From 078ff20d758b7d3219f5c10735b3b1757db1eff0 Mon Sep 17 00:00:00 2001 From: Vsevolod Stakhov Date: Fri, 6 Feb 2015 14:10:44 +0000 Subject: Add curve25519 and poly1305 by @agl / @floodyberry --- src/libcryptobox/curve25519/curve25519-donna.c | 912 +++++++++++++++++++++++++ 1 file changed, 912 insertions(+) create mode 100644 src/libcryptobox/curve25519/curve25519-donna.c (limited to 'src/libcryptobox/curve25519/curve25519-donna.c') diff --git a/src/libcryptobox/curve25519/curve25519-donna.c b/src/libcryptobox/curve25519/curve25519-donna.c new file mode 100644 index 000000000..f9f19a632 --- /dev/null +++ b/src/libcryptobox/curve25519/curve25519-donna.c @@ -0,0 +1,912 @@ +/* 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 + * + * Derived from public domain C code by Daniel J. Bernstein + * + * 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 +#include + +#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. + * + * output[x] <= 14 * the largest product of the input limbs. */ +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. + * + * On entry: |output[i]| < 14*2^54 + * On exit: |output[0..8]| < 280*2^54 */ +static void freduce_degree (limb *output) +{ + /* Each of these shifts and adds ends up multiplying the value by 19. + * + * For output[0..8], the absolute entry value is < 14*2^54 and we add, at + * most, 19*14*2^54 thus, on exit, |output[0..8]| < 280*2^54. */ + 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. + * + * On entry: v can take any value. */ +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. + * + * On entry: v can take any value. */ +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; +} + +/* Reduce all coefficients of the short form input so that |x| < 2^26. + * + * On entry: |output[i]| < 280*2^54 */ +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]); + /* The entry condition (that |output[i]| < 280*2^54) means that over is, at + * most, 280*2^28 in the first iteration of this loop. This is added to the + * next limb and we can approximate the resulting bound of that limb by + * 281*2^54. */ + output[i] -= over << 26; + output[i + 1] += over; + + /* For the first iteration, |output[i+1]| < 281*2^54, thus |over| < + * 281*2^29. When this is added to the next limb, the resulting bound can + * be approximated as 281*2^54. + * + * For subsequent iterations of the loop, 281*2^54 remains a conservative + * bound and no overflow occurs. */ + over = div_by_2_25 (output[i + 1]); + output[i + 1] -= over << 25; + output[i + 2] += over; + } + /* Now |output[10]| < 281*2^29 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*281*2^29 + * So |over| will be no more than 2^16. */ + { + 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 + 2^16 < 2^26. The + * bound on |output[1]| is sufficient to meet our needs. */ +} + +/* A helpful wrapper around fproduct: output = in * in2. + * + * On entry: |in[i]| < 2^27 and |in2[i]| < 2^27. + * + * output must be distinct to both inputs. The output is reduced degree + * (indeed, one need only provide storage for 10 limbs) and |output[i]| < 2^26. */ +static void fmul (limb *output, const limb *in, const limb *in2) +{ + limb t[19]; + fproduct (t, in, in2); + /* |t[i]| < 14*2^54 */ + freduce_degree (t); + freduce_coefficients (t); + /* |t[i]| < 2^26 */ + memcpy (output, t, sizeof(limb) * 10); +} + +/* Square a number: output = in**2 + * + * output must be distinct from the input. The inputs are reduced coefficient + * form, the output is not. + * + * output[x] <= 14 * the largest