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/* Copyright 2008, Google Inc.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following disclaimer
* in the documentation and/or other materials provided with the
* distribution.
* * Neither the name of Google Inc. nor the names of its
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* curve25519-donna: Curve25519 elliptic curve, public key function
*
* http://code.google.com/p/curve25519-donna/
*
* Adam Langley <agl@imperialviolet.org>
*
* Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
*
* More information about curve25519 can be found here
* http://cr.yp.to/ecdh.html
*
* djb's sample implementation of curve25519 is written in a special assembly
* language called qhasm and uses the floating point registers.
*
* This is, almost, a clean room reimplementation from the curve25519 paper. It
* uses many of the tricks described therein. Only the crecip function is taken
* from the sample implementation.
*/
#include <string.h>
#include <stdint.h>
#ifdef _MSC_VER
#define inline __inline
#endif
typedef uint8_t u8;
typedef int32_t s32;
typedef int64_t limb;
/* Field element representation:
*
* Field elements are written as an array of signed, 64-bit limbs, least
* significant first. The value of the field element is:
* x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ...
*
* i.e. the limbs are 26, 25, 26, 25, ... bits wide.
*/
/* Sum two numbers: output += in */
static void fsum(limb *output, const limb *in) {
unsigned i;
for (i = 0; i < 10; i += 2) {
output[0+i] = (output[0+i] + in[0+i]);
output[1+i] = (output[1+i] + in[1+i]);
}
}
/* Find the difference of two numbers: output = in - output
* (note the order of the arguments!)
*/
static void fdifference(limb *output, const limb *in) {
unsigned i;
for (i = 0; i < 10; ++i) {
output[i] = (in[i] - output[i]);
}
}
/* Multiply a number by a scalar: output = in * scalar */
static void fscalar_product(limb *output, const limb *in, const limb scalar) {
unsigned i;
for (i = 0; i < 10; ++i) {
output[i] = in[i] * scalar;
}
}
/* Multiply two numbers: output = in2 * in
*
* output must be distinct to both inputs. The inputs are reduced coefficient
* form, the output is not.
*/
static void fproduct(limb *output, const limb *in2, const limb *in) {
output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]);
output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) +
((limb) ((s32) in2[1])) * ((s32) in[0]);
output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) +
((limb) ((s32) in2[0])) * ((s32) in[2]) +
((limb) ((s32) in2[2])) * ((s32) in[0]);
output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) +
((limb) ((s32) in2[2])) * ((s32) in[1]) +
((limb) ((s32) in2[0])) * ((s32) in[3]) +
((limb) ((s32) in2[3])) * ((s32) in[0]);
output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) +
2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) +
((limb) ((s32) in2[3])) * ((s32) in[1])) +
((limb) ((s32) in2[0])) * ((s32) in[4]) +
((limb) ((s32) in2[4])) * ((s32) in[0]);
output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) +
((limb) ((s32) in2[3])) * ((s32) in[2]) +
((limb) ((s32) in2[1])) * ((s32) in[4]) +
((limb) ((s32) in2[4])) * ((s32) in[1]) +
((limb) ((s32) in2[0])) * ((s32) in[5]) +
((limb) ((s32) in2[5])) * ((s32) in[0]);
output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) +
((limb) ((s32) in2[1])) * ((s32) in[5]) +
((limb) ((s32) in2[5])) * ((s32) in[1])) +
((limb) ((s32) in2[2])) * ((s32) in[4]) +
((limb) ((s32) in2[4])) * ((s32) in[2]) +
((limb) ((s32) in2[0])) * ((s32) in[6]) +
((limb) ((s32) in2[6])) * ((s32) in[0]);
output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) +
((limb) ((s32) in2[4])) * ((s32) in[3]) +
((limb) ((s32) in2[2])) * ((s32) in[5]) +
((limb) ((s32) in2[5])) * ((s32) in[2]) +
((limb) ((s32) in2[1])) * ((s32) in[6]) +
((limb) ((s32) in2[6])) * ((s32) in[1]) +
((limb) ((s32) in2[0])) * ((s32) in[7]) +
