296 lines
10 KiB
C
296 lines
10 KiB
C
/* 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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#if default_RNG_defined
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static uECC_RNG_Function g_rng_function = &default_CSPRNG;
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#else
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static uECC_RNG_Function g_rng_function = 0;
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#endif
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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 (!g_rng_function) {
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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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