From 326e7de416493999cc7f67318d64c9850ecdabd3 Mon Sep 17 00:00:00 2001 From: Zhi Guan Date: Tue, 20 Feb 2024 11:24:00 +0800 Subject: [PATCH] Add SM2 Z256 implementation --- CMakeLists.txt | 10 +- include/gmssl/sm2_z256.h | 87 + src/sm2_z256.c | 1004 ++++++++ src/sm2_z256_table.c | 4835 ++++++++++++++++++++++++++++++++++++++ tests/sm2_z256test.c | 626 +---- 5 files changed, 6054 insertions(+), 508 deletions(-) create mode 100644 include/gmssl/sm2_z256.h create mode 100644 src/sm2_z256.c create mode 100644 src/sm2_z256_table.c diff --git a/CMakeLists.txt b/CMakeLists.txt index 57f2626d0..0635e7b48 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -313,9 +313,13 @@ if (ENABLE_SM4_XTS) endif() - - - +option(ENABLE_SM2_Z256 "Enable SM2 z256 implementation" OFF) +if (ENABLE_SM2_Z256) + message(STATUS "ENABLE_SM2_Z256 is ON") + add_definitions(-DENABLE_SM2_Z256) + list(APPEND src src/sm2_z256.c src/sm2_z256_table.c) + list(APPEND tests sm2_z256) +endif() option(ENABLE_SM2_EXTS "Enable SM2 Extensions" OFF) diff --git a/include/gmssl/sm2_z256.h b/include/gmssl/sm2_z256.h new file mode 100644 index 000000000..6ce939dff --- /dev/null +++ b/include/gmssl/sm2_z256.h @@ -0,0 +1,87 @@ +/* + * Copyright 2014-2024 The GmSSL Project. All Rights Reserved. + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + + + +#ifndef GMSSL_SM2_Z256_H +#define GMSSL_SM2_Z256_H + +#include +#include +#include + +#ifdef __cplusplus +extern "C" { +#endif + + +void sm2_z256_copy(uint64_t r[4], const uint64_t a[4]); +void sm2_z256_copy_conditional(uint64_t dst[4], const uint64_t src[4], uint64_t move); +void sm2_z256_from_bytes(uint64_t r[4], const uint8_t in[32]); +void sm2_z256_to_bytes(const uint64_t a[4], uint8_t out[32]); +int sm2_z256_cmp(const uint64_t a[4], const uint64_t b[4]); +uint64_t sm2_z256_equ(const uint64_t a[4], const uint64_t b[4]); +uint64_t sm2_z256_add(uint64_t r[4], const uint64_t a[4], const uint64_t b[4]); +uint64_t sm2_z256_sub(uint64_t r[4], const uint64_t a[4], const uint64_t b[4]); +void sm2_z256_mul(uint64_t r[8], const uint64_t a[4], const uint64_t b[4]); +uint64_t sm2_z512_add(uint64_t r[8], const uint64_t a[8], const uint64_t b[8]); +int sm2_z256_get_booth(const uint64_t a[4], unsigned int window_size, int i); +void sm2_z256_from_hex(uint64_t r[4], const char *hex); +int sm2_z256_print(FILE *fp, int ind, int fmt, const char *label, const uint64_t a[4]); +int sm2_z512_print(FILE *fp, int ind, int fmt, const char *label, const uint64_t a[8]); + +void sm2_z256_modp_add(uint64_t r[4], const uint64_t a[4], const uint64_t b[4]); +void sm2_z256_modp_sub(uint64_t r[4], const uint64_t a[4], const uint64_t b[4]); +void sm2_z256_modp_neg(uint64_t r[4], const uint64_t a[4]); +void sm2_z256_modp_mul_by_2(uint64_t r[4], const uint64_t a[4]); +void sm2_z256_modp_mul_by_3(uint64_t r[4], const uint64_t a[4]); +void sm2_z256_modp_div_by_2(uint64_t r[4], const uint64_t a[4]); + +void sm2_z256_to_mont(const uint64_t a[4], uint64_t r[4]); +void sm2_z256_from_mont(uint64_t r[4], const uint64_t a[4]); +void sm2_z256_mont_mul(uint64_t r[4], const uint64_t a[4], const uint64_t b[4]); +void sm2_z256_mont_sqr(uint64_t r[4], const uint64_t a[4]); +void sm2_z256_mont_inv(uint64_t r[4], const uint64_t a[4]); +int sm2_z256_mont_print(FILE *fp, int ind, int fmt, const char *label, const uint64_t a[4]); + + +typedef struct { + uint64_t X[4]; + uint64_t Y[4]; + uint64_t Z[4]; +} SM2_Z256_POINT; + +void sm2_z256_point_to_bytes(const SM2_Z256_POINT *P, uint8_t out[64]); +void sm2_z256_point_dbl(SM2_Z256_POINT *R, const SM2_Z256_POINT *A); +void sm2_z256_point_add(SM2_Z256_POINT *r, const SM2_Z256_POINT *a, const SM2_Z256_POINT *b); +void sm2_z256_point_neg(SM2_Z256_POINT *R, const SM2_Z256_POINT *P); +void sm2_z256_point_sub(SM2_Z256_POINT *R, const SM2_Z256_POINT *A, const SM2_Z256_POINT *B); +void sm2_z256_point_get_affine(const SM2_Z256_POINT *P, uint64_t x[4], uint64_t y[4]); +int sm2_z256_point_print(FILE *fp, int fmt, int ind, const char *label, const SM2_Z256_POINT *P); + + +typedef struct { + uint64_t x[4]; + uint64_t y[4]; +} SM2_Z256_POINT_AFFINE; + +void sm2_z256_point_copy_affine(SM2_Z256_POINT *R, const SM2_Z256_POINT_AFFINE *P); +void sm2_z256_point_add_affine(SM2_Z256_POINT *r, const SM2_Z256_POINT *a, const SM2_Z256_POINT_AFFINE *b); +void sm2_z256_point_sub_affine(SM2_Z256_POINT *R, const SM2_Z256_POINT *A, const SM2_Z256_POINT_AFFINE *B); +int sm2_z256_point_affine_print(FILE *fp, int fmt, int ind, const char *label, const SM2_Z256_POINT_AFFINE *P); + +void sm2_z256_point_mul_generator(SM2_Z256_POINT *R, const uint64_t k[4]); +void sm2_z256_point_mul(SM2_Z256_POINT *R, const SM2_Z256_POINT *P, const uint64_t k[4]); +void sm2_z256_point_mul_sum(SM2_Z256_POINT *R, const uint64_t t[4], const SM2_Z256_POINT *P, const uint64_t s[4]); + + +#ifdef __cplusplus +} +#endif +#endif diff --git a/src/sm2_z256.c b/src/sm2_z256.c new file mode 100644 index 000000000..d3ae135c1 --- /dev/null +++ b/src/sm2_z256.c @@ -0,0 +1,1004 @@ +/* + * Copyright 2014-2024 The GmSSL Project. All Rights Reserved. + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ +/* + * Copyright 2014-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ +/****************************************************************************** + * * + * Copyright 2014 Intel Corporation * + * * + * Licensed under the Apache License, Version 2.0 (the "License"); * + * you may not use this file except in compliance with the License. * + * You may obtain a copy of the License at * + * * + * http://www.apache.org/licenses/LICENSE-2.0 * + * * + * Unless required by applicable law or agreed to in writing, software * + * distributed under the License is distributed on an "AS IS" BASIS, * + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * + * See the License for the specific language governing permissions and * + * limitations under the License. * + * * + ****************************************************************************** + * * + * Developers and authors: * + * Shay Gueron (1, 2), and Vlad Krasnov (1) * + * (1) Intel Corporation, Israel Development Center * + * (2) University of Haifa * + * Reference: * + * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with * + * 256 Bit Primes" * + * * + ******************************************************************************/ + + +#include +#include +#include +#include +#include +#include +#include +#include + + +// z256 + +void sm2_z256_copy(uint64_t r[4], const uint64_t a[4]) +{ + r[3] = a[3]; + r[2] = a[2]; + r[1] = a[1]; + r[0] = a[0]; +} + +void sm2_z256_copy_conditional(uint64_t dst[4], const uint64_t src[4], uint64_t move) +{ + uint64_t mask1 = 0-move; + uint64_t mask2 = ~mask1; + + dst[0] = (src[0] & mask1) ^ (dst[0] & mask2); + dst[1] = (src[1] & mask1) ^ (dst[1] & mask2); + dst[2] = (src[2] & mask1) ^ (dst[2] & mask2); + dst[3] = (src[3] & mask1) ^ (dst[3] & mask2); +} + +void sm2_z256_from_bytes(uint64_t r[4], const uint8_t in[32]) +{ + r[3] = GETU64(in); + r[2] = GETU64(in + 8); + r[1] = GETU64(in + 16); + r[0] = GETU64(in + 24); +} + +void sm2_z256_to_bytes(const uint64_t a[4], uint8_t out[32]) +{ + PUTU64(out, a[3]); + PUTU64(out + 8, a[2]); + PUTU64(out + 16, a[1]); + PUTU64(out + 24, a[0]); +} + +static uint64_t is_zero(uint64_t in) +{ + in |= (0 - in); + in = ~in; + in >>= 63; + return in; +} + +uint64_t sm2_z256_equ(const uint64_t a[4], const uint64_t b[4]) +{ + uint64_t res; + + res = a[0] ^ b[0]; + res |= a[1] ^ b[1]; + res |= a[2] ^ b[2]; + res |= a[3] ^ b[3]; + + return is_zero(res); +} + +int sm2_z256_cmp(const uint64_t a[4], const uint64_t b[4]) +{ + if (a[3] > b[3]) return 1; + else if (a[3] < b[3]) return -1; + if (a[2] > b[2]) return 1; + else if (a[2] < b[2]) return -1; + if (a[1] > b[1]) return 1; + else if (a[1] < b[1]) return -1; + if (a[0] > b[0]) return 1; + else if (a[0] < b[0]) return -1; + return 0; +} + +uint64_t sm2_z256_add(uint64_t r[4], const uint64_t a[4], const uint64_t b[4]) +{ + uint64_t t, c = 0; + + t = a[0] + b[0]; + c = t < a[0]; + r[0] = t; + + t = a[1] + c; + c = t < a[1]; + r[1] = t + b[1]; + c += r[1] < t; + + t = a[2] + c; + c = t < a[2]; + r[2] = t + b[2]; + c += r[2] < t; + + t = a[3] + c; + c = t < a[3]; + r[3] = t + b[3]; + c += r[3] < t; + + return c; +} + +uint64_t sm2_z256_sub(uint64_t r[4], const uint64_t a[4], const uint64_t b[4]) +{ + uint64_t t, c = 0; + + t = a[0] - b[0]; + c = t > a[0]; + r[0] = t; + + t = a[1] - c; + c = t > a[1]; + r[1] = t - b[1]; + c += r[1] > t; + + t = a[2] - c; + c = t > a[2]; + r[2] = t - b[2]; + c += r[2] > t; + + t = a[3] - c; + c = t > a[3]; + r[3] = t - b[3]; + c += r[3] > t; + + return c; +} + +void sm2_z256_mul(uint64_t r[8], const uint64_t a[4], const uint64_t b[4]) +{ + uint64_t a_[8]; + uint64_t b_[8]; + uint64_t s[16] = {0}; + uint64_t u; + int i, j; + + for (i = 0; i < 4; i++) { + a_[2 * i] = a[i] & 0xffffffff; + b_[2 * i] = b[i] & 0xffffffff; + a_[2 * i + 1] = a[i] >> 32; + b_[2 * i + 1] = b[i] >> 32; + } + + for (i = 0; i < 8; i++) { + u = 0; + for (j = 0; j < 8; j++) { + u = s[i + j] + a_[i] * b_[j] + u; + s[i + j] = u & 0xffffffff; + u >>= 32; + } + s[i + 8] = u; + } + + for (i = 0; i < 8; i++) { + r[i] = (s[2 * i + 1] << 32) | s[2 * i]; + } +} + +uint64_t sm2_z512_add(uint64_t r[8], const uint64_t a[8], const uint64_t b[8]) +{ + uint64_t t, c = 0; + + t = a[0] + b[0]; + c = t < a[0]; + r[0] = t; + + t = a[1] + c; + c = t < a[1]; + r[1] = t + b[1]; + c += r[1] < t; + + t = a[2] + c; + c = t < a[2]; + r[2] = t + b[2]; + c += r[2] < t; + + t = a[3] + c; + c = t < a[3]; + r[3] = t + b[3]; + c += r[3] < t; + + t = a[4] + c; + c = t < a[4]; + r[4] = t + b[4]; + c += r[4] < t; + + t = a[5] + c; + c = t < a[5]; + r[5] = t + b[5]; + c += r[5] < t; + + t = a[6] + c; + c = t < a[6]; + r[6] = t + b[6]; + c += r[6] < t; + + t = a[7] + c; + c = t < a[7]; + r[7] = t + b[7]; + c += r[7] < t; + + return c; +} + +int sm2_z256_get_booth(const uint64_t a[4], unsigned int window_size, int i) +{ + uint64_t mask = (1 << window_size) - 1; + uint64_t wbits; + int n, j; + + if (i == 0) { + return ((a[0] << 1) & mask) - (a[0] & mask); + } + + j = i * window_size - 1; + n = j / 64; + j = j % 64; + + wbits = a[n] >> j; + if ((64 - j) < (window_size + 1) && n < 3) { + wbits |= a[n + 1] << (64 - j); + } + return (wbits & mask) - ((wbits >> 1) & mask); +} + +void sm2_z256_from_hex(uint64_t r[4], const char *hex) +{ + uint8_t bytes[32]; + size_t len; + + hex_to_bytes(hex, 64, bytes, &len); + sm2_z256_from_bytes(r, bytes); +} + +int sm2_z256_print(FILE *fp, int ind, int fmt, const char *label, const uint64_t a[4]) +{ + format_print(fp, ind, fmt, "%s: %016llx%016llx%016llx%016llx\n", label, a[3], a[2], a[1], a[0]); + return 1; +} + +int sm2_z512_print(FILE *fp, int ind, int fmt, const char *label, const uint64_t a[8]) +{ + format_print(fp, ind, fmt, "%s: %016llx%016llx%016llx%016llx%016llx%016llx%016llx%016llx\n", + label, a[7], a[6], a[5], a[4], a[3], a[2], a[1], a[0]); + return 1; +} + + +// z256 mod p + +// p = 2^256 - 2^224 - 2^96 + 2^64 - 1 +const uint64_t SM2_Z256_P[4] = { + 0xffffffffffffffff, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffeffffffff +}; + +// mont(1) = 2^256 mod p = 2^224 + 2^96 - 2^64 + 1 +const uint64_t SM2_Z256_NEG_P[4] = { + 1, ((uint64_t)1 << 32) - 1, 0, ((uint64_t)1 << 32) }; + + +void sm2_z256_modp_add(uint64_t r[4], const uint64_t a[4], const uint64_t b[4]) +{ + uint64_t c; + + c = sm2_z256_add(r, a, b); + + if (c) { + // a + b - p = (a + b - 2^256) + (2^256 - p) + (void)sm2_z256_add(r, r, SM2_Z256_NEG_P); + return; + } + + if (sm2_z256_cmp(r, SM2_Z256_P) >= 0) { + + (void)sm2_z256_sub(r, r, SM2_Z256_P); + } +} + +void sm2_z256_modp_sub(uint64_t r[4], const uint64_t a[4], const uint64_t b[4]) +{ + uint64_t c; + + c = sm2_z256_sub(r, a, b); + + if (c) { + // a - b + p = (a - b + 2^256) - (2^256 - p) + (void)sm2_z256_sub(r, r, SM2_Z256_NEG_P); + } +} + +void sm2_z256_modp_mul_by_2(uint64_t r[4], const uint64_t a[4]) +{ + sm2_z256_modp_add(r, a, a); +} + +void sm2_z256_modp_mul_by_3(uint64_t r[4], const uint64_t a[4]) +{ + uint64_t t[4]; + sm2_z256_modp_add(t, a, a); + sm2_z256_modp_add(r, t, a); +} + +void sm2_z256_modp_div_by_2(uint64_t r[4], const uint64_t a[4]) +{ + uint64_t c = 0; + + if (a[0] & 1) { + c = sm2_z256_add(r, a, SM2_Z256_P); + } else { + r[0] = a[0]; + r[1] = a[1]; + r[2] = a[2]; + r[3] = a[3]; + } + + r[0] = (r[0] >> 1) | ((r[1] & 1) << 63); + r[1] = (r[1] >> 1) | ((r[2] & 1) << 63); + r[2] = (r[2] >> 1) | ((r[3] & 1) << 63); + r[3] = (r[3] >> 1) | ((c & 1) << 63); +} + +void sm2_z256_modp_neg(uint64_t r[4], const uint64_t a[4]) +{ + (void)sm2_z256_sub(r, SM2_Z256_P, a); +} + + +// montegomery + +const uint64_t *SM2_Z256_MONT_ONE = SM2_Z256_NEG_P; + +// z = xy +// c = (z + (z * p' mod 2^256) * p)/2^256 +void sm2_z256_mont_mul(uint64_t r[4], const uint64_t a[4], const uint64_t b[4]) +{ + uint64_t z[8]; + uint64_t t[8]; + uint64_t c; + + // p' = -p^(-1) mod 2^256 = fffffffc00000001fffffffe00000000ffffffff000000010000000000000001 + const uint64_t p_[4] = { + 0x0000000000000001, 0xffffffff00000001, 0xfffffffe00000000, 0xfffffffc00000001 + }; + + //sm2_z256_print(stderr, 0, 0, "a", a); + //sm2_z256_print(stderr, 0, 0, "b", b); + + // z = a * b + sm2_z256_mul(z, a, b); + //sm2_z512_print(stderr, 0, 0, "z", z); + + // t = low(z) * p' + sm2_z256_mul(t, z, p_); + //sm2_z256_print(stderr, 0, 0, "z * p' mod 2^256", t); + + // t = low(t) * p + sm2_z256_mul(t, t, SM2_Z256_P); + //sm2_z512_print(stderr, 0, 0, "(z * p' mod 2^256) * p", t); + + // z = z + t + c = sm2_z512_add(z, z, t); + //sm2_z512_print(stderr, 0, 0, "z", z); + + // r = high(r) + sm2_z256_copy(r, z + 4); + //sm2_z256_print(stderr, 0, 0, "r", r); + + if (c) { + sm2_z256_add(r, r, SM2_Z256_MONT_ONE); + //sm2_z256_print(stderr, 0, 0, "r1", r); + + } else if (sm2_z256_cmp(r, SM2_Z256_P) >= 0) { + (void)sm2_z256_sub(r, r, SM2_Z256_P); + //sm2_z256_print(stderr, 0, 0, "r2", r); + } +} + +void sm2_z256_mont_sqr(uint64_t r[4], const uint64_t a[4]) +{ + sm2_z256_mont_mul(r, a, a); +} + +void sm2_z256_mont_inv(uint64_t r[4], const uint64_t a[4]) +{ + uint64_t a1[4]; + uint64_t a2[4]; + uint64_t a3[4]; + uint64_t a4[4]; + uint64_t a5[4]; + int i; + + sm2_z256_mont_sqr(a1, a); + sm2_z256_mont_mul(a2, a1, a); + sm2_z256_mont_sqr(a3, a2); + sm2_z256_mont_sqr(a3, a3); + sm2_z256_mont_mul(a3, a3, a2); + sm2_z256_mont_sqr(a4, a3); + sm2_z256_mont_sqr(a4, a4); + sm2_z256_mont_sqr(a4, a4); + sm2_z256_mont_sqr(a4, a4); + sm2_z256_mont_mul(a4, a4, a3); + sm2_z256_mont_sqr(a5, a4); + for (i = 1; i < 8; i++) { + sm2_z256_mont_sqr(a5, a5); + } + sm2_z256_mont_mul(a5, a5, a4); + for (i = 0; i < 8; i++) { + sm2_z256_mont_sqr(a5, a5); + } + sm2_z256_mont_mul(a5, a5, a4); + for (i = 0; i < 4; i++) { + sm2_z256_mont_sqr(a5, a5); + } + sm2_z256_mont_mul(a5, a5, a3); + sm2_z256_mont_sqr(a5, a5); + sm2_z256_mont_sqr(a5, a5); + sm2_z256_mont_mul(a5, a5, a2); + sm2_z256_mont_sqr(a5, a5); + sm2_z256_mont_mul(a5, a5, a); + sm2_z256_mont_sqr(a4, a5); + sm2_z256_mont_mul(a3, a4, a1); + sm2_z256_mont_sqr(a5, a4); + for (i = 1; i< 31; i++) { + sm2_z256_mont_sqr(a5, a5); + } + sm2_z256_mont_mul(a4, a5, a4); + sm2_z256_mont_sqr(a4, a4); + sm2_z256_mont_mul(a4, a4, a); + sm2_z256_mont_mul(a3, a4, a2); + for (i = 0; i < 33; i++) { + sm2_z256_mont_sqr(a5, a5); + } + sm2_z256_mont_mul(a2, a5, a3); + sm2_z256_mont_mul(a3, a2, a3); + for (i = 0; i < 32; i++) { + sm2_z256_mont_sqr(a5, a5); + } + sm2_z256_mont_mul(a2, a5, a3); + sm2_z256_mont_mul(a3, a2, a3); + sm2_z256_mont_mul(a4, a2, a4); + for (i = 0; i < 32; i++) { + sm2_z256_mont_sqr(a5, a5); + } + sm2_z256_mont_mul(a2, a5, a3); + sm2_z256_mont_mul(a3, a2, a3); + sm2_z256_mont_mul(a4, a2, a4); + for (i = 0; i < 32; i++) { + sm2_z256_mont_sqr(a5, a5); + } + sm2_z256_mont_mul(a2, a5, a3); + sm2_z256_mont_mul(a3, a2, a3); + sm2_z256_mont_mul(a4, a2, a4); + for (i = 0; i < 32; i++) { + sm2_z256_mont_sqr(a5, a5); + } + sm2_z256_mont_mul(a2, a5, a3); + sm2_z256_mont_mul(a3, a2, a3); + sm2_z256_mont_mul(a4, a2, a4); + for (i = 0; i < 32; i++) { + sm2_z256_mont_sqr(a5, a5); + } + sm2_z256_mont_mul(r, a4, a5); +} + +// mont(mont(a), 1) = aR * 1 * R^-1 (mod p) = a (mod p) +void sm2_z256_from_mont(uint64_t r[4], const uint64_t a[4]) +{ + const uint64_t SM2_Z256_ONE[4] = { 1,0,0,0 }; + sm2_z256_mont_mul(r, a, SM2_Z256_ONE); +} + +// mont(a) = a * 2^256 (mod p) = mont_mul(a, 2^512 mod p) +void sm2_z256_to_mont(const uint64_t a[4], uint64_t r[4]) +{ + // 2^512 (mod p) + const uint64_t SM2_Z256_2e512modp[4] = { + 0x0000000200000003, 0x00000002ffffffff, 0x0000000100000001, 0x0000000400000002 + }; + + sm2_z256_mont_mul(r, a, SM2_Z256_2e512modp); +} + +int sm2_z256_mont_print(FILE *fp, int ind, int fmt, const char *label, const uint64_t a[4]) +{ + uint64_t r[4]; + sm2_z256_from_mont(r, a); + sm2_z256_print(fp, ind, fmt, label, r); + return 1; +} + +// Jacobian Point with Montgomery coordinates + +void sm2_z256_point_dbl(SM2_Z256_POINT *R, const SM2_Z256_POINT *A) +{ + const uint64_t *X1 = A->X; + const uint64_t *Y1 = A->Y; + const uint64_t *Z1 = A->Z; + uint64_t *X3 = R->X; + uint64_t *Y3 = R->Y; + uint64_t *Z3 = R->Z; + uint64_t S[4]; + uint64_t M[4]; + uint64_t Zsqr[4]; + uint64_t tmp0[4]; + + // S = 2*Y1 + sm2_z256_modp_mul_by_2(S, Y1); + //sm2_z256_mont_print(stderr, 0, 0, "1", S); + + // Zsqr = Z1^2 + sm2_z256_mont_sqr(Zsqr, Z1); + //sm2_z256_mont_print(stderr, 0, 0, "2", Zsqr); + + // S = S^2 = 4*Y1^2 + sm2_z256_mont_sqr(S, S); + //sm2_z256_mont_print(stderr, 0, 0, "3", S); + + // Z3 = Z1 * Y1 + sm2_z256_mont_mul(Z3, Z1, Y1); + //sm2_z256_mont_print(stderr, 0, 0, "4", Z3); + + // Z3 = 2 * Z3 = 2*Y1*Z1 + sm2_z256_modp_mul_by_2(Z3, Z3); + //sm2_z256_mont_print(stderr, 0, 0, "5", Z3); + + // M = X1 + Zsqr = X1 + Z1^2 + sm2_z256_modp_add(M, X1, Zsqr); + //sm2_z256_mont_print(stderr, 0, 0, "6", M); + + // Zsqr = X1 - Zsqr = X1 - Z1^2 + sm2_z256_modp_sub(Zsqr, X1, Zsqr); + //sm2_z256_mont_print(stderr, 0, 0, "7", Zsqr); + + // Y3 = S^2 = 16 * Y1^4 + sm2_z256_mont_sqr(Y3, S); + //sm2_z256_mont_print(stderr, 0, 0, "8", Y3); + + // Y3 = Y3/2 = 8 * Y1^4 + sm2_z256_modp_div_by_2(Y3, Y3); + //sm2_z256_mont_print(stderr, 0, 0, "9", Y3); + + // M = M * Zsqr = (X1 + Z1^2)(X1 - Z1^2) + sm2_z256_mont_mul(M, M, Zsqr); + //sm2_z256_mont_print(stderr, 0, 0, "10", M); + + // M = 3*M = 3(X1 + Z1^2)(X1 - Z1^2) + sm2_z256_modp_mul_by_3(M, M); + //sm2_z256_mont_print(stderr, 0, 0, "11", M); + + // S = S * X1 = 4 * X1 * Y1^2 + sm2_z256_mont_mul(S, S, X1); + //sm2_z256_mont_print(stderr, 0, 0, "12", S); + + // tmp0 = 2 * S = 8 * X1 * Y1^2 + sm2_z256_modp_mul_by_2(tmp0, S); + //sm2_z256_mont_print(stderr, 0, 0, "13", tmp0); + + // X3 = M^2 = (3(X1 + Z1^2)(X1 - Z1^2))^2 + sm2_z256_mont_sqr(X3, M); + //sm2_z256_mont_print(stderr, 0, 0, "14", X3); + + // X3 = X3 - tmp0 = (3(X1 + Z1^2)(X1 - Z1^2))^2 - 8 * X1 * Y1^2 + sm2_z256_modp_sub(X3, X3, tmp0); + //sm2_z256_mont_print(stderr, 0, 0, "15", X3); + + // S = S - X3 = 4 * X1 * Y1^2 - X3 + sm2_z256_modp_sub(S, S, X3); + //sm2_z256_mont_print(stderr, 0, 0, "16", S); + + // S = S * M = 3(X1 + Z1^2)(X1 - Z1^2)(4 * X1 * Y1^2 - X3) + sm2_z256_mont_mul(S, S, M); + //sm2_z256_mont_print(stderr, 0, 0, "17", S); + + // Y3 = S - Y3 = 3(X1 + Z1^2)(X1 - Z1^2)(4 * X1 * Y1^2 - X3) - 8 * Y1^4 + sm2_z256_modp_sub(Y3, S, Y3); + //sm2_z256_mont_print(stderr, 0, 0, "18", Y3); +} + +void sm2_z256_point_add(SM2_Z256_POINT *r, const SM2_Z256_POINT *a, const SM2_Z256_POINT *b) +{ + uint64_t U2[4], S2[4]; + uint64_t U1[4], S1[4]; + uint64_t Z1sqr[4]; + uint64_t Z2sqr[4]; + uint64_t H[4], R[4]; + uint64_t Hsqr[4]; + uint64_t Rsqr[4]; + uint64_t Hcub[4]; + + uint64_t res_x[4]; + uint64_t res_y[4]; + uint64_t res_z[4]; + + uint64_t in1infty, in2infty; + + const uint64_t *in1_x = a->X; + const uint64_t *in1_y = a->Y; + const uint64_t *in1_z = a->Z; + + const uint64_t *in2_x = b->X; + const uint64_t *in2_y = b->Y; + const uint64_t *in2_z = b->Z; + + /* + * Infinity in encoded as (,,0) + */ + in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]); + + in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[3]); + + in1infty = is_zero(in1infty); + in2infty = is_zero(in2infty); + + sm2_z256_mont_sqr(Z2sqr, in2_z); /* Z2^2 */ + sm2_z256_mont_sqr(Z1sqr, in1_z); /* Z1^2 */ + + sm2_z256_mont_mul(S1, Z2sqr, in2_z); /* S1 = Z2^3 */ + sm2_z256_mont_mul(S2, Z1sqr, in1_z); /* S2 = Z1^3 */ + + sm2_z256_mont_mul(S1, S1, in1_y); /* S1 = Y1*Z2^3 */ + sm2_z256_mont_mul(S2, S2, in2_y); /* S2 = Y2*Z1^3 */ + sm2_z256_modp_sub(R, S2, S1); /* R = S2 - S1 */ + + sm2_z256_mont_mul(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */ + sm2_z256_mont_mul(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */ + sm2_z256_modp_sub(H, U2, U1); /* H = U2 - U1 */ + + /* + * This should not happen during sign/ecdh, so no constant time violation + */ + if (sm2_z256_equ(U1, U2) && !in1infty && !in2infty) { + if (sm2_z256_equ(S1, S2)) { + sm2_z256_point_dbl(r, a); + return; + } else { + memset(r, 0, sizeof(*r)); + return; + } + } + + sm2_z256_mont_sqr(Rsqr, R); /* R^2 */ + sm2_z256_mont_mul(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */ + sm2_z256_mont_sqr(Hsqr, H); /* H^2 */ + sm2_z256_mont_mul(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */ + sm2_z256_mont_mul(Hcub, Hsqr, H); /* H^3 */ + + sm2_z256_mont_mul(U2, U1, Hsqr); /* U1*H^2 */ + sm2_z256_modp_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */ + + sm2_z256_modp_sub(res_x, Rsqr, Hsqr); + sm2_z256_modp_sub(res_x, res_x, Hcub); + + sm2_z256_modp_sub(res_y, U2, res_x); + + sm2_z256_mont_mul(S2, S1, Hcub); + sm2_z256_mont_mul(res_y, R, res_y); + sm2_z256_modp_sub(res_y, res_y, S2); + + sm2_z256_copy_conditional(res_x, in2_x, in1infty); + sm2_z256_copy_conditional(res_y, in2_y, in1infty); + sm2_z256_copy_conditional(res_z, in2_z, in1infty); + + sm2_z256_copy_conditional(res_x, in1_x, in2infty); + sm2_z256_copy_conditional(res_y, in1_y, in2infty); + sm2_z256_copy_conditional(res_z, in1_z, in2infty); + + memcpy(r->X, res_x, sizeof(res_x)); + memcpy(r->Y, res_y, sizeof(res_y)); + memcpy(r->Z, res_z, sizeof(res_z)); +} + +void sm2_z256_point_neg(SM2_Z256_POINT *R, const SM2_Z256_POINT *P) +{ + sm2_z256_copy(R->X, P->X); + sm2_z256_modp_neg(R->Y, P->Y); + sm2_z256_copy(R->Z, P->Z); +} + +void sm2_z256_point_sub(SM2_Z256_POINT *R, const SM2_Z256_POINT *A, const SM2_Z256_POINT *B) +{ + SM2_Z256_POINT neg_B; + sm2_z256_point_neg(&neg_B, B); + sm2_z256_point_add(R, A, &neg_B); +} + +void sm2_z256_point_get_affine(const SM2_Z256_POINT *P, uint64_t x[4], uint64_t y[4]) +{ + uint64_t z_inv[4]; + uint64_t x_out[4]; + uint64_t y_out[4]; + + // z_inv = 1/Z + sm2_z256_mont_inv(z_inv, P->Z); + + // y_out = Y/Z + if (y) { + sm2_z256_mont_mul(y_out, P->Y, z_inv); + } + + // z_inv = 1/Z^2 + sm2_z256_mont_sqr(z_inv, z_inv); + + // x_out = X/Z^2 + sm2_z256_mont_mul(x_out, P->X, z_inv); + sm2_z256_from_mont(x, x_out); + + if (y) { + // y_out = Y/Z^3 + sm2_z256_mont_mul(y_out, y_out, z_inv); + sm2_z256_from_mont(y, y_out); + } +} + + + + +void sm2_z256_point_copy_affine(SM2_Z256_POINT *R, const SM2_Z256_POINT_AFFINE *P) +{ + memcpy(R, P, sizeof(SM2_Z256_POINT_AFFINE)); + sm2_z256_copy(R->Z, SM2_Z256_MONT_ONE); +} + +void sm2_z256_point_add_affine(SM2_Z256_POINT *r, const SM2_Z256_POINT *a, const SM2_Z256_POINT_AFFINE *b) +{ + uint64_t U2[4], S2[4]; + uint64_t Z1sqr[4]; + uint64_t H[4], R[4]; + uint64_t Hsqr[4]; + uint64_t Rsqr[4]; + uint64_t Hcub[4]; + + uint64_t res_x[4]; + uint64_t res_y[4]; + uint64_t res_z[4]; + + uint64_t in1infty, in2infty; + + const uint64_t *in1_x = a->X; + const uint64_t *in1_y = a->Y; + const uint64_t *in1_z = a->Z; + + const uint64_t *in2_x = b->x; + const uint64_t *in2_y = b->y; + + /* + * Infinity in encoded as (,,0) + */ + in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]); + + /* + * In affine representation we encode infinity as (0,0), which is + * not on the curve, so it is OK + */ + in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] | in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]); + + in1infty = is_zero(in1infty); + in2infty = is_zero(in2infty); + + + /* Z1^2 */ + sm2_z256_mont_sqr(Z1sqr, in1_z); + + /* U2 = X2*Z1^2 */ + sm2_z256_mont_mul(U2, in2_x, Z1sqr); + /* H = U2 - U1 */ + sm2_z256_modp_sub(H, U2, in1_x); + + sm2_z256_mont_mul(S2, Z1sqr, in1_z); /* S2 = Z1^3 */ + + sm2_z256_mont_mul(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */ + + sm2_z256_mont_mul(S2, S2, in2_y); /* S2 = Y2*Z1^3 */ + sm2_z256_modp_sub(R, S2, in1_y); /* R = S2 - S1 */ + + sm2_z256_mont_sqr(Hsqr, H); /* H^2 */ + sm2_z256_mont_sqr(Rsqr, R); /* R^2 */ + sm2_z256_mont_mul(Hcub, Hsqr, H); /* H^3 */ + + sm2_z256_mont_mul(U2, in1_x, Hsqr); /* U1*H^2 */ + sm2_z256_modp_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */ + + sm2_z256_modp_sub(res_x, Rsqr, Hsqr); + sm2_z256_modp_sub(res_x, res_x, Hcub); + sm2_z256_modp_sub(H, U2, res_x); + + sm2_z256_mont_mul(S2, in1_y, Hcub); + sm2_z256_mont_mul(H, H, R); + sm2_z256_modp_sub(res_y, H, S2); + + sm2_z256_copy_conditional(res_x, in2_x, in1infty); + sm2_z256_copy_conditional(res_x, in1_x, in2infty); + + sm2_z256_copy_conditional(res_y, in2_y, in1infty); + sm2_z256_copy_conditional(res_y, in1_y, in2infty); + + sm2_z256_copy_conditional(res_z, SM2_Z256_MONT_ONE, in1infty); + sm2_z256_copy_conditional(res_z, in1_z, in2infty); + + memcpy(r->X, res_x, sizeof(res_x)); + memcpy(r->Y, res_y, sizeof(res_y)); + memcpy(r->Z, res_z, sizeof(res_z)); +} + +void sm2_z256_point_sub_affine(SM2_Z256_POINT *R, + const SM2_Z256_POINT *A, const SM2_Z256_POINT_AFFINE *B) +{ + SM2_Z256_POINT_AFFINE neg_B; + + sm2_z256_copy(neg_B.x, B->x); + sm2_z256_modp_neg(neg_B.y, B->y); + + sm2_z256_point_add_affine(R, A, &neg_B); +} + +int sm2_z256_point_print(FILE *fp, int fmt, int ind, const char *label, const SM2_Z256_POINT *P) +{ + uint64_t x[4]; + uint64_t y[4]; + uint8_t affine[64]; + + sm2_z256_point_get_affine(P, x, y); + sm2_z256_to_bytes(x, affine); + sm2_z256_to_bytes(y, affine + 32); + + format_bytes(fp, fmt, ind, label, affine, 64); + return 1; +} + +int sm2_z256_point_affine_print(FILE *fp, int fmt, int ind, const char *label, const SM2_Z256_POINT_AFFINE *P) +{ + uint8_t affine[64]; + uint64_t a[4]; + + sm2_z256_from_mont(a, P->x); + sm2_z256_to_bytes(a, affine); + + sm2_z256_from_mont(a, P->y); + sm2_z256_to_bytes(a, affine + 32); + + format_bytes(fp, fmt, ind, label, affine, 64); + return 1; +} + +extern const uint64_t sm2_z256_pre_comp[37][64 * 4 * 2]; +static SM2_Z256_POINT_AFFINE (*g_pre_comp)[64] = (SM2_Z256_POINT_AFFINE (*)[64])sm2_z256_pre_comp; + +void sm2_z256_point_mul_generator(SM2_Z256_POINT *R, const uint64_t k[4]) +{ + size_t window_size = 7; + int R_infinity = 1; + int n = (256 + window_size - 1)/window_size; + int i; + + for (i = n - 1; i >= 0; i--) { + int booth = sm2_z256_get_booth(k, window_size, i); + + if (R_infinity) { + if (booth != 0) { + sm2_z256_point_copy_affine(R, &g_pre_comp[i][booth - 1]); + R_infinity = 0; + } + } else { + if (booth > 0) { + sm2_z256_point_add_affine(R, R, &g_pre_comp[i][booth - 1]); + } else if (booth < 0) { + sm2_z256_point_sub_affine(R, R, &g_pre_comp[i][-booth - 1]); + } + } + } + + if (R_infinity) { + memset(R, 0, sizeof(*R)); + } +} + +void sm2_z256_point_mul(SM2_Z256_POINT *R, const SM2_Z256_POINT *P, const uint64_t k[4]) +{ + int window_size = 5; + SM2_Z256_POINT T[16]; + int R_infinity = 1; + int n = (256 + window_size - 1)/window_size; + int i; + + // T[i] = (i + 1) * P + memcpy(&T[0], P, sizeof(SM2_Z256_POINT)); + sm2_z256_point_dbl(&T[ 1], &T[ 0]); + sm2_z256_point_add(&T[ 2], &T[ 1], P); + sm2_z256_point_dbl(&T[ 3], &T[ 1]); + sm2_z256_point_add(&T[ 4], &T[ 3], P); + sm2_z256_point_dbl(&T[ 5], &T[ 2]); + sm2_z256_point_add(&T[ 6], &T[ 5], P); + sm2_z256_point_dbl(&T[ 7], &T[ 3]); + sm2_z256_point_add(&T[ 8], &T[ 7], P); + sm2_z256_point_dbl(&T[ 9], &T[ 4]); + sm2_z256_point_add(&T[10], &T[ 9], P); + sm2_z256_point_dbl(&T[11], &T[ 5]); + sm2_z256_point_add(&T[12], &T[11], P); + sm2_z256_point_dbl(&T[13], &T[ 6]); + sm2_z256_point_add(&T[14], &T[13], P); + sm2_z256_point_dbl(&T[15], &T[ 7]); + + for (i = n - 1; i >= 0; i--) { + int booth = sm2_z256_get_booth(k, window_size, i); + + if (R_infinity) { + if (booth != 0) { + *R = T[booth - 1]; + R_infinity = 0; + } + } else { + sm2_z256_point_dbl(R, R); + sm2_z256_point_dbl(R, R); + sm2_z256_point_dbl(R, R); + sm2_z256_point_dbl(R, R); + sm2_z256_point_dbl(R, R); + + if (booth > 0) { + sm2_z256_point_add(R, R, &T[booth - 1]); + } else if (booth < 0) { + sm2_z256_point_sub(R, R, &T[-booth - 1]); + } + } + } + + if (R_infinity) { + memset(R, 0, sizeof(*R)); + } +} + +// R = t*P + s*G +void sm2_z256_point_mul_sum(SM2_Z256_POINT *R, const uint64_t t[4], const SM2_Z256_POINT *P, const uint64_t s[4]) +{ + SM2_Z256_POINT Q; + sm2_z256_point_mul_generator(R, s); + sm2_z256_point_mul(&Q, P, t); + sm2_z256_point_add(R, R, &Q); +} + + +void sm2_z256_point_to_bytes(const SM2_Z256_POINT *P, uint8_t out[64]) +{ + uint64_t x[4]; + uint64_t y[4]; + + sm2_z256_point_get_affine(P, x, y); + sm2_z256_to_bytes(x, out); + sm2_z256_to_bytes(y, out + 32); +} + + + + + + + diff --git a/src/sm2_z256_table.c b/src/sm2_z256_table.c new file mode 100644 index 000000000..38aa7d811 --- /dev/null +++ b/src/sm2_z256_table.c @@ -0,0 +1,4835 @@ +/* + * Copyright 2014-2024 The GmSSL Project. All Rights Reserved. + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + + +#include +#include +#include +#include + + +#if defined(__GNUC__) +__attribute((aligned(4096))) +#elif defined(_MSC_VER) +__declspec(align(4096)) +#endif + + +const uint64_t sm2_z256_pre_comp[37][64 * 4 * 2] = { + { + 0x61328990f418029e, 0x3e7981eddca6c050, 0xd6a1ed99ac24c3c3, 0x91167a5ee1c13b05, + 0xc1354e593c2d0ddd, 0xc1f5e5788d3295fa, 0x8d4cfb066e2a48f8, 0x63cd65d481d735bd, + 0x0af037bfbc3be46a, 0x83bdc9ba2d8fa938, 0x5349d94b5788cd24, 0x0d7e9c18caa5736a, + 0x6a7e1a1d69db9ac1, 0xccbd8d37c4a8e82b, 0xc7b145169b7157ac, 0x947e74656c21bdf5, + 0x1cda54fdab589e4a, 0x26765289db4f0a0d, 0x0a265a308ceb4a0a, 0x3019fd6bfe887c64, + 0x0a10fbe94b2fc190, 0xf40aa52b87cbce60, 0xcc496bfa6dc13c97, 0x28ad34785bb3fbb4, + 0x393f7c5a98615060, 0x487ea27fe9016209, 0x8a86bcb4a09f9020, 0x50dc8e3ac899dbe1, + 0xfc099043fd619998, 0x1de135ea7c7383bd, 0x4d0bd55632cf70ed, 0x6ffc31c525bce9e3, + 0x9a5756336a9c8162, 0x15aa58f221dfcc53, 0x7ad354bf1ef5f4c5, 0x0f443ef363f875b9, + 0x2e81d68fd3450133, 0xb30f4bbde3607d18, 0xb1826a4c362258ef, 0x7b415276142a6768, + 0x136a9c4c0acd72ba, 0xb1274a255e7ec73c, 0xf15a876e5de34db6, 0x85e74ca08cba8047, + 0x08454cddb469eb37, 0x8fbf6d1fc99754f8, 0x1060e7f8ec30e984, 0xb568bc974b8c598a, + 0xaa3531c781f06784, 0x0b89419307132520, 0x84ee5b69acfe18c5, 0xbbf492e0d9fbec28, + 0x313a35c1e5f6186d, 0x0e449a2e757a01b8, 0x96c9b9922bd99baf, 0x2ba05a8f3b84d777, + 0xde523a1c09122670, 0x90be6f2a22cc810c, 0x086e63414387df9e, 0x115c2fc0d9c44134, + 0x9334430d8799302a, 0x693b3500e27b7ea4, 0xcbe1136f9a8f3382, 0xe77fd5f2b5778247, + 0x98e795c330fbde86, 0x8e5e0495ab21af8f, 0x3925bf83b48669b4, 0x77d88740469522c8, + 0x8fbf8b5b987b04ce, 0x63c563a83aff4428, 0x5dc1116553a6e969, 0x822a6c2432697f4c, + 0x6774298a642cb143, 0xecdb60d82d110e71, 0xe810b11b1388728e, 0x2e8237d8d8603a8a, + 0x673968fc50aeeae1, 0x08c65d196746a3f4, 0x7a61a6b5d7dd7165, 0xe31bbfd9a9b6df3a, + 0x2b252ad03421e115, 0x7557c8c7c6affc01, 0xd90c19fd8a509267, 0x483da168e0d871c8, + 0x72d6f9b3c10729bf, 0x5dd8402115b7061e, 0x9bfea2db9f2c587d, 0x528398a798641ec2, + 0x18a65d8df3afdd62, 0x89f38500d6d7e4e4, 0x65708c6a9d8d4f07, 0xb90ea13cd0bdc7f4, + 0x589858558c3e2b32, 0xfa48d5c5bcfad3a1, 0x5c3544e762385ffa, 0xb6bd39ed7e72aeb7, + 0x34e51c6a8000fe4e, 0x7da2bdfd89c46941, 0x667ba91de1bc2b2e, 0x3c80c9d010a73e5c, + 0x4fadebbec7f5c64d, 0xaef09eb43ea35052, 0x167ee11b26ec55f9, 0x45fa508a85189260, + 0xa0e9a43922542fc3, 0x3f194a6cddac78dc, 0xa75ae72d6f74d053, 0x0f8babeb097c6617, + 0x1d12bc5c4303c247, 0xfe0c027abd1e246c, 0xe9ca1a99b69b55ad, 0xff6cd2b0117cd63a, + 0xf3489343dde97d4d, 0x9c14e38abbb2ce1f, 0x25866911cfddf221, 0x0df89411460efef1, + 0xf713f30e73ae8326, 0xd9be66a8cdd274a1, 0xdf915ae236885947, 0x2c5c1e9e7878b781, + 0xf71560c939e8a120, 0x7121d6b87273b59a, 0x649535ce8ef4639d, 0xcd01076e14cc6d58, + 0x2705729a96e74f8a, 0xb07e32305533037e, 0x0846dcc1663c5c62, 0x6a4759c110fc3ac1, + 0x3c126193cfbdfeff, 0x4a31dd204996d845, 0x48a76ba019f2b658, 0xbe3301428890a8bc, + 0x287b34e1308aa041, 0xcbf5da24813adf29, 0xcdfc5a58cdcdc439, 0xbda3bda2198a6075, + 0x639f92bc1497fe38, 0x8ed8eeacd58bd278, 0xcf5d7ce6b417bfe4, 0xf617c54e44400c59, + 0xde6356357d8dc939, 0x2e6a3a75241baaff, 0x02f324e5e07e8e97, 0xeb71548770f9fc9d, + 0xbefd338086712116, 0x9b9e9707884efe46, 0x611a1eec8c9e513f, 0xe2d8e3f53b6dbcec, + 0x7cedab1c4f8964e4, 0xee12d062f4e139f8, 0x8e63c9c09a9af4f3, 0xe3246dbb8b907b23, + 0x70d5bda271099001, 0x3d876d4a15fae7dd, 0xaba0500f7b69c20e, 0xa8e3e0949834adf2, + 0x69db851b980b21b9, 0x274c1de2788c2a30, 0x5caa5336d47d153d, 0xada6987757cef318, + 0x83879486a0551c80, 0x1611dea0658e61be, 0x1fe95c821b935068, 0x8f01e0195b229223, + 0x23017e057e93c389, 0xce4ac99d9840dd64, 0xddc9b9001de86399, 0x6abe5cc388015785, + 0xc09545a9b3c50898, 0xbd4433616c05d902, 0xed71f70c2c6bcc8c, 0x8dbc0b88bdf8e908, + 0x56eb5b984fcbcd9a, 0xafb6fedc08114397, 0x0500ce5bb35f7927, 0x7005bcf995efe710, + 0x125cbed22eba7f39, 0xc7c42e766c488d44, 0xdb8991f9676915c4, 0xdf6ae5949183839f, + 0x4f69c304c79f8bd1, 0x638cb070aa1662fa, 0xc7f68c72ba6f2599, 0x11bb84d91f6edfa9, + 0x9ed156eca215fda2, 0x19de7a9120c5ddb6, 0xc1ed949d0668c65d, 0x96683044d0826f6a, + 0x1e6325e01adaa8ff, 0xbc53bc2407ac392a, 0x2c342db5d9f06e44, 0x3f52938530db8c1a, + 0xc5957d29e7492326, 0x3addc3df0663f829, 0x8faa3169728cfdc1, 0xde53aa7c6b975134, + 0xf481759befddc764, 0xd605474b09edaff3, 0xc7df1eb9653d48c9, 0xa71e6854c5040212, + 0x136d8342afe945b5, 0x91707e7de9d239c7, 0xeda23dc5fb2e80de, 0x892bed73ff614966, + 0x2ded2367838dc12d, 0x73fd298cb002bd9c, 0xc548b4262c4629df, 0x93605d178f7e03b7, + 0x32861816d37c24cc, 0x5bb54ee2e427975a, 0x6da013d232f943a9, 0x0746a77a9bc202e5, + 0x6db07a84cd1def5b, 0x9421fe7f861d9f9b, 0x71767292692181fb, 0x0560e7e5c9d2441d, + 0xf1496afd4d7e922a, 0x67f42a3fe11fa533, 0x9f903e5b977956cd, 0x37671e241eb49608, + 0x967950a021fb2047, 0x141f96fb35da3c6b, 0xe07c3c40d27bba59, 0xbde5ed1d0e1af754, + 0xdc64c4b054f1f257, 0xecb033c8b01196dc, 0x54e65f4d8202d5bd, 0x63afcc932b2fd451, + 0x1e929a3930640fb7, 0xdc91387e5b361718, 0x10aadecbf8f0bbe8, 0x81d8f4660977e2bb, + 0xdcaa3790bd64cd96, 0xbc8ac152cee698d3, 0xde7192f7a1143c45, 0xf7c9d826f5fb9ea0, + 0x54aea92ec9468f50, 0x340f4459cc427ed4, 0x3fec5be902ad5467, 0xec780d9c2cc6c8b5, + 0x7b179a8bb889c78a, 0x069a7ab90aca32c5, 0xe4e5215e591b9a36, 0x7802fb3e3bd54630, + 0x9a479313233c6eeb, 0x18c612ad4e1cbabc, 0x28a29273c0e36f3b, 0xf4e2dfb17d3deb26, + 0xa6c11369adbb3c8b, 0xd78af40b4c8ec378, 0xffb3a80d03f0a982, 0x550e3e71a83be50a, + 0x845c0fb2418ee45b, 0x5297cf430791b964, 0x676b638ccc47e33b, 0xb1c52facfecf85b2, + 0xf011b5e53dba2c0e, 0xa6c68448026d4f11, 0x11596db3c3f206fb, 0xc91c76dc29414a3c, + 0x1839b9d1b94ddc7c, 0xdfb20ce756ae8610, 0x3e2b1cd9d8734400, 0x59f9329af01ea540, + 0x7d4c140c2351a2a9, 0x575c1e1bbf4c9823, 0x8f11c2ca31068df9, 0xe3c17aa005e6def0, + 0xe6281c70501c8630, 0xad240917c88a412e, 0x6f21bfb7390492d7, 0x61ea1385c3a3ccb7, + 0x60494a8333733cbc, 0x8da622a027ed8157, 0x0022b1540471ad90, 0x3bd0a4c5d3568003, + 0xdc8e2d03d932df23, 0x859ed9407a1f5159, 