/* * Copyright 2014-2016 The OpenSSL Project Authors. All Rights Reserved. * Copyright (c) 2014, Intel Corporation. All Rights Reserved. * * Licensed under the OpenSSL license (the "License"). You may not use * this file except in compliance with the License. You can obtain a copy * in the file LICENSE in the source distribution or at * https://www.openssl.org/source/license.html * * Originally written by Shay Gueron (1, 2), and Vlad Krasnov (1) * (1) Intel Corporation, Israel Development Center, Haifa, Israel * (2) University of Haifa, Israel * * Reference: * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with * 256 Bit Primes" */ #include <openssl/ec.h> #include <assert.h> #include <stdint.h> #include <string.h> #include <openssl/bn.h> #include <openssl/crypto.h> #include <openssl/err.h> #include "../bn/internal.h" #include "../delocate.h" #include "../../internal.h" #include "internal.h" #include "p256-nistz.h" #if !defined(OPENSSL_NO_ASM) && \ (defined(OPENSSL_X86_64) || defined(OPENSSL_AARCH64)) && \ !defined(OPENSSL_SMALL) typedef P256_POINT_AFFINE PRECOMP256_ROW[64]; // One converted into the Montgomery domain static const BN_ULONG ONE[P256_LIMBS] = { TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000), TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe), }; // Precomputed tables for the default generator #include "p256-nistz-table.h" // Recode window to a signed digit, see |ec_GFp_nistp_recode_scalar_bits| in // util.c for details static crypto_word_t booth_recode_w5(crypto_word_t in) { crypto_word_t s, d; s = ~((in >> 5) - 1); d = (1 << 6) - in - 1; d = (d & s) | (in & ~s); d = (d >> 1) + (d & 1); return (d << 1) + (s & 1); } static crypto_word_t booth_recode_w7(crypto_word_t in) { crypto_word_t s, d; s = ~((in >> 7) - 1); d = (1 << 8) - in - 1; d = (d & s) | (in & ~s); d = (d >> 1) + (d & 1); return (d << 1) + (s & 1); } // copy_conditional copies |src| to |dst| if |move| is one and leaves it as-is // if |move| is zero. // // WARNING: this breaks the usual convention of constant-time functions // returning masks. static void copy_conditional(BN_ULONG dst[P256_LIMBS], const BN_ULONG src[P256_LIMBS], BN_ULONG move) { BN_ULONG mask1 = ((BN_ULONG)0) - move; BN_ULONG mask2 = ~mask1; dst[0] = (src[0] & mask1) ^ (dst[0] & mask2); dst[1] = (src[1] & mask1) ^ (dst[1] & mask2); dst[2] = (src[2] & mask1) ^ (dst[2] & mask2); dst[3] = (src[3] & mask1) ^ (dst[3] & mask2); if (P256_LIMBS == 8) { dst[4] = (src[4] & mask1) ^ (dst[4] & mask2); dst[5] = (src[5] & mask1) ^ (dst[5] & mask2); dst[6] = (src[6] & mask1) ^ (dst[6] & mask2); dst[7] = (src[7] & mask1) ^ (dst[7] & mask2); } } // is_not_zero returns one iff in != 0 and zero otherwise. // // WARNING: this breaks the usual convention of constant-time functions // returning masks. // // (define-fun is_not_zero ((in (_ BitVec 64))) (_ BitVec 64) // (bvlshr (bvor in (bvsub #x0000000000000000 in)) #x000000000000003f) // ) // // (declare-fun x () (_ BitVec 64)) // // (assert (and (= x #x0000000000000000) (= (is_not_zero x) #x0000000000000001))) // (check-sat) // // (assert (and (not (= x #x0000000000000000)) (= (is_not_zero x) #x0000000000000000))) // (check-sat) // static BN_ULONG is_not_zero(BN_ULONG in) { in |= (0 - in); in >>= BN_BITS2 - 1; return in; } // ecp_nistz256_mod_inverse_sqr_mont sets |r| to (|in| * 2^-256)^-2 * 2^256 mod // p. That is, |r| is the modular inverse square of |in| for input and output in // the Montgomery domain. static void ecp_nistz256_mod_inverse_sqr_mont(BN_ULONG r[P256_LIMBS], const BN_ULONG in[P256_LIMBS]) { // This implements the addition chain described in // https://briansmith.org/ecc-inversion-addition-chains-01#p256_field_inversion BN_ULONG x2[P256_LIMBS], x3[P256_LIMBS], x6[P256_LIMBS], x12[P256_LIMBS], x15[P256_LIMBS], x30[P256_LIMBS], x32[P256_LIMBS]; ecp_nistz256_sqr_mont(x2, in); // 2^2 - 2^1 ecp_nistz256_mul_mont(x2, x2, in); // 2^2 - 2^0 ecp_nistz256_sqr_mont(x3, x2); // 2^3 - 2^1 ecp_nistz256_mul_mont(x3, x3, in); // 2^3 - 2^0 ecp_nistz256_sqr_mont(x6, x3); for (int i = 1; i < 3; i++) { ecp_nistz256_sqr_mont(x6, x6); } // 2^6 - 2^3 ecp_nistz256_mul_mont(x6, x6, x3); // 2^6 - 2^0 ecp_nistz256_sqr_mont(x12, x6); for (int i = 1; i < 6; i++) { ecp_nistz256_sqr_mont(x12, x12); } // 2^12 - 2^6 ecp_nistz256_mul_mont(x12, x12, x6); // 2^12 - 2^0 ecp_nistz256_sqr_mont(x15, x12); for (int i = 1; i < 3; i++) { ecp_nistz256_sqr_mont(x15, x15); } // 2^15 - 2^3 ecp_nistz256_mul_mont(x15, x15, x3); // 2^15 - 2^0 ecp_nistz256_sqr_mont(x30, x15); for (int i = 1; i < 15; i++) { ecp_nistz256_sqr_mont(x30, x30); } // 2^30 - 2^15 ecp_nistz256_mul_mont(x30, x30, x15); // 2^30 - 2^0 ecp_nistz256_sqr_mont(x32, x30); ecp_nistz256_sqr_mont(x32, x32); // 2^32 - 2^2 ecp_nistz256_mul_mont(x32, x32, x2); // 2^32 - 2^0 BN_ULONG ret[P256_LIMBS]; ecp_nistz256_sqr_mont(ret, x32); for (int i = 1; i < 31 + 1; i++) { ecp_nistz256_sqr_mont(ret, ret); } // 2^64 - 2^32 ecp_nistz256_mul_mont(ret, ret, in); // 2^64 - 2^32 + 2^0 for (int i = 0; i < 96 + 32; i++) { ecp_nistz256_sqr_mont(ret, ret); } // 2^192 - 2^160 + 2^128 ecp_nistz256_mul_mont(ret, ret, x32); // 2^192 - 2^160 + 2^128 + 2^32 - 2^0 for (int i = 0; i < 32; i++) { ecp_nistz256_sqr_mont(ret, ret); } // 2^224 - 2^192 + 2^160 + 2^64 - 2^32 ecp_nistz256_mul_mont(ret, ret, x32); // 2^224 - 2^192 + 2^160 + 2^64 - 2^0 for (int i = 0; i < 30; i++) { ecp_nistz256_sqr_mont(ret, ret); } // 2^254 - 2^222 + 2^190 + 2^94 - 2^30 ecp_nistz256_mul_mont(ret, ret, x30); // 2^254 - 2^222 + 2^190 + 2^94 - 2^0 ecp_nistz256_sqr_mont(ret, ret); ecp_nistz256_sqr_mont(r, ret); // 2^256 - 2^224 + 2^192 + 2^96 - 2^2 } // r = p * p_scalar static void ecp_nistz256_windowed_mul(const EC_GROUP *group, P256_POINT *r, const EC_JACOBIAN *p, const EC_SCALAR *p_scalar) { assert(p != NULL); assert(p_scalar != NULL); assert(group->field.N.width == P256_LIMBS); static const size_t kWindowSize = 5; static const crypto_word_t kMask = (1 << (5 /* kWindowSize */ + 1)) - 1; // A |P256_POINT| is (3 * 32) = 96 