817 строки
20 KiB
C
817 строки
20 KiB
C
/*
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* Copyright (c) 2013, Kenneth MacKay
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are
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* met:
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* * Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* * Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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* HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#include <linux/random.h>
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#include "ecc.h"
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/* 256-bit curve */
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#define ECC_BYTES 32
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#define MAX_TRIES 16
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/* Number of u64's needed */
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#define NUM_ECC_DIGITS (ECC_BYTES / 8)
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struct ecc_point {
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u64 x[NUM_ECC_DIGITS];
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u64 y[NUM_ECC_DIGITS];
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};
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typedef struct {
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u64 m_low;
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u64 m_high;
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} uint128_t;
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#define CURVE_P_32 { 0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull, \
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0x0000000000000000ull, 0xFFFFFFFF00000001ull }
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#define CURVE_G_32 { \
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{ 0xF4A13945D898C296ull, 0x77037D812DEB33A0ull, \
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0xF8BCE6E563A440F2ull, 0x6B17D1F2E12C4247ull }, \
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{ 0xCBB6406837BF51F5ull, 0x2BCE33576B315ECEull, \
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0x8EE7EB4A7C0F9E16ull, 0x4FE342E2FE1A7F9Bull } \
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}
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#define CURVE_N_32 { 0xF3B9CAC2FC632551ull, 0xBCE6FAADA7179E84ull, \
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0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFF00000000ull }
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static u64 curve_p[NUM_ECC_DIGITS] = CURVE_P_32;
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static struct ecc_point curve_g = CURVE_G_32;
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static u64 curve_n[NUM_ECC_DIGITS] = CURVE_N_32;
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static void vli_clear(u64 *vli)
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{
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int i;
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for (i = 0; i < NUM_ECC_DIGITS; i++)
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vli[i] = 0;
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}
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/* Returns true if vli == 0, false otherwise. */
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static bool vli_is_zero(const u64 *vli)
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{
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int i;
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for (i = 0; i < NUM_ECC_DIGITS; i++) {
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if (vli[i])
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return false;
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}
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return true;
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}
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/* Returns nonzero if bit bit of vli is set. */
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static u64 vli_test_bit(const u64 *vli, unsigned int bit)
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{
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return (vli[bit / 64] & ((u64) 1 << (bit % 64)));
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}
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/* Counts the number of 64-bit "digits" in vli. */
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static unsigned int vli_num_digits(const u64 *vli)
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{
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int i;
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/* Search from the end until we find a non-zero digit.
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* We do it in reverse because we expect that most digits will
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* be nonzero.
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*/
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for (i = NUM_ECC_DIGITS - 1; i >= 0 && vli[i] == 0; i--);
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return (i + 1);
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}
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/* Counts the number of bits required for vli. */
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static unsigned int vli_num_bits(const u64 *vli)
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{
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unsigned int i, num_digits;
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u64 digit;
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num_digits = vli_num_digits(vli);
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if (num_digits == 0)
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return 0;
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digit = vli[num_digits - 1];
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for (i = 0; digit; i++)
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digit >>= 1;
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return ((num_digits - 1) * 64 + i);
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}
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/* Sets dest = src. */
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static void vli_set(u64 *dest, const u64 *src)
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{
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int i;
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for (i = 0; i < NUM_ECC_DIGITS; i++)
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dest[i] = src[i];
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}
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/* Returns sign of left - right. */
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static int vli_cmp(const u64 *left, const u64 *right)
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{
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int i;
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for (i = NUM_ECC_DIGITS - 1; i >= 0; i--) {
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if (left[i] > right[i])
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return 1;
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else if (left[i] < right[i])
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return -1;
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}
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return 0;
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}
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/* Computes result = in << c, returning carry. Can modify in place
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* (if result == in). 0 < shift < 64.
