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539 lines
20 KiB
C
539 lines
20 KiB
C
/* ecc.h - TinyCrypt interface to common ECC functions */
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/*
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* Copyright (c) 2019, Arm Limited (or its affiliates), All Rights Reserved.
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* SPDX-License-Identifier: BSD-3-Clause
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*/
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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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*
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* * Redistributions of source code must retain the above copyright notice, this
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* list of conditions and the following disclaimer.
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*
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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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/*
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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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/**
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* @file
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* @brief -- Interface to common ECC functions.
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*
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* Overview: This software is an implementation of common functions
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* necessary to elliptic curve cryptography. This implementation uses
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* curve NIST p-256.
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*
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* Security: The curve NIST p-256 provides approximately 128 bits of security.
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*
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*/
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#if defined(MBEDTLS_USE_TINYCRYPT)
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#ifndef __TC_UECC_H__
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#define __TC_UECC_H__
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#include <stdint.h>
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#ifdef __cplusplus
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extern "C" {
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#endif
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/* Word size (4 bytes considering 32-bits architectures) */
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#define uECC_WORD_SIZE 4
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/* setting max number of calls to prng: */
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#ifndef uECC_RNG_MAX_TRIES
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#define uECC_RNG_MAX_TRIES 64
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#endif
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/* defining data types to store word and bit counts: */
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typedef int8_t wordcount_t;
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typedef int16_t bitcount_t;
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/* defining data type for comparison result: */
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typedef int8_t cmpresult_t;
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/* defining data type to store ECC coordinate/point in 32bits words: */
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typedef unsigned int uECC_word_t;
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/* defining data type to store an ECC coordinate/point in 64bits words: */
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typedef uint64_t uECC_dword_t;
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/* defining masks useful for ecc computations: */
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#define HIGH_BIT_SET 0x80000000
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#define uECC_WORD_BITS 32
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#define uECC_WORD_BITS_SHIFT 5
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#define uECC_WORD_BITS_MASK 0x01F
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/* Number of words of 32 bits to represent an element of the the curve p-256: */
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#define NUM_ECC_WORDS 8
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/* Number of bytes to represent an element of the the curve p-256: */
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#define NUM_ECC_BYTES (uECC_WORD_SIZE*NUM_ECC_WORDS)
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#define NUM_ECC_BITS 256
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/* structure that represents an elliptic curve (e.g. p256):*/
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struct uECC_Curve_t;
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typedef const struct uECC_Curve_t * uECC_Curve;
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struct uECC_Curve_t {
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wordcount_t num_words;
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wordcount_t num_bytes;
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bitcount_t num_n_bits;
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uECC_word_t p[NUM_ECC_WORDS];
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uECC_word_t n[NUM_ECC_WORDS];
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uECC_word_t G[NUM_ECC_WORDS * 2];
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uECC_word_t b[NUM_ECC_WORDS];
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void (*double_jacobian)(uECC_word_t * X1, uECC_word_t * Y1, uECC_word_t * Z1,
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uECC_Curve curve);
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void (*x_side)(uECC_word_t *result, const uECC_word_t *x, uECC_Curve curve);
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void (*mmod_fast)(uECC_word_t *result, uECC_word_t *product);
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};
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/*
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* @brief computes doubling of point ion jacobian coordinates, in place.
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* @param X1 IN/OUT -- x coordinate
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* @param Y1 IN/OUT -- y coordinate
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* @param Z1 IN/OUT -- z coordinate
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* @param curve IN -- elliptic curve
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*/
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void double_jacobian_default(uECC_word_t * X1, uECC_word_t * Y1,
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uECC_word_t * Z1, uECC_Curve curve);
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/*
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* @brief Computes x^3 + ax + b. result must not overlap x.
