n, b->n); +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= 8); + secp256k1_fe_verify(a); +#endif + secp256k1_fe_sqr_inner(r->n, a->n); +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) { + uint64_t mask0, mask1; + mask0 = flag + ~((uint64_t)0); + mask1 = ~mask0; + r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); + r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); + r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); + r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); + r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1); +#ifdef VERIFY + if (a->magnitude > r->magnitude) { + r->magnitude = a->magnitude; + } + r->normalized &= a->normalized; +#endif +} + +static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) { + uint64_t mask0, mask1; + mask0 = flag + ~((uint64_t)0); + mask1 = ~mask0; + r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); + r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); + r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); + r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); +} + +static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); +#endif + r->n[0] = a->n[0] | a->n[1] << 52; + r->n[1] = a->n[1] >> 12 | a->n[2] << 40; + r->n[2] = a->n[2] >> 24 | a->n[3] << 28; + r->n[3] = a->n[3] >> 36 | a->n[4] << 16; +} + +static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) { + r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL; + r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL); + r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL); + r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL); + r->n[4] = a->n[3] >> 16; +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; +#endif +} + +#endif /* SECP256K1_FIELD_REPR_IMPL_H */ diff --git a/src/secp256k1_tests/field_5x52_int128_impl.h b/src/secp256k1_tests/field_5x52_int128_impl.h new file mode 100644 index 0000000..bcbfb92 --- /dev/null +++ b/src/secp256k1_tests/field_5x52_int128_impl.h @@ -0,0 +1,279 @@ +/********************************************************************** + * 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_FIELD_INNER5X52_IMPL_H +#define SECP256K1_FIELD_INNER5X52_IMPL_H + +#include + +#ifdef VERIFY +#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0) +#else +#define VERIFY_BITS(x, n) do { } while(0) +#endif + +SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) { + uint128_t c, d; + uint64_t t3, t4, tx, u0; + uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4]; + const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL; + + VERIFY_BITS(a[0], 56); + VERIFY_BITS(a[1], 56); + VERIFY_BITS(a[2], 56); + VERIFY_BITS(a[3], 56); + VERIFY_BITS(a[4], 52); + VERIFY_BITS(b[0], 56); + VERIFY_BITS(b[1], 56); + VERIFY_BITS(b[2], 56); + VERIFY_BITS(b[3], 56); + VERIFY_BITS(b[4], 52); + VERIFY_CHECK(r != b); + VERIFY_CHECK(a != b); + + /* [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n. + * for 0 <= x <= 4, px is a shorthand for sum(a[i]*b[x-i], i=0..x). + * for 4 <= x <= 8, px is a shorthand for sum(a[i]*b[x-i], i=(x-4)..4) + * Note that [x 0 0 0 0 0] = [x*R]. + */ + + d = (uint128_t)a0 * b[3] + + (uint128_t)a1 * b[2] + + (uint128_t)a2 * b[1] + + (uint128_t)a3 * b[0]; + VERIFY_BITS(d, 114); + /* [d 0 0 0] = [p3 0 0 0] */ + c = (uint128_t)a4 * b[4]; + VERIFY_BITS(c, 112); + /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + d += (c & M) * R; c >>= 52; + VERIFY_BITS(d, 115); + VERIFY_BITS(c, 60); + /* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + t3 = d & M; d >>= 52; + VERIFY_BITS(t3, 52); + VERIFY_BITS(d, 63); + /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + + d += (uint128_t)a0 * b[4] + + (uint128_t)a1 * b[3] + + (uint128_t)a2 * b[2] + + (uint128_t)a3 * b[1] + + (uint128_t)a4 * b[0]; + VERIFY_BITS(d, 115); + /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + d += c * R; + VERIFY_BITS(d, 116); + /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + t4 = d & M; d >>= 52; + VERIFY_BITS(t4, 52); + VERIFY_BITS(d, 64); + /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + tx = (t4 >> 48); t4 &= (M >> 4); + VERIFY_BITS(tx, 4); + VERIFY_BITS(t4, 48); + /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + + c = (uint128_t)a0 * b[0]; + VERIFY_BITS(c, 112); + /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */ + d += (uint128_t)a1 * b[4] + + (uint128_t)a2 * b[3] + + (uint128_t)a3 * b[2] + + (uint128_t)a4 * b[1]; + VERIFY_BITS(d, 115); + /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + u0 = d & M; d >>= 52; + VERIFY_BITS(u0, 52); + VERIFY_BITS(d, 63); + /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + u0 = (u0 << 4) | tx; + VERIFY_BITS(u0, 56); + /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + c += (uint128_t)u0 * (R >> 4); + VERIFY_BITS(c, 115); + /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + r[0] = c & M; c >>= 52; + VERIFY_BITS(r[0], 52); + VERIFY_BITS(c, 61); + /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */ + + c += (uint128_t)a0 * b[1] + + (uint128_t)a1 * b[0]; + VERIFY_BITS(c, 114); + /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */ + d += (uint128_t)a2 * b[4] + + (uint128_t)a3 * b[3] + + (uint128_t)a4 * b[2]; + VERIFY_BITS(d, 114); + /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + c += (d & M) * R; d >>= 52; + VERIFY_BITS(c, 115); + VERIFY_BITS(d, 62); + /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + r[1] = c & M; c >>= 52; + VERIFY_BITS(r[1], 52); + VERIFY_BITS(c, 63); + /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + + c += (uint128_t)a0 * b[2] + + (uint128_t)a1 * b[1] + + (uint128_t)a2 * b[0]; + VERIFY_BITS(c, 114); + /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint128_t)a3 * b[4] + + (uint128_t)a4 * b[3]; + VERIFY_BITS(d, 114); + /* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += (d & M) * R; d >>= 52; + VERIFY_BITS(c, 115); + VERIFY_BITS(d, 62); + /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[2] = c & M; c >>= 52; + VERIFY_BITS(r[2], 52); + VERIFY_BITS(c, 63); + /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += d * R + t3; + VERIFY_BITS(c, 100); + /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[3] = c & M; c >>= 52; + VERIFY_BITS(r[3], 52); + VERIFY_BITS(c, 48); + /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += t4; + VERIFY_BITS(c, 49); + /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[4] = c; + VERIFY_BITS(r[4], 49); + /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ +} + +SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) { + uint128_t c, d; + uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4]; + int64_t t3, t4, tx, u0; + const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL; + + VERIFY_BITS(a[0], 56); + VERIFY_BITS(a[1], 56); + VERIFY_BITS(a[2], 56); + VERIFY_BITS(a[3], 56); + VERIFY_BITS(a[4], 52); + + /** [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n. + * px is a shorthand for sum(a[i]*a[x-i], i=0..x). + * Note that [x 0 0 0 0 0] = [x*R]. + */ + + d = (uint128_t)(a0*2) * a3 + + (uint128_t)(a1*2) * a2; + VERIFY_BITS(d, 114); + /* [d 0 0 0] = [p3 0 0 0] */ + c = (uint128_t)a4 * a4; + VERIFY_BITS(c, 112); + /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + d += (c & M) * R; c >>= 52; + VERIFY_BITS(d, 115); + VERIFY_BITS(c, 60); + /* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + t3 = d & M; d >>= 52; + VERIFY_BITS(t3, 52); + VERIFY_BITS(d, 63); + /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + + a4 *= 2; + d += (uint128_t)a0 * a4 + + (uint128_t)(a1*2) * a3 + + (uint128_t)a2 * a2; + VERIFY_BITS(d, 115); + /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + d += c * R; + VERIFY_BITS(d, 116); + /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + t4 = d & M; d >>= 52; + VERIFY_BITS(t4, 52); + VERIFY_BITS(d, 64); + /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + tx = (t4 >> 48); t4 &= (M >> 4); + VERIFY_BITS(tx, 4); + VERIFY_BITS(t4, 48); + /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + + c = (uint128_t)a0 * a0; + VERIFY_BITS(c, 112); + /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */ + d += (uint128_t)a1 * a4 + + (uint128_t)(a2*2) * a3; + VERIFY_BITS(d, 114); + /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + u0 = d & M; d >>= 52; + VERIFY_BITS(u0, 52); + VERIFY_BITS(d, 62); + /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + u0 = (u0 << 4) | tx; + VERIFY_BITS(u0, 56); + /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + c += (uint128_t)u0 * (R >> 4); + VERIFY_BITS(c, 113); + /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + r[0] = c & M; c >>= 52; + VERIFY_BITS(r[0], 52); + VERIFY_BITS(c, 61); + /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */ + + a0 *= 2; + c += (uint128_t)a0 * a1; + VERIFY_BITS(c, 114); + /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */ + d += (uint128_t)a2 * a4 + + (uint128_t)a3 * a3; + VERIFY_BITS(d, 114); + /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + c += (d & M) * R; d >>= 52; + VERIFY_BITS(c, 115); + VERIFY_BITS(d, 62); + /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + r[1] = c & M; c >>= 52; + VERIFY_BITS(r[1], 52); + VERIFY_BITS(c, 63); + /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + + c += (uint128_t)a0 * a2 + + (uint128_t)a1 * a1; + VERIFY_BITS(c, 114); + /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint128_t)a3 * a4; + VERIFY_BITS(d, 114); + /* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += (d & M) * R; d >>= 52; + VERIFY_BITS(c, 115); + VERIFY_BITS(d, 62); + /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[2] = c & M; c >>= 52; + VERIFY_BITS(r[2], 52); + VERIFY_BITS(c, 63); + /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + c += d * R + t3; + VERIFY_BITS(c, 100); + /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[3] = c & M; c >>= 52; + VERIFY_BITS(r[3], 52); + VERIFY_BITS(c, 48); + /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += t4; + VERIFY_BITS(c, 49); + /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[4] = c; + VERIFY_BITS(r[4], 49); + /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ +} + +#endif /* SECP256K1_FIELD_INNER5X52_IMPL_H */ diff --git a/src/secp256k1_tests/field_impl.h b/src/secp256k1_tests/field_impl.h new file mode 100644 index 0000000..6070cac --- /dev/null +++ b/src/secp256k1_tests/field_impl.h @@ -0,0 +1,318 @@ +/********************************************************************** + * 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_FIELD_IMPL_H +#define SECP256K1_FIELD_IMPL_H + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include "util.h" +#include "num.h" + +#if defined(USE_FIELD_10X26) +#include "field_10x26_impl.h" +#elif defined(USE_FIELD_5X52) +#include "field_5x52_impl.h" +#else +#error "Please select field implementation" +#endif + +SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) { + secp256k1_fe na; + secp256k1_fe_negate(&na, a, 1); + secp256k1_fe_add(&na, b); + return secp256k1_fe_normalizes_to_zero(&na); +} + +SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b) { + secp256k1_fe na; + secp256k1_fe_negate(&na, a, 1); + secp256k1_fe_add(&na, b); + return secp256k1_fe_normalizes_to_zero_var(&na); +} + +static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a) { + /** Given that p is congruent to 3 mod 4, we can compute the square root of + * a mod p as the (p+1)/4'th power of a. + * + * As (p+1)/4 is an even number, it will have the same result for a and for + * (-a). Only one of these two numbers actually has a square root however, + * so we test at the end by squaring and comparing to the input. + * Also because (p+1)/4 is an even number, the computed square root is + * itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)). + */ + secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1; + int j; + + VERIFY_CHECK(r != a); + + /** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in + * { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block: + * 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223] + */ + + secp256k1_fe_sqr(&x2, a); + secp256k1_fe_mul(&x2, &x2, a); + + secp256k1_fe_sqr(&x3, &x2); + secp256k1_fe_mul(&x3, &x3, a); + + x6 = x3; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x6, &x6); + } + secp256k1_fe_mul(&x6, &x6, &x3); + + x9 = x6; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x9, &x9); + } + secp256k1_fe_mul(&x9, &x9, &x3); + + x11 = x9; + for (j=0; j<2; j++) { + secp256k1_fe_sqr(&x11, &x11); + } + secp256k1_fe_mul(&x11, &x11, &x2); + + x22 = x11; + for (j=0; j<11; j++) { + secp256k1_fe_sqr(&x22, &x22); + } + secp256k1_fe_mul(&x22, &x22, &x11); + + x44 = x22; + for (j=0; j<22; j++) { + secp256k1_fe_sqr(&x44, &x44); + } + secp256k1_fe_mul(&x44, &x44, &x22); + + x88 = x44; + for (j=0; j<44; j++) { + secp256k1_fe_sqr(&x88, &x88); + } + secp256k1_fe_mul(&x88, &x88, &x44); + + x176 = x88; + for (j=0; j<88; j++) { + secp256k1_fe_sqr(&x176, &x176); + } + secp256k1_fe_mul(&x176, &x176, &x88); + + x220 = x176; + for (j=0; j<44; j++) { + secp256k1_fe_sqr(&x220, &x220); + } + secp256k1_fe_mul(&x220, &x220, &x44); + + x223 = x220; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x223, &x223); + } + secp256k1_fe_mul(&x223, &x223, &x3); + + /* The final result is then assembled using a sliding window over the blocks. */ + + t1 = x223; + for (j=0; j<23; j++) { + secp256k1_fe_sqr(&t1, &t1); + } + secp256k1_fe_mul(&t1, &t1, &x22); + for (j=0; j<6; j++) { + secp256k1_fe_sqr(&t1, &t1); + } + secp256k1_fe_mul(&t1, &t1, &x2); + secp256k1_fe_sqr(&t1, &t1); + secp256k1_fe_sqr(r, &t1); + + /* Check that a square root was actually calculated */ + + secp256k1_fe_sqr(&t1, r); + return secp256k1_fe_equal(&t1, a); +} + +static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) { + secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1; + int j; + + /** The binary representation of (p - 2) has 5 blocks of 1s, with lengths in + * { 1, 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block: + * [1], [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223] + */ + + secp256k1_fe_sqr(&x2, a); + secp256k1_fe_mul(&x2, &x2, a); + + secp256k1_fe_sqr(&x3, &x2); + secp256k1_fe_mul(&x3, &x3, a); + + x6 = x3; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x6, &x6); + } + secp256k1_fe_mul(&x6, &x6, &x3); + + x9 = x6; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x9, &x9); + } + secp256k1_fe_mul(&x9, &x9, &x3); + + x11 = x9; + for (j=0; j<2; j++) { + secp256k1_fe_sqr(&x11, &x11); + } + secp256k1_fe_mul(&x11, &x11, &x2); + + x22 = x11; + for (j=0; j<11; j++) { + secp256k1_fe_sqr(&x22, &x22); + } + secp256k1_fe_mul(&x22, &x22, &x11); + + x44 = x22; + for (j=0; j<22; j++) { + secp256k1_fe_sqr(&x44, &x44); + } + secp256k1_fe_mul(&x44, &x44, &x22); + + x88 = x44; + for (j=0; j<44; j++) { + secp256k1_fe_sqr(&x88, &x88); + } + secp256k1_fe_mul(&x88, &x88, &x44); + + x176 = x88; + for (j=0; j<88; j++) { + secp256k1_fe_sqr(&x176, &x176); + } + secp256k1_fe_mul(&x176, &x176, &x88); + + x220 = x176; + for (j=0; j<44; j++) { + secp256k1_fe_sqr(&x220, &x220); + } + secp256k1_fe_mul(&x220, &x220, &x44); + + x223 = x220; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x223, &x223); + } + secp256k1_fe_mul(&x223, &x223, &x3); + + /* The final result is then assembled using a sliding window over the blocks. */ + + t1 = x223; + for (j=0; j<23; j++) { + secp256k1_fe_sqr(&t1, &t1); + } + secp256k1_fe_mul(&t1, &t1, &x22); + for (j=0; j<5; j++) { + secp256k1_fe_sqr(&t1, &t1); + } + secp256k1_fe_mul(&t1, &t1, a); + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&t1, &t1); + } + secp256k1_fe_mul(&t1, &t1, &x2); + for (j=0; j<2; j++) { + secp256k1_fe_sqr(&t1, &t1); + } + secp256k1_fe_mul(r, a, &t1); +} + +static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) { +#if defined(USE_FIELD_INV_BUILTIN) + secp256k1_fe_inv(r, a); +#elif defined(USE_FIELD_INV_NUM) + secp256k1_num n, m; + static const secp256k1_fe negone = SECP256K1_FE_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, 0xFFFFFC2EUL + ); + /* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */ + static const unsigned char prime[32] = { + 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,0x2F + }; + unsigned char b[32]; + int res; + secp256k1_fe c = *a; + secp256k1_fe_normalize_var(&c); + secp256k1_fe_get_b32(b, &c); + secp256k1_num_set_bin(&n, b, 32); + secp256k1_num_set_bin(&m, prime, 32); + secp256k1_num_mod_inverse(&n, &n, &m); + secp256k1_num_get_bin(b, 32, &n); + res = secp256k1_fe_set_b32(r, b); + (void)res; + VERIFY_CHECK(res); + /* Verify the result is the (unique) valid inverse using non-GMP code. */ + secp256k1_fe_mul(&c, &c, r); + secp256k1_fe_add(&c, &negone); + CHECK(secp256k1_fe_normalizes_to_zero_var(&c)); +#else +#error "Please select field inverse implementation" +#endif +} + +static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len) { + secp256k1_fe u; + size_t i; + if (len < 1) { + return; + } + + VERIFY_CHECK((r + len <= a) || (a + len <= r)); + + r[0] = a[0]; + + i = 0; + while (++i < len) { + secp256k1_fe_mul(&r[i], &r[i - 1], &a[i]); + } + + secp256k1_fe_inv_var(&u, &r[--i]); + + while (i > 0) { + size_t j = i--; + secp256k1_fe_mul(&r[j], &r[i], &u); + secp256k1_fe_mul(&u, &u, &a[j]); + } + + r[0] = u; +} + +static int secp256k1_fe_is_quad_var(const secp256k1_fe *a) { +#ifndef USE_NUM_NONE + unsigned char b[32]; + secp256k1_num n; + secp256k1_num m; + /* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */ + static const unsigned char prime[32] = { + 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,0x2F + }; + + secp256k1_fe c = *a; + secp256k1_fe_normalize_var(&c); + secp256k1_fe_get_b32(b, &c); + secp256k1_num_set_bin(&n, b, 32); + secp256k1_num_set_bin(&m, prime, 32); + return secp256k1_num_jacobi(&n, &m) >= 0; +#else + secp256k1_fe r; + return secp256k1_fe_sqrt(&r, a); +#endif +} + +#endif /* SECP256K1_FIELD_IMPL_H */ diff --git a/src/secp256k1_tests/group.h b/src/secp256k1_tests/group.h new file mode 100644 index 0000000..8e122ab --- /dev/null +++ b/src/secp256k1_tests/group.h @@ -0,0 +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); + +/** 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_tests/group_impl.h b/src/secp256k1_tests/group_impl.h new file mode 100644 index 0000000..9b93c39 --- /dev/null +++ b/src/secp256k1_tests/group_impl.h @@ -0,0 +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) { + secp256k1_fe u; + size_t i; + size_t last_i = SIZE_MAX; + + for (i = 0; i < len; i++) { + if (!a[i].infinity) { + /* 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); + + i = last_i; + while (i > 0) { + i--; + if (!a[i].infinity) { + secp256k1_fe_mul(&r[last_i].x, &r[i].x, &u); + secp256k1_fe_mul(&u, &u, &a[last_i].z); + last_i = i; + } + } + VERIFY_CHECK(!a[last_i].infinity); + r[last_i].x = u; + + 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_tests/hash.h b/src/secp256k1_tests/hash.h new file mode 100644 index 0000000..de26e4b --- /dev/null +++ b/src/secp256k1_tests/hash.h @@ -0,0 +1,41 @@ +/********************************************************************** + * Copyright (c) 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_HASH_H +#define SECP256K1_HASH_H + +#include +#include + +typedef struct { + uint32_t s[8]; + uint32_t buf[16]; /* In big endian */ + size_t bytes; +} secp256k1_sha256; + +static void secp256k1_sha256_initialize(secp256k1_sha256 *hash); +static void secp256k1_sha256_write(secp256k1_sha256 *hash, const unsigned char *data, size_t size); +static void secp256k1_sha256_finalize(secp256k1_sha256 *hash, unsigned char *out32); + +typedef struct { + secp256k1_sha256 inner, outer; +} secp256k1_hmac_sha256; + +static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256 *hash, const unsigned char *key, size_t size); +static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256 *hash, const unsigned char *data, size_t size); +static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256 *hash, unsigned char *out32); + +typedef struct { + unsigned char v[32]; + unsigned char k[32]; + int retry; +} secp256k1_rfc6979_hmac_sha256; + +static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256 *rng, const unsigned char *key, size_t keylen); +static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256 *rng, unsigned char *out, size_t outlen); +static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256 *rng); + +#endif /* SECP256K1_HASH_H */ diff --git a/src/secp256k1_tests/hash_impl.h b/src/secp256k1_tests/hash_impl.h new file mode 100644 index 0000000..009f26b --- /dev/null +++ b/src/secp256k1_tests/hash_impl.h @@ -0,0 +1,282 @@ +/********************************************************************** + * Copyright (c) 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_HASH_IMPL_H +#define SECP256K1_HASH_IMPL_H + +#include "hash.h" + +#include +#include +#include + +#define Ch(x,y,z) ((z) ^ ((x) & ((y) ^ (z)))) +#define Maj(x,y,z) (((x) & (y)) | ((z) & ((x) | (y)))) +#define Sigma0(x) (((x) >> 2 | (x) << 30) ^ ((x) >> 13 | (x) << 19) ^ ((x) >> 22 | (x) << 10)) +#define Sigma1(x) (((x) >> 6 | (x) << 26) ^ ((x) >> 11 | (x) << 21) ^ ((x) >> 25 | (x) << 7)) +#define sigma0(x) (((x) >> 7 | (x) << 25) ^ ((x) >> 18 | (x) << 14) ^ ((x) >> 3)) +#define sigma1(x) (((x) >> 17 | (x) << 15) ^ ((x) >> 19 | (x) << 13) ^ ((x) >> 10)) + +#define Round(a,b,c,d,e,f,g,h,k,w) do { \ + uint32_t t1 = (h) + Sigma1(e) + Ch((e), (f), (g)) + (k) + (w); \ + uint32_t t2 = Sigma0(a) + Maj((a), (b), (c)); \ + (d) += t1; \ + (h) = t1 + t2; \ +} while(0) + +#ifdef WORDS_BIGENDIAN +#define BE32(x) (x) +#else +#define BE32(p) ((((p) & 0xFF) << 24) | (((p) & 0xFF00) << 8) | (((p) & 0xFF0000) >> 8) | (((p) & 0xFF000000) >> 24)) +#endif + +static void secp256k1_sha256_initialize(secp256k1_sha256 *hash) { + hash->s[0] = 0x6a09e667ul; + hash->s[1] = 0xbb67ae85ul; + hash->s[2] = 0x3c6ef372ul; + hash->s[3] = 0xa54ff53aul; + hash->s[4] = 0x510e527ful; + hash->s[5] = 0x9b05688cul; + hash->s[6] = 0x1f83d9abul; + hash->s[7] = 0x5be0cd19ul; + hash->bytes = 0; +} + +/** Perform one SHA-256 transformation, processing 16 big endian 32-bit words. */ +static void secp256k1_sha256_transform(uint32_t* s, const uint32_t* chunk) { + uint32_t a = s[0], b = s[1], c = s[2], d = s[3], e = s[4], f = s[5], g = s[6], h = s[7]; + uint32_t w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15; + + Round(a, b, c, d, e, f, g, h, 0x428a2f98, w0 = BE32(chunk[0])); + Round(h, a, b, c, d, e, f, g, 0x71374491, w1 = BE32(chunk[1])); + Round(g, h, a, b, c, d, e, f, 0xb5c0fbcf, w2 = BE32(chunk[2])); + Round(f, g, h, a, b, c, d, e, 0xe9b5dba5, w3 = BE32(chunk[3])); + Round(e, f, g, h, a, b, c, d, 0x3956c25b, w4 = BE32(chunk[4])); + Round(d, e, f, g, h, a, b, c, 0x59f111f1, w5 = BE32(chunk[5])); + Round(c, d, e, f, g, h, a, b, 0x923f82a4, w6 = BE32(chunk[6])); + Round(b, c, d, e, f, g, h, a, 0xab1c5ed5, w7 = BE32(chunk[7])); + Round(a, b, c, d, e, f, g, h, 0xd807aa98, w8 = BE32(chunk[8])); + Round(h, a, b, c, d, e, f, g, 0x12835b01, w9 = BE32(chunk[9])); + Round(g, h, a, b, c, d, e, f, 0x243185be, w10 = BE32(chunk[10])); + Round(f, g, h, a, b, c, d, e, 0x550c7dc3, w11 = BE32(chunk[11])); + Round(e, f, g, h, a, b, c, d, 0x72be5d74, w12 = BE32(chunk[12])); + Round(d, e, f, g, h, a, b, c, 0x80deb1fe, w13 = BE32(chunk[13])); + Round(c, d, e, f, g, h, a, b, 0x9bdc06a7, w14 = BE32(chunk[14])); + Round(b, c, d, e, f, g, h, a, 0xc19bf174, w15 = BE32(chunk[15])); + + Round(a, b, c, d, e, f, g, h, 0xe49b69c1, w0 += sigma1(w14) + w9 + sigma0(w1)); + Round(h, a, b, c, d, e, f, g, 0xefbe4786, w1 += sigma1(w15) + w10 + sigma0(w2)); + Round(g, h, a, b, c, d, e, f, 0x0fc19dc6, w2 += sigma1(w0) + w11 + sigma0(w3)); + Round(f, g, h, a, b, c, d, e, 0x240ca1cc, w3 += sigma1(w1) + w12 + sigma0(w4)); + Round(e, f, g, h, a, b, c, d, 0x2de92c6f, w4 += sigma1(w2) + w13 + sigma0(w5)); + Round(d, e, f, g, h, a, b, c, 0x4a7484aa, w5 += sigma1(w3) + w14 + sigma0(w6)); + Round(c, d, e, f, g, h, a, b, 0x5cb0a9dc, w6 += sigma1(w4) + w15 + sigma0(w7)); + Round(b, c, d, e, f, g, h, a, 0x76f988da, w7 += sigma1(w5) + w0 + sigma0(w8)); + Round(a, b, c, d, e, f, g, h, 0x983e5152, w8 += sigma1(w6) + w1 + sigma0(w9)); + Round(h, a, b, c, d, e, f, g, 0xa831c66d, w9 += sigma1(w7) + w2 + sigma0(w10)); + Round(g, h, a, b, c, d, e, f, 0xb00327c8, w10 += sigma1(w8) + w3 + sigma0(w11)); + Round(f, g, h, a, b, c, d, e, 0xbf597fc7, w11 += sigma1(w9) + w4 + sigma0(w12)); + Round(e, f, g, h, a, b, c, d, 0xc6e00bf3, w12 += sigma1(w10) + w5 + sigma0(w13)); + Round(d, e, f, g, h, a, b, c, 0xd5a79147, w13 += sigma1(w11) + w6 + sigma0(w14)); + Round(c, d, e, f, g, h, a, b, 0x06ca6351, w14 += sigma1(w12) + w7 + sigma0(w15)); + Round(b, c, d, e, f, g, h, a, 0x14292967, w15 += sigma1(w13) + w8 + sigma0(w0)); + + Round(a, b, c, d, e, f, g, h, 0x27b70a85, w0 += sigma1(w14) + w9 + sigma0(w1)); + Round(h, a, b, c, d, e, f, g, 0x2e1b2138, w1 += sigma1(w15) + w10 + sigma0(w2)); + Round(g, h, a, b, c, d, e, f, 0x4d2c6dfc, w2 += sigma1(w0) + w11 + sigma0(w3)); + Round(f, g, h, a, b, c, d, e, 0x53380d13, w3 += sigma1(w1) + w12 + sigma0(w4)); + Round(e, f, g, h, a, b, c, d, 0x650a7354, w4 += sigma1(w2) + w13 + sigma0(w5)); + Round(d, e, f, g, h, a, b, c, 0x766a0abb, w5 += sigma1(w3) + w14 + sigma0(w6)); + Round(c, d, e, f, g, h, a, b, 0x81c2c92e, w6 += sigma1(w4) + w15 + sigma0(w7)); + Round(b, c, d, e, f, g, h, a, 0x92722c85, w7 += sigma1(w5) + w0 + sigma0(w8)); + Round(a, b, c, d, e, f, g, h, 0xa2bfe8a1, w8 += sigma1(w6) + w1 + sigma0(w9)); + Round(h, a, b, c, d, e, f, g, 0xa81a664b, w9 += sigma1(w7) + w2 + sigma0(w10)); + Round(g, h, a, b, c, d, e, f, 0xc24b8b70, w10 += sigma1(w8) + w3 + sigma0(w11)); + Round(f, g, h, a, b, c, d, e, 0xc76c51a3, w11 += sigma1(w9) + w4 + sigma0(w12)); + Round(e, f, g, h, a, b, c, d, 0xd192e819, w12 += sigma1(w10) + w5 + sigma0(w13)); + Round(d, e, f, g, h, a, b, c, 0xd6990624, w13 += sigma1(w11) + w6 + sigma0(w14)); + Round(c, d, e, f, g, h, a, b, 0xf40e3585, w14 += sigma1(w12) + w7 + sigma0(w15)); + Round(b, c, d, e, f, g, h, a, 0x106aa070, w15 += sigma1(w13) + w8 + sigma0(w0)); + + Round(a, b, c, d, e, f, g, h, 0x19a4c116, w0 += sigma1(w14) + w9 + sigma0(w1)); + Round(h, a, b, c, d, e, f, g, 0x1e376c08, w1 += sigma1(w15) + w10 + sigma0(w2)); + Round(g, h, a, b, c, d, e, f, 0x2748774c, w2 += sigma1(w0) + w11 + sigma0(w3)); + Round(f, g, h, a, b, c, d, e, 0x34b0bcb5, w3 += sigma1(w1) + w12 + sigma0(w4)); + Round(e, f, g, h, a, b, c, d, 0x391c0cb3, w4 += sigma1(w2) + w13 + sigma0(w5)); + Round(d, e, f, g, h, a, b, c, 0x4ed8aa4a, w5 += sigma1(w3) + w14 + sigma0(w6)); + Round(c, d, e, f, g, h, a, b, 0x5b9cca4f, w6 += sigma1(w4) + w15 + sigma0(w7)); + Round(b, c, d, e, f, g, h, a, 0x682e6ff3, w7 += sigma1(w5) + w0 + sigma0(w8)); + Round(a, b, c, d, e, f, g, h, 0x748f82ee, w8 += sigma1(w6) + w1 + sigma0(w9)); + Round(h, a, b, c, d, e, f, g, 0x78a5636f, w9 += sigma1(w7) + w2 + sigma0(w10)); + Round(g, h, a, b, c, d, e, f, 0x84c87814, w10 += sigma1(w8) + w3 + sigma0(w11)); + Round(f, g, h, a, b, c, d, e, 0x8cc70208, w11 += sigma1(w9) + w4 + sigma0(w12)); + Round(e, f, g, h, a, b, c, d, 0x90befffa, w12 += sigma1(w10) + w5 + sigma0(w13)); + Round(d, e, f, g, h, a, b, c, 0xa4506ceb, w13 += sigma1(w11) + w6 + sigma0(w14)); + Round(c, d, e, f, g, h, a, b, 0xbef9a3f7, w14 + sigma1(w12) + w7 + sigma0(w15)); + Round(b, c, d, e, f, g, h, a, 0xc67178f2, w15 + sigma1(w13) + w8 + sigma0(w0)); + + s[0] += a; + s[1] += b; + s[2] += c; + s[3] += d; + s[4] += e; + s[5] += f; + s[6] += g; + s[7] += h; +} + +static void secp256k1_sha256_write(secp256k1_sha256 *hash, const unsigned char *data, size_t len) { + size_t bufsize = hash->bytes & 0x3F; + hash->bytes += len; + while (bufsize + len >= 64) { + /* Fill the buffer, and process it. */ + size_t chunk_len = 64 - bufsize; + memcpy(((unsigned char*)hash->buf) + bufsize, data, chunk_len); + data += chunk_len; + len -= chunk_len; + secp256k1_sha256_transform(hash->s, hash->buf); + bufsize = 0; + } + if (len) { + /* Fill the buffer with what remains. */ + memcpy(((unsigned char*)hash->buf) + bufsize, data, len); + } +} + +static void secp256k1_sha256_finalize(secp256k1_sha256 *hash, unsigned char *out32) { + static const unsigned char pad[64] = {0x80, 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, 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, 0}; + uint32_t sizedesc[2]; + uint32_t out[8]; + int i = 0; + sizedesc[0] = BE32(hash->bytes >> 29); + sizedesc[1] = BE32(hash->bytes << 3); + secp256k1_sha256_write(hash, pad, 1 + ((119 - (hash->bytes % 64)) % 64)); + secp256k1_sha256_write(hash, (const unsigned char*)sizedesc, 8); + for (i = 0; i < 8; i++) { + out[i] = BE32(hash->s[i]); + hash->s[i] = 0; + } + memcpy(out32, (const unsigned char*)out, 32); +} + +static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256 *hash, const unsigned char *key, size_t keylen) { + size_t n; + unsigned char rkey[64]; + if (keylen <= sizeof(rkey)) { + memcpy(rkey, key, keylen); + memset(rkey + keylen, 0, sizeof(rkey) - keylen); + } else { + secp256k1_sha256 sha256; + secp256k1_sha256_initialize(&sha256); + secp256k1_sha256_write(&sha256, key, keylen); + secp256k1_sha256_finalize(&sha256, rkey); + memset(rkey + 32, 0, 32); + } + + secp256k1_sha256_initialize(&hash->outer); + for (n = 0; n < sizeof(rkey); n++) { + rkey[n] ^= 0x5c; + } + secp256k1_sha256_write(&hash->outer, rkey, sizeof(rkey)); + + secp256k1_sha256_initialize(&hash->inner); + for (n = 0; n < sizeof(rkey); n++) { + rkey[n] ^= 0x5c ^ 0x36; + } + secp256k1_sha256_write(&hash->inner, rkey, sizeof(rkey)); + memset(rkey, 0, sizeof(rkey)); +} + +static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256 *hash, const unsigned char *data, size_t size) { + secp256k1_sha256_write(&hash->inner, data, size); +} + +static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256 *hash, unsigned char *out32) { + unsigned char temp[32]; + secp256k1_sha256_finalize(&hash->inner, temp); + secp256k1_sha256_write(&hash->outer, temp, 32); + memset(temp, 0, 32); + secp256k1_sha256_finalize(&hash->outer, out32); +} + + +static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256 *rng, const unsigned char *key, size_t keylen) { + secp256k1_hmac_sha256 hmac; + static const unsigned char zero[1] = {0x00}; + static const unsigned char one[1] = {0x01}; + + memset(rng->v, 0x01, 32); /* RFC6979 3.2.b. */ + memset(rng->k, 0x00, 32); /* RFC6979 3.2.c. */ + + /* RFC6979 3.2.d. */ + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_write(&hmac, zero, 1); + secp256k1_hmac_sha256_write(&hmac, key, keylen); + secp256k1_hmac_sha256_finalize(&hmac, rng->k); + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_finalize(&hmac, rng->v); + + /* RFC6979 3.2.f. */ + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_write(&hmac, one, 1); + secp256k1_hmac_sha256_write(&hmac, key, keylen); + secp256k1_hmac_sha256_finalize(&hmac, rng->k); + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_finalize(&hmac, rng->v); + rng->retry = 0; +} + +static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256 *rng, unsigned char *out, size_t outlen) { + /* RFC6979 3.2.h. */ + static const unsigned char zero[1] = {0x00}; + if (rng->retry) { + secp256k1_hmac_sha256 hmac; + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_write(&hmac, zero, 1); + secp256k1_hmac_sha256_finalize(&hmac, rng->k); + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_finalize(&hmac, rng->v); + } + + while (outlen > 0) { + secp256k1_hmac_sha256 hmac; + int now = outlen; + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_finalize(&hmac, rng->v); + if (now > 32) { + now = 32; + } + memcpy(out, rng->v, now); + out += now; + outlen -= now; + } + + rng->retry = 1; +} + +static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256 *rng) { + memset(rng->k, 0, 32); + memset(rng->v, 0, 32); + rng->retry = 0; +} + +#undef BE32 +#undef Round +#undef sigma1 +#undef sigma0 +#undef Sigma1 +#undef Sigma0 +#undef Maj +#undef Ch + +#endif /* SECP256K1_HASH_IMPL_H */ diff --git a/src/secp256k1_tests/include/secp256k1.h b/src/secp256k1_tests/include/secp256k1.h new file mode 100644 index 0000000..43af09c --- /dev/null +++ b/src/secp256k1_tests/include/secp256k1.h @@ -0,0 +1,666 @@ +#ifndef SECP256K1_H +#define SECP256K1_H + +#ifdef __cplusplus +extern "C" { +#endif + +#include + +/* These rules specify the order of arguments in API calls: + * + * 1. Context pointers go first, followed by output arguments, combined + * output/input arguments, and finally input-only arguments. + * 2. Array lengths always immediately the follow the argument whose length + * they describe, even if this violates rule 1. + * 3. Within the OUT/OUTIN/IN groups, pointers to data that is typically generated + * later go first. This means: signatures, public nonces, private nonces, + * messages, public keys, secret keys, tweaks. + * 4. Arguments that are not data pointers go last, from more complex to less + * complex: function pointers, algorithm names, messages, void pointers, + * counts, flags, booleans. + * 5. Opaque data pointers follow the function pointer they are to be passed to. + */ + +/** Opaque data structure that holds context information (precomputed tables etc.). + * + * The purpose of context structures is to cache large precomputed data tables + * that are expensive to construct, and also to maintain the randomization data + * for blinding. + * + * Do not create a new context object for each operation, as construction is + * far slower than all other API calls (~100 times slower than an ECDSA + * verification). + * + * A constructed context can safely be used from multiple threads + * simultaneously, but API call that take a non-const pointer to a context + * need exclusive access to it. In particular this is the case for + * secp256k1_context_destroy and secp256k1_context_randomize. + * + * Regarding randomization, either do it once at creation time (in which case + * you do not need any locking for the other calls), or use a read-write lock. + */ +typedef struct secp256k1_context_struct secp256k1_context; + +/** Opaque data structure that holds rewriteable "scratch space" + * + * The purpose of this structure is to replace dynamic memory allocations, + * because we target architectures where this may not be available. It is + * essentially a resizable (within specified parameters) block of bytes, + * which is initially created either by memory allocation or TODO as a pointer + * into some fixed rewritable space. + * + * Unlike the context object, this cannot safely be shared between threads + * without additional synchronization logic. + */ +typedef struct secp256k1_scratch_space_struct secp256k1_scratch_space; + +/** Opaque data structure that holds a parsed and valid public key. + * + * The exact representation of data inside is implementation defined and not + * guaranteed to be portable between different platforms or versions. It is + * however guaranteed to be 64 bytes in size, and can be safely copied/moved. + * If you need to convert to a format suitable for storage, transmission, or + * comparison, use secp256k1_ec_pubkey_serialize and secp256k1_ec_pubkey_parse. + */ +typedef struct { + unsigned char data[64]; +} secp256k1_pubkey; + +/** Opaque data structured that holds a parsed ECDSA signature. + * + * The exact representation of data inside is implementation defined and not + * guaranteed to be portable between different platforms or versions. It is + * however guaranteed to be 64 bytes in size, and can be safely copied/moved. + * If you need to convert to a format suitable for storage, transmission, or + * comparison, use the secp256k1_ecdsa_signature_serialize_* and + * secp256k1_ecdsa_signature_parse_* functions. + */ +typedef struct { + unsigned char data[64]; +} secp256k1_ecdsa_signature; + +/** A pointer to a function to deterministically generate a nonce. + * + * Returns: 1 if a nonce was successfully generated. 