diff --git a/src/secp256k1/src/ecmult_const_impl.h b/src/secp256k1/src/ecmult_const_impl.h index 7d7a172b7..d8697e0e9 100644 --- a/src/secp256k1/src/ecmult_const_impl.h +++ b/src/secp256k1/src/ecmult_const_impl.h @@ -1,3 +1,5 @@ +#ifndef ENABLE_MODULE_MUSIG + /********************************************************************** * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra * * Distributed under the MIT software license, see the accompanying * @@ -238,3 +240,265 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons } #endif /* SECP256K1_ECMULT_CONST_IMPL_H */ + +#else +/********************************************************************** + * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_ECMULT_CONST_IMPL_H +#define SECP256K1_ECMULT_CONST_IMPL_H + +#include "scalar.h" +#include "group.h" +#include "ecmult_const.h" +#include "ecmult_impl.h" + +/* This is like `ECMULT_TABLE_GET_GE` but is constant time */ +#define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \ +int m; \ +int abs_n = (n) * (((n) > 0) * 2 - 1); \ +int idx_n = abs_n / 2; \ +secp256k1_fe neg_y; \ +VERIFY_CHECK(((n) & 1) == 1); \ +VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \ +VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \ +VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \ +VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \ +for (m = 0; m < ECMULT_TABLE_SIZE(w); m++) { \ +/* This loop is used to avoid secret data in array indices. See +* the comment in ecmult_gen_impl.h for rationale. */ \ +secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \ +secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \ +} \ +(r)->infinity = 0; \ +secp256k1_fe_negate(&neg_y, &(r)->y, 1); \ +secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \ +} while(0) + + +/** Convert a number to WNAF notation. + * The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val. + * It has the following guarantees: + * - each wnaf[i] an odd integer between -(1 << w) and (1 << w) + * - each wnaf[i] is nonzero + * - the number of words set is always WNAF_SIZE(w) + 1 + * + * Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar + * Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.) + * CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlagy Berlin Heidelberg 2003 + * + * Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335 + */ +static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w, int size) { + int global_sign; + int skew = 0; + int word = 0; + + /* 1 2 3 */ + int u_last; + int u; + + int flip; + int bit; + secp256k1_scalar neg_s; + int not_neg_one; + /* Note that we cannot handle even numbers by negating them to be odd, as is + * done in other implementations, since if our scalars were specified to have + * width < 256 for performance reasons, their negations would have width 256 + * and we'd lose any performance benefit. Instead, we use a technique from + * Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even) + * or 2 (for odd) to the number we are encoding, returning a skew value indicating + * this, and having the caller compensate after doing the multiplication. + * + * In fact, we _do_ want to negate numbers to minimize their bit-lengths (and in + * particular, to ensure that the outputs from the endomorphism-split fit into + * 128 bits). If we negate, the parity of our number flips, inverting which of + * {1, 2} we want to add to the scalar when ensuring that it's odd. Further + * complicating things, -1 interacts badly with `secp256k1_scalar_cadd_bit` and + * we need to special-case it in this logic. */ + flip = secp256k1_scalar_is_high(&s); + /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */ + bit = flip ^ !secp256k1_scalar_is_even(&s); + /* We check for negative one, since adding 2 to it will cause an overflow */ + secp256k1_scalar_negate(&neg_s, &s); + not_neg_one = !secp256k1_scalar_is_one(&neg_s); + secp256k1_scalar_cadd_bit(&s, bit, not_neg_one); + /* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects + * that we added two to it and flipped it. In fact for -1 these operations are + * identical. We only flipped, but since skewing is required (in the sense that + * the skew must be 1 or 2, never zero) and flipping is not, we need to change + * our flags to claim that we only skewed. */ + global_sign = secp256k1_scalar_cond_negate(&s, flip); + global_sign *= not_neg_one * 2 - 1; + skew = 1 << bit; + + /* 4 */ + u_last = secp256k1_scalar_shr_int(&s, w); + while (word * w < size) { + int sign; + int even; + + /* 4.1 4.4 */ + u = secp256k1_scalar_shr_int(&s, w); + /* 4.2 */ + even = ((u & 