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* @param result OUT -- x^3 + ax + b
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* @param x IN -- value of x
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* @param curve IN -- elliptic curve
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*/
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void x_side_default(uECC_word_t *result, const uECC_word_t *x,
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uECC_Curve curve);
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/*
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* @brief Computes result = product % curve_p
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* from http://www.nsa.gov/ia/_files/nist-routines.pdf
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* @param result OUT -- product % curve_p
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* @param product IN -- value to be reduced mod curve_p
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*/
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void vli_mmod_fast_secp256r1(unsigned int *result, unsigned int *product);
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/* Bytes to words ordering: */
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#define BYTES_TO_WORDS_8(a, b, c, d, e, f, g, h) 0x##d##c##b##a, 0x##h##g##f##e
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#define BYTES_TO_WORDS_4(a, b, c, d) 0x##d##c##b##a
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#define BITS_TO_WORDS(num_bits) \
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((num_bits + ((uECC_WORD_SIZE * 8) - 1)) / (uECC_WORD_SIZE * 8))
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#define BITS_TO_BYTES(num_bits) ((num_bits + 7) / 8)
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/* definition of curve NIST p-256: */
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static const struct uECC_Curve_t curve_secp256r1 = {
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NUM_ECC_WORDS,
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NUM_ECC_BYTES,
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256, /* num_n_bits */ {
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BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF),
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BYTES_TO_WORDS_8(FF, FF, FF, FF, 00, 00, 00, 00),
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BYTES_TO_WORDS_8(00, 00, 00, 00, 00, 00, 00, 00),
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BYTES_TO_WORDS_8(01, 00, 00, 00, FF, FF, FF, FF)
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}, {
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BYTES_TO_WORDS_8(51, 25, 63, FC, C2, CA, B9, F3),
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BYTES_TO_WORDS_8(84, 9E, 17, A7, AD, FA, E6, BC),
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BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF),
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BYTES_TO_WORDS_8(00, 00, 00, 00, FF, FF, FF, FF)
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}, {
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BYTES_TO_WORDS_8(96, C2, 98, D8, 45, 39, A1, F4),
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BYTES_TO_WORDS_8(A0, 33, EB, 2D, 81, 7D, 03, 77),
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BYTES_TO_WORDS_8(F2, 40, A4, 63, E5, E6, BC, F8),
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BYTES_TO_WORDS_8(47, 42, 2C, E1, F2, D1, 17, 6B),
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BYTES_TO_WORDS_8(F5, 51, BF, 37, 68, 40, B6, CB),
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BYTES_TO_WORDS_8(CE, 5E, 31, 6B, 57, 33, CE, 2B),
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BYTES_TO_WORDS_8(16, 9E, 0F, 7C, 4A, EB, E7, 8E),
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BYTES_TO_WORDS_8(9B, 7F, 1A, FE, E2, 42, E3, 4F)
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}, {
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BYTES_TO_WORDS_8(4B, 60, D2, 27, 3E, 3C, CE, 3B),
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BYTES_TO_WORDS_8(F6, B0, 53, CC, B0, 06, 1D, 65),
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BYTES_TO_WORDS_8(BC, 86, 98, 76, 55, BD, EB, B3),
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BYTES_TO_WORDS_8(E7, 93, 3A, AA, D8, 35, C6, 5A)
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},
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&double_jacobian_default,
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&x_side_default,
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&vli_mmod_fast_secp256r1
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};
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uECC_Curve uECC_secp256r1(void);
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/*
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* @brief Generates a random integer in the range 0 < random < top.
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* Both random and top have num_words words.
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* @param random OUT -- random integer in the range 0 < random < top
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* @param top IN -- upper limit
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* @param num_words IN -- number of words
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* @return a random integer in the range 0 < random < top
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*/
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int uECC_generate_random_int(uECC_word_t *random, const uECC_word_t *top,
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wordcount_t num_words);
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/* uECC_RNG_Function type
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* The RNG function should fill 'size' random bytes into 'dest'. It should
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* return 1 if 'dest' was filled with random data, or 0 if the random data could
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* not be generated. The filled-in values should be either truly random, or from
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* a cryptographically-secure PRNG.
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*
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* A correctly functioning RNG function must be set (using uECC_set_rng())
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* before calling uECC_make_key() or uECC_sign().
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*
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* Setting a correctly functioning RNG function improves the resistance to
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* side-channel attacks for uECC_shared_secret().
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*
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* A correct RNG function is set by default. If you are building on another
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* POSIX-compliant system that supports /dev/random or /dev/urandom, you can
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* define uECC_POSIX to use the predefined RNG.
