ecc: added ecc implementation for EAP-PWD
The file, src/ecc.c was taken from the bluez project: https://git.kernel.org/pub/scm/bluetooth/bluez.git/tree/src/shared/ecc.c There were minor changes made, e.g. changing some functions to globals for access in EAP-PWD as well as removing some unneeded code. There was also some code appended which allows for point addition, modulus inverse as well as a function to compute a Y value given an X.
This commit is contained in:
James Prestwood
Denis Kenzior
parent
b8c80060d3
commit
fdee72dffc
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@ -106,6 +106,7 @@ src_iwd_SOURCES = src/main.c linux/nl80211.h \
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src/plugin.h src/plugin.c \
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src/eap-peap.c \
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src/eap-gtc.c \
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src/ecc.h src/ecc.c \
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$(builtin_sources)
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src_iwd_LDADD = ell/libell-internal.la -ldl
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@ -0,0 +1,871 @@
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/*
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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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#ifdef HAVE_CONFIG_H
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#include <config.h>
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#endif
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#include <fcntl.h>
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#include <unistd.h>
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#include <sys/types.h>
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#include <string.h>
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#include "ecc.h"
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#define MAX_TRIES 16
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typedef struct {
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uint64_t m_low;
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uint64_t m_high;
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} uint128_t;
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static uint64_t curve_p[NUM_ECC_DIGITS] = CURVE_P_32;
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static uint64_t curve_b[NUM_ECC_DIGITS] = CURVE_B_32;
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static void vli_clear(uint64_t *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 uint64_t *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 uint64_t vli_test_bit(const uint64_t *vli, unsigned int bit)
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{
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return (vli[bit / 64] & ((uint64_t) 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 uint64_t *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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unsigned int vli_num_bits(const uint64_t *vli)
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{
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unsigned int i, num_digits;
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uint64_t 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(uint64_t *dest, const uint64_t *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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int vli_cmp(const uint64_t *left, const uint64_t *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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/* Constant-time comparison function - secure way to compare long integers */
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/* Returns one if left == right, zero otherwise. */
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static bool vli_equal(const uint64_t *left, const uint64_t *right)
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{
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uint64_t diff = 0;
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int i;
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for (i = NUM_ECC_DIGITS - 1; i >= 0; --i)
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diff |= (left[i] ^ right[i]);
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return (diff == 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 uint64_t vli_lshift(uint64_t *result, const uint64_t *in,
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unsigned int shift)
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{
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uint64_t carry = 0;
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int i;
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for (i = 0; i < NUM_ECC_DIGITS; i++) {
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uint64_t 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(uint64_t *vli)
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{
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uint64_t *end = vli;
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uint64_t carry = 0;
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vli += NUM_ECC_DIGITS;
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while (vli-- > end) {
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uint64_t 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 uint64_t vli_add(uint64_t *result, const uint64_t *left,
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const uint64_t *right)
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{
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uint64_t carry = 0;
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int i;
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for (i = 0; i < NUM_ECC_DIGITS; i++) {
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uint64_t 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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uint64_t vli_sub(uint64_t *result, const uint64_t *left,
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const uint64_t *right)
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{
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uint64_t borrow = 0;
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int i;
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for (i = 0; i < NUM_ECC_DIGITS; i++) {
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uint64_t 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(uint64_t left, uint64_t right)
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{
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uint64_t a0 = left & 0xffffffffull;