0xad670e632a375b0f, 0x15922fae9520db97, + 0xfb73d16f59eb1a9b, 0x3ee8cc1f8511e541, 0x20d72d591590c321, 0x62eab5663bd075d4, + 0xac07a7c7fae123ab, 0x83b89abf1f10af6e, 0x469962ec1da8ac5d, 0x09761c358c58c3b3, + 0x2c086d5e7da90fc9, 0x458e5ffd5cc27782, 0xc3f48611b9268939, 0x39fed873de4b9110, + 0x16ef8f78fda698cc, 0xb028dc21a973bb50, 0x45eb849ee29b725b, 0xd41b5b6d14c6eae9, + 0x5e931b21c55d5720, 0xb628ccb2a0e40b19, 0x42044ffe000651a5, 0x2130b4de076544e7, + 0x384285943677c70f, 0xfdcdb038f8945d86, 0xfb2e3d4c4169ae44, 0xd4695e9b0d13bce2, + 0x45191390039d646d, 0x983b7a2eb12ba339, 0xdfd30d3e5923e7d6, 0xae3590f0ba9d206a, + 0x7d58d334b6d5e62a, 0xb15b05447e402b12, 0xac57e11362ae8e01, 0x4d83804cf473edee, + 0x2faa7c4dc81bc828, 0xb16ed9d7fb62561f, 0x4c9da27049c2fa93, 0x3b014c73b311d90d, + 0xd29c5d65f5443332, 0xb6457d54eebdb7c2, 0xc6a0bf3a4cce9480, 0xd434a3b085355854, + 0x178ca01b8b2c703c, 0x605bba530ab71a51, 0x2140948e3db948d5, 0xc45b26895fb6b8c1, + 0x421f66def17b47bd, 0x57627a5a2e9b3ee5, 0xedf3920a66614339, 0x7ea619034b638a46, + 0x7203d5423c030643, 0x7112bb3d5e631461, 0x2604eac72bc3da9c, 0x2e4964e732d2541b, + 0x940faf46e8b6482a, 0x8f772fcb24d27c9e, 0x125c34d7ca7c5f88, 0x9903eadbd1f47795, + 0x11aaa417e2147129, 0x3ccef5c2f88a0a30, 0x78d5207a90283f97, 0xba1261e9d25226b6, + 0xbfc79248d1e7a01c, 0x373f1cd5941ab2bd, 0xf0881e2119a0668b, 0x7b7937891f77bf0a, + 0x49c2769b63d4523d, 0xf8df2cbaf0399eaf, 0x5ae94c6922a2a74d, 0xd08f8d45efd1e193, + 0x64341fc4c681f376, 0x3a8e25c8ec918711, 0xdf35304d0608f50f, 0x9b4c69679a973742, + 0xb5c1f5d3bfba043b, 0xaff4f896e975f03b, 0xea1f39bdae2cbb01, 0x4cc1c4cba62915ff, + 0x5eb4afa389e943b8, 0x8c4d27e5154e565a, 0x4e2e5a7e7f2bced6, 0x7af408e24487f6a3, + 0xe5dacbae97a60de7, 0x9774834c4401b0ad, 0x7683bb008a9113f9, 0xc6fe7e8b42b2ba67, + 0xc0c0564d54e760c8, 0xf7b05401118606c2, 0x554a9b0fec3cd7b9, 0xce75ecfb27916a21, + 0xf663899712118abd, 0x2ba6e754097da3a7, 0x1df820850fdf9985, 0xbf73502a546c864a, + 0xdfde9323c02d9ce0, 0x580491e2e4dd0e7d, 0xe71522d2ae43b9b4, 0x876e36276a231a41, + 0xfa8ff511b36362ec, 0x11c5a9f634085959, 0x272b86f29770c62b, 0xf06262257c7e8827, + 0x929168bfea1e13eb, 0xdb892971ce59b0f5, 0x6769e31d4f826f34, 0xfa1dd9340a955cec, + 0x123d9ca2a294d7ea, 0x8699063b4492569b, 0x6a50eae9a8dd86c3, 0x3d757d1012c06c38, + 0x5a92c2c03e41e556, 0xa64595eb6330c21a, 0x70d8141ae184d925, 0x8543f2cea2f10304, + 0x4559b0a29eaca504, 0xb9843a4b2617bc9b, 0x5b28d4ee1b641003, 0x3e9af8e14ced538a, + 0x3790fe897bdf7dc2, 0xc7c74941c32549ee, 0xdcc8295babcd2f42, 0x48b29a4fead078b6, + 0x8e8b28e32040178e, 0xceff8f3e971725fc, 0x4a97b6fafcee2cc1, 0x775df6a9bac85b56, + 0x32e5cbe6d28a21cc, 0xe8b86adaae2b82db, 0x44dfbb5086e38e96, 0x45d3fe7d1afc2d4b, + 0x838b356ed23f620d, 0x2e8fa8ac4592fe4b, 0x1396e1b33af5b1d8, 0x9c0c2ef3cbf50fb0, + 0xd9efb6c9836e93e9, 0xe6eb58700899163f, 0x3a2f6d77dca00d1b, 0x36f55f89b40ba0d6, + 0xf3b1701f32866e57, 0xf076847359de0f2e, 0xe55d7aedab57962d, 0x450049852b60cabb, + 0x8d539d6ed5498888, 0x176ce1a0a5e0ff6a, 0xcb7c15efdc088c50, 0x90393d7ac9a9ae2f, + 0xd9c1a140d396bdce, 0x4215b78b6fb2800f, 0x8939109f2f76b0df, 0x0f2508972adb40a8, + 0x4db0007c3a86e009, 0x6ef0ad95f968a635, 0x58a82d4b8eaefa78, 0xe8a181cb493604a4, + 0x36c84e34520d216d, 0x2b2ef6b5c666171c, 0x9469b91f2ce29d37, 0x3ecd84e7c15f20aa, + 0xf1090635292edd2c, 0x6d4393627c3447f6, 0x51b9a0a93eea3fdf, 0x68e0d1f89e57e450, + 0x25d249d57380931e, 0x87f03fad2011a45b, 0x89df0324efde1ca3, 0x52ae43cd9a9b4330, + 0xfe48bc64a1867c1b, 0xdd874f669866920e, 0x6942a7e4fcf50251, 0xf5c100489c5f6298, + 0x305183eb00973d66, 0x1ce6676095baf07c, 0x74c9d97174822e13, 0x2ccd7fbb76b5e6ef, + 0x51688b49a3e1ca18, 0x1beb5bbba603f2f1, 0x09a231d1962534b6, 0x70417ce1afa92f75, + 0xb86b6d82e154bc00, 0x5a0b19e8895483e5, 0xb15f6c05a0ff1e44, 0x2938b88afdd8615d, + 0x81800a05971615c3, 0x6be6d56bc03d2039, 0xff3e57d2c476ce64, 0x5b509b7b6f583ee8, + 0x1d92c36c7c1f5d3b, 0x1e60b19be11df757, 0x20261501e37e36f6, 0xb68a9aaa29bc86e3, + 0xfba81eaaf61d23ca, 0x63440834d5adaa18, 0xa80d76eda5f93bb8, 0x3264283d5a728480, + 0xd6171111e4b8c48e, 0x3ee227a1de557cca, 0x2bebc09a3cb59841, 0x2f8047fe99bf6205, + 0xb78b243e4c43845f, 0x484ac18346d3b5e0, 0xa07be4760314524d, 0xc0a3aa351ab4c447, + 0x2f302d589c341f84, 0x264911a784f130ba, 0x30bed4083ee64343, 0xd7d6e92d5dc5868a, + 0x9207456880adb3fb, 0x005ab33ca133123e, 0x105119fd42e1da50, 0x6987117db7f6b1e8, + 0xa2315af3c2bccb7a, 0x95ddd3ee8672c98a, 0xa90326455f48f607, 0x76861e62c5273603, + 0x71aaa35f88817217, 0x57e95b6c2892afac, 0xf65e909b9e84c791, 0x257bcc2daa52f3b1, + 0xd5f6110a865c665a, 0xddc3afe130c08b4c, 0x4df3d04aefec26fc, 0xf229bddfb035af5d, + 0x364913cfd191b439, 0xf41b8f6d5a7fa8a4, 0x677cc51b6f6c1219, 0x593afe4a148b7f64, + 0x80ffa5ae0d038ad4, 0xf44d3df336256c8f, 0x0a3077c8bc978dce, 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0x2601981695782b24, + 0x945c172ca66c0ccd, 0x6c25f635b440719a, 0x917d5dbaa49f681a, 0xc0cad047b2dc5df4, + 0xd45bcf4c5960ef1c, 0xbabcb16d8c6979d5, 0x8e3be750ae9090d6, 0x9481d261ac0eb728, + 0x46b436cd0d6a7d46, 0x6eb1a6a31f976501, 0x5984ffa2dbe1064f, 0xe6575fb1f809dc20, + 0xf0426d804d974a81, 0x61304f0f97a74be6, 0x2346ff98a9486531, 0xa1242ccaf53d781a, + 0x482f03df97355f15, 0xc607ed33bd6058cf, 0x03bc8cd468aefe28, 0xa6e7de5a851307e4, + 0x2c07df0fc6af7d44, 0x310b251fb15a9188, 0xd42661ced3e15c2f, 0x5198fd901b4d8313, + 0x7a6062cdda8368a1, 0x1a905d115e9c2542, 0x1d752b70dae37cee, 0x3ed8c1a516bf84ca, + 0x5190fb0feecc2f22, 0x3df210f3698d8e60, 0xcce57d3af5f3ce72, 0xb2fb6223312b8fc6, + 0x7994700571867c84, 0x141cd92cbe139ebe, 0x415efc9e5de7944e, 0xae9ee91945821058, + 0xd696e1d95bf363dc, 0x6a1bcfc08251449c, 0xa1b82dffa5fa53e9, 0x6c56b5beeef05378, + 0xaf9efe4cc0e74dc3, 0x3d9a7ae9e5c1f1a0, 0x34b385772823c3e5, 0x69f297dc41fbabac, + 0xf01aff98d74c5a65, 0x979931041951a915, 0x8b211915723096a6, 0xf85910c4a769ef1f, + 0x30cefb9e8ddc0eb4, 0xd5957eefbb09607b, 0x2e139c9c2355b499, 0x5749531dc1789013, + 0x1603ca645475f2d2, 0x57190e0e0a336508, 0x2203b703cea7d558, 0xf16eba4dfb5503e3, + 0x62e2ce3db7344a98, 0xebf5b2439a4efa7a, 0x962124551c914064, 0xd2c5e31cbe5bbc07, + 0x2b5f2f7706c30b28, 0x0931841dbc9823d3, 0xd16fb08badfa6fdb, 0x8892bae2d6fd441e, + 0x3fc646302e576983, 0x08c60fb607b05529, 0x32b283b17afc1d4d, 0xc9c56965a2f0e37f, + 0x8e7191784644e173, 0x4c2a11ecf88b43ff, 0xb13644e67d3ddbb3, 0xd4746056c3d8703c, + 0x6611395f55dca667, 0x6359671227c91d73, 0x4ca68a87ea2ff489, 0x2864a816337adc1d, + 0x8aa830ae224d4f21, 0xda6c122e9f7845dc, 0xb0c61ffcfb240793, 0xf4df6842ce8580e9, + 0x94372aaa0a990dc7, 0x42968cd35ce1aa24, 0x177c5ff04df363a5, 0xa8c3f73768c4546f, + 0xc69750d5bd21c524, 0xbf3b485722a6c4ae, 0xcefcbb98e2883a1d, 0x6ffef743ae13f22b, + 0x6316ba605defea01, 0x0a89e6a74ba63810, 0x7f9af1de15ab0e11, 0x6247ca15385911c9, + 0x6f7b1a6a32f9eaf5, 0x2c440f94acfc13dc, 0x2cf39bc566b18adf, 0xb9939fe89f01533f, + 0x031c4553383a6450, 0x16d96ad3f0102087, 0xcbd6fa95501f1360, 0x667d3ea065f96c08, + 0xa5a7cbfa68a1a680, 0xf131d77942041db7, 0xbefee3acd85d377f, 0x6d0ed6b73b62dfa2, + 0xef683f0f1baacfbd, 0xc586c4f2c976cebd, 0x3a4120dc3b163339, 0x9ac9b950c79e5c1f, + 0xaf1ff35fe294926a, 0x2703bab8a2103168, 0xc645560a658a52bf, 0x5ff3ccd9e466fd97, + 0xe62fdc0154867f14, 0x435ef9509cdba39e, 0x2a7bbffd92828acc, 0xe7538fdbfe763981, + 0xedf451738bfe9773, 0xd187fa01471b8b9c, 0x34506c3578fa54df, 0x73cab9fdc2767589, + 0xf8f76c656726f305, 0xea45012d8de332b2, 0xb746f40d87970e03, 0xb2b2279a1ba8fbd6, + 0x79cdc61021147dbc, 0x738ef6809939a3cc, 0xd66d6ce68101bd8b, 0x65612acb09323caa, + 0x6874b37210310a29, 0x3cf30f0a5ee9ecfa, 0x4e1026ad8cfe1df8, 0x75a153f7d5989af5, + 0xc362ccee8b8e0c49, 0x8adfc0d2b533f3dd, 0xe02ab03ba109572e, 0x06efacdcfd3066ec, + 0xf136a8ba3fa28700, 0x48a1e987308cceb9, 0xe8ee7c0368253387, 0x47febbe8c2b463c7, + 0x485195f239a5c4d3, 0xf42e000ea26241ec, 0x08c64f90cd05368d, 0x46fbd381857cdbdb, + 0xf711df8b4c7e16ae, 0x95637e46e4edea42, 0x2df8b206ad171465, 0xa31ea8954bccedce, + 0x28dbcb7750743bb6, 0x13d12f8ef9cf84b9, 0x39e3d3afc8f7d408, 0x5824117feba591d4, + 0xd8ef7c9a1bead2d6, 0x9003a559caf53dd7, 0x33b2365c174cb9a9, 0x1149d080adb33afb, + 0x55231d00aea9bd3c, 0x07e107c9fdf3f015, 0xf535947dec9d8fce, 0x8b64ed8abba349a7, + 0xdd5881fd049301df, 0xefac9c43e6490fd0, 0xd990285273740a78, 0x6eef3724942c326c, + 0x5671a6e95cfb3c8c, 0x040aabd20ea29721, 0x24e92ca6eac8da18, 0xc34d3d79a31170c3, + 0xf81dd15fb061e416, 0xff7be70e85f80af0, 0xa9faba4bade45cd4, 0x42a6ab05505fddd4, + 0x17d5821d0a793534, 0x9e094e54ce0ade43, 0xa127fb6dc42cb4d2, 0x43865428db12dc99, + 0xb6b1b34759e3bfc1, 0x0b0076a91ec5b810, 0xbf2dd17aa6864982, 0x0c45947f9d523c87, + 0x9f53372f4c5dd59e, 0x3d0ceaeaca5ce09f, 0xf3ff88e87c0337fb, 0xb4fa4593faa022c7, + 0x575240a7d65ea54d, 0xa4ec0a39adb92fb0, 0xc20e737c79429eb1, 0xcea931d169addec4, + 0x7a29011f3e09f46a, 0x9c36865e0e578a5b, 0x8746ea5171d805f4, 0xf024de85e12d3024, + 0xc397b46c15a7f6be, 0x612db6fb1b0580d7, 0xe5342f76f736d087, 0x652768538c1e844c, + 0xedf48adc113841a5, 