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commit 3f0cc5f09c8ced3abe2452f6feb0b901ec7aceeb Author: makejian <[email protected]> AuthorDate: Thu Aug 7 14:04:39 2025 +0800 crypto: export algorithm about ecc Transplanting the ECC algorithm from https://github.com/jestan/easy-ecc which is BSD lisence Signed-off-by: makejian <[email protected]> --- crypto/CMakeLists.txt | 1 + crypto/Makefile | 1 + crypto/ecc.c | 1731 +++++++++++++++++++++++++++++++++++++++++++++++++ include/crypto/ecc.h | 143 ++++ 4 files changed, 1876 insertions(+) diff --git a/crypto/CMakeLists.txt b/crypto/CMakeLists.txt index dbe5098fbac..ea47feefc10 100644 --- a/crypto/CMakeLists.txt +++ b/crypto/CMakeLists.txt @@ -45,6 +45,7 @@ if(CONFIG_CRYPTO) list(APPEND SRCS chachapoly.c) list(APPEND SRCS ecb_enc.c) list(APPEND SRCS ecb3_enc.c) + list(APPEND SRCS ecc.c) list(APPEND SRCS set_key.c) list(APPEND SRCS md5.c) list(APPEND SRCS poly1305.c) diff --git a/crypto/Makefile b/crypto/Makefile index f315dd81f58..3c879e6c504 100644 --- a/crypto/Makefile +++ b/crypto/Makefile @@ -49,6 +49,7 @@ CRYPTO_CSRCS += cast.c CRYPTO_CSRCS += chachapoly.c CRYPTO_CSRCS += ecb_enc.c CRYPTO_CSRCS += ecb3_enc.c +CRYPTO_CSRCS += ecc.c CRYPTO_CSRCS += set_key.c CRYPTO_CSRCS += md5.c CRYPTO_CSRCS += poly1305.c diff --git a/crypto/ecc.c b/crypto/ecc.c new file mode 100644 index 00000000000..0a94621aa6f --- /dev/null +++ b/crypto/ecc.c @@ -0,0 +1,1731 @@ +/**************************************************************************** + * crypto/ecc.c + * + * Copyright (c) 2013, 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 + * SPECIAL, HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, 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. + ****************************************************************************/ + +/**************************************************************************** + * Included Files + ****************************************************************************/ + +#include <fcntl.h> +#include <stdlib.h> +#include <string.h> +#include <unistd.h> +#include <sys/types.h> + +#include <crypto/ecc.h> +#include <nuttx/macro.h> + +/**************************************************************************** + * Pre-processor Definitions + ****************************************************************************/ + +#define NUM_ECC_DIGITS (ECC_BYTES / 8) +#define MAX_TRIES 16 + +#define EVEN(vli) (!(vli[0] & 1)) + +#define curve_p_16 { 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFDFFFFFFFF } +#define curve_p_24 { 0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFFFFFFFFFEull, \ + 0xFFFFFFFFFFFFFFFFull } +#define curve_p_32 { 0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull, \ + 0x0000000000000000ull, 0xFFFFFFFF00000001ull } +#define curve_p_48 { 0x00000000FFFFFFFF, 0xFFFFFFFF00000000, \ + 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, \ + 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF } + +#define curve_b_16 { 0xD824993C2CEE5ED3, 0xE87579C11079F43D } +#define curve_b_24 { 0xFEB8DEECC146B9B1ull, 0x0FA7E9AB72243049ull, \ + 0x64210519E59C80E7ull } +#define curve_b_32 { 0x3BCE3C3E27D2604Bull, 0x651D06B0CC53B0F6ull, \ + 0xB3EBBD55769886BCull, 0x5AC635D8AA3A93E7ull } +#define curve_b_48 { 0x2A85C8EDD3EC2AEF, 0xC656398D8A2ED19D, \ + 0x0314088F5013875A, 0x181D9C6EFE814112, \ + 0x988E056BE3F82D19, 0xB3312FA7E23EE7E4 } + +#define curve_g_16 { \ + { 0x0C28607CA52C5B86, 0x161FF7528B899B2D }, \ + { 0xC02DA292DDED7A83, 0xCF5AC8395BAFEB13 }} + +#define curve_g_24 { \ + { 0xF4FF0AFD82FF1012ull, 0x7CBF20EB43A18800ull, 0x188DA80EB03090F6ull }, \ + { 0x73F977A11E794811ull, 0x631011ED6B24CDD5ull, 0x07192B95FFC8DA78ull }} + +#define curve_g_32 { \ + { 0xF4A13945D898C296ull, 0x77037D812DEB33A0ull, \ + 0xF8BCE6E563A440F2ull, 0x6B17D1F2E12C4247ull }, \ + { 0xCBB6406837BF51F5ull, 0x2BCE33576B315ECEull, \ + 0x8EE7EB4A7C0F9E16ull, 0x4FE342E2FE1A7F9Bull }} + +#define curve_g_48 { \ + { 0x3A545E3872760AB7, 0x5502F25DBF55296C, 0x59F741E082542A38, \ + 0x6E1D3B628BA79B98, 0x8EB1C71EF320AD74, 0xAA87CA22BE8B0537}, \ + { 0x7A431D7C90EA0E5F, 0x0A60B1CE1D7E819D, 0xE9DA3113B5F0B8C0, \ + 0xF8F41DBD289A147C, 0x5D9E98BF9292DC29, 0x3617DE4A96262C6F }} + +#define curve_n_16 { 0x75A30D1B9038A115, 0xFFFFFFFE00000000 } +#define curve_n_24 { 0x146BC9B1B4D22831ull, 0xFFFFFFFF99DEF836ull, \ + 0xFFFFFFFFFFFFFFFFull } +#define curve_n_32 { 0xF3B9CAC2FC632551ull, 0xBCE6FAADA7179E84ull, \ + 0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFF00000000ull } +#define curve_n_48 { 0xECEC196ACCC52973, 0x581A0DB248B0A77A, \ + 0xC7634D81F4372DDF, 0xFFFFFFFFFFFFFFFF, \ + 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF } + +#if defined(__SIZEOF_INT128__) +# define SUPPORTS_INT128 1 +#else +# define SUPPORTS_INT128 0 +#endif + +/**************************************************************************** + * Private Type Definitions + ****************************************************************************/ + +typedef unsigned int uint; + +#if SUPPORTS_INT128 +typedef unsigned __int128 uint128_t; +#else +typedef struct +{ + uint64_t m_low; + uint64_t m_high; +} uint128_t; +#endif + +typedef struct +{ + uint64_t x[NUM_ECC_DIGITS]; + uint64_t