| /* ec_dsa.c - TinyCrypt implementation of EC-DSA */ |
| |
| /* Copyright (c) 2014, Kenneth MacKay |
| * All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions are met: |
| * * Redistributions of source code must retain the above copyright notice, |
| * this list of conditions and the following disclaimer. |
| * * Redistributions in binary form must reproduce the above copyright notice, |
| * this list of conditions and the following disclaimer in the documentation |
| * and/or other materials provided with the distribution. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE |
| * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| * POSSIBILITY OF SUCH DAMAGE.*/ |
| |
| /* |
| * Copyright (C) 2017 by Intel Corporation, All Rights Reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions are met: |
| * |
| * - Redistributions of source code must retain the above copyright notice, |
| * this list of conditions and the following disclaimer. |
| * |
| * - Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution. |
| * |
| * - Neither the name of Intel Corporation nor the names of its contributors |
| * may be used to endorse or promote products derived from this software |
| * without specific prior written permission. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE |
| * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| * POSSIBILITY OF SUCH DAMAGE. |
| */ |
| |
| #include <tinycrypt/constants.h> |
| #include <tinycrypt/ecc.h> |
| #include <tinycrypt/ecc_dsa.h> |
| |
| #if default_RNG_defined |
| static uECC_RNG_Function g_rng_function = &default_CSPRNG; |
| #else |
| static uECC_RNG_Function g_rng_function = 0; |
| #endif |
| |
| static void bits2int(uECC_word_t *native, const uint8_t *bits, |
| unsigned bits_size, uECC_Curve curve) |
| { |
| unsigned num_n_bytes = BITS_TO_BYTES(curve->num_n_bits); |
| unsigned num_n_words = BITS_TO_WORDS(curve->num_n_bits); |
| int shift; |
| uECC_word_t carry; |
| uECC_word_t *ptr; |
| |
| if (bits_size > num_n_bytes) { |
| bits_size = num_n_bytes; |
| } |
| |
| uECC_vli_clear(native, num_n_words); |
| uECC_vli_bytesToNative(native, bits, bits_size); |
| if (bits_size * 8 <= (unsigned)curve->num_n_bits) { |
| return; |
| } |
| shift = bits_size * 8 - curve->num_n_bits; |
| carry = 0; |
| ptr = native + num_n_words; |
| while (ptr-- > native) { |
| uECC_word_t temp = *ptr; |
| *ptr = (temp >> shift) | carry; |
| carry = temp << (uECC_WORD_BITS - shift); |
| } |
| |
| /* Reduce mod curve_n */ |
| if (uECC_vli_cmp_unsafe(curve->n, native, num_n_words) != 1) { |
| uECC_vli_sub(native, native, curve->n, num_n_words); |
| } |
| } |
| |
| int uECC_sign_with_k(const uint8_t *private_key, const uint8_t *message_hash, |
| unsigned hash_size, uECC_word_t *k, uint8_t *signature, |
| uECC_Curve curve) |
| { |
| |
| uECC_word_t tmp[NUM_ECC_WORDS]; |
| uECC_word_t s[NUM_ECC_WORDS]; |
| uECC_word_t *k2[2] = {tmp, s}; |
| uECC_word_t p[NUM_ECC_WORDS * 2]; |
| uECC_word_t carry; |
| wordcount_t num_words = curve->num_words; |
| wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits); |
| bitcount_t num_n_bits = curve->num_n_bits; |
| |