bytes, and the 64-byte alignment should // add no more than 63 bytes of overhead. Thus, |table| should require // ~1599 ((96 * 16) + 63) bytes of stack space. alignas(64) P256_POINT table[16]; uint8_t p_str[33]; OPENSSL_memcpy(p_str, p_scalar->words, 32); p_str[32] = 0; // table[0] is implicitly (0,0,0) (the point at infinity), therefore it is // not stored. All other values are actually stored with an offset of -1 in // table. P256_POINT *row = table; assert(group->field.N.width == P256_LIMBS); OPENSSL_memcpy(row[1 - 1].X, p->X.words, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(row[1 - 1].Y, p->Y.words, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(row[1 - 1].Z, p->Z.words, P256_LIMBS * sizeof(BN_ULONG)); ecp_nistz256_point_double(&row[2 - 1], &row[1 - 1]); ecp_nistz256_point_add(&row[3 - 1], &row[2 - 1], &row[1 - 1]); ecp_nistz256_point_double(&row[4 - 1], &row[2 - 1]); ecp_nistz256_point_double(&row[6 - 1], &row[3 - 1]); ecp_nistz256_point_double(&row[8 - 1], &row[4 - 1]); ecp_nistz256_point_double(&row[12 - 1], &row[6 - 1]); ecp_nistz256_point_add(&row[5 - 1], &row[4 - 1], &row[1 - 1]); ecp_nistz256_point_add(&row[7 - 1], &row[6 - 1], &row[1 - 1]); ecp_nistz256_point_add(&row[9 - 1], &row[8 - 1], &row[1 - 1]); ecp_nistz256_point_add(&row[13 - 1], &row[12 - 1], &row[1 - 1]); ecp_nistz256_point_double(&row[14 - 1], &row[7 - 1]); ecp_nistz256_point_double(&row[10 - 1], &row[5 - 1]); ecp_nistz256_point_add(&row[15 - 1], &row[14 - 1], &row[1 - 1]); ecp_nistz256_point_add(&row[11 - 1], &row[10 - 1], &row[1 - 1]); ecp_nistz256_point_double(&row[16 - 1], &row[8 - 1]); BN_ULONG tmp[P256_LIMBS]; alignas(32) P256_POINT h; size_t index = 255; crypto_word_t wvalue = p_str[(index - 1) / 8]; wvalue = (wvalue >> ((index - 1) % 8)) & kMask; ecp_nistz256_select_w5(r, table, booth_recode_w5(wvalue) >> 1); while (index >= 5) { if (index != 255) { size_t off = (index - 1) / 8; wvalue = (crypto_word_t)p_str[off] | (crypto_word_t)p_str[off + 1] << 8; wvalue = (wvalue >> ((index - 1) % 8)) & kMask; wvalue = booth_recode_w5(wvalue); ecp_nistz256_select_w5(&h, table, wvalue >> 1); ecp_nistz256_neg(tmp, h.Y); copy_conditional(h.Y, tmp, (wvalue & 1)); ecp_nistz256_point_add(r, r, &h); } index -= kWindowSize; ecp_nistz256_point_double(r, r); ecp_nistz256_point_double(r, r); ecp_nistz256_point_double(r, r); ecp_nistz256_point_double(r, r); ecp_nistz256_point_double(r, r); } // Final window wvalue = p_str[0]; wvalue = (wvalue << 1) & kMask; wvalue = booth_recode_w5(wvalue); ecp_nistz256_select_w5(&h, table, wvalue >> 1); ecp_nistz256_neg(tmp, h.Y); copy_conditional(h.Y, tmp, wvalue & 1); ecp_nistz256_point_add(r, r, &h); } static crypto_word_t calc_first_wvalue(size_t *index, const uint8_t p_str[33]) { static const size_t kWindowSize = 7; static const crypto_word_t kMask = (1 << (7 /* kWindowSize */ + 1)) - 1; *index = kWindowSize; crypto_word_t wvalue = (p_str[0] << 1) & kMask; return booth_recode_w7(wvalue); } static crypto_word_t calc_wvalue(size_t *index, const