diff --git a/src/sm9_math.c b/src/sm9_math.c new file mode 100644 index 00000000..e7aa840b --- /dev/null +++ b/src/sm9_math.c @@ -0,0 +1,1951 @@ +/* + * Copyright (c) 2014 - 2020 The GmSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the GmSSL Project. + * (http://gmssl.org/)" + * + * 4. The name "GmSSL Project" must not be used to endorse or promote + * products derived from this software without prior written + * permission. For written permission, please contact + * guanzhi1980@gmail.com. + * + * 5. Products derived from this software may not be called "GmSSL" + * nor may "GmSSL" appear in their names without prior written + * permission of the GmSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the GmSSL Project + * (http://gmssl.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE GmSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE GmSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#include +#include +#include +#include +#include +#include +#include "endian.h" + + +const sm9_bn_t SM9_ZERO = {0,0,0,0,0,0,0,0}; +const sm9_bn_t SM9_ONE = {1,0,0,0,0,0,0,0}; +const sm9_bn_t SM9_TWO = {2,0,0,0,0,0,0,0}; +const sm9_bn_t SM9_FIVE = {5,0,0,0,0,0,0,0}; + + +// p = b640000002a3a6f1d603ab4ff58ec74521f2934b1a7aeedbe56f9b27e351457d +// n = b640000002a3a6f1d603ab4ff58ec74449f2934b18ea8beee56ee19cd69ecf25 +// mu = 2^512 // p = 167980e0beb5759a655f73aebdcd1312af2665f6d1e36081c71188f90d5c22146 +const sm9_bn_t SM9_P = {0xe351457d, 0xe56f9b27, 0x1a7aeedb, 0x21f2934b, 0xf58ec745, 0xd603ab4f, 0x02a3a6f1, 0xb6400000}; +const sm9_bn_t SM9_P_MINUS_ONE = {0xe351457c, 0xe56f9b27, 0x1a7aeedb, 0x21f2934b, 0xf58ec745, 0xd603ab4f, 0x02a3a6f1, 0xb6400000}; +const sm9_bn_t SM9_N = {0xd69ecf25, 0xe56ee19c, 0x18ea8bee, 0x49f2934b, 0xf58ec744, 0xd603ab4f, 0x02a3a6f1, 0xb6400000}; +const sm9_barrett_bn_t SM9_MU = {0xd5c22146, 0x71188f90, 0x1e36081c, 0xf2665f6d, 0xdcd1312a, 0x55f73aeb, 0xeb5759a6, 0x67980e0b, 0x00000001}; + + +// P1.X 0x93DE051D62BF718FF5ED0704487D01D6E1E4086909DC3280E8C4E4817C66DDDD +// P1.Y 0x21FE8DDA4F21E607631065125C395BBC1C1C00CBFA6024350C464CD70A3EA616 +const sm9_point_t _SM9_P1 = { + {0x7c66dddd, 0xe8c4e481, 0x09dc3280, 0xe1e40869, 0x487d01d6, 0xf5ed0704, 0x62bf718f, 0x93de051d}, + {0x0a3ea616, 0x0c464cd7, 0xfa602435, 0x1c1c00cb, 0x5c395bbc, 0x63106512, 0x4f21e607, 0x21fe8dda}, + {1,0,0,0,0,0,0,0} +}; +const sm9_point_t *SM9_P1 = &_SM9_P1; + + +/* + X : [0x3722755292130b08d2aab97fd34ec120ee265948d19c17abf9b7213baf82d65bn, + 0x85aef3d078640c98597b6027b441a01ff1dd2c190f5e93c454806c11d8806141n], + Y : [0xa7cf28d519be3da65f3170153d278ff247efba98a71a08116215bba5c999a7c7n, + 0x17509b092e845c1266ba0d262cbee6ed0736a96fa347c8bd856dc76b84ebeb96n], + Z : [1n, 0n], +*/ +const sm9_twist_point_t _SM9_P2 = { + {{0xAF82D65B, 0xF9B7213B, 0xD19C17AB, 0xEE265948, 0xD34EC120, 0xD2AAB97F, 0x92130B08, 0x37227552}, + {0xD8806141, 0x54806C11, 0x0F5E93C4, 0xF1DD2C19, 0xB441A01F, 0x597B6027, 0x78640C98, 0x85AEF3D0}}, + {{0xC999A7C7, 0x6215BBA5, 0xA71A0811, 0x47EFBA98, 0x3D278FF2, 0x5F317015, 0x19BE3DA6, 0xA7CF28D5}, + {0x84EBEB96, 0x856DC76B, 0xA347C8BD, 0x0736A96F, 0x2CBEE6ED, 0x66BA0D26, 0x2E845C12, 0x17509B09}}, + {{1,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0}}, +}; +const sm9_twist_point_t *SM9_P2 = &_SM9_P2; + + +const sm9_twist_point_t _SM9_Ppubs = { + {{0x96EA5E32, 0x8F14D656, 0x386A92DD, 0x414D2177, 0x24A3B573, 0x6CE843ED, 0x152D1F78, 0x29DBA116}, + {0x1B94C408, 0x0AB1B679, 0x5E392CFB, 0x1CE0711C, 0x41B56501, 0xE48AFF4B, 0x3084F733, 0x9F64080B}}, + {{0xB4E3216D, 0x0E75C05F, 0x5CDFF073, 0x1006E85F, 0xB7A46F74, 0x1A7CE027, 0xDDA532DA, 0x41E00A53}, + {0xD0EF1C25, 0xE89E1408, 0x1A77F335, 0xAD3E2FDB, 0x47E3A0CB, 0xB57329F4, 0xABEA0112, 0x69850938}}, + {{1,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0}}, +}; +const sm9_twist_point_t *SM9_Ppubs = &_SM9_Ppubs; + + +void sm9_bn_to_bytes(const sm9_bn_t a, uint8_t out[32]) +{ + int i; + for (i = 7; i >= 0; i--) { + PUTU32(out, (uint32_t)a[i]); + out += sizeof(uint32_t); + } +} + +void sm9_bn_from_bytes(sm9_bn_t r, const uint8_t in[32]) +{ + int i; + for (i = 7; i >= 0; i--) { + r[i] = GETU32(in); + in += sizeof(uint32_t); + } +} + +int sm9_bn_from_hex(sm9_bn_t r, const char hex[65]) +{ + uint8_t buf[32]; + size_t len; + if (hex_to_bytes(hex, 64, buf, &len) < 0) { + return -1; + } + sm9_bn_from_bytes(r, buf); + return 0; +} + +void sm9_bn_to_hex(const sm9_bn_t a, char hex[65]) +{ + int i; + for (i = 7; i >= 0; i--) { + (void)sprintf(hex + 8*(7-i), "%08x", (uint32_t)a[i]); + //hex += 8; + } + hex[64] = 0; +} + +void sm9_print_bn(const char *prefix, const sm9_bn_t a) +{ + char hex[65]; + sm9_bn_to_hex(a, hex); + printf("%s\n%s\n", prefix, hex); +} + +void sm9_bn_to_bits(const sm9_bn_t a, char bits[256]) +{ + int i, j; + for (i = 7; i >= 0; i--) { + uint32_t w = a[i]; + for (j = 0; j < 32; j++) { + *bits++ = (w & 0x80000000) ? '1' : '0'; + w <<= 1; + } + } +} + +int sm9_bn_cmp(const sm9_bn_t a, const sm9_bn_t b) +{ + int i; + for (i = 7; i >= 0; i--) { + if (a[i] > b[i]) + return 1; + if (a[i] < b[i]) + return -1; + } + return 0; +} + +int sm9_bn_equ_hex(const sm9_bn_t a, const char *hex) +{ + sm9_bn_t b; + sm9_bn_from_hex(b, hex); + return (sm9_bn_cmp(a, b) == 0); +} + +void sm9_bn_set_word(sm9_bn_t r, uint32_t a) +{ + sm9_bn_set_zero(r); + r[0] = a; +} + +void sm9_bn_add(sm9_bn_t r, const sm9_bn_t a, const sm9_bn_t b) +{ + int i; + r[0] = a[0] + b[0]; + for (i = 1; i < 8; i++) { + r[i] = a[i] + b[i] + (r[i-1] >> 32); + } + for (i = 0; i < 7; i++) { + r[i] &= 0xffffffff; + } +} + +void sm9_bn_sub(sm9_bn_t ret, const sm9_bn_t a, const sm9_bn_t b) +{ + int i; + sm9_bn_t