((limb) ((s32) in2[7])) * ((s32) in[0]);
output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) +
2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) +
((limb) ((s32) in2[5])) * ((s32) in[3]) +
((limb) ((s32) in2[1])) * ((s32) in[7]) +
((limb) ((s32) in2[7])) * ((s32) in[1])) +
((limb) ((s32) in2[2])) * ((s32) in[6]) +
((limb) ((s32) in2[6])) * ((s32) in[2]) +
((limb) ((s32) in2[0])) * ((s32) in[8]) +
((limb) ((s32) in2[8])) * ((s32) in[0]);
output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) +
((limb) ((s32) in2[5])) * ((s32) in[4]) +
((limb) ((s32) in2[3])) * ((s32) in[6]) +
((limb) ((s32) in2[6])) * ((s32) in[3]) +
((limb) ((s32) in2[2])) * ((s32) in[7]) +
((limb) ((s32) in2[7])) * ((s32) in[2]) +
((limb) ((s32) in2[1])) * ((s32) in[8]) +
((limb) ((s32) in2[8])) * ((s32) in[1]) +
((limb) ((s32) in2[0])) * ((s32) in[9]) +
((limb) ((s32) in2[9])) * ((s32) in[0]);
output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) +
((limb) ((s32) in2[3])) * ((s32) in[7]) +
((limb) ((s32) in2[7])) * ((s32) in[3]) +
((limb) ((s32) in2[1])) * ((s32) in[9]) +
((limb) ((s32) in2[9])) * ((s32) in[1])) +
((limb) ((s32) in2[4])) * ((s32) in[6]) +
((limb) ((s32) in2[6])) * ((s32) in[4]) +
((limb) ((s32) in2[2])) * ((s32) in[8]) +
((limb) ((s32) in2[8])) * ((s32) in[2]);
output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) +
((limb) ((s32) in2[6])) * ((s32) in[5]) +
((limb) ((s32) in2[4])) * ((s32) in[7]) +
((limb) ((s32) in2[7])) * ((s32) in[4]) +
((limb) ((s32) in2[3])) * ((s32) in[8]) +
((limb) ((s32) in2[8])) * ((s32) in[3]) +
((limb) ((s32) in2[2])) * ((s32) in[9]) +
((limb) ((s32) in2[9])) * ((s32) in[2]);
output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) +
2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) +
((limb) ((s32) in2[7])) * ((s32) in[5]) +
((limb) ((s32) in2[3])) * ((s32) in[9]) +
((limb) ((s32) in2[9])) * ((s32) in[3])) +
((limb) ((s32) in2[4])) * ((s32) in[8]) +
((limb) ((s32) in2[8])) * ((s32) in[4]);
output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) +
((limb) ((s32) in2[7])) * ((s32) in[6]) +
((limb) ((s32) in2[5])) * ((s32) in[8]) +
((limb) ((s32) in2[8])) * ((s32) in[5]) +
((limb) ((s32) in2[4])) * ((s32) in[9]) +
((limb) ((s32) in2[9])) * ((s32) in[4]);
output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) +
((limb) ((s32) in2[5])) * ((s32) in[9]) +
((limb) ((s32) in2[9])) * ((s32) in[5])) +
((limb) ((s32) in2[6])) * ((s32) in[8]) +
((limb) ((s32) in2[8])) * ((s32) in[6]);
output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) +
((limb) ((s32) in2[8])) * ((s32) in[7]) +
((limb) ((s32) in2[6])) * ((s32) in[9]) +
((limb) ((s32) in2[9])) * ((s32) in[6]);
output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) +
2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) +
((limb) ((s32) in2[9])) * ((s32) in[7]));
output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) +
((limb) ((s32) in2[9])) * ((s32) in[8]);
output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]);
}
/* Reduce a long form to a short form by taking the input mod 2^255 - 19. */
static void freduce_degree(limb *output) {
/* Each of these shifts and adds ends up multiplying the value by 19. */
output[8] += output[18] << 4;
output[8] += output[18] << 1;
output[8] += output[18];
output[7] += output[17] << 4;
output[7] += output[17] << 1;
output[7] += output[17];
output[6] += output[16] << 4;
output[6] += output[16] << 1;
output[6] += output[16];
output[5] += output[15] << 4;
output[5] += output[15] << 1;
output[5] += output[15];
output[4] += output[14] << 4;
output[4] += output[14] << 1;
output[4] += output[14];
output[3] += output[13] << 4;
output[3] += output[13] << 1;
output[3] += output[13];
output[2] += output[12] << 4;
output[2] += output[12] << 1;
output[2] += output[12];
output[1] += output[11] << 4;
output[1] += output[11] << 1;
output[1] += output[11];
output[0] += output[10] << 4;
