| // Copyright 2020 The BoringSSL Authors |
| // |
| // Licensed under the Apache License, Version 2.0 (the "License"); |
| // you may not use this file except in compliance with the License. |
| // You may obtain a copy of the License at |
| // |
| // https://www.apache.org/licenses/LICENSE-2.0 |
| // |
| // Unless required by applicable law or agreed to in writing, software |
| // distributed under the License is distributed on an "AS IS" BASIS, |
| // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| // See the License for the specific language governing permissions and |
| // limitations under the License. |
| |
| // An implementation of the NIST P-256 elliptic curve point multiplication. |
| // 256-bit Montgomery form for 64 and 32-bit. Field operations are generated by |
| // Fiat, which lives in //third_party/fiat. |
| |
| #include <openssl/base.h> |
| |
| #include <openssl/bn.h> |
| #include <openssl/ec.h> |
| #include <openssl/err.h> |
| #include <openssl/mem.h> |
| |
| #include <assert.h> |
| #include <string.h> |
| |
| #include <iterator> |
| |
| #include "../../internal.h" |
| #include "../delocate.h" |
| #include "./internal.h" |
| |
| #include "../../../third_party/fiat/p256_field.c.inc" |
| #include "../../../third_party/fiat/p256_point.br.c.inc" |
| |
| // utility functions, handwritten |
| |
| #if defined(OPENSSL_64_BIT) |
| #define FIAT_P256_NLIMBS 4 |
| typedef uint64_t fiat_p256_limb_t; |
| typedef uint64_t fiat_p256_felem[FIAT_P256_NLIMBS]; |
| static const fiat_p256_felem fiat_p256_one = {0x1, 0xffffffff00000000, |
| 0xffffffffffffffff, 0xfffffffe}; |
| #else // 64BIT; else 32BIT |
| #define FIAT_P256_NLIMBS 8 |
| typedef uint32_t fiat_p256_limb_t; |
| typedef uint32_t fiat_p256_felem[FIAT_P256_NLIMBS]; |
| static const fiat_p256_felem fiat_p256_one = { |
| 0x1, 0x0, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffe, 0x0}; |
| #endif // 64BIT |
| |
| |
| static void fiat_p256_copy(fiat_p256_limb_t out[FIAT_P256_NLIMBS], |
| const fiat_p256_limb_t in1[FIAT_P256_NLIMBS]) { |
| for (size_t i = 0; i < FIAT_P256_NLIMBS; i++) { |
| out[i] = in1[i]; |
| } |
| } |
| |
| static void fiat_p256_cmovznz(fiat_p256_limb_t out[FIAT_P256_NLIMBS], |
| fiat_p256_limb_t t, |
| const fiat_p256_limb_t z[FIAT_P256_NLIMBS], |
| const fiat_p256_limb_t nz[FIAT_P256_NLIMBS]) { |
| fiat_p256_selectznz(out, !!t, z, nz); |
| } |
| |
| static void fiat_p256_from_words(fiat_p256_felem out, |
| const BN_ULONG in[32 / sizeof(BN_ULONG)]) { |
| // Typically, |BN_ULONG| and |fiat_p256_limb_t| will be the same type, but on |
| // 64-bit platforms without |uint128_t|, they are different. However, on |
| // little-endian systems, |uint64_t[4]| and |uint32_t[8]| have the same |
| // layout. |
| OPENSSL_memcpy(out, in, 32); |
| } |
| |
| static void fiat_p256_from_generic(fiat_p256_felem out, const EC_FELEM *in) { |
