232 lines
9.4 KiB
C
232 lines
9.4 KiB
C
/***********************************************************************
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* Copyright (c) 2015 Pieter Wuille, Andrew Poelstra *
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* Distributed under the MIT software license, see the accompanying *
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* file COPYING or https://www.opensource.org/licenses/mit-license.php.*
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***********************************************************************/
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#ifndef SECP256K1_ECMULT_CONST_IMPL_H
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#define SECP256K1_ECMULT_CONST_IMPL_H
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#include "scalar.h"
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#include "group.h"
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#include "ecmult_const.h"
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#include "ecmult_impl.h"
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/** Fill a table 'pre' with precomputed odd multiples of a.
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*
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* The resulting point set is brought to a single constant Z denominator, stores the X and Y
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* coordinates as ge_storage points in pre, and stores the global Z in globalz.
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* It only operates on tables sized for WINDOW_A wnaf multiples.
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*/
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static void rustsecp256k1_v0_8_0_ecmult_odd_multiples_table_globalz_windowa(rustsecp256k1_v0_8_0_ge *pre, rustsecp256k1_v0_8_0_fe *globalz, const rustsecp256k1_v0_8_0_gej *a) {
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rustsecp256k1_v0_8_0_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)];
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rustsecp256k1_v0_8_0_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), pre, zr, globalz, a);
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rustsecp256k1_v0_8_0_ge_table_set_globalz(ECMULT_TABLE_SIZE(WINDOW_A), pre, zr);
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}
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/* This is like `ECMULT_TABLE_GET_GE` but is constant time */
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#define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
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int m = 0; \
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/* Extract the sign-bit for a constant time absolute-value. */ \
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int mask = (n) >> (sizeof(n) * CHAR_BIT - 1); \
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int abs_n = ((n) + mask) ^ mask; \
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int idx_n = abs_n >> 1; \
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rustsecp256k1_v0_8_0_fe neg_y; \
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VERIFY_CHECK(((n) & 1) == 1); \
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VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
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VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
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VERIFY_SETUP(rustsecp256k1_v0_8_0_fe_clear(&(r)->x)); \
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VERIFY_SETUP(rustsecp256k1_v0_8_0_fe_clear(&(r)->y)); \
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/* Unconditionally set r->x = (pre)[m].x. r->y = (pre)[m].y. because it's either the correct one \
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* or will get replaced in the later iterations, this is needed to make sure `r` is initialized. */ \
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(r)->x = (pre)[m].x; \
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(r)->y = (pre)[m].y; \
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for (m = 1; m < ECMULT_TABLE_SIZE(w); m++) { \
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/* This loop is used to avoid secret data in array indices. See
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* the comment in ecmult_gen_impl.h for rationale. */ \
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rustsecp256k1_v0_8_0_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \
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rustsecp256k1_v0_8_0_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \
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} \
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(r)->infinity = 0; \
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rustsecp256k1_v0_8_0_fe_negate(&neg_y, &(r)->y, 1); \
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rustsecp256k1_v0_8_0_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \
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} while(0)
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/** Convert a number to WNAF notation.
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* The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val.
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* It has the following guarantees:
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* - each wnaf[i] an odd integer between -(1 << w) and (1 << w)
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* - each wnaf[i] is nonzero
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* - the number of words set is always WNAF_SIZE(w) + 1
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*
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* Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar
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* Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.)
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* CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlag Berlin Heidelberg 2003
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*
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* Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335
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*/
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static int rustsecp256k1_v0_8_0_wnaf_const(int *wnaf, const rustsecp256k1_v0_8_0_scalar *scalar, int w, int size) {
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int global_sign;
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int skew;
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int word = 0;
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/* 1 2 3 */
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int u_last;
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int u;
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int flip;
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rustsecp256k1_v0_8_0_scalar s = *scalar;
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VERIFY_CHECK(w > 0);
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VERIFY_CHECK(size > 0);
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/* Note that we cannot handle even numbers by negating them to be odd, as is
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* done in other implementations, since if our scalars were specified to have
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* width < 256 for performance reasons, their negations would have width 256
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* and we'd lose any performance benefit. Instead, we use a variation of a
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* technique from Section 4.2 of the Okeya/Tagaki paper, which is to add 1 to the
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* number we are encoding when it is even, returning a skew value indicating
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* this, and having the caller compensate after doing the multiplication.