0xc21b67e1e5c482f0, 0xe43b0138684a540b, 0xc4f2782ba5d4b266, + 0x184e240c397f3664, 0x968e89e70d8788f8, 0xec3eba1a377e18bf, 0x4d03cbbc36002652, + 0x21eedee71005a953, 0xc178ddf175ba987e, 0xd0d577f6c4ba43f6, 0x9486f46c4d6f24fd, + 0x3d33c574c5421895, 0x5be6cb4c842e52ab, 0x3809690d9debc9ff, 0xe4b1c692a84a5b6f, + 0x58b966add7e18b57, 0x7ff0b61e77c94715, 0x0e295883f06add82, 0x7c3c04fd65c7f5a4, + 0x4ea9266060223be5, 0x5d843a5789262bfd, 0x35bf4aef36da11c0, 0xa6692f14af859eb1, + 0xca1fc13ba12fdf41, 0xd798c04b8224f5d2, 0x22f4594e1dd5872b, 0xdee12df51bddfda8, + 0x96473ff0ed83420a, 0xf41cf1c78daa27f4, 0x2772cd56aecefd8a, 0xd5ddaf184902b47f, + 0xff77551fc0798101, 0x8baa01d626946bda, 0xd0087e47100525f2, 0x521d62544c0de308, + 0x4a0f45eb9bbce049, 0x5ee33cbea6c6b96e, 0x9a6af4b7d6a22345, 0x0d0d35e738b1b406, + 0x9e71252dbbedc29b, 0x3aa70bb6cad1455e, 0xa406fb7a42a1778c, 0xd94f9646f0897613, + 0x5256370ff57f66c8, 0x95891e354432f679, 0x75d6423abcb6b3d3, 0x79d9ea012367483f, + 0x1e36ccc69efb0473, 0x3e64b034dfdc0cec, 0x13bfd326028bb238, 0x171e9d96209edd95, + 0xda25838007b22424, 0xe31e97f6d41b8023, 0xdd4ed3907269cecd, 0x810fb3c812d5cec6, + 0x2f956519babeec88, 0xb0350c52455baf52, 0xa7fb548a48d5abf1, 0xcb81bd0cca5e2d9f, + 0xda5ecd39a6d17b19, 0xd2588bab508e5149, 0x1a30cff5c3e23cfd, 0x2dd398b4f89f8712, + 0x2a9118005b304005, 0xd091be7ad9dece69, 0x147e93daf6cabc89, 0x7eac201844935824, + 0xd4aaf2be32f5de9b, 0xe302bc41d9396cd1, 0x3c2794cf2c069d1a, 0xf9197eaaa9d433ae, + 0x98f822ef4445e8c2, 0xc578360e1383ece8, 0xa5372c1201869457, 0x1c6ed00d787d6644, + 0x77fb08cd86531814, 0xeff6ee2663a70db8, 0x980be15380976119, 0x534a09bdd69d60c5, + 0x71a58b0c759dba20, 0x34d5f06c679c0b40, 0xdc0e7e5fceed2f9f, 0xaaa5996e48808edb, + 0x8ca96ff0bcdd88e5, 0x91b02d67c37c2b46, 0xbe4f394895526319, 0x4315c7f289be56d1, + 0xa312a3c0dc85bba1, 0x3328fa8e431ca797, 0x5438bf1c68fd219a, 0x98812c6f85837d74, + 0xe88c4913f8c96d49, 0xcc62e79cc2442aca, 0x4ef3c7d4046655f1, 0x04a362eddadab1ea, + 0x975e2f3c30a199cf, 0x831e04a9014a165a, 0x1e1d3c53aa126719, 0xc42661e01bf707a0, + 0x295b0738aa2da264, 0xb45f5ed865d4ba34, 0x27fb5a129f3938fa, 0x25fba614cb26f86c, + 0x6bd41981cf3c1c4d, 0xd6f9239ca0dedafd, 0x46882526ae55b97f, 0x8e6fa99481b628d4, + 0xbdb314dddc0aa158, 0x3534367812ba2a17, 0xac018e8332e2e431, 0x43a64e35e65cc63e, + 0x887f3a2a0b6603ea, 0xe015426c76b2673f, 0x59dc553027edfe8a, 0xea9eacf368d9ebf3, + 0x40301c8ecc3e07ca, 0xd8cb9b5b0f57a2e6, 0x542e6b5260ec5864, 0xb8791dd617f6affe, + 0x6735bd1c798d9993, 0x006d8b25d5da393c, 0x1d675bdb49e6d0d2, 0x331d9a108607f99e, + 0x4ff8ab749dc4cd07, 0xa87d4ae164ea3192, 0xdde0d92e41196b5b, 0xa15ad47bb2e010eb, + 0x23e6003fa5522a75, 0xc6ef3f1b84afa749, 0x9a723f75146d10a3, 0x5fa99480119106b0, + 0x01d500dbc0013dba, 0x10b30ada548edbe0, 0xb2eb046eb04ffc6b, 0xa57088f364f25ee2, + 0xc0c919c383a068a3, 0x8139559dfbde282f, 0x4e2b5d139fec9a99, 0x53bad712fbefa7e6, + 0xa6befe0d2860bd4f, 0x6ea0ae150011bd15, 0xc1ef34632bce3779, 0xc09ecb305d742dbb, + 0x29526afdf73db19d, 0x7c02c9056a029a40, 0xa778460fde5a48ba, 0xda05993e77c105f6, + 0xb6d599f9c9ddece9, 0x9f9df6680cfc33ca, 0xdcd8ef4fa0aa67a8, 0x31277019c3f4d178, + 0x98e05abf53e86ae1, 0xc1dc4d903850830d, 0xbd7fd806e06bc33c, 0x1ac330d6acf1286f, + 0x28ce2303e1588c1e, 0xdc25e54b1b7e9c19, 0x11e51e494b7149f2, 0x551b8391b5c7fa25, + 0xa2fc251c1bf69873, 0x099b7b532aec1574, 0x9ff981567c53296a, 0xaf3f8d08a2dc60de, + 0x18dd295c59b72d6c, 0x165c9063e75f44fc, 0x9046ee7c427a0c55, 0x317ea24dc79ffdb3, + 0x6835a3150ef0447d, 0xb2b9c7868068e7c7, 0xe63527140e646af5, 0xc5554a91442baaa0, + 0x671febc56d0ba1ea, 0x44f9ef7b0cf649ed, 0x4aa0cd610c1dac6b, 0x865f3c236e393e68, + 0xf6886bcda71dee29, 0x934b0455da44ffae, 0xda7621c4016d6039, 0xf36c41bf3ad35493, + 0x9063135ee5f6ab8d, 0xb0e8eaba47bdc0a8, 0x625306164c737cf3, 0x8046423e64f6b6cb, + 0x11e50ad77958e3dc, 0x4dab4e16b57234ab, 0x6ccfe2c6e0916210, 0x4d5dbc3b80f49d40, + 0x2b8ff368ef1b2b1b, 0xf2afb326752fea2a, 0xffa48ea70246e36b, 0x3a4bae9b589b7444, + 0x80ff984a6ff3efcf, 0x7af53f3056b77b47, 0x1f1c33b09320cae6, 0xce1f1c4826fc4ad4, + 0x9cac662bad350ee5, 0xf4c72fffe27a7dbd, 0xd766f986703184e5, 0x36d3efd57c5b241e, + 0xd4d6e358f7ff5804, 0xa832b3028f5e0bf6, 0x4b3d73f7453d9a22, 0xb4dae072df938705, + 0x6bff7b2e92401620, 0x96b8494e9bfa61cd, 0x4bcda341b74dc1e5, 0x383fe3d2c19c393d, + 0xa375fb70077e8821, 0xea35e04bc17eb9bc, 0x941d21ba7c4dd076, 0x916c0a593d0c3d8a, + 0x2c1304e315b2cf47, 0x9233ebf3d0c955c0, 0x77acdd072b2fc935, 0xd71b6a7ac04276bf, + 0x789ea49bd2ee8d68, 0x89552b460a84a920, 0xe629d5de1a4ea456, 0xddfefe8722ddd405, + 0x3d56f6971cdb9e7b, 0x95a861b0a8bf715b, 0xb01248d67896c993, 0x3c4e3d9801a3085c, + 0x674939e19085b360, 0xae67dea9b589a287, 0xc563856f2bfdcfc9, 0x62fa9a80313b685d, + 0x36ff33d97ad501d9, 0xf8bab4dd730ab349, 0x18fd59f3c46ba69d, 0x81e08665e65278e9, + 0x5a5e803feb8a1e84, 0x5b4eef3547243604, 0x0ee71ee0393d6cdf, 0xde4d9deac3a9c6db, + 0x0c14c37664466b53, 0xc2ce964289e3b45e, 0x6aa8012f54a2de21, 0x519759c129b6bc2c, + 0x17768527e4667322, 0x09fdfe4dac83b2ea, 0xd422125d04a0d5f5, 0x02e8ff962b86b310, + 0xf033628dd7ee97af, 0x778a846c7d72e0e6, 0x06fde613882f63d6, 0x9e258b0d8d434f14, + 0x5cdda529ccdcd600, 0x37038b38033c4535, 0xd6a1d639391c1d7d, 0x4f6489e431d4ce6b, + 0xd1b82f175754e08c, 0x7df268ee75db7bd6, 0x1e4a1202ad14dcfa, 0x7ab92ce2ccfb9b77, + 0x61388e0323aef997, 0x9981f5bf06440ce3, 0x8d7631dac67d0edd, 0xc6ea593fc0a93516, + 0x064a06e0ee841b38, 0x0d1d4f57521ce83f, 0xf7a0e0c370df2613, 0x1506cccb84c071ab, + 0x42a138ec328565e9, 0xe16b4578b8130d16, 0x0628ff2245ba251a, 0x016a84ca210e22e8, + 0x8ba14bb494592d43, 0xffee4308785274a5, 0x01fc21ab01354b75, 0xc37ce45f7e424674, + 0x71e153afa7fe2735, 0x000fcee9c307721f, 0x3b189004805b56e3, 0x2f1435aa7f504d9b, + 0xd9aa1ebaa083bd72, 0xf1145036720ccf3d, 0x95b29e274084fa32, 0x8862d21301f94f0c, + 0x23fc5ddf1510a406, 0x475a78f4c9f0e98d, 0xb6d681c4e72843a0, 0xa90af2a44a00c5a6, + 0x95fc6d45a34f4412, 0x60f9c0e2e7f5d703, 0x2bc0642bad110925, 0x79abfc10be24a4d5, + }, +}; diff --git a/tests/sm2_z256test.c b/tests/sm2_z256test.c index 75a48c13b..0374deb01 100644 --- a/tests/sm2_z256test.c +++ b/tests/sm2_z256test.c @@ -1,5 +1,5 @@ /* - * Copyright 2014-2023 The GmSSL Project. All Rights Reserved. + * Copyright 2014-2024 The GmSSL Project. All Rights Reserved. * * Licensed under the Apache License, Version 2.0 (the License); you may * not use this file except in compliance with the License. @@ -12,462 +12,91 @@ #include #include #include +#include #include +#include #include -#include - - - -static int sm2_z256_equ_hex(const uint64_t a[4], const char *hex) -{ - uint64_t b[4]; - sm2_z256_from_hex(b, hex); - return (sm2_z256_cmp(a, b) == 0); -} - - -int sm2_z256_mont_equ_hex(const uint64_t a[4], const char *hex) -{ - uint64_t a_[4]; - uint64_t b[4]; - - sm2_z256_from_mont(a_, a); - sm2_z256_from_hex(b, hex); - return (sm2_z256_cmp(a_, b) == 0); -} - -static int test_sm2_z256_add(void) -{ - char *hex_x = "32c4ae2c1f1981195f9904466a39c9948fe30bbff2660be1715a4589334c74c7"; - char *hex_y = "bc3736a2f4f6779c59bdcee36b692153d0a9877cc62a474002df32e52139f0a0"; - char *hex_add_x_y = "eefbe4cf140ff8b5b956d329d5a2eae8608c933cb89053217439786e54866567"; - char *hex_2y = "786e6d45e9ecef38b37b9dc6d6d242a7a1530ef98c548e8005be65ca4273e140"; - - uint64_t x[4]; - uint64_t y[4]; - uint64_t r[4]; - uint64_t c; - - sm2_z256_from_hex(x, hex_x); - sm2_z256_from_hex(y, hex_y); - - c = sm2_z256_add(r, x, y); - if (c != 0 || sm2_z256_equ_hex(r, hex_add_x_y) != 1) { - error_print(); - return -1; - } - - c = sm2_z256_add(r, y, y); - if (c != 1 || sm2_z256_equ_hex(r, hex_2y) != 1) { - error_print(); - return -1; - } - - printf("%s() ok\n", __FUNCTION__); - return 1; -} - -static int test_sm2_z256_sub(void) -{ - char *hex_x = "32c4ae2c1f1981195f9904466a39c9948fe30bbff2660be1715a4589334c74c7"; - char *hex_y = "bc3736a2f4f6779c59bdcee36b692153d0a9877cc62a474002df32e52139f0a0"; - char *hex_sub_x_y = "768d77892a23097d05db3562fed0a840bf3984432c3bc4a16e7b12a412128427"; - char *hex_sub_y_x = "89728876d5dcf682fa24ca9d012f57bf40c67bbcd3c43b5e9184ed5beded7bd9"; - uint64_t x[4]; - uint64_t y[4]; - uint64_t r[4]; - uint64_t c; - - sm2_z256_from_hex(x, hex_x); - sm2_z256_from_hex(y, hex_y); - - c = sm2_z256_sub(r, x, y); - if (c != 1 || sm2_z256_equ_hex(r, hex_sub_x_y) != 1) { - error_print(); - return -1; - } - - c = sm2_z256_sub(r, y, x); - if (c != 0 || sm2_z256_equ_hex(r, hex_sub_y_x) != 1) { - error_print(); - return -1; - } - - printf("%s() ok\n", __FUNCTION__); - return 1; -} - -static int test_sm2_z256_mul(void) -{ - char *hex_x = "32c4ae2c1f1981195f9904466a39c9948fe30bbff2660be1715a4589334c74c7"; - char *hex_y = "bc3736a2f4f6779c59bdcee36b692153d0a9877cc62a474002df32e52139f0a0"; - char *hex_mul_x_y = - "255362ffa019467e48add0ebbe29d15e82fab48f15592867dbdab16dde8d0673" - "dd4057dd755d04ff86dad43f0ecaf69ddccd043ba61f523ebe51b0ee64928c60"; - - uint64_t x[4]; - uint64_t y[4]; - uint64_t