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uint64_t a1 = left >> 32;
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uint64_t b0 = right & 0xffffffffull;
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uint64_t b1 = right >> 32;
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uint64_t m0 = a0 * b0;
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uint64_t m1 = a0 * b1;
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uint64_t m2 = a1 * b0;
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uint64_t 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(uint64_t *result, const uint64_t *left,
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const uint64_t *right)
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{
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uint128_t r01 = { 0, 0 };
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uint64_t 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(uint64_t *result, const uint64_t *left)
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{
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uint128_t r01 = { 0, 0 };
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uint64_t 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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void vli_mod_add(uint64_t *result, const uint64_t *left,
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const uint64_t *right, const uint64_t *mod)
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{
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uint64_t 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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void vli_mod_sub(uint64_t *result, const uint64_t *left,
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const uint64_t *right, const uint64_t *mod)
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{
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uint64_t 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(uint64_t *result, const uint64_t *product)
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{
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uint64_t 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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void vli_mod_mult_fast(uint64_t *result, const uint64_t *left,
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const uint64_t *right)
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{
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uint64_t 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(uint64_t *result, const uint64_t *left)
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{
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uint64_t 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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void vli_mod_inv(uint64_t *result, const uint64_t *input,
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const uint64_t *mod)
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{
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uint64_t a[NUM_ECC_DIGITS], b[NUM_ECC_DIGITS];
|
||||
uint64_t u[NUM_ECC_DIGITS], v[NUM_ECC_DIGITS];
|
||||
uint64_t carry;
|
||||
int cmp_result;
|
||||
|
||||
if (vli_is_zero(input)) {
|
||||
vli_clear(result);
|
||||
return;
|
||||
}
|
||||
|
||||
vli_set(a, input);
|
||||
vli_set(b, mod);
|
||||
vli_clear(u);
|
||||
u[0] = 1;
|
||||
vli_clear(v);
|
||||
|
||||
while ((cmp_result = vli_cmp(a, b)) != 0) {
|
||||
carry = 0;
|
||||
|
||||
if (EVEN(a)) {
|
||||
vli_rshift1(a);
|
||||
|
||||
if (!EVEN(u))
|
||||
carry = vli_add(u, u, mod);
|
||||
|
||||
vli_rshift1(u);
|
||||
if (carry)
|
||||
u[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
|
||||
} else if (EVEN(b)) {
|
||||
vli_rshift1(b);
|
||||
|
||||
if (!EVEN(v))
|
||||
carry = vli_add(v, v, mod);
|
||||
|
||||
vli_rshift1(v);
|
||||
if (carry)
|
||||
v[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
|
||||
} else if (cmp_result > 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))
|
||||
carry = vli_add(u, u, mod);
|
||||
|
||||
vli_rshift1(u);
|
||||
if (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))
|
||||
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(uint64_t *x1, uint64_t *y1, uint64_t *z1)
|
||||
{
|
||||
/* t1 = x, t2 = y, t3 = z */
|
||||
uint64_t t4[NUM_ECC_DIGITS];
|
||||
uint64_t 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)) {
|
||||
uint64_t 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(uint64_t *x1, uint64_t *y1, uint64_t *z)
|
||||
{
|
||||
uint64_t 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(uint64_t *x1, uint64_t *y1, uint64_t *x2,
|
||||
uint64_t *y2, uint64_t *p_initial_z)
|
||||
{
|
||||
uint64_t 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(uint64_t *x1, uint64_t *y1, uint64_t *x2, uint64_t *y2)
|
||||
{
|
||||
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
|
||||
uint64_t 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(uint64_t *x1, uint64_t *y1, uint64_t *x2, 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];
|
||||
|
||||
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);
|
||||
}
|
||||
|
||||
void ecc_point_mult(struct ecc_point *result,
|
||||
const struct ecc_point *point,
|
||||
uint64_t *scalar, uint64_t *initial_z,
|
||||
int num_bits)
|
||||
{
|
||||
/* R0 and R1 */
|
||||
uint64_t rx[2][NUM_ECC_DIGITS];
|
||||
uint64_t ry[2][NUM_ECC_DIGITS];
|
||||
uint64_t 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]);
|
||||
}
|
||||
|
||||
bool ecc_valid_point(struct ecc_point *point)
|
||||
{
|
||||
uint64_t tmp1[NUM_ECC_DIGITS];
|
||||
uint64_t tmp2[NUM_ECC_DIGITS];
|
||||
uint64_t _3[NUM_ECC_DIGITS] = { 3 }; /* -a = 3 */
|
||||
|
||||
/* The point at infinity is invalid. */
|
||||
if (ecc_point_is_zero(point))
|
||||
return false;
|
||||
|
||||
/* x and y must be smaller than p. */
|
||||
if (vli_cmp(curve_p, point->x) != 1 ||
|
||||
vli_cmp(curve_p, point->y) != 1)
|
||||
return false;
|
||||
|
||||
/* Computes result = y^2. */
|
||||
vli_mod_square_fast(tmp1, point->y);
|
||||
|
||||
/* Computes result = x^3 + ax + b. result must not overlap x. */
|
||||
vli_mod_square_fast(tmp2, point->x); /* r = x^2 */
|
||||
vli_mod_sub(tmp2, tmp2, _3, curve_p); /* r = x^2 - 3 */
|
||||
vli_mod_mult_fast(tmp2, tmp2, point->x); /* r = x^3 - 3x */
|
||||
vli_mod_add(tmp2, tmp2, curve_b, curve_p); /* r = x^3 - 3x + b */
|
||||
|
||||
/* Make sure that y^2 == x^3 + ax + b */
|
||||
return vli_equal(tmp1, tmp2);
|
||||
}
|
||||
|
||||
/*
|
||||
* The code below was not in the original file and was added to support EAP-PWD.
|
||||
* The above ECC implementation did not include functionality for point
|
||||
* addition or the ability to solve for Y value given some X.
