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Add micro-ecc based ecc-files to mbedtls

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The files are from https://github.com/intel/tinycrypt
Using commit 6e0eb53fc8403988f97345e94081b0453f47231d as a base.
This commit is contained in:
Jarno Lamsa 2019-04-24 15:40:43 +03:00
parent 7326bc8577
commit 18987a420b
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/* ecc.h - TinyCrypt interface to common ECC functions */
/* Copyright (c) 2014, Kenneth MacKay
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
/*
* Copyright (C) 2017 by Intel Corporation, All Rights Reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* - Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* - Neither the name of Intel Corporation nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
/**
* @file
* @brief -- Interface to common ECC functions.
*
* Overview: This software is an implementation of common functions
* necessary to elliptic curve cryptography. This implementation uses
* curve NIST p-256.
*
* Security: The curve NIST p-256 provides approximately 128 bits of security.
*
*/
#ifndef __TC_UECC_H__
#define __TC_UECC_H__
#include <stdint.h>
#ifdef __cplusplus
extern "C" {
#endif
/* Word size (4 bytes considering 32-bits architectures) */
#define uECC_WORD_SIZE 4
/* setting max number of calls to prng: */
#ifndef uECC_RNG_MAX_TRIES
#define uECC_RNG_MAX_TRIES 64
#endif
/* defining data types to store word and bit counts: */
typedef int8_t wordcount_t;
typedef int16_t bitcount_t;
/* defining data type for comparison result: */
typedef int8_t cmpresult_t;
/* defining data type to store ECC coordinate/point in 32bits words: */
typedef unsigned int uECC_word_t;
/* defining data type to store an ECC coordinate/point in 64bits words: */
typedef uint64_t uECC_dword_t;
/* defining masks useful for ecc computations: */
#define HIGH_BIT_SET 0x80000000
#define uECC_WORD_BITS 32
#define uECC_WORD_BITS_SHIFT 5
#define uECC_WORD_BITS_MASK 0x01F
/* Number of words of 32 bits to represent an element of the the curve p-256: */
#define NUM_ECC_WORDS 8
/* Number of bytes to represent an element of the the curve p-256: */
#define NUM_ECC_BYTES (uECC_WORD_SIZE*NUM_ECC_WORDS)
/* structure that represents an elliptic curve (e.g. p256):*/
struct uECC_Curve_t;
typedef const struct uECC_Curve_t * uECC_Curve;
struct uECC_Curve_t {
wordcount_t num_words;
wordcount_t num_bytes;
bitcount_t num_n_bits;
uECC_word_t p[NUM_ECC_WORDS];
uECC_word_t n[NUM_ECC_WORDS];
uECC_word_t G[NUM_ECC_WORDS * 2];
uECC_word_t b[NUM_ECC_WORDS];
void (*double_jacobian)(uECC_word_t * X1, uECC_word_t * Y1, uECC_word_t * Z1,
uECC_Curve curve);
void (*x_side)(uECC_word_t *result, const uECC_word_t *x, uECC_Curve curve);
void (*mmod_fast)(uECC_word_t *result, uECC_word_t *product);
};
/*
* @brief computes doubling of point ion jacobian coordinates, in place.
* @param X1 IN/OUT -- x coordinate
* @param Y1 IN/OUT -- y coordinate
* @param Z1 IN/OUT -- z coordinate
* @param curve IN -- elliptic curve
*/
void double_jacobian_default(uECC_word_t * X1, uECC_word_t * Y1,
uECC_word_t * Z1, uECC_Curve curve);
/*
* @brief Computes x^3 + ax + b. result must not overlap x.
* @param result OUT -- x^3 + ax + b
* @param x IN -- value of x
* @param curve IN -- elliptic curve
*/
void x_side_default(uECC_word_t *result, const uECC_word_t *x,
uECC_Curve curve);
/*
* @brief Computes result = product % curve_p
* from http://www.nsa.gov/ia/_files/nist-routines.pdf
* @param result OUT -- product % curve_p
* @param product IN -- value to be reduced mod curve_p
*/
void vli_mmod_fast_secp256r1(unsigned int *result, unsigned int *product);
/* Bytes to words ordering: */
#define BYTES_TO_WORDS_8(a, b, c, d, e, f, g, h) 0x##d##c##b##a, 0x##h##g##f##e
#define BYTES_TO_WORDS_4(a, b, c, d) 0x##d##c##b##a
#define BITS_TO_WORDS(num_bits) \
((num_bits + ((uECC_WORD_SIZE * 8) - 1)) / (uECC_WORD_SIZE * 8))
#define BITS_TO_BYTES(num_bits) ((num_bits + 7) / 8)
/* definition of curve NIST p-256: */
static const struct uECC_Curve_t curve_secp256r1 = {
NUM_ECC_WORDS,
NUM_ECC_BYTES,
256, /* num_n_bits */ {
BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF),
BYTES_TO_WORDS_8(FF, FF, FF, FF, 00, 00, 00, 00),
BYTES_TO_WORDS_8(00, 00, 00, 00, 00, 00, 00, 00),
BYTES_TO_WORDS_8(01, 00, 00, 00, FF, FF, FF, FF)
}, {
BYTES_TO_WORDS_8(51, 25, 63, FC, C2, CA, B9, F3),
BYTES_TO_WORDS_8(84, 9E, 17, A7, AD, FA, E6, BC),
BYTES_TO_WORDS_8(FF, FF, FF, FF, FF, FF, FF, FF),
BYTES_TO_WORDS_8(00, 00, 00, 00, FF, FF, FF, FF)
}, {
BYTES_TO_WORDS_8(96, C2, 98, D8, 45, 39, A1, F4),
BYTES_TO_WORDS_8(A0, 33, EB, 2D, 81, 7D, 03, 77),
BYTES_TO_WORDS_8(F2, 40, A4, 63, E5, E6, BC, F8),
BYTES_TO_WORDS_8(47, 42, 2C, E1, F2, D1, 17, 6B),
BYTES_TO_WORDS_8(F5, 51, BF, 37, 68, 40, B6, CB),
BYTES_TO_WORDS_8(CE, 5E, 31, 6B, 57, 33, CE, 2B),
BYTES_TO_WORDS_8(16, 9E, 0F, 7C, 4A, EB, E7, 8E),
BYTES_TO_WORDS_8(9B, 7F, 1A, FE, E2, 42, E3, 4F)
}, {
BYTES_TO_WORDS_8(4B, 60, D2, 27, 3E, 3C, CE, 3B),
BYTES_TO_WORDS_8(F6, B0, 53, CC, B0, 06, 1D, 65),
BYTES_TO_WORDS_8(BC, 86, 98, 76, 55, BD, EB, B3),
BYTES_TO_WORDS_8(E7, 93, 3A, AA, D8, 35, C6, 5A)
},
&double_jacobian_default,
&x_side_default,
&vli_mmod_fast_secp256r1
};
uECC_Curve uECC_secp256r1(void);
/*
* @brief Generates a random integer in the range 0 < random < top.
* Both random and top have num_words words.
* @param random OUT -- random integer in the range 0 < random < top
* @param top IN -- upper limit
* @param num_words IN -- number of words
* @return a random integer in the range 0 < random < top
*/
int uECC_generate_random_int(uECC_word_t *random, const uECC_word_t *top,
wordcount_t num_words);
/* uECC_RNG_Function type
* The RNG function should fill 'size' random bytes into 'dest'. It should
* return 1 if 'dest' was filled with random data, or 0 if the random data could
* not be generated. The filled-in values should be either truly random, or from
* a cryptographically-secure PRNG.
