17cf2cb1d2
Most C standard library functions are undefined if passed NULL, even when the corresponding length is zero. This gives them (and, in turn, all functions which call them) surprising behavior on empty arrays. Some compilers will miscompile code due to this rule. See also https://www.imperialviolet.org/2016/06/26/nonnull.html Add OPENSSL_memcpy, etc., wrappers which avoid this problem. BUG=23 Change-Id: I95f42b23e92945af0e681264fffaf578e7f8465e Reviewed-on: https://boringssl-review.googlesource.com/12928 Commit-Queue: David Benjamin <davidben@google.com> Reviewed-by: Adam Langley <agl@google.com>
4939 lines
181 KiB
C
4939 lines
181 KiB
C
/* Copyright (c) 2015, Google Inc.
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*
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* Permission to use, copy, modify, and/or distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
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* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
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* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
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* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
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/* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
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* 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as
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* public domain but this file has the ISC license just to keep licencing
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* simple.
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*
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* The field functions are shared by Ed25519 and X25519 where possible. */
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#include <openssl/curve25519.h>
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#include <string.h>
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#include <openssl/cpu.h>
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#include <openssl/mem.h>
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#include <openssl/rand.h>
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#include <openssl/sha.h>
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#include "internal.h"
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#include "../internal.h"
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static const int64_t kBottom25Bits = INT64_C(0x1ffffff);
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static const int64_t kBottom26Bits = INT64_C(0x3ffffff);
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static const int64_t kTop39Bits = INT64_C(0xfffffffffe000000);
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static const int64_t kTop38Bits = INT64_C(0xfffffffffc000000);
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static uint64_t load_3(const uint8_t *in) {
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uint64_t result;
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result = (uint64_t)in[0];
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result |= ((uint64_t)in[1]) << 8;
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result |= ((uint64_t)in[2]) << 16;
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return result;
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}
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static uint64_t load_4(const uint8_t *in) {
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uint64_t result;
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result = (uint64_t)in[0];
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result |= ((uint64_t)in[1]) << 8;
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result |= ((uint64_t)in[2]) << 16;
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result |= ((uint64_t)in[3]) << 24;
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return result;
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}
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static void fe_frombytes(fe h, const uint8_t *s) {
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/* Ignores top bit of h. */
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int64_t h0 = load_4(s);
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int64_t h1 = load_3(s + 4) << 6;
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int64_t h2 = load_3(s + 7) << 5;
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int64_t h3 = load_3(s + 10) << 3;
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int64_t h4 = load_3(s + 13) << 2;
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int64_t h5 = load_4(s + 16);
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int64_t h6 = load_3(s + 20) << 7;
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int64_t h7 = load_3(s + 23) << 5;
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int64_t h8 = load_3(s + 26) << 4;
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int64_t h9 = (load_3(s + 29) & 8388607) << 2;
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int64_t carry0;
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int64_t carry1;
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int64_t carry2;
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int64_t carry3;
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int64_t carry4;
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int64_t carry5;
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int64_t carry6;
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int64_t carry7;
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int64_t carry8;
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int64_t carry9;
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carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
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carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
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carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
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carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
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carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
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carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
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carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
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carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
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carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
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carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
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h[0] = h0;
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h[1] = h1;
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h[2] = h2;
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h[3] = h3;
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h[4] = h4;
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h[5] = h5;
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h[6] = h6;
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h[7] = h7;
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h[8] = h8;
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h[9] = h9;
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}
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/* Preconditions:
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* |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
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*
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* Write p=2^255-19; q=floor(h/p).
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* Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
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*
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* Proof:
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* Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
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* Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
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*
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* Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
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* Then 0<y<1.
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*
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* Write r=h-pq.
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* Have 0<=r<=p-1=2^255-20.
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* Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
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*
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* Write x=r+19(2^-255)r+y.