| fiat_p256_from_words(out, in->words); |
| } |
| |
| static void fiat_p256_to_generic(EC_FELEM *out, const fiat_p256_felem in) { |
| // See |fiat_p256_from_words|. |
| OPENSSL_memcpy(out->words, in, 32); |
| } |
| |
| // fiat_p256_inv_square calculates |out| = |in|^{-2} |
| // |
| // Based on Fermat's Little Theorem: |
| // a^p = a (mod p) |
| // a^{p-1} = 1 (mod p) |
| // a^{p-3} = a^{-2} (mod p) |
| static void fiat_p256_inv_square(fiat_p256_felem out, |
| const fiat_p256_felem in) { |
| // This implements the addition chain described in |
| // https://briansmith.org/ecc-inversion-addition-chains-01#p256_field_inversion |
| fiat_p256_felem x2, x3, x6, x12, x15, x30, x32; |
| fiat_p256_square(x2, in); // 2^2 - 2^1 |
| fiat_p256_mul(x2, x2, in); // 2^2 - 2^0 |
| |
| fiat_p256_square(x3, x2); // 2^3 - 2^1 |
| fiat_p256_mul(x3, x3, in); // 2^3 - 2^0 |
| |
| fiat_p256_square(x6, x3); |
| for (int i = 1; i < 3; i++) { |
| fiat_p256_square(x6, x6); |
| } // 2^6 - 2^3 |
| fiat_p256_mul(x6, x6, x3); // 2^6 - 2^0 |
| |
| fiat_p256_square(x12, x6); |
| for (int i = 1; i < 6; i++) { |
| fiat_p256_square(x12, x12); |
| } // 2^12 - 2^6 |
| fiat_p256_mul(x12, x12, x6); // 2^12 - 2^0 |
| |
| fiat_p256_square(x15, x12); |
| for (int i = 1; i < 3; i++) { |
| fiat_p256_square(x15, x15); |
| } // 2^15 - 2^3 |
| fiat_p256_mul(x15, x15, x3); // 2^15 - 2^0 |
| |
| fiat_p256_square(x30, x15); |
| for (int i = 1; i < 15; i++) { |
| fiat_p256_square(x30, x30); |
| } // 2^30 - 2^15 |
| fiat_p256_mul(x30, x30, x15); // 2^30 - 2^0 |
| |
| fiat_p256_square(x32, x30); |
| fiat_p256_square(x32, x32); // 2^32 - 2^2 |
| fiat_p256_mul(x32, x32, x2); // 2^32 - 2^0 |
| |
| fiat_p256_felem ret; |
| fiat_p256_square(ret, x32); |
| for (int i = 1; i < 31 + 1; i++) { |
| fiat_p256_square(ret, ret); |
| } // 2^64 - 2^32 |
| fiat_p256_mul(ret, ret, in); // 2^64 - 2^32 + 2^0 |
| |
| for (int i = 0; i < 96 + 32; i++) { |
| fiat_p256_square(ret, ret); |
| } // 2^192 - 2^160 + 2^128 |
| fiat_p256_mul(ret, ret, x32); // 2^192 - 2^160 + 2^128 + 2^32 - 2^0 |
| |
| for (int i = 0; i < 32; i++) { |
| fiat_p256_square(ret, ret); |
| } // 2^224 - 2^192 + 2^160 + 2^64 - 2^32 |
| fiat_p256_mul(ret, ret, x32); // 2^224 - 2^192 + 2^160 + 2^64 - 2^0 |
| |
| for (int i = 0; i < 30; i++) { |
| fiat_p256_square(ret, ret); |
| } // 2^254 - 2^222 + 2^190 + 2^94 - 2^30 |
| fiat_p256_mul(ret, ret, x30); // 2^254 - 2^222 + 2^190 + 2^94 - 2^0 |
| |
| fiat_p256_square(ret, ret); |
| fiat_p256_square(out, ret); // 2^256 - 2^224 + 2^192 + 2^96 - 2^2 |
| } |
| |
| // Group operations |
| // ---------------- |
| // |
| // Building on top of the field operations we have the operations on the |
| // elliptic curve group itself. Points on the curve are represented in Jacobian |
| // coordinates. |
| |