r; + r[0] = ((uint64_t)1 << 32) + a[0] - b[0]; + for (i = 1; i < 7; i++) { + r[i] = 0xffffffff + a[i] - b[i] + (r[i - 1] >> 32); + r[i - 1] &= 0xffffffff; + } + r[i] = a[i] - b[i] + (r[i - 1] >> 32) - 1; + r[i - 1] &= 0xffffffff; + sm9_bn_copy(ret, r); +} + +void sm9_bn_rand_range(sm9_bn_t r, const sm9_bn_t range) +{ + FILE *fp; + uint8_t buf[256]; + + fp = fopen("/dev/urandom", "rb"); + do { + fread(buf, 1, 256, fp); + sm9_bn_from_bytes(r, buf); + } while (sm9_bn_cmp(r, range) >= 0); + fclose(fp); +} + +int sm9_fp_equ(const sm9_fp_t a, const sm9_fp_t b) +{ + int i; + for (i = 0; i < 8; i++) { + if (a[i] != b[i]) + return 0; + } + return 1; +} + +void sm9_fp_add(sm9_fp_t r, const sm9_fp_t a, const sm9_fp_t b) +{ + sm9_bn_add(r, a, b); + if (sm9_bn_cmp(r, SM9_P) >= 0) + return sm9_bn_sub(r, r, SM9_P); +} + +void sm9_fp_sub(sm9_fp_t r, const sm9_fp_t a, const sm9_fp_t b) +{ + if (sm9_bn_cmp(a, b) >= 0) { + sm9_bn_sub(r, a, b); + } else { + sm9_bn_t t; + sm9_bn_sub(t, SM9_P, b); + sm9_bn_add(r, t, a); + } +} + +void sm9_fp_dbl(sm9_fp_t r, const sm9_fp_t a) +{ + sm9_fp_add(r, a, a); +} + +void sm9_fp_tri(sm9_fp_t r, const sm9_fp_t a) +{ + sm9_fp_t t; + sm9_fp_dbl(t, a); + sm9_fp_add(r, t, a); +} + +void sm9_fp_div2(sm9_fp_t r, const sm9_fp_t a) +{ + int i; + sm9_bn_copy(r, a); + if (r[0] & 0x01) { + sm9_bn_add(r, r, SM9_P); + } + for (i = 0; i < 7; i++) { + r[i] = (r[i] >> 1) | ((r[i + 1] & 0x01) << 31); + } + r[i] >>= 1; +} + +void sm9_fp_neg(sm9_fp_t r, const sm9_fp_t a) +{ + if (sm9_bn_is_zero(a)) { + sm9_bn_copy(r, a); + } else { + sm9_bn_sub(r, SM9_P, a); + } +} + +int sm9_barrett_bn_cmp(const sm9_barrett_bn_t a, const sm9_barrett_bn_t b) +{ + int i; + for (i = 8; i >= 0; i--) { + if (a[i] > b[i]) + return 1; + if (a[i] < b[i]) + return -1; + } + return 0; +} + +void sm9_barrett_bn_add(sm9_barrett_bn_t r, const sm9_barrett_bn_t a, const sm9_barrett_bn_t b) +{ + int i; + r[0] = a[0] + b[0]; + for (i = 1; i < 9; i++) { + r[i] = a[i] + b[i] + (r[i-1] >> 32); + } + for (i = 0; i < 8; i++) { + r[i] &= 0xffffffff; + } +} + +void sm9_barrett_bn_sub(sm9_barrett_bn_t ret, const sm9_barrett_bn_t a, const sm9_barrett_bn_t b) +{ + sm9_barrett_bn_t r; + int i; + r[0] = ((uint64_t)1 << 32) + a[0] - b[0]; + for (i = 1; i < 8; i++) { + r[i] = 0xffffffff + a[i] - b[i] + (r[i - 1] >> 32); + r[i - 1] &= 0xffffffff; + } + r[i] = a[i] - b[i] + (r[i - 1] >> 32) - 1; + r[i - 1] &= 0xffffffff; + for (i = 0; i < 9; i++) { + ret[i] = r[i]; + } +} + +void sm9_fp_mul(sm9_fp_t r, const sm9_fp_t a, const sm9_fp_t b) +{ + uint64_t s[18]; + sm9_barrett_bn_t zh, zl, q; + uint64_t w; + int i, j; + + /* z = a * b */ + for (i = 0; i < 8; i++) { + s[i] = 0; + } + for (i = 0; i < 8; i++) { + w = 0; + for (j = 0; j < 8; j++) { + w += s[i + j] + a[i] * b[j]; + s[i + j] = w & 0xffffffff; + w >>= 32; + } + s[i + 8] = w; + } + + /* zl = z mod (2^32)^9 = z[0..8] + * zh = z // (2^32)^7 = z[7..15] */ + for (i = 0; i < 9; i++) { + zl[i] = s[i]; + zh[i] = s[7 + i]; + } + + /* q = zh * mu // (2^32)^9 */ + for (i = 0; i < 18; i++) { + s[i] = 0; + } + for (i = 0; i < 9; i++) { + w = 0; + for (j = 0; j < 9; j++) { + w += s[i + j] + zh[i] * SM9_MU[j]; + s[i + j] = w & 0xffffffff; + w >>= 32; + } + s[i + 9] = w; + } + for (i = 0; i < 9; i++) { + q[i] = s[9 + i]; + } + + /* q = q * p mod (2^32)^9 */ + for (i = 0; i < 18; i++) { + s[i] = 0; + } + for (i = 0; i < 9; i++) { + w = 0; + for (j = 0; j < 8; j++) { + w += s[i + j] + q[i] * SM9_P[j]; + s[i + j] = w & 0xffffffff; + w >>= 32; + } + s[i + 8] = w; + } + for (i = 0; i < 9; i++) { + q[i] = s[i]; + } + + /* r = zl - q (mod (2^32)^9) */ + + if (sm9_barrett_bn_cmp(zl, q)) { + sm9_barrett_bn_sub(zl, zl, q); + } else { + sm9_barrett_bn_t c = {0,0,0,0,0,0,0,0,0x100000000}; + sm9_barrett_bn_sub(q, c, q); + sm9_barrett_bn_add(zl, q, zl); + } + + + for (i = 0; i < 8; i++) { + r[i] = zl[i]; + } + + r[7] += (zl[8] << 32); + + /* while r >= p do: r = r - p */ + while (sm9_bn_cmp(r, SM9_P) >= 0) { + + sm9_bn_sub(r, r, SM9_P); + } +} + +void sm9_fp_sqr(sm9_fp_t r, const sm9_fp_t a) +{ + sm9_fp_mul(r, a, a); +} + +void sm9_fp_pow(sm9_fp_t r, const sm9_fp_t a, const sm9_bn_t e) +{ + sm9_fp_t t; + uint32_t w; + int i, j; + + assert(sm9_bn_cmp(e, SM9_P_MINUS_ONE) < 0); + + sm9_bn_set_one(t); + for (i = 7; i >= 0; i--) { + w = (uint32_t)e[i]; + for (j = 0; j < 32; j++) { + sm9_fp_sqr(t, t); + if (w & 0x80000000) + sm9_fp_mul(t, t, a); + w <<= 1; + } + } + sm9_bn_copy(r, t); +} + +void sm9_fp_inv(sm9_fp_t r, const sm9_fp_t a) +{ + sm9_fp_t e; + sm9_bn_sub(e, SM9_P, SM9_TWO); + sm9_fp_pow(r, a, e); +} + +const sm9_fp2_t SM9_FP2_ZERO = {{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}; +const sm9_fp2_t SM9_FP2_ONE = {{1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}; +const sm9_fp2_t SM9_FP2_U = {{0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0}}; +const sm9_fp2_t SM9_FP2_5U = {{0,0,0,0,0,0,0,0},{5,0,0,0,0,0,0,0}}; + +void sm9_fp2_from_hex(sm9_fp2_t r, const char hex[65 * 2]) +{ + sm9_fp_from_hex(r[1], hex); + sm9_fp_from_hex(r[0], hex + 65); +} + +void sm9_fp2_to_hex(const sm9_fp2_t a, char hex[65 * 2]) +{ + sm9_fp_to_hex(a[1], hex); + hex[64] = '\n'; + sm9_fp_to_hex(a[0], hex + 65); +} + +void sm9_fp2_print(const char *prefix, const sm9_fp2_t a) +{ + char hex[65 * 2]; + sm9_fp2_to_hex(a, hex); + printf("%s\n%s\n", prefix, hex); +} + +void sm9_fp2_set_fp(sm9_fp2_t r, const sm9_fp_t a) +{ + sm9_fp_copy(r[0], a); + sm9_fp_set_zero(r[1]); +} + +void sm9_fp2_set(sm9_fp2_t r, const sm9_fp_t a0, const sm9_fp_t a1) +{ + sm9_fp_copy(r[0], a0); + sm9_fp_copy(r[1], a1); +} + +void sm9_fp2_add(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b) +{ + sm9_fp_add(r[0], a[0], b[0]); + sm9_fp_add(r[1], a[1], b[1]); +} + +void sm9_fp2_dbl(sm9_fp2_t r, const sm9_fp2_t a) +{ + sm9_fp_dbl(r[0], a[0]); + sm9_fp_dbl(r[1], a[1]); +} + +void sm9_fp2_tri(sm9_fp2_t r, const sm9_fp2_t a) +{ + sm9_fp_tri(r[0], a[0]); + sm9_fp_tri(r[1], a[1]); +} + +void sm9_fp2_sub(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b) +{ + sm9_fp_sub(r[0], a[0], b[0]); + sm9_fp_sub(r[1], a[1], b[1]); +} + +void sm9_fp2_neg(sm9_fp2_t r, const sm9_fp2_t a) +{ + sm9_fp_neg(r[0], a[0]); + sm9_fp_neg(r[1], a[1]); +} + +void sm9_fp2_mul(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b) +{ + sm9_fp_t r0, r1, t; + + // r0 = a0 * b0 - 2 * a1 * b1 + sm9_fp_mul(r0, a[0], b[0]); + sm9_fp_mul(t, a[1], b[1]); + sm9_fp_dbl(t, t); + sm9_fp_sub(r0, r0, t); + + // r1 = a0 * b1 + a1 * b0 + sm9_fp_mul(r1, a[0], b[1]); + sm9_fp_mul(t, a[1], b[0]); + sm9_fp_add(r1, r1, t); + + sm9_fp_copy(r[0], r0); + sm9_fp_copy(r[1], r1); +} + +void sm9_fp2_mul_u(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b) +{ + sm9_fp_t r0, r1, t; + + // r0 = -2 * (a0 * b1 + a1 * b0) + sm9_fp_mul(r0, a[0], b[1]); + sm9_fp_mul(t, a[1], b[0]); + sm9_fp_add(r0, r0, t); + sm9_fp_dbl(r0, r0); + sm9_fp_neg(r0, r0); + + // r1 = a0 * b0 - 2 * a1 * b1 + sm9_fp_mul(r1, a[0], b[0]); + sm9_fp_mul(t, a[1], b[1]); + sm9_fp_dbl(t, t); + sm9_fp_sub(r1, r1, t); + + sm9_fp_copy(r[0], r0); + sm9_fp_copy(r[1], r1); +} + +void sm9_fp2_mul_fp(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp_t k) +{ + sm9_fp_mul(r[0], a[0], k); + sm9_fp_mul(r[1], a[1], k); +} + +void sm9_fp2_sqr(sm9_fp2_t r, const sm9_fp2_t a) +{ + sm9_fp_t r0, r1, t; + + // a0^2 - 2 * a1^2 + sm9_fp_sqr(r0, a[0]); + sm9_fp_sqr(t, a[1]); + sm9_fp_dbl(t, t); + sm9_fp_sub(r0, r0, t); + + // r1 = 2 * a0 * a1 + sm9_fp_mul(r1, a[0], a[1]); + sm9_fp_dbl(r1, r1); + + sm9_bn_copy(r[0], r0); + sm9_bn_copy(r[1], r1); +} + +void sm9_fp2_sqr_u(sm9_fp2_t r, const sm9_fp2_t a) +{ + sm9_fp_t r0, r1, t; + + // r0 = -4 * a0 * a1 + sm9_fp_mul(r0, a[0], a[1]); + sm9_fp_dbl(r0, r0); + sm9_fp_dbl(r0, r0); + sm9_fp_neg(r0, r0); + + // r1 = a0^2 - 2 * a1^2 + sm9_fp_sqr(r1, a[0]); + sm9_fp_sqr(t, a[1]); + sm9_fp_dbl(t, t); + sm9_fp_sub(r1, r1, t); + + sm9_fp_copy(r[0], r0); + sm9_fp_copy(r[1], r1); + +} + +void sm9_fp2_inv(sm9_fp2_t r, const sm9_fp2_t a) +{ + if (sm9_fp_is_zero(a[0])) { + // r0 = 0 + sm9_fp_set_zero(r[0]); + // r1 = -(2 * a1)^-1 + sm9_fp_dbl(r[1], a[1]); + sm9_fp_inv(r[1], r[1]); + sm9_fp_neg(r[1], r[1]); + + } else if (sm9_fp_is_zero(a[1])) { + /* r1 = 0 */ + sm9_fp_set_zero(r[1]); + /* r0 = a0^-1 */ + sm9_fp_inv(r[0], a[0]); + + } else { + sm9_fp_t k, t; + + // k = (a[0]^2 + 2 * a[1]^2)^-1 + sm9_fp_sqr(k, a[0]); + sm9_fp_sqr(t, a[1]); + sm9_fp_dbl(t, t); + sm9_fp_add(k, k, t); + sm9_fp_inv(k, k); + + // r[0] = a[0] * k + sm9_fp_mul(r[0], a[0], k); + + // r[1] = -a[1] * k + sm9_fp_mul(r[1], a[1], k); + sm9_fp_neg(r[1], r[1]); + } +} + +void sm9_fp2_div(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b) +{ + sm9_fp2_t t; + sm9_fp2_inv(t, b); + sm9_fp2_mul(r, a, t); +} + +void sm9_fp2_div2(sm9_fp2_t r, const sm9_fp2_t a) +{ + sm9_fp_div2(r[0], a[0]); + sm9_fp_div2(r[1], a[1]); +} + +const sm9_fp4_t SM9_FP4_ZERO = {{{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}}}; +const sm9_fp4_t SM9_FP4_ONE = {{{1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}, {{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}}; +const sm9_fp4_t SM9_FP4_U = {{{0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0}}, {{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}}; +const sm9_fp4_t SM9_FP4_V = {{{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}, {{1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}}; + +void sm9_fp4_from_hex(sm9_fp4_t r, const char hex[65 * 4]) +{ + sm9_fp2_from_hex(r[1], hex); + sm9_fp2_from_hex(r[0], hex + 65 * 2); +} + +void sm9_fp4_to_hex(const sm9_fp4_t a, char hex[65 * 4]) +{ + sm9_fp2_to_hex(a[1], hex); + hex[65 + 64] = '\n'; + sm9_fp2_to_hex(a[0], hex + 65 * 2); +} + +void sm9_fp4_set_fp(sm9_fp4_t r, const sm9_fp_t a) +{ + sm9_fp2_set_fp(r[0], a); + sm9_fp2_set_zero(r[1]); +} + +void sm9_fp4_set_fp2(sm9_fp4_t r, const sm9_fp2_t a) +{ + sm9_fp2_copy(r[0], a); + sm9_fp2_set_zero(r[1]); +} + +void sm9_fp4_set(sm9_fp4_t r, const sm9_fp2_t a0, const sm9_fp2_t a1) +{ + sm9_fp2_copy(r[0], a0); + sm9_fp2_copy(r[1], a1); +} + +/* +void sm9_fp4_set_one(sm9_fp4_t r) +{ + sm9_fp2_set_one(r[0]); + sm9_fp2_set_zero(r[1]); +} +*/ + +void sm9_fp4_set_u(sm9_fp4_t r) +{ + sm9_fp2_set_u(r[0]); + sm9_fp2_set_zero(r[1]); +} + +void sm9_fp4_set_v(sm9_fp4_t r) +{ + sm9_fp2_set_zero(r[0]); + sm9_fp2_set_one(r[1]); +} + +void sm9_fp4_add(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp4_t b) +{ + sm9_fp2_add(r[0], a[0], b[0]); + sm9_fp2_add(r[1], a[1], b[1]); +} + +void sm9_fp4_dbl(sm9_fp4_t r, const sm9_fp4_t a) +{ + sm9_fp2_dbl(r[0], a[0]); + sm9_fp2_dbl(r[1], a[1]); +} + +void sm9_fp4_sub(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp4_t b) +{ + sm9_fp2_sub(r[0], a[0], b[0]); + sm9_fp2_sub(r[1], a[1], b[1]); +} + +void sm9_fp4_neg(sm9_fp4_t r, const sm9_fp4_t a) +{ + sm9_fp2_neg(r[0], a[0]); + sm9_fp2_neg(r[1], a[1]); +} + +void sm9_fp4_mul(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp4_t b) +{ + sm9_fp2_t r0, r1, t; + + sm9_fp2_mul(r0, a[0], b[0]); + sm9_fp2_mul_u(t, a[1], b[1]); + sm9_fp2_add(r0, r0, t); + + sm9_fp2_mul(r1, a[0], b[1]); + sm9_fp2_mul(t, a[1], b[0]); + sm9_fp2_add(r1, r1, t); + + sm9_fp2_copy(r[0], r0); + sm9_fp2_copy(r[1], r1); +} + +void sm9_fp4_mul_fp(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp_t