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* Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
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*
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* Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
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* so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */
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static void fe_tobytes(uint8_t *s, const fe h) {
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int32_t h0 = h[0];
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int32_t h1 = h[1];
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int32_t h2 = h[2];
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int32_t h3 = h[3];
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int32_t h4 = h[4];
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int32_t h5 = h[5];
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int32_t h6 = h[6];
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int32_t h7 = h[7];
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int32_t h8 = h[8];
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int32_t h9 = h[9];
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int32_t q;
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q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
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q = (h0 + q) >> 26;
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q = (h1 + q) >> 25;
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q = (h2 + q) >> 26;
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q = (h3 + q) >> 25;
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q = (h4 + q) >> 26;
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q = (h5 + q) >> 25;
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q = (h6 + q) >> 26;
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q = (h7 + q) >> 25;
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q = (h8 + q) >> 26;
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q = (h9 + q) >> 25;
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/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
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h0 += 19 * q;
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/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
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h1 += h0 >> 26; h0 &= kBottom26Bits;
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h2 += h1 >> 25; h1 &= kBottom25Bits;
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h3 += h2 >> 26; h2 &= kBottom26Bits;
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h4 += h3 >> 25; h3 &= kBottom25Bits;
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h5 += h4 >> 26; h4 &= kBottom26Bits;
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h6 += h5 >> 25; h5 &= kBottom25Bits;
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h7 += h6 >> 26; h6 &= kBottom26Bits;
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h8 += h7 >> 25; h7 &= kBottom25Bits;
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h9 += h8 >> 26; h8 &= kBottom26Bits;
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h9 &= kBottom25Bits;
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/* h10 = carry9 */
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/* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
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* Have h0+...+2^230 h9 between 0 and 2^255-1;
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* evidently 2^255 h10-2^255 q = 0.
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* Goal: Output h0+...+2^230 h9. */
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s[0] = h0 >> 0;
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s[1] = h0 >> 8;
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s[2] = h0 >> 16;
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s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2);
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s[4] = h1 >> 6;
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s[5] = h1 >> 14;
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s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3);
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s[7] = h2 >> 5;
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s[8] = h2 >> 13;
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s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5);
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s[10] = h3 >> 3;
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s[11] = h3 >> 11;
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s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6);
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s[13] = h4 >> 2;
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s[14] = h4 >> 10;
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s[15] = h4 >> 18;
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s[16] = h5 >> 0;
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s[17] = h5 >> 8;
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s[18] = h5 >> 16;
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s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1);
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s[20] = h6 >> 7;
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s[21] = h6 >> 15;
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s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3);
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s[23] = h7 >> 5;
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s[24] = h7 >> 13;
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s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4);
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s[26] = h8 >> 4;
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s[27] = h8 >> 12;
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s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6);
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s[29] = h9 >> 2;
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s[30] = h9 >> 10;
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s[31] = h9 >> 18;
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}
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/* h = f */
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static void fe_copy(fe h, const fe f) {
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OPENSSL_memmove(h, f, sizeof(int32_t) * 10);
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}
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/* h = 0 */
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static void fe_0(fe h) { OPENSSL_memset(h, 0, sizeof(int32_t) * 10); }
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/* h = 1 */
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static void fe_1(fe h) {
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OPENSSL_memset(h, 0, sizeof(int32_t) * 10);
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h[0] = 1;
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}
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/* h = f + g
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* Can overlap h with f or g.
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*
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* Preconditions:
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* |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
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* |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
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*
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* Postconditions:
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* |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
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static void fe_add(fe h, const fe f, const fe g) {
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unsigned i;
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for (i = 0; i < 10; i++) {
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h[i] = f[i] + g[i];
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}
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}
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/* h = f - g
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* Can overlap h with f or g.
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*
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* Preconditions:
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* |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
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* |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
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*
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* Postconditions:
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* |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
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static void fe_sub(fe h, const fe f, const fe g) {
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unsigned i;
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for (i = 0; i < 10; i++) {
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h[i] = f[i] - g[i];
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}
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}
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/* h = f * g
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* Can overlap h with f or g.
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*
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* Preconditions:
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* |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
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* |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
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*
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* Postconditions:
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* |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
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*
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* Notes on implementation strategy:
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*
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* Using schoolbook multiplication.
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* Karatsuba would save a little in some cost models.