| static void fiat_p256_point_double(fiat_p256_felem x_out, fiat_p256_felem y_out, |
| fiat_p256_felem z_out, |
| const fiat_p256_felem x_in, |
| const fiat_p256_felem y_in, |
| const fiat_p256_felem z_in) { |
| uint8_t out[3*32], in[3*32]; |
| static_assert(sizeof(fiat_p256_felem) == 32); |
| OPENSSL_memcpy(&in[0], x_in, 32); |
| OPENSSL_memcpy(&in[32], y_in, 32); |
| OPENSSL_memcpy(&in[64], z_in, 32); |
| p256_point_double((br_word_t)out, (br_word_t)in); |
| OPENSSL_memcpy(x_out, &out[0], 32); |
| OPENSSL_memcpy(y_out, &out[32], 32); |
| OPENSSL_memcpy(z_out, &out[64], 32); |
| } |
| |
| static void fiat_p256_point_add(fiat_p256_felem x3, fiat_p256_felem y3, |
| fiat_p256_felem z3, const fiat_p256_felem x1, |
| const fiat_p256_felem y1, |
| const fiat_p256_felem z1, |
| const fiat_p256_felem x2, |
| const fiat_p256_felem y2, |
| const fiat_p256_felem z2) { |
| uint8_t out[3 * 32], in1[3 * 32], in2[3 * 32]; |
| static_assert(sizeof(fiat_p256_felem) == 32); |
| OPENSSL_memcpy(&in1[0], x1, 32); |
| OPENSSL_memcpy(&in1[32], y1, 32); |
| OPENSSL_memcpy(&in1[64], z1, 32); |
| OPENSSL_memcpy(&in2[0], x2, 32); |
| OPENSSL_memcpy(&in2[32], y2, 32); |
| OPENSSL_memcpy(&in2[64], z2, 32); |
| p256_point_add_vartime_if_doubling((br_word_t)out, (br_word_t)in1, |
| (br_word_t)in2); |
| OPENSSL_memcpy(x3, &out[0], 32); |
| OPENSSL_memcpy(y3, &out[32], 32); |
| OPENSSL_memcpy(z3, &out[64], 32); |
| } |
| #include "./p256_table.h" |
| |
| // fiat_p256_select_point_affine selects the |idx-1|th point from a |
| // precomputation table and copies it to out. If |idx| is zero, the output is |
| // the point at infinity. |
| static void fiat_p256_select_point_affine( |
| const fiat_p256_limb_t idx, size_t size, |
| const fiat_p256_felem pre_comp[/*size*/][2], fiat_p256_felem out[3]) { |
| OPENSSL_memset(out, 0, sizeof(fiat_p256_felem) * 3); |
| for (size_t i = 0; i < size; i++) { |
| fiat_p256_limb_t mismatch = i ^ (idx - 1); |
| fiat_p256_cmovznz(out[0], mismatch, pre_comp[i][0], out[0]); |
| fiat_p256_cmovznz(out[1], mismatch, pre_comp[i][1], out[1]); |
| } |
| fiat_p256_cmovznz(out[2], idx, out[2], fiat_p256_one); |
| } |
| |
| // fiat_p256_select_point selects the |idx|th point from a precomputation table |
| // and copies it to out. |
| static void fiat_p256_select_point(const fiat_p256_limb_t idx, size_t size, |
| const fiat_p256_felem pre_comp[/*size*/][3], |
| fiat_p256_felem out[3]) { |
| OPENSSL_memset(out, 0, sizeof(fiat_p256_felem) * 3); |
| for (size_t i = 0; i < size; i++) { |
| fiat_p256_limb_t mismatch = i ^ idx; |
| fiat_p256_cmovznz(out[0], mismatch, pre_comp[i][0], out[0]); |
| fiat_p256_cmovznz(out[1], mismatch, pre_comp[i][1], out[1]); |
| fiat_p256_cmovznz(out[2], mismatch, pre_comp[i][2], out[2]); |
| } |
| } |
| |
| // fiat_p256_get_bit returns the |i|th bit in |in|. |