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*/
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static u64 vli_lshift(u64 *result, const u64 *in,
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unsigned int shift)
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{
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u64 carry = 0;
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int i;
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for (i = 0; i < NUM_ECC_DIGITS; i++) {
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u64 temp = in[i];
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result[i] = (temp << shift) | carry;
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carry = temp >> (64 - shift);
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}
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return carry;
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}
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/* Computes vli = vli >> 1. */
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static void vli_rshift1(u64 *vli)
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{
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u64 *end = vli;
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u64 carry = 0;
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vli += NUM_ECC_DIGITS;
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while (vli-- > end) {
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u64 temp = *vli;
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*vli = (temp >> 1) | carry;
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carry = temp << 63;
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}
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}
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/* Computes result = left + right, returning carry. Can modify in place. */
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static u64 vli_add(u64 *result, const u64 *left,
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const u64 *right)
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{
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u64 carry = 0;
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int i;
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for (i = 0; i < NUM_ECC_DIGITS; i++) {
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u64 sum;
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sum = left[i] + right[i] + carry;
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if (sum != left[i])
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carry = (sum < left[i]);
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result[i] = sum;
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}
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return carry;
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}
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/* Computes result = left - right, returning borrow. Can modify in place. */
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static u64 vli_sub(u64 *result, const u64 *left, const u64 *right)
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{
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u64 borrow = 0;
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int i;
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for (i = 0; i < NUM_ECC_DIGITS; i++) {
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u64 diff;
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diff = left[i] - right[i] - borrow;
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if (diff != left[i])
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borrow = (diff > left[i]);
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result[i] = diff;
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}
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return borrow;
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}
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static uint128_t mul_64_64(u64 left, u64 right)
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{
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u64 a0 = left & 0xffffffffull;
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u64 a1 = left >> 32;
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u64 b0 = right & 0xffffffffull;
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u64 b1 = right >> 32;
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u64 m0 = a0 * b0;
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u64 m1 = a0 * b1;
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u64 m2 = a1 * b0;
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u64 m3 = a1 * b1;
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uint128_t result;
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m2 += (m0 >> 32);
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m2 += m1;
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/* Overflow */
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if (m2 < m1)
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m3 += 0x100000000ull;
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result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
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result.m_high = m3 + (m2 >> 32);
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return result;
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}
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static uint128_t add_128_128(uint128_t a, uint128_t b)
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{
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uint128_t result;
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result.m_low = a.m_low + b.m_low;
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result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low);
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return result;
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}
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static void vli_mult(u64 *result, const u64 *left, const u64 *right)
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{
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uint128_t r01 = { 0, 0 };
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u64 r2 = 0;
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unsigned int i, k;
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/* Compute each digit of result in sequence, maintaining the
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* carries.
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*/
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for (k = 0; k < NUM_ECC_DIGITS * 2 - 1; k++) {
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unsigned int min;
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if (k < NUM_ECC_DIGITS)
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min = 0;
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else
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min = (k + 1) - NUM_ECC_DIGITS;
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for (i = min; i <= k && i < NUM_ECC_DIGITS; i++) {
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uint128_t product;
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product = mul_64_64(left[i], right[k - i]);
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r01 = add_128_128(r01, product);
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r2 += (r01.m_high < product.m_high);
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}
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result[k] = r01.m_low;
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r01.m_low = r01.m_high;
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r01.m_high = r2;
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r2 = 0;
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}
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result[NUM_ECC_DIGITS * 2 - 1] = r01.m_low;
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}
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static void vli_square(u64 *result, const u64 *left)
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{
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uint128_t r01 = { 0, 0 };
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u64 r2 = 0;
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int i, k;
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for (k = 0; k < NUM_ECC_DIGITS * 2 - 1; k++) {
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unsigned int min;
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if (k < NUM_ECC_DIGITS)
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min = 0;
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else
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min = (k + 1) - NUM_ECC_DIGITS;
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for (i = min; i <= k && i <= k - i; i++) {
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uint128_t product;
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product = mul_64_64(left[i], left[k - i]);
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if (i < k - i) {
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r2 += product.m_high >> 63;
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product.m_high = (product.m_high << 1) |
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(product.m_low >> 63);
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product.m_low <<= 1;
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}
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r01 = add_128_128(r01, product);
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r2 += (r01.m_high < product.m_high);
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}
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result[k] = r01.m_low;
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r01.m_low = r01.m_high;
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r01.m_high = r2;
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r2 = 0;
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}
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result[NUM_ECC_DIGITS * 2 - 1] = r01.m_low;
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}
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/* Computes result = (left + right) % mod.