*
* A correctly functioning RNG function must be set (using uECC_set_rng())
* before calling uECC_make_key() or uECC_sign().
*
* Setting a correctly functioning RNG function improves the resistance to
* side-channel attacks for uECC_shared_secret().
*
* A correct RNG function is set by default. If you are building on another
* POSIX-compliant system that supports /dev/random or /dev/urandom, you can
* define uECC_POSIX to use the predefined RNG.
*/
typedef int(*uECC_RNG_Function)(uint8_t *dest, unsigned int size);
/*
* @brief Set the function that will be used to generate random bytes. The RNG
* function should return 1 if the random data was generated, or 0 if the random
* data could not be generated.
*
* @note On platforms where there is no predefined RNG function, this must be
* called before uECC_make_key() or uECC_sign() are used.
*
* @param rng_function IN -- function that will be used to generate random bytes
*/
void uECC_set_rng(uECC_RNG_Function rng_function);
/*
* @brief provides current uECC_RNG_Function.
* @return Returns the function that will be used to generate random bytes.
*/
uECC_RNG_Function uECC_get_rng(void);
/*
* @brief computes the size of a private key for the curve in bytes.
* @param curve IN -- elliptic curve
* @return size of a private key for the curve in bytes.
*/
int uECC_curve_private_key_size(uECC_Curve curve);
/*
* @brief computes the size of a public key for the curve in bytes.
* @param curve IN -- elliptic curve
* @return the size of a public key for the curve in bytes.
*/
int uECC_curve_public_key_size(uECC_Curve curve);
/*
* @brief Compute the corresponding public key for a private key.
* @param private_key IN -- The private key to compute the public key for
* @param public_key OUT -- Will be filled in with the corresponding public key
* @param curve
* @return Returns 1 if key was computed successfully, 0 if an error occurred.
*/
int uECC_compute_public_key(const uint8_t *private_key,
uint8_t *public_key, uECC_Curve curve);
/*
* @brief Compute public-key.
* @return corresponding public-key.
* @param result OUT -- public-key
* @param private_key IN -- private-key
* @param curve IN -- elliptic curve
*/
uECC_word_t EccPoint_compute_public_key(uECC_word_t *result,
uECC_word_t *private_key, uECC_Curve curve);
/*
* @brief Regularize the bitcount for the private key so that attackers cannot
* use a side channel attack to learn the number of leading zeros.
* @return Regularized k
* @param k IN -- private-key
* @param k0 IN/OUT -- regularized k
* @param k1 IN/OUT -- regularized k
* @param curve IN -- elliptic curve
*/
uECC_word_t regularize_k(const uECC_word_t * const k, uECC_word_t *k0,
uECC_word_t *k1, uECC_Curve curve);
/*
* @brief Point multiplication algorithm using Montgomery's ladder with co-Z
* coordinates. See http://eprint.iacr.org/2011/338.pdf.
* @note Result may overlap point.
* @param result OUT -- returns scalar*point
* @param point IN -- elliptic curve point
* @param scalar IN -- scalar
* @param initial_Z IN -- initial value for z
* @param num_bits IN -- number of bits in scalar
* @param curve IN -- elliptic curve
*/
void EccPoint_mult(uECC_word_t * result, const uECC_word_t * point,
const uECC_word_t * scalar, const uECC_word_t * initial_Z,
bitcount_t num_bits, uECC_Curve curve);
/*
* @brief Constant-time comparison to zero - secure way to compare long integers
* @param vli IN -- very long integer
* @param num_words IN -- number of words in the vli
* @return 1 if vli == 0, 0 otherwise.
*/
uECC_word_t uECC_vli_isZero(const uECC_word_t *vli, wordcount_t num_words);
/*
* @brief Check if 'point' is the point at infinity
* @param point IN -- elliptic curve point
* @param curve IN -- elliptic curve
* @return if 'point' is the point at infinity, 0 otherwise.
*/
uECC_word_t EccPoint_isZero(const uECC_word_t *point, uECC_Curve curve);
/*
* @brief computes the sign of left - right, in constant time.
* @param left IN -- left term to be compared
* @param right IN -- right term to be compared
* @param num_words IN -- number of words
* @return the sign of left - right
*/
cmpresult_t uECC_vli_cmp(const uECC_word_t *left, const uECC_word_t *right,
wordcount_t num_words);
/*
* @brief computes sign of left - right, not in constant time.
* @note should not be used if inputs are part of a secret
* @param left IN -- left term to be compared
* @param right IN -- right term to be compared
* @param num_words IN -- number of words
* @return the sign of left - right
*/
cmpresult_t uECC_vli_cmp_unsafe(const uECC_word_t *left, const uECC_word_t *right,
wordcount_t num_words);
/*
* @brief Computes result = (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 -- leftright term in modular subtraction
* @param right IN -- right term in modular subtraction
* @param mod IN -- mod
* @param num_words IN -- number of words
*/
void uECC_vli_modSub(uECC_word_t *result, const uECC_word_t *left,
const uECC_word_t *right, const uECC_word_t *mod,
wordcount_t num_words);
/*
* @brief Computes P' = (x1', y1', Z3), P + Q = (x3, y3, Z3) or
* P => P', Q => P + Q
* @note assumes Input P = (x1, y1, Z), Q = (x2, y2, Z)
* @param X1 IN -- x coordinate of P
* @param Y1 IN -- y coordinate of P
* @param X2 IN -- x coordinate of Q
* @param Y2 IN -- y coordinate of Q
* @param curve IN -- elliptic curve
*/
void XYcZ_add(uECC_word_t * X1, uECC_word_t * Y1, uECC_word_t * X2,
uECC_word_t * Y2, uECC_Curve curve);
/*
* @brief Computes (x1 * z^2, y1 * z^3)
* @param X1 IN -- previous x1 coordinate
* @param Y1 IN -- previous y1 coordinate
* @param Z IN -- z value
* @param curve IN -- elliptic curve
*/
void apply_z(uECC_word_t * X1, uECC_word_t * Y1, const uECC_word_t * const Z,
uECC_Curve curve);
/*
* @brief Check if bit is set.
* @return Returns nonzero if bit 'bit' of vli is set.
* @warning It is assumed that the value provided in 'bit' is within the
* boundaries of the word-array 'vli'.
* @note The bit ordering layout assumed for vli is: {31, 30, ..., 0},
* {63, 62, ..., 32}, {95, 94, ..., 64}, {127, 126,..., 96} for a vli consisting
* of 4 uECC_word_t elements.
*/
uECC_word_t uECC_vli_testBit(const uECC_word_t *vli, bitcount_t bit);
/*
* @brief Computes result = product % mod, where product is 2N words long.
* @param result OUT -- product % mod
* @param mod IN -- module
* @param num_words IN -- number of words
* @warning Currently only designed to work for curve_p or curve_n.
*/
void uECC_vli_mmod(uECC_word_t *result, uECC_word_t *product,
const uECC_word_t *mod, wordcount_t num_words);
/*
* @brief Computes modular product (using curve->mmod_fast)
* @param result OUT -- (left * right) mod % curve_p
* @param left IN -- left term in product
* @param right IN -- right term in product
* @param curve IN -- elliptic curve
*/
void uECC_vli_modMult_fast(uECC_word_t *result, const uECC_word_t *left,
const uECC_word_t *right, uECC_Curve curve);
/*
* @brief Computes result = left - right.
* @note Can modify in place.