k) +{ + sm9_fp2_mul_fp(r[0], a[0], k); + sm9_fp2_mul_fp(r[1], a[1], k); +} + +void sm9_fp4_mul_fp2(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp2_t b0) +{ + sm9_fp2_mul(r[0], a[0], b0); + sm9_fp2_mul(r[1], a[1], b0); +} + +void sm9_fp4_mul_v(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp4_t b) +{ + sm9_fp2_t r0, r1, t; + + sm9_fp2_mul_u(r0, a[0], b[1]); + sm9_fp2_mul_u(t, a[1], b[0]); + sm9_fp2_add(r0, r0, t); + + sm9_fp2_mul(r1, a[0], b[0]); + sm9_fp2_mul_u(t, a[1], b[1]); + sm9_fp2_add(r1, r1, t); + + sm9_fp2_copy(r[0], r0); + sm9_fp2_copy(r[1], r1); +} + +void sm9_fp4_sqr(sm9_fp4_t r, const sm9_fp4_t a) +{ + sm9_fp2_t r0, r1, t; + + sm9_fp2_sqr(r0, a[0]); + sm9_fp2_sqr_u(t, a[1]); + sm9_fp2_add(r0, r0, t); + + sm9_fp2_mul(r1, a[0], a[1]); + sm9_fp2_dbl(r1, r1); + sm9_fp2_copy(r[0], r0); + sm9_fp2_copy(r[1], r1); +} + +void sm9_fp4_sqr_v(sm9_fp4_t r, const sm9_fp4_t a) +{ + sm9_fp2_t r0, r1, t; + + sm9_fp2_mul_u(t, a[0], a[1]); + sm9_fp2_dbl(r0, t); + + sm9_fp2_sqr(r1, a[0]); + sm9_fp2_sqr_u(t, a[1]); + sm9_fp2_add(r1, r1, t); + + sm9_fp2_copy(r[0], r0); + sm9_fp2_copy(r[1], r1); +} + +void sm9_fp4_inv(sm9_fp4_t r, const sm9_fp4_t a) +{ + sm9_fp2_t r0, r1, k; + + sm9_fp2_sqr_u(k, a[1]); + sm9_fp2_sqr(r0, a[0]); + sm9_fp2_sub(k, k, r0); + sm9_fp2_inv(k, k); + + sm9_fp2_mul(r0, a[0], k); + sm9_fp2_neg(r0, r0); + + sm9_fp2_mul(r1, a[1], k); + + sm9_fp2_copy(r[0], r0); + sm9_fp2_copy(r[1], r1); +} + +void sm9_fp12_set_one(sm9_fp12_t r) +{ + sm9_fp4_set_one(r[0]); + sm9_fp4_set_zero(r[1]); + sm9_fp4_set_zero(r[2]); +} + +int sm9_fp12_is_one(const sm9_fp12_t a) +{ + return sm9_fp4_is_one(a[0]) + && sm9_fp4_is_zero(a[1]) + && sm9_fp4_is_zero(a[2]); +} + +int sm9_fp12_is_zero(const sm9_fp12_t a) +{ + return sm9_fp4_is_zero(a[0]) + && sm9_fp4_is_zero(a[1]) + && sm9_fp4_is_zero(a[2]); +} + +void sm9_fp12_from_hex(sm9_fp12_t r, const char hex[65 * 12]) +{ + sm9_fp4_from_hex(r[2], hex); + sm9_fp4_from_hex(r[1], hex + 65 * 4); + sm9_fp4_from_hex(r[0], hex + 65 * 8); +} + +void sm9_fp12_to_hex(const sm9_fp12_t a, char hex[65 * 12]) +{ + sm9_fp4_to_hex(a[2], hex); + hex[65 * 4 - 1] = '\n'; + sm9_fp4_to_hex(a[1], hex + 65 * 4); + hex[65 * 8 - 1] = '\n'; + sm9_fp4_to_hex(a[0], hex + 65 * 8); +} + +void sm9_fp12_print(const char *prefix, const sm9_fp12_t a) +{ + char hex[65 * 12]; + sm9_fp12_to_hex(a, hex); + printf("%s\n%s\n", prefix, hex); +} + +void sm9_fp12_set(sm9_fp12_t r, const sm9_fp4_t a0, const sm9_fp4_t a1, const sm9_fp4_t a2) +{ + sm9_fp4_copy(r[0], a0); + sm9_fp4_copy(r[1], a1); + sm9_fp4_copy(r[2], a2); +} + +void sm9_fp12_set_fp(sm9_fp12_t r, const sm9_fp_t a) +{ + sm9_fp4_set_fp(r[0], a); + sm9_fp4_set_zero(r[1]); + sm9_fp4_set_zero(r[2]); +} + +void sm9_fp12_set_fp2(sm9_fp12_t r, const sm9_fp2_t a) +{ + sm9_fp4_set_fp2(r[0], a); + sm9_fp4_set_zero(r[1]); + sm9_fp4_set_zero(r[2]); +} + +void sm9_fp12_set_fp4(sm9_fp12_t r, const sm9_fp4_t a) +{ + sm9_fp4_copy(r[0], a); + sm9_fp4_set_zero(r[1]); + sm9_fp4_set_zero(r[2]); +} + +void sm9_fp12_set_u(sm9_fp12_t r) +{ + sm9_fp4_set_u(r[0]); + sm9_fp4_set_zero(r[1]); + sm9_fp4_set_zero(r[2]); +} + +void sm9_fp12_set_v(sm9_fp12_t r) +{ + sm9_fp4_set_v(r[0]); + sm9_fp4_set_zero(r[1]); + sm9_fp4_set_zero(r[2]); +} + +void sm9_fp12_set_w(sm9_fp12_t r) +{ + sm9_fp4_set_zero(r[0]); + sm9_fp4_set_one(r[1]); + sm9_fp4_set_zero(r[2]); +} + +void sm9_fp12_set_w_sqr(sm9_fp12_t r) +{ + sm9_fp4_set_zero(r[0]); + sm9_fp4_set_zero(r[1]); + sm9_fp4_set_one(r[2]); +} + +int sm9_fp12_equ(const sm9_fp12_t a, const sm9_fp12_t b) +{ + return sm9_fp4_equ(a[0], b[0]) + && sm9_fp4_equ(a[1], b[1]) + && sm9_fp4_equ(a[2], b[2]); +} + +void sm9_fp12_add(sm9_fp12_t r, const sm9_fp12_t a, const sm9_fp12_t b) +{ + sm9_fp4_add(r[0], a[0], b[0]); + sm9_fp4_add(r[1], a[1], b[1]); + sm9_fp4_add(r[2], a[2], b[2]); +} + +void sm9_fp12_dbl(sm9_fp12_t r, const sm9_fp12_t a) +{ + sm9_fp4_dbl(r[0], a[0]); + sm9_fp4_dbl(r[1], a[1]); + sm9_fp4_dbl(r[2], a[2]); +} + +void sm9_fp12_tri(sm9_fp12_t r, const sm9_fp12_t a) +{ + sm9_fp12_t t; + sm9_fp12_dbl(t, a); + sm9_fp12_add(r, t, a); +} + +void sm9_fp12_sub(sm9_fp12_t r, const sm9_fp12_t a, const sm9_fp12_t b) +{ + sm9_fp4_sub(r[0], a[0], b[0]); + sm9_fp4_sub(r[1], a[1], b[1]); + sm9_fp4_sub(r[2], a[2], b[2]); +} + +void sm9_fp12_neg(sm9_fp12_t r, const sm9_fp12_t a) +{ + sm9_fp4_neg(r[0], a[0]); + sm9_fp4_neg(r[1], a[1]); + sm9_fp4_neg(r[2], a[2]); +} + +void sm9_fp12_mul(sm9_fp12_t r, const sm9_fp12_t a, const sm9_fp12_t b) +{ + sm9_fp4_t r0, r1, r2, t; + + sm9_fp4_mul(r0, a[0], b[0]); + sm9_fp4_mul_v(t, a[1], b[2]); + sm9_fp4_add(r0, r0, t); + sm9_fp4_mul_v(t, a[2], b[1]); + sm9_fp4_add(r0, r0, t); + + sm9_fp4_mul(r1, a[0], b[1]); + sm9_fp4_mul(t, a[1], b[0]); + sm9_fp4_add(r1, r1, t); + sm9_fp4_mul_v(t, a[2], b[2]); + sm9_fp4_add(r1, r1, t); + + sm9_fp4_mul(r2, a[0], b[2]); + sm9_fp4_mul(t, a[1], b[1]); + sm9_fp4_add(r2, r2, t); + sm9_fp4_mul(t, a[2], b[0]); + sm9_fp4_add(r2, r2, t); + + sm9_fp4_copy(r[0], r0); + sm9_fp4_copy(r[1], r1); + sm9_fp4_copy(r[2], r2); +} + +void sm9_fp12_sqr(sm9_fp12_t r, const sm9_fp12_t a) +{ + sm9_fp4_t r0, r1, r2, t; + + sm9_fp4_sqr(r0, a[0]); + sm9_fp4_mul_v(t, a[1], a[2]); + sm9_fp4_dbl(t, t); + sm9_fp4_add(r0, r0, t); + + sm9_fp4_mul(r1, a[0], a[1]); + sm9_fp4_dbl(r1, r1); + sm9_fp4_sqr_v(t, a[2]); + sm9_fp4_add(r1, r1, t); + + sm9_fp4_mul(r2, a[0], a[2]); + sm9_fp4_dbl(r2, r2); + sm9_fp4_sqr(t, a[1]); + sm9_fp4_add(r2, r2, t); + + sm9_fp4_copy(r[0], r0); + sm9_fp4_copy(r[1], r1); + sm9_fp4_copy(r[2], r2); +} + +void sm9_fp12_inv(sm9_fp12_t r, const sm9_fp12_t a) +{ + if (sm9_fp4_is_zero(a[2])) { + sm9_fp4_t