0 will cause signing to fail. + * Out: nonce32: pointer to a 32-byte array to be filled by the function. + * In: msg32: the 32-byte message hash being verified (will not be NULL) + * key32: pointer to a 32-byte secret key (will not be NULL) + * algo16: pointer to a 16-byte array describing the signature + * algorithm (will be NULL for ECDSA for compatibility). + * data: Arbitrary data pointer that is passed through. + * attempt: how many iterations we have tried to find a nonce. + * This will almost always be 0, but different attempt values + * are required to result in a different nonce. + * + * Except for test cases, this function should compute some cryptographic hash of + * the message, the algorithm, the key and the attempt. + */ +typedef int (*secp256k1_nonce_function)( + unsigned char *nonce32, + const unsigned char *msg32, + const unsigned char *key32, + const unsigned char *algo16, + void *data, + unsigned int attempt +); + +# if !defined(SECP256K1_GNUC_PREREQ) +# if defined(__GNUC__)&&defined(__GNUC_MINOR__) +# define SECP256K1_GNUC_PREREQ(_maj,_min) \ + ((__GNUC__<<16)+__GNUC_MINOR__>=((_maj)<<16)+(_min)) +# else +# define SECP256K1_GNUC_PREREQ(_maj,_min) 0 +# endif +# endif + +# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) ) +# if SECP256K1_GNUC_PREREQ(2,7) +# define SECP256K1_INLINE __inline__ +# elif (defined(_MSC_VER)) +# define SECP256K1_INLINE __inline +# else +# define SECP256K1_INLINE +# endif +# else +# define SECP256K1_INLINE inline +# endif + +#ifndef SECP256K1_API +# if defined(_WIN32) +# ifdef SECP256K1_BUILD +# define SECP256K1_API __declspec(dllexport) +# else +# define SECP256K1_API +# endif +# elif defined(__GNUC__) && defined(SECP256K1_BUILD) +# define SECP256K1_API __attribute__ ((visibility ("default"))) +# else +# define SECP256K1_API +# endif +#endif + +/**Warning attributes + * NONNULL is not used if SECP256K1_BUILD is set to avoid the compiler optimizing out + * some paranoid null checks. */ +# if defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4) +# define SECP256K1_WARN_UNUSED_RESULT __attribute__ ((__warn_unused_result__)) +# else +# define SECP256K1_WARN_UNUSED_RESULT +# endif +# if !defined(SECP256K1_BUILD) && defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4) +# define SECP256K1_ARG_NONNULL(_x) __attribute__ ((__nonnull__(_x))) +# else +# define SECP256K1_ARG_NONNULL(_x) +# endif + +/** All flags' lower 8 bits indicate what they're for. Do not use directly. */ +#define SECP256K1_FLAGS_TYPE_MASK ((1 << 8) - 1) +#define SECP256K1_FLAGS_TYPE_CONTEXT (1 << 0) +#define SECP256K1_FLAGS_TYPE_COMPRESSION (1 << 1) +/** The higher bits contain the actual data. Do not use directly. */ +#define SECP256K1_FLAGS_BIT_CONTEXT_VERIFY (1 << 8) +#define SECP256K1_FLAGS_BIT_CONTEXT_SIGN (1 << 9) +#define SECP256K1_FLAGS_BIT_COMPRESSION (1 << 8) + +/** Flags to pass to secp256k1_context_create. */ +#define SECP256K1_CONTEXT_VERIFY (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_VERIFY) +#define SECP256K1_CONTEXT_SIGN (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_SIGN) +#define SECP256K1_CONTEXT_NONE (SECP256K1_FLAGS_TYPE_CONTEXT) + +/** Flag to pass to secp256k1_ec_pubkey_serialize and secp256k1_ec_privkey_export. */ +#define SECP256K1_EC_COMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION | SECP256K1_FLAGS_BIT_COMPRESSION) +#define SECP256K1_EC_UNCOMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION) + +/** Prefix byte used to tag various encoded curvepoints for specific purposes */ +#define SECP256K1_TAG_PUBKEY_EVEN 0x02 +#define SECP256K1_TAG_PUBKEY_ODD 0x03 +#define SECP256K1_TAG_PUBKEY_UNCOMPRESSED 0x04 +#define SECP256K1_TAG_PUBKEY_HYBRID_EVEN 0x06 +#define SECP256K1_TAG_PUBKEY_HYBRID_ODD 0x07 + +/** A simple secp256k1 context object with no precomputed tables. These are useful for + * type serialization/parsing functions which require a context object to maintain + * API consistency, but currently do not require expensive precomputations or dynamic + * allocations. + */ +SECP256K1_API extern const secp256k1_context *secp256k1_context_no_precomp; + +/** Create a secp256k1 context object. + * + * Returns: a newly created context object. + * In: flags: which parts of the context to initialize. + * + * See also secp256k1_context_randomize. + */ +SECP256K1_API secp256k1_context* secp256k1_context_create( + unsigned int flags +) SECP256K1_WARN_UNUSED_RESULT; + +/** Copies a secp256k1 context object. + * + * Returns: a newly created context object. + * Args: ctx: an existing context to copy (cannot be NULL) + */ +SECP256K1_API secp256k1_context* secp256k1_context_clone( + const secp256k1_context* ctx +) SECP256K1_ARG_NONNULL(1) SECP256K1_WARN_UNUSED_RESULT; + +/** Destroy a secp256k1 context object. + * + * The context pointer may not be used afterwards. + * Args: ctx: an existing context to destroy (cannot be NULL) + */ +SECP256K1_API void secp256k1_context_destroy( + secp256k1_context* ctx +); + +/** Set a callback function to be called when an illegal argument is passed to + * an API call. It will only trigger for violations that are mentioned + * explicitly in the header. + * + * The philosophy is that these shouldn't be dealt with through a + * specific return value, as calling code should not have branches to deal with + * the case that this code itself is broken. + * + * On the other hand, during debug stage, one would want to be informed about + * such mistakes, and the default (crashing) may be inadvisable. + * When this callback is triggered, the API function called is guaranteed not + * to cause a crash, though its return value and output arguments are + * undefined. + * + * Args: ctx: an existing context object (cannot be NULL) + * In: fun: a pointer to a function to call when an illegal argument is + * passed to the API, taking a message and an opaque pointer + * (NULL restores a default handler that calls abort). + * data: the opaque pointer to pass to fun above. + */ +SECP256K1_API void secp256k1_context_set_illegal_callback( + secp256k1_context* ctx, + void (*fun)(const char* message, void* data), + const void* data +) SECP256K1_ARG_NONNULL(1); + +/** Set a callback function to be called when an internal consistency check + * fails. The default is crashing. + * + * This can only trigger in case of a hardware failure, miscompilation, + * memory corruption, serious bug in the library, or other error would can + * otherwise result in undefined behaviour. It will not trigger due to mere + * incorrect usage of the API (see secp256k1_context_set_illegal_callback + * for that). After this callback returns, anything may happen, including + * crashing. + * + * Args: ctx: an existing context object (cannot be NULL) + * In: fun: a pointer to a function to call when an internal error occurs, + * taking a message and an opaque pointer (NULL restores a default + * handler that calls abort). + * data: the opaque pointer to pass to fun above. + */ +SECP256K1_API void secp256k1_context_set_error_callback( + secp256k1_context* ctx, + void (*fun)(const char* message, void* data), + const void* data +) SECP256K1_ARG_NONNULL(1); + +/** Create a secp256k1 scratch space object. + * + * Returns: a newly created scratch space. + * Args: ctx: an existing context object (cannot be NULL) + * In: max_size: maximum amount of memory to allocate + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT secp256k1_scratch_space* secp256k1_scratch_space_create( + const secp256k1_context* ctx, + size_t max_size +) SECP256K1_ARG_NONNULL(1); + +/** Destroy a secp256k1 scratch space. + * + * The pointer may not be used afterwards. + * Args: scratch: space to destroy + */ +SECP256K1_API void secp256k1_scratch_space_destroy( + secp256k1_scratch_space* scratch +); + +/** Parse a variable-length public key into the pubkey object. + * + * Returns: 1 if the public key was fully valid. + * 0 if the public key could not be parsed or is invalid. + * Args: ctx: a secp256k1 context object. + * Out: pubkey: pointer to a pubkey object. If 1 is returned, it is set to a + * parsed version of input. If not, its value is undefined. + * In: input: pointer to a serialized public key + * inputlen: length of the array pointed to by input + * + * This function supports parsing compressed (33 bytes, header byte 0x02 or + * 0x03), uncompressed (65 bytes, header byte 0x04), or hybrid (65 bytes, header + * byte 0x06 or 0x07) format public keys. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_parse( + const secp256k1_context* ctx, + secp256k1_pubkey* pubkey, + const unsigned char *input, + size_t inputlen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Serialize a pubkey object into a serialized byte sequence. + * + * Returns: 1 always. + * Args: ctx: a secp256k1 context object. + * Out: output: a pointer to a 65-byte (if compressed==0) or 33-byte (if + * compressed==1) byte array to place the serialized key + * in. + * In/Out: outputlen: a pointer to an integer which is initially set to the + * size of output, and is overwritten with the written + * size. + * In: pubkey: a pointer to a secp256k1_pubkey containing an + * initialized public key. + * flags: SECP256K1_EC_COMPRESSED if serialization should be in + * compressed format, otherwise SECP256K1_EC_UNCOMPRESSED. + */ +SECP256K1_API int secp256k1_ec_pubkey_serialize( + const secp256k1_context* ctx, + unsigned char *output, + size_t *outputlen, + const secp256k1_pubkey* pubkey, + unsigned int flags +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Parse an ECDSA signature in compact (64 bytes) format. + * + * Returns: 1 when the signature could be parsed, 0 otherwise. + * Args: ctx: a secp256k1 context object + * Out: sig: a pointer to a signature object + * In: input64: a pointer to the 64-byte array to parse + * + * The signature must consist of a 32-byte big endian R value, followed by a + * 32-byte big endian S value. If R or S fall outside of [0..order-1], the + * encoding is invalid. R and S with value 0 are allowed in the encoding. + * + * After the call, sig will always be initialized. If parsing failed or R or + * S are zero, the resulting sig value is guaranteed to fail validation for any + * message and public key. + */ +SECP256K1_API int secp256k1_ecdsa_signature_parse_compact( + const secp256k1_context* ctx, + secp256k1_ecdsa_signature* sig, + const unsigned char *input64 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Parse a DER ECDSA signature. + * + * Returns: 1 when the signature could be parsed, 0 otherwise. + * Args: ctx: a secp256k1 context object + * Out: sig: a pointer to a signature object + * In: input: a pointer to the signature to be parsed + * inputlen: the length of the array pointed to be input + * + * This function will accept any valid DER encoded signature, even if the + * encoded numbers are out of range. + * + * After the call, sig will always be initialized. If parsing failed or the + * encoded numbers are out of range, signature validation with it is + * guaranteed to fail for every message and public key. + */ +SECP256K1_API int secp256k1_ecdsa_signature_parse_der( + const secp256k1_context* ctx, + secp256k1_ecdsa_signature* sig, + const unsigned char *input, + size_t inputlen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Serialize an ECDSA signature in DER format. + * + * Returns: 1 if enough space was available to serialize, 0 otherwise + * Args: ctx: a secp256k1 context object + * Out: output: a pointer to an array to store the DER serialization + * In/Out: outputlen: a pointer to a length integer. Initially, this integer + * should be set to the length of output. After the call + * it will be set to the length of the serialization (even + * if 0 was returned). + * In: sig: a pointer to an initialized signature object + */ +SECP256K1_API int secp256k1_ecdsa_signature_serialize_der( + const secp256k1_context* ctx, + unsigned char *output, + size_t *outputlen, + const secp256k1_ecdsa_signature* sig +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Serialize an ECDSA signature in compact (64 byte) format. + * + * Returns: 1 + * Args: ctx: a secp256k1 context object + * Out: output64: a pointer to a 64-byte array to store the compact serialization + * In: sig: a pointer to an initialized signature object + * + * See secp256k1_ecdsa_signature_parse_compact for details about the encoding. + */ +SECP256K1_API int secp256k1_ecdsa_signature_serialize_compact( + const secp256k1_context* ctx, + unsigned char *output64, + const secp256k1_ecdsa_signature* sig +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Verify an ECDSA signature. + * + * Returns: 1: correct signature + * 0: incorrect or unparseable signature + * Args: ctx: a secp256k1 context object, initialized for verification. + * In: sig: the signature being verified (cannot be NULL) + * msg32: the 32-byte message hash being verified (cannot be NULL) + * pubkey: pointer to an initialized public key to verify with (cannot be NULL) + * + * To avoid accepting malleable signatures, only ECDSA signatures in lower-S + * form are accepted. + * + * If you need to accept ECDSA signatures from sources that do not obey this + * rule, apply secp256k1_ecdsa_signature_normalize to the signature prior to + * validation, but be aware that doing so results in malleable signatures. + * + * For details, see the comments for that function. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_verify( + const secp256k1_context* ctx, + const secp256k1_ecdsa_signature *sig, + const unsigned char *msg32, + const secp256k1_pubkey *pubkey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Convert a signature to a normalized lower-S form. + * + * Returns: 1 if sigin was not normalized, 0 if it already was. + * Args: ctx: a secp256k1 context object + * Out: sigout: a pointer to a signature to fill with the normalized form, + * or copy if the input was already normalized. (can be NULL if + * you're only interested in whether the input was already + * normalized). + * In: sigin: a pointer to a signature to check/normalize (cannot be NULL, + * can be identical to sigout) + * + * With ECDSA a third-party can forge a second distinct signature of the same + * message, given a single initial signature, but without knowing the key. This + * is done by negating the S value modulo the order of the curve, 'flipping' + * the sign of the random point R which is not included in the signature. + * + * Forgery of the same message isn't universally problematic, but in systems + * where message malleability or uniqueness of signatures is important this can + * cause issues. This forgery can be blocked by all verifiers forcing signers + * to use a normalized form. + * + * The lower-S form reduces the size of signatures slightly on average when + * variable length encodings (such as DER) are used and is cheap to verify, + * making it a good choice. Security of always using lower-S is assured because + * anyone can trivially modify a signature after the fact to enforce this + * property anyway. + * + * The lower S value is always between 0x1 and + * 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0, + * inclusive. + * + * No other forms of ECDSA malleability are known and none seem likely, but + * there is no formal proof that ECDSA, even with this additional restriction, + * is free of other malleability. Commonly used serialization schemes will also + * accept various non-unique encodings, so care should be taken when this + * property is required for an application. + * + * The secp256k1_ecdsa_sign function will by default create signatures in the + * lower-S form, and secp256k1_ecdsa_verify will not accept others. In case + * signatures come from a system that cannot enforce this property, + * secp256k1_ecdsa_signature_normalize must be called before verification. + */ +SECP256K1_API int secp256k1_ecdsa_signature_normalize( + const secp256k1_context* ctx, + secp256k1_ecdsa_signature *sigout, + const secp256k1_ecdsa_signature *sigin +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3); + +/** An implementation of RFC6979 (using HMAC-SHA256) as nonce generation function. + * If a data pointer is passed, it is assumed to be a pointer to 32 bytes of + * extra entropy. + */ +SECP256K1_API extern const secp256k1_nonce_function secp256k1_nonce_function_rfc6979; + +/** A default safe nonce generation function (currently equal to secp256k1_nonce_function_rfc6979). */ +SECP256K1_API extern const secp256k1_nonce_function secp256k1_nonce_function_default; + +/** Create an ECDSA signature. + * + * Returns: 1: signature created + * 0: the nonce generation function failed, or the private key was invalid. + * Args: ctx: pointer to a context object, initialized for signing (cannot be NULL) + * Out: sig: pointer to an array where the signature will be placed (cannot be NULL) + * In: msg32: the 32-byte message hash being signed (cannot be NULL) + * seckey: pointer to a 32-byte secret key (cannot be NULL) + * noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used + * ndata: pointer to arbitrary data used by the nonce generation function (can be NULL) + * + * The created signature is always in lower-S form. See + * secp256k1_ecdsa_signature_normalize for more details. + */ +SECP256K1_API int secp256k1_ecdsa_sign( + const secp256k1_context* ctx, + secp256k1_ecdsa_signature *sig, + const unsigned char *msg32, + const unsigned char *seckey, + secp256k1_nonce_function noncefp, + const void *ndata +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Verify an ECDSA secret key. + * + * Returns: 1: secret key is valid + * 0: secret key is invalid + * Args: ctx: pointer to a context object (cannot be NULL) + * In: seckey: pointer to a 32-byte secret key (cannot be NULL) + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_verify( + const secp256k1_context* ctx, + const unsigned char *seckey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2); + +/** Compute the public key for a secret key. + * + * Returns: 1: secret was valid, public key stores + * 0: secret was invalid, try again + * Args: ctx: pointer to a context object, initialized for signing (cannot be NULL) + * Out: pubkey: pointer to the created public key (cannot be NULL) + * In: seckey: pointer to a 32-byte private key (cannot be NULL) + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create( + const secp256k1_context* ctx, + secp256k1_pubkey *pubkey, + const unsigned char *seckey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Negates a private key in place. + * + * Returns: 1 always + * Args: ctx: pointer to a context object + * In/Out: seckey: pointer to the 32-byte private key to be negated (cannot be NULL) + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_negate( + const secp256k1_context* ctx, + unsigned char *seckey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2); + +/** Negates a public key in place. + * + * Returns: 1 always + * Args: ctx: pointer to a context object + * In/Out: pubkey: pointer to the public key to be negated (cannot be NULL) + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_negate( + const secp256k1_context* ctx, + secp256k1_pubkey *pubkey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2); + +/** Tweak a private key by adding tweak to it. + * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for + * uniformly random 32-byte arrays, or if the resulting private key + * would be invalid (only when the tweak is the complement of the + * private key). 1 otherwise. + * Args: ctx: pointer to a context object (cannot be NULL). + * In/Out: seckey: pointer to a 32-byte private key. + * In: tweak: pointer to a 32-byte tweak. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add( + const secp256k1_context* ctx, + unsigned char *seckey, + const unsigned char *tweak +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Tweak a public key by adding tweak times the generator to it. + * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for + * uniformly random 32-byte arrays, or if the resulting public key + * would be invalid (only when the tweak is the complement of the + * corresponding private key). 1 otherwise. + * Args: ctx: pointer to a context object initialized for validation + * (cannot be NULL). + * In/Out: pubkey: pointer to a public key object. + * In: tweak: pointer to a 32-byte tweak. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add( + const secp256k1_context* ctx, + secp256k1_pubkey *pubkey, + const unsigned char *tweak +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Tweak a private key by multiplying it by a tweak. + * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for + * uniformly random 32-byte arrays, or equal to zero. 1 otherwise. + * Args: ctx: pointer to a context object (cannot be NULL). + * In/Out: seckey: pointer to a 32-byte private key. + * In: tweak: pointer to a 32-byte tweak. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul( + const secp256k1_context* ctx, + unsigned char *seckey, + const unsigned char *tweak +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Tweak a public key by multiplying it by a tweak value. + * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for + * uniformly random 32-byte arrays, or equal to zero. 1 otherwise. + * Args: ctx: pointer to a context object initialized for validation + * (cannot be NULL). + * In/Out: pubkey: pointer to a public key obkect. + * In: tweak: pointer to a 32-byte tweak. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul( + const secp256k1_context* ctx, + secp256k1_pubkey *pubkey, + const unsigned char *tweak +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Updates the context randomization to protect against side-channel leakage. + * Returns: 1: randomization successfully updated or nothing to randomize + * 0: error + * Args: ctx: pointer to a context object (cannot be NULL) + * In: seed32: pointer to a 32-byte random seed (NULL resets to initial state) + * + * While secp256k1 code is written to be constant-time no matter what secret + * values are, it's possible that a future compiler may output code which isn't, + * and also that the CPU may not emit the same radio frequencies or draw the same + * amount power for all values. + * + * This function provides a seed which is combined into the blinding value: that + * blinding value is added before each multiplication (and removed afterwards) so + * that it does not affect function results, but shields against attacks which + * rely on any input-dependent behaviour. + * + * This function has currently an effect only on contexts initialized for signing + * because randomization is currently used only for signing. However, this is not + * guaranteed and may change in the future. It is safe to call this function on + * contexts not initialized for signing; then it will have no effect and return 1. + * + * You should call this after secp256k1_context_create or + * secp256k1_context_clone, and may call this repeatedly afterwards. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_context_randomize( + secp256k1_context* ctx, + const unsigned char *seed32 +) SECP256K1_ARG_NONNULL(1); + +/** Add a number of public keys together. + * Returns: 1: the sum of the public keys is valid. + * 0: the sum of the public keys is not valid. + * Args: ctx: pointer to a context object + * Out: out: pointer to a public key object for placing the resulting public key + * (cannot be NULL) + * In: ins: pointer to array of pointers to public keys (cannot be NULL) + * n: the number of public keys to add together (must be at least 1) + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_combine( + const secp256k1_context* ctx, + secp256k1_pubkey *out, + const secp256k1_pubkey * const * ins, + size_t n +) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_H */ diff --git a/src/secp256k1_tests/include/secp256k1_recovery.h b/src/secp256k1_tests/include/secp256k1_recovery.h new file mode 100644 index 0000000..cf6c5ed --- /dev/null +++ b/src/secp256k1_tests/include/secp256k1_recovery.h @@ -0,0 +1,110 @@ +#ifndef SECP256K1_RECOVERY_H +#define SECP256K1_RECOVERY_H + +#include "secp256k1.h" + +#ifdef __cplusplus +extern "C" { +#endif + +/** Opaque data structured that holds a parsed ECDSA signature, + * supporting pubkey recovery. + * + * The exact representation of data inside is implementation defined and not + * guaranteed to be portable between different platforms or versions. It is + * however guaranteed to be 65 bytes in size, and can be safely copied/moved. + * If you need to convert to a format suitable for storage or transmission, use + * the secp256k1_ecdsa_signature_serialize_* and + * secp256k1_ecdsa_signature_parse_* functions. + * + * Furthermore, it is guaranteed that identical signatures (including their + * recoverability) will have identical representation, so they can be + * memcmp'ed. + */ +typedef struct { + unsigned char data[65]; +} secp256k1_ecdsa_recoverable_signature; + +/** Parse a compact ECDSA signature (64 bytes + recovery id). + * + * Returns: 1 when the signature could be parsed, 0 otherwise + * Args: ctx: a secp256k1 context object + * Out: sig: a pointer to a signature object + * In: input64: a pointer to a 64-byte compact signature + * recid: the recovery id (0, 1, 2 or 3) + */ +SECP256K1_API int secp256k1_ecdsa_recoverable_signature_parse_compact( + const secp256k1_context* ctx, + secp256k1_ecdsa_recoverable_signature* sig, + const unsigned char *input64, + int recid +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Convert a recoverable signature into a normal signature. + * + * Returns: 1 + * Out: sig: a pointer to a normal signature (cannot be NULL). + * In: sigin: a pointer to a recoverable signature (cannot be NULL). + */ +SECP256K1_API int secp256k1_ecdsa_recoverable_signature_convert( + const secp256k1_context* ctx, + secp256k1_ecdsa_signature* sig, + const secp256k1_ecdsa_recoverable_signature* sigin +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Serialize an ECDSA signature in compact format (64 bytes + recovery id). + * + * Returns: 1 + * Args: ctx: a secp256k1 context object + * Out: output64: a pointer to a 64-byte array of the compact signature (cannot be NULL) + * recid: a pointer to an integer to hold the recovery id (can be NULL). + * In: sig: a pointer to an initialized signature object (cannot be NULL) + */ +SECP256K1_API int secp256k1_ecdsa_recoverable_signature_serialize_compact( + const secp256k1_context* ctx, + unsigned char *output64, + int *recid, + const secp256k1_ecdsa_recoverable_signature* sig +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Create a recoverable ECDSA signature. + * + * Returns: 1: signature created + * 0: the nonce generation function failed, or the private key was invalid. + * Args: ctx: pointer to a context object, initialized for signing (cannot be NULL) + * Out: sig: pointer to an array where the signature will be placed (cannot be NULL) + * In: msg32: the 32-byte message hash being signed (cannot be NULL) + * seckey: pointer to a 32-byte secret key (cannot be NULL) + * noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used + * ndata: pointer to arbitrary data used by the nonce generation function (can be NULL) + */ +SECP256K1_API int secp256k1_ecdsa_sign_recoverable( + const secp256k1_context* ctx, + secp256k1_ecdsa_recoverable_signature *sig, + const unsigned char *msg32, + const unsigned char *seckey, + secp256k1_nonce_function noncefp, + const void *ndata +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Recover an ECDSA public key from a signature. + * + * Returns: 1: public key successfully recovered (which guarantees a correct signature). + * 0: otherwise. + * Args: ctx: pointer to a context object, initialized for verification (cannot be NULL) + * Out: pubkey: pointer to the recovered public key (cannot be NULL) + * In: sig: pointer to initialized signature that supports pubkey recovery (cannot be NULL) + * msg32: the 32-byte message hash assumed to be signed (cannot be NULL) + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_recover( + const secp256k1_context* ctx, + secp256k1_pubkey *pubkey, + const secp256k1_ecdsa_recoverable_signature *sig, + const unsigned char *msg32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_RECOVERY_H */ diff --git a/src/secp256k1_tests/libsecp256k1-config.h b/src/secp256k1_tests/libsecp256k1-config.h new file mode 100644 index 0000000..464ebbe --- /dev/null +++ b/src/secp256k1_tests/libsecp256k1-config.h @@ -0,0 +1,147 @@ +/* src/libsecp256k1-config.h. Generated from libsecp256k1-config.h.in by configure. */ +/* src/libsecp256k1-config.h.in. Generated from configure.ac by autoheader. */ + +#ifndef LIBSECP256K1_CONFIG_H + +#define LIBSECP256K1_CONFIG_H + +/* Define if building universal (internal helper macro) */ +/* #undef AC_APPLE_UNIVERSAL_BUILD */ + +/* Define this symbol to compile out all VERIFY code */ +/* #undef COVERAGE */ + +/* Define this symbol to enable the ECDH module */ +/* #undef ENABLE_MODULE_ECDH */ + +/* Define this symbol to enable the ECDSA pubkey recovery module */ +/* #undef ENABLE_MODULE_RECOVERY */ + +/* Define this symbol if OpenSSL EC functions are available */ +/* #undef ENABLE_OPENSSL_TESTS */ + +/* Define to 1 if you have the header file. */ +#define HAVE_DLFCN_H 1 + +/* Define to 1 if you have the header file. */ +#define HAVE_INTTYPES_H 1 + +/* Define this symbol if libcrypto is installed */ +#define HAVE_LIBCRYPTO 1 + +/* Define this symbol if libgmp is installed */ +/* #undef HAVE_LIBGMP */ + +/* Define to 1 if you have the header file. */ +#define HAVE_MEMORY_H 1 + +/* Define to 1 if you have the header file. */ +#define HAVE_STDINT_H 1 + +/* Define to 1 if you have the header file. */ +#define HAVE_STDLIB_H 1 + +/* Define to 1 if you have the header file. */ +#define HAVE_STRINGS_H 1 + +/* Define to 1 if you have the header file. */ +#define HAVE_STRING_H 1 + +/* Define to 1 if you have the header file. */ +#define HAVE_SYS_STAT_H 1 + +/* Define to 1 if you have the header file. */ +#define HAVE_SYS_TYPES_H 1 + +/* Define to 1 if you have the header file. */ +#define HAVE_UNISTD_H 1 + +/* Define to 1 if the system has the type `__int128'. */ +#define HAVE___INT128 1 + +/* Define to the sub-directory where libtool stores uninstalled libraries. */ +#define LT_OBJDIR ".libs/" + +/* Name of package */ +#define PACKAGE "libsecp256k1" + +/* Define to the address where bug reports for this package should be sent. */ +#define PACKAGE_BUGREPORT "" + +/* Define to the full name of this package. */ +#define PACKAGE_NAME "libsecp256k1" + +/* Define to the full name and version of this package. */ +#define PACKAGE_STRING "libsecp256k1 0.1" + +/* Define to the one symbol short name of this package. */ +#define PACKAGE_TARNAME "libsecp256k1" + +/* Define to the home page for this package. */ +#define PACKAGE_URL "" + +/* Define to the version of this package. */ +#define PACKAGE_VERSION "0.1" + +/* Define to 1 if you have the ANSI C header files. */ +#define STDC_HEADERS 1 + +/* Define this symbol to enable x86_64 assembly optimizations */ +/* #undef USE_ASM_X86_64 */ + +/* Define this symbol to use a statically generated ecmult table */ +#define USE_ECMULT_STATIC_PRECOMPUTATION 1 + +/* Define this symbol to use endomorphism optimization */ +/* #undef USE_ENDOMORPHISM */ + +/* Define this symbol if an external (non-inline) assembly implementation is + used */ +/* #undef USE_EXTERNAL_ASM */ + +/* Define this symbol to use the FIELD_10X26 implementation */ +/* #undef USE_FIELD_10X26 */ + +/* Define this symbol to use the FIELD_5X52 implementation */ +#define USE_FIELD_5X52 1 + +/* Define this symbol to use the native field inverse implementation */ +#define USE_FIELD_INV_BUILTIN 1 + +/* Define this symbol to use the num-based field inverse implementation */ +/* #undef USE_FIELD_INV_NUM */ + +/* Define this symbol to use the gmp implementation for num */ +/* #undef USE_NUM_GMP */ + +/* Define this symbol to use no num implementation */ +#define USE_NUM_NONE 1 + +/* Define this symbol to use the 4x64 scalar implementation */ +#define USE_SCALAR_4X64 1 + +/* Define this symbol to use the 8x32 scalar implementation */ +/* #undef USE_SCALAR_8X32 */ + +/* Define this symbol to use the native scalar inverse implementation */ +#define USE_SCALAR_INV_BUILTIN 1 + +/* Define this symbol to use the num-based scalar inverse implementation */ +/* #undef USE_SCALAR_INV_NUM */ + +/* Version number of package */ +#define VERSION "0.1" + +/* Define WORDS_BIGENDIAN to 1 if your processor stores words with the most + significant byte first (like Motorola and SPARC, unlike Intel). */ +#if defined AC_APPLE_UNIVERSAL_BUILD +# if defined __BIG_ENDIAN__ +# define WORDS_BIGENDIAN 1 +# endif +#else +# ifndef WORDS_BIGENDIAN +/* # undef WORDS_BIGENDIAN */ +# endif +#endif + +#endif /*LIBSECP256K1_CONFIG_H*/ diff --git a/src/secp256k1_tests/num.h b/src/secp256k1_tests/num.h new file mode 100644 index 0000000..49f2dd7 --- /dev/null +++ b/src/secp256k1_tests/num.h @@ -0,0 +1,74 @@ +/********************************************************************** + * 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_NUM_H +#define SECP256K1_NUM_H + +#ifndef USE_NUM_NONE + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#if defined(USE_NUM_GMP) +#include "num_gmp.h" +#else +#error "Please select num implementation" +#endif + +/** Copy a number. */ +static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a); + +/** Convert a number's absolute value to a binary big-endian string. + * There must be enough place. */ +static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a); + +/** Set a number to the value of a binary big-endian string. */ +static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen); + +/** Compute a modular inverse. The input must be less than the modulus. */ +static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m); + +/** Compute the jacobi symbol (a|b). b must be positive and odd. */ +static int secp256k1_num_jacobi(const secp256k1_num *a, const secp256k1_num *b); + +/** Compare the absolute value of two numbers. */ +static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b); + +/** Test whether two number are equal (including sign). */ +static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b); + +/** Add two (signed) numbers. */ +static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b); + +/** Subtract two (signed) numbers. */ +static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b); + +/** Multiply two (signed) numbers. */ +static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b); + +/** Replace a number by its remainder modulo m. M's sign is ignored. The result is a number between 0 and m-1, + even if r was negative. */ +static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m); + +/** Right-shift the passed number by bits bits. */ +static void secp256k1_num_shift(secp256k1_num *r, int bits); + +/** Check whether a number is zero. */ +static int secp256k1_num_is_zero(const secp256k1_num *a); + +/** Check whether a number is one. */ +static int secp256k1_num_is_one(const secp256k1_num *a); + +/** Check whether a number is strictly negative. */ +static int secp256k1_num_is_neg(const secp256k1_num *a); + +/** Change a number's sign. */ +static void secp256k1_num_negate(secp256k1_num *r); + +#endif + +#endif /* SECP256K1_NUM_H */ diff --git a/src/secp256k1_tests/num_impl.h b/src/secp256k1_tests/num_impl.h new file mode 100644 index 0000000..c45193b --- /dev/null +++ b/src/secp256k1_tests/num_impl.h @@ -0,0 +1,24 @@ +/********************************************************************** + * 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_NUM_IMPL_H +#define SECP256K1_NUM_IMPL_H + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include "num.h" + +#if defined(USE_NUM_GMP) +#include "num_gmp_impl.h" +#elif defined(USE_NUM_NONE) +/* Nothing. */ +#else +#error "Please select num implementation" +#endif + +#endif /* SECP256K1_NUM_IMPL_H */ diff --git a/src/secp256k1_tests/scalar.h b/src/secp256k1_tests/scalar.h new file mode 100644 index 0000000..59304cb --- /dev/null +++ b/src/secp256k1_tests/scalar.h @@ -0,0 +1,106 @@ +/********************************************************************** + * Copyright (c) 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_SCALAR_H +#define SECP256K1_SCALAR_H + +#include "num.h" + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#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" +#else +#error "Please select scalar implementation" +#endif + +/** Clear a scalar to prevent the leak of sensitive data. */ +static void secp256k1_scalar_clear(secp256k1_scalar *r); + +/** Access bits from a scalar. All requested bits must belong to the same 32-bit limb. */ +static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count); + +/** Access bits from a scalar. Not constant time. */ +static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count); + +/** Set a scalar from a big endian byte array. */ +static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *bin, int *overflow); + +/** Set a scalar to an unsigned integer. */ +static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v); + +/** Convert a scalar to a byte array. */ +static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a); + +/** Add two scalars together (modulo the group order). Returns whether it overflowed. */ +static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b); + +/** Conditionally add a power of two to a scalar. The result is not allowed to overflow. */ +static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag); + +/** Multiply two scalars (modulo the group order). */ +static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b); + +/** Shift a scalar right by some amount strictly between 0 and 16, returning + * the low bits that were shifted off */ +static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n); + +/** Compute the square of a scalar (modulo the group order). */ +static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a); + +/** Compute the inverse of a scalar (modulo the group order). */ +static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *a); + +/** Compute the inverse of a scalar (modulo the group order), without constant-time guarantee. */ +static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *a); + +/** Compute the complement of a scalar (modulo the group order). */ +static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a); + +/** Check whether a scalar equals zero. */ +static int secp256k1_scalar_is_zero(const secp256k1_scalar *a); + +/** Check whether a scalar equals one. */ +static int secp256k1_scalar_is_one(const secp256k1_scalar *a); + +/** Check whether a scalar, considered as an nonnegative integer, is even. */ +static int secp256k1_scalar_is_even(const secp256k1_scalar *a); + +/** Check whether a scalar is higher than the group order divided by 2. */ +static int secp256k1_scalar_is_high(const secp256k1_scalar *a); + +/** Conditionally negate a number, in constant time. + * Returns -1 if the number was negated, 1 otherwise */ +static int secp256k1_scalar_cond_negate(secp256k1_scalar *a, int flag); + +#ifndef USE_NUM_NONE +/** Convert a scalar to a number. */ +static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a); + +/** Get the order of the group as a number. */ +static void secp256k1_scalar_order_get_num(secp256k1_num *r); +#endif + +/** Compare two scalars. */ +static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b); + +#ifdef USE_ENDOMORPHISM +/** Find r1 and r2 such that r1+r2*2^128 = a. */ +static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a); +/** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (see secp256k1_gej_mul_lambda). */ +static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a); +#endif + +/** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */ +static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift); + +#endif /* SECP256K1_SCALAR_H */ diff --git a/src/secp256k1_tests/scalar_4x64.h b/src/secp256k1_tests/scalar_4x64.h new file mode 100644 index 0000000..19c7495 --- /dev/null +++ b/src/secp256k1_tests/scalar_4x64.h @@ -0,0 +1,19 @@ +/********************************************************************** + * Copyright (c) 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_SCALAR_REPR_H +#define SECP256K1_SCALAR_REPR_H + +#include + +/** A scalar modulo the group order of the secp256k1 curve. */ +typedef struct { + uint64_t d[4]; +} secp256k1_scalar; + +#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{((uint64_t)(d1)) << 32 | (d0), ((uint64_t)(d3)) << 32 | (d2), ((uint64_t)(d5)) << 32 | (d4), ((uint64_t)(d7)) << 32 | (d6)}} + +#endif /* SECP256K1_SCALAR_REPR_H */ diff --git a/src/secp256k1_tests/scalar_4x64_impl.h b/src/secp256k1_tests/scalar_4x64_impl.h new file mode 100644 index 0000000..d378335 --- /dev/null +++ b/src/secp256k1_tests/scalar_4x64_impl.h @@ -0,0 +1,949 @@ +/********************************************************************** + * 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_SCALAR_REPR_IMPL_H +#define SECP256K1_SCALAR_REPR_IMPL_H + +/* Limbs of the secp256k1 order. */ +#define SECP256K1_N_0 ((uint64_t)0xBFD25E8CD0364141ULL) +#define SECP256K1_N_1 ((uint64_t)0xBAAEDCE6AF48A03BULL) +#define SECP256K1_N_2 ((uint64_t)0xFFFFFFFFFFFFFFFEULL) +#define SECP256K1_N_3 ((uint64_t)0xFFFFFFFFFFFFFFFFULL) + +/* Limbs of 2^256 minus the secp256k1 order. */ +#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1) +#define SECP256K1_N_C_1 (~SECP256K1_N_1) +#define SECP256K1_N_C_2 (1) + +/* Limbs of half the secp256k1 order. */ +#define SECP256K1_N_H_0 ((uint64_t)0xDFE92F46681B20A0ULL) +#define SECP256K1_N_H_1 ((uint64_t)0x5D576E7357A4501DULL) +#define SECP256K1_N_H_2 ((uint64_t)0xFFFFFFFFFFFFFFFFULL) +#define SECP256K1_N_H_3 ((uint64_t)0x7FFFFFFFFFFFFFFFULL) + +SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) { + r->d[0] = 0; + r->d[1] = 0; + r->d[2] = 0; + r->d[3] = 0; +} + +SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) { + r->d[0] = v; + r->d[1] = 0; + r->d[2] = 0; + r->d[3] = 0; +} + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + VERIFY_CHECK((offset + count - 1) >> 6 == offset >> 6); + return (a->d[offset >> 6] >> (offset & 0x3F)) & ((((uint64_t)1) << count) - 1); +} + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + VERIFY_CHECK(count < 32); + VERIFY_CHECK(offset + count <= 256); + if ((offset + count - 1) >> 6 == offset >> 6) { + return secp256k1_scalar_get_bits(a, offset, count); + } else { + VERIFY_CHECK((offset >> 6) + 1 < 4); + return ((a->d[offset >> 6] >> (offset & 0x3F)) | (a->d[(offset >> 6) + 1] << (64 - (offset & 0x3F)))) & ((((uint64_t)1) << count) - 1); + } +} + +SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) { + int yes = 0; + int no = 0; + no |= (a->d[3] < SECP256K1_N_3); /* No need for a > check. */ + no |= (a->d[2] < SECP256K1_N_2); + yes |= (a->d[2] > SECP256K1_N_2) & ~no; + no |= (a->d[1] < SECP256K1_N_1); + yes |= (a->d[1] > SECP256K1_N_1) & ~no; + yes |= (a->d[0] >= SECP256K1_N_0) & ~no; + return yes; +} + +SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, unsigned int overflow) { + uint128_t t; + VERIFY_CHECK(overflow <= 1); + t = (uint128_t)r->d[0] + overflow * SECP256K1_N_C_0; + r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)r->d[1] + overflow * SECP256K1_N_C_1; + r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)r->d[2] + overflow * SECP256K1_N_C_2; + r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint64_t)r->d[3]; + r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; + return overflow; +} + +static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + int overflow; + uint128_t t = (uint128_t)a->d[0] + b->d[0]; + r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)a->d[1] + b->d[1]; + r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)a->d[2] + b->d[2]; + r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)a->d[3] + b->d[3]; + r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + overflow = t + secp256k1_scalar_check_overflow(r); + VERIFY_CHECK(overflow == 0 || overflow == 1); + secp256k1_scalar_reduce(r, overflow); + return overflow; +} + +static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) { + uint128_t t; + VERIFY_CHECK(bit < 256); + bit += ((uint32_t) flag - 1) & 0x100; /* forcing (bit >> 6) > 3 makes this a noop */ + t = (uint128_t)r->d[0] + (((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F)); + r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)r->d[1] + (((uint64_t)((bit >> 6) == 1)) << (bit & 0x3F)); + r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)r->d[2] + (((uint64_t)((bit >> 6) == 2)) << (bit & 0x3F)); + r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)r->d[3] + (((uint64_t)((bit >> 6) == 3)) << (bit & 0x3F)); + r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; +#ifdef VERIFY + VERIFY_CHECK((t >> 64) == 0); + VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0); +#endif +} + +static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) { + int over; + r->d[0] = (uint64_t)b32[31] | (uint64_t)b32[30] << 8 | (uint64_t)b32[29] << 16 | (uint64_t)b32[28] << 24 | (uint64_t)b32[27] << 32 | (uint64_t)b32[26] << 40 | (uint64_t)b32[25] << 48 | (uint64_t)b32[24] << 56; + r->d[1] = (uint64_t)b32[23] | (uint64_t)b32[22] << 8 | (uint64_t)b32[21] << 16 | (uint64_t)b32[20] << 24 | (uint64_t)b32[19] << 32 | (uint64_t)b32[18] << 40 | (uint64_t)b32[17] << 48 | (uint64_t)b32[16] << 56; + r->d[2] = (uint64_t)b32[15] | (uint64_t)b32[14] << 8 | (uint64_t)b32[13] << 16 | (uint64_t)b32[12] << 24 | (uint64_t)b32[11] << 32 | (uint64_t)b32[10] << 40 | (uint64_t)b32[9] << 48 | (uint64_t)b32[8] << 56; + r->d[3] = (uint64_t)b32[7] | (uint64_t)b32[6] << 8 | (uint64_t)b32[5] << 16 | (uint64_t)b32[4] << 24 | (uint64_t)b32[3] << 32 | (uint64_t)b32[2] << 40 | (uint64_t)b32[1] << 48 | (uint64_t)b32[0] << 56; + over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r)); + if (overflow) { + *overflow = over; + } +} + +static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) { + bin[0] = a->d[3] >> 56; bin[1] = a->d[3] >> 48; bin[2] = a->d[3] >> 40; bin[3] = a->d[3] >> 32; bin[4] = a->d[3] >> 24; bin[5] = a->d[3] >> 16; bin[6] = a->d[3] >> 8; bin[7] = a->d[3]; + bin[8] = a->d[2] >> 56; bin[9] = a->d[2] >> 48; bin[10] = a->d[2] >> 40; bin[11] = a->d[2] >> 32; bin[12] = a->d[2] >> 24; bin[13] = a->d[2] >> 16; bin[14] = a->d[2] >> 8; bin[15] = a->d[2]; + bin[16] = a->d[1] >> 56; bin[17] = a->d[1] >> 48; bin[18] = a->d[1] >> 40; bin[19] = a->d[1] >> 32; bin[20] = a->d[1] >> 24; bin[21] = a->d[1] >> 16; bin[22] = a->d[1] >> 8; bin[23] = a->d[1]; + bin[24] = a->d[0] >> 56; bin[25] = a->d[0] >> 48; bin[26] = a->d[0] >> 40; bin[27] = a->d[0] >> 32; bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0]; +} + +SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) { + return (a->d[0] | a->d[1] | a->d[2] | a->d[3]) == 0; +} + +static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) { + uint64_t nonzero = 0xFFFFFFFFFFFFFFFFULL * (secp256k1_scalar_is_zero(a) == 0); + uint128_t t = (uint128_t)(~a->d[0]) + SECP256K1_N_0 + 1; + r->d[0] = t & nonzero; t >>= 64; + t += (uint128_t)(~a->d[1]) + SECP256K1_N_1; + r->d[1] = t & nonzero; t >>= 64; + t += (uint128_t)(~a->d[2]) + SECP256K1_N_2; + r->d[2] = t & nonzero; t >>= 64; + t += (uint128_t)(~a->d[3]) + SECP256K1_N_3; + r->d[3] = t & nonzero; +} + +SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) { + return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3]) == 0; +} + +static int secp256k1_scalar_is_high(const secp256k1_scalar *a) { + int yes = 0; + int no = 0; + no |= (a->d[3] < SECP256K1_N_H_3); + yes |= (a->d[3] > SECP256K1_N_H_3) & ~no; + no |= (a->d[2] < SECP256K1_N_H_2) & ~yes; /* No need for a > check. */ + no |= (a->d[1] < SECP256K1_N_H_1) & ~yes; + yes |= (a->d[1] > SECP256K1_N_H_1) & ~no; + yes |= (a->d[0] > SECP256K1_N_H_0) & ~no; + return yes; +} + +static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) { + /* If we are flag = 0, mask = 00...00 and this is a no-op; + * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */ + uint64_t mask = !flag - 1; + uint64_t nonzero = (secp256k1_scalar_is_zero(r) != 0) - 1; + uint128_t t = (uint128_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask); + r->d[0] = t & nonzero; t >>= 64; + t += (uint128_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask); + r->d[1] = t & nonzero; t >>= 64; + t += (uint128_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask); + r->d[2] = t & nonzero; t >>= 64; + t += (uint128_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask); + r->d[3] = t & nonzero; + return 2 * (mask == 0) - 1; +} + +/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */ + +/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */ +#define muladd(a,b) { \ + uint64_t tl, th; \ + { \ + uint128_t t = (uint128_t)a * b; \ + th = t >> 64; /* at most 0xFFFFFFFFFFFFFFFE */ \ + tl = t; \ + } \ + c0 += tl; /* overflow is handled on the next line */ \ + th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFFFFFFFFFF */ \ + c1 += th; /* overflow is handled on the next line */ \ + c2 += (c1 < th) ? 1 : 0; /* never overflows by contract (verified in the next line) */ \ + VERIFY_CHECK((c1 >= th) || (c2 != 0)); \ +} + +/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */ +#define muladd_fast(a,b) { \ + uint64_t tl, th; \ + { \ + uint128_t t = (uint128_t)a * b; \ + th = t >> 64; /* at most 0xFFFFFFFFFFFFFFFE */ \ + tl = t; \ + } \ + c0 += tl; /* overflow is handled on the next line */ \ + th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFFFFFFFFFF */ \ + c1 += th; /* never overflows by contract (verified in the next line) */ \ + VERIFY_CHECK(c1 >= th); \ +} + +/** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */ +#define muladd2(a,b) { \ + uint64_t tl, th, th2, tl2; \ + { \ + uint128_t t = (uint128_t)a * b; \ + th = t >> 64; /* at most 0xFFFFFFFFFFFFFFFE */ \ + tl = t; \ + } \ + th2 = th + th; /* at most 0xFFFFFFFFFFFFFFFE (in case th was 0x7FFFFFFFFFFFFFFF) */ \ + c2 += (th2 < th) ? 1 : 0; /* never overflows by contract (verified the next line) */ \ + VERIFY_CHECK((th2 >= th) || (c2 != 0)); \ + tl2 = tl + tl; /* at most 0xFFFFFFFFFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFFFFFFFFFF) */ \ + th2 += (tl2 < tl) ? 1 : 0; /* at most 0xFFFFFFFFFFFFFFFF */ \ + c0 += tl2; /* overflow is handled on the next line */ \ + th2 += (c0 < tl2) ? 1 : 0; /* second overflow is handled on the next line */ \ + c2 += (c0 < tl2) & (th2 == 0); /* never overflows by contract (verified the next line) */ \ + VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \ + c1 += th2; /* overflow is handled on the next line */ \ + c2 += (c1 < th2) ? 1 : 0; /* never overflows by contract (verified the next line) */ \ + VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \ +} + +/** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */ +#define sumadd(a) { \ + unsigned int over; \ + c0 += (a); /* overflow is handled on the next line */ \ + over = (c0 < (a)) ? 1 : 0; \ + c1 += over; /* overflow is handled on the next line */ \ + c2 += (c1 < over) ? 1 : 0; /* never overflows by contract */ \ +} + +/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */ +#define sumadd_fast(a) { \ + c0 += (a); /* overflow is handled on the next line */ \ + c1 += (c0 < (a)) ? 1 : 0; /* never overflows by contract (verified the next line) */ \ + VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \ + VERIFY_CHECK(c2 == 0); \ +} + +/** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. */ +#define extract(n) { \ + (n) = c0; \ + c0 = c1; \ + c1 = c2; \ + c2 = 0; \ +} + +/** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. c2 is required to be zero. */ +#define extract_fast(n) { \ + (n) = c0; \ + c0 = c1; \ + c1 = 0; \ + VERIFY_CHECK(c2 == 0); \ +} + +static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l) { +#ifdef USE_ASM_X86_64 + /* Reduce 512 bits into 385. */ + uint64_t m0, m1, m2, m3, m4, m5, m6; + uint64_t p0, p1, p2, p3, p4; + uint64_t c; + + __asm__ __volatile__( + /* Preload. */ + "movq 32(%%rsi), %%r11\n" + "movq 40(%%rsi), %%r12\n" + "movq 48(%%rsi), %%r13\n" + "movq 56(%%rsi), %%r14\n" + /* Initialize r8,r9,r10 */ + "movq 0(%%rsi), %%r8\n" + "xorq %%r9, %%r9\n" + "xorq %%r10, %%r10\n" + /* (r8,r9) += n0 * c0 */ + "movq %8, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + /* extract m0 */ + "movq %%r8, %q0\n" + "xorq %%r8, %%r8\n" + /* (r9,r10) += l1 */ + "addq 8(%%rsi), %%r9\n" + "adcq $0, %%r10\n" + /* (r9,r10,r8) += n1 * c0 */ + "movq %8, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += n0 * c1 */ + "movq %9, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* extract m1 */ + "movq %%r9, %q1\n" + "xorq %%r9, %%r9\n" + /* (r10,r8,r9) += l2 */ + "addq 16(%%rsi), %%r10\n" + "adcq $0, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += n2 * c0 */ + "movq %8, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += n1 * c1 */ + "movq %9, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += n0 */ + "addq %%r11, %%r10\n" + "adcq $0, %%r8\n" + "adcq $0, %%r9\n" + /* extract m2 */ + "movq %%r10, %q2\n" + "xorq %%r10, %%r10\n" + /* (r8,r9,r10) += l3 */ + "addq 24(%%rsi), %%r8\n" + "adcq $0, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += n3 * c0 */ + "movq %8, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += n2 * c1 */ + "movq %9, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += n1 */ + "addq %%r12, %%r8\n" + "adcq $0, %%r9\n" + "adcq $0, %%r10\n" + /* extract m3 */ + "movq %%r8, %q3\n" + "xorq %%r8, %%r8\n" + /* (r9,r10,r8) += n3 * c1 */ + "movq %9, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += n2 */ + "addq %%r13, %%r9\n" + "adcq $0, %%r10\n" + "adcq $0, %%r8\n" + /* extract m4 */ + "movq %%r9, %q4\n" + /* (r10,r8) += n3 */ + "addq %%r14, %%r10\n" + "adcq $0, %%r8\n" + /* extract m5 */ + "movq %%r10, %q5\n" + /* extract m6 */ + "movq %%r8, %q6\n" + : "=g"(m0), "=g"(m1), "=g"(m2), "=g"(m3), "=g"(m4), "=g"(m5), "=g"(m6) + : "S"(l), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1) + : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc"); + + /* Reduce 385 bits into 258. */ + __asm__ __volatile__( + /* Preload */ + "movq %q9, %%r11\n" + "movq %q10, %%r12\n" + "movq %q11, %%r13\n" + /* Initialize (r8,r9,r10) */ + "movq %q5, %%r8\n" + "xorq %%r9, %%r9\n" + "xorq %%r10, %%r10\n" + /* (r8,r9) += m4 * c0 */ + "movq %12, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + /* extract p0 */ + "movq %%r8, %q0\n" + "xorq %%r8, %%r8\n" + /* (r9,r10) += m1 */ + "addq %q6, %%r9\n" + "adcq $0, %%r10\n" + /* (r9,r10,r8) += m5 * c0 */ + "movq %12, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += m4 * c1 */ + "movq %13, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* extract p1 */ + "movq %%r9, %q1\n" + "xorq %%r9, %%r9\n" + /* (r10,r8,r9) += m2 */ + "addq %q7, %%r10\n" + "adcq $0, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += m6 * c0 */ + "movq %12, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += m5 * c1 */ + "movq %13, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += m4 */ + "addq %%r11, %%r10\n" + "adcq $0, %%r8\n" + "adcq $0, %%r9\n" + /* extract p2 */ + "movq %%r10, %q2\n" + /* (r8,r9) += m3 */ + "addq %q8, %%r8\n" + "adcq $0, %%r9\n" + /* (r8,r9) += m6 * c1 */ + "movq %13, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + /* (r8,r9) += m5 */ + "addq %%r12, %%r8\n" + "adcq $0, %%r9\n" + /* extract p3 */ + "movq %%r8, %q3\n" + /* (r9) += m6 */ + "addq %%r13, %%r9\n" + /* extract p4 */ + "movq %%r9, %q4\n" + : "=&g"(p0), "=&g"(p1), "=&g"(p2), "=g"(p3), "=g"(p4) + : "g"(m0), "g"(m1), "g"(m2), "g"(m3), "g"(m4), "g"(m5), "g"(m6), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1) + : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "cc"); + + /* Reduce 258 bits into 256. */ + __asm__ __volatile__( + /* Preload */ + "movq %q5, %%r10\n" + /* (rax,rdx) = p4 * c0 */ + "movq %7, %%rax\n" + "mulq %%r10\n" + /* (rax,rdx) += p0 */ + "addq %q1, %%rax\n" + "adcq $0, %%rdx\n" + /* extract r0 */ + "movq %%rax, 0(%q6)\n" + /* Move to (r8,r9) */ + "movq %%rdx, %%r8\n" + "xorq %%r9, %%r9\n" + /* (r8,r9) += p1 */ + "addq %q2, %%r8\n" + "adcq $0, %%r9\n" + /* (r8,r9) += p4 * c1 */ + "movq %8, %%rax\n" + "mulq %%r10\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + /* Extract r1 */ + "movq %%r8, 8(%q6)\n" + "xorq %%r8, %%r8\n" + /* (r9,r8) += p4 */ + "addq %%r10, %%r9\n" + "adcq $0, %%r8\n" + /* (r9,r8) += p2 */ + "addq %q3, %%r9\n" + "adcq $0, %%r8\n" + /* Extract r2 */ + "movq %%r9, 16(%q6)\n" + "xorq %%r9, %%r9\n" + /* (r8,r9) += p3 */ + "addq %q4, %%r8\n" + "adcq $0, %%r9\n" + /* Extract r3 */ + "movq %%r8, 24(%q6)\n" + /* Extract c */ + "movq %%r9, %q0\n" + : "=g"(c) + : "g"(p0), "g"(p1), "g"(p2), "g"(p3), "g"(p4), "D"(r), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1) + : "rax", "rdx", "r8", "r9", "r10", "cc", "memory"); +#else + uint128_t c; + uint64_t c0, c1, c2; + uint64_t n0 = l[4], n1 = l[5], n2 = l[6], n3 = l[7]; + uint64_t m0, m1, m2, m3, m4, m5; + uint32_t m6; + uint64_t p0, p1, p2, p3; + uint32_t p4; + + /* Reduce 512 bits into 385. */ + /* m[0..6] = l[0..3] + n[0..3] * SECP256K1_N_C. */ + c0 = l[0]; c1 = 0; c2 = 0; + muladd_fast(n0, SECP256K1_N_C_0); + extract_fast(m0); + sumadd_fast(l[1]); + muladd(n1, SECP256K1_N_C_0); + muladd(n0, SECP256K1_N_C_1); + extract(m1); + sumadd(l[2]); + muladd(n2, SECP256K1_N_C_0); + muladd(n1, SECP256K1_N_C_1); + sumadd(n0); + extract(m2); + sumadd(l[3]); + muladd(n3, SECP256K1_N_C_0); + muladd(n2, SECP256K1_N_C_1); + sumadd(n1); + extract(m3); + muladd(n3, SECP256K1_N_C_1); + sumadd(n2); + extract(m4); + sumadd_fast(n3); + extract_fast(m5); + VERIFY_CHECK(c0 <= 1); + m6 = c0; + + /* Reduce 385 bits into 258. */ + /* p[0..4] = m[0..3] + m[4..6] * SECP256K1_N_C. */ + c0 = m0; c1 = 0; c2 = 0; + muladd_fast(m4, SECP256K1_N_C_0); + extract_fast(p0); + sumadd_fast(m1); + muladd(m5, SECP256K1_N_C_0); + muladd(m4, SECP256K1_N_C_1); + extract(p1); + sumadd(m2); + muladd(m6, SECP256K1_N_C_0); + muladd(m5, SECP256K1_N_C_1); + sumadd(m4); + extract(p2); + sumadd_fast(m3); + muladd_fast(m6, SECP256K1_N_C_1); + sumadd_fast(m5); + extract_fast(p3); + p4 = c0 + m6; + VERIFY_CHECK(p4 <= 2); + + /* Reduce 258 bits into 256. */ + /* r[0..3] = p[0..3] + p[4] * SECP256K1_N_C. */ + c = p0 + (uint128_t)SECP256K1_N_C_0 * p4; + r->d[0] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64; + c += p1 + (uint128_t)SECP256K1_N_C_1 * p4; + r->d[1] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64; + c += p2 + (uint128_t)p4; + r->d[2] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64; + c += p3; + r->d[3] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64; +#endif + + /* Final reduction of r. */ + secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r)); +} + +static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar *a, const secp256k1_scalar *b) { +#ifdef USE_ASM_X86_64 + const uint64_t *pb = b->d; + __asm__ __volatile__( + /* Preload */ + "movq 0(%%rdi), %%r15\n" + "movq 8(%%rdi), %%rbx\n" + "movq 16(%%rdi), %%rcx\n" + "movq 0(%%rdx), %%r11\n" + "movq 8(%%rdx), %%r12\n" + "movq 16(%%rdx), %%r13\n" + "movq 24(%%rdx), %%r14\n" + /* (rax,rdx) = a0 * b0 */ + "movq %%r15, %%rax\n" + "mulq %%r11\n" + /* Extract l0 */ + "movq %%rax, 0(%%rsi)\n" + /* (r8,r9,r10) = (rdx) */ + "movq %%rdx, %%r8\n" + "xorq %%r9, %%r9\n" + "xorq %%r10, %%r10\n" + /* (r8,r9,r10) += a0 * b1 */ + "movq %%r15, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += a1 * b0 */ + "movq %%rbx, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* Extract l1 */ + "movq %%r8, 8(%%rsi)\n" + "xorq %%r8, %%r8\n" + /* (r9,r10,r8) += a0 * b2 */ + "movq %%r15, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += a1 * b1 */ + "movq %%rbx, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += a2 * b0 */ + "movq %%rcx, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* Extract l2 */ + "movq %%r9, 16(%%rsi)\n" + "xorq %%r9, %%r9\n" + /* (r10,r8,r9) += a0 * b3 */ + "movq %%r15, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* Preload a3 */ + "movq 24(%%rdi), %%r15\n" + /* (r10,r8,r9) += a1 * b2 */ + "movq %%rbx, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += a2 * b1 */ + "movq %%rcx, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += a3 * b0 */ + "movq %%r15, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* Extract l3 */ + "movq %%r10, 24(%%rsi)\n" + "xorq %%r10, %%r10\n" + /* (r8,r9,r10) += a1 * b3 */ + "movq %%rbx, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += a2 * b2 */ + "movq %%rcx, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += a3 * b1 */ + "movq %%r15, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* Extract l4 */ + "movq %%r8, 32(%%rsi)\n" + "xorq %%r8, %%r8\n" + /* (r9,r10,r8) += a2 * b3 */ + "movq %%rcx, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += a3 * b2 */ + "movq %%r15, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* Extract l5 */ + "movq %%r9, 40(%%rsi)\n" + /* (r10,r8) += a3 * b3 */ + "movq %%r15, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + /* Extract l6 */ + "movq %%r10, 48(%%rsi)\n" + /* Extract l7 */ + "movq %%r8, 56(%%rsi)\n" + : "+d"(pb) + : "S"(l), "D"(a->d) + : "rax", "rbx", "rcx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "r15", "cc", "memory"); +#else + /* 160 bit accumulator. */ + uint64_t c0 = 0, c1 = 0; + uint32_t c2 = 0; + + /* l[0..7] = a[0..3] * b[0..3]. */ + muladd_fast(a->d[0], b->d[0]); + extract_fast(l[0]); + muladd(a->d[0], b->d[1]); + muladd(a->d[1], b->d[0]); + extract(l[1]); + muladd(a->d[0], b->d[2]); + muladd(a->d[1], b->d[1]); + muladd(a->d[2], b->d[0]); + extract(l[2]); + muladd(a->d[0], b->d[3]); + muladd(a->d[1], b->d[2]); + muladd(a->d[2], b->d[1]); + muladd(a->d[3], b->d[0]); + extract(l[3]); + muladd(a->d[1], b->d[3]); + muladd(a->d[2], b->d[2]); + muladd(a->d[3], b->d[1]); + extract(l[4]); + muladd(a->d[2], b->d[3]); + muladd(a->d[3], b->d[2]); + extract(l[5]); + muladd_fast(a->d[3], b->d[3]); + extract_fast(l[6]); + VERIFY_CHECK(c1 == 0); + l[7] = c0; +#endif +} + +static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar *a) { +#ifdef USE_ASM_X86_64 + __asm__ __volatile__( + /* Preload */ + "movq 0(%%rdi), %%r11\n" + "movq 8(%%rdi), %%r12\n" + "movq 16(%%rdi), %%r13\n" + "movq 24(%%rdi), %%r14\n" + /* (rax,rdx) = a0 * a0 */ + "movq %%r11, %%rax\n" + "mulq %%r11\n" + /* Extract l0 */ + "movq %%rax, 0(%%rsi)\n" + /* (r8,r9,r10) = (rdx,0) */ + "movq %%rdx, %%r8\n" + "xorq %%r9, %%r9\n" + "xorq %%r10, %%r10\n" + /* (r8,r9,r10) += 2 * a0 * a1 */ + "movq %%r11, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* Extract l1 */ + "movq %%r8, 8(%%rsi)\n" + "xorq %%r8, %%r8\n" + /* (r9,r10,r8) += 2 * a0 * a2 */ + "movq %%r11, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += a1 * a1 */ + "movq %%r12, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* Extract l2 */ + "movq %%r9, 16(%%rsi)\n" + "xorq %%r9, %%r9\n" + /* (r10,r8,r9) += 2 * a0 * a3 */ + "movq %%r11, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += 2 * a1 * a2 */ + "movq %%r12, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* Extract l3 */ + "movq %%r10, 24(%%rsi)\n" + "xorq %%r10, %%r10\n" + /* (r8,r9,r10) += 2 * a1 * a3 */ + "movq %%r12, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += a2 * a2 */ + "movq %%r13, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* Extract l4 */ + "movq %%r8, 32(%%rsi)\n" + "xorq %%r8, %%r8\n" + /* (r9,r10,r8) += 2 * a2 * a3 */ + "movq %%r13, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* Extract l5 */ + "movq %%r9, 40(%%rsi)\n" + /* (r10,r8) += a3 * a3 */ + "movq %%r14, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + /* Extract l6 */ + "movq %%r10, 48(%%rsi)\n" + /* Extract l7 */ + "movq %%r8, 56(%%rsi)\n" + : + : "S"(l), "D"(a->d) + : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc", "memory"); +#else + /* 160 bit accumulator. */ + uint64_t c0 = 0, c1 = 0; + uint32_t c2 = 0; + + /* l[0..7] = a[0..3] * b[0..3]. */ + muladd_fast(a->d[0], a->d[0]); + extract_fast(l[0]); + muladd2(a->d[0], a->d[1]); + extract(l[1]); + muladd2(a->d[0], a->d[2]); + muladd(a->d[1], a->d[1]); + extract(l[2]); + muladd2(a->d[0], a->d[3]); + muladd2(a->d[1], a->d[2]); + extract(l[3]); + muladd2(a->d[1], a->d[3]); + muladd(a->d[2], a->d[2]); + extract(l[4]); + muladd2(a->d[2], a->d[3]); + extract(l[5]); + muladd_fast(a->d[3], a->d[3]); + extract_fast(l[6]); + VERIFY_CHECK(c1 == 0); + l[7] = c0; +#endif +} + +#undef sumadd +#undef sumadd_fast +#undef muladd +#undef muladd_fast +#undef muladd2 +#undef extract +#undef extract_fast + +static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + uint64_t l[8]; + secp256k1_scalar_mul_512(l, a, b); + secp256k1_scalar_reduce_512(r, l); +} + +static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) { + int ret; + VERIFY_CHECK(n > 0); + VERIFY_CHECK(n < 16); + ret = r->d[0] & ((1 << n) - 1); + r->d[0] = (r->d[0] >> n) + (r->d[1] << (64 - n)); + r->d[1] = (r->d[1] >> n) + (r->d[2] << (64 - n)); + r->d[2] = (r->d[2] >> n) + (r->d[3] << (64 - n)); + r->d[3] = (r->d[3] >> n); + return ret; +} + +static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) { + uint64_t l[8]; + secp256k1_scalar_sqr_512(l, a); + secp256k1_scalar_reduce_512(r, l); +} + +#ifdef USE_ENDOMORPHISM +static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) { + r1->d[0] = a->d[0]; + r1->d[1] = a->d[1]; + r1->d[2] = 0; + r1->d[3] = 0; + r2->d[0] = a->d[2]; + r2->d[1] = a->d[3]; + r2->d[2] = 0; + r2->d[3] = 0; +} +#endif + +SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) { + return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3])) == 0; +} + +SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) { + uint64_t l[8]; + unsigned int shiftlimbs; + unsigned int shiftlow; + unsigned int shifthigh; + VERIFY_CHECK(shift >= 256); + secp256k1_scalar_mul_512(l, a, b); + shiftlimbs = shift >> 6; + shiftlow = shift & 0x3F; + shifthigh = 64 - shiftlow; + r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[1] = shift < 448 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[2] = shift < 384 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[3] = shift < 320 ? (l[3 + shiftlimbs] >> shiftlow) : 0; + secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1); +} + +#endif /* SECP256K1_SCALAR_REPR_IMPL_H */ diff --git a/src/secp256k1_tests/scalar_impl.h b/src/secp256k1_tests/scalar_impl.h new file mode 100644 index 0000000..fa79057 --- /dev/null +++ b/src/secp256k1_tests/scalar_impl.h @@ -0,0 +1,333 @@ +/********************************************************************** + * Copyright (c) 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_SCALAR_IMPL_H +#define SECP256K1_SCALAR_IMPL_H + +#include "group.h" +#include "scalar.h" + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#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" +#else +#error "Please select scalar implementation" +#endif + +#ifndef USE_NUM_NONE +static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a) { + unsigned char c[32]; + secp256k1_scalar_get_b32(c, a); + secp256k1_num_set_bin(r, c, 32); +} + +/** 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 xN as x ^ (2^N - 1) for some values of N, + * and uM as x ^ M for some values of M. */ + secp256k1_scalar x2, x3, x6, x8, x14, x28, x56, x112, x126; + secp256k1_scalar u2, u5, u9, u11, u13; + + secp256k1_scalar_sqr(&u2, x); + secp256k1_scalar_mul(&x2, &u2, x); + secp256k1_scalar_mul(&u5, &u2, &x2); + secp256k1_scalar_mul(&x3, &u5, &u2); + secp256k1_scalar_mul(&u9, &x3, &u2); + secp256k1_scalar_mul(&u11, &u9, &u2); + secp256k1_scalar_mul(&u13, &u11, &u2); + + secp256k1_scalar_sqr(&x6, &u13); + secp256k1_scalar_sqr(&x6, &x6); + secp256k1_scalar_mul(&x6, &x6, &u11); + + secp256k1_scalar_sqr(&x8, &x6); + secp256k1_scalar_sqr(&x8, &x8); + secp256k1_scalar_mul(&x8, &x8, &x2); + + secp256k1_scalar_sqr(&x14, &x8); + for (i = 0; i < 5; i++) { + secp256k1_scalar_sqr(&x14, &x14); + } + secp256k1_scalar_mul(&x14, &x14, &x6); + + secp256k1_scalar_sqr(&x28, &x14); + for (i = 0; i < 13; i++) { + secp256k1_scalar_sqr(&x28, &x28); + } + secp256k1_scalar_mul(&x28, &x28, &x14); + + secp256k1_scalar_sqr(&x56, &x28); + for (i = 0; i < 27; i++) { + secp256k1_scalar_sqr(&x56, &x56); + } + secp256k1_scalar_mul(&x56, &x56, &x28); + + secp256k1_scalar_sqr(&x112, &x56); + for (i = 0; i < 55; i++) { + secp256k1_scalar_sqr(&x112, &x112); + } + secp256k1_scalar_mul(&x112, &x112, &x56); + + secp256k1_scalar_sqr(&x126, &x112); + for (i = 0; i < 13; i++) { + secp256k1_scalar_sqr(&x126, &x126); + } + secp256k1_scalar_mul(&x126, &x126, &x14); + + /* Then accumulate the final result (t starts at x126). */ + t = &x126; + for (i = 0; i < 3; i++) { + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u5); /* 101 */ + for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x3); /* 111 */ + for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u5); /* 101 */ + for (i = 0; i < 5; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u11); /* 1011 */ + for (i = 0; i < 4; i++) { + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u11); /* 1011 */ + for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x3); /* 111 */ + for (i = 0; i < 5; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x3); /* 111 */ + for (i = 0; i < 6; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u13); /* 1101 */ + for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u5); /* 101 */ + for (i = 0; i < 3; i++) { + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x3); /* 111 */ + for (i = 0; i < 5; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u9); /* 1001 */ + for (i = 0; i < 6; i++) { /* 000 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u5); /* 101 */ + for (i = 0; i < 10; i++) { /* 0000000 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x3); /* 111 */ + for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x3); /* 111 */ + for (i = 0; i < 9; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x8); /* 11111111 */ + for (i = 0; i < 5; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u9); /* 1001 */ + for (i = 0; i < 6; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u11); /* 1011 */ + for (i = 0; i < 4; i++) { + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u13); /* 1101 */ + for (i = 0; i < 5; i++) { + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x2); /* 11 */ + for (i = 0; i < 6; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u13); /* 1101 */ + for (i = 0; i < 10; i++) { /* 000000 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u13); /* 1101 */ + for (i = 0; i < 4; i++) { + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u9); /* 1001 */ + for (i = 0; i < 6; i++) { /* 00000 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, x); /* 1 */ + for (i = 0; i < 8; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(r, t, &x6); /* 111111 */ +} + +SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) { + 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) + secp256k1_scalar_inverse(r, x); +#elif defined(USE_SCALAR_INV_NUM) + unsigned char b[32]; + secp256k1_num n, m; + secp256k1_scalar t = *x; + secp256k1_scalar_get_b32(b, &t); + secp256k1_num_set_bin(&n, b, 32); + secp256k1_scalar_order_get_num(&m); + secp256k1_num_mod_inverse(&n, &n, &m); + secp256k1_num_get_bin(b, 32, &n); + secp256k1_scalar_set_b32(r, b, NULL); + /* Verify that the inverse was computed correctly, without GMP code. */ + secp256k1_scalar_mul(&t, &t, r); + CHECK(secp256k1_scalar_is_one(&t)); +#else +#error "Please select scalar inverse implementation" +#endif +} + +#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, + * 0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72} + * + * "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm + * (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1 + * and k2 have a small size. + * It relies on constants a1, b1, a2, b2. These constants for the value of lambda above are: + * + * - a1 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15} + * - b1 = -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3} + * - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8} + * - b2 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15} + * + * The algorithm then computes c1 = round(b1 * k / n) and c2 = round(b2 * k / n), and gives + * k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and + * compute k1 as k - k2 * lambda, avoiding the need for constants a1 and a2. + * + * g1, g2 are precomputed constants used to replace division with a rounded multiplication + * when decomposing the scalar for an endomorphism-based point multiplication. + * + * The possibility of using precomputed estimates is mentioned in "Guide to Elliptic Curve + * Cryptography" (Hankerson, Menezes, Vanstone) in section 3.5. + * + * The derivation is described in the paper "Efficient Software Implementation of Public-Key + * Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez), + * Section 4.3 (here we use a somewhat higher-precision estimate): + * d = a1*b2 - b1*a2 + * g1 = round((2^272)*b2/d) + * g2 = round((2^272)*b1/d) + * + * (Note that 'd' is also equal to the curve order here because [a1,b1] and [a2,b2] are found + * as outputs of the Extended Euclidean Algorithm on inputs 'order' and 'lambda'). + * + * The function below splits a in r1 and r2, such that r1 + lambda * r2 == a (mod order). + */ + +static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) { + secp256k1_scalar c1, c2; + static const secp256k1_scalar minus_lambda = SECP256K1_SCALAR_CONST( + 0xAC9C52B3UL, 0x3FA3CF1FUL, 0x5AD9E3FDUL, 0x77ED9BA4UL, + 0xA880B9FCUL, 0x8EC739C2UL, 0xE0CFC810UL, 0xB51283CFUL + ); + static const secp256k1_scalar minus_b1 = SECP256K1_SCALAR_CONST( + 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL, + 0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL + ); + static const secp256k1_scalar minus_b2 = SECP256K1_SCALAR_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, + 0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL + ); + static const secp256k1_scalar g1 = SECP256K1_SCALAR_CONST( + 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00003086UL, + 0xD221A7D4UL, 0x6BCDE86CUL, 0x90E49284UL, 0xEB153DABUL + ); + static const secp256k1_scalar g2 = SECP256K1_SCALAR_CONST( + 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0000E443UL, + 0x7ED6010EUL, 0x88286F54UL, 0x7FA90ABFUL, 0xE4C42212UL + ); + VERIFY_CHECK(r1 != a); + VERIFY_CHECK(r2 != a); + /* these _var calls are constant time since the shift amount is constant */ + secp256k1_scalar_mul_shift_var(&c1, a, &g1, 272); + secp256k1_scalar_mul_shift_var(&c2, a, &g2, 272); + secp256k1_scalar_mul(&c1, &c1, &minus_b1); + secp256k1_scalar_mul(&c2, &c2, &minus_b2); + secp256k1_scalar_add(r2, &c1, &c2); + secp256k1_scalar_mul(r1, r2, &minus_lambda); + secp256k1_scalar_add(r1, r1, a); +} +#endif +#endif + +#endif /* SECP256K1_SCALAR_IMPL_H */ diff --git a/src/secp256k1_tests/scalar_low.h b/src/secp256k1_tests/scalar_low.h new file mode 100644 index 0000000..5836feb --- /dev/null +++ b/src/secp256k1_tests/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_H +#define SECP256K1_SCALAR_REPR_H + +#include + +/** A scalar modulo the group order of the secp256k1 curve. */ +typedef uint32_t secp256k1_scalar; + +#endif /* SECP256K1_SCALAR_REPR_H */ diff --git a/src/secp256k1_tests/scalar_low_impl.h b/src/secp256k1_tests/scalar_low_impl.h new file mode 100644 index 0000000..c80e70c --- /dev/null +++ b/src/secp256k1_tests/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 /* SECP256K1_SCALAR_REPR_IMPL_H */ diff --git a/src/secp256k1_tests/scratch.h b/src/secp256k1_tests/scratch.h new file mode 100644 index 0000000..fef377a --- /dev/null +++ b/src/secp256k1_tests/scratch.h @@ -0,0 +1,39 @@ +/********************************************************************** + * Copyright (c) 2017 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef _SECP256K1_SCRATCH_ +#define _SECP256K1_SCRATCH_ + +#define SECP256K1_SCRATCH_MAX_FRAMES 5 + +/* The typedef is used internally; the struct name is used in the public API + * (where it is exposed as a different typedef) */ +typedef struct secp256k1_scratch_space_struct { + void *data[SECP256K1_SCRATCH_MAX_FRAMES]; + size_t offset[SECP256K1_SCRATCH_MAX_FRAMES]; + size_t frame_size[SECP256K1_SCRATCH_MAX_FRAMES]; + size_t frame; + size_t max_size; + const secp256k1_callback* error_callback; +} secp256k1_scratch; + +static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* error_callback, size_t max_size); + +static void secp256k1_scratch_destroy(secp256k1_scratch* scratch); + +/** Attempts to allocate a new stack frame with `n` available bytes. Returns 1 on success, 0 on failure */ +static int secp256k1_scratch_allocate_frame(secp256k1_scratch* scratch, size_t n, size_t objects); + +/** Deallocates a stack frame */ +static void secp256k1_scratch_deallocate_frame(secp256k1_scratch* scratch); + +/** Returns the maximum allocation the scratch space will allow */ +static size_t secp256k1_scratch_max_allocation(const secp256k1_scratch* scratch, size_t n_objects); + +/** Returns a pointer into the most recently allocated frame, or NULL if there is insufficient available space */ +static void *secp256k1_scratch_alloc(secp256k1_scratch* scratch, size_t n); + +#endif diff --git a/src/secp256k1_tests/scratch_impl.h b/src/secp256k1_tests/scratch_impl.h new file mode 100644 index 0000000..abed713 --- /dev/null +++ b/src/secp256k1_tests/scratch_impl.h @@ -0,0 +1,86 @@ +/********************************************************************** + * Copyright (c) 2017 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef _SECP256K1_SCRATCH_IMPL_H_ +#define _SECP256K1_SCRATCH_IMPL_H_ + +#include "scratch.h" + +/* Using 16 bytes alignment because common architectures never have alignment + * requirements above 8 for any of the types we care about. In addition we + * leave some room because currently we don't care about a few bytes. + * TODO: Determine this at configure time. */ +#define ALIGNMENT 16 + +static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* error_callback, size_t max_size) { + secp256k1_scratch* ret = (secp256k1_scratch*)checked_malloc(error_callback, sizeof(*ret)); + if (ret != NULL) { + memset(ret, 0, sizeof(*ret)); + ret->max_size = max_size; + ret->error_callback = error_callback; + } + return ret; +} + +static void secp256k1_scratch_destroy(secp256k1_scratch* scratch) { + if (scratch != NULL) { + VERIFY_CHECK(scratch->frame == 0); + free(scratch); + } +} + +static size_t secp256k1_scratch_max_allocation(const secp256k1_scratch* scratch, size_t objects) { + size_t i = 0; + size_t allocated = 0; + for (i = 0; i < scratch->frame; i++) { + allocated += scratch->frame_size[i]; + } + if (scratch->max_size - allocated <= objects * ALIGNMENT) { + return 0; + } + return scratch->max_size - allocated - objects * ALIGNMENT; +} + +static int secp256k1_scratch_allocate_frame(secp256k1_scratch* scratch, size_t n, size_t objects) { + VERIFY_CHECK(scratch->frame < SECP256K1_SCRATCH_MAX_FRAMES); + + if (n <= secp256k1_scratch_max_allocation(scratch, objects)) { + n += objects * ALIGNMENT; + scratch->data[scratch->frame] = checked_malloc(scratch->error_callback, n); + if (scratch->data[scratch->frame] == NULL) { + return 0; + } + scratch->frame_size[scratch->frame] = n; + scratch->offset[scratch->frame] = 0; + scratch->frame++; + return 1; + } else { + return 0; + } +} + +static void secp256k1_scratch_deallocate_frame(secp256k1_scratch* scratch) { + VERIFY_CHECK(scratch->frame > 0); + scratch->frame -= 1; + free(scratch->data[scratch->frame]); +} + +static void *secp256k1_scratch_alloc(secp256k1_scratch* scratch, size_t size) { + void *ret; + size_t frame = scratch->frame - 1; + size = ((size + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT; + + if (scratch->frame == 0 || size + scratch->offset[frame] > scratch->frame_size[frame]) { + return NULL; + } + ret = (void *) ((unsigned char *) scratch->data[frame] + scratch->offset[frame]); + memset(ret, 0, size); + scratch->offset[frame] += size; + + return ret; +} + +#endif diff --git a/src/secp256k1_tests/secp256k1_c.h b/src/secp256k1_tests/secp256k1_c.h new file mode 100644 index 0000000..15981f4 --- /dev/null +++ b/src/secp256k1_tests/secp256k1_c.h @@ -0,0 +1,609 @@ +/********************************************************************** + * Copyright (c) 2013-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#include "include/secp256k1.h" + +#include "util.h" +#include "num_impl.h" +#include "field_impl.h" +#include "scalar_impl.h" +#include "group_impl.h" +#include "ecmult_impl.h" +#include "ecmult_const_impl.h" +#include "ecmult_gen_impl.h" +#include "ecdsa_impl.h" +#include "eckey_impl.h" +#include "hash_impl.h" +#include "scratch_impl.h" + +#define ARG_CHECK(cond) do { \ + if (EXPECT(!(cond), 0)) { \ + secp256k1_callback_call(&ctx->illegal_callback, #cond); \ + return 0; \ + } \ +} while(0) + +static void default_illegal_callback_fn(const char* str, void* data) { + (void)data; + fprintf(stderr, "[libsecp256k1] illegal argument: %s\n", str); + abort(); +} + +static const secp256k1_callback default_illegal_callback = { + default_illegal_callback_fn, + NULL +}; + +static void default_error_callback_fn(const char* str, void* data) { + (void)data; + fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str); + abort(); +} + +static const secp256k1_callback default_error_callback = { + default_error_callback_fn, + NULL +}; + + +struct secp256k1_context_struct { + secp256k1_ecmult_context ecmult_ctx; + secp256k1_ecmult_gen_context ecmult_gen_ctx; + secp256k1_callback illegal_callback; + secp256k1_callback error_callback; +}; + +static const secp256k1_context secp256k1_context_no_precomp_ = { + { 0 }, + { 0 }, + { default_illegal_callback_fn, 0 }, + { default_error_callback_fn, 0 } +}; +const secp256k1_context *secp256k1_context_no_precomp = &secp256k1_context_no_precomp_; + +secp256k1_context* secp256k1_context_create(unsigned int flags) { + secp256k1_context* ret = (secp256k1_context*)checked_malloc(&default_error_callback, sizeof(secp256k1_context)); + ret->illegal_callback = default_illegal_callback; + ret->error_callback = default_error_callback; + + if (EXPECT((flags & SECP256K1_FLAGS_TYPE_MASK) != SECP256K1_FLAGS_TYPE_CONTEXT, 0)) { + secp256k1_callback_call(&ret->illegal_callback, + "Invalid flags"); + free(ret); + return NULL; + } + + secp256k1_ecmult_context_init(&ret->ecmult_ctx); + secp256k1_ecmult_gen_context_init(&ret->ecmult_gen_ctx); + + if (flags & SECP256K1_FLAGS_BIT_CONTEXT_SIGN) { + secp256k1_ecmult_gen_context_build(&ret->ecmult_gen_ctx, &ret->error_callback); + } + if (flags & SECP256K1_FLAGS_BIT_CONTEXT_VERIFY) { + secp256k1_ecmult_context_build(&ret->ecmult_ctx, &ret->error_callback); + } + + return ret; +} + +secp256k1_context* secp256k1_context_clone(const secp256k1_context* ctx) { + secp256k1_context* ret = (secp256k1_context*)checked_malloc(&ctx->error_callback, sizeof(secp256k1_context)); + ret->illegal_callback = ctx->illegal_callback; + ret->error_callback = ctx->error_callback; + secp256k1_ecmult_context_clone(&ret->ecmult_ctx, &ctx->ecmult_ctx, &ctx->error_callback); + secp256k1_ecmult_gen_context_clone(&ret->ecmult_gen_ctx, &ctx->ecmult_gen_ctx, &ctx->error_callback); + return ret; +} + +void secp256k1_context_destroy(secp256k1_context* ctx) { + CHECK(ctx != secp256k1_context_no_precomp); + if (ctx != NULL) { + secp256k1_ecmult_context_clear(&ctx->ecmult_ctx); + secp256k1_ecmult_gen_context_clear(&ctx->ecmult_gen_ctx); + + free(ctx); + } +} + +void secp256k1_context_set_illegal_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) { + CHECK(ctx != secp256k1_context_no_precomp); + if (fun == NULL) { + fun = default_illegal_callback_fn; + } + ctx->illegal_callback.fn = fun; + ctx->illegal_callback.data = data; +} + +void secp256k1_context_set_error_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) { + CHECK(ctx != secp256k1_context_no_precomp); + if (fun == NULL) { + fun = default_error_callback_fn; + } + ctx->error_callback.fn = fun; + ctx->error_callback.data = data; +} + +secp256k1_scratch_space* secp256k1_scratch_space_create(const secp256k1_context* ctx, size_t max_size) { + VERIFY_CHECK(ctx != NULL); + return secp256k1_scratch_create(&ctx->error_callback, max_size); +} + +void secp256k1_scratch_space_destroy(secp256k1_scratch_space* scratch) { + secp256k1_scratch_destroy(scratch); +} + +static int secp256k1_pubkey_load(const secp256k1_context* ctx, secp256k1_ge* ge, const secp256k1_pubkey* pubkey) { + if (sizeof(secp256k1_ge_storage) == 64) { + /* When the secp256k1_ge_storage type is exactly 64 byte, use its + * representation inside secp256k1_pubkey, as conversion is very fast. + * Note that secp256k1_pubkey_save must use the same representation. */ + secp256k1_ge_storage s; + memcpy(&s, &pubkey->data[0], sizeof(s)); + secp256k1_ge_from_storage(ge, &s); + } else { + /* Otherwise, fall back to 32-byte big endian for X and Y. */ + secp256k1_fe x, y; + secp256k1_fe_set_b32(&x, pubkey->data); + secp256k1_fe_set_b32(&y, pubkey->data + 32); + secp256k1_ge_set_xy(ge, &x, &y); + } + ARG_CHECK(!secp256k1_fe_is_zero(&ge->x)); + return 1; +} + +static void secp256k1_pubkey_save(secp256k1_pubkey* pubkey, secp256k1_ge* ge) { + if (sizeof(secp256k1_ge_storage) == 64) { + secp256k1_ge_storage s; + secp256k1_ge_to_storage(&s, ge); + memcpy(&pubkey->data[0], &s, sizeof(s)); + } else { + VERIFY_CHECK(!secp256k1_ge_is_infinity(ge)); + secp256k1_fe_normalize_var(&ge->x); + secp256k1_fe_normalize_var(&ge->y); + secp256k1_fe_get_b32(pubkey->data, &ge->x); + secp256k1_fe_get_b32(pubkey->data + 32, &ge->y); + } +} + +int secp256k1_ec_pubkey_parse(const secp256k1_context* ctx, secp256k1_pubkey* pubkey, const unsigned char *input, size_t inputlen) { + secp256k1_ge Q; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + memset(pubkey, 0, sizeof(*pubkey)); + ARG_CHECK(input != NULL); + if (!secp256k1_eckey_pubkey_parse(&Q, input, inputlen)) { + return 0; + } + secp256k1_pubkey_save(pubkey, &Q); + secp256k1_ge_clear(&Q); + return 1; +} + +int secp256k1_ec_pubkey_serialize(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_pubkey* pubkey, unsigned int flags) { + secp256k1_ge Q; + size_t len; + int ret = 0; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(outputlen != NULL); + ARG_CHECK(*outputlen >= ((flags & SECP256K1_FLAGS_BIT_COMPRESSION) ? 33 : 65)); + len = *outputlen; + *outputlen = 0; + ARG_CHECK(output != NULL); + memset(output, 0, len); + ARG_CHECK(pubkey != NULL); + ARG_CHECK((flags & SECP256K1_FLAGS_TYPE_MASK) == SECP256K1_FLAGS_TYPE_COMPRESSION); + if (secp256k1_pubkey_load(ctx, &Q, pubkey)) { + ret = secp256k1_eckey_pubkey_serialize(&Q, output, &len, flags & SECP256K1_FLAGS_BIT_COMPRESSION); + if (ret) { + *outputlen = len; + } + } + return ret; +} + +static void secp256k1_ecdsa_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_ecdsa_signature* sig) { + (void)ctx; + if (sizeof(secp256k1_scalar) == 32) { + /* When the secp256k1_scalar type is exactly 32 byte, use its + * representation inside secp256k1_ecdsa_signature, as conversion is very fast. + * Note that secp256k1_ecdsa_signature_save must use the same representation. */ + memcpy(r, &sig->data[0], 32); + memcpy(s, &sig->data[32], 32); + } else { + secp256k1_scalar_set_b32(r, &sig->data[0], NULL); + secp256k1_scalar_set_b32(s, &sig->data[32], NULL); + } +} + +static void secp256k1_ecdsa_signature_save(secp256k1_ecdsa_signature* sig, const secp256k1_scalar* r, const secp256k1_scalar* s) { + if (sizeof(secp256k1_scalar) == 32) { + memcpy(&sig->data[0], r, 32); + memcpy(&sig->data[32], s, 32); + } else { + secp256k1_scalar_get_b32(&sig->data[0], r); + secp256k1_scalar_get_b32(&sig->data[32], s); + } +} + +int secp256k1_ecdsa_signature_parse_der(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) { + secp256k1_scalar r, s; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(input != NULL); + + if (secp256k1_ecdsa_sig_parse(&r, &s, input, inputlen)) { + secp256k1_ecdsa_signature_save(sig, &r, &s); + return 1; + } else { + memset(sig, 0, sizeof(*sig)); + return 0; + } +} + +int secp256k1_ecdsa_signature_parse_compact(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input64) { + secp256k1_scalar r, s; + int ret = 1; + int overflow = 0; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(input64 != NULL); + + secp256k1_scalar_set_b32(&r, &input64[0], &overflow); + ret &= !overflow; + secp256k1_scalar_set_b32(&s, &input64[32], &overflow); + ret &= !overflow; + if (ret) { + secp256k1_ecdsa_signature_save(sig, &r, &s); + } else { + memset(sig, 0, sizeof(*sig)); + } + return ret; +} + +int secp256k1_ecdsa_signature_serialize_der(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_ecdsa_signature* sig) { + secp256k1_scalar r, s; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output != NULL); + ARG_CHECK(outputlen != NULL); + ARG_CHECK(sig != NULL); + + secp256k1_ecdsa_signature_load(ctx, &r, &s, sig); + return secp256k1_ecdsa_sig_serialize(output, outputlen, &r, &s); +} + +int secp256k1_ecdsa_signature_serialize_compact(const secp256k1_context* ctx, unsigned char *output64, const secp256k1_ecdsa_signature* sig) { + secp256k1_scalar r, s; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output64 != NULL); + ARG_CHECK(sig != NULL); + + secp256k1_ecdsa_signature_load(ctx, &r, &s, sig); + secp256k1_scalar_get_b32(&output64[0], &r); + secp256k1_scalar_get_b32(&output64[32], &s); + return 1; +} + +int secp256k1_ecdsa_signature_normalize(const secp256k1_context* ctx, secp256k1_ecdsa_signature *sigout, const secp256k1_ecdsa_signature *sigin) { + secp256k1_scalar r, s; + int ret = 0; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sigin != NULL); + + secp256k1_ecdsa_signature_load(ctx, &r, &s, sigin); + ret = secp256k1_scalar_is_high(&s); + if (sigout != NULL) { + if (ret) { + secp256k1_scalar_negate(&s, &s); + } + secp256k1_ecdsa_signature_save(sigout, &r, &s); + } + + return ret; +} + +int secp256k1_ecdsa_verify(const secp256k1_context* ctx, const secp256k1_ecdsa_signature *sig, const unsigned char *msg32, const secp256k1_pubkey *pubkey) { + secp256k1_ge q; + secp256k1_scalar r, s; + secp256k1_scalar m; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx)); + ARG_CHECK(msg32 != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(pubkey != NULL); + + secp256k1_scalar_set_b32(&m, msg32, NULL); + secp256k1_ecdsa_signature_load(ctx, &r, &s, sig); + return (!secp256k1_scalar_is_high(&s) && + secp256k1_pubkey_load(ctx, &q, pubkey) && + secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &r, &s, &q, &m)); +} + +static SECP256K1_INLINE void buffer_append(unsigned char *buf, unsigned int *offset, const void *data, unsigned int len) { + memcpy(buf + *offset, data, len); + *offset += len; +} + +static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) { + unsigned char keydata[112]; + unsigned int offset = 0; + secp256k1_rfc6979_hmac_sha256 rng; + unsigned int i; + /* We feed a byte array to the PRNG as input, consisting of: + * - the private key (32 bytes) and message (32 bytes), see RFC 6979 3.2d. + * - optionally 32 extra bytes of data, see RFC 6979 3.6 Additional Data. + * - optionally 16 extra bytes with the algorithm name. + * Because the arguments have distinct fixed lengths it is not possible for + * different argument mixtures to emulate each other and result in the same + * nonces. + */ + buffer_append(keydata, &offset, key32, 32); + buffer_append(keydata, &offset, msg32, 32); + if (data != NULL) { + buffer_append(keydata, &offset, data, 32); + } + if (algo16 != NULL) { + buffer_append(keydata, &offset, algo16, 16); + } + secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, offset); + memset(keydata, 0, sizeof(keydata)); + for (i = 0; i <= counter; i++) { + secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32); + } + secp256k1_rfc6979_hmac_sha256_finalize(&rng); + return 1; +} + +const secp256k1_nonce_function secp256k1_nonce_function_rfc6979 = nonce_function_rfc6979; +const secp256k1_nonce_function secp256k1_nonce_function_default = nonce_function_rfc6979; + +int secp256k1_ecdsa_sign(const secp256k1_context* ctx, secp256k1_ecdsa_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) { + secp256k1_scalar r, s; + secp256k1_scalar sec, non, msg; + int ret = 0; + int overflow = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); + ARG_CHECK(msg32 != NULL); + ARG_CHECK(signature != NULL); + ARG_CHECK(seckey != NULL); + if (noncefp == NULL) { + noncefp = secp256k1_nonce_function_default; + } + + secp256k1_scalar_set_b32(&sec, seckey, &overflow); + /* Fail if the secret key is invalid. */ + if (!overflow && !secp256k1_scalar_is_zero(&sec)) { + unsigned char nonce32[32]; + unsigned int count = 0; + secp256k1_scalar_set_b32(&msg, msg32, NULL); + while (1) { + ret = noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count); + if (!ret) { + break; + } + secp256k1_scalar_set_b32(&non, nonce32, &overflow); + if (!overflow && !secp256k1_scalar_is_zero(&non)) { + if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, NULL)) { + break; + } + } + count++; + } + memset(nonce32, 0, 32); + secp256k1_scalar_clear(&msg); + secp256k1_scalar_clear(&non); + secp256k1_scalar_clear(&sec); + } + if (ret) { + secp256k1_ecdsa_signature_save(signature, &r, &s); + } else { + memset(signature, 0, sizeof(*signature)); + } + return ret; +} + +int secp256k1_ec_seckey_verify(const secp256k1_context* ctx, const unsigned char *seckey) { + secp256k1_scalar sec; + int ret; + int overflow; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(seckey != NULL); + + secp256k1_scalar_set_b32(&sec, seckey, &overflow); + ret = !overflow && !secp256k1_scalar_is_zero(&sec); + secp256k1_scalar_clear(&sec); + return ret; +} + +int secp256k1_ec_pubkey_create(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *seckey) { + secp256k1_gej pj; + secp256k1_ge p; + secp256k1_scalar sec; + int overflow; + int ret = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + memset(pubkey, 0, sizeof(*pubkey)); + ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); + ARG_CHECK(seckey != NULL); + + secp256k1_scalar_set_b32(&sec, seckey, &overflow); + ret = (!overflow) & (!secp256k1_scalar_is_zero(&sec)); + if (ret) { + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pj, &sec); + secp256k1_ge_set_gej(&p, &pj); + secp256k1_pubkey_save(pubkey, &p); + } + secp256k1_scalar_clear(&sec); + return ret; +} + +int secp256k1_ec_privkey_negate(const secp256k1_context* ctx, unsigned char *seckey) { + secp256k1_scalar sec; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(seckey != NULL); + + secp256k1_scalar_set_b32(&sec, seckey, NULL); + secp256k1_scalar_negate(&sec, &sec); + secp256k1_scalar_get_b32(seckey, &sec); + + return 1; +} + +int secp256k1_ec_pubkey_negate(const secp256k1_context* ctx, secp256k1_pubkey *pubkey) { + int ret = 0; + secp256k1_ge p; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + + ret = secp256k1_pubkey_load(ctx, &p, pubkey); + memset(pubkey, 0, sizeof(*pubkey)); + if (ret) { + secp256k1_ge_neg(&p, &p); + secp256k1_pubkey_save(pubkey, &p); + } + return ret; +} + +int secp256k1_ec_privkey_tweak_add(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) { + secp256k1_scalar term; + secp256k1_scalar sec; + int ret = 0; + int overflow = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(seckey != NULL); + ARG_CHECK(tweak != NULL); + + secp256k1_scalar_set_b32(&term, tweak, &overflow); + secp256k1_scalar_set_b32(&sec, seckey, NULL); + + ret = !overflow && secp256k1_eckey_privkey_tweak_add(&sec, &term); + memset(seckey, 0, 32); + if (ret) { + secp256k1_scalar_get_b32(seckey, &sec); + } + + secp256k1_scalar_clear(&sec); + secp256k1_scalar_clear(&term); + return ret; +} + +int secp256k1_ec_pubkey_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) { + secp256k1_ge p; + secp256k1_scalar term; + int ret = 0; + int overflow = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx)); + ARG_CHECK(pubkey != NULL); + ARG_CHECK(tweak != NULL); + + secp256k1_scalar_set_b32(&term, tweak, &overflow); + ret = !overflow && secp256k1_pubkey_load(ctx, &p, pubkey); + memset(pubkey, 0, sizeof(*pubkey)); + if (ret) { + if (secp256k1_eckey_pubkey_tweak_add(&ctx->ecmult_ctx, &p, &term)) { + secp256k1_pubkey_save(pubkey, &p); + } else { + ret = 0; + } + } + + return ret; +} + +int secp256k1_ec_privkey_tweak_mul(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) { + secp256k1_scalar factor; + secp256k1_scalar sec; + int ret = 0; + int overflow = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(seckey != NULL); + ARG_CHECK(tweak != NULL); + + secp256k1_scalar_set_b32(&factor, tweak, &overflow); + secp256k1_scalar_set_b32(&sec, seckey, NULL); + ret = !overflow && secp256k1_eckey_privkey_tweak_mul(&sec, &factor); + memset(seckey, 0, 32); + if (ret) { + secp256k1_scalar_get_b32(seckey, &sec); + } + + secp256k1_scalar_clear(&sec); + secp256k1_scalar_clear(&factor); + return ret; +} + +int secp256k1_ec_pubkey_tweak_mul(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) { + secp256k1_ge p; + secp256k1_scalar factor; + int ret = 0; + int overflow = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx)); + ARG_CHECK(pubkey != NULL); + ARG_CHECK(tweak != NULL); + + secp256k1_scalar_set_b32(&factor, tweak, &overflow); + ret = !overflow && secp256k1_pubkey_load(ctx, &p, pubkey); + memset(pubkey, 0, sizeof(*pubkey)); + if (ret) { + if (secp256k1_eckey_pubkey_tweak_mul(&ctx->ecmult_ctx, &p, &factor)) { + secp256k1_pubkey_save(pubkey, &p); + } else { + ret = 0; + } + } + + return ret; +} + +int secp256k1_context_randomize(secp256k1_context* ctx, const unsigned char *seed32) { + VERIFY_CHECK(ctx != NULL); + if (secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)) { + secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32); + } + return 1; +} + +int secp256k1_ec_pubkey_combine(const secp256k1_context* ctx, secp256k1_pubkey *pubnonce, const secp256k1_pubkey * const *pubnonces, size_t n) { + size_t i; + secp256k1_gej Qj; + secp256k1_ge Q; + + ARG_CHECK(pubnonce != NULL); + memset(pubnonce, 0, sizeof(*pubnonce)); + ARG_CHECK(n >= 1); + ARG_CHECK(pubnonces != NULL); + + secp256k1_gej_set_infinity(&Qj); + + for (i = 0; i < n; i++) { + secp256k1_pubkey_load(ctx, &Q, pubnonces[i]); + secp256k1_gej_add_ge(&Qj, &Qj, &Q); + } + if (secp256k1_gej_is_infinity(&Qj)) { + return 0; + } + secp256k1_ge_set_gej(&Q, &Qj); + secp256k1_pubkey_save(pubnonce, &Q); + return 1; +} + +#ifdef ENABLE_MODULE_ECDH +# include "modules/ecdh/main_impl.h" +#endif + +#ifdef ENABLE_MODULE_RECOVERY +# include "modules/recovery/main_impl.h" +#endif diff --git a/src/secp256k1_tests/testrand.h b/src/secp256k1_tests/testrand.h new file mode 100644 index 0000000..f1f9be0 --- /dev/null +++ b/src/secp256k1_tests/testrand.h @@ -0,0 +1,38 @@ +/********************************************************************** + * 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_TESTRAND_H +#define SECP256K1_TESTRAND_H + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +/* A non-cryptographic RNG used only for test infrastructure. */ + +/** Seed the pseudorandom number generator for testing. */ +SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16); + +/** Generate a pseudorandom number in the range [0..2**32-1]. */ +static uint32_t secp256k1_rand32(void); + +/** Generate a pseudorandom number in the range [0..2**bits-1]. Bits must be 1 or + * more. */ +static uint32_t secp256k1_rand_bits(int bits); + +/** Generate a pseudorandom number in the range [0..range-1]. */ +static uint32_t secp256k1_rand_int(uint32_t range); + +/** Generate a pseudorandom 32-byte array. */ +static void secp256k1_rand256(unsigned char *b32); + +/** Generate a pseudorandom 32-byte array with long sequences of zero and one bits. */ +static void secp256k1_rand256_test(unsigned char *b32); + +/** Generate pseudorandom bytes with long sequences of zero and one bits. */ +static void secp256k1_rand_bytes_test(unsigned char *bytes, size_t len); + +#endif /* SECP256K1_TESTRAND_H */ diff --git a/src/secp256k1_tests/testrand_impl.h b/src/secp256k1_tests/testrand_impl.h new file mode 100644 index 0000000..30a91e5 --- /dev/null +++ b/src/secp256k1_tests/testrand_impl.h @@ -0,0 +1,110 @@ +/********************************************************************** + * Copyright (c) 2013-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_TESTRAND_IMPL_H +#define SECP256K1_TESTRAND_IMPL_H + +#include +#include + +#include "testrand.h" +#include "hash.h" + +static secp256k1_rfc6979_hmac_sha256 secp256k1_test_rng; +static uint32_t secp256k1_test_rng_precomputed[8]; +static int secp256k1_test_rng_precomputed_used = 8; +static uint64_t secp256k1_test_rng_integer; +static int secp256k1_test_rng_integer_bits_left = 0; + +SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16) { + secp256k1_rfc6979_hmac_sha256_initialize(&secp256k1_test_rng, seed16, 16); +} + +SECP256K1_INLINE static uint32_t secp256k1_rand32(void) { + if (secp256k1_test_rng_precomputed_used == 8) { + secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, (unsigned char*)(&secp256k1_test_rng_precomputed[0]), sizeof(secp256k1_test_rng_precomputed)); + secp256k1_test_rng_precomputed_used = 0; + } + return secp256k1_test_rng_precomputed[secp256k1_test_rng_precomputed_used++]; +} + +static uint32_t secp256k1_rand_bits(int bits) { + uint32_t ret; + if (secp256k1_test_rng_integer_bits_left < bits) { + secp256k1_test_rng_integer |= (((uint64_t)secp256k1_rand32()) << secp256k1_test_rng_integer_bits_left); + secp256k1_test_rng_integer_bits_left += 32; + } + ret = secp256k1_test_rng_integer; + secp256k1_test_rng_integer >>= bits; + secp256k1_test_rng_integer_bits_left -= bits; + ret &= ((~((uint32_t)0)) >> (32 - bits)); + return ret; +} + +static uint32_t secp256k1_rand_int(uint32_t range) { + /* We want a uniform integer between 0 and range-1, inclusive. + * B is the smallest number such that range <= 2**B. + * two mechanisms implemented here: + * - generate B bits numbers until one below range is found, and return it + * - find the largest multiple M of range that is <= 2**(B+A), generate B+A + * bits numbers until one below M is found, and return it modulo range + * The second mechanism consumes A more bits of entropy in every iteration, + * but may need fewer iterations due to M being closer to 2**(B+A) then + * range is to 2**B. The array below (indexed by B) contains a 0 when the + * first mechanism is to be used, and the number A otherwise. + */ + static const int addbits[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 0}; + uint32_t trange, mult; + int bits = 0; + if (range <= 1) { + return 0; + } + trange = range - 1; + while (trange > 0) { + trange >>= 1; + bits++; + } + if (addbits[bits]) { + bits = bits + addbits[bits]; + mult = ((~((uint32_t)0)) >> (32 - bits)) / range; + trange = range * mult; + } else { + trange = range; + mult = 1; + } + while(1) { + uint32_t x = secp256k1_rand_bits(bits); + if (x < trange) { + return (mult == 1) ? x : (x % range); + } + } +} + +static void secp256k1_rand256(unsigned char *b32) { + secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, b32, 32); +} + +static void secp256k1_rand_bytes_test(unsigned char *bytes, size_t len) { + size_t bits = 0; + memset(bytes, 0, len); + while (bits < len * 8) { + int now; + uint32_t val; + now = 1 + (secp256k1_rand_bits(6) * secp256k1_rand_bits(5) + 16) / 31; + val = secp256k1_rand_bits(1); + while (now > 0 && bits < len * 8) { + bytes[bits / 8] |= val << (bits % 8); + now--; + bits++; + } + } +} + +static void secp256k1_rand256_test(unsigned char *b32) { + secp256k1_rand_bytes_test(b32, 32); +} + +#endif /* SECP256K1_TESTRAND_IMPL_H */ diff --git a/src/secp256k1_tests/tests.c b/src/secp256k1_tests/tests.c new file mode 100644 index 0000000..4027f8b --- /dev/null +++ b/src/secp256k1_tests/tests.c @@ -0,0 +1,5215 @@ +/********************************************************************** + * 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.* + **********************************************************************/ +#define HAVE_CONFIG_H +#define VERIFY +#define SECP256K1_BUILD + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include +#include +#include + +#include + +#include "sysctl.h" +#include "uarths.h" +#include "sleep.h" + +#include "secp256k1_c.h" +#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.h" +#include "contrib/lax_der_privatekey_parsing.c.h" + +#if !defined(VG_CHECK) +# if defined(VALGRIND) +# include +# 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 = 4; /* reduced from 64 to make the tests run in reasonable time */ +static secp256k1_context *ctx = NULL; + +//#define fprintf(file, fmt, ...) printf(fmt, ##__VA_ARGS__) + +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_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_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_all[i], &gej[i]); + } + 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); +} + +void test_ecmult_multi_batch_size_helper(void) { + size_t n_batches, n_batch_points, max_n_batch_points, n; + + max_n_batch_points = 0; + n = 1; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 0); + + max_n_batch_points = 1; + n = 0; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == 0); + CHECK(n_batch_points == 0); + + max_n_batch_points = 2; + n = 5; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == 3); + CHECK(n_batch_points == 2); + + max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH; + n = ECMULT_MAX_POINTS_PER_BATCH; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == 1); + CHECK(n_batch_points == ECMULT_MAX_POINTS_PER_BATCH); + + max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH + 1; + n = ECMULT_MAX_POINTS_PER_BATCH + 1; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == 2); + CHECK(n_batch_points == ECMULT_MAX_POINTS_PER_BATCH/2 + 1); + + max_n_batch_points = 1; + n = SIZE_MAX; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == SIZE_MAX); + CHECK(n_batch_points == 1); + + max_n_batch_points = 2; + n = SIZE_MAX; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == SIZE_MAX/2 + 1); + CHECK(n_batch_points == 2); +} + +/** + * 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(NULL, 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_batch_size_helper(); + 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_RECOVERY +# include "modules/recovery/tests_impl.h" +#endif + +int main(int argc, char **argv) { + if (current_coreid() != 0) { + while (1) + asm volatile ("wfi"); + } + + sysctl_pll_set_freq(SYSCTL_PLL0, 800000000UL); + + uarths_init(); + usleep(100000); + + unsigned char seed16[16] = {0}; + unsigned char run32[32] = {0}; +#if 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); + } + } +#endif + 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 */ + printf("run_context_tests()\n"); + run_context_tests(); + printf("run_scratch_tests()\n"); + 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)); + } + + printf("num_rand_bits\n"); + run_rand_bits(); + printf("num_rand_int\n"); + run_rand_int(); + + printf("run_sha256_tests\n"); + run_sha256_tests(); + printf("run_hmac_sha256_tests\n"); + run_hmac_sha256_tests(); + printf("run_rfc6979_hmac_sha256_tests\n"); + run_rfc6979_hmac_sha256_tests(); + +#ifndef USE_NUM_NONE + /* num tests */ + printf("run_num_smalltests\n"); + run_num_smalltests(); +#endif + + /* scalar tests */ + printf("run_scalar_tests\n"); + run_scalar_tests(); + + /* field tests */ + printf("field tests\n"); + printf(" run_field_inv\n"); + run_field_inv(); + printf(" run_field_inv_var\n"); + run_field_inv_var(); + printf(" run_field_inv_all_var\n"); + run_field_inv_all_var(); + printf(" run_field_misc\n"); + run_field_misc(); + printf(" run_field_convert\n"); + run_field_convert(); + printf(" run_sqr\n"); + run_sqr(); + printf(" run_sqrt\n"); + run_sqrt(); + + /* group tests */ + printf("group tests\n"); + printf(" run_ge\n"); + run_ge(); + printf(" run_group_decompress\n"); + run_group_decompress(); + + /* ecmult tests */ + printf("ecmult tests\n"); + printf(" run_wnaf\n"); + run_wnaf(); + printf(" run_point_times_order\n"); + run_point_times_order(); + printf(" run_ecmult_chain\n"); + run_ecmult_chain(); + printf(" run_ecmult_constants\n"); + run_ecmult_constants(); + printf(" run_ecmult_gen_blind\n"); + run_ecmult_gen_blind(); + printf(" run_ecmult_const_tests\n"); + run_ecmult_const_tests(); + // Runs out of memory + //printf(" run_ecmult_multi_tests\n"); + //run_ecmult_multi_tests(); + printf(" run_ec_combine\n"); + run_ec_combine(); + + /* endomorphism tests */ +#ifdef USE_ENDOMORPHISM + printf("endomorphism tests\n"); + run_endomorphism_tests(); +#endif + + /* EC point parser test */ + printf("run_ec_pubkey_parse_test\n"); + run_ec_pubkey_parse_test(); + + /* EC key edge cases */ + printf("run_eckey_edge_case_test\n"); + run_eckey_edge_case_test(); + +#ifdef ENABLE_MODULE_ECDH + /* ecdh tests */ + printf("run_ecdh_tests\n"); + run_ecdh_tests(); +#endif + + /* ecdsa tests */ + printf("ecdsa tests\n"); + printf(" run_random_pubkeys\n"); + run_random_pubkeys(); + printf(" run_ecdsa_der_parse\n"); + run_ecdsa_der_parse(); + printf(" run_ecdsa_sign_verify\n"); + run_ecdsa_sign_verify(); + printf(" run_ecdsa_end_to_end\n"); + run_ecdsa_end_to_end(); + printf(" run_ecdsa_edge_cases\n"); + run_ecdsa_edge_cases(); +#ifdef ENABLE_OPENSSL_TESTS + run_ecdsa_openssl(); +#endif + +#ifdef ENABLE_MODULE_RECOVERY + /* ECDSA pubkey recovery tests */ + printf("run_recovery_tests\n"); + run_recovery_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"); + + while (1) + asm volatile ("wfi"); + return 0; +} diff --git a/src/secp256k1_tests/util.h b/src/secp256k1_tests/util.h new file mode 100644 index 0000000..e1f5b76 --- /dev/null +++ b/src/secp256k1_tests/util.h @@ -0,0 +1,121 @@ +/********************************************************************** + * 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_UTIL_H +#define SECP256K1_UTIL_H + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include +#include +#include + +typedef struct { + void (*fn)(const char *text, void* data); + const void* data; +} secp256k1_callback; + +static SECP256K1_INLINE void secp256k1_callback_call(const secp256k1_callback * const cb, const char * const text) { + cb->fn(text, (void*)cb->data); +} + +#ifdef DETERMINISTIC +#define TEST_FAILURE(msg) do { \ + fprintf(stderr, "%s\n", msg); \ + abort(); \ +} while(0); +#else +#define TEST_FAILURE(msg) do { \ + fprintf(stderr, "%s:%d: %s\n", __FILE__, __LINE__, msg); \ + abort(); \ +} while(0) +#endif + +#if SECP256K1_GNUC_PREREQ(3, 0) +#define EXPECT(x,c) __builtin_expect((x),(c)) +#else +#define EXPECT(x,c) (x) +#endif + +#ifdef DETERMINISTIC +#define CHECK(cond) do { \ + if (EXPECT(!(cond), 0)) { \ + TEST_FAILURE("test condition failed"); \ + } \ +} while(0) +#else +#define CHECK(cond) do { \ + if (EXPECT(!(cond), 0)) { \ + TEST_FAILURE("test condition failed: " #cond); \ + } \ +} while(0) +#endif + +/* Like assert(), but when VERIFY is defined, and side-effect safe. */ +#if defined(COVERAGE) +#define VERIFY_CHECK(check) +#define VERIFY_SETUP(stmt) +#elif defined(VERIFY) +#define VERIFY_CHECK CHECK +#define VERIFY_SETUP(stmt) do { stmt; } while(0) +#else +#define VERIFY_CHECK(cond) do { (void)(cond); } while(0) +#define VERIFY_SETUP(stmt) +#endif + +static SECP256K1_INLINE void *checked_malloc(const secp256k1_callback* cb, size_t size) { + void *ret = malloc(size); + if (ret == NULL) { + secp256k1_callback_call(cb, "Out of memory"); + } + return ret; +} + +static SECP256K1_INLINE void *checked_realloc(const secp256k1_callback* cb, void *ptr, size_t size) { + void *ret = realloc(ptr, size); + if (ret == NULL) { + secp256k1_callback_call(cb, "Out of memory"); + } + return ret; +} + +/* Macro for restrict, when available and not in a VERIFY build. */ +#if defined(SECP256K1_BUILD) && defined(VERIFY) +# define SECP256K1_RESTRICT +#else +# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) ) +# if SECP256K1_GNUC_PREREQ(3,0) +# define SECP256K1_RESTRICT __restrict__ +# elif (defined(_MSC_VER) && _MSC_VER >= 1400) +# define SECP256K1_RESTRICT __restrict +# else +# define SECP256K1_RESTRICT +# endif +# else +# define SECP256K1_RESTRICT restrict +# endif +#endif + +#if defined(_WIN32) +# define I64FORMAT "I64d" +# define I64uFORMAT "I64u" +#else +# define I64FORMAT "lld" +# define I64uFORMAT "llu" +#endif + +#if defined(HAVE___INT128) +# if defined(__GNUC__) +# define SECP256K1_GNUC_EXT __extension__ +# else +# define SECP256K1_GNUC_EXT +# endif +SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t; +#endif + +#endif /* SECP256K1_UTIL_H */