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* Assumes that left < mod and right < mod, result != mod.
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*/
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static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
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const u64 *mod)
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{
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u64 carry;
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carry = vli_add(result, left, right);
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/* result > mod (result = mod + remainder), so subtract mod to
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* get remainder.
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*/
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if (carry || vli_cmp(result, mod) >= 0)
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vli_sub(result, result, mod);
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}
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/* Computes result = (left - right) % mod.
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* Assumes that left < mod and right < mod, result != mod.
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*/
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static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
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const u64 *mod)
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{
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u64 borrow = vli_sub(result, left, right);
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/* In this case, p_result == -diff == (max int) - diff.
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* Since -x % d == d - x, we can get the correct result from
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* result + mod (with overflow).
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*/
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if (borrow)
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vli_add(result, result, mod);
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}
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/* Computes result = product % curve_p
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from http://www.nsa.gov/ia/_files/nist-routines.pdf */
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static void vli_mmod_fast(u64 *result, const u64 *product)
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{
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u64 tmp[NUM_ECC_DIGITS];
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int carry;
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/* t */
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vli_set(result, product);
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/* s1 */
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tmp[0] = 0;
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tmp[1] = product[5] & 0xffffffff00000000ull;
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tmp[2] = product[6];
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tmp[3] = product[7];
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carry = vli_lshift(tmp, tmp, 1);
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carry += vli_add(result, result, tmp);
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/* s2 */
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tmp[1] = product[6] << 32;
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tmp[2] = (product[6] >> 32) | (product[7] << 32);
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tmp[3] = product[7] >> 32;
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carry += vli_lshift(tmp, tmp, 1);
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carry += vli_add(result, result, tmp);
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/* s3 */
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tmp[0] = product[4];
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tmp[1] = product[5] & 0xffffffff;
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tmp[2] = 0;
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tmp[3] = product[7];
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carry += vli_add(result, result, tmp);
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/* s4 */
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tmp[0] = (product[4] >> 32) | (product[5] << 32);
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tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
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tmp[2] = product[7];
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tmp[3] = (product[6] >> 32) | (product[4] << 32);
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carry += vli_add(result, result, tmp);
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/* d1 */
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tmp[0] = (product[5] >> 32) | (product[6] << 32);
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tmp[1] = (product[6] >> 32);
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tmp[2] = 0;
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tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
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carry -= vli_sub(result, result, tmp);
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/* d2 */
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tmp[0] = product[6];
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tmp[1] = product[7];
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tmp[2] = 0;
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tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
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carry -= vli_sub(result, result, tmp);
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/* d3 */
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tmp[0] = (product[6] >> 32) | (product[7] << 32);
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tmp[1] = (product[7] >> 32) | (product[4] << 32);
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tmp[2] = (product[4] >> 32) | (product[5] << 32);
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tmp[3] = (product[6] << 32);
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carry -= vli_sub(result, result, tmp);
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/* d4 */
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tmp[0] = product[7];
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tmp[1] = product[4] & 0xffffffff00000000ull;
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tmp[2] = product[5];
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tmp[3] = product[6] & 0xffffffff00000000ull;
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carry -= vli_sub(result, result, tmp);
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if (carry < 0) {
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do {
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carry += vli_add(result, result, curve_p);
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} while (carry < 0);
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} else {
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while (carry || vli_cmp(curve_p, result) != 1)
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carry -= vli_sub(result, result, curve_p);
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}
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}
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/* Computes result = (left * right) % curve_p. */
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static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right)
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{
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u64 product[2 * NUM_ECC_DIGITS];
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vli_mult(product, left, right);
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vli_mmod_fast(result, product);
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}
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/* Computes result = left^2 % curve_p. */
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static void vli_mod_square_fast(u64 *result, const u64 *left)
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{
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u64 product[2 * NUM_ECC_DIGITS];
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vli_square(product, left);
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vli_mmod_fast(result, product);
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}
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#define EVEN(vli) (!(vli[0] & 1))
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/* Computes result = (1 / p_input) % mod. All VLIs are the same size.