k, t; + + sm9_fp4_sqr(k, a[0]); + sm9_fp4_mul(k, k, a[0]); + sm9_fp4_sqr_v(t, a[1]); + sm9_fp4_mul(t, t, a[1]); + sm9_fp4_add(k, k, t); + sm9_fp4_inv(k, k); + + sm9_fp4_sqr(r[2], a[1]); + sm9_fp4_mul(r[2], r[2], k); + + sm9_fp4_mul(r[1], a[0], a[1]); + sm9_fp4_mul(r[1], r[1], k); + sm9_fp4_neg(r[1], r[1]); + + sm9_fp4_sqr(r[0], a[0]); + sm9_fp4_mul(r[0], r[0], k); + + } else { + sm9_fp4_t t0, t1, t2, t3; + + sm9_fp4_sqr(t0, a[1]); + sm9_fp4_mul(t1, a[0], a[2]); + sm9_fp4_sub(t0, t0, t1); + + sm9_fp4_mul(t1, a[0], a[1]); + sm9_fp4_sqr_v(t2, a[2]); + sm9_fp4_sub(t1, t1, t2); + + sm9_fp4_sqr(t2, a[0]); + sm9_fp4_mul_v(t3, a[1], a[2]); + sm9_fp4_sub(t2, t2, t3); + + sm9_fp4_sqr(t3, t1); + sm9_fp4_mul(r[0], t0, t2); + sm9_fp4_sub(t3, t3, r[0]); + sm9_fp4_inv(t3, t3); + sm9_fp4_mul(t3, a[2], t3); + + sm9_fp4_mul(r[0], t2, t3); + + sm9_fp4_mul(r[1], t1, t3); + sm9_fp4_neg(r[1], r[1]); + + sm9_fp4_mul(r[2], t0, t3); + } +} + +void sm9_fp12_pow(sm9_fp12_t r, const sm9_fp12_t a, const sm9_bn_t k) +{ + char kbits[257]; + sm9_fp12_t t; + int i; + + assert(sm9_bn_cmp(k, SM9_P_MINUS_ONE) < 0); + sm9_fp12_set_zero(t); + + sm9_bn_to_bits(k, kbits); + sm9_fp12_copy(t, a); + for (i = 1; i < 256; i++) { + sm9_fp12_sqr(t, t); + if (kbits[i] == '1') { + sm9_fp12_mul(t, t, a); + } + } + sm9_fp12_copy(r, t); +} + +void sm9_fp2_conjugate(sm9_fp2_t r, const sm9_fp2_t a) +{ + sm9_fp_copy(r[0], a[0]); + sm9_fp_neg (r[1], a[1]); + +} + +void sm9_fp2_frobenius(sm9_fp2_t r, const sm9_fp2_t a) +{ + return sm9_fp2_conjugate(r, a); +} + +// beta = 0x6c648de5dc0a3f2cf55acc93ee0baf159f9d411806dc5177f5b21fd3da24d011 +// alpha1 = 0x3f23ea58e5720bdb843c6cfa9c08674947c5c86e0ddd04eda91d8354377b698b +// alpha2 = 0xf300000002a3a6f2780272354f8b78f4d5fc11967be65334 +// alpha3 = 0x6c648de5dc0a3f2cf55acc93ee0baf159f9d411806dc5177f5b21fd3da24d011 +// alpha4 = 0xf300000002a3a6f2780272354f8b78f4d5fc11967be65333 +// alpha5 = 0x2d40a38cf6983351711e5f99520347cc57d778a9f8ff4c8a4c949c7fa2a96686 +const sm9_fp2_t SM9_BETA = {{0xda24d011, 0xf5b21fd3, 0x06dc5177, 0x9f9d4118, 0xee0baf15, 0xf55acc93, 0xdc0a3f2c, 0x6c648de5}, {0}}; +const sm9_fp_t SM9_ALPHA1 = {0x377b698b, 0xa91d8354, 0x0ddd04ed, 0x47c5c86e, 0x9c086749, 0x843c6cfa, 0xe5720bdb, 0x3f23ea58}; +const sm9_fp_t SM9_ALPHA2 = {0x7be65334, 0xd5fc1196, 0x4f8b78f4, 0x78027235, 0x02a3a6f2, 0xf3000000, 0x0, 0x0 }; +const sm9_fp_t SM9_ALPHA3 = {0xda24d011, 0xf5b21fd3, 0x06dc5177, 0x9f9d4118, 0xee0baf15, 0xf55acc93, 0xdc0a3f2c, 0x6c648de5}; +const sm9_fp_t SM9_ALPHA4 = {0x7be65333, 0xd5fc1196, 0x4f8b78f4, 0x78027235, 0x02a3a6f2, 0xf3000000, 0x0, 0x0 }; +const sm9_fp_t SM9_ALPHA5 = {0xa2a96686, 0x4c949c7f, 0xf8ff4c8a, 0x57d778a9, 0x520347cc, 0x711e5f99, 0xf6983351, 0x2d40a38c}; + + +void sm9_fp4_frobenius(sm9_fp4_t r, const sm9_fp4_t a) +{ + sm9_fp2_conjugate(r[0], a[0]); + sm9_fp2_conjugate(r[1], a[1]); + sm9_fp2_mul(r[1], r[1], SM9_BETA); +} + +void sm9_fp4_conjugate(sm9_fp4_t r, const sm9_fp4_t a) +{ + sm9_fp2_copy(r[0], a[0]); + sm9_fp2_neg(r[1], a[1]); +} + +void sm9_fp4_frobenius2(sm9_fp4_t r, const sm9_fp4_t a) +{ + return sm9_fp4_conjugate(r, a); +} + +void sm9_fp4_frobenius3(sm9_fp4_t r, const sm9_fp4_t a) +{ + sm9_fp2_conjugate(r[0], a[0]); + sm9_fp2_conjugate(r[1], a[1]); + sm9_fp2_mul(r[1], r[1], SM9_BETA); + sm9_fp2_neg(r[1], r[1]); +} + +void sm9_fp12_frobenius(sm9_fp12_t r, const sm9_fp12_t x) +{ + const sm9_fp2_t *xa = x[0]; + const sm9_fp2_t *xb = x[1]; + const sm9_fp2_t *xc = x[2]; + sm9_fp4_t ra; + sm9_fp4_t rb; + sm9_fp4_t rc; + + sm9_fp2_conjugate(ra[0], xa[0]); + sm9_fp2_conjugate(ra[1], xa[1]); + sm9_fp2_mul_fp(ra[1], ra[1], SM9_ALPHA3); + + sm9_fp2_conjugate(rb[0], xb[0]); + sm9_fp2_mul_fp(rb[0], rb[0], SM9_ALPHA1); + sm9_fp2_conjugate(rb[1], xb[1]); + sm9_fp2_mul_fp(rb[1], rb[1], SM9_ALPHA4); + + sm9_fp2_conjugate(rc[0], xc[0]); + sm9_fp2_mul_fp(rc[0], rc[0], SM9_ALPHA2); + sm9_fp2_conjugate(rc[1], xc[1]); + sm9_fp2_mul_fp(rc[1], rc[1], SM9_ALPHA5); + + sm9_fp12_set(r, ra, rb, rc); +} + +void sm9_fp12_frobenius2(sm9_fp12_t r, const sm9_fp12_t x) +{ + sm9_fp4_t a; + sm9_fp4_t b; + sm9_fp4_t c; + + sm9_fp4_conjugate(a, x[0]); + sm9_fp4_conjugate(b, x[1]); + sm9_fp4_mul_fp(b, b, SM9_ALPHA2); + sm9_fp4_conjugate(c, x[2]); + sm9_fp4_mul_fp(c, c, SM9_ALPHA4); + + sm9_fp4_copy(r[0], a); + sm9_fp4_copy(r[1], b); + sm9_fp4_copy(r[2], c); +} + +void sm9_fp12_frobenius3(sm9_fp12_t r, const sm9_fp12_t x) +{ + const sm9_fp2_t *xa = x[0]; + const sm9_fp2_t *xb = x[1]; + const sm9_fp2_t *xc = x[2]; + sm9_fp4_t ra; + sm9_fp4_t rb; + sm9_fp4_t rc; + + sm9_fp2_conjugate(ra[0], xa[0]); + sm9_fp2_conjugate(ra[1], xa[1]); + sm9_fp2_mul(ra[1], ra[1], SM9_BETA); + sm9_fp2_neg(ra[1], ra[1]); + + sm9_fp2_conjugate(rb[0], xb[0]); + sm9_fp2_mul(rb[0], rb[0], SM9_BETA); + sm9_fp2_conjugate(rb[1], xb[1]); + + sm9_fp2_conjugate(rc[0], xc[0]); + sm9_fp2_neg(rc[0], rc[0]); + sm9_fp2_conjugate(rc[1], xc[1]); + sm9_fp2_mul(rc[1], rc[1], SM9_BETA); + + sm9_fp4_copy(r[0], ra); + sm9_fp4_copy(r[1], rb); + sm9_fp4_copy(r[2], rc); +} + +void sm9_fp12_frobenius6(sm9_fp12_t r, const sm9_fp12_t x) +{ + sm9_fp4_t a; + sm9_fp4_t b; + sm9_fp4_t c; + + sm9_fp4_copy(a, x[0]); + sm9_fp4_copy(b, x[1]); + sm9_fp4_copy(c, x[2]); + + sm9_fp4_conjugate(a, a); + sm9_fp4_conjugate(b, b); + sm9_fp4_neg(b, b); + sm9_fp4_conjugate(c, c); + + sm9_fp4_copy(r[0], a); + sm9_fp4_copy(r[1], b); + sm9_fp4_copy(r[2], c); +} + + +void sm9_point_init(sm9_point_t *R) +{ + sm9_fp_set_zero(R->X); + sm9_fp_set_zero(R->Y); + sm9_fp_set_one(R->Z); +} + +void sm9_point_from_hex(sm9_point_t *R, const char hex[65 * 2]) +{ + sm9_bn_from_hex(R->X, hex); + sm9_bn_from_hex(R->Y, hex + 65); + sm9_bn_set_one(R->Z); +} + +int sm9_point_is_at_infinity(const sm9_point_t *P) { + return sm9_fp_is_zero(P->X); +} + +void sm9_point_set_infinity(sm9_point_t *R) { + sm9_fp_set_one(R->X); + sm9_fp_set_one(R->Y); + sm9_fp_set_zero(R->Z); +} + +void sm9_point_get_xy(const sm9_point_t *P, sm9_fp_t x, sm9_fp_t y) +{ + sm9_fp_t z_inv; + + assert(!sm9_fp_is_zero(P->Z)); + + if (sm9_fp_is_one(P->Z)) { + sm9_fp_copy(x, P->X); + sm9_fp_copy(y, P->Y); + } + + sm9_fp_inv(z_inv, P->Z); + if (y) + sm9_fp_mul(y, P->Y, z_inv); + sm9_fp_sqr(z_inv, z_inv); + sm9_fp_mul(x, P->X, z_inv); + if (y) + sm9_fp_mul(y, y, z_inv); +} + +int sm9_point_equ(const sm9_point_t *P, const sm9_point_t *Q) +{ + sm9_fp_t t1, t2, t3, t4; + sm9_fp_sqr(t1, P->Z); + sm9_fp_sqr(t2, Q->Z); + sm9_fp_mul(t3, P->X, t2); + sm9_fp_mul(t4, Q->X, t1); + if (!sm9_fp_equ(t3, t4)) { + return 0; + } + sm9_fp_mul(t1, t1, P->Z); + sm9_fp_mul(t2, t2, Q->Z); + sm9_fp_mul(t3, P->Y, t2); + sm9_fp_mul(t4, Q->Y, t1); + return sm9_fp_equ(t3, t4); +} + +int sm9_point_is_on_curve(const sm9_point_t *P) +{ + sm9_fp_t t0, t1, t2; + if (sm9_fp_is_one(P->Z)) { + sm9_fp_sqr(t0, P->Y); + sm9_fp_sqr(t1, P->X); + sm9_fp_mul(t1, t1, P->X); + sm9_fp_add(t1, t1, SM9_FIVE); + } else { + sm9_fp_sqr(t0, P->X); + sm9_fp_mul(t0, t0, P->X); + sm9_fp_sqr(t1, P->Z); + sm9_fp_sqr(t2, t1); + sm9_fp_mul(t1, t1, t2); + sm9_fp_mul(t1, t1, SM9_FIVE); + sm9_fp_add(t1, t0, t1); + sm9_fp_sqr(t0, P->Y); + } + return sm9_fp_equ(t0, t1); +} + +void sm9_point_dbl(sm9_point_t *R, const sm9_point_t *P) +{ + const uint64_t *X1 = P->X; + const uint64_t *Y1 = P->Y; + const uint64_t *Z1 = P->Z; + sm9_fp_t X3, Y3, Z3, T1, T2, T3; + + if (sm9_point_is_at_infinity(P)) { + sm9_point_copy(R, P); + return; + } + + sm9_fp_sqr(T2, X1); + sm9_fp_tri(T2, T2); + sm9_fp_dbl(Y3, Y1); + sm9_fp_mul(Z3, Y3, Z1); + sm9_fp_sqr(Y3, Y3); + sm9_fp_mul(T3, Y3, X1); + sm9_fp_sqr(Y3, Y3); + sm9_fp_div2(Y3, Y3); + sm9_fp_sqr(X3, T2); + sm9_fp_dbl(T1, T3); + sm9_fp_sub(X3, X3, T1); + sm9_fp_sub(T1, T3, X3); + sm9_fp_mul(T1, T1, T2); + sm9_fp_sub(Y3, T1, Y3); + + sm9_fp_copy(R->X, X3); + sm9_fp_copy(R->Y, Y3); + sm9_fp_copy(R->Z, Z3); +} + +void sm9_point_add(sm9_point_t *R, const sm9_point_t *P, const sm9_point_t *Q) +{ + const uint64_t *X1 = P->X; + const uint64_t *Y1 = P->Y; + const uint64_t *Z1 = P->Z; + const uint64_t *x2 = Q->X; + const uint64_t *y2 = Q->Y; + sm9_fp_t X3, Y3, Z3, T1, T2, T3, T4; + + if (sm9_point_is_at_infinity(Q)) { + sm9_point_copy(R, P); + return; + } + if (sm9_point_is_at_infinity(P)) { + sm9_point_copy(R, Q); + return; + } + + sm9_fp_sqr(T1, Z1); + sm9_fp_mul(T2, T1, Z1); + sm9_fp_mul(T1, T1, x2); + sm9_fp_mul(T2, T2, y2); + sm9_fp_sub(T1, T1, X1); + sm9_fp_sub(T2, T2, Y1); + + if (sm9_fp_is_zero(T1)) { + if (sm9_fp_is_zero(T2)) { + sm9_point_dbl(R, Q); + return; + } else { + sm9_point_set_infinity(R); + return; + } + } + + sm9_fp_mul(Z3, Z1, T1); + sm9_fp_sqr(T3, T1); + sm9_fp_mul(T4, T3, T1); + sm9_fp_mul(T3, T3, X1); + sm9_fp_dbl(T1, T3); + sm9_fp_sqr(X3, T2); + sm9_fp_sub(X3, X3, T1); + sm9_fp_sub(X3, X3, T4); + sm9_fp_sub(T3, T3, X3); + sm9_fp_mul(T3, T3, T2); + sm9_fp_mul(T4, T4, Y1); + sm9_fp_sub(Y3, T3, T4); + + sm9_fp_copy(R->X, X3); + sm9_fp_copy(R->Y, Y3); + sm9_fp_copy(R->Z, Z3); +} + +void sm9_point_neg(sm9_point_t *R, const sm9_point_t *P) +{ + sm9_fp_copy(R->X, P->X); + sm9_fp_neg(R->Y, P->Y); + sm9_fp_copy(R->Z, P->Z); +} + +void sm9_point_sub(sm9_point_t *R, const sm9_point_t *P, const sm9_point_t *Q) +{ + sm9_point_t _T, *T = &_T; + sm9_point_neg(T, Q); + sm9_point_add(R, P, T); +} + +void sm9_point_mul(sm9_point_t *R, const sm9_bn_t k, const sm9_point_t *P) +{ + char kbits[257]; + sm9_point_t _Q, *Q = &_Q; + int i; + + sm9_bn_to_bits(k, kbits); + for (i = 0; i < 256; i++) { + sm9_point_dbl(Q, Q); + if (kbits[i] == '1') { + sm9_point_add(Q, Q, P); + } + } + sm9_point_copy(R, Q); +} + +void sm9_point_mul_generator(sm9_point_t *R, const sm9_bn_t k) +{ + sm9_point_mul(R, k, SM9_P1); +} + + +void sm9_twist_point_from_hex(sm9_twist_point_t *R, const char hex[65 * 4]) +{ + sm9_fp2_from_hex(R->X, hex); + sm9_fp2_from_hex(R->Y, hex + 65 * 2); + sm9_fp2_set_one(R->Z); +} + +int sm9_twist_point_is_at_infinity(const sm9_twist_point_t *P) +{ + return sm9_fp2_is_zero(P->Z); +} + +void sm9_twist_point_set_infinity(sm9_twist_point_t *R) +{ + sm9_fp2_set_one(R->X); + sm9_fp2_set_one(R->Y); + sm9_fp2_set_zero(R->Z); +} + +void sm9_twist_point_get_xy(const sm9_twist_point_t *P, sm9_fp2_t x, sm9_fp2_t y) +{ + sm9_fp2_t z_inv; + + assert(!sm9_fp2_is_zero(P->Z)); + + if (sm9_fp2_is_one(P->Z)) { + sm9_fp2_copy(x, P->X); + sm9_fp2_copy(y, P->Y); + } + + sm9_fp2_inv(z_inv, P->Z); + if (y) + sm9_fp2_mul(y, P->Y, z_inv); + sm9_fp2_sqr(z_inv, z_inv); + sm9_fp2_mul(x, P->X, z_inv); + if (y) + sm9_fp2_mul(y, y, z_inv); +} + + +int sm9_twist_point_equ(const sm9_twist_point_t *P, const sm9_twist_point_t *Q) +{ + sm9_fp2_t t1, t2, t3, t4; + + sm9_fp2_sqr(t1, P->Z); + sm9_fp2_sqr(t2, Q->Z); + sm9_fp2_mul(t3, P->X, t2); + sm9_fp2_mul(t4, Q->X, t1); + if (!sm9_fp2_equ(t3, t4)) { + return 0; + } + sm9_fp2_mul(t1, t1, P->Z); + sm9_fp2_mul(t2, t2, Q->Z); + sm9_fp2_mul(t3, P->Y, t2); + sm9_fp2_mul(t4, Q->Y, t1); + return sm9_fp2_equ(t3, t4); +} + +int sm9_twist_point_is_on_curve(const sm9_twist_point_t *P) +{ + sm9_fp2_t t0, t1, t2; + + if (sm9_fp2_is_one(P->Z)) { + sm9_fp2_sqr(t0, P->Y); + sm9_fp2_sqr(t1, P->X); + sm9_fp2_mul(t1, t1, P->X); + sm9_fp2_add(t1, t1, SM9_FP2_5U); + + } else { + sm9_fp2_sqr(t0, P->X); + sm9_fp2_mul(t0, t0, P->X); + sm9_fp2_sqr(t1, P->Z); + sm9_fp2_sqr(t2, t1); + sm9_fp2_mul(t1, t1, t2); + sm9_fp2_mul(t1, t1, SM9_FP2_5U); + sm9_fp2_add(t1, t0, t1); + sm9_fp2_sqr(t0, P->Y); + } + + return