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*
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* Most multiplications by 2 and 19 are 32-bit precomputations;
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* cheaper than 64-bit postcomputations.
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*
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* There is one remaining multiplication by 19 in the carry chain;
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* one *19 precomputation can be merged into this,
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* but the resulting data flow is considerably less clean.
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*
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* There are 12 carries below.
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* 10 of them are 2-way parallelizable and vectorizable.
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* Can get away with 11 carries, but then data flow is much deeper.
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*
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* With tighter constraints on inputs can squeeze carries into int32. */
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static void fe_mul(fe h, const fe f, const fe g) {
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int32_t f0 = f[0];
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int32_t f1 = f[1];
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int32_t f2 = f[2];
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int32_t f3 = f[3];
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int32_t f4 = f[4];
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int32_t f5 = f[5];
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int32_t f6 = f[6];
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int32_t f7 = f[7];
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int32_t f8 = f[8];
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int32_t f9 = f[9];
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int32_t g0 = g[0];
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int32_t g1 = g[1];
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int32_t g2 = g[2];
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int32_t g3 = g[3];
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int32_t g4 = g[4];
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int32_t g5 = g[5];
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int32_t g6 = g[6];
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int32_t g7 = g[7];
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int32_t g8 = g[8];
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int32_t g9 = g[9];
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int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
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int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
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int32_t g3_19 = 19 * g3;
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int32_t g4_19 = 19 * g4;
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int32_t g5_19 = 19 * g5;
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int32_t g6_19 = 19 * g6;
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int32_t g7_19 = 19 * g7;
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int32_t g8_19 = 19 * g8;
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int32_t g9_19 = 19 * g9;
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int32_t f1_2 = 2 * f1;
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int32_t f3_2 = 2 * f3;
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int32_t f5_2 = 2 * f5;
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int32_t f7_2 = 2 * f7;
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int32_t f9_2 = 2 * f9;
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int64_t f0g0 = f0 * (int64_t) g0;
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int64_t f0g1 = f0 * (int64_t) g1;
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int64_t f0g2 = f0 * (int64_t) g2;
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int64_t f0g3 = f0 * (int64_t) g3;
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int64_t f0g4 = f0 * (int64_t) g4;
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int64_t f0g5 = f0 * (int64_t) g5;
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int64_t f0g6 = f0 * (int64_t) g6;
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int64_t f0g7 = f0 * (int64_t) g7;
