| /* 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 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 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 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, 0x1ffffff); |
| #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; |
| } |