* @param result OUT -- left - right
* @param left IN -- left term in subtraction
* @param right IN -- right term in subtraction
* @param num_words IN -- number of words
* @return borrow
*/
uECC_word_t uECC_vli_sub(uECC_word_t *result, const uECC_word_t *left,
const uECC_word_t *right, wordcount_t num_words);
/*
* @brief Constant-time comparison function(secure way to compare long ints)
* @param left IN -- left term in comparison
* @param right IN -- right term in comparison
* @param num_words IN -- number of words
* @return Returns 0 if left == right, 1 otherwise.
*/
uECC_word_t uECC_vli_equal(const uECC_word_t *left, const uECC_word_t *right,
wordcount_t num_words);
/*
* @brief Computes (left * right) % mod
* @param result OUT -- (left * right) % mod
* @param left IN -- left term in product
* @param right IN -- right term in product
* @param mod IN -- mod
* @param num_words IN -- number of words
*/
void uECC_vli_modMult(uECC_word_t *result, const uECC_word_t *left,
const uECC_word_t *right, const uECC_word_t *mod,
wordcount_t num_words);
/*
* @brief Computes (1 / input) % mod
* @note All VLIs are the same size.
* @note See "Euclid's GCD to Montgomery Multiplication to the Great Divide"
* @param result OUT -- (1 / input) % mod
* @param input IN -- value to be modular inverted
* @param mod IN -- mod
* @param num_words -- number of words
*/
void uECC_vli_modInv(uECC_word_t *result, const uECC_word_t *input,
const uECC_word_t *mod, wordcount_t num_words);
/*
* @brief Sets dest = src.
* @param dest OUT -- destination buffer
* @param src IN -- origin buffer
* @param num_words IN -- number of words
*/
void uECC_vli_set(uECC_word_t *dest, const uECC_word_t *src,
wordcount_t num_words);
/*
* @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,
const wordcount_t max_words);
/*
* @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__ */

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/* ecc_dh.h - TinyCrypt interface to EC-DH implementation */
/*
* Copyright (c) 2014, Kenneth MacKay
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
/* Copyright (C) 2017 by Intel Corporation, All Rights Reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* - Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* - Neither the name of Intel Corporation nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
/**
* @file
* @brief -- Interface to EC-DH implementation.
*
* Overview: This software is an implementation of EC-DH. This implementation
* uses curve NIST p-256.
*
* Security: The curve NIST p-256 provides approximately 128 bits of security.
*/
#ifndef __TC_ECC_DH_H__
#define __TC_ECC_DH_H__
#include <tinycrypt/ecc.h>
#ifdef __cplusplus
extern "C" {
#endif
/**
* @brief Create a public/private key pair.
* @return returns TC_CRYPTO_SUCCESS (1) if the key pair was generated successfully
* returns TC_CRYPTO_FAIL (0) if error while generating key pair
*
* @param p_public_key OUT -- Will be filled in with the public key. Must be at
* least 2 * the curve size (in bytes) long. For curve secp256r1, p_public_key
* must be 64 bytes long.
* @param p_private_key OUT -- Will be filled in with the private key. Must be as
* long as the curve order (for secp256r1, p_private_key must be 32 bytes long).
*
* @note side-channel countermeasure: algorithm strengthened against timing
* attack.
* @warning A cryptographically-secure PRNG function must be set (using
* uECC_set_rng()) before calling uECC_make_key().
*/
int uECC_make_key(uint8_t *p_public_key, uint8_t *p_private_key, uECC_Curve curve);
#ifdef ENABLE_TESTS
/**
* @brief Create a public/private key pair given a specific d.
*
* @note THIS FUNCTION SHOULD BE CALLED ONLY FOR TEST PURPOSES. Refer to
* uECC_make_key() function for real applications.
*/
int uECC_make_key_with_d(uint8_t *p_public_key, uint8_t *p_private_key,
unsigned int *d, uECC_Curve curve);
#endif
/**
* @brief Compute a shared secret given your secret key and someone else's
* public key.
* @return returns TC_CRYPTO_SUCCESS (1) if the shared secret was computed successfully
* returns TC_CRYPTO_FAIL (0) otherwise
*
* @param p_secret OUT -- Will be filled in with the shared secret value. Must be
* the same size as the curve size (for curve secp256r1, secret must be 32 bytes
* long.
* @param p_public_key IN -- The public key of the remote party.
* @param p_private_key IN -- Your private key.
*
* @warning It is recommended to use the output of uECC_shared_secret() as the
* input of a recommended Key Derivation Function (see NIST SP 800-108) in
* order to produce a cryptographically secure symmetric key.
*/
int uECC_shared_secret(const uint8_t *p_public_key, const uint8_t *p_private_key,
uint8_t *p_secret, uECC_Curve curve);
#ifdef __cplusplus
}
#endif
#endif /* __TC_ECC_DH_H__ */

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/* ecc_dh.h - TinyCrypt interface to EC-DSA implementation */
/*
* Copyright (c) 2014, Kenneth MacKay
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
/*
* Copyright (C) 2017 by Intel Corporation, All Rights Reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* - Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* - Neither the name of Intel Corporation nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
/**
* @file
* @brief -- Interface to EC-DSA implementation.
*
* Overview: This software is an implementation of EC-DSA. This implementation
* uses curve NIST p-256.
*
* Security: The curve NIST p-256 provides approximately 128 bits of security.
*
* Usage: - To sign: Compute a hash of the data you wish to sign (SHA-2 is
* recommended) and pass it in to ecdsa_sign function along with your
* private key and a random number. You must use a new non-predictable
* random number to generate each new signature.
* - To verify a signature: Compute the hash of the signed data using
* the same hash as the signer and pass it to this function along with
* the signer's public key and the signature values (r and s).
*/
#ifndef __TC_ECC_DSA_H__
#define __TC_ECC_DSA_H__
#include <tinycrypt/ecc.h>
#ifdef __cplusplus
extern "C" {
#endif
/**
* @brief Generate an ECDSA signature for a given hash value.
* @return returns TC_CRYPTO_SUCCESS (1) if the signature generated successfully
* returns TC_CRYPTO_FAIL (0) if an error occurred.
*
* @param p_private_key IN -- Your private key.
* @param p_message_hash IN -- The hash of the message to sign.
* @param p_hash_size IN -- The size of p_message_hash in bytes.
* @param p_signature OUT -- Will be filled in with the signature value. Must be
* at least 2 * curve size long (for secp256r1, signature must be 64 bytes long).
*
* @warning A cryptographically-secure PRNG function must be set (using
* uECC_set_rng()) before calling uECC_sign().
* @note Usage: Compute a hash of the data you wish to sign (SHA-2 is
* recommended) and pass it in to this function along with your private key.
* @note side-channel countermeasure: algorithm strengthened against timing
* attack.
*/
int uECC_sign(const uint8_t *p_private_key, const uint8_t *p_message_hash,
unsigned p_hash_size, uint8_t *p_signature, uECC_Curve curve);
#ifdef ENABLE_TESTS
/*
* THIS FUNCTION SHOULD BE CALLED FOR TEST PURPOSES ONLY.
* Refer to uECC_sign() function for real applications.
*/
int uECC_sign_with_k(const uint8_t *private_key, const uint8_t *message_hash,
unsigned int hash_size, uECC_word_t *k, uint8_t *signature,
uECC_Curve curve);
#endif
/**
* @brief Verify an ECDSA signature.
* @return returns TC_SUCCESS (1) if the signature is valid
* returns TC_FAIL (0) if the signature is invalid.
*
* @param p_public_key IN -- The signer's public key.
* @param p_message_hash IN -- The hash of the signed data.
* @param p_hash_size IN -- The size of p_message_hash in bytes.
* @param p_signature IN -- The signature values.