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* See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
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* https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
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*/
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static void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod)
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{
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u64 a[NUM_ECC_DIGITS], b[NUM_ECC_DIGITS];
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u64 u[NUM_ECC_DIGITS], v[NUM_ECC_DIGITS];
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u64 carry;
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int cmp_result;
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if (vli_is_zero(input)) {
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vli_clear(result);
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return;
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}
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vli_set(a, input);
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vli_set(b, mod);
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vli_clear(u);
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u[0] = 1;
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vli_clear(v);
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while ((cmp_result = vli_cmp(a, b)) != 0) {
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carry = 0;
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if (EVEN(a)) {
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vli_rshift1(a);
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if (!EVEN(u))
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carry = vli_add(u, u, mod);
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vli_rshift1(u);
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if (carry)
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u[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
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} else if (EVEN(b)) {
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vli_rshift1(b);
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if (!EVEN(v))
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carry = vli_add(v, v, mod);
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vli_rshift1(v);
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if (carry)
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v[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
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} else if (cmp_result > 0) {
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vli_sub(a, a, b);
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vli_rshift1(a);
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if (vli_cmp(u, v) < 0)
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vli_add(u, u, mod);
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vli_sub(u, u, v);
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if (!EVEN(u))
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carry = vli_add(u, u, mod);
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vli_rshift1(u);
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if (carry)
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u[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
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} else {
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vli_sub(b, b, a);
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vli_rshift1(b);
|
|
|
|
if (vli_cmp(v, u) < 0)
|
|
vli_add(v, v, mod);
|
|
|
|
vli_sub(v, v, u);
|
|
if (!EVEN(v))
|
|
carry = vli_add(v, v, mod);
|
|
|
|
vli_rshift1(v);
|
|
if (carry)
|
|
v[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
|
|
}
|
|
}
|
|
|
|
vli_set(result, u);
|
|
}
|
|
|
|
/* ------ Point operations ------ */
|
|
|
|
/* Returns true if p_point is the point at infinity, false otherwise. */
|
|
static bool ecc_point_is_zero(const struct ecc_point *point)
|
|
{
|
|
return (vli_is_zero(point->x) && vli_is_zero(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 ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1)
|
|
{
|
|
/* t1 = x, t2 = y, t3 = z */
|
|
u64 t4[NUM_ECC_DIGITS];
|
|
u64 t5[NUM_ECC_DIGITS];
|
|
|
|
if (vli_is_zero(z1))
|
|
return;
|
|
|
|
vli_mod_square_fast(t4, y1); /* t4 = y1^2 */
|
|
vli_mod_mult_fast(t5, x1, t4); /* t5 = x1*y1^2 = A */
|
|
vli_mod_square_fast(t4, t4); /* t4 = y1^4 */
|
|
vli_mod_mult_fast(y1, y1, z1); /* t2 = y1*z1 = z3 */
|
|
vli_mod_square_fast(z1, z1); /* t3 = z1^2 */
|
|
|
|
vli_mod_add(x1, x1, z1, curve_p); /* t1 = x1 + z1^2 */
|
|
vli_mod_add(z1, z1, z1, curve_p); /* t3 = 2*z1^2 */
|
|
vli_mod_sub(z1, x1, z1, curve_p); /* t3 = x1 - z1^2 */
|
|
vli_mod_mult_fast(x1, x1, z1); /* t1 = x1^2 - z1^4 */
|
|
|
|
vli_mod_add(z1, x1, x1, curve_p); /* t3 = 2*(x1^2 - z1^4) */
|
|
vli_mod_add(x1, x1, z1, curve_p); /* t1 = 3*(x1^2 - z1^4) */
|
|
if (vli_test_bit(x1, 0)) {
|
|
u64 carry = vli_add(x1, x1, curve_p);
|
|
vli_rshift1(x1);
|
|
x1[NUM_ECC_DIGITS - 1] |= carry << 63;
|
|
} else {
|
|
vli_rshift1(x1);
|
|
}
|
|
/* t1 = 3/2*(x1^2 - z1^4) = B */
|
|
|
|
vli_mod_square_fast(z1, x1); /* t3 = B^2 */
|
|
vli_mod_sub(z1, z1, t5, curve_p); /* t3 = B^2 - A */
|
|
vli_mod_sub(z1, z1, t5, curve_p); /* t3 = B^2 - 2A = x3 */
|
|
vli_mod_sub(t5, t5, z1, curve_p); /* t5 = A - x3 */
|
|
vli_mod_mult_fast(x1, x1, t5); /* t1 = B * (A - x3) */
|
|
vli_mod_sub(t4, x1, t4, curve_p); /* t4 = B * (A - x3) - y1^4 = y3 */
|
|
|
|
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(u64 *x1, u64 *y1, u64 *z)
|
|
{
|
|
u64 t1[NUM_ECC_DIGITS];
|
|
|
|
vli_mod_square_fast(t1, z); /* z^2 */
|
|
vli_mod_mult_fast(x1, x1, t1); /* x1 * z^2 */
|
|
vli_mod_mult_fast(t1, t1, z); /* z^3 */
|
|
vli_mod_mult_fast(y1, y1, t1); /* y1 * z^3 */
|
|
}
|
|
|
|
/* P = (x1, y1) => 2P, (x2, y2) => P' */
|
|
static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
|
|
u64 *p_initial_z)
|
|
{
|
|
u64 z[NUM_ECC_DIGITS];
|
|
|
