| /* 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" |
| |
| |
| void ec_GFp_mont_mul(const EC_GROUP *group, EC_JACOBIAN *r, |
| const EC_JACOBIAN *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_JACOBIAN 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_JACOBIAN tmp; |
| OPENSSL_memset(&tmp, 0, sizeof(EC_JACOBIAN)); |
| for (size_t j = 0; j < OPENSSL_ARRAY_SIZE(precomp); j++) { |
| BN_ULONG mask = constant_time_eq_w(j, window); |
| ec_point_select(group, &tmp, mask, &precomp[j], &tmp); |
| } |
| |
| 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_base(const EC_GROUP *group, EC_JACOBIAN *r, |
| const EC_SCALAR *scalar) { |
| ec_GFp_mont_mul(group, r, &group->generator->raw, scalar); |
| } |
| |
| static void ec_GFp_mont_batch_precomp(const EC_GROUP *group, EC_JACOBIAN *out, |
| size_t num, const EC_JACOBIAN *p) { |
| assert(num > 1); |
| ec_GFp_simple_point_set_to_infinity(group, &out[0]); |
| ec_GFp_simple_point_copy(&out[1], p); |
| for (size_t j = 2; j < num; j++) { |
| if (j & 1) { |
| ec_GFp_mont_add(group, &out[j], &out[1], &out[j - 1]); |
| } else { |
| ec_GFp_mont_dbl(group, &out[j], &out[j / 2]); |
| } |
| } |
| } |
| |
| static void ec_GFp_mont_batch_get_window(const EC_GROUP *group, |
| EC_JACOBIAN *out, |
| const EC_JACOBIAN precomp[17], |
| const EC_SCALAR *scalar, unsigned i) { |
| const size_t width = group->order.width; |
| uint8_t window = bn_is_bit_set_words(scalar->words, width, i + 4) << 5; |
| window |= bn_is_bit_set_words(scalar->words, width, i + 3) << 4; |
| window |= bn_is_bit_set_words(scalar->words, width, i + 2) << 3; |
| window |= bn_is_bit_set_words(scalar->words, width, i + 1) << 2; |
| window |= bn_is_bit_set_words(scalar->words, width, i) << 1; |
| if (i > 0) { |
| window |= bn_is_bit_set_words(scalar->words, width, i - 1); |
| } |
| crypto_word_t sign, digit; |
| ec_GFp_nistp_recode_scalar_bits(&sign, &digit, window); |
| |
| // Select the entry in constant-time. |
| OPENSSL_memset(out, 0, sizeof(EC_JACOBIAN)); |
| for (size_t j = 0; j < 17; j++) { |
| BN_ULONG mask = constant_time_eq_w(j, digit); |
| ec_point_select(group, out, mask, &precomp[j], out); |
| } |
| |
| // Negate if necessary. |
| EC_FELEM neg_Y; |
| ec_felem_neg(group, &neg_Y, &out->Y); |
| crypto_word_t sign_mask = sign; |
| sign_mask = 0u - sign_mask; |
| ec_felem_select(group, &out->Y, sign_mask, &neg_Y, &out->Y); |
| } |
| |
| void ec_GFp_mont_mul_batch(const EC_GROUP *group, EC_JACOBIAN *r, |
| const EC_JACOBIAN *p0, const EC_SCALAR *scalar0, |
| const EC_JACOBIAN *p1, const EC_SCALAR *scalar1, |
| const EC_JACOBIAN *p2, const EC_SCALAR *scalar2) { |
| EC_JACOBIAN precomp[3][17]; |
| ec_GFp_mont_batch_precomp(group, precomp[0], 17, p0); |
| ec_GFp_mont_batch_precomp(group, precomp[1], 17, p1); |
| if (p2 != NULL) { |
| ec_GFp_mont_batch_precomp(group, precomp[2], 17, p2); |
| } |
| |
| // Divide bits in |scalar| into windows. |
| unsigned bits = BN_num_bits(&group->order); |
| int r_is_at_infinity = 1; |
| for (unsigned i = bits; i <= bits; i--) { |
| if (!r_is_at_infinity) { |
| ec_GFp_mont_dbl(group, r, r); |
| } |
| if (i % 5 == 0) { |
| EC_JACOBIAN tmp; |
| ec_GFp_mont_batch_get_window(group, &tmp, precomp[0], scalar0, i); |
| 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); |
| } |
| |
| ec_GFp_mont_batch_get_window(group, &tmp, precomp[1], scalar1, i); |
| ec_GFp_mont_add(group, r, r, &tmp); |
| |
| if (p2 != NULL) { |
| ec_GFp_mont_batch_get_window(group, &tmp, precomp[2], scalar2, i); |
| ec_GFp_mont_add(group, r, r, &tmp); |
| } |
| } |
| } |
| if (r_is_at_infinity) { |
| ec_GFp_simple_point_set_to_infinity(group, r); |
| } |
| } |
| |
| static unsigned ec_GFp_mont_comb_stride(const EC_GROUP *group) { |
| return (BN_num_bits(&group->field) + EC_MONT_PRECOMP_COMB_SIZE - 1) / |