*
* @note Usage: Compute the hash of the signed data using the same hash as the
* signer and pass it to this function along with the signer's public key and
* the signature values (hash_size and signature).
*/
int uECC_verify(const uint8_t *p_public_key, const uint8_t *p_message_hash,
unsigned int p_hash_size, const uint8_t *p_signature, uECC_Curve curve);
#ifdef __cplusplus
}
#endif
#endif /* __TC_ECC_DSA_H__ */

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/* ecc.c - TinyCrypt implementation of common ECC functions */
/*
* Copyright (c) 2014, Kenneth MacKay
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
* ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
* ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* Copyright (C) 2017 by Intel Corporation, All Rights Reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* - Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* - Neither the name of Intel Corporation nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
#include <tinycrypt/ecc.h>
#include <tinycrypt/ecc_platform_specific.h>
#include <string.h>
/* IMPORTANT: Make sure a cryptographically-secure PRNG is set and the platform
* has access to enough entropy in order to feed the PRNG regularly. */
#if default_RNG_defined
static uECC_RNG_Function g_rng_function = &default_CSPRNG;
#else
static uECC_RNG_Function g_rng_function = 0;
#endif
void uECC_set_rng(uECC_RNG_Function rng_function)
{
g_rng_function = rng_function;
}
uECC_RNG_Function uECC_get_rng(void)
{
return g_rng_function;
}
int uECC_curve_private_key_size(uECC_Curve curve)
{
return BITS_TO_BYTES(curve->num_n_bits);
}
int uECC_curve_public_key_size(uECC_Curve curve)
{
return 2 * curve->num_bytes;
}
void uECC_vli_clear(uECC_word_t *vli, wordcount_t num_words)
{
wordcount_t i;
for (i = 0; i < num_words; ++i) {
vli[i] = 0;
}
}
uECC_word_t uECC_vli_isZero(const uECC_word_t *vli, wordcount_t num_words)
{
uECC_word_t bits = 0;
wordcount_t i;
for (i = 0; i < num_words; ++i) {
bits |= vli[i];
}
return (bits == 0);
}
uECC_word_t uECC_vli_testBit(const uECC_word_t *vli, bitcount_t bit)
{
return (vli[bit >> uECC_WORD_BITS_SHIFT] &
((uECC_word_t)1 << (bit & uECC_WORD_BITS_MASK)));
}
/* Counts the number of words in vli. */
static wordcount_t vli_numDigits(const uECC_word_t *vli,
const wordcount_t max_words)
{
wordcount_t i;
/* Search from the end until we find a non-zero digit. We do it in reverse
* because we expect that most digits will be nonzero. */
for (i = max_words - 1; i >= 0 && vli[i] == 0; --i) {
}
return (i + 1);
}
bitcount_t uECC_vli_numBits(const uECC_word_t *vli,
const wordcount_t max_words)
{
uECC_word_t i;
uECC_word_t digit;
wordcount_t num_digits = vli_numDigits(vli, max_words);
if (num_digits == 0) {
return 0;
}
digit = vli[num_digits - 1];
for (i = 0; digit; ++i) {
digit >>= 1;
}
return (((bitcount_t)(num_digits - 1) << uECC_WORD_BITS_SHIFT) + i);
}
void uECC_vli_set(uECC_word_t *dest, const uECC_word_t *src,
wordcount_t num_words)
{
wordcount_t i;
for (i = 0; i < num_words; ++i) {
dest[i] = src[i];
}
}
cmpresult_t uECC_vli_cmp_unsafe(const uECC_word_t *left,
const uECC_word_t *right,
wordcount_t num_words)
{
wordcount_t i;
for (i = num_words - 1; i >= 0; --i) {
if (left[i] > right[i]) {
return 1;
} else if (left[i] < right[i]) {
return -1;
}
}
return 0;
}
uECC_word_t uECC_vli_equal(const uECC_word_t *left, const uECC_word_t *right,
wordcount_t num_words)
{
uECC_word_t diff = 0;
wordcount_t i;
for (i = num_words - 1; i >= 0; --i) {
diff |= (left[i] ^ right[i]);
}
return !(diff == 0);
}
uECC_word_t cond_set(uECC_word_t p_true, uECC_word_t p_false, unsigned int cond)
{
return (p_true*(cond)) | (p_false*(!cond));
}
/* Computes result = left - right, returning borrow, in constant time.
* Can modify in place. */
uECC_word_t uECC_vli_sub(uECC_word_t *result, const uECC_word_t *left,
const uECC_word_t *right, wordcount_t num_words)
{
uECC_word_t borrow = 0;
wordcount_t i;
for (i = 0; i < num_words; ++i) {
uECC_word_t diff = left[i] - right[i] - borrow;
uECC_word_t val = (diff > left[i]);
borrow = cond_set(val, borrow, (diff != left[i]));
result[i] = diff;
}
return borrow;
}
/* Computes result = left + right, returning carry, in constant time.
* Can modify in place. */
static uECC_word_t uECC_vli_add(uECC_word_t *result, const uECC_word_t *left,
const uECC_word_t *right, wordcount_t num_words)
{
uECC_word_t carry = 0;
wordcount_t i;
for (i = 0; i < num_words; ++i) {
uECC_word_t sum = left[i] + right[i] + carry;
uECC_word_t val = (sum < left[i]);
carry = cond_set(val, carry, (sum != left[i]));
result[i] = sum;
}
return carry;
}
cmpresult_t uECC_vli_cmp(const uECC_word_t *left, const uECC_word_t *right,
wordcount_t num_words)
{
uECC_word_t tmp[NUM_ECC_WORDS];
uECC_word_t neg = !!uECC_vli_sub(tmp, left, right, num_words);
uECC_word_t equal = uECC_vli_isZero(tmp, num_words);
return (!equal - 2 * neg);
}
/* Computes vli = vli >> 1. */
static void uECC_vli_rshift1(uECC_word_t *vli, wordcount_t num_words)
{
uECC_word_t *end = vli;
uECC_word_t carry = 0;
vli += num_words;
while (vli-- > end) {
uECC_word_t temp = *vli;
*vli = (temp >> 1) | carry;
carry = temp << (uECC_WORD_BITS - 1);
}
}
static void muladd(uECC_word_t a, uECC_word_t b, uECC_word_t *r0,
uECC_word_t *r1, uECC_word_t *r2)
{
uECC_dword_t p = (uECC_dword_t)a * b;
uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0;
r01 += p;
*r2 += (r01 < p);
*r1 = r01 >> uECC_WORD_BITS;
*r0 = (uECC_word_t)r01;
}
/* Computes result = left * right. Result must be 2 * num_words long. */
static void uECC_vli_mult(uECC_word_t *result, const uECC_word_t *left,
const uECC_word_t *right, wordcount_t num_words)
{
uECC_word_t r0 = 0;
uECC_word_t r1 = 0;
uECC_word_t r2 = 0;
wordcount_t i, k;
/* Compute each digit of result in sequence, maintaining the carries. */
for (k = 0; k < num_words; ++k) {
for (i = 0; i <= k; ++i) {
