diff --git a/src/secp256k1/src/scalar_4x64_impl.h b/src/secp256k1/src/scalar_4x64_impl.h index a12c80626..b1b62ac1f 100644 --- a/src/secp256k1/src/scalar_4x64_impl.h +++ b/src/secp256k1/src/scalar_4x64_impl.h @@ -2001,6 +2001,6 @@ static void secp256k1_scalar_chacha20(secp256k1_scalar *r1, secp256k1_scalar *r2 #undef LE32 #endif /* SECP256K1_SCALAR_REPR_IMPL_H */ -xxx + #endif diff --git a/src/secp256k1/src/scalar_impl.h b/src/secp256k1/src/scalar_impl.h index dec541aed..d69a94880 100644 --- a/src/secp256k1/src/scalar_impl.h +++ b/src/secp256k1/src/scalar_impl.h @@ -1,3 +1,4 @@ +#ifndef ENABLE_MODULE_MUSIG /********************************************************************** * Copyright (c) 2014 Pieter Wuille * @@ -333,3 +334,340 @@ static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar #endif /* SECP256K1_SCALAR_IMPL_H */ + +#else +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_SCALAR_IMPL_H +#define SECP256K1_SCALAR_IMPL_H + +#include "group.h" +#include "scalar.h" + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#if defined(EXHAUSTIVE_TEST_ORDER) +#include "scalar_low_impl.h" +#elif defined(USE_SCALAR_4X64) +#include "scalar_4x64_impl.h" +#elif defined(USE_SCALAR_8X32) +#include "scalar_8x32_impl.h" +#else +#error "Please select scalar implementation" +#endif + +#ifndef USE_NUM_NONE +static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a) { + unsigned char c[32]; + secp256k1_scalar_get_b32(c, a); + secp256k1_num_set_bin(r, c, 32); +} + +/** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */ +static void secp256k1_scalar_order_get_num(secp256k1_num *r) { +#if defined(EXHAUSTIVE_TEST_ORDER) + static const unsigned char order[32] = { + 0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,EXHAUSTIVE_TEST_ORDER + }; +#else + static const unsigned char order[32] = { + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, + 0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B, + 0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41 + }; +#endif + secp256k1_num_set_bin(r, order, 32); +} +#endif + +static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) { +#if defined(EXHAUSTIVE_TEST_ORDER) + int i; + *r = 0; + for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) + if ((i * *x) % EXHAUSTIVE_TEST_ORDER == 1) + *r = i; + /* If this VERIFY_CHECK triggers we were given a noninvertible scalar (and thus + * have a composite group order; fix it in exhaustive_tests.c). */ + VERIFY_CHECK(*r != 0); +} +#else +secp256k1_scalar *t; +int i; +/* First compute xN as x ^ (2^N - 1) for some values of N, + * and uM as x ^ M for some values of M. */ +secp256k1_scalar x2, x3, x6, x8, x14, x28, x56, x112, x126; +secp256k1_scalar u2, u5, u9, u11, u13; + +secp256k1_scalar_sqr(&u2, x); +secp256k1_scalar_mul(&x2, &u2, x); +secp256k1_scalar_mul(&u5, &u2, &x2); +secp256k1_scalar_mul(&x3, &u5, &u2); +secp256k1_scalar_mul(&u9, &x3, &u2); +secp256k1_scalar_mul(&u11, &u9, &u2); +secp256k1_scalar_mul(&u13, &u11, &u2); + +secp256k1_scalar_sqr(&x6, &u13); +secp256k1_scalar_sqr(&x6, &x6); +secp256k1_scalar_mul(&x6, &x6, &u11); + +secp256k1_scalar_sqr(&x8, &x6); +secp256k1_scalar_sqr(&x8, &x8); +secp256k1_scalar_mul(&x8, &x8, &x2); + +secp256k1_scalar_sqr(&x14, &x8); +for (i = 0; i < 5; i++) { + secp256k1_scalar_sqr(&x14, &x14); +} +secp256k1_scalar_mul(&x14, &x14, &x6); + +secp256k1_scalar_sqr(&x28, &x14); +for (i = 0; i < 13; i++) { + secp256k1_scalar_sqr(&x28, &x28); +} +secp256k1_scalar_mul(&x28, &x28, &x14); + +secp256k1_scalar_sqr(&x56, &x28); +for (i = 0; i < 27; i++) { + secp256k1_scalar_sqr(&x56, &x56); +} +secp256k1_scalar_mul(&x56, &x56, &x28); + +secp256k1_scalar_sqr(&x112, &x56); +for (i = 0; i < 55; i++) { + secp256k1_scalar_sqr(&x112, &x112); +} +secp256k1_scalar_mul(&x112, &x112, &x56); + +secp256k1_scalar_sqr(&x126, &x112); +for (i = 0; i < 13; i++) { + secp256k1_scalar_sqr(&x126, &x126); +} +secp256k1_scalar_mul(&x126, &x126, &x14); + +/* Then accumulate the final result (t starts at x126). */ +t = &x126; +for (i = 0; i < 3; i++) { + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &u5); /* 101 */ +for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &x3); /* 111 */ +for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &u5); /* 101 */ +for (i = 0; i < 5; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &u11); /* 1011 */ +for (i = 0; i < 4; i++) { + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &u11); /* 1011 */ +for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &x3); /* 111 */ +for (i = 0; i < 5; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &x3); /* 111 */ +for (i = 0; i < 6; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &u13); /* 1101 */ +for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &u5); /* 101 */ +for (i = 0; i < 3; i++) { + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &x3); /* 111 */ +for (i = 0; i < 5; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &u9); /* 1001 */ +for (i = 0; i < 6; i++) { /* 000 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &u5); /* 101 */ +for (i = 0; i < 10; i++) { /* 0000000 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &x3); /* 111 */ +for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &x3); /* 111 */ +for (i = 0; i < 9; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &x8); /* 11111111 */ +for (i = 0; i < 5; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &u9); /* 1001 */ +for (i = 0; i < 6; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &u11); /* 1011 */ +for (i = 0; i < 4; i++) { + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &u13); /* 1101 */ +for (i = 0; i < 5; i++) { + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &x2); /* 11 */ +for (i = 0; i < 6; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &u13); /* 1101 */ +for (i = 0; i < 10; i++) { /* 000000 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &u13); /* 1101 */ +for (i = 0; i < 4; i++) { + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, &u9); /* 1001 */ +for (i = 0; i < 6; i++) { /* 00000 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(t, t, x); /* 1 */ +for (i = 0; i < 8; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); +} +secp256k1_scalar_mul(r, t, &x6); /* 111111 */ +} + +SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) { + return !(a->d[0] & 1); +} +#endif + +static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) { +#if defined(USE_SCALAR_INV_BUILTIN) + secp256k1_scalar_inverse(r, x); +#elif defined(USE_SCALAR_INV_NUM) + unsigned char b[32]; + secp256k1_num n, m; + secp256k1_scalar t = *x; + secp256k1_scalar_get_b32(b, &t); + secp256k1_num_set_bin(&n, b, 32); + secp256k1_scalar_order_get_num(&m); + secp256k1_num_mod_inverse(&n, &n, &m); + secp256k1_num_get_bin(b, 32, &n); + secp256k1_scalar_set_b32(r, b, NULL); + /* Verify that the inverse was computed correctly, without GMP code. */ + secp256k1_scalar_mul(&t, &t, r); + CHECK(secp256k1_scalar_is_one(&t)); +#else +#error "Please select scalar inverse implementation" +#endif +} + +#ifdef USE_ENDOMORPHISM +#if defined(EXHAUSTIVE_TEST_ORDER) +/** + * Find k1 and k2 given k, such that k1 + k2 * lambda == k mod n; unlike in the + * full case we don't bother making k1 and k2 be small, we just want them to be + * nontrivial to get full test coverage for the exhaustive tests. We therefore + * (arbitrarily) set k2 = k + 5 and