sm9_fp2_equ(t0, t1); +} + +void sm9_twist_point_neg(sm9_twist_point_t *R, const sm9_twist_point_t *P) +{ + sm9_fp2_copy(R->X, P->X); + sm9_fp2_neg(R->Y, P->Y); + sm9_fp2_copy(R->Z, P->Z); +} + +void sm9_twist_point_dbl(sm9_twist_point_t *R, const sm9_twist_point_t *P) +{ + const sm9_fp_t *X1 = P->X; + const sm9_fp_t *Y1 = P->Y; + const sm9_fp_t *Z1 = P->Z; + sm9_fp2_t X3, Y3, Z3, T1, T2, T3; + + if (sm9_twist_point_is_at_infinity(P)) { + sm9_twist_point_copy(R, P); + return; + } + sm9_fp2_sqr(T2, X1); + sm9_fp2_tri(T2, T2); + sm9_fp2_dbl(Y3, Y1); + sm9_fp2_mul(Z3, Y3, Z1); + sm9_fp2_sqr(Y3, Y3); + sm9_fp2_mul(T3, Y3, X1); + sm9_fp2_sqr(Y3, Y3); + sm9_fp2_div2(Y3, Y3); + sm9_fp2_sqr(X3, T2); + sm9_fp2_dbl(T1, T3); + sm9_fp2_sub(X3, X3, T1); + sm9_fp2_sub(T1, T3, X3); + sm9_fp2_mul(T1, T1, T2); + sm9_fp2_sub(Y3, T1, Y3); + + sm9_fp2_copy(R->X, X3); + sm9_fp2_copy(R->Y, Y3); + sm9_fp2_copy(R->Z, Z3); +} + +void sm9_twist_point_add(sm9_twist_point_t *R, const sm9_twist_point_t *P, const sm9_twist_point_t *Q) +{ + const sm9_fp_t *X1 = P->X; + const sm9_fp_t *Y1 = P->Y; + const sm9_fp_t *Z1 = P->Z; + const sm9_fp_t *x2 = Q->X; + const sm9_fp_t *y2 = Q->Y; + sm9_fp2_t X3, Y3, Z3, T1, T2, T3, T4; + + if (sm9_twist_point_is_at_infinity(Q)) { + sm9_twist_point_copy(R, P); + return; + } + if (sm9_twist_point_is_at_infinity(P)) { + sm9_twist_point_copy(R, Q); + return; + } + + sm9_fp2_sqr(T1, Z1); + sm9_fp2_mul(T2, T1, Z1); + sm9_fp2_mul(T1, T1, x2); + sm9_fp2_mul(T2, T2, y2); + sm9_fp2_sub(T1, T1, X1); + sm9_fp2_sub(T2, T2, Y1); + if (sm9_fp2_is_zero(T1)) { + if (sm9_fp2_is_zero(T2)) { + sm9_twist_point_dbl(R, Q); + return; + } else { + sm9_twist_point_set_infinity(R); + return; + } + } + sm9_fp2_mul(Z3, Z1, T1); + sm9_fp2_sqr(T3, T1); + sm9_fp2_mul(T4, T3, T1); + sm9_fp2_mul(T3, T3, X1); + sm9_fp2_dbl(T1, T3); + sm9_fp2_sqr(X3, T2); + sm9_fp2_sub(X3, X3, T1); + sm9_fp2_sub(X3, X3, T4); + sm9_fp2_sub(T3, T3, X3); + sm9_fp2_mul(T3, T3, T2); + sm9_fp2_mul(T4, T4, Y1); + sm9_fp2_sub(Y3, T3, T4); + + sm9_fp2_copy(R->X, X3); + sm9_fp2_copy(R->Y, Y3); + sm9_fp2_copy(R->Z, Z3); +} + +void sm9_twist_point_sub(sm9_twist_point_t *R, const sm9_twist_point_t *P, const sm9_twist_point_t *Q) +{ + sm9_twist_point_t _T, *T = &_T; + sm9_twist_point_neg(T, Q); + sm9_twist_point_add(R, P, T); +} + +void sm9_twist_point_add_full(sm9_twist_point_t *R, const sm9_twist_point_t *P, const sm9_twist_point_t *Q) +{ + const sm9_fp_t *X1 = P->X; + const sm9_fp_t *Y1 = P->Y; + const sm9_fp_t *Z1 = P->Z; + const sm9_fp_t *X2 = Q->X; + const sm9_fp_t *Y2 = Q->Y; + const sm9_fp_t *Z2 = Q->Z; + sm9_fp2_t T1, T2, T3, T4, T5, T6, T7, T8; + + if (sm9_twist_point_is_at_infinity(Q)) { + sm9_twist_point_copy(R, P); + return; + } + if (sm9_twist_point_is_at_infinity(P)) { + sm9_twist_point_copy(R, Q); + return; + } + + sm9_fp2_sqr(T1, Z1); + sm9_fp2_sqr(T2, Z2); + sm9_fp2_mul(T3, X2, T1); + sm9_fp2_mul(T4, X1, T2); + sm9_fp2_add(T5, T3, T4); + sm9_fp2_sub(T3, T3, T4); + sm9_fp2_mul(T1, T1, Z1); + sm9_fp2_mul(T1, T1, Y2); + sm9_fp2_mul(T2, T2, Z2); + sm9_fp2_mul(T2, T2, Y1); + sm9_fp2_add(T6, T1, T2); + sm9_fp2_sub(T1, T1, T2); + + if (sm9_fp2_is_zero(T1) && sm9_fp2_is_zero(T3)) { + return sm9_twist_point_dbl(R, P); + } + if (sm9_fp2_is_zero(T1) && sm9_fp2_is_zero(T6)) { + return sm9_twist_point_set_infinity(R); + } + + sm9_fp2_sqr(T6, T1); + sm9_fp2_mul(T7, T3, Z1); + sm9_fp2_mul(T7, T7, Z2); + sm9_fp2_sqr(T8, T3); + sm9_fp2_mul(T5, T5, T8); + sm9_fp2_mul(T3, T3, T8); + sm9_fp2_mul(T4, T4, T8); + sm9_fp2_sub(T6, T6, T5); + sm9_fp2_sub(T4, T4, T6); + sm9_fp2_mul(T1, T1, T4); + sm9_fp2_mul(T2, T2, T3); + sm9_fp2_sub(T1, T1, T2); + + sm9_fp2_copy(R->X, T6); + sm9_fp2_copy(R->Y, T1); + sm9_fp2_copy(R->Z, T7); +} + +void sm9_twist_point_mul(sm9_twist_point_t *R, const sm9_bn_t k, const sm9_twist_point_t *P) +{ + sm9_twist_point_t _Q, *Q = &_Q; + char kbits[256]; + int i; + + sm9_bn_to_bits(k, kbits); + for (i = 0; i < 256; i++) { + sm9_twist_point_dbl(Q, Q); + if (kbits[i] == '1') { + sm9_twist_point_add(Q, Q, P); + } + } + sm9_twist_point_copy(R, Q); +} + +void sm9_twist_point_mul_G(sm9_twist_point_t *R, const sm9_bn_t k) +{ + sm9_twist_point_mul(R, k, SM9_P2); +} + +void sm9_eval_g_tangent(sm9_fp12_t num, sm9_fp12_t den, const sm9_twist_point_t *P, const sm9_point_t *Q) +{ + const sm9_fp_t *XP = P->X; + const sm9_fp_t *YP = P->Y; + const sm9_fp_t *ZP = P->Z; + const uint64_t *xQ = Q->X; + const uint64_t *yQ = Q->Y; + + sm9_fp_t *a0 = num[0][0]; + sm9_fp_t *a1 = num[0][1]; + sm9_fp_t *a4 = num[2][0]; + sm9_fp_t *b1 = den[0][1]; + + sm9_fp2_t t0; + sm9_fp2_t t1; + sm9_fp2_t t2; + + + sm9_fp12_set_zero(num); + sm9_fp12_set_zero(den); + + sm9_fp2_sqr(t0, ZP); + sm9_fp2_mul(t1, t0, ZP); + sm9_fp2_mul(b1, t1, YP); + + sm9_fp2_mul_fp(t2, b1, yQ); + sm9_fp2_neg(a1, t2); + + sm9_fp2_sqr(t1, XP); + sm9_fp2_mul(t0, t0, t1); + sm9_fp2_mul_fp(t0, t0, xQ); + sm9_fp2_tri(t0, t0); + sm9_fp2_div2(a4, t0); + + sm9_fp2_mul(t1, t1, XP); + sm9_fp2_tri(t1, t1); + sm9_fp2_div2(t1, t1); + sm9_fp2_sqr(t0, YP); + sm9_fp2_sub(a0, t0, t1); +} + +void sm9_eval_g_line(sm9_fp12_t num, sm9_fp12_t den, const sm9_twist_point_t *T, const sm9_twist_point_t *P, const sm9_point_t *Q) +{ + const sm9_fp_t *XT = T->X; + const sm9_fp_t *YT = T->Y; + const sm9_fp_t *ZT = T->Z; + const sm9_fp_t *XP = P->X; + const sm9_fp_t *YP = P->Y; + const sm9_fp_t *ZP = P->Z; + const uint64_t *xQ = Q->X; + const uint64_t *yQ = Q->Y; + + sm9_fp_t *a0 = num[0][0]; + sm9_fp_t *a1 = num[0][1]; + sm9_fp_t *a4 = num[2][0]; + sm9_fp_t *b1 = den[0][1]; + + sm9_fp2_t T0, T1, T2, T3, T4; + + + sm9_fp12_set_zero(num); + sm9_fp12_set_zero(den); + + sm9_fp2_sqr(T0, ZP); + sm9_fp2_mul(T1, T0, XT); + sm9_fp2_mul(T0, T0, ZP); + sm9_fp2_sqr(T2, ZT); + sm9_fp2_mul(T3, T2, XP); + sm9_fp2_mul(T2, T2, ZT); + sm9_fp2_mul(T2, T2, YP); + sm9_fp2_sub(T1, T1, T3); + sm9_fp2_mul(T1, T1, ZT); + sm9_fp2_mul(T1, T1, ZP); + sm9_fp2_mul(T4, T1, T0); + sm9_fp2_copy(b1, T4); + sm9_fp2_mul(T1, T1, YP); + sm9_fp2_mul(T3, T0, YT); + sm9_fp2_sub(T3, T3, T2); + sm9_fp2_mul(T0, T0, T3); + sm9_fp2_mul_fp(T0, T0, xQ); + sm9_fp2_copy(a4, T0); + sm9_fp2_mul(T3, T3, XP); + sm9_fp2_mul(T3, T3, ZP); + sm9_fp2_sub(T1, T1, T3); + sm9_fp2_copy(a0, T1); + sm9_fp2_mul_fp(T2, T4, yQ); + sm9_fp2_neg(T2, T2); + sm9_fp2_copy(a1, T2); +} + +void sm9_twist_point_pi1(sm9_twist_point_t *R, const sm9_twist_point_t *P) +{ + //const c = 0x3f23ea58e5720bdb843c6cfa9c08674947c5c86e0ddd04eda91d8354377b698bn; + const sm9_fp_t c = { + 0x377b698b, 0xa91d8354, 0x0ddd04ed, 0x47c5c86e, + 0x9c086749, 0x843c6cfa, 0xe5720bdb, 0x3f23ea58, + }; + sm9_fp2_conjugate(R->X, P->X); + sm9_fp2_conjugate(R->Y, P->Y); + sm9_fp2_conjugate(R->Z, P->Z); + sm9_fp2_mul_fp(R->Z, R->Z, c); + +} + +void sm9_twist_point_pi2(sm9_twist_point_t *R, const sm9_twist_point_t *P) +{ + //c = 0xf300000002a3a6f2780272354f8b78f4d5fc11967be65334 + const sm9_fp_t c = { + 0x7be65334, 0xd5fc1196, 0x4f8b78f4, 0x78027235, + 0x02a3a6f2, 0xf3000000, 0, 0, + }; + sm9_fp2_copy(R->X, P->X); + sm9_fp2_copy(R->Y, P->Y); + sm9_fp2_mul_fp(R->Z, P->Z, c); +} + +void sm9_twist_point_neg_pi2(sm9_twist_point_t *R, const sm9_twist_point_t *P) +{ + // c = 0xf300000002a3a6f2780272354f8b78f4d5fc11967be65334 + const sm9_fp_t c = { + 0x7be65334, 0xd5fc1196, 0x4f8b78f4, 0x78027235, + 0x02a3a6f2, 0xf3000000, 0, 0, + }; + sm9_fp2_copy(R->X, P->X); + sm9_fp2_neg(R->Y, P->Y); + sm9_fp2_mul_fp(R->Z, P->Z, c); +} + + +void sm9_final_exponent_hard_part(sm9_fp12_t r, const sm9_fp12_t f) +{ + // a2 = 0xd8000000019062ed0000b98b0cb27659 + // a3 = 0x2400000000215d941 + const sm9_bn_t a2 = {0xcb27659, 0x0000b98b, 0x019062ed, 0xd8000000, 0, 0, 0, 0}; + const sm9_bn_t a3 = {0x215d941, 0x40000000, 0x2, 0, 0, 0, 0, 0}; + const sm9_bn_t nine = {9,0,0,0,0,0,0,0}; + sm9_fp12_t t0, t1, t2, t3; + + sm9_fp12_pow(t0, f, a3); + sm9_fp12_inv(t0, t0); + sm9_fp12_frobenius(t1, t0); + sm9_fp12_mul(t1, t0, t1); + + sm9_fp12_mul(t0, t0, t1); + sm9_fp12_frobenius(t2, f); + sm9_fp12_mul(t3, t2, f); + sm9_fp12_pow(t3, t3, nine); + + sm9_fp12_mul(t0, t0, t3); + sm9_fp12_sqr(t3, f); + sm9_fp12_sqr(t3, t3); + sm9_fp12_mul(t0, t0, t3); + sm9_fp12_sqr(t2, t2); + sm9_fp12_mul(t2, t2, t1); + sm9_fp12_frobenius2(t1, f); + sm9_fp12_mul(t1, t1, t2); + + sm9_fp12_pow(t2, t1, a2); + sm9_fp12_mul(t0, t2, t0); + sm9_fp12_frobenius3(t1, f); + sm9_fp12_mul(t1, t1, t0); + + sm9_fp12_copy(r, t1); +} + +void sm9_final_exponent(sm9_fp12_t r, const sm9_fp12_t f) +{ + sm9_fp12_t t0; + sm9_fp12_t t1; + + sm9_fp12_frobenius6(t0, f); + sm9_fp12_inv(t1, f); + sm9_fp12_mul(t0, t0, t1); + sm9_fp12_frobenius2(t1, t0); + sm9_fp12_mul(t0, t0, t1); + sm9_final_exponent_hard_part(t0, t0); + + sm9_fp12_copy(r, t0); +} + +void sm9_pairing(sm9_fp12_t r, const sm9_twist_point_t *Q, const sm9_point_t *P) { + const char *abits = "00100000000000000000000000000000000000010000101011101100100111110"; + + sm9_twist_point_t _T, *T = &_T; + sm9_twist_point_t _Q1, *Q1 = &_Q1; + sm9_twist_point_t _Q2, *Q2 = &_Q2; + + sm9_fp12_t f_num; + sm9_fp12_t f_den; + sm9_fp12_t g_num; + sm9_fp12_t g_den; + int i; + + sm9_twist_point_copy(T, Q); + + sm9_fp12_set_one(f_num); + sm9_fp12_set_one(f_den); + + for (i = 0; i < strlen(abits); i++) { + + sm9_fp12_sqr(f_num, f_num); + sm9_fp12_sqr(f_den, f_den); + sm9_eval_g_tangent(g_num, g_den, T, P); + sm9_fp12_mul(f_num, f_num, g_num); + sm9_fp12_mul(f_den, f_den, g_den); + + sm9_twist_point_dbl(T, T); + + if (abits[i] == '1') { + sm9_eval_g_line(g_num, g_den, T, Q, P); + sm9_fp12_mul(f_num, f_num, g_num); + sm9_fp12_mul(f_den, f_den, g_den); + sm9_twist_point_add(T, T, Q); + } + } + + sm9_twist_point_pi1(Q1, Q); + sm9_twist_point_neg_pi2(Q2, Q); + + sm9_eval_g_line(g_num, g_den, T, Q1, P); + sm9_fp12_mul(f_num, f_num, g_num); + sm9_fp12_mul(f_den, f_den, g_den); + sm9_twist_point_add_full(T, T, Q1); + + sm9_eval_g_line(g_num, g_den, T, Q2, P); + sm9_fp12_mul(f_num, f_num, g_num); + sm9_fp12_mul(f_den, f_den, g_den); + sm9_twist_point_add_full(T, T, Q2); + + sm9_fp12_inv(f_den, f_den); + sm9_fp12_mul(r, f_num, f_den); + + sm9_final_exponent(r, r); +} + +void sm9_pairing_test() +{ + sm9_fp12_t r; + sm9_fp12_init(r); + + const char *sm9_g_hex[] = { + "aab9f06a4eeba4323a7833db202e4e35639d93fa3305af73f0f071d7d284fcfb\n", + "84b87422330d7936eaba1109fa5a7a7181ee16f2438b0aeb2f38fd5f7554e57a\n", + "4c744e69c4a2e1c8ed72f796d151a17ce2325b943260fc460b9f73cb57c9014b\n", + "b3129a75d31d17194675a1bc56947920898fbf390a5bf5d931ce6cbb3340f66d\n", + "93634f44fa13af76169f3cc8fbea880adaff8475d5fd28a75deb83c44362b439\n", + "1604a3fcfa9783e667ce9fcb1062c2a5c6685c316dda62de0548baa6ba30038b\n", + "5a1ae172102efd95df7338dbc577c66d8d6c15e0a0158c7507228efb078f42a6\n", + "67e0e0c2eed7a6993dce28fe9aa2ef56834307860839677f96685f2b44d0911f\n", + "a01f2c8bee81769609462c69c96aa923fd863e209d3ce26dd889b55e2e3873db\n", + "38bffe40a22d529a0c66124b2c308dac9229912656f62b4facfced408e02380f\n", + "28b3404a61908f5d6198815c99af1990c8af38655930058c28c21bb539ce0000\n", + "4e378fb5561cd0668f906b731ac58fee25738edf09cadc7a29c0abc0177aea6d\n", + }; + + sm9_pairing(r, SM9_Ppubs, SM9_P1); + //printf("test pairing: %d\n", sm9_fp12_equ(&r, sm9_fp12_from_hex(g))); +} +