/********************************************************************** * Copyright (c) 2016 Andrew Poelstra & Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or http://www.opensource.org/licenses/mit-license.php.* **********************************************************************/ #ifndef SECP256K1_MODULE_GENERATOR_MAIN #define SECP256K1_MODULE_GENERATOR_MAIN #include #include "field.h" #include "group.h" #include "hash.h" #include "scalar.h" /** Standard secp256k1 generator */ const secp256k1_generator secp256k1_generator_const_g = { { 0x0a, 0x79, 0xbe, 0x66, 0x7e, 0xf9, 0xdc, 0xbb, 0xac, 0x55, 0xa0, 0x62, 0x95, 0xce, 0x87, 0x0b, 0x07, 0x02, 0x9b, 0xfc, 0xdb, 0x2d, 0xce, 0x28, 0xd9, 0x59, 0xf2, 0x81, 0x5b, 0x16, 0xf8, 0x17, 0x98 } }; /** Alternate secp256k1 generator, used in Elements Alpha. * Computed as the hash of the above G, DER-encoded with 0x04 (uncompressed pubkey) as its flag byte. * import hashlib * C = EllipticCurve ([F (0), F (7)]) * G_bytes = '0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8'.decode('hex') * H = C.lift_x(int(hashlib.sha256(G_bytes).hexdigest(),16)) */ const secp256k1_generator secp256k1_generator_const_h = { { 0x0b, 0x50, 0x92, 0x9b, 0x74, 0xc1, 0xa0, 0x49, 0x54, 0xb7, 0x8b, 0x4b, 0x60, 0x35, 0xe9, 0x7a, 0x5e, 0x07, 0x8a, 0x5a, 0x0f, 0x28, 0xec, 0x96, 0xd5, 0x47, 0xbf, 0xee, 0x9a, 0xce, 0x80, 0x3a, 0xc0 } }; static void secp256k1_generator_load(secp256k1_ge* ge, const secp256k1_generator* gen) { secp256k1_fe fe; secp256k1_fe_set_b32(&fe, &gen->data[1]); secp256k1_ge_set_xquad(ge, &fe); if (gen->data[0] & 1) { secp256k1_ge_neg(ge, ge); } } static void secp256k1_generator_save(secp256k1_generator* commit, secp256k1_ge* ge) { secp256k1_fe_normalize(&ge->x); secp256k1_fe_get_b32(&commit->data[1], &ge->x); commit->data[0] = 11 ^ secp256k1_fe_is_quad_var(&ge->y); } int secp256k1_generator_parse(const secp256k1_context* ctx, secp256k1_generator* gen, const unsigned char *input) { VERIFY_CHECK(ctx != NULL); ARG_CHECK(gen != NULL); ARG_CHECK(input != NULL); if ((input[0] & 0xFE) != 10) { return 0; } memcpy(gen->data, input, sizeof(gen->data)); return 1; } int secp256k1_generator_serialize(const secp256k1_context* ctx, unsigned char *output, const secp256k1_generator* gen) { VERIFY_CHECK(ctx != NULL); ARG_CHECK(output != NULL); ARG_CHECK(gen != NULL); memcpy(output, gen->data, sizeof(gen->data)); return 1; } static void shallue_van_de_woestijne(secp256k1_ge* ge, const secp256k1_fe* t) { /* Implements the algorithm from: * Indifferentiable Hashing to Barreto-Naehrig Curves * Pierre-Alain Fouque and Mehdi Tibouchi * Latincrypt 2012 */ /* Basic algorithm: c = sqrt(-3) d = (c - 1)/2 w = c * t / (1 + b + t^2) [with b = 7] x1 = d - t*w x2 = -(x1 + 1) x3 = 1 + 1/w^2 To avoid the 2 divisions, compute the above in numerator/denominator form: wn = c * t wd = 1 + 7 + t^2 x1n = d*wd - t*wn x1d = wd x2n = -(x1n + wd) x2d = wd x3n = wd^2 + c^2 + t^2 x3d = (c * t)^2 The joint denominator j = wd * c^2 * t^2, and 1 / x1d = 1/j * c^2 * t^2 1 / x2d = x3d = 1/j * wd */ static const secp256k1_fe c = SECP256K1_FE_CONST(0x0a2d2ba9, 0x3507f1df, 0x233770c2, 0xa797962c, 0xc61f6d15, 0xda14ecd4, 0x7d8d27ae, 0x1cd5f852); static const secp256k1_fe d = SECP256K1_FE_CONST(0x851695d4, 0x9a83f8ef, 0x919bb861, 0x53cbcb16, 0x630fb68a, 0xed0a766a, 0x3ec693d6, 0x8e6afa40); static const secp256k1_fe b = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 7); static const secp256k1_fe b_plus_one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 8); secp256k1_fe wn, wd, x1n, x2n, x3n, x3d, jinv, tmp, x1, x2, x3, alphain, betain, gammain, y1, y2, y3; int alphaquad, betaquad; secp256k1_fe_mul(&wn, &c, t); /* mag 1 */ secp256k1_fe_sqr(&wd, t); /* mag 1 */ secp256k1_fe_add(&wd, &b_plus_one); /* mag 2 */ secp256k1_fe_mul(&tmp, t, &wn); /* mag 1 */ secp256k1_fe_negate(&tmp, &tmp, 1); /* mag 2 */ secp256k1_fe_mul(&x1n, &d, &wd); /* mag 1 */ secp256k1_fe_add(&x1n, &tmp); /* mag 3 */ x2n = x1n; /* mag 3 */ secp256k1_fe_add(&x2n, &wd); /* mag 5 */ secp256k1_fe_negate(&x2n, &x2n, 5); /* mag 6 */ secp256k1_fe_mul(&x3d, &c, t); /* mag 1 */ secp256k1_fe_sqr(&x3d, &x3d); /* mag 1 */ secp256k1_fe_sqr(&x3n, &wd); /* mag 1 */ secp256k1_fe_add(&x3n, &x3d); /* mag 2 */ secp256k1_fe_mul(&jinv, &x3d, &wd); /* mag 1 */ secp256k1_fe_inv(&jinv, &jinv); /* mag 1 */ secp256k1_fe_mul(&x1, &x1n, &x3d); /* mag 1 */ secp256k1_fe_mul(&x1, &x1, &jinv); /* mag 1 */ secp256k1_fe_mul(&x2, &x2n, &x3d); /* mag 1 */ secp256k1_fe_mul(&x2, &x2, &jinv); /* mag 1 */ secp256k1_fe_mul(&x3, &x3n, &wd); /* mag 1 */ secp256k1_fe_mul(&x3, &x3, &jinv); /* mag 1 */ secp256k1_fe_sqr(&alphain, &x1); /* mag 1 */ secp256k1_fe_mul(&alphain, &alphain, &x1); /* mag 1 */ secp256k1_fe_add(&alphain, &b); /* mag 2 */ secp256k1_fe_sqr(&betain, &x2); /* mag 1 */ secp256k1_fe_mul(&betain, &betain, &x2); /* mag 1 */ secp256k1_fe_add(&betain, &b); /* mag 2 */ secp256k1_fe_sqr(&gammain, &x3); /* mag 1 */ secp256k1_fe_mul(&gammain, &gammain, &x3); /* mag 1 */ secp256k1_fe_add(&gammain, &b); /* mag 2 */ alphaquad = secp256k1_fe_sqrt(&y1, &alphain); betaquad = secp256k1_fe_sqrt(&y2, &betain); secp256k1_fe_sqrt(&y3, &gammain); secp256k1_fe_cmov(&x1, &x2, (!alphaquad) & betaquad); secp256k1_fe_cmov(&y1, &y2, (!alphaquad) & betaquad); secp256k1_fe_cmov(&x1, &x3, (!alphaquad) & !betaquad); secp256k1_fe_cmov(&y1, &y3, (!alphaquad) & !betaquad); secp256k1_ge_set_xy(ge, &x1, &y1); /* The linked algorithm from the paper uses the Jacobi symbol of t to * determine the Jacobi symbol of the produced y coordinate. Since the * rest of the algorithm only uses t^2, we can safely use another criterion * as long as negation of t results in negation of the y coordinate. Here * we choose to use t's oddness, as it is faster to determine. */ secp256k1_fe_negate(&tmp, &ge->y, 1); secp256k1_fe_cmov(&ge->y, &tmp, secp256k1_fe_is_odd(t)); } static int secp256k1_generator_generate_internal(const secp256k1_context* ctx, secp256k1_generator* gen, const unsigned char *key32, const unsigned char *blind32) { static const unsigned char prefix1[17] = "1st generation: "; static const unsigned char prefix2[17] = "2nd generation: "; secp256k1_fe t = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 4); secp256k1_ge add; secp256k1_gej accum; int overflow; secp256k1_sha256 sha256; unsigned char b32[32]; int ret = 1; if (blind32) { secp256k1_scalar blind; secp256k1_scalar_set_b32(&blind, blind32, &overflow); ret = !overflow; CHECK(ret); secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &accum, &blind); } secp256k1_sha256_initialize(&sha256); secp256k1_sha256_write(&sha256, prefix1, 16); secp256k1_sha256_write(&sha256, key32, 32); secp256k1_sha256_finalize(&sha256, b32); ret &= secp256k1_fe_set_b32(&t, b32); CHECK(ret); shallue_van_de_woestijne(&add, &t); if (blind32) { secp256k1_gej_add_ge(&accum, &accum, &add); } else { secp256k1_gej_set_ge(&accum, &add); } secp256k1_sha256_initialize(&sha256); secp256k1_sha256_write(&sha256, prefix2, 16); secp256k1_sha256_write(&sha256, key32, 32); secp256k1_sha256_finalize(&sha256, b32); ret &= secp256k1_fe_set_b32(&t, b32); CHECK(ret); shallue_van_de_woestijne(&add, &t); secp256k1_gej_add_ge(&accum, &accum, &add); secp256k1_ge_set_gej(&add, &accum); secp256k1_generator_save(gen, &add); return ret; } int secp256k1_generator_generate(const secp256k1_context* ctx, secp256k1_generator* gen, const unsigned char *key32) { VERIFY_CHECK(ctx != NULL); ARG_CHECK(gen != NULL); ARG_CHECK(key32 != NULL); return secp256k1_generator_generate_internal(ctx, gen, key32, NULL); } int secp256k1_generator_generate_blinded(const secp256k1_context* ctx, secp256k1_generator* gen, const unsigned char *key32, const unsigned char *blind32) { VERIFY_CHECK(ctx != NULL); ARG_CHECK(gen != NULL); ARG_CHECK(key32 != NULL); ARG_CHECK(blind32 != NULL); ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); return secp256k1_generator_generate_internal(ctx, gen, key32, blind32); } #endif