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*/
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typedef int(*uECC_RNG_Function)(uint8_t *dest, unsigned int size);
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/*
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* @brief Set the function that will be used to generate random bytes. The RNG
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* function should return 1 if the random data was generated, or 0 if the random
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* data could not be generated.
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*
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* @note On platforms where there is no predefined RNG function, this must be
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* called before uECC_make_key() or uECC_sign() are used.
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*
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* @param rng_function IN -- function that will be used to generate random bytes
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*/
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void uECC_set_rng(uECC_RNG_Function rng_function);
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/*
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* @brief provides current uECC_RNG_Function.
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* @return Returns the function that will be used to generate random bytes.
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*/
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uECC_RNG_Function uECC_get_rng(void);
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/*
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* @brief computes the size of a private key for the curve in bytes.
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* @param curve IN -- elliptic curve
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* @return size of a private key for the curve in bytes.
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*/
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int uECC_curve_private_key_size(uECC_Curve curve);
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/*
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* @brief computes the size of a public key for the curve in bytes.
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* @param curve IN -- elliptic curve
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* @return the size of a public key for the curve in bytes.
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*/
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int uECC_curve_public_key_size(uECC_Curve curve);
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/*
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* @brief Compute the corresponding public key for a private key.
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* @param private_key IN -- The private key to compute the public key for
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* @param public_key OUT -- Will be filled in with the corresponding public key
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* @param curve
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* @return Returns 1 if key was computed successfully, 0 if an error occurred.
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*/
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int uECC_compute_public_key(const uint8_t *private_key,
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uint8_t *public_key, uECC_Curve curve);
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/*
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* @brief Compute public-key.
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* @return corresponding public-key.
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* @param result OUT -- public-key
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* @param private_key IN -- private-key
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* @param curve IN -- elliptic curve
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*/
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uECC_word_t EccPoint_compute_public_key(uECC_word_t *result,
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uECC_word_t *private_key, uECC_Curve curve);
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/*
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* @brief Point multiplication algorithm using Montgomery's ladder with co-Z
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* coordinates. See http://eprint.iacr.org/2011/338.pdf.
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* Uses scalar regularization and coordinate randomization (if a global RNG
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* function is set) in order to protect against some side channel attacks.
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* @note Result may overlap point.
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* @param result OUT -- returns scalar*point
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* @param point IN -- elliptic curve point
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* @param scalar IN -- scalar
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* @param curve IN -- elliptic curve
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*/
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int EccPoint_mult_safer(uECC_word_t * result, const uECC_word_t * point,
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const uECC_word_t * scalar, uECC_Curve curve);
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/*
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* @brief Constant-time comparison to zero - secure way to compare long integers
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* @param vli IN -- very long integer
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* @param num_words IN -- number of words in the vli
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* @return 1 if vli == 0, 0 otherwise.
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*/
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uECC_word_t uECC_vli_isZero(const uECC_word_t *vli);
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/*
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* @brief Check if 'point' is the point at infinity
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* @param point IN -- elliptic curve point
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* @param curve IN -- elliptic curve
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* @return if 'point' is the point at infinity, 0 otherwise.
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*/
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uECC_word_t EccPoint_isZero(const uECC_word_t *point, uECC_Curve curve);
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/*
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* @brief computes the sign of left - right, in constant time.
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* @param left IN -- left term to be compared
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* @param right IN -- right term to be compared
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* @param num_words IN -- number of words
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* @return the sign of left - right
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*/
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cmpresult_t uECC_vli_cmp(const uECC_word_t *left, const uECC_word_t *right,
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wordcount_t num_words);
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/*
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* @brief computes sign of left - right, not in constant time.
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* @note should not be used if inputs are part of a secret
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* @param left IN -- left term to be compared
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* @param right IN -- right term to be compared
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* @param num_words IN -- number of words
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* @return the sign of left - right
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*/
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cmpresult_t uECC_vli_cmp_unsafe(const uECC_word_t *left, const uECC_word_t *right,
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wordcount_t num_words);
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/*
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* @brief Computes result = (left - right) % mod.
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* @note Assumes that (left < mod) and (right < mod), and that result does not
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* overlap mod.