| static crypto_word_t fiat_p256_get_bit(const EC_SCALAR *in, int i) { |
| if (i < 0 || i >= 256) { |
| return 0; |
| } |
| #if defined(OPENSSL_64_BIT) |
| static_assert(sizeof(BN_ULONG) == 8, "BN_ULONG was not 64-bit"); |
| return (in->words[i >> 6] >> (i & 63)) & 1; |
| #else |
| static_assert(sizeof(BN_ULONG) == 4, "BN_ULONG was not 32-bit"); |
| return (in->words[i >> 5] >> (i & 31)) & 1; |
| #endif |
| } |
| |
| // OPENSSL EC_METHOD FUNCTIONS |
| |
| // Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = |
| // (X/Z^2, Y/Z^3). |
| static int ec_GFp_nistp256_point_get_affine_coordinates( |
| const EC_GROUP *group, const EC_JACOBIAN *point, EC_FELEM *x_out, |
| EC_FELEM *y_out) { |
| if (constant_time_declassify_int( |
| ec_GFp_simple_is_at_infinity(group, point))) { |
| OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY); |
| return 0; |
| } |
| |
| fiat_p256_felem z1, z2; |
| fiat_p256_from_generic(z1, &point->Z); |
| fiat_p256_inv_square(z2, z1); |
| |
| if (x_out != NULL) { |
| fiat_p256_felem x; |
| fiat_p256_from_generic(x, &point->X); |
| fiat_p256_mul(x, x, z2); |
| fiat_p256_to_generic(x_out, x); |
| } |
| |
| if (y_out != NULL) { |
| fiat_p256_felem y; |
| fiat_p256_from_generic(y, &point->Y); |
| fiat_p256_square(z2, z2); // z^-4 |
| fiat_p256_mul(y, y, z1); // y * z |
| fiat_p256_mul(y, y, z2); // y * z^-3 |
| fiat_p256_to_generic(y_out, y); |
| } |
| |
| return 1; |
| } |
| |
| static void ec_GFp_nistp256_add(const EC_GROUP *group, EC_JACOBIAN *r, |
| const EC_JACOBIAN *a, const EC_JACOBIAN *b) { |
| fiat_p256_felem x1, y1, z1, x2, y2, z2; |
| fiat_p256_from_generic(x1, &a->X); |
| fiat_p256_from_generic(y1, &a->Y); |
| fiat_p256_from_generic(z1, &a->Z); |
| fiat_p256_from_generic(x2, &b->X); |
| fiat_p256_from_generic(y2, &b->Y); |
| fiat_p256_from_generic(z2, &b->Z); |
| fiat_p256_point_add(x1, y1, z1, x1, y1, z1, x2, y2, z2); |
| fiat_p256_to_generic(&r->X, x1); |
| fiat_p256_to_generic(&r->Y, y1); |
| fiat_p256_to_generic(&r->Z, z1); |
| } |
| |
| static void ec_GFp_nistp256_dbl(const EC_GROUP *group, EC_JACOBIAN *r, |
| const EC_JACOBIAN *a) { |
| fiat_p256_felem x, y, z; |
| fiat_p256_from_generic(x, &a->X); |
| fiat_p256_from_generic(y, &a->Y); |
| fiat_p256_from_generic(z, &a->Z); |
| fiat_p256_point_double(x, y, z, x, y, z); |
| fiat_p256_to_generic(&r->X, x); |
| fiat_p256_to_generic(&r->Y, y); |
| fiat_p256_to_generic(&r->Z, z); |
| } |
| |
| static void ec_GFp_nistp256_point_mul(const EC_GROUP *group, EC_JACOBIAN *r, |
| const EC_JACOBIAN *p, |
| const EC_SCALAR *scalar) { |
| fiat_p256_felem p_pre_comp[17][3]; |
| OPENSSL_memset(&p_pre_comp, 0, sizeof(p_pre_comp)); |
| // Precompute multiples. |
| fiat_p256_from_generic(p_pre_comp[1][0], &p->X); |
| fiat_p256_from_generic(p_pre_comp[1][1], &p->Y); |
| fiat_p256_from_generic(p_pre_comp[1][2], &p->Z); |