y[NUM_ECC_DIGITS]; +} eccpoint_t; + +/**************************************************************************** + * Private Data + ****************************************************************************/ + +static uint64_t g_curve_p[NUM_ECC_DIGITS] = CONCATENATE(curve_p_, ECC_CURVE); +static uint64_t g_curve_b[NUM_ECC_DIGITS] = CONCATENATE(curve_b_, ECC_CURVE); +static uint64_t g_curve_n[NUM_ECC_DIGITS] = CONCATENATE(curve_n_, ECC_CURVE); +static eccpoint_t g_curve_g = CONCATENATE(curve_g_, ECC_CURVE); + +/**************************************************************************** + * Private Functions + ****************************************************************************/ + +static void vli_clear(FAR uint64_t *vli) +{ + uint i; + + for (i = 0; i < NUM_ECC_DIGITS; ++i) + { + vli[i] = 0; + } +} + +/* Returns 1 if vli == 0, 0 otherwise. */ + +static int vli_iszero(FAR uint64_t *vli) +{ + uint i; + + for (i = 0; i < NUM_ECC_DIGITS; ++i) + { + if (vli[i]) + { + return 0; + } + } + + return 1; +} + +/* Returns nonzero if bit bit of vli is set. */ + +static uint64_t vli_testbit(FAR uint64_t *vli, uint bit) +{ + return vli[bit / 64] & ((uint64_t)1 << (bit % 64)); +} + +/* Counts the number of 64-bit "digits" in vli. */ + +static uint vli_numdigits(FAR uint64_t *vli) +{ + int 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 = NUM_ECC_DIGITS - 1; i >= 0 && vli[i] == 0; --i) + { + } + + return i + 1; +} + +/* Counts the number of bits required for vli. */ + +static uint vli_numbits(FAR uint64_t *vli) +{ + uint64_t l_digit; + uint l_numdigits = vli_numdigits(vli); + uint i; + + if (l_numdigits == 0) + { + return 0; + } + + l_digit = vli[l_numdigits - 1]; + for (i = 0; l_digit; ++i) + { + l_digit >>= 1; + } + + return (l_numdigits - 1) * 64 + i; +} + +/* Sets dest = src. */ + +static void vli_set(FAR uint64_t *dest, FAR uint64_t *src) +{ + uint i; + + for (i = 0; i < NUM_ECC_DIGITS; ++i) + { + dest[i] = src[i]; + } +} + +/* Returns sign of left - right. */ + +static int vli_cmp(FAR uint64_t *left, FAR uint64_t *right) +{ + int i; + + for (i = NUM_ECC_DIGITS - 1; i >= 0; --i) + { + if (left[i] > right[i]) + { + return 1; + } + else if (left[i] < right[i]) + { + return -1; + } + } + + return 0; +} + +/* Computes result = in << c, returning carry. + * Can modify in place (if result == in). 0 < shift < 64. + */ + +static uint64_t vli_lshift(FAR uint64_t *result, FAR uint64_t *in, + uint shift) +{ + uint64_t l_carry = 0; + uint64_t l_temp; + uint i; + + for (i = 0; i < NUM_ECC_DIGITS; ++i) + { + l_temp = in[i]; + result[i] = (l_temp << shift) | l_carry; + l_carry = l_temp >> (64 - shift); + } + + return l_carry; +} + +/* Computes vli = vli >> 1. */ + +static void vli_rshift1(FAR uint64_t *vli) +{ + FAR uint64_t *l_end = vli; + uint64_t l_carry = 0; + uint64_t l_temp; + + vli += NUM_ECC_DIGITS; + while (vli-- > l_end) + { + l_temp = *vli; + *vli = (l_temp >> 1) | l_carry; + l_carry = l_temp << 63; + } +} + +/* Computes result = left + right, returning carry. Can modify in place. */ + +static uint64_t vli_add(FAR uint64_t *result, FAR uint64_t *left, + FAR uint64_t *right) +{ + uint64_t l_carry = 0; + uint64_t l_sum; + uint i; + + for (i = 0; i < NUM_ECC_DIGITS; ++i) + { + l_sum = left[i] + right[i] + l_carry; + if (l_sum != left[i]) + { + l_carry = (l_sum < left[i]); + } + + result[i] = l_sum; + } + + return l_carry; +} + +/* Computes result = left - right, returning borrow. Can modify in place. */ + +static uint64_t vli_sub(FAR uint64_t *result, FAR uint64_t *left, + FAR uint64_t *right) +{ + uint64_t l_borrow = 0; + uint64_t l_diff; + uint i; + + for (i = 0; i < NUM_ECC_DIGITS; ++i) + { + l_diff = left[i] - right[i] - l_borrow; + if (l_diff != left[i]) + { + l_borrow = (l_diff > left[i]); + } + + result[i] = l_diff; + } + + return l_borrow; +} + +#if SUPPORTS_INT128 + +/* Computes result = left * right. */ + +static void vli_mult(FAR uint64_t *result, FAR uint64_t *left, + FAR uint64_t *right) +{ + uint128_t l_product; + uint128_t r01 = 0; + uint64_t r2 = 0; + uint l_min; + uint i; + uint k; + + /* Compute each digit of result in sequence, maintaining the carries. */ + + for (k = 0; k < NUM_ECC_DIGITS * 2 - 1; ++k) + { + l_min = (k < NUM_ECC_DIGITS ? 0 : (k + 1) - NUM_ECC_DIGITS); + for (i = l_min; i <= k && i < NUM_ECC_DIGITS; ++i) + { + l_product = (uint128_t)left[i] * right[k - i]; + r01 += l_product; + r2 += (r01 < l_product); + } + + result[k] = (uint64_t)r01; + r01 = (r01 >> 64) | (((uint128_t)r2) << 64); + r2 = 0; + } + + result[NUM_ECC_DIGITS * 2 - 1] = (uint64_t)r01; +} + +/* Computes result = left^2. */ + +static void vli_square(FAR uint64_t *result, FAR uint64_t *left) +{ + uint128_t l_product; + uint128_t r01 = 0; + uint64_t r2 = 0; + uint l_min; + uint i; + uint k; + + for (k = 0; k < NUM_ECC_DIGITS * 2 - 1; ++k) + { + l_min = (k < NUM_ECC_DIGITS ? 