r[8]; - - sm2_z256_from_hex(x, hex_x); - sm2_z256_from_hex(y, hex_y); - - sm2_z256_mul(r, x, y); - - if (sm2_z256_equ_hex(r + 4, hex_mul_x_y) != 1 - || sm2_z256_equ_hex(r, hex_mul_x_y + 64) != 1) { - error_print(); - return -1; - } - - printf("%s() ok\n", __FUNCTION__); - return 1; -} - -static int test_sm2_z256_cmp(void) -{ - char *hex_x = "32c4ae2c1f1981195f9904466a39c9948fe30bbff2660be1715a4589334c74c7"; - char *hex_y = "bc3736a2f4f6779c59bdcee36b692153d0a9877cc62a474002df32e52139f0a0"; - - uint64_t x[4]; - uint64_t y[4]; - - sm2_z256_from_hex(x, hex_x); - sm2_z256_from_hex(y, hex_y); - - if (sm2_z256_cmp(x, y) != -1 - || sm2_z256_cmp(x, x) != 0 - || sm2_z256_cmp(y, y) != 0 - || sm2_z256_cmp(y, x) != 1) { - error_print(); - return -1; - } - - printf("%s() ok\n", __FUNCTION__); - return 1; -} - -static int test_sm2_z256_modp_add(void) -{ - char *hex_x = "32c4ae2c1f1981195f9904466a39c9948fe30bbff2660be1715a4589334c74c7"; - char *hex_y = "bc3736a2f4f6779c59bdcee36b692153d0a9877cc62a474002df32e52139f0a0"; - char *hex_modp_add_x_y = "eefbe4cf140ff8b5b956d329d5a2eae8608c933cb89053217439786e54866567"; - char *hex_neg_x = "cd3b51d2e0e67ee6a066fbb995c6366b701cf43f0d99f41f8ea5ba76ccb38b38"; - char *hex_p_sub_1 = "fffffffeffffffffffffffffffffffffffffffff00000000fffffffffffffffe"; - char *hex_2 = "0000000000000000000000000000000000000000000000000000000000000002"; - char *hex_1 = "0000000000000000000000000000000000000000000000000000000000000001"; - char *hex_0 = "0000000000000000000000000000000000000000000000000000000000000000"; - char *hex_modp_2y = "786e6d46e9ecef38b37b9dc6d6d242a7a1530efa8c548e7f05be65ca4273e141"; - - uint64_t x[4]; - uint64_t y[4]; - uint64_t r[4]; - - sm2_z256_from_hex(x, hex_x); - sm2_z256_from_hex(y, hex_y); - - // x + y < p - sm2_z256_modp_add(r, x, y); - if (sm2_z256_equ_hex(r, hex_modp_add_x_y) != 1) { - error_print(); - return -1; - } - - // x + y > 2^256 - sm2_z256_modp_add(r, y, y); - if (sm2_z256_equ_hex(r, hex_modp_2y) != 1) { - error_print(); - return -1; - } - - // x + y = p - sm2_z256_from_hex(r, hex_neg_x); - sm2_z256_modp_add(r, r, x); - if (sm2_z256_equ_hex(r, hex_0) != 1) { - error_print(); - return -1; - } - - // p < x + y < 2^256 - sm2_z256_from_hex(x, hex_p_sub_1); - sm2_z256_from_hex(y, hex_2); - sm2_z256_modp_add(r, x, y); - if (sm2_z256_equ_hex(r, hex_1) != 1) { - error_print(); - return -1; - } - - printf("%s() ok\n", __FUNCTION__); - return 1; -} - -static int test_sm2_z256_modp_sub(void) -{ - char *hex_x = "32c4ae2c1f1981195f9904466a39c9948fe30bbff2660be1715a4589334c74c7"; - char *hex_y = "bc3736a2f4f6779c59bdcee36b692153d0a9877cc62a474002df32e52139f0a0"; - char *hex_modp_sub_x_y = "768d77882a23097d05db3562fed0a840bf3984422c3bc4a26e7b12a412128426"; - char *hex_modp_sub_y_x = "89728876d5dcf682fa24ca9d012f57bf40c67bbcd3c43b5e9184ed5beded7bd9"; - char *hex_0 = "0000000000000000000000000000000000000000000000000000000000000000"; - - uint64_t x[4]; - uint64_t y[4]; - uint64_t r[4]; - - sm2_z256_from_hex(x, hex_x); - sm2_z256_from_hex(y, hex_y); - - sm2_z256_modp_sub(r, x, y); - if (sm2_z256_equ_hex(r, hex_modp_sub_x_y) != 1) { - error_print(); - return -1; - } - - sm2_z256_modp_sub(r, y, x); - if (sm2_z256_equ_hex(r, hex_modp_sub_y_x) != 1) { - error_print(); - return -1; - } - - sm2_z256_modp_sub(r, x, x); - if (sm2_z256_equ_hex(r, hex_0) != 1) { - error_print(); - return -1; - } - - printf("%s() ok\n", __FUNCTION__); - return 1; -} - -static int test_sm2_z256_modp_div_by_2(void) -{ - char *hex_x = "32c4ae2c1f1981195f9904466a39c9948fe30bbff2660be1715a4589334c74c7"; - char *hex_y = "bc3736a2f4f6779c59bdcee36b692153d0a9877cc62a474002df32e52139f0a0"; - char *hex_modp_x_div_2 = "996257158f8cc08cafcc8223351ce4ca47f185df793305f138ad22c499a63a63"; - char *hex_modp_y_div_2 = "5e1b9b517a7b3bce2cdee771b5b490a9e854c3be631523a0016f9972909cf850"; - - uint64_t x[4]; - uint64_t y[4]; - uint64_t r[4]; - - sm2_z256_from_hex(x, hex_x); - sm2_z256_from_hex(y, hex_y); - - sm2_z256_modp_div_by_2(r, x); - if (sm2_z256_equ_hex(r, hex_modp_x_div_2) != 1) { - error_print(); - return -1; - } - - sm2_z256_modp_div_by_2(r, y); - if (sm2_z256_equ_hex(r, hex_modp_y_div_2) != 1) { - error_print(); - return -1; - } - printf("%s ok\n", __FUNCTION__); - return 1; -} - -static int test_sm2_z256_modp_mul(void) -{ - char *hex_x = "32c4ae2c1f1981195f9904466a39c9948fe30bbff2660be1715a4589334c74c7"; - char *hex_y = "bc3736a2f4f6779c59bdcee36b692153d0a9877cc62a474002df32e52139f0a0"; - char *hex_modp_mul_x_y = "edd7e745bdc4630ccfa1da1057033a525346dbf202f082f3c431349991ace76a"; - char *hex_0 = "0000000000000000000000000000000000000000000000000000000000000000"; - - uint64_t x[4]; - uint64_t y[4]; - uint64_t r[4]; - - sm2_z256_from_hex(x, hex_x); - sm2_z256_from_hex(y, hex_y); - - sm2_z256_to_mont(x, x); - sm2_z256_to_mont(y, y); - sm2_z256_mont_mul(r, x, y); - sm2_z256_from_mont(r, r); - - if (sm2_z256_equ_hex(r, hex_modp_mul_x_y) != 1) { - error_print(); - return -1; - } - - printf("%s() ok\n", __FUNCTION__); - return 1; -} - -static int test_sm2_z256_modp_inv(void) -{ - char *hex_x = "32c4ae2c1f1981195f9904466a39c9948fe30bbff2660be1715a4589334c74c7"; - char *hex_y = "bc3736a2f4f6779c59bdcee36b692153d0a9877cc62a474002df32e52139f0a0"; - char *hex_modp_inv_x = "053b878fb82e213c17e554b9a574b7bd31775222704b7fd9c7d6f8441026cd80"; - char *hex_modp_inv_y = "7adc850505c462b280f710414ab54e922551dbc97eefbc04e99cb743624c729f"; - char *hex_0 = "0000000000000000000000000000000000000000000000000000000000000000"; - char *hex_1 = "0000000000000000000000000000000000000000000000000000000000000001"; - - uint64_t x[4]; - uint64_t y[4]; - uint64_t r[4]; - - sm2_z256_from_hex(x, hex_x); - sm2_z256_from_hex(y, hex_y); - - sm2_z256_to_mont(x, x); - sm2_z256_mont_inv(r, x); - sm2_z256_from_mont(r ,r); - if (sm2_z256_equ_hex(r, hex_modp_inv_x) != 1) { - error_print(); - return -1; - } - - sm2_z256_to_mont(y, y); - sm2_z256_mont_inv(r, y); - sm2_z256_from_mont(r ,r); - if (sm2_z256_equ_hex(r, hex_modp_inv_y) != 1) { - error_print(); - return -1; - } - - printf("%s() ok\n", __FUNCTION__); - return 1; -} - - - -static const uint64_t SM2_Z256_MONT_X[4] = { - 0x61328990f418029e, 0x3e7981eddca6c050, 0xd6a1ed99ac24c3c3, 0x91167a5ee1c13b05, -}; - -static const uint64_t SM2_Z256_MONT_Y[4] = { - 0xc1354e593c2d0ddd, 0xc1f5e5788d3295fa, 0x8d4cfb066e2a48f8, 0x63cd65d481d735bd, -}; - -static int test_sm2_z256_point_get_affine(void) -{ - const char *hex_x = "32c4ae2c1f1981195f9904466a39c9948fe30bbff2660be1715a4589334c74c7"; - const char *hex_y = "bc3736a2f4f6779c59bdcee36b692153d0a9877cc62a474002df32e52139f0a0"; - SM2_Z256_POINT P; - uint64_t x[4]; - uint64_t y[4]; - - sm2_z256_copy(P.X, SM2_Z256_MONT_X); - sm2_z256_copy(P.Y, SM2_Z256_MONT_Y); - sm2_z256_copy(P.Z, SM2_Z256_MONT_ONE); - - sm2_z256_point_get_affine(&P, x, y); - - if (sm2_z256_equ_hex(x, hex_x) != 1 || sm2_z256_equ_hex(y, hex_y) != 1) { - error_print(); - return -1; - } - - printf("%s() ok\n", __FUNCTION__); - return 1; -} - -static int test_sm2_z256_point_dbl(void) -{ - char *hex_x_2G = "56cefd60d7c87c000d58ef57fa73ba4d9c0dfa08c08a7331495c2e1da3f2bd52"; - char *hex_y_2G = "31b7e7e6cc8189f668535ce0f8eaf1bd6de84c182f6c8e716f780d3a970a23c3"; - SM2_Z256_POINT P; - uint64_t x[4]; - uint64_t y[4]; - - sm2_z256_copy(P.X, SM2_Z256_MONT_X); - sm2_z256_copy(P.Y, SM2_Z256_MONT_Y); - sm2_z256_copy(P.Z, SM2_Z256_MONT_ONE); - - sm2_z256_point_dbl(&P, &P); - sm2_z256_point_get_affine(&P, x, y); - - if (sm2_z256_equ_hex(x, hex_x_2G) != 1 || sm2_z256_equ_hex(y, hex_y_2G) != 1) { - error_print(); - return -1; - } - printf("%s() ok\n", __FUNCTION__); - return 1; - -} - -static int test_sm2_z256_point_add_affine(void) +static int test_sm2_z256_point_mul_generator(void) { - char *hex_x_3G = "a97f7cd4b3c993b4be2daa8cdb41e24ca13f6bd945302244e26918f1d0509ebf"; - char *hex_y_3G = "530b5dd88c688ef5ccc5cec08a72150f7c400ee5cd045292aaacdd037458f6e6"; - SM2_Z256_POINT P; - SM2_Z256_POINT Q; - uint64_t x[4]; - uint64_t y[4]; - - sm2_z256_copy(P.X, SM2_Z256_MONT_X); - sm2_z256_copy(P.Y, SM2_Z256_MONT_Y); - sm2_z256_copy(P.Z, SM2_Z256_MONT_ONE); - - sm2_z256_point_dbl(&Q, &P); - sm2_z256_point_add_affine(&Q, &Q, (SM2_Z256_POINT_AFFINE *)&P); - sm2_z256_point_get_affine(&Q, x, y); - - if (sm2_z256_equ_hex(x, hex_x_3G) != 1 || sm2_z256_equ_hex(y, hex_y_3G) != 1) { - error_print(); - return -1; - } - - printf("%s() ok\n", __FUNCTION__); - return 1; -} + struct { + char *k; + char *kG; + } tests[] = { + // k = 0 + {"0000000000000000000000000000000000000000000000000000000000000000", + "0000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000"}, + // k = 1 + {"0000000000000000000000000000000000000000000000000000000000000001", + "32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7" + "BC3736A2F4F6779C59BDCEE36B692153D0A9877CC62A474002DF32E52139F0A0"}, + // k = 2 + {"0000000000000000000000000000000000000000000000000000000000000002", + "56CEFD60D7C87C000D58EF57FA73BA4D9C0DFA08C08A7331495C2E1DA3F2BD52" + "31B7E7E6CC8189F668535CE0F8EAF1BD6DE84C182F6C8E716F780D3A970A23C3"}, + // k = 3 + {"0000000000000000000000000000000000000000000000000000000000000003", + "A97F7CD4B3C993B4BE2DAA8CDB41E24CA13F6BD945302244E26918F1D0509EBF" + "530B5DD88C688EF5CCC5CEC08A72150F7C400EE5CD045292AAACDD037458F6E6"}, + // k = 4 + {"0000000000000000000000000000000000000000000000000000000000000004", + "C239507105C683242A81052FF641ED69009A084AD5CC937DB21646CD34A0CED5" + "B1BF7EC4080F3C8735F1294AC0DB19686BEE2E96AB8C71FB7A253666CB66E009"}, + // k = 5 + {"0000000000000000000000000000000000000000000000000000000000000005", + "C749061668652E26040E008FDD5EB77A344A417B7FCE19DBA575DA57CC372A9E" + "F2DF5DB2D144E9454504C622B51CF38F5006206EB579FF7DA6976EFF5FBE6480"}, + // k = 6 + {"0000000000000000000000000000000000000000000000000000000000000006", + "0927AFB57D93483BBB17C93E71F22A3105FF8856A66016892C8B1A1A3C4B0D30" + "150C6B1AB4D1FC7EAC1C0EF6EBF2664581ADF1F0855A064DD572103000088F63"}, + // k = 7 + {"0000000000000000000000000000000000000000000000000000000000000007", + "DDF092555409C19DFDBE86A75C139906A80198337744EE78CD27E384D9FCAF15" + "847D18FFB38E87065CD6B6E9C12D2922037937707D6A49A2223B949657E52BC1"}, + // k = G.x + {"32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7", + "782E1941B8A8C802543BC831E19F3548235C94A9C42AAD1EA8952CEAAECF12BA" + "EEE0D9A6939E87F3B47A85863F873B324B9859136E2BF3235E17B3270164202D"}, + // k = G.y + {"BC3736A2F4F6779C59BDCEE36B692153D0A9877CC62A474002DF32E52139F0A0", + "1000165E3FFF85F1DFFFB3AA1DF9F5E62B9A86A9A2927B4FF1AC16D19FEFF330" + "3116F22B65320DD3B7F73DCF4A4028063A9BE6EFBD1DB0915C72F1EE067C5ECF"}, + // k = n - 1 = -1 + {"FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54122", + "32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7" + "43C8C95C0B098863A642311C9496DEAC2F56788239D5B8C0FD20CD1ADEC60F5F"}, + // k = n = 0 + {"FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123", + "0000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000"}, + // k = n + 1 = 1 + {"FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54124", + "32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7" + "BC3736A2F4F6779C59BDCEE36B692153D0A9877CC62A474002DF32E52139F0A0"}, + // k = 2^256 - 1 + {"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", + "B3217D884BC175E6BA6B360EB0E6D4396EAEA725C3D66E87BFA5BEB6C0D3456B" + "A5199445C54B56602AA60025E1907BFD26B30E867DB6C58A034263AE4A2E27C2"}, + }; -static int test_sm2_z256_point_add(void) -{ - char *hex_x_5G = "c749061668652e26040e008fdd5eb77a344a417b7fce19dba575da57cc372a9e"; - char *hex_y_5G = "f2df5db2d144e9454504c622b51cf38f5006206eb579ff7da6976eff5fbe6480"; - SM2_Z256_POINT G; + uint64_t k[4]; SM2_Z256_POINT P; - SM2_Z256_POINT Q; - SM2_Z256_POINT R; - uint64_t x[4]; - uint64_t y[4]; - - sm2_z256_copy(G.X, SM2_Z256_MONT_X); - sm2_z256_copy(G.Y, SM2_Z256_MONT_Y); - sm2_z256_copy(G.Z, SM2_Z256_MONT_ONE); + uint8_t P_bytes[64]; + uint8_t kG_bytes[64]; + size_t i, len; - // P = 2*G - sm2_z256_point_dbl(&P, &G); + for (i = 0; i < sizeof(tests)/sizeof(tests[0]); i++) { - // Q = 3*G - sm2_z256_point_add_affine(&Q, &P, (SM2_Z256_POINT_AFFINE *)&G); + sm2_z256_from_hex(k, tests[i].k); + hex_to_bytes(tests[i].kG, strlen(tests[i].kG), kG_bytes, &len); - // R = P + Q - sm2_z256_point_add(&R, &P, &Q); + sm2_z256_point_mul_generator(&P, k); + sm2_z256_point_to_bytes(&P, P_bytes); - sm2_z256_point_get_affine(&R, x, y); - - if (sm2_z256_equ_hex(x, hex_x_5G) != 1 || sm2_z256_equ_hex(y, hex_y_5G) != 1) { - error_print(); - return -1; - } - - printf("%s() ok\n", __FUNCTION__); - return 1; -} - -static int test_sm2_z256_get_booth(void) -{ - char *hex_a = "7a648a77d0cbe0b9ee841433be0c132aa98f6757da70a18c74999774fa587762"; - - // window_size = 7, len(booth) = (256 + 6)/7 = 7 - int booth_a[37] = { - -30, -17, -30, -45, -48, -17, -26, -51, -11, 25, 6, 5, 39, -5, -42, 52, - 15, -45, 43, 25, -63, -62, -16, 26, 20, 8, 58, -49, 12, -4, 51, -24, -8, - 21, 18, -45, 8 - }; - uint64_t a[4]; - int i = 0; - - sm2_z256_from_hex(a, hex_a); - - for (i = 0; i < 37; i++) { - if (sm2_z256_get_booth(a, 7, i) != booth_a[i]) { + if (memcmp(P_bytes, kG_bytes, 64) != 0) { error_print(); return -1; } @@ -477,81 +106,68 @@ static int test_sm2_z256_get_booth(void) return 1; } -static int test_sm2_z256_point_mul_generator(void) +int main(void) { - char *hex_b = "28e9fa9e9d9f5e344d5a9e4bcf6509a7f39789f515ab8f92ddbcbd414d940e93"; - char *hex_x = "528470bc74a6ebc663c06fc4cfa1b630d1e9d4a80c0a127b47f73c324c46c0ba"; - char *hex_y = "832cf9c5a15b997e60962b4cf6e2c9cee488faaec98d20599d323d4cabfc1bf4"; +/* + SM2_POINT P; + uint8_t k[32] = {0}; + uint8_t i; - uint64_t b[4]; - SM2_Z256_POINT P; - uint64_t x[4]; - uint64_t y[4]; + for (i = 0; i < 8; i++) { + k[31] = i; - sm2_z256_from_hex(b, hex_b); - sm2_z256_point_mul_generator(&P, b); - sm2_z256_point_get_affine(&P, x, y); + format_bytes(stderr, 0, 0, "k", k, 32); - if (sm2_z256_equ_hex(x, hex_x) != 1 || sm2_z256_equ_hex(y, hex_y) != 1) { - error_print(); - return -1; + sm2_point_mul_generator(&P, k); + sm2_point_print(stdout, 0, 4, "kG", &P); } - printf("%s() ok\n", __FUNCTION__); - return 1; -} + size_t len; + char *xG = "32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7"; + char *yG = "BC3736A2F4F6779C59BDCEE36B692153D0A9877CC62A474002DF32E52139F0A0"; -static int test_sm2_z256_point_mul(void) -{ - char *hex_b = "28e9fa9e9d9f5e344d5a9e4bcf6509a7f39789f515ab8f92ddbcbd414d940e93"; - char *hex_x = "528470bc74a6ebc663c06fc4cfa1b630d1e9d4a80c0a127b47f73c324c46c0ba"; - char *hex_y = "832cf9c5a15b997e60962b4cf6e2c9cee488faaec98d20599d323d4cabfc1bf4"; + hex_to_bytes(xG, strlen(xG), k, &len); - uint64_t b[4]; - SM2_Z256_POINT G; - SM2_Z256_POINT P; - uint64_t x[4]; - uint64_t y[4]; + sm2_point_mul_generator(&P, k); + format_bytes(stderr, 0, 0, "k", k, 32); + sm2_point_print(stdout, 0, 4, "kG", &P); - sm2_z256_from_hex(b, hex_b); + hex_to_bytes(yG, strlen(yG), k, &len); + sm2_point_mul_generator(&P, k); + format_bytes(stderr, 0, 0, "k", k, 32); + sm2_point_print(stdout, 0, 4, "kG", &P); - sm2_z256_copy(G.X, SM2_Z256_MONT_X); - sm2_z256_copy(G.Y, SM2_Z256_MONT_Y); - sm2_z256_copy(G.Z, SM2_Z256_MONT_ONE); + char *n = "fffffffeffffffffffffffffffffffff7203df6b21c6052b53bbf40939d54123"; + char *n_minus_one = "fffffffeffffffffffffffffffffffff7203df6b21c6052b53bbf40939d54122"; + char *n_plus_one = "fffffffeffffffffffffffffffffffff7203df6b21c6052b53bbf40939d54124"; + char *max256 = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"; - sm2_z256_point_mul(&P, &G, b); - sm2_z256_point_get_affine(&P, x, y); + hex_to_bytes(n_minus_one, strlen(n_minus_one), k, &len); + sm2_point_mul_generator(&P, k); + format_bytes(stderr, 0, 0, "n-1", k, 32); + sm2_point_print(stdout, 0, 4, "kG", &P); - if (sm2_z256_equ_hex(x, hex_x) != 1 || sm2_z256_equ_hex(y, hex_y) != 1) { - error_print(); - return -1; - } + hex_to_bytes(n, strlen(n), k, &len); + sm2_point_mul_generator(&P, k); + format_bytes(stderr, 0, 0, "n", k, 32); + sm2_point_print(stdout, 0, 4, "kG", &P); - printf("%s() ok\n", __FUNCTION__); - return 1; -} + hex_to_bytes(n_plus_one, strlen(n_plus_one), k, &len); + sm2_point_mul_generator(&P, k); + format_bytes(stderr, 0, 0, "n+1", k, 32); + sm2_point_print(stdout, 0, 4, "kG", &P); -int main(void) -{ - if (test_sm2_z256_add() != 1) { error_print(); return -1; } - if (test_sm2_z256_sub() != 1) { error_print(); return -1; } - if (test_sm2_z256_mul() != 1) { error_print(); return -1; } - if (test_sm2_z256_cmp() != 1) { error_print(); return -1; } - if (test_sm2_z256_modp_add() != 1) { error_print(); return -1; } - if (test_sm2_z256_modp_sub() != 1) { error_print(); return -1; } - if (test_sm2_z256_modp_mul() != 1) { error_print(); return -1; } - if (test_sm2_z256_modp_inv() != 1) { error_print(); return -1; } - if (test_sm2_z256_modp_div_by_2() != 1) { error_print(); return -1; } - if (test_sm2_z256_get_booth() != 1) { error_print(); return -1; } - if (test_sm2_z256_point_get_affine() != 1) { error_print(); return -1; } - if (test_sm2_z256_point_dbl() != 1) { error_print(); return -1; } - if (test_sm2_z256_point_add_affine() != 1) { error_print(); return -1; } - if (test_sm2_z256_point_add() != 1) { error_print(); return -1; } - if (test_sm2_z256_point_mul_generator() != 1) { error_print(); return -1; } - if (test_sm2_z256_point_mul() != 1) { error_print(); return -1; } + hex_to_bytes(max256, strlen(max256), k, &len); + sm2_point_mul_generator(&P, k); + format_bytes(stderr, 0, 0, "n+1", k, 32); + sm2_point_print(stdout, 0, 4, "kG", &P); +*/ + if (test_sm2_z256_point_mul_generator() != 1) goto err; printf("%s all tests passed\n", __FILE__); return 0; +err: + error_print(); + return 1; } -