output[0] += output[10] << 1;
output[0] += output[10];
}
#if (-1 & 3) != 3
#error "This code only works on a two's complement system"
#endif
/* return v / 2^26, using only shifts and adds. */
static inline limb
div_by_2_26(const limb v)
{
/* High word of v; no shift needed*/
const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
/* Set to all 1s if v was negative; else set to 0s. */
const int32_t sign = ((int32_t) highword) >> 31;
/* Set to 0x3ffffff if v was negative; else set to 0. */
const int32_t roundoff = ((uint32_t) sign) >> 6;
/* Should return v / (1<<26) */
return (v + roundoff) >> 26;
}
/* return v / (2^25), using only shifts and adds. */
static inline limb
div_by_2_25(const limb v)
{
/* High word of v; no shift needed*/
const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
/* Set to all 1s if v was negative; else set to 0s. */
const int32_t sign = ((int32_t) highword) >> 31;
/* Set to 0x1ffffff if v was negative; else set to 0. */
const int32_t roundoff = ((uint32_t) sign) >> 7;
/* Should return v / (1<<25) */
return (v + roundoff) >> 25;
}
static inline s32
div_s32_by_2_25(const s32 v)
{
const s32 roundoff = ((uint32_t)(v >> 31)) >> 7;
return (v + roundoff) >> 25;
}
/* Reduce all coefficients of the short form input so that |x| < 2^26.
*
* On entry: |output[i]| < 2^62
*/
static void freduce_coefficients(limb *output) {
unsigned i;
output[10] = 0;
for (i = 0; i < 10; i += 2) {
limb over = div_by_2_26(output[i]);
output[i] -= over << 26;
output[i+1] += over;
over = div_by_2_25(output[i+1]);
output[i+1] -= over << 25;
output[i+2] += over;
}
/* Now |output[10]| < 2 ^ 38 and all other coefficients are reduced. */
output[0] += output[10] << 4;
output[0] += output[10] << 1;
output[0] += output[10];
output[10] = 0;
/* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19 * 2^38
* So |over| will be no more than 77825 */
{
limb over = div_by_2_26(output[0]);
output[0] -= over << 26;
output[1] += over;
}
/* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 77825
* So |over| will be no more than 1. */
{
/* output[1] fits in 32 bits, so we can use div_s32_by_2_25 here. */
s32 over32 = div_s32_by_2_25((s32) output[1]);
output[1] -= over32 << 25;
output[2] += over32;
}
/* Finally, output[0,1,3..9] are reduced, and output[2] is "nearly reduced":
* we have |output[2]| <= 2^26. This is good enough for all of our math,
* but it will require an extra freduce_coefficients before fcontract. */
}
/* A helpful wrapper around fproduct: output = in * in2.
*
* output must be distinct to both inputs. The output is reduced degree and
* reduced coefficient.
*/
static void
fmul(limb *output, const limb *in, const limb *in2) {
limb t[19];
fproduct(t, in, in2);
freduce_degree(t);
freduce_coefficients(t);
memcpy(output, t, sizeof(limb) * 10);
}
static void fsquare_inner(limb *output, const limb *in) {
output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]);
output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]);
output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) +
((limb) ((s32) in[0])) * ((s32) in[2]));
output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) +
((limb) ((s32) in[0])) * ((s32) in[3]));
output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) +
4 * ((limb) ((s32) in[1])) * ((s32) in[3]) +
2 * ((limb) ((s32) in[0])) * ((s32) in[4]);
output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) +
((limb) ((s32) in[1])) * ((s32) in[4]) +
((limb) ((s32) in[0])) * ((s32) in[5]));
output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) +
((limb) ((s32) in[2])) * ((s32) in[4]) +
((limb) ((s32) in[0])) * ((s32) in[6]) +
2 * ((limb) ((s32) in[1])) * ((s32) in[5]));
output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) +
((limb) ((s32) in[2])) * ((s32) in[5]) +
((limb) ((s32) in[1])) * ((s32) in[6]) +
((limb) ((s32) in[0])) * ((s32) in[7]));
output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) +