muladd(left[i], right[k - i], &r0, &r1, &r2);
}
result[k] = r0;
r0 = r1;
r1 = r2;
r2 = 0;
}
for (k = num_words; k < num_words * 2 - 1; ++k) {
for (i = (k + 1) - num_words; i < num_words; ++i) {
muladd(left[i], right[k - i], &r0, &r1, &r2);
}
result[k] = r0;
r0 = r1;
r1 = r2;
r2 = 0;
}
result[num_words * 2 - 1] = r0;
}
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)
{
uECC_word_t carry = uECC_vli_add(result, left, right, num_words);
if (carry || uECC_vli_cmp_unsafe(mod, result, num_words) != 1) {
/* result > mod (result = mod + remainder), so subtract mod to get
* remainder. */
uECC_vli_sub(result, result, mod, num_words);
}
}
void uECC_vli_modSub(uECC_word_t *result, const uECC_word_t *left,
const uECC_word_t *right, const uECC_word_t *mod,
wordcount_t num_words)
{
uECC_word_t l_borrow = uECC_vli_sub(result, left, right, num_words);
if (l_borrow) {
/* In this case, result == -diff == (max int) - diff. Since -x % d == d - x,
* we can get the correct result from result + mod (with overflow). */
uECC_vli_add(result, result, mod, num_words);
}
}
/* Computes result = product % mod, where product is 2N words long. */
/* Currently only designed to work for curve_p or curve_n. */
void uECC_vli_mmod(uECC_word_t *result, uECC_word_t *product,
const uECC_word_t *mod, wordcount_t num_words)
{
uECC_word_t mod_multiple[2 * NUM_ECC_WORDS];
uECC_word_t tmp[2 * NUM_ECC_WORDS];
uECC_word_t *v[2] = {tmp, product};
uECC_word_t index;
/* Shift mod so its highest set bit is at the maximum position. */
bitcount_t shift = (num_words * 2 * uECC_WORD_BITS) -
uECC_vli_numBits(mod, num_words);
wordcount_t word_shift = shift / uECC_WORD_BITS;
wordcount_t bit_shift = shift % uECC_WORD_BITS;
uECC_word_t carry = 0;
uECC_vli_clear(mod_multiple, word_shift);
if (bit_shift > 0) {
for(index = 0; index < (uECC_word_t)num_words; ++index) {
mod_multiple[word_shift + index] = (mod[index] << bit_shift) | carry;
carry = mod[index] >> (uECC_WORD_BITS - bit_shift);
}
} else {
uECC_vli_set(mod_multiple + word_shift, mod, num_words);
}
for (index = 1; shift >= 0; --shift) {
uECC_word_t borrow = 0;
wordcount_t i;
for (i = 0; i < num_words * 2; ++i) {
uECC_word_t diff = v[index][i] - mod_multiple[i] - borrow;
if (diff != v[index][i]) {
borrow = (diff > v[index][i]);
}
v[1 - index][i] = diff;
}
/* Swap the index if there was no borrow */
index = !(index ^ borrow);
uECC_vli_rshift1(mod_multiple, num_words);
mod_multiple[num_words - 1] |= mod_multiple[num_words] <<
(uECC_WORD_BITS - 1);
uECC_vli_rshift1(mod_multiple + num_words, num_words);
}
uECC_vli_set(result, v[index], num_words);
}
void uECC_vli_modMult(uECC_word_t *result, const uECC_word_t *left,
const uECC_word_t *right, const uECC_word_t *mod,
wordcount_t num_words)
{
uECC_word_t product[2 * NUM_ECC_WORDS];
uECC_vli_mult(product, left, right, num_words);
uECC_vli_mmod(result, product, mod, num_words);
}
void uECC_vli_modMult_fast(uECC_word_t *result, const uECC_word_t *left,
const uECC_word_t *right, uECC_Curve curve)
{
uECC_word_t product[2 * NUM_ECC_WORDS];
uECC_vli_mult(product, left, right, curve->num_words);
curve->mmod_fast(result, product);
}
static void uECC_vli_modSquare_fast(uECC_word_t *result,
const uECC_word_t *left,
uECC_Curve curve)
{
uECC_vli_modMult_fast(result, left, left, curve);
}
#define EVEN(vli) (!(vli[0] & 1))
static void vli_modInv_update(uECC_word_t *uv,
const uECC_word_t *mod,
wordcount_t num_words)
{
uECC_word_t carry = 0;
if (!EVEN(uv)) {
carry = uECC_vli_add(uv, uv, mod, num_words);
}
uECC_vli_rshift1(uv, num_words);
if (carry) {
uv[num_words - 1] |= HIGH_BIT_SET;
}
}
void uECC_vli_modInv(uECC_word_t *result, const uECC_word_t *input,
const uECC_word_t *mod, wordcount_t num_words)
{
uECC_word_t a[NUM_ECC_WORDS], b[NUM_ECC_WORDS];
uECC_word_t u[NUM_ECC_WORDS], v[NUM_ECC_WORDS];
cmpresult_t cmpResult;
if (uECC_vli_isZero(input, num_words)) {
uECC_vli_clear(result, num_words);
return;
}
uECC_vli_set(a, input, num_words);
uECC_vli_set(b, mod, num_words);
uECC_vli_clear(u, num_words);
u[0] = 1;
uECC_vli_clear(v, num_words);
while ((cmpResult = uECC_vli_cmp_unsafe(a, b, num_words)) != 0) {
if (EVEN(a)) {
uECC_vli_rshift1(a, num_words);
vli_modInv_update(u, mod, num_words);
} else if (EVEN(b)) {
uECC_vli_rshift1(b, num_words);
vli_modInv_update(v, mod, num_words);
} else if (cmpResult > 0) {
uECC_vli_sub(a, a, b, num_words);
uECC_vli_rshift1(a, num_words);
if (uECC_vli_cmp_unsafe(u, v, num_words) < 0) {
uECC_vli_add(u, u, mod, num_words);
}
uECC_vli_sub(u, u, v, num_words);
vli_modInv_update(u, mod, num_words);
} else {
uECC_vli_sub(b, b, a, num_words);
uECC_vli_rshift1(b, num_words);
if (uECC_vli_cmp_unsafe(v, u, num_words) < 0) {
uECC_vli_add(v, v, mod, num_words);
}
uECC_vli_sub(v, v, u, num_words);
vli_modInv_update(v, mod, num_words);
}
}
uECC_vli_set(result, u, num_words);
}
/* ------ Point operations ------ */
void double_jacobian_default(uECC_word_t * X1, uECC_word_t * Y1,
uECC_word_t * Z1, uECC_Curve curve)
{
/* t1 = X, t2 = Y, t3 = Z */
uECC_word_t t4[NUM_ECC_WORDS];
uECC_word_t t5[NUM_ECC_WORDS];
wordcount_t num_words = curve->num_words;
if (uECC_vli_isZero(Z1, num_words)) {
return;
}
uECC_vli_modSquare_fast(t4, Y1, curve); /* t4 = y1^2 */
uECC_vli_modMult_fast(t5, X1, t4, curve); /* t5 = x1*y1^2 = A */
uECC_vli_modSquare_fast(t4, t4, curve); /* t4 = y1^4 */
uECC_vli_modMult_fast(Y1, Y1, Z1, curve); /* t2 = y1*z1 = z3 */
uECC_vli_modSquare_fast(Z1, Z1, curve); /* t3 = z1^2 */
uECC_vli_modAdd(X1, X1, Z1, curve->p, num_words); /* t1 = x1 + z1^2 */
uECC_vli_modAdd(Z1, Z1, Z1, curve->p, num_words); /* t3 = 2*z1^2 */
uECC_vli_modSub(Z1, X1, Z1, curve->p, num_words); /* t3 = x1 - z1^2 */
uECC_vli_modMult_fast(X1, X1, Z1, curve); /* t1 = x1^2 - z1^4 */
uECC_vli_modAdd(Z1, X1, X1, curve->p, num_words); /* t3 = 2*(x1^2 - z1^4) */
uECC_vli_modAdd(X1, X1, Z1, curve->p, num_words); /* t1 = 3*(x1^2 - z1^4) */
