diff options
Diffstat (limited to 'web/server/h2o/libh2o/deps/picotls/deps/cifra/src/curve25519.donna.c')
-rw-r--r-- | web/server/h2o/libh2o/deps/picotls/deps/cifra/src/curve25519.donna.c | 867 |
1 files changed, 0 insertions, 867 deletions
diff --git a/web/server/h2o/libh2o/deps/picotls/deps/cifra/src/curve25519.donna.c b/web/server/h2o/libh2o/deps/picotls/deps/cifra/src/curve25519.donna.c deleted file mode 100644 index 3c597d37c..000000000 --- a/web/server/h2o/libh2o/deps/picotls/deps/cifra/src/curve25519.donna.c +++ /dev/null @@ -1,867 +0,0 @@ -/* 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 "curve25519.h" - -#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. - * - * 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); -} - -void cf_curve25519_mul(u8 out[32], const u8 scalar[32], const u8 point[32]) -{ - limb bp[10], x[10], z[11], zmone[10]; - uint8_t e[32]; - int i; - - for (i = 0; i < 32; ++i) e[i] = scalar[i]; - e[0] &= 248; - e[31] &= 127; - e[31] |= 64; - - fexpand(bp, point); - cmult(x, z, e, bp); - crecip(zmone, z); - fmul(z, x, zmone); - fcontract(out, z); -} - -void cf_curve25519_mul_base(u8 out[32], const u8 scalar[32]) -{ - uint8_t base[32] = { 9 }; - cf_curve25519_mul(out, scalar, base); -} |