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int64_t f0g8 = f0 * (int64_t) g8;
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int64_t f0g9 = f0 * (int64_t) g9;
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int64_t f1g0 = f1 * (int64_t) g0;
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int64_t f1g1_2 = f1_2 * (int64_t) g1;
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int64_t f1g2 = f1 * (int64_t) g2;
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int64_t f1g3_2 = f1_2 * (int64_t) g3;
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int64_t f1g4 = f1 * (int64_t) g4;
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int64_t f1g5_2 = f1_2 * (int64_t) g5;
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int64_t f1g6 = f1 * (int64_t) g6;
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int64_t f1g7_2 = f1_2 * (int64_t) g7;
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int64_t f1g8 = f1 * (int64_t) g8;
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int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
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int64_t f2g0 = f2 * (int64_t) g0;
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int64_t f2g1 = f2 * (int64_t) g1;
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int64_t f2g2 = f2 * (int64_t) g2;
|
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int64_t f2g3 = f2 * (int64_t) g3;
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int64_t f2g4 = f2 * (int64_t) g4;
|
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int64_t f2g5 = f2 * (int64_t) g5;
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int64_t f2g6 = f2 * (int64_t) g6;
|
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int64_t f2g7 = f2 * (int64_t) g7;
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int64_t f2g8_19 = f2 * (int64_t) g8_19;
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int64_t f2g9_19 = f2 * (int64_t) g9_19;
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int64_t f3g0 = f3 * (int64_t) g0;
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int64_t f3g1_2 = f3_2 * (int64_t) g1;
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int64_t f3g2 = f3 * (int64_t) g2;
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int64_t f3g3_2 = f3_2 * (int64_t) g3;
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int64_t f3g4 = f3 * (int64_t) g4;
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int64_t f3g5_2 = f3_2 * (int64_t) g5;
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int64_t f3g6 = f3 * (int64_t) g6;
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int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
|
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int64_t f3g8_19 = f3 * (int64_t) g8_19;
|
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int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
|
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int64_t f4g0 = f4 * (int64_t) g0;
|
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int64_t f4g1 = f4 * (int64_t) g1;
|
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int64_t f4g2 = f4 * (int64_t) g2;
|
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int64_t f4g3 = f4 * (int64_t) g3;
|
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int64_t f4g4 = f4 * (int64_t) g4;
|
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int64_t f4g5 = f4 * (int64_t) g5;
|
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int64_t f4g6_19 = f4 * (int64_t) g6_19;
|
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int64_t f4g7_19 = f4 * (int64_t) g7_19;
|
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int64_t f4g8_19 = f4 * (int64_t) g8_19;
|
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int64_t f4g9_19 = f4 * (int64_t) g9_19;
|
||
int64_t f5g0 = f5 * (int64_t) g0;
|
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int64_t f5g1_2 = f5_2 * (int64_t) g1;
|
||
int64_t f5g2 = f5 * (int64_t) g2;
|
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int64_t f5g3_2 = f5_2 * (int64_t) g3;
|
||
int64_t f5g4 = f5 * (int64_t) g4;
|
||
int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
|
||
int64_t f5g6_19 = f5 * (int64_t) g6_19;
|
||
int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
|
||
int64_t f5g8_19 = f5 * (int64_t) g8_19;
|
||
int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
|
||
int64_t f6g0 = f6 * (int64_t) g0;
|
||
int64_t f6g1 = f6 * (int64_t) g1;
|
||
int64_t f6g2 = f6 * (int64_t) g2;
|
||
int64_t f6g3 = f6 * (int64_t) g3;
|
||
int64_t f6g4_19 = f6 * (int64_t) g4_19;
|
||
int64_t f6g5_19 = f6 * (int64_t) g5_19;
|
||