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*
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* In fact, we _do_ want to negate numbers to minimize their bit-lengths (and in
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* particular, to ensure that the outputs from the endomorphism-split fit into
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* 128 bits). If we negate, the parity of our number flips, affecting whether
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* we want to add to the scalar to ensure that it's odd. */
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flip = rustsecp256k1_v0_8_0_scalar_is_high(&s);
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skew = flip ^ rustsecp256k1_v0_8_0_scalar_is_even(&s);
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rustsecp256k1_v0_8_0_scalar_cadd_bit(&s, 0, skew);
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global_sign = rustsecp256k1_v0_8_0_scalar_cond_negate(&s, flip);
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/* 4 */
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u_last = rustsecp256k1_v0_8_0_scalar_shr_int(&s, w);
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do {
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int even;
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/* 4.1 4.4 */
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u = rustsecp256k1_v0_8_0_scalar_shr_int(&s, w);
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/* 4.2 */
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even = ((u & 1) == 0);
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/* In contrast to the original algorithm, u_last is always > 0 and
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* therefore we do not need to check its sign. In particular, it's easy
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* to see that u_last is never < 0 because u is never < 0. Moreover,
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* u_last is never = 0 because u is never even after a loop
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* iteration. The same holds analogously for the initial value of
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* u_last (in the first loop iteration). */
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VERIFY_CHECK(u_last > 0);
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VERIFY_CHECK((u_last & 1) == 1);
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u += even;
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u_last -= even * (1 << w);
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/* 4.3, adapted for global sign change */
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wnaf[word++] = u_last * global_sign;
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u_last = u;
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} while (word * w < size);
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wnaf[word] = u * global_sign;
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VERIFY_CHECK(rustsecp256k1_v0_8_0_scalar_is_zero(&s));
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VERIFY_CHECK(word == WNAF_SIZE_BITS(size, w));
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return skew;
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}
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static void rustsecp256k1_v0_8_0_ecmult_const(rustsecp256k1_v0_8_0_gej *r, const rustsecp256k1_v0_8_0_ge *a, const rustsecp256k1_v0_8_0_scalar *scalar, int size) {
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rustsecp256k1_v0_8_0_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
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rustsecp256k1_v0_8_0_ge tmpa;
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rustsecp256k1_v0_8_0_fe Z;
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int skew_1;
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rustsecp256k1_v0_8_0_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
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int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
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int skew_lam;
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rustsecp256k1_v0_8_0_scalar q_1, q_lam;
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int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
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int i;
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/* build wnaf representation for q. */
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int rsize = size;
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if (size > 128) {
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rsize = 128;
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/* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */
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rustsecp256k1_v0_8_0_scalar_split_lambda(&q_1, &q_lam, scalar);
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skew_1 = rustsecp256k1_v0_8_0_wnaf_const(wnaf_1, &q_1, WINDOW_A - 1, 128);
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skew_lam = rustsecp256k1_v0_8_0_wnaf_const(wnaf_lam, &q_lam, WINDOW_A - 1, 128);
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} else
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{
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skew_1 = rustsecp256k1_v0_8_0_wnaf_const(wnaf_1, scalar, WINDOW_A - 1, size);
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skew_lam = 0;
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}
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/* Calculate odd multiples of a.
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* All multiples are brought to the same Z 'denominator', which is stored
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* in Z. Due to secp256k1' isomorphism we can do all operations pretending
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* that the Z coordinate was 1, use affine addition formulae, and correct
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* the Z coordinate of the result once at the end.
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*/
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VERIFY_CHECK(!a->infinity);
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rustsecp256k1_v0_8_0_gej_set_ge(r, a);
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rustsecp256k1_v0_8_0_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r);
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for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
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rustsecp256k1_v0_8_0_fe_normalize_weak(&pre_a[i].y);
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}
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if (size > 128) {
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for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
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rustsecp256k1_v0_8_0_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
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}
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}
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/* first loop iteration (separated out so we can directly set r, rather
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* than having it start at infinity, get doubled several times, then have
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* its new value added to it) */
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i = wnaf_1[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)];
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VERIFY_CHECK(i != 0);
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ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
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rustsecp256k1_v0_8_0_gej_set_ge(r, &tmpa);
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if (size > 128) {
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i = wnaf_lam[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)];
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VERIFY_CHECK(i != 0);
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ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A);
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rustsecp256k1_v0_8_0_gej_add_ge(r, r, &tmpa);
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}
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/* remaining loop iterations */
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for (i = WNAF_SIZE_BITS(rsize, WINDOW_A - 1) - 1; i >= 0; i--) {
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int n;
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int j;
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for (j = 0; j < WINDOW_A - 1; ++j) {
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rustsecp256k1_v0_8_0_gej_double(r, r);
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}
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n = wnaf_1[i];
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ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
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VERIFY_CHECK(n != 0);
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rustsecp256k1_v0_8_0_gej_add_ge(r, r, &tmpa);
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if (size > 128) {
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n = wnaf_lam[i];
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ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
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VERIFY_CHECK(n != 0);
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rustsecp256k1_v0_8_0_gej_add_ge(r, r, &tmpa);
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}
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}
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{
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/* Correct for wNAF skew */
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rustsecp256k1_v0_8_0_gej tmpj;
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rustsecp256k1_v0_8_0_ge_neg(&tmpa, &pre_a[0]);
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rustsecp256k1_v0_8_0_gej_add_ge(&tmpj, r, &tmpa);
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rustsecp256k1_v0_8_0_gej_cmov(r, &tmpj, skew_1);
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if (size > 128) {
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rustsecp256k1_v0_8_0_ge_neg(&tmpa, &pre_a_lam[0]);
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rustsecp256k1_v0_8_0_gej_add_ge(&tmpj, r, &tmpa);
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rustsecp256k1_v0_8_0_gej_cmov(r, &tmpj, skew_lam);
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}
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}
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rustsecp256k1_v0_8_0_fe_mul(&r->z, &r->z, &Z);
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}
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#endif /* SECP256K1_ECMULT_CONST_IMPL_H */
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