product of the input limbs. */ +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]); +} + +/* fsquare sets output = in^2. + * + * On entry: The |in| argument is in reduced coefficients form and |in[i]| < + * 2^27. + * + * On exit: The |output| argument is in reduced coefficients form (indeed, one + * need only provide storage for 10 limbs) and |out[i]| < 2^26. */ +static void fsquare (limb *output, const limb *in) +{ + limb t[19]; + fsquare_inner (t, in); + /* |t[i]| < 14*2^54 because the largest product of two limbs will be < + * 2^(27+27) and fsquare_inner adds together, at most, 14 of those + * products. */ + freduce_degree (t); + freduce_coefficients (t); + /* |t[i]| < 2^26 */ + 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 + +/* s32_eq returns 0xffffffff iff a == b and zero otherwise. */ +static s32 s32_eq (s32 a, s32 b) +{ + a = ~(a ^ b); + a &= a << 16; + a &= a << 8; + a &= a << 4; + a &= a << 2; + a &= a << 1; + return a >> 31; +} + +/* s32_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are + * both non-negative. */ +static s32 s32_gte (s32 a, s32 b) +{ + a -= b; + /* a >= 0 iff a >= b. */ + return ~(a >> 31); +} + +/* Take a fully reduced polynomial form number and contract it into a + * little-endian, 32-byte array. + * + * On entry: |input_limbs[i]| < 2^26 */ +static void fcontract (u8 *output, limb *input_limbs) +{ + int i; + int j; + s32 input[10]; + s32 mask; + + /* |input_limbs[i]| < 2^26, so it's valid to convert to an s32. */ + for (i = 0; i < 10; i++) { + input[i] = input_limbs[i]; + } + + 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] + * non-negative by borrowing from the next-larger limb. */ + const s32 mask = input[i] >> 31; + const s32 carry = -((input[i] & mask) >> 25); + input[i] = input[i] + (carry << 25); + input[i + 1] = input[i + 1] - carry; + } + else { + const s32 mask = input[i] >> 31; + const s32 carry = -((input[i] & mask) >> 26); + input[i] = input[i] + (carry << 26); + input[i + 1] = input[i + 1] - carry; + } + } + + /* There's no greater limb for input[9] to borrow from, but we can multiply + * by 19 and borrow from input[0], which is valid mod 2^255-19. */ + { + const s32 mask = input[9] >> 31; + const s32 carry = -((input[9] & mask) >> 25); + input[9] = input[9] + (carry << 25); + input[0] = input[0] - (carry * 19); + } + + /* After the first iteration, input[1..9] are non-negative and fit within + * 25 or 26 bits, depending on position. However, input[0] may be + * negative. */ + } + + /* The first borrow-propagation pass above ended with every limb + except (possibly) input[0] non-negative. + + If input[0] was negative after the first pass, then it was because of a + carry from input[9]. On entry, input[9] < 2^26 so the carry was, at most, + one, since (2**26-1) >> 25 = 1. Thus input[0] >= -19. + + In the second pass, each limb is decreased by at most one. Thus 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 = input[0] >> 31; + const s32 carry = -((input[0] & mask) >> 26); + input[0] = input[0] + (carry << 26); + input[1] = input[1] - carry; + } + + /* All input[i] are now non-negative. However, there might be values between + * 2^25 and 2^26 in a limb which is, nominally, 25 bits wide. */ + for (j = 0; j < 2; j++) { + for (i = 0; i < 9; i++) { + if ((i & 1) == 1) { + const s32 carry = input[i] >> 25; + input[i] &= 0x1ffffff; + input[i + 1] += carry; + } + else { + const s32 carry = input[i] >> 26; + input[i] &= 0x3ffffff; + input[i + 1] += carry; + } + } + + { + const s32 carry = input[9] >> 