0 : (k + 1) - NUM_ECC_DIGITS); + for (i = l_min; i <= k && i <= k - i; ++i) + { + l_product = (uint128_t)left[i] * left[k - i]; + if (i < k - i) + { + r2 += l_product >> 127; + l_product *= 2; + } + + r01 += l_product; + r2 += (r01 < l_product); + } + + result[k] = (uint64_t)r01; + r01 = (r01 >> 64) | (((uint128_t)r2) << 64); + r2 = 0; + } + + result[NUM_ECC_DIGITS * 2 - 1] = (uint64_t)r01; +} + +#else /* #if SUPPORTS_INT128 */ + +static uint128_t mul_64_64(uint64_t left, uint64_t right) +{ + uint128_t l_result; + uint64_t a0 = left & 0xffffffffull; + uint64_t a1 = left >> 32; + uint64_t b0 = right & 0xffffffffull; + uint64_t b1 = right >> 32; + uint64_t m0 = a0 * b0; + uint64_t m1 = a0 * b1; + uint64_t m2 = a1 * b0; + uint64_t m3 = a1 * b1; + + m2 += (m0 >> 32); + m2 += m1; + if (m2 < m1) + { + m3 += 0x100000000ull; + } + + l_result.m_low = (m0 & 0xffffffffull) | (m2 << 32); + l_result.m_high = m3 + (m2 >> 32); + + return l_result; +} + +static uint128_t add_128_128(uint128_t a, uint128_t b) +{ + uint128_t l_result; + + l_result.m_low = a.m_low + b.m_low; + l_result.m_high = a.m_high + b.m_high + (l_result.m_low < a.m_low); + return l_result; +} + +static void vli_mult(FAR uint64_t *result, FAR uint64_t *left, + FAR uint64_t *right) +{ + uint64_t r2 = 0; + uint i; + uint k; + uint128_t l_product; + uint128_t r01 = + { + 0, 0 + }; + + /* Compute each digit of result in sequence, maintaining the carries. */ + + for (k = 0; k < NUM_ECC_DIGITS * 2 - 1; ++k) + { + uint l_min = (k < NUM_ECC_DIGITS ? 0 : (k + 1) - NUM_ECC_DIGITS); + for (i = l_min; i <= k && i < NUM_ECC_DIGITS; ++i) + { + l_product = mul_64_64(left[i], right[k - i]); + r01 = add_128_128(r01, l_product); + r2 += (r01.m_high < l_product.m_high); + } + + result[k] = r01.m_low; + r01.m_low = r01.m_high; + r01.m_high = r2; + r2 = 0; + } + + result[NUM_ECC_DIGITS * 2 - 1] = r01.m_low; +} + +static void vli_square(FAR uint64_t *result, FAR uint64_t *left) +{ + uint64_t r2 = 0; + uint l_min; + uint i; + uint k; + uint128_t l_product; + uint128_t r01 = + { + 0, 0 + }; + + for (k = 0; k < NUM_ECC_DIGITS * 2 - 1; ++k) + { + l_min = (k < NUM_ECC_DIGITS ? 0 : (k + 1) - NUM_ECC_DIGITS); + for (i = l_min; i <= k && i <= k - i; ++i) + { + l_product = mul_64_64(left[i], left[k - i]); + if (i < k - i) + { + r2 += l_product.m_high >> 63; + l_product.m_high = (l_product.m_high << 1) | + (l_product.m_low >> 63); + l_product.m_low <<= 1; + } + + r01 = add_128_128(r01, l_product); + r2 += (r01.m_high < l_product.m_high); + } + + result[k] = r01.m_low; + r01.m_low = r01.m_high; + r01.m_high = r2; + r2 = 0; + } + + result[NUM_ECC_DIGITS * 2 - 1] = r01.m_low; +} + +#endif /* SUPPORTS_INT128 */ + +/* Computes result = (left + right) % mod. + * Assumes that left < mod and right < mod, result != mod. + */ + +static void vli_modadd(FAR uint64_t *result, FAR uint64_t *left, + FAR uint64_t *right, FAR uint64_t *mod) +{ + uint64_t l_carry = vli_add(result, left, right); + + if (l_carry || vli_cmp(result, mod) >= 0) + { + /* result > mod (result = mod + remainder), + * so subtract mod to get remainder. + */ + + vli_sub(result, result, mod); + } +} + +/* Computes result = (left - right) % mod. + * Assumes that left < mod and right < mod, result != mod. + */ + +static void vli_modsub(FAR uint64_t *result, FAR uint64_t *left, + FAR uint64_t *right, FAR uint64_t *mod) +{ + uint64_t l_borrow = vli_sub(result, left, right); + + 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). + */ + + vli_add(result, result, mod); + } +} + +#if ECC_CURVE == secp128r1 + +/* Computes result = product % g_curve_p. + * See algorithm 5 and 6 from + * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf + */ + +static void vli_mmod_fast(FAR uint64_t *result, + FAR uint64_t *product) +{ + uint64_t l_tmp[NUM_ECC_DIGITS]; + int l_carry; + + vli_set(result, product); + + l_tmp[0] = product[2]; + l_tmp[1] = (product[3] & 0x1ffffffffull) | (product[2] << 33); + l_carry = vli_add(result, result, l_tmp); + + l_tmp[0] = (product[2] >> 31) | (product[3] << 33); + l_tmp[1] = (product[3] >> 31) | + ((product[2] & 0xffffffff80000000ull) << 2); + l_carry += vli_add(result, result, l_tmp); + + l_tmp[0] = (product[2] >> 62) | (product[3] << 2); + l_tmp[1] = (product[3] >> 62) | + ((product[2] & 0xc000000000000000ull) >> 29) | + (product[3] << 35); + l_carry += vli_add(result, result, l_tmp); + + l_tmp[0] = (product[3] >> 29); + l_tmp[1] = ((product[3] & 0xffffffffe0000000ull) << 4); + l_carry += vli_add(result, result, l_tmp); + + l_tmp[0] = (product[3] >> 60); + l_tmp[1] = (product[3] & 0xfffffffe00000000ull); + l_carry += vli_add(result, result, l_tmp); + + l_tmp[0] = 0; + l_tmp[1] = ((product[3] & 0xf000000000000000ull) >> 27); + l_carry += vli_add(result, result, l_tmp); + + while (l_carry || vli_cmp(g_curve_p, result) != 1) + { + l_carry -= vli_sub(result, result, g_curve_p); + } +} + +#elif ECC_CURVE == secp192r1 + +/* Computes result = product % g_curve_p. + * See algorithm 5 and 6 from + * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf + */ + +static void vli_mmod_fast(FAR uint64_t *result, + FAR uint64_t *product) +{ + uint64_t l_tmp[NUM_ECC_DIGITS]; + int l_carry; + + vli_set(result, product); + + vli_set(l_tmp, &product[3]); + l_carry = vli_add(result, result, l_tmp); + + l_tmp[0] = 0; + l_tmp[1] = product[3]; + l_tmp[2] = product[4]; + l_carry += vli_add(result, result, l_tmp); + + l_tmp[0] = l_tmp[1] = product[5]; + l_tmp[2] = 0; + l_carry += vli_add(result, result, l_tmp); + + while (l_carry || vli_cmp(g_curve_p, result) != 1) + { + l_carry -= vli_sub(result, result, g_curve_p); + } +} + +#elif ECC_CURVE == secp256r1 + +/* Computes result = product % g_curve_p + * from http://www.nsa.gov/ia/_files/nist-routines.pdf + */ + +static void vli_mmod_fast(FAR uint64_t *result, + FAR uint64_t *product) +{ + uint64_t l_tmp[NUM_ECC_DIGITS]; + int l_carry; + + /* t */ + + vli_set(result, product); + + /* s1 */ + + l_tmp[0] = 0; + l_tmp[1] = product[5] & 0xffffffff00000000ull; + l_tmp[2] = product[6]; + l_tmp[3] = product[7]; + l_carry = vli_lshift(l_tmp, l_tmp, 1); + l_carry += vli_add(result, result, l_tmp); + + /* s2 */ + + l_tmp[1] = product[6] << 32; + l_tmp[2] = (product[6] >> 32) | (product[7] << 32); + l_tmp[3] = product[7] >> 32; + l_carry += vli_lshift(l_tmp, l_tmp, 1); + l_carry += vli_add(result, result, l_tmp); + + /* s3 */ + + l_tmp[0] = product[4]; + l_tmp[1] = product[5] & 0xffffffff; + l_tmp[2] = 0; + l_tmp[3] = product[7]; + l_carry += vli_add(result, result, l_tmp); + + /* s4 */ + + l_tmp[0] = (product[4] >> 32) | (product[5] << 32); + l_tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull); + l_tmp[2] = product[7]; + l_tmp[3] = (product[6] >> 32) | (product[4] << 32); + l_carry += vli_add(result, result, l_tmp); + + /* d1 */ + + l_tmp[0] = (product[5] >> 32) | (product[6] << 32); + l_tmp[1] = (product[6] >> 32); + l_tmp[2] = 0; + l_tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32); + l_carry -= vli_sub(result, result, l_tmp); + + /* d2 */ + + l_tmp[0] = product[6]; + l_tmp[1] = product[7]; + l_tmp[2] = 0; + l_tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull); + l_carry -= vli_sub(result, result, l_tmp); + + /* d3 */ + + l_tmp[0] = (product[6] >> 32) | (product[7] << 32); + l_tmp[1] = (product[7] >> 32) | (product[4] << 32); + l_tmp[2] = (product[4] >> 32) | (product[5] << 32); + l_tmp[3] = (product[6] << 32); + l_carry -= vli_sub(result, result, l_tmp); + + /* d4 */ + + l_tmp[0] = product[7]; + l_tmp[1] = product[4] & 0xffffffff00000000ull; + l_tmp[2] = product[5]; + l_tmp[3] = product[6] & 0xffffffff00000000ull; + l_carry -= vli_sub(result, result, l_tmp); + + if (l_carry < 0) + { + do + { + l_carry += vli_add(result, result, g_curve_p); + } + while (l_carry < 0); + } + else + { + while (l_carry || vli_cmp(g_curve_p, result) != 1) + { + l_carry -= vli_sub(result, result, g_curve_p); + } + } +} + +#elif ECC_CURVE == secp384r1 + +static void omega_mult(uint64_t *result, uint64_t *right) +{ + uint64_t l_tmp[NUM_ECC_DIGITS]; + uint64_t l_carry; + uint64_t l_diff; + uint i; + + /* Multiply by (2^128 + 2^96 - 2^32 + 1). */ + + vli_set(result, right); /* 1 */ + l_carry = vli_lshift(l_tmp, right, 32); + result[1 + NUM_ECC_DIGITS] = l_carry + vli_add(result + 1, result + 1, l_tmp); /* 2^96 + 1 */ + + /* 2^128 + 2^96 + 1 */ + + result[2 + NUM_ECC_DIGITS] = vli_add(result + 2, result + 2, right); + + /* 2^128 + 2^96 - 2^32 + 1 */ + + l_carry += vli_sub(result, result, l_tmp); + l_diff = result[NUM_ECC_DIGITS] - l_carry; + if (l_diff > result[NUM_ECC_DIGITS]) + { + /* Propagate borrow if necessary. */ + + for (i = 1 + NUM_ECC_DIGITS; ; ++i) + { + --result[i]; + if (result[i] != (uint64_t)-1) + { + break; + } + } + } + + result[NUM_ECC_DIGITS] = l_diff; +} + +/* Computes result = product % g_curve_p + * see PDF "Comparing Elliptic Curve Cryptography and RSA on 8-bit CPUs" + * section "Curve-Specific Optimizations" + */ + +static void vli_mmod_fast(uint64_t *result, uint64_t *product) +{ + uint64_t l_tmp[2 * NUM_ECC_DIGITS]; + uint64_t l_carry; + uint64_t l_sum; + uint i; + + while (!vli_iszero(product + NUM_ECC_DIGITS)) /* While c1 != 0 */ + { + l_carry = 0; + + vli_clear(l_tmp); + vli_clear(l_tmp + NUM_ECC_DIGITS); + omega_mult(l_tmp, product + NUM_ECC_DIGITS); /* tmp = w * c1 */ + + /* p = c0 */ + + vli_clear(product + NUM_ECC_DIGITS); + + /* (c1, c0) = c0 + w * c1 */ + + for (i = 0; i < NUM_ECC_DIGITS + 3; ++i) + { + l_sum = product[i] + l_tmp[i] + l_carry; + if (l_sum != product[i]) + { + l_carry = (l_sum < product[i]); + } + + product[i] = l_sum; + } + } + + while (vli_cmp(product, g_curve_p) > 0) + { + vli_sub(product, product, g_curve_p); + } + + vli_set(result, product); +} + +#endif + +/* Computes result = (left * right) % g_curve_p. */ + +static void vli_modmult_fast(FAR uint64_t *result, FAR uint64_t *left, + FAR uint64_t *right) +{ + uint64_t l_product[2 * NUM_ECC_DIGITS]; + + vli_mult(l_product, left, right); + vli_mmod_fast(result, l_product); +} + +/* Computes result = left^2 % g_curve_p. */ + +static void vli_modsquare_fast(FAR uint64_t *result, + FAR uint64_t *left) +{ + uint64_t l_product[2 * NUM_ECC_DIGITS]; + + vli_square(l_product, left); + vli_mmod_fast(result, l_product); +} + +/* Computes result = (1 / input) % mod. All VLIs are the same size. + * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide" + * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf + */ + +static void vli_modinv(FAR uint64_t *result, FAR uint64_t *input, + FAR uint64_t *mod) +{ + uint64_t a[NUM_ECC_DIGITS]; + uint64_t b[NUM_ECC_DIGITS]; + uint64_t u[NUM_ECC_DIGITS]; + uint64_t v[NUM_ECC_DIGITS]; + uint64_t l_carry; + int l_cmpresult; + + if (vli_iszero(input)) + { + vli_clear(result); + return; + } + + vli_set(a, input); + vli_set(b, mod); + vli_clear(u); + u[0] = 1; + vli_clear(v); + + while ((l_cmpresult = vli_cmp(a, b)) != 0) + { + l_carry = 0; + if (EVEN(a)) + { + vli_rshift1(a); + if (!EVEN(u)) + { + l_carry = vli_add(u, u, mod); + } + + vli_rshift1(u); + if (l_carry) + { + u[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull; + } + } + else if (EVEN(b)) + { + vli_rshift1(b); + if (!EVEN(v)) + { + l_carry = vli_add(v, v, mod); + } + + vli_rshift1(v); + if (l_carry) + { + v[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull; + } + } + else if (l_cmpresult > 0) + { + vli_sub(a, a, b); + vli_rshift1(a); + if (vli_cmp(u, v) < 0) + { + vli_add(u, u, mod); + } + + vli_sub(u, u, v); + if (!EVEN(u)) + { + l_carry = vli_add(u, u, mod); + } + + vli_rshift1(u); + if (l_carry) + { + u[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull; + } + } + else + { + vli_sub(b, b, a); + vli_rshift1(b); + if (vli_cmp(v, u) < 0) + { + vli_add(v, v, mod); + } + + vli_sub(v, v, u); + if (!EVEN(v)) + { + l_carry = vli_add(v, v, mod); + } + + vli_rshift1(v); + if (l_carry) + { + v[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull; + } + } + } + + vli_set(result, u); +} + +/* ------ Point operations ------ */ + +/* Returns 1 if point is the point at infinity, 0 otherwise. */ + +static int eccpoint_iszero(FAR eccpoint_t *point) +{ + return vli_iszero(point->x) && vli_iszero(point->y); +} + +/* Point multiplication algorithm using Montgomery's ladder with + * co-Z coordinates. From http://eprint.iacr.org/2011/338.pdf + */ + +/* Double in place */ + +static void eccpoint_double_jacobian(FAR uint64_t *X1, + FAR uint64_t *Y1, + FAR uint64_t *Z1) +{ + /* t1 = X, t2 = Y, t3 = Z */ + + uint64_t t4[NUM_ECC_DIGITS]; + uint64_t t5[NUM_ECC_DIGITS]; + uint64_t l_carry; + + if (vli_iszero(Z1)) + { + return; + } + + vli_modsquare_fast(t4, Y1); /* t4 = y1^2 */ + vli_modmult_fast(t5, X1, t4); /* t5 = x1*y1^2 = A */ + vli_modsquare_fast(t4, t4); /* t4 = y1^4 */ + vli_modmult_fast(Y1, Y1, Z1); /* t2 = y1*z1 = z3 */ + vli_modsquare_fast(Z1, Z1); /* t3 = z1^2 */ + + vli_modadd(X1, X1, Z1, g_curve_p); /* t1 = x1 + z1^2 */ + vli_modadd(Z1, Z1, Z1, g_curve_p); /* t3 = 2*z1^2 */ + vli_modsub(Z1, X1, Z1, g_curve_p); /* t3 = x1 - z1^2 */ + + /* t1 = x1^2 - z1^4 */ + + vli_modmult_fast(X1, X1, Z1); + + vli_modadd(Z1, X1, X1, g_curve_p); /* t3 = 2*(x1^2 - z1^4) */ + vli_modadd(X1, X1, Z1, g_curve_p); /* t1 = 3*(x1^2 - z1^4) */ + if (vli_testbit(X1, 0)) + { + l_carry = vli_add(X1, X1, g_curve_p); + vli_rshift1(X1); + X1[NUM_ECC_DIGITS - 1] |= l_carry << 63; + } + else + { + vli_rshift1(X1); + } + + /* t1 = 3/2*(x1^2 - z1^4) = B */ + + /* t3 = B^2 */ + + vli_modsquare_fast(Z1, X1); + + /* t3 = B^2 - A */ + + vli_modsub(Z1, Z1, t5, g_curve_p); + + /* t3 = B^2 - 2A = x3 */ + + vli_modsub(Z1, Z1, t5, g_curve_p); + + /* t5 = A - x3 */ + + vli_modsub(t5, t5, Z1, g_curve_p); + + /* t1 = B * (A - x3) */ + + vli_modmult_fast(X1, X1, t5); + + /* t4 = B * (A - x3) - y1^4 = y3 */ + + vli_modsub(t4, X1, t4, g_curve_p); + + vli_set(X1, Z1); + vli_set(Z1, Y1); + vli_set(Y1, t4); +} + +/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */ + +static void apply_z(FAR uint64_t *X1, FAR uint64_t *Y1, + FAR uint64_t *Z) +{ + uint64_t t1[NUM_ECC_DIGITS]; + + /* z^2 */ + + vli_modsquare_fast(t1, Z); + + /* x1 * z^2 */ + + vli_modmult_fast(X1, X1, t1); + + /* z^3 */ + + vli_modmult_fast(t1, t1, Z); + + /* y1 * z^3 */ + + vli_modmult_fast(Y1, Y1, t1); +} + +/* P = (x1, y1) => 2P, (x2, y2) => P' */ + +static void xycz_initial_double(FAR uint64_t *X1, FAR uint64_t *Y1, + FAR uint64_t *X2, FAR uint64_t *Y2, + FAR uint64_t *initialz) +{ + uint64_t z[NUM_ECC_DIGITS]; + + vli_set(X2, X1); + vli_set(Y2, Y1); + + vli_clear(z); + z[0] = 1; + if (initialz) + { + vli_set(z, initialz); + } + + apply_z(X1, Y1, z); + + eccpoint_double_jacobian(X1, Y1, z); + + apply_z(X2, Y2, z); +} + +/* Input P = (x1, y1, Z), Q = (x2, y2, Z) + * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3) + * or P => P', Q => P + Q + */ + +static void xycz_add(FAR uint64_t *X1, FAR uint64_t *Y1, + FAR uint64_t *X2, FAR uint64_t *Y2) +{ + /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ + + uint64_t t5[NUM_ECC_DIGITS]; + + /* t5 = x2 - x1 */ + + vli_modsub(t5, X2, X1, g_curve_p); + + /* t5 = (x2 - x1)^2 = A */ + + vli_modsquare_fast(t5, t5); + + /* t1 = x1*A = B */ + + vli_modmult_fast(X1, X1, t5); + + /* t3 = x2*A = C */ + + vli_modmult_fast(X2, X2, t5); + + /* t4 = y2 - y1 */ + + vli_modsub(Y2, Y2, Y1, g_curve_p); + + /* t5 = (y2 - y1)^2 = D */ + + vli_modsquare_fast(t5, Y2); + + /* t5 = D - B */ + + vli_modsub(t5, t5, X1, g_curve_p); + + /* t5 = D - B - C = x3 */ + + vli_modsub(t5, t5, X2, g_curve_p); + + /* t3 = C - B */ + + vli_modsub(X2, X2, X1, g_curve_p); + + /* t2 = y1*(C - B) */ + + vli_modmult_fast(Y1, Y1, X2); + + /* t3 = B - x3 */ + + vli_modsub(X2, X1, t5, g_curve_p); + + /* t4 = (y2 - y1)*(B - x3) */ + + vli_modmult_fast(Y2, Y2, X2); + + /* t4 = y3 */ + + vli_modsub(Y2, Y2, Y1, g_curve_p); + vli_set(X2, t5); +} + +/* 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(FAR uint64_t *X1, FAR uint64_t *Y1, + FAR uint64_t *X2, FAR uint64_t *Y2) +{ + /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ + + uint64_t t5[NUM_ECC_DIGITS]; + uint64_t t6[NUM_ECC_DIGITS]; + uint64_t t7[NUM_ECC_DIGITS]; + + /* t5 = x2 - x1 */ + + vli_modsub(t5, X2, X1, g_curve_p); + + /* t5 = (x2 - x1)^2 = A */ + + vli_modsquare_fast(t5, t5); + + /* t1 = x1*A = B */ + + vli_modmult_fast(X1, X1, t5); + + /* t3 = x2*A = C */ + + vli_modmult_fast(X2, X2, t5); + + /* t4 = y2 + y1 */ + + vli_modadd(t5, Y2, Y1, g_curve_p); + + /* t4 = y2 - y1 */ + + vli_modsub(Y2, Y2, Y1, g_curve_p); + + /* t6 = C - B */ + + vli_modsub(t6, X2, X1, g_curve_p); + + /* t2 = y1 * (C - B) */ + + vli_modmult_fast(Y1, Y1, t6); + + /* t6 = B + C */ + + vli_modadd(t6, X1, X2, g_curve_p); + + /* t3 = (y2 - y1)^2 */ + + vli_modsquare_fast(X2, Y2); + + /* t3 = x3 */ + + vli_modsub(X2, X2, t6, g_curve_p); + + /* t7 = B - x3 */ + + vli_modsub(t7, X1, X2, g_curve_p); + + /* t4 = (y2 - y1)*(B - x3) */ + + vli_modmult_fast(Y2, Y2, t7); + + /* t4 = y3 */ + + vli_modsub(Y2, Y2, Y1, g_curve_p); + + /* t7 = (y2 + y1)^2 = F */ + + vli_modsquare_fast(t7, t5); + + /* t7 = x3' */ + + vli_modsub(t7, t7, t6, g_curve_p); + + /* t6 = x3' - B */ + + vli_modsub(t6, t7, X1, g_curve_p); + + /* t6 = (y2 + y1)*(x3' - B) */ + + vli_modmult_fast(t6, t6, t5); + + /* t2 = y3' */ + + vli_modsub(Y1, t6, Y1, g_curve_p); + + vli_set(X1, t7); +} + +static void eccpoint_mult(FAR eccpoint_t *result, FAR eccpoint_t *point, + FAR uint64_t *scalar, FAR uint64_t *initialz) +{ + /* R0 and R1 */ + + uint64_t rx[2][NUM_ECC_DIGITS]; + uint64_t ry[2][NUM_ECC_DIGITS]; + uint64_t z[NUM_ECC_DIGITS]; + int nb; + int i; + + vli_set(rx[1], point->x); + vli_set(ry[1], point->y); + + xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initialz); + + for (i = vli_numbits(scalar) - 2; i > 0; --i) + { + nb = !vli_testbit(scalar, i); + xycz_addc(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb]); + xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb]); + } + + nb = !vli_testbit(scalar, 0); + xycz_addc(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb]); + + /* Find final 1/Z value. */ + + /* X1 - X0 */ + + vli_modsub(z, rx[1], rx[0], g_curve_p); + + /* Yb * (X1 - X0) */ + + vli_modmult_fast(z, z, ry[1 - nb]); + + /* xP * Yb * (X1 - X0) */ + + vli_modmult_fast(z, z, point->x); + + /* 1 / (xP * Yb * (X1 - X0)) */ + + vli_modinv(z, z, g_curve_p); + + /* yP / (xP * Yb * (X1 - X0)) */ + + vli_modmult_fast(z, z, point->y); + + /* Xb * yP / (xP * Yb * (X1 - X0)) */ + + vli_modmult_fast(z, z, rx[1 - nb]); + + /* End 1/Z calculation */ + + xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb]); + + apply_z(rx[0], ry[0], z); + + vli_set(result->x, rx[0]); + vli_set(result->y, ry[0]); +} + +static void ecc_bytes2native(uint64_t native[NUM_ECC_DIGITS], + const uint8_t bytes[ECC_BYTES]) +{ + FAR const uint8_t *digit; + unsigned i; + + for (i = 0; i < NUM_ECC_DIGITS; ++i) + { + digit = bytes + 8 * (NUM_ECC_DIGITS - 1 - i); + native[i] = ((uint64_t)digit[0] << 56) | ((uint64_t)digit[1] << 48) | + ((uint64_t)digit[2] << 40) | ((uint64_t)digit[3] << 32) | + ((uint64_t)digit[4] << 24) | ((uint64_t)digit[5] << 16) | + ((uint64_t)digit[6] << 8) | (uint64_t)digit[7]; + } +} + +static void ecc_native2bytes(uint8_t bytes[ECC_BYTES], + const uint64_t native[NUM_ECC_DIGITS]) +{ + FAR uint8_t *digit; + unsigned i; + + for (i = 0; i < NUM_ECC_DIGITS; ++i) + { + digit = bytes + 8 * (NUM_ECC_DIGITS - 1 - i); + digit[0] = native[i] >> 56; + digit[1] = native[i] >> 48; + digit[2] = native[i] >> 40; + digit[3] = native[i] >> 32; + digit[4] = native[i] >> 24; + digit[5] = native[i] >> 16; + digit[6] = native[i] >> 8; + digit[7] = native[i]; + } +} + +/* Compute a = sqrt(a) (mod g_curve_p). */ + +static void mod_sqrt(uint64_t a[NUM_ECC_DIGITS]) +{ + unsigned i; + uint64_t l_result[NUM_ECC_DIGITS] = + { + 1 + }; + + uint64_t p1[NUM_ECC_DIGITS] = + { + 1 + }; + + /* Since g_curve_p == 3 (mod 4) for all supported curves, we can + * compute sqrt(a) = a^((g_curve_p + 1) / 4) (mod g_curve_p). + */ + + vli_add(p1, g_curve_p, p1); /* p1 = g_curve_p + 1 */ + for (i = vli_numbits(p1) - 1; i > 1; --i) + { + vli_modsquare_fast(l_result, l_result); + if (vli_testbit(p1, i)) + { + vli_modmult_fast(l_result, l_result, a); + } + } + + vli_set(a, l_result); +} + +static void +ecc_point_decompress(FAR eccpoint_t *point, + const uint8_t compressed[ECC_BYTES + 1]) +{ + /* -a = 3 */ + + uint64_t _3[NUM_ECC_DIGITS] = + { + 3 + }; + + ecc_bytes2native(point->x, compressed + 1); + + /* y = x^2 */ + + vli_modsquare_fast(point->y, point->x); + + /* y = x^2 - 3 */ + + vli_modsub(point->y, point->y, _3, g_curve_p); + + /* y = x^3 - 3x */ + + vli_modmult_fast(point->y, point->y, point->x); + + /* y = x^3 - 3x + b */ + + vli_modadd(point->y, point->y, g_curve_b, g_curve_p); + + mod_sqrt(point->y); + + if ((point->y[0] & 0x01) != (compressed[0] & 0x01)) + { + vli_sub(point->y, g_curve_p, point->y); + } +} + +/* -------- ECDSA code -------- */ + +/* Computes result = (left * right) % mod. */ + +static void vli_modmult(FAR uint64_t *result, FAR uint64_t *left, + FAR uint64_t *right, FAR uint64_t *mod) +{ + uint64_t l_product[2 * NUM_ECC_DIGITS]; + uint64_t l_modmultiple[2 * NUM_ECC_DIGITS]; + uint64_t l_carry; + uint l_modbits = vli_numbits(mod); + uint l_productbits; + uint l_digitshift; + uint l_bitshift; + int l_cmp; + + vli_mult(l_product, left, right); + l_productbits = vli_numbits(l_product + NUM_ECC_DIGITS); + if (l_productbits) + { + l_productbits += NUM_ECC_DIGITS * 64; + } + else + { + l_productbits = vli_numbits(l_product); + } + + if (l_productbits < l_modbits) + { + /* l_product < mod. */ + + vli_set(result, l_product); + return; + } + + /* Shift mod by (l_leftBits - l_modbits). + * This multiplies mod by the largest power of two possible + * while still resulting in a number less than left. + */ + + vli_clear(l_modmultiple); + vli_clear(l_modmultiple + NUM_ECC_DIGITS); + l_digitshift = (l_productbits - l_modbits) / 64; + l_bitshift = (l_productbits - l_modbits) % 64; + if (l_bitshift) + { + l_modmultiple[l_digitshift + NUM_ECC_DIGITS] = + vli_lshift(l_modmultiple + l_digitshift, mod, l_bitshift); + } + else + { + vli_set(l_modmultiple + l_digitshift, mod); + } + + /* Subtract all multiples of mod to get the remainder. */ + + vli_clear(result); + + /* Use result as a temp var to store 1 (for subtraction) */ + + result[0] = 1; + while (l_productbits > NUM_ECC_DIGITS * 64 || + vli_cmp(l_modmultiple, mod) >= 0) + { + l_cmp = vli_cmp(l_modmultiple + NUM_ECC_DIGITS, + l_product + NUM_ECC_DIGITS); + if (l_cmp < 0 || + (l_cmp == 0 && vli_cmp(l_modmultiple, l_product) <= 0)) + { + if (vli_sub(l_product, l_product, l_modmultiple)) + { + /* borrow */ + + vli_sub(l_product + NUM_ECC_DIGITS, + l_product + NUM_ECC_DIGITS, result); + } + + vli_sub(l_product + NUM_ECC_DIGITS, l_product + NUM_ECC_DIGITS, + l_modmultiple + NUM_ECC_DIGITS); + } + + l_carry = (l_modmultiple[NUM_ECC_DIGITS] & 0x01) << 63; + vli_rshift1(l_modmultiple + NUM_ECC_DIGITS); + vli_rshift1(l_modmultiple); + l_modmultiple[NUM_ECC_DIGITS - 1] |= l_carry; + --l_productbits; + } + + vli_set(result, l_product); +} + +static uint umax(uint a, uint b) +{ + return a > b ? a : b; +} + +/**************************************************************************** + * Public Functions + ****************************************************************************/ + +int ecc_make_key(uint8_t publickey[ECC_BYTES + 1], + uint8_t privatekey[ECC_BYTES]) +{ + uint64_t l_private[NUM_ECC_DIGITS]; + eccpoint_t l_public; + unsigned l_tries = 0; + + do + { + if (l_tries++ >= MAX_TRIES) + { + return 0; + } + + arc4random_buf(l_private, NUM_ECC_DIGITS); + + if (vli_iszero(l_private)) + { + continue; + } + + /* Make sure the private key is in the range [1, n-1]. + * For the supported curves, n is always large enough that we only + * need to subtract once at most. + */ + + if (vli_cmp(g_curve_n, l_private) != 1) + { + vli_sub(l_private, l_private, g_curve_n); + } + + eccpoint_mult(&l_public, &g_curve_g, l_private, NULL); + } + while (eccpoint_iszero(&l_public)); + + ecc_native2bytes(privatekey, l_private); + ecc_native2bytes(publickey + 1, l_public.x); + publickey[0] = 2 + (l_public.y[0] & 0x01); + return 1; +} + +int ecdh_shared_secret(const uint8_t publickey[ECC_BYTES + 1], + const uint8_t privatekey[ECC_BYTES], + uint8_t secret[ECC_BYTES]) +{ + eccpoint_t l_product; + eccpoint_t l_public; + uint64_t l_private[NUM_ECC_DIGITS]; + uint64_t l_random[NUM_ECC_DIGITS]; + + arc4random_buf(l_random, NUM_ECC_DIGITS); + ecc_point_decompress(&l_public, publickey); + ecc_bytes2native(l_private, privatekey); + + eccpoint_mult(&l_product, &l_public, l_private, l_random); + + ecc_native2bytes(secret, l_product.x); + + return !eccpoint_iszero(&l_product); +} + +int ecdsa_sign(const uint8_t privatekey[ECC_BYTES], + const uint8_t hash[ECC_BYTES], + uint8_t signature[ECC_BYTES * 2]) +{ + uint64_t k[NUM_ECC_DIGITS]; + uint64_t l_tmp[NUM_ECC_DIGITS]; + uint64_t l_s[NUM_ECC_DIGITS]; + unsigned l_tries = 0; + eccpoint_t p; + + do + { + if (l_tries++ >= MAX_TRIES) + { + return 0; + } + + arc4random_buf(k, NUM_ECC_DIGITS); + + if (vli_iszero(k)) + { + continue; + } + + if (vli_cmp(g_curve_n, k) != 1) + { + vli_sub(k, k, g_curve_n); + } + + /* tmp = k * G */ + + eccpoint_mult(&p, &g_curve_g, k, NULL); + + /* r = x1 (mod n) */ + + if (vli_cmp(g_curve_n, p.x) != 1) + { + vli_sub(p.x, p.x, g_curve_n); + } + } + while (vli_iszero(p.x)); + + ecc_native2bytes(signature, p.x); + + ecc_bytes2native(l_tmp, privatekey); + vli_modmult(l_s, p.x, l_tmp, g_curve_n); /* s = r*d */ + ecc_bytes2native(l_tmp, hash); + vli_modadd(l_s, l_tmp, l_s, g_curve_n); /* s = e + r*d */ + + /* k = 1 / k */ + + vli_modinv(k, k, g_curve_n); + + /* s = (e + r*d) / k */ + + vli_modmult(l_s, l_s, k, g_curve_n); + ecc_native2bytes(signature + ECC_BYTES, l_s); + + return 1; +} + +int ecdsa_verify(const uint8_t publickey[ECC_BYTES + 1], + const uint8_t hash[ECC_BYTES], + const uint8_t signature[ECC_BYTES * 2]) +{ + uint64_t u1[NUM_ECC_DIGITS]; + uint64_t u2[NUM_ECC_DIGITS]; + uint64_t z[NUM_ECC_DIGITS]; + uint64_t rx[NUM_ECC_DIGITS]; + uint64_t ry[NUM_ECC_DIGITS]; + uint64_t tx[NUM_ECC_DIGITS]; + uint64_t ty[NUM_ECC_DIGITS]; + uint64_t tz[NUM_ECC_DIGITS]; + uint64_t l_r[NUM_ECC_DIGITS]; + uint64_t l_s[NUM_ECC_DIGITS]; + uint l_numbits; + eccpoint_t *l_point; + eccpoint_t l_public; + eccpoint_t l_sum; + int l_index; + int i; + + /* Use Shamir's trick to calculate u1*G + u2*Q */ + + eccpoint_t *l_points[4] = + { + NULL, &g_curve_g, &l_public, &l_sum + }; + + ecc_point_decompress(&l_public, publickey); + ecc_bytes2native(l_r, signature); + ecc_bytes2native(l_s, signature + ECC_BYTES); + + if (vli_iszero(l_r) || vli_iszero(l_s)) + { + /* r, s must not be 0. */ + + return 0; + } + + if (vli_cmp(g_curve_n, l_r) != 1 || vli_cmp(g_curve_n, l_s) != 1) + { + /* r, s must be < n. */ + + return 0; + } + + /* Calculate u1 and u2. */ + + vli_modinv(z, l_s, g_curve_n); /* Z = s^-1 */ + ecc_bytes2native(u1, hash); + vli_modmult(u1, u1, z, g_curve_n); /* u1 = e/s */ + + /* u2 = r/s */ + + vli_modmult(u2, l_r, z, g_curve_n); + + /* Calculate l_sum = G + Q. */ + + vli_set(l_sum.x, l_public.x); + vli_set(l_sum.y, l_public.y); + vli_set(tx, g_curve_g.x); + vli_set(ty, g_curve_g.y); + vli_modsub(z, l_sum.x, tx, g_curve_p); /* Z = x2 - x1 */ + xycz_add(tx, ty, l_sum.x, l_sum.y); + vli_modinv(z, z, g_curve_p); /* Z = 1/Z */ + apply_z(l_sum.x, l_sum.y, z); + + l_numbits = umax(vli_numbits(u1), vli_numbits(u2)); + + l_point = l_points[(!!vli_testbit(u1, l_numbits - 1)) | + ((!!vli_testbit(u2, l_numbits - 1)) << 1)]; + vli_set(rx, l_point->x); + vli_set(ry, l_point->y); + vli_clear(z); + z[0] = 1; + + for (i = l_numbits - 2; i >= 0; --i) + { + eccpoint_double_jacobian(rx, ry, z); + + l_index = (!!vli_testbit(u1, i)) | ((!!vli_testbit(u2, i)) << 1); + l_point = l_points[l_index]; + if (l_point) + { + vli_set(tx, l_point->x); + vli_set(ty, l_point->y); + apply_z(tx, ty, z); + vli_modsub(tz, rx, tx, g_curve_p); /* Z = x2 - x1 */ + xycz_add(tx, ty, rx, ry); + vli_modmult_fast(z, z, tz); + } + } + + vli_modinv(z, z, g_curve_p); /* Z = 1/Z */ + apply_z(rx, ry, z); + + /* v = x1 (mod n) */ + + if (vli_cmp(g_curve_n, rx) != 1) + { + vli_sub(rx, rx, g_curve_n); + } + + /* Accept only if v == r. */ + + return vli_cmp(rx, l_r) == 0; +} diff --git a/include/crypto/ecc.h b/include/crypto/ecc.h new file mode 100644 index 00000000000..eb3898eaabd --- /dev/null +++ b/include/crypto/ecc.h @@ -0,0 +1,143 @@ +/**************************************************************************** + * include/crypto/ecc.h + * + * Copyright (c) 2013, 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 + * SPECIAL, HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, 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. + ****************************************************************************/ + +#ifndef __INCLUDE_CRYPTO_ECC_H +#define __INCLUDE_CRYPTO_ECC_H + +/**************************************************************************** + * Included Files + ****************************************************************************/ + +#include <stdint.h> + +/**************************************************************************** + * Pre-processor Definitions + ****************************************************************************/ + +/* Curve selection options. */ + +#define secp128r1 16 +#define secp192r1 24 +#define secp256r1 32 +#define secp384r1 48 + +#ifndef ECC_CURVE +# define ECC_CURVE secp256r1 +#endif + +#if (ECC_CURVE != secp128r1 && \ + ECC_CURVE != secp192r1 && \ + ECC_CURVE != secp256r1 && \ + ECC_CURVE != secp384r1) +# error "Must define ECC_CURVE to one of the available curves" +#endif + +#define ECC_BYTES ECC_CURVE + +#ifdef __cplusplus +extern "C" +{ +#endif + +/* ecc_make_key() function. + * Create a public/private key pair. + * + * Outputs: + * publickey - Will be filled in with the public key. + * privatekey - Will be filled in with the private key. + * + * Returns 1 if the key pair was generated successfully, + * 0 if an error occurred. + */ + +int ecc_make_key(uint8_t publickey[ECC_BYTES + 1], + uint8_t privatekey[ECC_BYTES]); + +/* ecdh_shared_secret() function. + * Compute a shared secret given your secret key and someone else's + * public key. + * Note: It is recommended that you hash the result of ecdh_shared_secret + * before using it for symmetric encryption or HMAC. + * + * Inputs: + * publickey - The public key of the remote party. + * privatekey - Your private key. + * + * Outputs: + * secret - Will be filled in with the shared secret value. + * + * Returns 1 if the shared secret was generated successfully, + * 0 if an error occurred. + */ + +int ecdh_shared_secret(const uint8_t publickey[ECC_BYTES + 1], + const uint8_t privatekey[ECC_BYTES], + uint8_t secret[ECC_BYTES]); + +/* ecdsa_sign() function. + * Generate an ECDSA signature for a given hash value. + * + * 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. + * + * Inputs: + * privatekey - Your private key. + * hash - The message hash to sign. + * + * Outputs: + * signature - Will be filled in with the signature value. + * + * Returns 1 if the signature generated successfully, 0 if an error occurred. + */ + +int ecdsa_sign(const uint8_t privatekey[ECC_BYTES], + const uint8_t hash[ECC_BYTES], + uint8_t signature[ECC_BYTES * 2]); + +/* ecdsa_verify() function. + * Verify an ECDSA signature. + * + * 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 (r and s). + * + * Inputs: + * publickey - The signer's public key + * hash - The hash of the signed data. + * signature - The signature value. + * + * Returns 1 if the signature is valid, 0 if it is invalid. + */ + +int ecdsa_verify(const uint8_t publickey[ECC_BYTES + 1], + const uint8_t hash[ECC_BYTES], + const uint8_t signature[ECC_BYTES * 2]); + +#ifdef __cplusplus +} +#endif + +#endif /* __INCLUDE_CRYPTO_ECC_H */