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* @param result OUT -- (left - right) % mod
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* @param left IN -- leftright term in modular subtraction
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* @param right IN -- right term in modular subtraction
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* @param mod IN -- mod
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* @param num_words IN -- number of words
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*/
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void uECC_vli_modSub(uECC_word_t *result, const uECC_word_t *left,
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const uECC_word_t *right, const uECC_word_t *mod,
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wordcount_t num_words);
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/*
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* @brief Computes P' = (x1', y1', Z3), P + Q = (x3, y3, Z3) or
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* P => P', Q => P + Q
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* @note assumes Input P = (x1, y1, Z), Q = (x2, y2, Z)
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* @param X1 IN -- x coordinate of P
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* @param Y1 IN -- y coordinate of P
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* @param X2 IN -- x coordinate of Q
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* @param Y2 IN -- y coordinate of Q
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* @param curve IN -- elliptic curve
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*/
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void XYcZ_add(uECC_word_t * X1, uECC_word_t * Y1, uECC_word_t * X2,
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uECC_word_t * Y2, uECC_Curve curve);
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/*
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* @brief Computes (x1 * z^2, y1 * z^3)
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* @param X1 IN -- previous x1 coordinate
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* @param Y1 IN -- previous y1 coordinate
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* @param Z IN -- z value
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* @param curve IN -- elliptic curve
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*/
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void apply_z(uECC_word_t * X1, uECC_word_t * Y1, const uECC_word_t * const Z);
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/*
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* @brief Check if bit is set.
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* @return Returns nonzero if bit 'bit' of vli is set.
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* @warning It is assumed that the value provided in 'bit' is within the
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* boundaries of the word-array 'vli'.
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* @note The bit ordering layout assumed for vli is: {31, 30, ..., 0},
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* {63, 62, ..., 32}, {95, 94, ..., 64}, {127, 126,..., 96} for a vli consisting
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* of 4 uECC_word_t elements.
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*/
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uECC_word_t uECC_vli_testBit(const uECC_word_t *vli, bitcount_t bit);
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/*
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* @brief Computes result = product % mod, where product is 2N words long.
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* @param result OUT -- product % mod
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* @param mod IN -- module
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* @param num_words IN -- number of words
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* @warning Currently only designed to work for curve_p or curve_n.
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*/
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void uECC_vli_mmod(uECC_word_t *result, uECC_word_t *product,
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const uECC_word_t *mod, wordcount_t num_words);
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/*
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* @brief Computes modular product (using curve->mmod_fast)
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* @param result OUT -- (left * right) mod % curve_p
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* @param left IN -- left term in product
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* @param right IN -- right term in product
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* @param curve IN -- elliptic curve
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*/
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void uECC_vli_modMult_fast(uECC_word_t *result, const uECC_word_t *left,
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const uECC_word_t *right);
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/*
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* @brief Computes result = left - right.
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* @note Can modify in place.
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* @param result OUT -- left - right
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* @param left IN -- left term in subtraction
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* @param right IN -- right term in subtraction
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* @param num_words IN -- number of words
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* @return borrow
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*/
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uECC_word_t uECC_vli_sub(uECC_word_t *result, const uECC_word_t *left,
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const uECC_word_t *right, wordcount_t num_words);
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/*
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* @brief Constant-time comparison function(secure way to compare long ints)
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* @param left IN -- left term in comparison
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* @param right IN -- right term in comparison
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* @param num_words IN -- number of words
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* @return Returns 0 if left == right, 1 otherwise.
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*/
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uECC_word_t uECC_vli_equal(const uECC_word_t *left, const uECC_word_t *right,
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wordcount_t num_words);
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|
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|
/*
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* @brief Computes (left * right) % mod
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* @param result OUT -- (left * right) % mod
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* @param left IN -- left term in product
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* @param right IN -- right term in product
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* @param mod IN -- mod
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* @param num_words IN -- number of words
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|
*/
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void uECC_vli_modMult(uECC_word_t *result, const uECC_word_t *left,
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const uECC_word_t *right, const uECC_word_t *mod,
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wordcount_t num_words);
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|
|
|
/*
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* @brief Computes (1 / input) % mod
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* @note All VLIs are the same size.