uint8_t p_str[33]) { static const size_t kWindowSize = 7; static const crypto_word_t kMask = (1 << (7 /* kWindowSize */ + 1)) - 1; const size_t off = (*index - 1) / 8; crypto_word_t wvalue = (crypto_word_t)p_str[off] | (crypto_word_t)p_str[off + 1] << 8; wvalue = (wvalue >> ((*index - 1) % 8)) & kMask; *index += kWindowSize; return booth_recode_w7(wvalue); } static void ecp_nistz256_point_mul(const EC_GROUP *group, EC_JACOBIAN *r, const EC_JACOBIAN *p, const EC_SCALAR *scalar) { alignas(32) P256_POINT out; ecp_nistz256_windowed_mul(group, &out, p, scalar); assert(group->field.N.width == P256_LIMBS); OPENSSL_memcpy(r->X.words, out.X, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(r->Y.words, out.Y, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(r->Z.words, out.Z, P256_LIMBS * sizeof(BN_ULONG)); } static void ecp_nistz256_point_mul_base(const EC_GROUP *group, EC_JACOBIAN *r, const EC_SCALAR *scalar) { uint8_t p_str[33]; OPENSSL_memcpy(p_str, scalar->words, 32); p_str[32] = 0; // First window size_t index = 0; crypto_word_t wvalue = calc_first_wvalue(&index, p_str); alignas(32) P256_POINT_AFFINE t; alignas(32) P256_POINT p; ecp_nistz256_select_w7(&t, ecp_nistz256_precomputed[0], wvalue >> 1); ecp_nistz256_neg(p.Z, t.Y); copy_conditional(t.Y, p.Z, wvalue & 1); // Convert |t| from affine to Jacobian coordinates. We set Z to zero if |t| // is infinity and |ONE| otherwise. |t| was computed from the table, so it // is infinity iff |wvalue >> 1| is zero. OPENSSL_memcpy(p.X, t.X, sizeof(p.X)); OPENSSL_memcpy(p.Y, t.Y, sizeof(p.Y)); OPENSSL_memset(p.Z, 0, sizeof(p.Z)); copy_conditional(p.Z, ONE, is_not_zero(wvalue >> 1)); for (int i = 1; i < 37; i++) { wvalue = calc_wvalue(&index, p_str); ecp_nistz256_select_w7(&t, ecp_nistz256_precomputed[i], wvalue >> 1); alignas(32) BN_ULONG neg_Y[P256_LIMBS]; ecp_nistz256_neg(neg_Y, t.Y); copy_conditional(t.Y, neg_Y, wvalue & 1); // Note |ecp_nistz256_point_add_affine| does not work if |p| and |t| are the // same non-infinity point. ecp_nistz256_point_add_affine(&p, &p, &t); } assert(group->field.N.width == P256_LIMBS); OPENSSL_memcpy(r->X.words, p.X, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(r->Y.words, p.Y, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(r->Z.words, p.Z, P256_LIMBS * sizeof(BN_ULONG)); } static void ecp_nistz256_points_mul_public(const EC_GROUP *group, EC_JACOBIAN *r, const EC_SCALAR *g_scalar, const EC_JACOBIAN *p_, const EC_SCALAR *p_scalar) { assert(p_ != NULL && p_scalar != NULL && g_scalar != NULL); alignas(32) P256_POINT p; uint8_t p_str[33]; OPENSSL_memcpy(p_str, g_scalar->words, 32); p_str[32] = 0; // First window size_t index = 0; size_t wvalue = calc_first_wvalue(&index, p_str); // Convert |p| from affine to Jacobian coordinates. We set Z to zero if |p| // is infinity and |ONE| otherwise. |p| was computed from the table, so it // is infinity iff |wvalue >> 1| is zero. if ((wvalue >> 1) != 0) { OPENSSL_memcpy(p.X, &ecp_nistz256_precomputed[0][(wvalue >> 1) - 