| for (size_t j = 2; j <= 16; ++j) { |
| if (j & 1) { |
| fiat_p256_point_add(p_pre_comp[j][0], p_pre_comp[j][1], p_pre_comp[j][2], |
| p_pre_comp[1][0], p_pre_comp[1][1], p_pre_comp[1][2], |
| p_pre_comp[j - 1][0], p_pre_comp[j - 1][1], |
| p_pre_comp[j - 1][2]); |
| } else { |
| fiat_p256_point_double(p_pre_comp[j][0], p_pre_comp[j][1], |
| p_pre_comp[j][2], p_pre_comp[j / 2][0], |
| p_pre_comp[j / 2][1], p_pre_comp[j / 2][2]); |
| } |
| } |
| |
| // Set nq to the point at infinity. |
| fiat_p256_felem nq[3] = {{0}, {0}, {0}}, ftmp, tmp[3]; |
| |
| // Loop over |scalar| msb-to-lsb, incorporating |p_pre_comp| every 5th round. |
| int skip = 1; // Save two point operations in the first round. |
| for (size_t i = 255; i < 256; i--) { |
| // double |
| if (!skip) { |
| fiat_p256_point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); |
| } |
| |
| // do other additions every 5 doublings |
| if (i % 5 == 0) { |
| crypto_word_t bits = fiat_p256_get_bit(scalar, i + 4) << 5; |
| bits |= fiat_p256_get_bit(scalar, i + 3) << 4; |
| bits |= fiat_p256_get_bit(scalar, i + 2) << 3; |
| bits |= fiat_p256_get_bit(scalar, i + 1) << 2; |
| bits |= fiat_p256_get_bit(scalar, i) << 1; |
| bits |= fiat_p256_get_bit(scalar, i - 1); |
| crypto_word_t sign, digit; |
| ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); |
| |
| // select the point to add or subtract, in constant time. |
| fiat_p256_select_point((fiat_p256_limb_t)digit, 17, |
| (const fiat_p256_felem(*)[3])p_pre_comp, tmp); |
| fiat_p256_opp(ftmp, tmp[1]); // (X, -Y, Z) is the negative point. |
| fiat_p256_cmovznz(tmp[1], (fiat_p256_limb_t)sign, tmp[1], ftmp); |
| |
| if (!skip) { |
| fiat_p256_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], tmp[0], |
| tmp[1], tmp[2]); |
| } else { |
| fiat_p256_copy(nq[0], tmp[0]); |
| fiat_p256_copy(nq[1], tmp[1]); |
| fiat_p256_copy(nq[2], tmp[2]); |
| skip = 0; |
| } |
| } |
| } |
| |
| fiat_p256_to_generic(&r->X, nq[0]); |
| fiat_p256_to_generic(&r->Y, nq[1]); |
| fiat_p256_to_generic(&r->Z, nq[2]); |
| } |
| |
| static void ec_GFp_nistp256_point_mul_base(const EC_GROUP *group, |
| EC_JACOBIAN *r, |
| const EC_SCALAR *scalar) { |
| // Set nq to the point at infinity. |
| fiat_p256_felem nq[3] = {{0}, {0}, {0}}, tmp[3]; |
| |
| int skip = 1; // Save two point operations in the first round. |
| for (size_t i = 31; i < 32; i--) { |
| if (!skip) { |
| fiat_p256_point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); |
| } |
| |
| // First, look 32 bits upwards. |
| crypto_word_t bits = fiat_p256_get_bit(scalar, i + 224) << 3; |
| bits |= fiat_p256_get_bit(scalar, i + 160) << 2; |
| bits |= fiat_p256_get_bit(scalar, i + 96) << 1; |
| bits |= fiat_p256_get_bit(scalar, i + 32); |
| // Select the point to add, in constant time. |
| fiat_p256_select_point_affine((fiat_p256_limb_t)bits, 15, |