if (uECC_vli_testBit(X1, 0)) {
uECC_word_t l_carry = uECC_vli_add(X1, X1, curve->p, num_words);
uECC_vli_rshift1(X1, num_words);
X1[num_words - 1] |= l_carry << (uECC_WORD_BITS - 1);
} else {
uECC_vli_rshift1(X1, num_words);
}
/* t1 = 3/2*(x1^2 - z1^4) = B */
uECC_vli_modSquare_fast(Z1, X1, curve); /* t3 = B^2 */
uECC_vli_modSub(Z1, Z1, t5, curve->p, num_words); /* t3 = B^2 - A */
uECC_vli_modSub(Z1, Z1, t5, curve->p, num_words); /* t3 = B^2 - 2A = x3 */
uECC_vli_modSub(t5, t5, Z1, curve->p, num_words); /* t5 = A - x3 */
uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = B * (A - x3) */
/* t4 = B * (A - x3) - y1^4 = y3: */
uECC_vli_modSub(t4, X1, t4, curve->p, num_words);
uECC_vli_set(X1, Z1, num_words);
uECC_vli_set(Z1, Y1, num_words);
uECC_vli_set(Y1, t4, num_words);
}
void x_side_default(uECC_word_t *result,
const uECC_word_t *x,
uECC_Curve curve)
{
uECC_word_t _3[NUM_ECC_WORDS] = {3}; /* -a = 3 */
wordcount_t num_words = curve->num_words;
uECC_vli_modSquare_fast(result, x, curve); /* r = x^2 */
uECC_vli_modSub(result, result, _3, curve->p, num_words); /* r = x^2 - 3 */
uECC_vli_modMult_fast(result, result, x, curve); /* r = x^3 - 3x */
/* r = x^3 - 3x + b: */
uECC_vli_modAdd(result, result, curve->b, curve->p, num_words);
}
uECC_Curve uECC_secp256r1(void)
{
return &curve_secp256r1;
}
void vli_mmod_fast_secp256r1(unsigned int *result, unsigned int*product)
{
unsigned int tmp[NUM_ECC_WORDS];
int carry;
/* t */
uECC_vli_set(result, product, NUM_ECC_WORDS);
/* s1 */
tmp[0] = tmp[1] = tmp[2] = 0;
tmp[3] = product[11];
tmp[4] = product[12];
tmp[5] = product[13];
tmp[6] = product[14];
tmp[7] = product[15];
carry = uECC_vli_add(tmp, tmp, tmp, NUM_ECC_WORDS);
carry += uECC_vli_add(result, result, tmp, NUM_ECC_WORDS);
/* s2 */
tmp[3] = product[12];
tmp[4] = product[13];
tmp[5] = product[14];
tmp[6] = product[15];
tmp[7] = 0;
carry += uECC_vli_add(tmp, tmp, tmp, NUM_ECC_WORDS);
carry += uECC_vli_add(result, result, tmp, NUM_ECC_WORDS);
/* s3 */
tmp[0] = product[8];
tmp[1] = product[9];
tmp[2] = product[10];
tmp[3] = tmp[4] = tmp[5] = 0;
tmp[6] = product[14];
tmp[7] = product[15];
carry += uECC_vli_add(result, result, tmp, NUM_ECC_WORDS);
/* s4 */
tmp[0] = product[9];
tmp[1] = product[10];
tmp[2] = product[11];
tmp[3] = product[13];
tmp[4] = product[14];
tmp[5] = product[15];
tmp[6] = product[13];
tmp[7] = product[8];
carry += uECC_vli_add(result, result, tmp, NUM_ECC_WORDS);
/* d1 */
tmp[0] = product[11];
tmp[1] = product[12];
tmp[2] = product[13];
tmp[3] = tmp[4] = tmp[5] = 0;
tmp[6] = product[8];
tmp[7] = product[10];
carry -= uECC_vli_sub(result, result, tmp, NUM_ECC_WORDS);
/* d2 */
tmp[0] = product[12];
tmp[1] = product[13];
tmp[2] = product[14];
tmp[3] = product[15];
tmp[4] = tmp[5] = 0;
tmp[6] = product[9];
tmp[7] = product[11];
carry -= uECC_vli_sub(result, result, tmp, NUM_ECC_WORDS);
/* d3 */
tmp[0] = product[13];
tmp[1] = product[14];
tmp[2] = product[15];
tmp[3] = product[8];
tmp[4] = product[9];
tmp[5] = product[10];
tmp[6] = 0;
tmp[7] = product[12];
carry -= uECC_vli_sub(result, result, tmp, NUM_ECC_WORDS);
/* d4 */
tmp[0] = product[14];
tmp[1] = product[15];
tmp[2] = 0;
tmp[3] = product[9];
tmp[4] = product[10];
tmp[5] = product[11];
tmp[6] = 0;
tmp[7] = product[13];
carry -= uECC_vli_sub(result, result, tmp, NUM_ECC_WORDS);
if (carry < 0) {
do {
carry += uECC_vli_add(result, result, curve_secp256r1.p, NUM_ECC_WORDS);
}
while (carry < 0);
} else {
while (carry ||
uECC_vli_cmp_unsafe(curve_secp256r1.p, result, NUM_ECC_WORDS) != 1) {
carry -= uECC_vli_sub(result, result, curve_secp256r1.p, NUM_ECC_WORDS);
}
}
}
uECC_word_t EccPoint_isZero(const uECC_word_t *point, uECC_Curve curve)
{
return uECC_vli_isZero(point, curve->num_words * 2);
}
void apply_z(uECC_word_t * X1, uECC_word_t * Y1, const uECC_word_t * const Z,
uECC_Curve curve)
{
uECC_word_t t1[NUM_ECC_WORDS];
uECC_vli_modSquare_fast(t1, Z, curve); /* z^2 */
uECC_vli_modMult_fast(X1, X1, t1, curve); /* x1 * z^2 */
uECC_vli_modMult_fast(t1, t1, Z, curve); /* z^3 */
uECC_vli_modMult_fast(Y1, Y1, t1, curve); /* y1 * z^3 */
}
/* P = (x1, y1) => 2P, (x2, y2) => P' */
static void XYcZ_initial_double(uECC_word_t * X1, uECC_word_t * Y1,
uECC_word_t * X2, uECC_word_t * Y2,
const uECC_word_t * const initial_Z,
uECC_Curve curve)
{
uECC_word_t z[NUM_ECC_WORDS];
wordcount_t num_words = curve->num_words;
if (initial_Z) {
uECC_vli_set(z, initial_Z, num_words);
} else {
uECC_vli_clear(z, num_words);
z[0] = 1;
}
uECC_vli_set(X2, X1, num_words);
uECC_vli_set(Y2, Y1, num_words);
apply_z(X1, Y1, z, curve);
curve->double_jacobian(X1, Y1, z, curve);
apply_z(X2, Y2, z, curve);
}
void XYcZ_add(uECC_word_t * X1, uECC_word_t * Y1,
uECC_word_t * X2, uECC_word_t * Y2,
uECC_Curve curve)
{
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
uECC_word_t t5[NUM_ECC_WORDS];
wordcount_t num_words = curve->num_words;
uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */
uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */
uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */
uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */
uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */
uECC_vli_modSquare_fast(t5, Y2, curve); /* t5 = (y2 - y1)^2 = D */
uECC_vli_modSub(t5, t5, X1, curve->p, num_words); /* t5 = D - B */
uECC_vli_modSub(t5, t5, X2, curve->p, num_words); /* t5 = D - B - C = x3 */
uECC_vli_modSub(X2, X2, X1, curve->p, num_words); /* t3 = C - B */
uECC_vli_modMult_fast(Y1, Y1, X2, curve); /* t2 = y1*(C - B) */
uECC_vli_modSub(X2, X1, t5, curve->p, num_words); /* t3 = B - x3 */
uECC_vli_modMult_fast(Y2, Y2, X2, curve); /* t4 = (y2 - y1)*(B - x3) */
uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y3 */
uECC_vli_set(X2, t5, num_words);
}
/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
or P => P - Q, Q => P + Q
*/
static void XYcZ_addC(uECC_word_t * X1, uECC_word_t * Y1,