2 * (((limb) ((s32) in[2])) * ((s32) in[6]) +
((limb) ((s32) in[0])) * ((s32) in[8]) +
2 * (((limb) ((s32) in[1])) * ((s32) in[7]) +
((limb) ((s32) in[3])) * ((s32) in[5])));
output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) +
((limb) ((s32) in[3])) * ((s32) in[6]) +
((limb) ((s32) in[2])) * ((s32) in[7]) +
((limb) ((s32) in[1])) * ((s32) in[8]) +
((limb) ((s32) in[0])) * ((s32) in[9]));
output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) +
((limb) ((s32) in[4])) * ((s32) in[6]) +
((limb) ((s32) in[2])) * ((s32) in[8]) +
2 * (((limb) ((s32) in[3])) * ((s32) in[7]) +
((limb) ((s32) in[1])) * ((s32) in[9])));
output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) +
((limb) ((s32) in[4])) * ((s32) in[7]) +
((limb) ((s32) in[3])) * ((s32) in[8]) +
((limb) ((s32) in[2])) * ((s32) in[9]));
output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) +
2 * (((limb) ((s32) in[4])) * ((s32) in[8]) +
2 * (((limb) ((s32) in[5])) * ((s32) in[7]) +
((limb) ((s32) in[3])) * ((s32) in[9])));
output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) +
((limb) ((s32) in[5])) * ((s32) in[8]) +
((limb) ((s32) in[4])) * ((s32) in[9]));
output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) +
((limb) ((s32) in[6])) * ((s32) in[8]) +
2 * ((limb) ((s32) in[5])) * ((s32) in[9]));
output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) +
((limb) ((s32) in[6])) * ((s32) in[9]));
output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) +
4 * ((limb) ((s32) in[7])) * ((s32) in[9]);
output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]);
output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]);
}
static void
fsquare(limb *output, const limb *in) {
limb t[19];
fsquare_inner(t, in);
freduce_degree(t);
freduce_coefficients(t);
memcpy(output, t, sizeof(limb) * 10);
}
/* Take a little-endian, 32-byte number and expand it into polynomial form */
static void
fexpand(limb *output, const u8 *input) {
#define F(n,start,shift,mask) \
output[n] = ((((limb) input[start + 0]) | \
((limb) input[start + 1]) << 8 | \
((limb) input[start + 2]) << 16 | \
((limb) input[start + 3]) << 24) >> shift) & mask;
F(0, 0, 0, 0x3ffffff);
F(1, 3, 2, 0x1ffffff);
F(2, 6, 3, 0x3ffffff);
F(3, 9, 5, 0x1ffffff);
F(4, 12, 6, 0x3ffffff);
F(5, 16, 0, 0x1ffffff);
F(6, 19, 1, 0x3ffffff);
F(7, 22, 3, 0x1ffffff);
F(8, 25, 4, 0x3ffffff);
F(9, 28, 6, 0x3ffffff);
#undef F
}
#if (-32 >> 1) != -16
#error "This code only works when >> does sign-extension on negative numbers"
#endif
/* Take a fully reduced polynomial form number and contract it into a
* little-endian, 32-byte array
*/
static void
fcontract(u8 *output, limb *input) {
int i;
int j;
for (j = 0; j < 2; ++j) {
for (i = 0; i < 9; ++i) {
if ((i & 1) == 1) {
/* This calculation is a time-invariant way to make input[i] positive
by borrowing from the next-larger limb.
*/
const s32 mask = (s32)(input[i]) >> 31;
const s32 carry = -(((s32)(input[i]) & mask) >> 25);
input[i] = (s32)(input[i]) + (carry << 25);
input[i+1] = (s32)(input[i+1]) - carry;
} else {
const s32 mask = (s32)(input[i]) >> 31;
const s32 carry = -(((s32)(input[i]) & mask) >> 26);
input[i] = (s32)(input[i]) + (carry << 26);
input[i+1] = (s32)(input[i+1]) - carry;
}
}
{
const s32 mask = (s32)(input[9]) >> 31;
const s32 carry = -(((s32)(input[9]) & mask) >> 25);
input[9] = (s32)(input[9]) + (carry << 25);
input[0] = (s32)(input[0]) - (carry * 19);
}
}
/* The first borrow-propagation pass above ended with every limb
except (possibly) input[0] non-negative.
Since each input limb except input[0] is decreased by at most 1
by a borrow-propagation pass, the second borrow-propagation pass
could only have wrapped around to decrease input[0] again if the
first pass left input[0] negative *and* input[1] through input[9]
were all zero. In that case, input[1] is now 2^25 - 1, and this
last borrow-propagation step will leave input[1] non-negative.