|
vli_set(x2, x1);
|
|
vli_set(y2, y1);
|
|
|
|
vli_clear(z);
|
|
z[0] = 1;
|
|
|
|
if (p_initial_z)
|
|
vli_set(z, p_initial_z);
|
|
|
|
apply_z(x1, y1, z);
|
|
|
|
ecc_point_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(u64 *x1, u64 *y1, u64 *x2, u64 *y2)
|
|
{
|
|
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
|
|
u64 t5[NUM_ECC_DIGITS];
|
|
|
|
vli_mod_sub(t5, x2, x1, curve_p); /* t5 = x2 - x1 */
|
|
vli_mod_square_fast(t5, t5); /* t5 = (x2 - x1)^2 = A */
|
|
vli_mod_mult_fast(x1, x1, t5); /* t1 = x1*A = B */
|
|
vli_mod_mult_fast(x2, x2, t5); /* t3 = x2*A = C */
|
|
vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y2 - y1 */
|
|
vli_mod_square_fast(t5, y2); /* t5 = (y2 - y1)^2 = D */
|
|
|
|
vli_mod_sub(t5, t5, x1, curve_p); /* t5 = D - B */
|
|
vli_mod_sub(t5, t5, x2, curve_p); /* t5 = D - B - C = x3 */
|
|
vli_mod_sub(x2, x2, x1, curve_p); /* t3 = C - B */
|
|
vli_mod_mult_fast(y1, y1, x2); /* t2 = y1*(C - B) */
|
|
vli_mod_sub(x2, x1, t5, curve_p); /* t3 = B - x3 */
|
|
vli_mod_mult_fast(y2, y2, x2); /* t4 = (y2 - y1)*(B - x3) */
|
|
vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y3 */
|
|
|
|
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_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2)
|
|
{
|
|
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
|
|
u64 t5[NUM_ECC_DIGITS];
|
|
u64 t6[NUM_ECC_DIGITS];
|
|
u64 t7[NUM_ECC_DIGITS];
|
|
|
|
vli_mod_sub(t5, x2, x1, curve_p); /* t5 = x2 - x1 */
|
|
vli_mod_square_fast(t5, t5); /* t5 = (x2 - x1)^2 = A */
|
|
vli_mod_mult_fast(x1, x1, t5); /* t1 = x1*A = B */
|
|
vli_mod_mult_fast(x2, x2, t5); /* t3 = x2*A = C */
|
|
vli_mod_add(t5, y2, y1, curve_p); /* t4 = y2 + y1 */
|
|
vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y2 - y1 */
|
|
|
|
vli_mod_sub(t6, x2, x1, curve_p); /* t6 = C - B */
|
|
vli_mod_mult_fast(y1, y1, t6); /* t2 = y1 * (C - B) */
|
|
vli_mod_add(t6, x1, x2, curve_p); /* t6 = B + C */
|
|
vli_mod_square_fast(x2, y2); /* t3 = (y2 - y1)^2 */
|
|
vli_mod_sub(x2, x2, t6, curve_p); /* t3 = x3 */
|
|
|
|
vli_mod_sub(t7, x1, x2, curve_p); /* t7 = B - x3 */
|
|
vli_mod_mult_fast(y2, y2, t7); /* t4 = (y2 - y1)*(B - x3) */
|
|
vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y3 */
|
|
|
|
vli_mod_square_fast(t7, t5); /* t7 = (y2 + y1)^2 = F */
|
|
vli_mod_sub(t7, t7, t6, curve_p); /* t7 = x3' */
|
|
vli_mod_sub(t6, t7, x1, curve_p); /* t6 = x3' - B */
|
|
vli_mod_mult_fast(t6, t6, t5); /* t6 = (y2 + y1)*(x3' - B) */
|
|
vli_mod_sub(y1, t6, y1, curve_p); /* t2 = y3' */
|
|
|
|
vli_set(x1, t7);
|
|
}
|
|
|
|
static void ecc_point_mult(struct ecc_point *result,
|
|
const struct ecc_point *point, u64 *scalar,
|
|
u64 *initial_z, int num_bits)
|
|
{
|
|
/* R0 and R1 */
|
|
u64 rx[2][NUM_ECC_DIGITS];
|
|
u64 ry[2][NUM_ECC_DIGITS];
|
|
u64 z[NUM_ECC_DIGITS];
|
|
int i, nb;
|
|
|
|
vli_set(rx[1], point->x);
|
|
vli_set(ry[1], point->y);
|
|
|
|
xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z);
|
|
|
|
for (i = num_bits - 2; i > 0; i--) {
|
|
nb = !vli_test_bit(scalar, i);
|
|
xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb]);
|
|
xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb]);
|
|
}
|
|
|
|
nb = !vli_test_bit(scalar, 0);
|
|
xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb]);
|
|
|
|
/* Find final 1/Z value. */
|
|
vli_mod_sub(z, rx[1], rx[0], curve_p); /* X1 - X0 */
|
|
vli_mod_mult_fast(z, z, ry[1 - nb]); /* Yb * (X1 - X0) */
|
|
vli_mod_mult_fast(z, z, point->x); /* xP * Yb * (X1 - X0) */
|
|
vli_mod_inv(z, z, curve_p); /* 1 / (xP * Yb * (X1 - X0)) */
|
|
vli_mod_mult_fast(z, z, point->y); /* yP / (xP * Yb * (X1 - X0)) */
|
|
vli_mod_mult_fast(z, z, rx[1 - nb]); /* Xb * yP / (xP * Yb * (X1 - X0)) */
|
|
/* 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(const u8 bytes[ECC_BYTES],
|
|
u64 native[NUM_ECC_DIGITS])
|
|
{
|
|
int i;
|
|
|
|
for (i = 0; i < NUM_ECC_DIGITS; i++) {
|
|
const u8 *digit = bytes + 8 * (NUM_ECC_DIGITS - 1 - i);
|
|
|
|
native[NUM_ECC_DIGITS - 1 - i] =
|
|
((u64) digit[0] << 0) |
|
|
((u64) digit[1] << 8) |
|
|
((u64) digit[2] << 16) |
|
|
((u64) digit[3] << 24) |
|
|
((u64) digit[4] << 32) |
|
|
((u64) digit[5] << 40) |
|
|
((u64) digit[6] << 48) |
|
|
((u64) digit[7] << 56);
|
|
}
|
|
}
|
|
|
|
static void ecc_native2bytes(const u64 native[NUM_ECC_DIGITS],
|
|
u8 bytes[ECC_BYTES])
|
|
{
|
|
int i;
|
|
|
|
for (i = 0; i < NUM_ECC_DIGITS; i++) {
|
|
u8 *digit = bytes + 8 * (NUM_ECC_DIGITS - 1 - i);
|
|
|
|
digit[0] = native[NUM_ECC_DIGITS - 1 - i] >> 0;
|
|
digit[1] = native[NUM_ECC_DIGITS - 1 - i] >> 8;
|
|
digit[2] = native[NUM_ECC_DIGITS - 1 - i] >> 16;
|
|
digit[3] = native[NUM_ECC_DIGITS - 1 - i] >> 24;
|
|
digit[4] = native[NUM_ECC_DIGITS - 1 - i] >> 32;
|
|
digit[5] = native[NUM_ECC_DIGITS - 1 - i] >> 40;
|
|
digit[6] = native[NUM_ECC_DIGITS - 1 - i] >> 48;
|
|
digit[7] = native[NUM_ECC_DIGITS - 1 - i] >> 56;
|
|
}
|
|
}
|
|
|
|
bool ecc_make_key(u8 public_key[64], u8 private_key[32])
|
|
{
|
|
struct ecc_point pk;
|
|
u64 priv[NUM_ECC_DIGITS];
|
|
unsigned int tries = 0;
|
|
|
|
do {
|
|
if (tries++ >= MAX_TRIES)
|
|
return false;
|
|
|
|
get_random_bytes(priv, ECC_BYTES);
|
|
|
|
if (vli_is_zero(priv))
|
|
continue;
|
|
|
|
/* Make sure the private key is in the range [1, n-1]. */
|
|
if (vli_cmp(curve_n, priv) != 1)
|
|
continue;
|
|
|
|
ecc_point_mult(&pk, &curve_g, priv, NULL, vli_num_bits(priv));
|
|
} while (ecc_point_is_zero(&pk));
|
|
|
|
ecc_native2bytes(priv, private_key);
|
|
ecc_native2bytes(pk.x, public_key);
|
|
ecc_native2bytes(pk.y, &public_key[32]);
|
|
|
|
return true;
|
|
}
|
|
|
|
bool ecdh_shared_secret(const u8 public_key[64], const u8 private_key[32],
|
|
u8 secret[32])
|
|
{
|
|
u64 priv[NUM_ECC_DIGITS];
|
|
u64 rand[NUM_ECC_DIGITS];
|
|
struct ecc_point product, pk;
|
|
|
|
get_random_bytes(rand, ECC_BYTES);
|
|
|
|
ecc_bytes2native(public_key, pk.x);
|
|
ecc_bytes2native(&public_key[32], pk.y);
|
|
ecc_bytes2native(private_key, priv);
|
|
|
|
ecc_point_mult(&product, &pk, priv, rand, vli_num_bits(priv));
|
|
|
|
ecc_native2bytes(product.x, secret);
|
|
|
|
return !ecc_point_is_zero(&product);
|
|
}
|