uECC_word_t * X2, uECC_word_t * Y2,
uECC_Curve curve)
{
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
uECC_word_t t5[NUM_ECC_WORDS];
uECC_word_t t6[NUM_ECC_WORDS];
uECC_word_t t7[NUM_ECC_WORDS];
wordcount_t num_words = curve->num_words;
uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */
uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */
uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */
uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */
uECC_vli_modAdd(t5, Y2, Y1, curve->p, num_words); /* t5 = y2 + y1 */
uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */
uECC_vli_modSub(t6, X2, X1, curve->p, num_words); /* t6 = C - B */
uECC_vli_modMult_fast(Y1, Y1, t6, curve); /* t2 = y1 * (C - B) = E */
uECC_vli_modAdd(t6, X1, X2, curve->p, num_words); /* t6 = B + C */
uECC_vli_modSquare_fast(X2, Y2, curve); /* t3 = (y2 - y1)^2 = D */
uECC_vli_modSub(X2, X2, t6, curve->p, num_words); /* t3 = D - (B + C) = x3 */
uECC_vli_modSub(t7, X1, X2, curve->p, num_words); /* t7 = B - x3 */
uECC_vli_modMult_fast(Y2, Y2, t7, curve); /* t4 = (y2 - y1)*(B - x3) */
/* t4 = (y2 - y1)*(B - x3) - E = y3: */
uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words);
uECC_vli_modSquare_fast(t7, t5, curve); /* t7 = (y2 + y1)^2 = F */
uECC_vli_modSub(t7, t7, t6, curve->p, num_words); /* t7 = F - (B + C) = x3' */
uECC_vli_modSub(t6, t7, X1, curve->p, num_words); /* t6 = x3' - B */
uECC_vli_modMult_fast(t6, t6, t5, curve); /* t6 = (y2+y1)*(x3' - B) */
/* t2 = (y2+y1)*(x3' - B) - E = y3': */
uECC_vli_modSub(Y1, t6, Y1, curve->p, num_words);
uECC_vli_set(X1, t7, num_words);
}
void EccPoint_mult(uECC_word_t * result, const uECC_word_t * point,
const uECC_word_t * scalar,
const uECC_word_t * initial_Z,
bitcount_t num_bits, uECC_Curve curve)
{
/* R0 and R1 */
uECC_word_t Rx[2][NUM_ECC_WORDS];
uECC_word_t Ry[2][NUM_ECC_WORDS];
uECC_word_t z[NUM_ECC_WORDS];
bitcount_t i;
uECC_word_t nb;
wordcount_t num_words = curve->num_words;
uECC_vli_set(Rx[1], point, num_words);
uECC_vli_set(Ry[1], point + num_words, num_words);
XYcZ_initial_double(Rx[1], Ry[1], Rx[0], Ry[0], initial_Z, curve);
for (i = num_bits - 2; i > 0; --i) {
nb = !uECC_vli_testBit(scalar, i);
XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], curve);
XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], curve);
}
nb = !uECC_vli_testBit(scalar, 0);
XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], curve);
/* Find final 1/Z value. */
uECC_vli_modSub(z, Rx[1], Rx[0], curve->p, num_words); /* X1 - X0 */
uECC_vli_modMult_fast(z, z, Ry[1 - nb], curve); /* Yb * (X1 - X0) */
uECC_vli_modMult_fast(z, z, point, curve); /* xP * Yb * (X1 - X0) */
uECC_vli_modInv(z, z, curve->p, num_words); /* 1 / (xP * Yb * (X1 - X0))*/
/* yP / (xP * Yb * (X1 - X0)) */
uECC_vli_modMult_fast(z, z, point + num_words, curve);
/* Xb * yP / (xP * Yb * (X1 - X0)) */
uECC_vli_modMult_fast(z, z, Rx[1 - nb], curve);
/* End 1/Z calculation */
XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], curve);
apply_z(Rx[0], Ry[0], z, curve);
uECC_vli_set(result, Rx[0], num_words);
uECC_vli_set(result + num_words, Ry[0], num_words);
}
uECC_word_t regularize_k(const uECC_word_t * const k, uECC_word_t *k0,
uECC_word_t *k1, uECC_Curve curve)
{
wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits);
bitcount_t num_n_bits = curve->num_n_bits;
uECC_word_t carry = uECC_vli_add(k0, k, curve->n, num_n_words) ||
(num_n_bits < ((bitcount_t)num_n_words * uECC_WORD_SIZE * 8) &&
uECC_vli_testBit(k0, num_n_bits));
uECC_vli_add(k1, k0, curve->n, num_n_words);
return carry;
}
uECC_word_t EccPoint_compute_public_key(uECC_word_t *result,
uECC_word_t *private_key,
uECC_Curve curve)
{
uECC_word_t tmp1[NUM_ECC_WORDS];
uECC_word_t tmp2[NUM_ECC_WORDS];
uECC_word_t *p2[2] = {tmp1, tmp2};
uECC_word_t carry;
/* Regularize the bitcount for the private key so that attackers cannot
* use a side channel attack to learn the number of leading zeros. */
carry = regularize_k(private_key, tmp1, tmp2, curve);
EccPoint_mult(result, curve->G, p2[!carry], 0, curve->num_n_bits + 1, curve);
if (EccPoint_isZero(result, curve)) {
return 0;
}
return 1;
}
/* Converts an integer in uECC native format to big-endian bytes. */
void uECC_vli_nativeToBytes(uint8_t *bytes, int num_bytes,
const unsigned int *native)
{
wordcount_t i;
for (i = 0; i < num_bytes; ++i) {
unsigned b = num_bytes - 1 - i;
bytes[i] = native[b / uECC_WORD_SIZE] >> (8 * (b % uECC_WORD_SIZE));
}
}
/* Converts big-endian bytes to an integer in uECC native format. */
void uECC_vli_bytesToNative(unsigned int *native, const uint8_t *bytes,
int num_bytes)
{
wordcount_t i;
uECC_vli_clear(native, (num_bytes + (uECC_WORD_SIZE - 1)) / uECC_WORD_SIZE);
for (i = 0; i < num_bytes; ++i) {
unsigned b = num_bytes - 1 - i;
native[b / uECC_WORD_SIZE] |=
(uECC_word_t)bytes[i] << (8 * (b % uECC_WORD_SIZE));
}
}
int uECC_generate_random_int(uECC_word_t *random, const uECC_word_t *top,
wordcount_t num_words)
{
uECC_word_t mask = (uECC_word_t)-1;
uECC_word_t tries;
bitcount_t num_bits = uECC_vli_numBits(top, num_words);
if (!g_rng_function) {
return 0;
}
for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) {
if (!g_rng_function((uint8_t *)random, num_words * uECC_WORD_SIZE)) {
return 0;
}
random[num_words - 1] &=
mask >> ((bitcount_t)(num_words * uECC_WORD_SIZE * 8 - num_bits));
if (!uECC_vli_isZero(random, num_words) &&
uECC_vli_cmp(top, random, num_words) == 1) {
return 1;
}
}
return 0;
}
int uECC_valid_point(const uECC_word_t *point, uECC_Curve curve)
{
uECC_word_t tmp1[NUM_ECC_WORDS];
uECC_word_t tmp2[NUM_ECC_WORDS];
wordcount_t num_words = curve->num_words;
/* The point at infinity is invalid. */
if (EccPoint_isZero(point, curve)) {
return -1;
}
/* x and y must be smaller than p. */
if (uECC_vli_cmp_unsafe(curve->p, point, num_words) != 1 ||
uECC_vli_cmp_unsafe(curve->p, point + num_words, num_words) != 1) {
