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