| fiat_p256_g_pre_comp[1], tmp); |
| |
| if (!skip) { |
| fiat_p256_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], tmp[0], |
| tmp[1], tmp[2]); |
| } else { |
| fiat_p256_copy(nq[0], tmp[0]); |
| fiat_p256_copy(nq[1], tmp[1]); |
| fiat_p256_copy(nq[2], tmp[2]); |
| skip = 0; |
| } |
| |
| // Second, look at the current position. |
| bits = fiat_p256_get_bit(scalar, i + 192) << 3; |
| bits |= fiat_p256_get_bit(scalar, i + 128) << 2; |
| bits |= fiat_p256_get_bit(scalar, i + 64) << 1; |
| bits |= fiat_p256_get_bit(scalar, i); |
| // Select the point to add, in constant time. |
| fiat_p256_select_point_affine((fiat_p256_limb_t)bits, 15, |
| fiat_p256_g_pre_comp[0], tmp); |
| fiat_p256_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], tmp[0], |
| tmp[1], tmp[2]); |
| } |
| |
| fiat_p256_to_generic(&r->X, nq[0]); |
| fiat_p256_to_generic(&r->Y, nq[1]); |
| fiat_p256_to_generic(&r->Z, nq[2]); |
| } |
| |
| static void ec_GFp_nistp256_point_mul_public(const EC_GROUP *group, |
| EC_JACOBIAN *r, |
| const EC_SCALAR *g_scalar, |
| const EC_JACOBIAN *p, |
| const EC_SCALAR *p_scalar) { |
| #define P256_WSIZE_PUBLIC 4 |
| // Precompute multiples of |p|. p_pre_comp[i] is (2*i+1) * |p|. |
| fiat_p256_felem p_pre_comp[1 << (P256_WSIZE_PUBLIC - 1)][3]; |
| fiat_p256_from_generic(p_pre_comp[0][0], &p->X); |
| fiat_p256_from_generic(p_pre_comp[0][1], &p->Y); |
| fiat_p256_from_generic(p_pre_comp[0][2], &p->Z); |
| fiat_p256_felem p2[3]; |
| fiat_p256_point_double(p2[0], p2[1], p2[2], p_pre_comp[0][0], |
| p_pre_comp[0][1], p_pre_comp[0][2]); |
| for (size_t i = 1; i < std::size(p_pre_comp); i++) { |
| fiat_p256_point_add(p_pre_comp[i][0], p_pre_comp[i][1], p_pre_comp[i][2], |
| p_pre_comp[i - 1][0], p_pre_comp[i - 1][1], |
| p_pre_comp[i - 1][2], p2[0], p2[1], p2[2]); |
| } |
| |
| // Set up the coefficients for |p_scalar|. |
| int8_t p_wNAF[257]; |
| ec_compute_wNAF(group, p_wNAF, p_scalar, 256, P256_WSIZE_PUBLIC); |
| |
| // Set |ret| to the point at infinity. |
| int skip = 1; // Save some point operations. |
| fiat_p256_felem ret[3] = {{0}, {0}, {0}}; |
| for (int i = 256; i >= 0; i--) { |
| if (!skip) { |
| fiat_p256_point_double(ret[0], ret[1], ret[2], ret[0], ret[1], ret[2]); |
| } |
| |
| // For the |g_scalar|, we use the precomputed table without the |
| // constant-time lookup. |
| if (i <= 31) { |
| // First, look 32 bits upwards. |
| crypto_word_t bits = fiat_p256_get_bit(g_scalar, i + 224) << 3; |
| bits |= fiat_p256_get_bit(g_scalar, i + 160) << 2; |
| bits |= fiat_p256_get_bit(g_scalar, i + 96) << 1; |
| bits |= fiat_p256_get_bit(g_scalar, i + 32); |
| if (bits != 0) { |
| size_t index = (size_t)(bits - 1); |
| fiat_p256_point_add(ret[0], ret[1], ret[2], ret[0], ret[1], ret[2], |
| fiat_p256_g_pre_comp[1][index][0], |
| fiat_p256_g_pre_comp[1][index][1], fiat_p256_one); |