int64_t f6g6_19 = f6 * (int64_t) g6_19;
|
||
int64_t f6g7_19 = f6 * (int64_t) g7_19;
|
||
int64_t f6g8_19 = f6 * (int64_t) g8_19;
|
||
int64_t f6g9_19 = f6 * (int64_t) g9_19;
|
||
int64_t f7g0 = f7 * (int64_t) g0;
|
||
int64_t f7g1_2 = f7_2 * (int64_t) g1;
|
||
int64_t f7g2 = f7 * (int64_t) g2;
|
||
int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
|
||
int64_t f7g4_19 = f7 * (int64_t) g4_19;
|
||
int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
|
||
int64_t f7g6_19 = f7 * (int64_t) g6_19;
|
||
int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
|
||
int64_t f7g8_19 = f7 * (int64_t) g8_19;
|
||
int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
|
||
int64_t f8g0 = f8 * (int64_t) g0;
|
||
int64_t f8g1 = f8 * (int64_t) g1;
|
||
int64_t f8g2_19 = f8 * (int64_t) g2_19;
|
||
int64_t f8g3_19 = f8 * (int64_t) g3_19;
|
||
int64_t f8g4_19 = f8 * (int64_t) g4_19;
|
||
int64_t f8g5_19 = f8 * (int64_t) g5_19;
|
||
int64_t f8g6_19 = f8 * (int64_t) g6_19;
|
||
int64_t f8g7_19 = f8 * (int64_t) g7_19;
|
||
int64_t f8g8_19 = f8 * (int64_t) g8_19;
|
||
int64_t f8g9_19 = f8 * (int64_t) g9_19;
|
||
int64_t f9g0 = f9 * (int64_t) g0;
|
||
int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
|
||
int64_t f9g2_19 = f9 * (int64_t) g2_19;
|
||
int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
|
||
int64_t f9g4_19 = f9 * (int64_t) g4_19;
|
||
int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
|
||
int64_t f9g6_19 = f9 * (int64_t) g6_19;
|
||
int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
|
||
int64_t f9g8_19 = f9 * (int64_t) g8_19;
|
||
int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
|
||
int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
|
||
int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
|
||
int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
|
||
int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
|
||
int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
|
||
int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
|
||
int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
|
||
int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
|
||
int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
|
||
int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
|
||
int64_t carry0;
|
||
int64_t carry1;
|
||
int64_t carry2;
|
||
int64_t carry3;
|
||
int64_t carry4;
|
||
int64_t carry5;
|
||
int64_t carry6;
|
||
int64_t carry7;
|
||
int64_t carry8;
|
||
int64_t carry9;
|
||
|
||
/* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
|
||
* i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
|
||
* |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
|
||
* i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
|
||
|
||
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
||
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||
/* |h0| <= 2^25 */
|
||
/* |h4| <= 2^25 */
|
||
/* |h1| <= 1.71*2^59 */
|
||
/* |h5| <= 1.71*2^59 */
|
||
|
||
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
||
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
|
||
/* |h1| <= 2^24; from now on fits into int32 */
|
||
/* |h5| <= 2^24; from now on fits into int32 */
|
||
/* |h2| <= 1.41*2^60 */
|
||
/* |h6| <= 1.41*2^60 */
|
||
|
||
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
||
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
|
||
/* |h2| <= 2^25; from now on fits into int32 unchanged */
|
||
/* |h6| <= 2^25; from now on fits into int32 unchanged */
|
||
/* |h3| <= 1.71*2^59 */
|
||
/* |h7| <= 1.71*2^59 */
|
||
|
||
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
||
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
|
||
/* |h3| <= 2^24; from now on fits into int32 unchanged */
|
||
/* |h7| <= 2^24; from now on fits into int32 unchanged */
|
||
/* |h4| <= 1.72*2^34 */
|
||
/* |h8| <= 1.41*2^60 */
|
||
|
||
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
|
||
/* |h4| <= 2^25; from now on fits into int32 unchanged */
|
||
/* |h8| <= 2^25; from now on fits into int32 unchanged */
|
||
/* |h5| <= 1.01*2^24 */
|
||
/* |h9| <= 1.71*2^59 */
|
||
|
||
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
|
||
/* |h9| <= 2^24; from now on fits into int32 unchanged */
|
||
/* |h0| <= 1.1*2^39 */
|
||
|
||
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
||
/* |h0| <= 2^25; from now on fits into int32 unchanged */
|
||
/* |h1| <= 1.01*2^24 */
|
||
|
||
h[0] = h0;
|
||
h[1] = h1;
|
||
h[2] = h2;
|
||
h[3] = h3;
|
||
h[4] = h4;
|
||
h[5] = h5;
|
||
h[6] = h6;
|
||
h[7] = h7;
|
||
h[8] = h8;
|
||
h[9] = h9;
|
||
}
|
||
|
||
/* h = f * f
|
||
* Can overlap h with f.