1].X, sizeof(p.X)); OPENSSL_memcpy(p.Y, &ecp_nistz256_precomputed[0][(wvalue >> 1) - 1].Y, sizeof(p.Y)); OPENSSL_memcpy(p.Z, ONE, sizeof(p.Z)); } else { OPENSSL_memset(p.X, 0, sizeof(p.X)); OPENSSL_memset(p.Y, 0, sizeof(p.Y)); OPENSSL_memset(p.Z, 0, sizeof(p.Z)); } if ((wvalue & 1) == 1) { ecp_nistz256_neg(p.Y, p.Y); } for (int i = 1; i < 37; i++) { wvalue = calc_wvalue(&index, p_str); if ((wvalue >> 1) == 0) { continue; } alignas(32) P256_POINT_AFFINE t; OPENSSL_memcpy(&t, &ecp_nistz256_precomputed[i][(wvalue >> 1) - 1], sizeof(t)); if ((wvalue & 1) == 1) { ecp_nistz256_neg(t.Y, t.Y); } // Note |ecp_nistz256_point_add_affine| does not work if |p| and |t| are // the same non-infinity point, so it is important that we compute the // |g_scalar| term before the |p_scalar| term. ecp_nistz256_point_add_affine(&p, &p, &t); } alignas(32) P256_POINT tmp; ecp_nistz256_windowed_mul(group, &tmp, p_, p_scalar); ecp_nistz256_point_add(&p, &p, &tmp); assert(group->field.N.width == P256_LIMBS); OPENSSL_memcpy(r->X.words, p.X, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(r->Y.words, p.Y, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(r->Z.words, p.Z, P256_LIMBS * sizeof(BN_ULONG)); } static int ecp_nistz256_get_affine(const EC_GROUP *group, const EC_JACOBIAN *point, EC_FELEM *x, EC_FELEM *y) { if (constant_time_declassify_int( ec_GFp_simple_is_at_infinity(group, point))) { OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY); return 0; } BN_ULONG z_inv2[P256_LIMBS]; assert(group->field.N.width == P256_LIMBS); ecp_nistz256_mod_inverse_sqr_mont(z_inv2, point->Z.words); if (x != NULL) { ecp_nistz256_mul_mont(x->words, z_inv2, point->X.words); } if (y != NULL) { ecp_nistz256_sqr_mont(z_inv2, z_inv2); // z^-4 ecp_nistz256_mul_mont(y->words, point->Y.words, point->Z.words); // y * z ecp_nistz256_mul_mont(y->words, y->words, z_inv2); // y * z^-3 } return 1; } static void ecp_nistz256_add(const EC_GROUP *group, EC_JACOBIAN *r, const EC_JACOBIAN *a_, const EC_JACOBIAN *b_) { P256_POINT a, b; OPENSSL_memcpy(a.X, a_->X.words, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(a.Y, a_->Y.words, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(a.Z, a_->Z.words, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(b.X, b_->X.words, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(b.Y, b_->Y.words, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(b.Z, b_->Z.words, P256_LIMBS * sizeof(BN_ULONG)); ecp_nistz256_point_add(&a, &a, &b); OPENSSL_memcpy(r->X.words, a.X, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(r->Y.words, a.Y, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(r->Z.words, a.Z, P256_LIMBS * sizeof(BN_ULONG)); } static void ecp_nistz256_dbl(const EC_GROUP *group, EC_JACOBIAN *r, const EC_JACOBIAN *a_) { P256_POINT a; OPENSSL_memcpy(a.X, a_->X.words, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(a.Y, a_->Y.words, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(a.Z, a_->Z.words, P256_LIMBS * sizeof(BN_ULONG)); ecp_nistz256_point_double(&a, &a); OPENSSL_memcpy(r->X.words, a.X, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(r->Y.words, a.Y, P256_LIMBS * sizeof(BN_ULONG)); OPENSSL_memcpy(r->Z.words, a.Z, P256_LIMBS * sizeof(BN_ULONG)); } static void ecp_nistz256_inv0_mod_ord(const EC_GROUP *group, EC_SCALAR *out, const EC_SCALAR *in) { // table[i] stores a power of |in| corresponding to the matching enum value. enum { // The following indices specify the power in binary. i_1 = 0, i_10, i_11, i_101, i_111, i_1010, i_1111, i_10101, i_101010, i_101111, // The following indices specify 2^N-1, or N ones in a row. i_x6, i_x8, i_x16, i_x32 }; BN_ULONG table[15][P256_LIMBS]; // https://briansmith.org/ecc-inversion-addition-chains-01#p256_scalar_inversion // // Even though this code path spares 12 squarings, 4.5%, and 13 // multiplications, 25%, the overall sign operation is not that much faster, // not more that 2%. Most of the performance of this function comes from the // scalar operations. // Pre-calculate powers. OPENSSL_memcpy(table[i_1], in->words, P256_LIMBS * sizeof(BN_ULONG)); ecp_nistz256_ord_sqr_mont(table[i_10], table[i_1], 1); ecp_nistz256_ord_mul_mont(table[i_11], table[i_1], table[i_10]); ecp_nistz256_ord_mul_mont(table[i_101], table[i_11], table[i_10]); ecp_nistz256_ord_mul_mont(table[i_111], table[i_101], table[i_10]); ecp_nistz256_ord_sqr_mont(table[i_1010], table[i_101], 1); ecp_nistz256_ord_mul_mont(table[i_1111], table[i_1010], table[i_101]); ecp_nistz256_ord_sqr_mont(table[i_10101], table[i_1010], 1); ecp_nistz256_ord_mul_mont(table[i_10101], table[i_10101], table[i_1]); ecp_nistz256_ord_sqr_mont(table[i_101010], table[i_10101], 1); ecp_nistz256_ord_mul_mont(table[i_101111], table[i_101010], table[i_101]); ecp_nistz256_ord_mul_mont(table[i_x6], table[i_101010], table[i_10101]); ecp_nistz256_ord_sqr_mont(table[i_x8], table[i_x6], 2); ecp_nistz256_ord_mul_mont(table[i_x8], table[i_x8], table[i_11]); ecp_nistz256_ord_sqr_mont(table[i_x16], table[i_x8], 8); ecp_nistz256_ord_mul_mont(table[i_x16], table[i_x16], table[i_x8]); ecp_nistz256_ord_sqr_mont(table[i_x32], table[i_x16], 16); ecp_nistz256_ord_mul_mont(table[i_x32], table[i_x32], table[i_x16]); // Compute |in| raised to the order-2. ecp_nistz256_ord_sqr_mont(out->words, table[i_x32], 64); ecp_nistz256_ord_mul_mont(out->words, out->words, table[i_x32]); static const struct { uint8_t p, i; } kChain[27] = {{32, i_x32}, {6, i_101111}, {5, i_111}, {4, i_11}, {5, i_1111}, {5, i_10101}, {4, i_101}, {3, i_101}, {3, i_101}, {5, i_111}, {9, i_101111}, {6, i_1111}, {2, i_1}, {5, i_1}, {6, i_1111}, {5, i_111}, {4, i_111}, {5, i_111}, {5, i_101}, {3, i_11}, {10, i_101111}, {2, i_11}, {5, i_11}, {5, i_11}, {3, i_1}, {7, i_10101}, {6, i_1111}}; for (size_t i = 0; i < OPENSSL_ARRAY_SIZE(kChain); i++) { ecp_nistz256_ord_sqr_mont(out->words, out->words, kChain[i].p); ecp_nistz256_ord_mul_mont(out->words, out->words, table[kChain[i].i]); } } static int ecp_nistz256_scalar_to_montgomery_inv_vartime(const EC_GROUP *group, EC_SCALAR *out, const EC_SCALAR *in) { #if defined(OPENSSL_X86_64) if (!CRYPTO_is_AVX_capable()) { // No AVX support; fallback to generic code. return ec_simple_scalar_to_montgomery_inv_vartime(group, out, in); } #endif assert(group->order.N.width == P256_LIMBS); if (!beeu_mod_inverse_vartime(out->words, in->words, group->order.N.d)) { return 0; } // The result should be returned in the Montgomery domain. ec_scalar_to_montgomery(group, out, out); return 1; } static int ecp_nistz256_cmp_x_coordinate(const EC_GROUP *group, const EC_JACOBIAN *p, const EC_SCALAR *r) { if (ec_GFp_simple_is_at_infinity(group, p)) { return 0; } assert(group->order.N.width == P256_LIMBS); assert(group->field.N.width == P256_LIMBS); // We wish to compare X/Z^2 with r. This is equivalent to comparing X with // r*Z^2. Note that X and Z are represented in Montgomery form, while r is // not. BN_ULONG r_Z2[P256_LIMBS], Z2_mont[P256_LIMBS], X[P256_LIMBS]; ecp_nistz256_mul_mont(Z2_mont, p->Z.words, p->Z.words); ecp_nistz256_mul_mont(r_Z2, r->words, Z2_mont); ecp_nistz256_from_mont(X, p->X.words); if (OPENSSL_memcmp(r_Z2, X, sizeof(r_Z2)) == 0) { return 1; } // During signing the x coefficient is reduced modulo the group order. // Therefore there is a small possibility, less than 1/2^128, that group_order // < p.x < P. in that case we need not only to compare against |r| but also to // compare against r+group_order. BN_ULONG carry = bn_add_words(r_Z2, r->words, group->order.N.d, P256_LIMBS); if (carry == 0 && bn_less_than_words(r_Z2, group->field.N.d, P256_LIMBS)) { // r + group_order < p, so compare (r + group_order) * Z^2 against X. ecp_nistz256_mul_mont(r_Z2, r_Z2, Z2_mont); if (OPENSSL_memcmp(r_Z2, X, sizeof(r_Z2)) == 0) { return 1; } } return 0; } DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_nistz256_method) { // TODO(crbug.com/42290548): The x86_64 assembly depends on initializing // |OPENSSL_ia32cap_P|. Move the dispatch to C. For now, explicitly initialize // things. OPENSSL_init_cpuid(); out->point_get_affine_coordinates = ecp_nistz256_get_affine; out->add = ecp_nistz256_add; out->dbl = ecp_nistz256_dbl; out->mul = ecp_nistz256_point_mul; out->mul_base = ecp_nistz256_point_mul_base; out->mul_public = ecp_nistz256_points_mul_public; out->felem_mul = ec_GFp_mont_felem_mul; out->felem_sqr = ec_GFp_mont_felem_sqr; out->felem_to_bytes = ec_GFp_mont_felem_to_bytes; out->felem_from_bytes = ec_GFp_mont_felem_from_bytes; out->felem_reduce = ec_GFp_mont_felem_reduce; // TODO(davidben): This should use the specialized field arithmetic // implementation, rather than the generic one. out->felem_exp = ec_GFp_mont_felem_exp; out->scalar_inv0_montgomery = ecp_nistz256_inv0_mod_ord; out->scalar_to_montgomery_inv_vartime = ecp_nistz256_scalar_to_montgomery_inv_vartime; out->cmp_x_coordinate = ecp_nistz256_cmp_x_coordinate; } #endif /* !defined(OPENSSL_NO_ASM) && \ (defined(OPENSSL_X86_64) || defined(OPENSSL_AARCH64)) && \ !defined(OPENSSL_SMALL) */
Codebase Browser
chromium