*/
{
const s32 mask = (s32)(input[0]) >> 31;
const s32 carry = -(((s32)(input[0]) & mask) >> 26);
input[0] = (s32)(input[0]) + (carry << 26);
input[1] = (s32)(input[1]) - carry;
}
/* Both passes through the above loop, plus the last 0-to-1 step, are
necessary: if input[9] is -1 and input[0] through input[8] are 0,
negative values will remain in the array until the end.
*/
input[1] <<= 2;
input[2] <<= 3;
input[3] <<= 5;
input[4] <<= 6;
input[6] <<= 1;
input[7] <<= 3;
input[8] <<= 4;
input[9] <<= 6;
#define F(i, s) \
output[s+0] |= input[i] & 0xff; \
output[s+1] = (input[i] >> 8) & 0xff; \
output[s+2] = (input[i] >> 16) & 0xff; \
output[s+3] = (input[i] >> 24) & 0xff;
output[0] = 0;
output[16] = 0;
F(0,0);
F(1,3);
F(2,6);
F(3,9);
F(4,12);
F(5,16);
F(6,19);
F(7,22);
F(8,25);
F(9,28);
#undef F
}
/* Input: Q, Q', Q-Q'
* Output: 2Q, Q+Q'
*
* x2 z3: long form
* x3 z3: long form
* x z: short form, destroyed
* xprime zprime: short form, destroyed
* qmqp: short form, preserved
*/
static void fmonty(limb *x2, limb *z2, /* output 2Q */
limb *x3, limb *z3, /* output Q + Q' */
limb *x, limb *z, /* input Q */
limb *xprime, limb *zprime, /* input Q' */
const limb *qmqp /* input Q - Q' */) {
limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19],
zzprime[19], zzzprime[19], xxxprime[19];
memcpy(origx, x, 10 * sizeof(limb));
fsum(x, z);
fdifference(z, origx); /* does x - z */
memcpy(origxprime, xprime, sizeof(limb) * 10);
fsum(xprime, zprime);
fdifference(zprime, origxprime);
fproduct(xxprime, xprime, z);
fproduct(zzprime, x, zprime);
freduce_degree(xxprime);
freduce_coefficients(xxprime);
freduce_degree(zzprime);
freduce_coefficients(zzprime);
memcpy(origxprime, xxprime, sizeof(limb) * 10);
fsum(xxprime, zzprime);
fdifference(zzprime, origxprime);
fsquare(xxxprime, xxprime);
fsquare(zzzprime, zzprime);
fproduct(zzprime, zzzprime, qmqp);
freduce_degree(zzprime);
freduce_coefficients(zzprime);
memcpy(x3, xxxprime, sizeof(limb) * 10);
memcpy(z3, zzprime, sizeof(limb) * 10);
fsquare(xx, x);
fsquare(zz, z);
fproduct(x2, xx, zz);
freduce_degree(x2);
freduce_coefficients(x2);
fdifference(zz, xx); /* does zz = xx - zz */
memset(zzz + 10, 0, sizeof(limb) * 9);
fscalar_product(zzz, zz, 121665);
/* No need to call freduce_degree here:
fscalar_product doesn't increase the degree of its input. */
freduce_coefficients(zzz);
fsum(zzz, xx);
fproduct(z2, zz, zzz);
freduce_degree(z2);
freduce_coefficients(z2);
}
/* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave
* them unchanged if 'iswap' is 0. Runs in data-invariant time to avoid
* side-channel attacks.
*
* NOTE that this function requires that 'iswap' be 1 or 0; other values give
* wrong results. Also, the two limb arrays must be in reduced-coefficient,
* reduced-degree form: the values in a[10..19] or b[10..19] aren't swapped,
* and all all values in a[0..9],b[0..9] must have magnitude less than
* INT32_MAX.