| /* Make sure 0 < k < curve_n */ |
| if (uECC_vli_isZero(k, num_words) || |
| uECC_vli_cmp(curve->n, k, num_n_words) != 1) { |
| return 0; |
| } |
| |
| carry = regularize_k(k, tmp, s, curve); |
| EccPoint_mult(p, curve->G, k2[!carry], 0, num_n_bits + 1, curve); |
| if (uECC_vli_isZero(p, num_words)) { |
| return 0; |
| } |
| |
| /* If an RNG function was specified, get a random number |
| to prevent side channel analysis of k. */ |
| if (!g_rng_function) { |
| uECC_vli_clear(tmp, num_n_words); |
| tmp[0] = 1; |
| } |
| else if (!uECC_generate_random_int(tmp, curve->n, num_n_words)) { |
| return 0; |
| } |
| |
| /* Prevent side channel analysis of uECC_vli_modInv() to determine |
| bits of k / the private key by premultiplying by a random number */ |
| uECC_vli_modMult(k, k, tmp, curve->n, num_n_words); /* k' = rand * k */ |
| uECC_vli_modInv(k, k, curve->n, num_n_words); /* k = 1 / k' */ |
| uECC_vli_modMult(k, k, tmp, curve->n, num_n_words); /* k = 1 / k */ |
| |
| uECC_vli_nativeToBytes(signature, curve->num_bytes, p); /* store r */ |
| |
| /* tmp = d: */ |
| uECC_vli_bytesToNative(tmp, private_key, BITS_TO_BYTES(curve->num_n_bits)); |
| |
| s[num_n_words - 1] = 0; |
| uECC_vli_set(s, p, num_words); |
| uECC_vli_modMult(s, tmp, s, curve->n, num_n_words); /* s = r*d */ |
| |
| bits2int(tmp, message_hash, hash_size, curve); |
| uECC_vli_modAdd(s, tmp, s, curve->n, num_n_words); /* s = e + r*d */ |
| uECC_vli_modMult(s, s, k, curve->n, num_n_words); /* s = (e + r*d) / k */ |
| if (uECC_vli_numBits(s, num_n_words) > (bitcount_t)curve->num_bytes * 8) { |
| return 0; |
| } |
| |
| uECC_vli_nativeToBytes(signature + curve->num_bytes, curve->num_bytes, s); |
| return 1; |
| } |
| |
| int uECC_sign(const uint8_t *private_key, const uint8_t *message_hash, |
| unsigned hash_size, uint8_t *signature, uECC_Curve curve) |
| { |
| uECC_word_t _random[2*NUM_ECC_WORDS]; |
| uECC_word_t k[NUM_ECC_WORDS]; |
| uECC_word_t tries; |
| |
| for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) { |
| /* Generating _random uniformly at random: */ |
| uECC_RNG_Function rng_function = uECC_get_rng(); |
| if (!rng_function || |
| !rng_function((uint8_t *)_random, 2*NUM_ECC_WORDS*uECC_WORD_SIZE)) { |
| return 0; |
| } |
| |
| // computing k as modular reduction of _random (see FIPS 186.4 B.5.1): |
| uECC_vli_mmod(k, _random, curve->n, BITS_TO_WORDS(curve->num_n_bits)); |
| |
| if (uECC_sign_with_k(private_key, message_hash, hash_size, k, signature, |
| curve)) { |
| return 1; |
| } |
| } |
| return 0; |
| } |
| |
| static bitcount_t smax(bitcount_t a, bitcount_t b) |
| { |
| return (a > b ? a : b); |
| } |
| |
| int uECC_verify(const uint8_t *public_key, const uint8_t *message_hash, |
| unsigned hash_size, const uint8_t *signature, |
| uECC_Curve curve) |
| { |
| |
| uECC_word_t u1[NUM_ECC_WORDS], u2[NUM_ECC_WORDS]; |
| uECC_word_t z[NUM_ECC_WORDS]; |
| uECC_word_t sum[NUM_ECC_WORDS * 2]; |
| uECC_word_t rx[NUM_ECC_WORDS]; |
| uECC_word_t ry[NUM_ECC_WORDS]; |
| uECC_word_t tx[NUM_ECC_WORDS]; |
| uECC_word_t ty[NUM_ECC_WORDS]; |
| uECC_word_t tz[NUM_ECC_WORDS]; |
| const uECC_word_t *points[4]; |