|
||
*
|
||
* Preconditions:
|
||
* |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
|
||
*
|
||
* Postconditions:
|
||
* |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
|
||
*
|
||
* See fe_mul.c for discussion of implementation strategy. */
|
||
static void fe_sq(fe h, const fe f) {
|
||
int32_t f0 = f[0];
|
||
int32_t f1 = f[1];
|
||
int32_t f2 = f[2];
|
||
int32_t f3 = f[3];
|
||
int32_t f4 = f[4];
|
||
int32_t f5 = f[5];
|
||
int32_t f6 = f[6];
|
||
int32_t f7 = f[7];
|
||
int32_t f8 = f[8];
|
||
int32_t f9 = f[9];
|
||
int32_t f0_2 = 2 * f0;
|
||
int32_t f1_2 = 2 * f1;
|
||
int32_t f2_2 = 2 * f2;
|
||
int32_t f3_2 = 2 * f3;
|
||
int32_t f4_2 = 2 * f4;
|
||
int32_t f5_2 = 2 * f5;
|
||
int32_t f6_2 = 2 * f6;
|
||
int32_t f7_2 = 2 * f7;
|
||
int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
|
||
int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
|
||
int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
|
||
int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
|
||
int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
|
||
int64_t f0f0 = f0 * (int64_t) f0;
|
||
int64_t f0f1_2 = f0_2 * (int64_t) f1;
|
||
int64_t f0f2_2 = f0_2 * (int64_t) f2;
|
||
int64_t f0f3_2 = f0_2 * (int64_t) f3;
|
||
int64_t f0f4_2 = f0_2 * (int64_t) f4;
|
||
int64_t f0f5_2 = f0_2 * (int64_t) f5;
|
||
int64_t f0f6_2 = f0_2 * (int64_t) f6;
|
||
int64_t f0f7_2 = f0_2 * (int64_t) f7;
|
||
int64_t f0f8_2 = f0_2 * (int64_t) f8;
|
||
int64_t f0f9_2 = f0_2 * (int64_t) f9;
|
||
int64_t f1f1_2 = f1_2 * (int64_t) f1;
|
||
int64_t f1f2_2 = f1_2 * (int64_t) f2;
|
||
int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
|
||
int64_t f1f4_2 = f1_2 * (int64_t) f4;
|
||
int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
|
||
int64_t f1f6_2 = f1_2 * (int64_t) f6;
|
||
int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
|
||
int64_t f1f8_2 = f1_2 * (int64_t) f8;
|
||
int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
|
||
int64_t f2f2 = f2 * (int64_t) f2;
|
||
int64_t f2f3_2 = f2_2 * (int64_t) f3;
|
||
int64_t f2f4_2 = f2_2 * (int64_t) f4;
|
||
int64_t f2f5_2 = f2_2 * (int64_t) f5;
|
||
int64_t f2f6_2 = f2_2 * (int64_t) f6;
|
||
int64_t f2f7_2 = f2_2 * (int64_t) f7;
|
||
int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
|
||
int64_t f2f9_38 = f2 * (int64_t) f9_38;
|
||
int64_t f3f3_2 = f3_2 * (int64_t) f3;
|
||
int64_t f3f4_2 = f3_2 * (int64_t) f4;
|
||
int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
|
||
int64_t f3f6_2 = f3_2 * (int64_t) f6;
|
||
int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
|
||
int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
|
||
int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
|
||
int64_t f4f4 = f4 * (int64_t) f4;
|
||
int64_t f4f5_2 = f4_2 * (int64_t) f5;
|
||
int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
|
||
int64_t f4f7_38 = f4 * (int64_t) f7_38;
|
||
int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
|
||
int64_t f4f9_38 = f4 * (int64_t) f9_38;
|
||
int64_t f5f5_38 = f5 * (int64_t) f5_38;
|
||
int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
|
||
int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
|
||
int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
|
||
int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
|
||
int64_t f6f6_19 = f6 * (int64_t) f6_19;
|
||
int64_t f6f7_38 = f6 * (int64_t) f7_38;
|
||
int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
|
||
int64_t f6f9_38 = f6 * (int64_t) f9_38;
|
||
int64_t f7f7_38 = f7 * (int64_t) f7_38;
|
||
int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
|
||
int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
|
||
int64_t f8f8_19 = f8 * (int64_t) f8_19;
|
||
int64_t f8f9_38 = f8 * (int64_t) f9_38;
|
||
int64_t f9f9_38 = f9 * (int64_t) f9_38;
|
||
int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
|
||