|
||||
*/
|
||||
|
||||
/* (rx, ry) = (px, py) + (qx, qy) */
|
||||
void ecc_point_add(struct ecc_point *ret, struct ecc_point *p,
|
||||
struct ecc_point *q)
|
||||
{
|
||||
/*
|
||||
* s = (py - qy)/(px - qx)
|
||||
*
|
||||
* rx = s^2 - px - qx
|
||||
* ry = s(px - rx) - py
|
||||
*/
|
||||
uint64_t s[NUM_ECC_DIGITS];
|
||||
uint64_t kp1[NUM_ECC_DIGITS];
|
||||
uint64_t kp2[NUM_ECC_DIGITS];
|
||||
uint64_t resx[NUM_ECC_DIGITS];
|
||||
uint64_t resy[NUM_ECC_DIGITS];
|
||||
|
||||
vli_clear(s);
|
||||
|
||||
/* kp1 = py - qy */
|
||||
vli_mod_sub(kp1, q->y, p->y, curve_p);
|
||||
/* kp2 = px - qx */
|
||||
vli_mod_sub(kp2, q->x, p->x, curve_p);
|
||||
/* s = kp1/kp2 */
|
||||
vli_mod_inv(kp2, kp2, curve_p);
|
||||
vli_mod_mult_fast(s, kp1, kp2);
|
||||
/* rx = s^2 - px - qx */
|
||||
vli_mod_mult_fast(kp1, s, s);
|
||||
vli_mod_sub(kp1, kp1, p->x, curve_p);
|
||||
vli_mod_sub(resx, kp1, q->x, curve_p);
|
||||
/* ry = s(px - rx) - py */
|
||||
vli_mod_sub(kp1, p->x, resx, curve_p);
|
||||
vli_mod_mult_fast(kp1, s, kp1);
|
||||
vli_mod_sub(resy, kp1, p->y, curve_p);
|
||||
|
||||
vli_set(ret->x, resx);
|
||||
vli_set(ret->y, resy);
|
||||
}
|
||||
|
||||
/* result = (base ^ exp) % p */
|
||||
void vli_mod_exp(uint64_t *result, uint64_t *base, uint64_t *exp,
|
||||
const uint64_t *mod)
|
||||
{
|
||||
int i;
|
||||
int bit;
|
||||
uint64_t n[NUM_ECC_DIGITS];
|
||||
uint64_t r[NUM_ECC_DIGITS] = { 1 };
|
||||
|
||||
vli_set(n, base);
|
||||
|
||||
for (i = 0; i < NUM_ECC_DIGITS; i++) {
|
||||
for (bit = 0; bit < 64; bit++) {
|
||||
uint64_t tmp[NUM_ECC_DIGITS];
|
||||
|
||||
if (exp[i] & (1ull << bit)) {
|
||||
vli_mod_mult_fast(tmp, r, n);
|
||||
memcpy(r, tmp, 32);
|
||||
}
|
||||
|
||||
vli_mod_mult_fast(tmp, n, n);
|
||||
memcpy(n, tmp, 32);
|
||||
}
|
||||
}
|
||||
|
||||
memcpy(result, r, 32);
|
||||
}
|
||||
|
||||
bool ecc_compute_y(uint64_t *y, uint64_t *x)
|
||||
{
|
||||
/*
|
||||
* y = sqrt(x^3 + ax + b) (mod p)
|
||||
*
|
||||
* Since our prime p satisfies p = 3 (mod 4), we can say:
|
||||
*
|
||||
* y = (x^3 - 3x + b)^((p + 1) / 4)
|
||||
*
|
||||
* This avoids the need for a square root function.
|
||||
*/
|
||||
|
||||
uint64_t sum[NUM_ECC_DIGITS] = { 0 };
|
||||
uint64_t expo[NUM_ECC_DIGITS] = { 0 };
|
||||
uint64_t one[NUM_ECC_DIGITS] = { 1ull };
|
||||
uint64_t check[NUM_ECC_DIGITS] = { 0 };
|
||||
uint64_t _3[NUM_ECC_DIGITS] = { 3ull }; /* -a = 3 */
|
||||
uint64_t tmp[NUM_ECC_DIGITS] = { 0 };
|
||||
|
||||
vli_set(expo, curve_p);
|
||||
|
||||
vli_mod_square_fast(sum, x);
|
||||
vli_mod_mult_fast(sum, sum, x); /* x^3 */
|
||||
vli_mod_mult_fast(tmp, _3, x);
|
||||
vli_mod_sub(sum, sum, tmp, curve_p); /* x^3 - ax */
|
||||
vli_mod_add(sum, sum, curve_b, curve_p); /* x^3 - ax + b */
|
||||
|
||||
/* (p + 1) / 4 == (p >> 2) + 1 */
|
||||
vli_rshift1(expo);
|
||||
vli_rshift1(expo);
|
||||
vli_mod_add(expo, expo, one, curve_p);
|
||||
/* sum ^ ((p + 1) / 4) */
|
||||
vli_mod_exp(y, sum, expo, curve_p);
|
||||
|
||||
/* square y to ensure we have a correct value */
|
||||
vli_mod_mult_fast(check, y, y);
|
||||
|
||||
if (vli_cmp(check, sum) != 0)
|
||||
return false;
|
||||
|
||||
return true;
|
||||
}
|
||||
|
|
@ -0,0 +1,85 @@
|
|||
/*
|
||||
*
|
||||
* Wireless daemon for Linux
|
||||
*
|
||||
* Copyright (C) 2018 Intel Corporation. All rights reserved.