1) == 0); + sign = 2 * (u_last > 0) - 1; + u += sign * even; + u_last -= sign * even * (1 << w); + + /* 4.3, adapted for global sign change */ + wnaf[word++] = u_last * global_sign; + + u_last = u; + } + wnaf[word] = u * global_sign; + + VERIFY_CHECK(secp256k1_scalar_is_zero(&s)); + VERIFY_CHECK(word == WNAF_SIZE_BITS(size, w)); + return skew; +} + +static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar, int size) { + secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)]; + secp256k1_ge tmpa; + secp256k1_fe Z; + + int skew_1; +#ifdef USE_ENDOMORPHISM + secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)]; + int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)]; + int skew_lam; + secp256k1_scalar q_1, q_lam; +#endif + int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)]; + + int i; + secp256k1_scalar sc = *scalar; + + /* build wnaf representation for q. */ + int rsize = size; +#ifdef USE_ENDOMORPHISM + if (size > 128) { + rsize = 128; + /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */ + secp256k1_scalar_split_lambda(&q_1, &q_lam, &sc); + skew_1 = secp256k1_wnaf_const(wnaf_1, q_1, WINDOW_A - 1, 128); + skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A - 1, 128); + } else +#endif + { + skew_1 = secp256k1_wnaf_const(wnaf_1, sc, WINDOW_A - 1, size); +#ifdef USE_ENDOMORPHISM + skew_lam = 0; +#endif + } + + /* Calculate odd multiples of a. + * All multiples are brought to the same Z 'denominator', which is stored + * in Z. Due to secp256k1' isomorphism we can do all operations pretending + * that the Z coordinate was 1, use affine addition formulae, and correct + * the Z coordinate of the result once at the end. + */ + secp256k1_gej_set_ge(r, a); + secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r); + for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { + secp256k1_fe_normalize_weak(&pre_a[i].y); + } +#ifdef USE_ENDOMORPHISM + if (size > 128) { + for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { + secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]); + } + } +#endif + + /* first loop iteration (separated out so we can directly set r, rather + * than having it start at infinity, get doubled several times, then have + * its new value added to it) */ + i = wnaf_1[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)]; + VERIFY_CHECK(i != 0); + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A); + secp256k1_gej_set_ge(r, &tmpa); +#ifdef USE_ENDOMORPHISM + if (size > 128) { + i = wnaf_lam[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)]; + VERIFY_CHECK(i != 0); + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A); + secp256k1_gej_add_ge(r, r, &tmpa); + } +#endif + /* remaining loop iterations */ + for (i = WNAF_SIZE_BITS(rsize, WINDOW_A - 1) - 1; i >= 0; i--) { + int n; + int j; + for (j = 0; j < WINDOW_A - 1; ++j) { + secp256k1_gej_double_nonzero(r, r, NULL); + } + + n = wnaf_1[i]; + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A); + VERIFY_CHECK(n != 0); + secp256k1_gej_add_ge(r, r, &tmpa); +#ifdef USE_ENDOMORPHISM + if (size > 128) { + n = wnaf_lam[i]; + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A); + VERIFY_CHECK(n != 0); + secp256k1_gej_add_ge(r, r, &tmpa); + } +#endif + } + + secp256k1_fe_mul(&r->z, &r->z, &Z); + + { + /* Correct for wNAF skew */ + secp256k1_ge correction = *a; + secp256k1_ge_storage correction_1_stor; +#ifdef USE_ENDOMORPHISM + secp256k1_ge_storage correction_lam_stor; +#endif + secp256k1_ge_storage a2_stor; + secp256k1_gej tmpj; + secp256k1_gej_set_ge(&tmpj, &correction); + secp256k1_gej_double_var(&tmpj, &tmpj, NULL); + secp256k1_ge_set_gej(&correction, &tmpj); + secp256k1_ge_to_storage(&correction_1_stor, a); +#ifdef USE_ENDOMORPHISM + if (size > 128) { + secp256k1_ge_to_storage(&correction_lam_stor, a); + } +#endif + secp256k1_ge_to_storage(&a2_stor, &correction); + + /* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */ + secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2); +#ifdef USE_ENDOMORPHISM + if (size > 128) { + secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2); + } +#endif + + /* Apply the correction */ + secp256k1_ge_from_storage(&correction, &correction_1_stor); + secp256k1_ge_neg(&correction, &correction); + secp256k1_gej_add_ge(r, r, &correction); + +#ifdef USE_ENDOMORPHISM + if (size > 128) { + secp256k1_ge_from_storage(&correction, &correction_lam_stor); + secp256k1_ge_neg(&correction, &correction); + secp256k1_ge_mul_lambda(&correction, &correction); + secp256k1_gej_add_ge(r, r, &correction); + } +#endif + } +} + +#endif /* SECP256K1_ECMULT_CONST_IMPL_H */ + +#endif +