| skip = 0; |
| } |
| |
| // Second, look at the current position. |
| bits = fiat_p256_get_bit(g_scalar, i + 192) << 3; |
| bits |= fiat_p256_get_bit(g_scalar, i + 128) << 2; |
| bits |= fiat_p256_get_bit(g_scalar, i + 64) << 1; |
| bits |= fiat_p256_get_bit(g_scalar, i); |
| if (bits != 0) { |
| size_t index = (size_t)(bits - 1); |
| fiat_p256_point_add(ret[0], ret[1], ret[2], ret[0], ret[1], ret[2], |
| fiat_p256_g_pre_comp[0][index][0], |
| fiat_p256_g_pre_comp[0][index][1], fiat_p256_one); |
| skip = 0; |
| } |
| } |
| |
| int digit = p_wNAF[i]; |
| if (digit != 0) { |
| assert(digit & 1); |
| size_t idx = (size_t)(digit < 0 ? (-digit) >> 1 : digit >> 1); |
| fiat_p256_felem *y = &p_pre_comp[idx][1], tmp; |
| if (digit < 0) { |
| fiat_p256_opp(tmp, p_pre_comp[idx][1]); |
| y = &tmp; |
| } |
| if (!skip) { |
| fiat_p256_point_add(ret[0], ret[1], ret[2], ret[0], ret[1], ret[2], |
| p_pre_comp[idx][0], *y, p_pre_comp[idx][2]); |
| } else { |
| fiat_p256_copy(ret[0], p_pre_comp[idx][0]); |
| fiat_p256_copy(ret[1], *y); |
| fiat_p256_copy(ret[2], p_pre_comp[idx][2]); |
| skip = 0; |
| } |
| } |
| } |
| |
| fiat_p256_to_generic(&r->X, ret[0]); |
| fiat_p256_to_generic(&r->Y, ret[1]); |
| fiat_p256_to_generic(&r->Z, ret[2]); |
| } |
| |
| static int ec_GFp_nistp256_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; |
| } |
| |
| // 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. |
| fiat_p256_felem Z2_mont; |
| fiat_p256_from_generic(Z2_mont, &p->Z); |
| fiat_p256_mul(Z2_mont, Z2_mont, Z2_mont); |
| |
| fiat_p256_felem r_Z2; |
| fiat_p256_from_words(r_Z2, r->words); // r < order < p, so this is valid. |
| fiat_p256_mul(r_Z2, r_Z2, Z2_mont); |
| |
| fiat_p256_felem X; |
| fiat_p256_from_generic(X, &p->X); |
| fiat_p256_from_montgomery(X, X); |
| |
| 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. |
| assert(group->field.N.width == group->order.N.width); |
| EC_FELEM tmp; |
| BN_ULONG carry = |
| bn_add_words(tmp.words, r->words, group->order.N.d, group->field.N.width); |
| if (carry == 0 && |
| bn_less_than_words(tmp.words, group->field.N.d, group->field.N.width)) { |
| fiat_p256_from_generic(r_Z2, &tmp); |
| fiat_p256_mul(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_nistp256_method) { |
| out->point_get_affine_coordinates = |
| ec_GFp_nistp256_point_get_affine_coordinates; |
| out->add = ec_GFp_nistp256_add; |
| out->dbl = ec_GFp_nistp256_dbl; |
| out->mul = ec_GFp_nistp256_point_mul; |
| out->mul_base = ec_GFp_nistp256_point_mul_base; |
| out->mul_public = ec_GFp_nistp256_point_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 = ec_simple_scalar_inv0_montgomery; |
| out->scalar_to_montgomery_inv_vartime = |
| ec_simple_scalar_to_montgomery_inv_vartime; |
| out->cmp_x_coordinate = ec_GFp_nistp256_cmp_x_coordinate; |
| } |