|
||||
*
|
||||
* This library is free software; you can redistribute it and/or
|
||||
* modify it under the terms of the GNU Lesser General Public
|
||||
* License as published by the Free Software Foundation; either
|
||||
* version 2.1 of the License, or (at your option) any later version.
|
||||
*
|
||||
* This library is distributed in the hope that it will be useful,
|
||||
* but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
||||
* Lesser General Public License for more details.
|
||||
*
|
||||
* You should have received a copy of the GNU Lesser General Public
|
||||
* License along with this library; if not, write to the Free Software
|
||||
* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
*
|
||||
*/
|
||||
|
||||
#ifdef HAVE_CONFIG_H
|
||||
#include <config.h>
|
||||
#endif
|
||||
|
||||
#include <stdio.h>
|
||||
#include <ell/ell.h>
|
||||
|
||||
/* 256-bit curve */
|
||||
#define ECC_BYTES 32
|
||||
|
||||
/* Number of uint64_t's needed */
|
||||
#define NUM_ECC_DIGITS (ECC_BYTES / 8)
|
||||
|
||||
#define CURVE_P_32 { 0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull, \
|
||||
0x0000000000000000ull, 0xFFFFFFFF00000001ull }
|
||||
|
||||
#define CURVE_G_32 { \
|
||||
{ 0xF4A13945D898C296ull, 0x77037D812DEB33A0ull, \
|
||||
0xF8BCE6E563A440F2ull, 0x6B17D1F2E12C4247ull }, \
|
||||
{ 0xCBB6406837BF51F5ull, 0x2BCE33576B315ECEull, \
|
||||
0x8EE7EB4A7C0F9E16ull, 0x4FE342E2FE1A7F9Bull } \
|
||||
}
|
||||
|
||||
#define CURVE_N_32 { 0xF3B9CAC2FC632551ull, 0xBCE6FAADA7179E84ull, \
|
||||
0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFF00000000ull }
|
||||
|
||||
#define CURVE_B_32 { 0x3BCE3C3E27D2604Bull, 0x651D06B0CC53B0F6ull, \
|
||||
0xB3EBBD55769886BCull, 0x5AC635D8AA3A93E7ull }
|
||||
|
||||
struct ecc_point {
|
||||
uint64_t x[NUM_ECC_DIGITS];
|
||||
uint64_t y[NUM_ECC_DIGITS];
|
||||
};
|
||||
|
||||
void ecc_point_mult(struct ecc_point *result, const struct ecc_point *point,
|
||||
uint64_t *scalar, uint64_t *initial_z, int num_bits);
|
||||
|
||||
void ecc_point_add(struct ecc_point *ret, struct ecc_point *p,
|
||||
struct ecc_point *q);
|
||||
|
||||
bool ecc_valid_point(struct ecc_point *point);
|
||||
|
||||
bool ecc_compute_y(uint64_t *y, uint64_t *x);
|
||||
|
||||
void vli_mod_inv(uint64_t *result, const uint64_t *input, const uint64_t *mod);
|
||||
|
||||
void vli_mod_sub(uint64_t *result, const uint64_t *left, const uint64_t *right,
|
||||
const uint64_t *mod);
|
||||
|
||||
void vli_mod_add(uint64_t *result, const uint64_t *left, const uint64_t *right,
|
||||
const uint64_t *mod);
|
||||
|
||||
uint64_t vli_sub(uint64_t *result, const uint64_t *left, const uint64_t *right);
|
||||
|
||||
void vli_mod_mult_fast(uint64_t *result, const uint64_t *left,
|
||||
const uint64_t *right);
|
||||
|
||||
void vli_mod_exp(uint64_t *result, uint64_t *base, uint64_t *exp,
|
||||
const uint64_t *mod);
|
||||
|
||||
int vli_cmp(const uint64_t *left, const uint64_t *right);
|
||||
|
||||
unsigned int vli_num_bits(const uint64_t *vli);
|
||||
Loading…
Reference in New Issue