| const uECC_word_t *point; |
| bitcount_t num_bits; |
| bitcount_t i; |
| |
| uECC_word_t _public[NUM_ECC_WORDS * 2]; |
| uECC_word_t r[NUM_ECC_WORDS], s[NUM_ECC_WORDS]; |
| wordcount_t num_words = curve->num_words; |
| wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits); |
| |
| rx[num_n_words - 1] = 0; |
| r[num_n_words - 1] = 0; |
| s[num_n_words - 1] = 0; |
| |
| uECC_vli_bytesToNative(_public, public_key, curve->num_bytes); |
| uECC_vli_bytesToNative(_public + num_words, public_key + curve->num_bytes, |
| curve->num_bytes); |
| uECC_vli_bytesToNative(r, signature, curve->num_bytes); |
| uECC_vli_bytesToNative(s, signature + curve->num_bytes, curve->num_bytes); |
| |
| /* r, s must not be 0. */ |
| if (uECC_vli_isZero(r, num_words) || uECC_vli_isZero(s, num_words)) { |
| return 0; |
| } |
| |
| /* r, s must be < n. */ |
| if (uECC_vli_cmp_unsafe(curve->n, r, num_n_words) != 1 || |
| uECC_vli_cmp_unsafe(curve->n, s, num_n_words) != 1) { |
| return 0; |
| } |
| |
| /* Calculate u1 and u2. */ |
| uECC_vli_modInv(z, s, curve->n, num_n_words); /* z = 1/s */ |
| u1[num_n_words - 1] = 0; |
| bits2int(u1, message_hash, hash_size, curve); |
| uECC_vli_modMult(u1, u1, z, curve->n, num_n_words); /* u1 = e/s */ |
| uECC_vli_modMult(u2, r, z, curve->n, num_n_words); /* u2 = r/s */ |
| |
| /* Calculate sum = G + Q. */ |
| uECC_vli_set(sum, _public, num_words); |
| uECC_vli_set(sum + num_words, _public + num_words, num_words); |
| uECC_vli_set(tx, curve->G, num_words); |
| uECC_vli_set(ty, curve->G + num_words, num_words); |
| uECC_vli_modSub(z, sum, tx, curve->p, num_words); /* z = x2 - x1 */ |
| XYcZ_add(tx, ty, sum, sum + num_words, curve); |
| uECC_vli_modInv(z, z, curve->p, num_words); /* z = 1/z */ |
| apply_z(sum, sum + num_words, z, curve); |
| |
| /* Use Shamir's trick to calculate u1*G + u2*Q */ |
| points[0] = 0; |
| points[1] = curve->G; |
| points[2] = _public; |
| points[3] = sum; |
| num_bits = smax(uECC_vli_numBits(u1, num_n_words), |
| uECC_vli_numBits(u2, num_n_words)); |
| |
| point = points[(!!uECC_vli_testBit(u1, num_bits - 1)) | |
| ((!!uECC_vli_testBit(u2, num_bits - 1)) << 1)]; |
| uECC_vli_set(rx, point, num_words); |
| uECC_vli_set(ry, point + num_words, num_words); |
| uECC_vli_clear(z, num_words); |
| z[0] = 1; |
| |
| for (i = num_bits - 2; i >= 0; --i) { |
| uECC_word_t index; |
| curve->double_jacobian(rx, ry, z, curve); |
| |
| index = (!!uECC_vli_testBit(u1, i)) | ((!!uECC_vli_testBit(u2, i)) << 1); |
| point = points[index]; |
| if (point) { |
| uECC_vli_set(tx, point, num_words); |
| uECC_vli_set(ty, point + num_words, num_words); |
| apply_z(tx, ty, z, curve); |
| uECC_vli_modSub(tz, rx, tx, curve->p, num_words); /* Z = x2 - x1 */ |
| XYcZ_add(tx, ty, rx, ry, curve); |
| uECC_vli_modMult_fast(z, z, tz, curve); |
| } |
| } |
| |
| uECC_vli_modInv(z, z, curve->p, num_words); /* Z = 1/Z */ |
| apply_z(rx, ry, z, curve); |
| |
| /* v = x1 (mod n) */ |
| if (uECC_vli_cmp_unsafe(curve->n, rx, num_n_words) != 1) { |
| uECC_vli_sub(rx, rx, curve->n, num_n_words); |
| } |
| |
| /* Accept only if v == r. */ |
| return (int)(uECC_vli_equal(rx, r, num_words) == 0); |
| } |
| |