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* @note See "Euclid's GCD to Montgomery Multiplication to the Great Divide"
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* @param result OUT -- (1 / input) % mod
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* @param input IN -- value to be modular inverted
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* @param mod IN -- mod
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|
* @param num_words -- number of words
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|
*/
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void uECC_vli_modInv(uECC_word_t *result, const uECC_word_t *input,
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const uECC_word_t *mod, wordcount_t num_words);
|
|
|
|
/*
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|
* @brief Sets dest = src.
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* @param dest OUT -- destination buffer
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* @param src IN -- origin buffer
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|
* @param num_words IN -- number of words
|
|
*/
|
|
void uECC_vli_set(uECC_word_t *dest, const uECC_word_t *src,
|
|
wordcount_t num_words);
|
|
|
|
/*
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|
* @brief Computes (left + right) % mod.
|
|
* @note Assumes that (left < mod) and right < mod), and that result does not
|
|
* overlap mod.
|
|
* @param result OUT -- (left + right) % mod.
|
|
* @param left IN -- left term in addition
|
|
* @param right IN -- right term in addition
|
|
* @param mod IN -- mod
|
|
* @param num_words IN -- number of words
|
|
*/
|
|
void uECC_vli_modAdd(uECC_word_t *result, const uECC_word_t *left,
|
|
const uECC_word_t *right, const uECC_word_t *mod,
|
|
wordcount_t num_words);
|
|
|
|
/*
|
|
* @brief Counts the number of bits required to represent vli.
|
|
* @param vli IN -- very long integer
|
|
* @param max_words IN -- number of words
|
|
* @return number of bits in given vli
|
|
*/
|
|
bitcount_t uECC_vli_numBits(const uECC_word_t *vli);
|
|
|
|
/*
|
|
* @brief Erases (set to 0) vli
|
|
* @param vli IN -- very long integer
|
|
* @param num_words IN -- number of words
|
|
*/
|
|
void uECC_vli_clear(uECC_word_t *vli);
|
|
|
|
/*
|
|
* @brief check if it is a valid point in the curve
|
|
* @param point IN -- point to be checked
|
|
* @param curve IN -- elliptic curve
|
|
* @return 0 if point is valid
|
|
* @exception returns -1 if it is a point at infinity
|
|
* @exception returns -2 if x or y is smaller than p,
|
|
* @exception returns -3 if y^2 != x^3 + ax + b.
|
|
*/
|
|
int uECC_valid_point(const uECC_word_t *point, uECC_Curve curve);
|
|
|
|
/*
|
|
* @brief Check if a public key is valid.
|
|
* @param public_key IN -- The public key to be checked.
|
|
* @return returns 0 if the public key is valid
|
|
* @exception returns -1 if it is a point at infinity
|
|
* @exception returns -2 if x or y is smaller than p,
|
|
* @exception returns -3 if y^2 != x^3 + ax + b.
|
|
* @exception returns -4 if public key is the group generator.
|
|
*
|
|
* @note Note that you are not required to check for a valid public key before
|
|
* using any other uECC functions. However, you may wish to avoid spending CPU
|
|
* time computing a shared secret or verifying a signature using an invalid
|
|
* public key.
|
|
*/
|
|
int uECC_valid_public_key(const uint8_t *public_key, uECC_Curve curve);
|
|
|
|
/*
|
|
* @brief Converts an integer in uECC native format to big-endian bytes.
|
|
* @param bytes OUT -- bytes representation
|
|
* @param num_bytes IN -- number of bytes
|
|
* @param native IN -- uECC native representation
|
|
*/
|
|
void uECC_vli_nativeToBytes(uint8_t *bytes, int num_bytes,
|
|
const unsigned int *native);
|
|
|
|
/*
|
|
* @brief Converts big-endian bytes to an integer in uECC native format.
|
|
* @param native OUT -- uECC native representation
|
|
* @param bytes IN -- bytes representation
|
|
* @param num_bytes IN -- number of bytes
|
|
*/
|
|
void uECC_vli_bytesToNative(unsigned int *native, const uint8_t *bytes,
|
|
int num_bytes);
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|
|
|
|
#endif /* __TC_UECC_H__ */
|
|
#endif /* MBEDTLS_USE_TINYCRYPT */
|