mirror of
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ef238283d5
This avoids the need for each calling site to manually regularize the scalar and randomize coordinates, which makes for simpler safe use and saves 50 bytes of code size in the library.
567 lines
21 KiB
C
567 lines
21 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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/* 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 Regularize the bitcount for the private key so that attackers cannot
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* use a side channel attack to learn the number of leading zeros.
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* @return Regularized k
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* @param k IN -- private-key
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* @param k0 IN/OUT -- regularized k
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* @param k1 IN/OUT -- regularized k
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* @param curve IN -- elliptic curve
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*/
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uECC_word_t regularize_k(const uECC_word_t * const k, uECC_word_t *k0,
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uECC_word_t *k1, 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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* @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 initial_Z IN -- initial value for z
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* @param num_bits IN -- number of bits in scalar
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* @param curve IN -- elliptic curve
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*/
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void EccPoint_mult(uECC_word_t * result, const uECC_word_t * point,
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const uECC_word_t * scalar, const uECC_word_t * initial_Z,
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bitcount_t num_bits, 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, wordcount_t num_words);
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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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uECC_Curve curve);
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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, uECC_Curve curve);
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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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* @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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/*
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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
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*/
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void uECC_vli_set(uECC_word_t *dest, const uECC_word_t *src,
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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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* @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 -- left term in addition
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* @param right IN -- right term in addition
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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_modAdd(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 Counts the number of bits required to represent vli.
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* @param vli IN -- very long integer
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|
* @param max_words IN -- number of words
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|
* @return number of bits in given vli
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|
*/
|
|
bitcount_t uECC_vli_numBits(const uECC_word_t *vli,
|
|
const wordcount_t max_words);
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|
|
|
/*
|
|
* @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, wordcount_t num_words);
|
|
|
|
/*
|
|
* @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 */
|