/* Copyright (c) 2018, Google Inc. * * Permission to use, copy, modify, and/or distribute this software for any * purpose with or without fee is hereby granted, provided that the above * copyright notice and this permission notice appear in all copies. * * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ #include <openssl/ec.h> #include <assert.h> #include "internal.h" #include "../bn/internal.h" #include "../../internal.h" static void ec_GFp_mont_mul_single(const EC_GROUP *group, EC_RAW_POINT *r, const EC_RAW_POINT *p, const EC_SCALAR *scalar) { // This is a generic implementation for uncommon curves that not do not // warrant a tuned one. It uses unsigned digits so that the doubling case in // |ec_GFp_mont_add| is always unreachable, erring on safety and simplicity. // Compute a table of the first 32 multiples of |p| (including infinity). EC_RAW_POINT precomp[32]; ec_GFp_simple_point_set_to_infinity(group, &precomp[0]); ec_GFp_simple_point_copy(&precomp[1], p); for (size_t j = 2; j < OPENSSL_ARRAY_SIZE(precomp); j++) { if (j & 1) { ec_GFp_mont_add(group, &precomp[j], &precomp[1], &precomp[j - 1]); } else { ec_GFp_mont_dbl(group, &precomp[j], &precomp[j / 2]); } } // Divide bits in |scalar| into windows. unsigned bits = BN_num_bits(&group->order); int r_is_at_infinity = 1; for (unsigned i = bits - 1; i < bits; i--) { if (!r_is_at_infinity) { ec_GFp_mont_dbl(group, r, r); } if (i % 5 == 0) { // Compute the next window value. const size_t width = group->order.width; uint8_t window = bn_is_bit_set_words(scalar->words, width, i + 4) << 4; window |= bn_is_bit_set_words(scalar->words, width, i + 3) << 3; window |= bn_is_bit_set_words(scalar->words, width, i + 2) << 2; window |= bn_is_bit_set_words(scalar->words, width, i + 1) << 1; window |= bn_is_bit_set_words(scalar->words, width, i); // Select the entry in constant-time. EC_RAW_POINT tmp; OPENSSL_memset(&tmp, 0, sizeof(EC_RAW_POINT)); for (size_t j = 0; j < OPENSSL_ARRAY_SIZE(precomp); j++) { BN_ULONG mask = constant_time_eq_w(j, window); ec_felem_select(group, &tmp.X, mask, &precomp[j].X, &tmp.X); ec_felem_select(group, &tmp.Y, mask, &precomp[j].Y, &tmp.Y); ec_felem_select(group, &tmp.Z, mask, &precomp[j].Z, &tmp.Z); } if (r_is_at_infinity) { ec_GFp_simple_point_copy(r, &tmp); r_is_at_infinity = 0; } else { ec_GFp_mont_add(group, r, r, &tmp); } } } if (r_is_at_infinity) { ec_GFp_simple_point_set_to_infinity(group, r); } } void ec_GFp_mont_mul(const EC_GROUP *group, EC_RAW_POINT *r, const EC_SCALAR *g_scalar, const EC_RAW_POINT *p, const EC_SCALAR *p_scalar) { assert(g_scalar != NULL || p_scalar != NULL); if (p_scalar == NULL) { ec_GFp_mont_mul_single(group, r, &group->generator->raw, g_scalar); } else if (g_scalar == NULL) { ec_GFp_mont_mul_single(group, r, p, p_scalar); } else { // Support constant-time two-point multiplication for compatibility. This // does not actually come up in keygen, ECDH, or ECDSA, so we implement it // the naive way. ec_GFp_mont_mul_single(group, r, &group->generator->raw, g_scalar); EC_RAW_POINT tmp; ec_GFp_mont_mul_single(group, &tmp, p, p_scalar); ec_GFp_mont_add(group, r, r, &tmp); } }