*/
static void
swap_conditional(limb a[19], limb b[19], limb iswap) {
unsigned i;
const s32 swap = (s32) -iswap;
for (i = 0; i < 10; ++i) {
const s32 x = swap & ( ((s32)a[i]) ^ ((s32)b[i]) );
a[i] = ((s32)a[i]) ^ x;
b[i] = ((s32)b[i]) ^ x;
}
}
/* Calculates nQ where Q is the x-coordinate of a point on the curve
*
* resultx/resultz: the x coordinate of the resulting curve point (short form)
* n: a little endian, 32-byte number
* q: a point of the curve (short form)
*/
static void
cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q) {
limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};
limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1};
limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
unsigned i, j;
memcpy(nqpqx, q, sizeof(limb) * 10);
for (i = 0; i < 32; ++i) {
u8 byte = n[31 - i];
for (j = 0; j < 8; ++j) {
const limb bit = byte >> 7;
swap_conditional(nqx, nqpqx, bit);
swap_conditional(nqz, nqpqz, bit);
fmonty(nqx2, nqz2,
nqpqx2, nqpqz2,
nqx, nqz,
nqpqx, nqpqz,
q);
swap_conditional(nqx2, nqpqx2, bit);
swap_conditional(nqz2, nqpqz2, bit);
t = nqx;
nqx = nqx2;
nqx2 = t;
t = nqz;
nqz = nqz2;
nqz2 = t;
t = nqpqx;
nqpqx = nqpqx2;
nqpqx2 = t;
t = nqpqz;
nqpqz = nqpqz2;
nqpqz2 = t;
byte <<= 1;
}
}
memcpy(resultx, nqx, sizeof(limb) * 10);
memcpy(resultz, nqz, sizeof(limb) * 10);
}
/* -----------------------------------------------------------------------------
* Shamelessly copied from djb's code
* ----------------------------------------------------------------------------- */
static void
crecip(limb *out, const limb *z) {
limb z2[10];
limb z9[10];
limb z11[10];
limb z2_5_0[10];
limb z2_10_0[10];
limb z2_20_0[10];
limb z2_50_0[10];
limb z2_100_0[10];
limb t0[10];
limb t1[10];
int i;
/* 2 */ fsquare(z2,z);
/* 4 */ fsquare(t1,z2);
/* 8 */ fsquare(t0,t1);
/* 9 */ fmul(z9,t0,z);
/* 11 */ fmul(z11,z9,z2);
/* 22 */ fsquare(t0,z11);
/* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9);
/* 2^6 - 2^1 */ fsquare(t0,z2_5_0);
/* 2^7 - 2^2 */ fsquare(t1,t0);
/* 2^8 - 2^3 */ fsquare(t0,t1);
/* 2^9 - 2^4 */ fsquare(t1,t0);
/* 2^10 - 2^5 */ fsquare(t0,t1);
/* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0);
/* 2^11 - 2^1 */ fsquare(t0,z2_10_0);
/* 2^12 - 2^2 */ fsquare(t1,t0);
/* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0);
/* 2^21 - 2^1 */ fsquare(t0,z2_20_0);
/* 2^22 - 2^2 */ fsquare(t1,t0);
/* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0);
/* 2^41 - 2^1 */ fsquare(t1,t0);
/* 2^42 - 2^2 */ fsquare(t0,t1);
/* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
/* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0);
/* 2^51 - 2^1 */ fsquare(t0,z2_50_0);
/* 2^52 - 2^2 */ fsquare(t1,t0);
/* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0);
/* 2^101 - 2^1 */ fsquare(t1,z2_100_0);
/* 2^102 - 2^2 */ fsquare(t0,t1);
/* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
/* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0);
/* 2^201 - 2^1 */ fsquare(t0,t1);
/* 2^202 - 2^2 */ fsquare(t1,t0);
/* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0);
/* 2^251 - 2^1 */ fsquare(t1,t0);
/* 2^252 - 2^2 */ fsquare(t0,t1);
/* 2^253 - 2^3 */ fsquare(t1,t0);
/* 2^254 - 2^4 */ fsquare(t0,t1);
/* 2^255 - 2^5 */ fsquare(t1,t0);
/* 2^255 - 21 */ fmul(out,t1,z11);
}
int curve25519_donna(u8 *, const u8 *, const u8 *);
int
curve25519_donna(u8 *mypublic, const u8 *secret, const u8 *basepoint) {
limb bp[10], x[10], z[11], zmone[10];
uint8_t e[32];
int i;
for (i = 0; i < 32; ++i) e[i] = secret[i];
e[0] &= 248;
e[31] &= 127;
e[31] |= 64;
fexpand(bp, basepoint);
cmult(x, z, e, bp);
crecip(zmone, z);
fmul(z, x, zmone);
freduce_coefficients(z);
fcontract(mypublic, z);
return 0;
}