k1 = k - k2 * lambda. + */ +static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) { + *r2 = (*a + 5) % EXHAUSTIVE_TEST_ORDER; + *r1 = (*a + (EXHAUSTIVE_TEST_ORDER - *r2) * EXHAUSTIVE_TEST_LAMBDA) % EXHAUSTIVE_TEST_ORDER; +} +#else +/** + * The Secp256k1 curve has an endomorphism, where lambda * (x, y) = (beta * x, y), where + * lambda is {0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a, + * 0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72} + * + * "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm + * (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1 + * and k2 have a small size. + * It relies on constants a1, b1, a2, b2. These constants for the value of lambda above are: + * + * - a1 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15} + * - b1 = -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3} + * - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8} + * - b2 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15} + * + * The algorithm then computes c1 = round(b1 * k / n) and c2 = round(b2 * k / n), and gives + * k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and + * compute k1 as k - k2 * lambda, avoiding the need for constants a1 and a2. + * + * g1, g2 are precomputed constants used to replace division with a rounded multiplication + * when decomposing the scalar for an endomorphism-based point multiplication. + * + * The possibility of using precomputed estimates is mentioned in "Guide to Elliptic Curve + * Cryptography" (Hankerson, Menezes, Vanstone) in section 3.5. + * + * The derivation is described in the paper "Efficient Software Implementation of Public-Key + * Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez), + * Section 4.3 (here we use a somewhat higher-precision estimate): + * d = a1*b2 - b1*a2 + * g1 = round((2^272)*b2/d) + * g2 = round((2^272)*b1/d) + * + * (Note that 'd' is also equal to the curve order here because [a1,b1] and [a2,b2] are found + * as outputs of the Extended Euclidean Algorithm on inputs 'order' and 'lambda'). + * + * The function below splits a in r1 and r2, such that r1 + lambda * r2 == a (mod order). + */ + +static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) { + secp256k1_scalar c1, c2; + static const secp256k1_scalar minus_lambda = SECP256K1_SCALAR_CONST( + 0xAC9C52B3UL, 0x3FA3CF1FUL, 0x5AD9E3FDUL, 0x77ED9BA4UL, + 0xA880B9FCUL, 0x8EC739C2UL, 0xE0CFC810UL, 0xB51283CFUL + ); + static const secp256k1_scalar minus_b1 = SECP256K1_SCALAR_CONST( + 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL, + 0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL + ); + static const secp256k1_scalar minus_b2 = SECP256K1_SCALAR_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, + 0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL + ); + static const secp256k1_scalar g1 = SECP256K1_SCALAR_CONST( + 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00003086UL, + 0xD221A7D4UL, 0x6BCDE86CUL, 0x90E49284UL, 0xEB153DABUL + ); + static const secp256k1_scalar g2 = SECP256K1_SCALAR_CONST( + 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0000E443UL, + 0x7ED6010EUL, 0x88286F54UL, 0x7FA90ABFUL, 0xE4C42212UL + ); + VERIFY_CHECK(r1 != a); + VERIFY_CHECK(r2 != a); + /* these _var calls are constant time since the shift amount is constant */ + secp256k1_scalar_mul_shift_var(&c1, a, &g1, 272); + secp256k1_scalar_mul_shift_var(&c2, a, &g2, 272); + secp256k1_scalar_mul(&c1, &c1, &minus_b1); + secp256k1_scalar_mul(&c2, &c2, &minus_b2); + secp256k1_scalar_add(r2, &c1, &c2); + secp256k1_scalar_mul(r1, r2, &minus_lambda); + secp256k1_scalar_add(r1, r1, a); +} +#endif +#endif + +#endif /* SECP256K1_SCALAR_IMPL_H */ +#endif +