return -2;
}
uECC_vli_modSquare_fast(tmp1, point + num_words, curve);
curve->x_side(tmp2, point, curve); /* tmp2 = x^3 + ax + b */
/* Make sure that y^2 == x^3 + ax + b */
if (uECC_vli_equal(tmp1, tmp2, num_words) != 0)
return -3;
return 0;
}
int uECC_valid_public_key(const uint8_t *public_key, uECC_Curve curve)
{
uECC_word_t _public[NUM_ECC_WORDS * 2];
uECC_vli_bytesToNative(_public, public_key, curve->num_bytes);
uECC_vli_bytesToNative(
_public + curve->num_words,
public_key + curve->num_bytes,
curve->num_bytes);
if (uECC_vli_cmp_unsafe(_public, curve->G, NUM_ECC_WORDS * 2) == 0) {
return -4;
}
return uECC_valid_point(_public, curve);
}
int uECC_compute_public_key(const uint8_t *private_key, uint8_t *public_key,
uECC_Curve curve)
{
uECC_word_t _private[NUM_ECC_WORDS];
uECC_word_t _public[NUM_ECC_WORDS * 2];
uECC_vli_bytesToNative(
_private,
private_key,
BITS_TO_BYTES(curve->num_n_bits));
/* Make sure the private key is in the range [1, n-1]. */
if (uECC_vli_isZero(_private, BITS_TO_WORDS(curve->num_n_bits))) {
return 0;
}
if (uECC_vli_cmp(curve->n, _private, BITS_TO_WORDS(curve->num_n_bits)) != 1) {
return 0;
}
/* Compute public key. */
if (!EccPoint_compute_public_key(_public, _private, curve)) {
return 0;
}
uECC_vli_nativeToBytes(public_key, curve->num_bytes, _public);
uECC_vli_nativeToBytes(
public_key +
curve->num_bytes, curve->num_bytes, _public + curve->num_words);
return 1;
}

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/* ec_dh.c - TinyCrypt implementation of EC-DH */
/*
* Copyright (c) 2014, Kenneth MacKay
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
/*
* Copyright (C) 2017 by Intel Corporation, All Rights Reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* - Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* - Neither the name of Intel Corporation nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
#include <tinycrypt/constants.h>
#include <tinycrypt/ecc.h>
#include <tinycrypt/ecc_dh.h>
#include <string.h>
#if default_RNG_defined
static uECC_RNG_Function g_rng_function = &default_CSPRNG;
#else
static uECC_RNG_Function g_rng_function = 0;
#endif
int uECC_make_key_with_d(uint8_t *public_key, uint8_t *private_key,
unsigned int *d, uECC_Curve curve)
{
uECC_word_t _private[NUM_ECC_WORDS];
uECC_word_t _public[NUM_ECC_WORDS * 2];
/* This function is designed for test purposes-only (such as validating NIST
* test vectors) as it uses a provided value for d instead of generating
* it uniformly at random. */
memcpy (_private, d, NUM_ECC_BYTES);
/* Computing public-key from private: */
if (EccPoint_compute_public_key(_public, _private, curve)) {
/* Converting buffers to correct bit order: */
uECC_vli_nativeToBytes(private_key,
BITS_TO_BYTES(curve->num_n_bits),
_private);
uECC_vli_nativeToBytes(public_key,
curve->num_bytes,
_public);
uECC_vli_nativeToBytes(public_key + curve->num_bytes,
curve->num_bytes,
_public + curve->num_words);
/* erasing temporary buffer used to store secret: */
memset(_private, 0, NUM_ECC_BYTES);
return 1;
}
return 0;
}
int uECC_make_key(uint8_t *public_key, uint8_t *private_key, uECC_Curve curve)
{
uECC_word_t _random[NUM_ECC_WORDS * 2];
uECC_word_t _private[NUM_ECC_WORDS];
uECC_word_t _public[NUM_ECC_WORDS * 2];
uECC_word_t tries;
for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) {
/* Generating _private uniformly at random: */
uECC_RNG_Function rng_function = uECC_get_rng();
if (!rng_function ||
!rng_function((uint8_t *)_random, 2 * NUM_ECC_WORDS*uECC_WORD_SIZE)) {
return 0;
}
/* computing modular reduction of _random (see FIPS 186.4 B.4.1): */
uECC_vli_mmod(_private, _random, curve->n, BITS_TO_WORDS(curve->num_n_bits));
/* Computing public-key from private: */
if (EccPoint_compute_public_key(_public, _private, curve)) {
/* Converting buffers to correct bit order: */
uECC_vli_nativeToBytes(private_key,
BITS_TO_BYTES(curve->num_n_bits),
_private);
uECC_vli_nativeToBytes(public_key,
curve->num_bytes,
_public);
uECC_vli_nativeToBytes(public_key + curve->num_bytes,
curve->num_bytes,
_public + curve->num_words);
/* erasing temporary buffer that stored secret: */
memset(_private, 0, NUM_ECC_BYTES);
return 1;
}
}
return 0;
}
int uECC_shared_secret(const uint8_t *public_key, const uint8_t *private_key,
uint8_t *secret, uECC_Curve curve)
{
uECC_word_t _public[NUM_ECC_WORDS * 2];
uECC_word_t _private[NUM_ECC_WORDS];
uECC_word_t tmp[NUM_ECC_WORDS];
uECC_word_t *p2[2] = {_private, tmp};
uECC_word_t *initial_Z = 0;
uECC_word_t carry;
wordcount_t num_words = curve->num_words;
wordcount_t num_bytes = curve->num_bytes;
int r;
/* Converting buffers to correct bit order: */
uECC_vli_bytesToNative(_private,
private_key,
BITS_TO_BYTES(curve->num_n_bits));
uECC_vli_bytesToNative(_public,
public_key,
num_bytes);
uECC_vli_bytesToNative(_public + num_words,
public_key + num_bytes,
num_bytes);
/* Regularize the bitcount for the private key so that attackers cannot use a
* side channel attack to learn the number of leading zeros. */
carry = regularize_k(_private, _private, tmp, curve);
/* If an RNG function was specified, try to get a random initial Z value to
* improve protection against side-channel attacks. */
if (g_rng_function) {
if (!uECC_generate_random_int(p2[carry], curve->p, num_words)) {
r = 0;
goto clear_and_out;
}
initial_Z = p2[carry];
}
EccPoint_mult(_public, _public, p2[!carry], initial_Z, curve->num_n_bits + 1,
curve);
uECC_vli_nativeToBytes(secret, num_bytes, _public);
r = !EccPoint_isZero(_public, curve);
clear_and_out:
/* erasing temporary buffer used to store secret: */
memset(p2, 0, sizeof(p2));
__asm__ __volatile__("" :: "g"(p2) : "memory");
memset(tmp, 0, sizeof(tmp));
__asm__ __volatile__("" :: "g"(tmp) : "memory");
memset(_private, 0, sizeof(_private));
__asm__ __volatile__("" :: "g"(_private) : "memory");
return r;
}

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