| EC_MONT_PRECOMP_COMB_SIZE; |
| } |
| |
| int ec_GFp_mont_init_precomp(const EC_GROUP *group, EC_PRECOMP *out, |
| const EC_JACOBIAN *p) { |
| // comb[i - 1] stores the ith element of the comb. That is, if i is |
| // b4 * 2^4 + b3 * 2^3 + ... + b0 * 2^0, it stores k * |p|, where k is |
| // b4 * 2^(4*stride) + b3 * 2^(3*stride) + ... + b0 * 2^(0*stride). stride |
| // here is |ec_GFp_mont_comb_stride|. We store at index i - 1 because the 0th |
| // comb entry is always infinity. |
| EC_JACOBIAN comb[(1 << EC_MONT_PRECOMP_COMB_SIZE) - 1]; |
| unsigned stride = ec_GFp_mont_comb_stride(group); |
| |
| // We compute the comb sequentially by the highest set bit. Initially, all |
| // entries up to 2^0 are filled. |
| comb[(1 << 0) - 1] = *p; |
| for (unsigned i = 1; i < EC_MONT_PRECOMP_COMB_SIZE; i++) { |
| // Compute entry 2^i by doubling the entry for 2^(i-1) |stride| times. |
| unsigned bit = 1 << i; |
| ec_GFp_mont_dbl(group, &comb[bit - 1], &comb[bit / 2 - 1]); |
| for (unsigned j = 1; j < stride; j++) { |
| ec_GFp_mont_dbl(group, &comb[bit - 1], &comb[bit - 1]); |
| } |
| // Compute entries from 2^i + 1 to 2^i + (2^i - 1) by adding entry 2^i to |
| // a previous entry. |
| for (unsigned j = 1; j < bit; j++) { |
| ec_GFp_mont_add(group, &comb[bit + j - 1], &comb[bit - 1], &comb[j - 1]); |
| } |
| } |
| |
| // Store the comb in affine coordinates to shrink the table. (This reduces |
| // cache pressure and makes the constant-time selects faster.) |
| static_assert(OPENSSL_ARRAY_SIZE(comb) == OPENSSL_ARRAY_SIZE(out->comb), |
| "comb sizes did not match"); |
| return ec_jacobian_to_affine_batch(group, out->comb, comb, |
| OPENSSL_ARRAY_SIZE(comb)); |
| } |
| |
| static void ec_GFp_mont_get_comb_window(const EC_GROUP *group, |
| EC_JACOBIAN *out, |
| const EC_PRECOMP *precomp, |
| const EC_SCALAR *scalar, unsigned i) { |
| const size_t width = group->order.width; |
| unsigned stride = ec_GFp_mont_comb_stride(group); |
| // Select the bits corresponding to the comb shifted up by |i|. |
| unsigned window = 0; |
| for (unsigned j = 0; j < EC_MONT_PRECOMP_COMB_SIZE; j++) { |
| window |= bn_is_bit_set_words(scalar->words, width, j * stride + i) |
| << j; |
| } |
| |
| // Select precomp->comb[window - 1]. If |window| is zero, |match| will always |
| // be zero, which will leave |out| at infinity. |
| OPENSSL_memset(out, 0, sizeof(EC_JACOBIAN)); |
| for (unsigned j = 0; j < OPENSSL_ARRAY_SIZE(precomp->comb); j++) { |
| BN_ULONG match = constant_time_eq_w(window, j + 1); |
| ec_felem_select(group, &out->X, match, &precomp->comb[j].X, &out->X); |
| ec_felem_select(group, &out->Y, match, &precomp->comb[j].Y, &out->Y); |
| } |
| BN_ULONG is_infinity = constant_time_is_zero_w(window); |
| ec_felem_select(group, &out->Z, is_infinity, &out->Z, &group->one); |
| } |
| |
| void ec_GFp_mont_mul_precomp(const EC_GROUP *group, EC_JACOBIAN *r, |
| const EC_PRECOMP *p0, const EC_SCALAR *scalar0, |
| const EC_PRECOMP *p1, const EC_SCALAR *scalar1, |
| const EC_PRECOMP *p2, const EC_SCALAR *scalar2) { |
| unsigned stride = ec_GFp_mont_comb_stride(group); |
| int r_is_at_infinity = 1; |
| for (unsigned i = stride - 1; i < stride; i--) { |
| if (!r_is_at_infinity) { |
| ec_GFp_mont_dbl(group, r, r); |
| } |
| |
| EC_JACOBIAN tmp; |
| ec_GFp_mont_get_comb_window(group, &tmp, p0, scalar0, i); |
| 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 (p1 != NULL) { |
| ec_GFp_mont_get_comb_window(group, &tmp, p1, scalar1, i); |
| ec_GFp_mont_add(group, r, r, &tmp); |
| } |
| |
| if (p2 != NULL) { |
| ec_GFp_mont_get_comb_window(group, &tmp, p2, scalar2, i); |
| ec_GFp_mont_add(group, r, r, &tmp); |
| } |
| } |
| if (r_is_at_infinity) { |
| ec_GFp_simple_point_set_to_infinity(group, r); |
| } |
| } |