25; + input[9] &= 0x1ffffff; + input[0] += 19 * carry; + } + } + + /* If the first carry-chain pass, just above, ended up with a carry from + * input[9], and that caused input[0] to be out-of-bounds, then input[0] was + * < 2^26 + 2*19, because the carry was, at most, two. + * + * If the second pass carried from input[9] again then input[0] is < 2*19 and + * the input[9] -> input[0] carry didn't push input[0] out of bounds. */ + + /* It still remains the case that input might be between 2^255-19 and 2^255. + * In this case, input[1..9] must take their maximum value and input[0] must + * be >= (2^255-19) & 0x3ffffff, which is 0x3ffffed. */ + mask = s32_gte (input[0], 0x3ffffed); + for (i = 1; i < 10; i++) { + if ((i & 1) == 1) { + mask &= s32_eq (input[i], 0x1ffffff); + } + else { + mask &= s32_eq (input[i], 0x3ffffff); + } + } + + /* mask is either 0xffffffff (if input >= 2^255-19) and zero otherwise. Thus + * this conditionally subtracts 2^255-19. */ + input[0] -= mask & 0x3ffffed; + + for (i = 1; i < 10; i++) { + if ((i & 1) == 1) { + input[i] -= mask & 0x1ffffff; + } + else { + input[i] -= mask & 0x3ffffff; + } + } + + 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 + * + * On entry and exit, the absolute value of the limbs of all inputs and outputs + * are < 2^26. */ +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); + /* |x[i]| < 2^27 */ + fdifference (z, origx); /* does x - z */ + /* |z[i]| < 2^27 */ + + memcpy (origxprime, xprime, sizeof(limb) * 10); + fsum (xprime, zprime); + /* |xprime[i]| < 2^27 */ + fdifference (zprime, origxprime); + /* |zprime[i]| < 2^27 */ + fproduct (xxprime, xprime, z); + /* |xxprime[i]| < 14*2^54: the largest product of two limbs will be < + * 2^(27+27) and fproduct adds together, at most, 14 of those products. + * (Approximating that to 2^58 doesn't work out.) */ + fproduct (zzprime, x, zprime); + /* |zzprime[i]| < 14*2^54 */ + freduce_degree (xxprime); + freduce_coefficients (xxprime); + /* |xxprime[i]| < 2^26 */ + freduce_degree (zzprime); + freduce_coefficients (zzprime); + /* |zzprime[i]| < 2^26 */ + memcpy (origxprime, xxprime, sizeof(limb) * 10); + fsum (xxprime, zzprime); + /* |xxprime[i]| < 2^27 */ + fdifference (zzprime, origxprime); + /* |zzprime[i]| < 2^27 */ + fsquare (xxxprime, xxprime); + /* |xxxprime[i]| < 2^26 */ + fsquare (zzzprime, zzprime); + /* |zzzprime[i]| < 2^26 */ + fproduct (zzprime, zzzprime, qmqp); + /* |zzprime[i]| < 14*2^52 */ + freduce_degree (zzprime); + freduce_coefficients (zzprime); + /* |zzprime[i]| < 2^26 */ + memcpy (x3, xxxprime, sizeof(limb) * 10); + memcpy (z3, zzprime, sizeof(limb) * 10); + + fsquare (xx, x); + /* |xx[i]| < 2^26 */ + fsquare (zz, z); + /* |zz[i]| < 2^26 */ + fproduct (x2, xx, zz); + /* |x2[i]| < 14*2^52 */ + freduce_degree (x2); + freduce_coefficients (x2); + /* |x2[i]| < 2^26 */ + fdifference (zz, xx); // does zz = xx - zz + /* |zz[i]| < 2^27 */ + memset (zzz + 10, 0, sizeof(limb) * 9); + fscalar_product (zzz, zz, 121665); + /* |zzz[i]| < 2^(27+17) */ + /* No need to call freduce_degree here: + fscalar_product doesn't increase the degree of its input. */ + freduce_coefficients (zzz); + /* |zzz[i]| < 2^26 */ + fsum (zzz, xx); + /* |zzz[i]| < 2^27 */ + fproduct (z2, zz, zzz); + /* |z2[i]| < 14*2^(26+27) */ + freduce_degree (z2); + freduce_coefficients (z2); + /* |z2|i| < 2^26 */ +} + +/* 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 (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); + fcontract (mypublic, z); + return 0; +} -- cgit v1.2.3