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Diffstat (limited to 'src/ecmult_const_impl.h')
| -rw-r--r-- | src/ecmult_const_impl.h | 260 |
1 files changed, 260 insertions, 0 deletions
diff --git a/src/ecmult_const_impl.h b/src/ecmult_const_impl.h new file mode 100644 index 0000000000..90ac94770e --- /dev/null +++ b/src/ecmult_const_impl.h @@ -0,0 +1,260 @@ +/********************************************************************** + * 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_ +#define _SECP256K1_ECMULT_CONST_IMPL_ + +#include "scalar.h" +#include "group.h" +#include "ecmult_const.h" +#include "ecmult_impl.h" + +#ifdef USE_ENDOMORPHISM + #define WNAF_BITS 128 +#else + #define WNAF_BITS 256 +#endif +#define WNAF_SIZE(w) ((WNAF_BITS + (w) - 1) / (w)) + +/* 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..return_val) + * with 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 returned; this is always (WNAF_BITS + w - 1) / w + * + * 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 global_sign; + int skew = 0; + int word = 0; + /* 1 2 3 */ + int u_last; + int u; + +#ifdef USE_ENDOMORPHISM + int flip; + int bit; + secp256k1_scalar neg_s; + int not_neg_one; + /* If we are using the endomorphism, we cannot handle even numbers by negating + * them, since we are working with 128-bit numbers whose negations would be 256 + * bits, eliminating the performance advantage. 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, then compensating after the + * multiplication. */ + /* Negative 128-bit numbers will be negated, since otherwise they are 256-bit */ + flip = secp256k1_scalar_is_high(&s); + /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */ + bit = flip ^ (s.d[0] & 1); + /* 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; +#else + /* Otherwise, we just negate to force oddness */ + int is_even = secp256k1_scalar_is_even(&s); + global_sign = secp256k1_scalar_cond_negate(&s, is_even); +#endif + + /* 4 */ + u_last = secp256k1_scalar_shr_int(&s, w); + while (word * w < WNAF_BITS) { + 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(w)); + return skew; +} + + +static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar) { + secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)]; + secp256k1_ge tmpa; + secp256k1_fe Z; + +#ifdef USE_ENDOMORPHISM + secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)]; + int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)]; + int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)]; + int skew_1; + int skew_lam; + secp256k1_scalar q_1, q_lam; +#else + int wnaf[1 + WNAF_SIZE(WINDOW_A - 1)]; +#endif + + int i; + secp256k1_scalar sc = *scalar; + + /* build wnaf representation for q. */ +#ifdef USE_ENDOMORPHISM + /* 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); + /* no need for zero correction when using endomorphism since even + * numbers have one added to them anyway */ + skew_1 = secp256k1_wnaf_const(wnaf_1, q_1, WINDOW_A - 1); + skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A - 1); +#else + int is_zero = secp256k1_scalar_is_zero(scalar); + /* the wNAF ladder cannot handle zero, so bump this to one .. we will + * correct the result after the fact */ + sc.d[0] += is_zero; + VERIFY_CHECK(!secp256k1_scalar_is_zero(&sc)); + + secp256k1_wnaf_const(wnaf, sc, WINDOW_A - 1); +#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 + 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) */ +#ifdef USE_ENDOMORPHISM + i = wnaf_1[WNAF_SIZE(WINDOW_A - 1)]; + VERIFY_CHECK(i != 0); + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A); + secp256k1_gej_set_ge(r, &tmpa); + + i = wnaf_lam[WNAF_SIZE(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); +#else + i = wnaf[WNAF_SIZE(WINDOW_A - 1)]; + VERIFY_CHECK(i != 0); + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A); + secp256k1_gej_set_ge(r, &tmpa); +#endif + /* remaining loop iterations */ + for (i = WNAF_SIZE(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); + } +#ifdef USE_ENDOMORPHISM + 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); + + 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); +#else + n = wnaf[i]; + VERIFY_CHECK(n != 0); + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A); + secp256k1_gej_add_ge(r, r, &tmpa); +#endif + } + + secp256k1_fe_mul(&r->z, &r->z, &Z); + +#ifdef USE_ENDOMORPHISM + { + /* Correct for wNAF skew */ + secp256k1_ge correction = *a; + secp256k1_ge_storage correction_1_stor; + secp256k1_ge_storage correction_lam_stor; + 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); + secp256k1_ge_to_storage(&correction_lam_stor, a); + 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); + secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2); + + /* Apply the correction */ + secp256k1_ge_from_storage(&correction, &correction_1_stor); + secp256k1_ge_neg(&correction, &correction); + secp256k1_gej_add_ge(r, r, &correction); + + 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); + } +#else + /* correct for zero */ + r->infinity |= is_zero; +#endif +} + +#endif |