int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
|
||
int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
|
||
int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
|
||
int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
|
||
int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
|
||
int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
|
||
int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
|
||
int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
|
||
int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
|
||
int64_t carry0;
|
||
int64_t carry1;
|
||
int64_t carry2;
|
||
int64_t carry3;
|
||
int64_t carry4;
|
||
int64_t carry5;
|
||
int64_t carry6;
|
||
int64_t carry7;
|
||
int64_t carry8;
|
||
int64_t carry9;
|
||
|
||
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
||
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||
|
||
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
||
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
|
||
|
||
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
||
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
|
||
|
||
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
||
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
|
||
|
||
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
|
||
|
||
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
|
||
|
||
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
||
|
||
h[0] = h0;
|
||
h[1] = h1;
|
||
h[2] = h2;
|
||
h[3] = h3;
|
||
h[4] = h4;
|
||
h[5] = h5;
|
||
h[6] = h6;
|
||
h[7] = h7;
|
||
h[8] = h8;
|
||
h[9] = h9;
|
||
}
|
||
|
||
static void fe_invert(fe out, const fe z) {
|
||
fe t0;
|
||
fe t1;
|
||
fe t2;
|
||
fe t3;
|
||
int i;
|
||
|
||
fe_sq(t0, z);
|
||
fe_sq(t1, t0);
|
||
for (i = 1; i < 2; ++i) {
|
||
fe_sq(t1, t1);
|
||
}
|
||
fe_mul(t1, z, t1);
|
||
fe_mul(t0, t0, t1);
|
||
fe_sq(t2, t0);
|
||
fe_mul(t1, t1, t2);
|
||
fe_sq(t2, t1);
|
||
for (i = 1; i < 5; ++i) {
|
||
fe_sq(t2, t2);
|
||
}
|
||
fe_mul(t1, t2, t1);
|
||
fe_sq(t2, t1);
|
||
for (i = 1; i < 10; ++i) {
|
||
fe_sq(t2, t2);
|
||
}
|
||
fe_mul(t2, t2, t1);
|
||
fe_sq(t3, t2);
|
||
for (i = 1; i < 20; ++i) {
|
||
fe_sq(t3, t3);
|
||
}
|
||
fe_mul(t2, t3, t2);
|
||
fe_sq(t2, t2);
|
||
for (i = 1; i < 10; ++i) {
|
||
fe_sq(t2, t2);
|
||
}
|
||
fe_mul(t1, t2, t1);
|
||
fe_sq(t2, t1);
|
||
for (i = 1; i < 50; ++i) {
|
||
fe_sq(t2, t2);
|
||
}
|
||
fe_mul(t2, t2, t1);
|
||
fe_sq(t3, t2);
|
||
for (i = 1; i < 100; ++i) {
|
||
fe_sq(t3, t3);
|
||
}
|
||
fe_mul(t2, t3, t2);
|
||
fe_sq(t2, t2);
|
||
for (i = 1; i < 50; ++i) {
|
||
fe_sq(t2, t2);
|
||
}
|
||
fe_mul(t1, t2, t1);
|
||
fe_sq(t1, t1);
|
||
for (i = 1; i < 5; ++i) {
|
||
fe_sq(t1, t1);
|
||
}
|
||
fe_mul(out, t1, t0);
|
||
}
|
||
|
||
/* h = -f
|
||
*
|
||
* Preconditions:
|
||
* |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|
||
*
|
||
* Postconditions:
|
||
* |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
|
||
static void fe_neg(fe h, const fe f) {
|
||
unsigned i;
|
||
for (i = 0; i < 10; i++) {
|
||
h[i] = -f[i];
|
||
}
|
||
}
|
||
|
||
/* Replace (f,g) with (g,g) if b == 1;
|
||
* replace (f,g) with (f,g) if b == 0.
|
||
*
|
||
* Preconditions: b in {0,1}. */
|
||
static void fe_cmov(fe f, const fe g, unsigned b) {
|
||
b = 0-b;
|
||
unsigned i;
|
||
for (i = 0; i < 10; i++) {
|
||
int32_t x = f[i] ^ g[i];
|
||
x &= b;
|
||
f[i] ^= x;
|
||
}
|
||
}
|
||
|
||
/* return 0 if f == 0
|
||
* return 1 if f != 0
|
||
*
|
||
* Preconditions:
|
||
* |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
|
||
static int fe_isnonzero(const fe f) {
|
||
uint8_t s[32];
|
||
fe_tobytes(s, f);
|
||
|
||
static const uint8_t zero[32] = {0};
|
||
return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
|
||
}
|
||
|
||
/* return 1 if f is in {1,3,5,...,q-2}
|
||
* return 0 if f is in {0,2,4,...,q-1}
|
||
*
|
||
* Preconditions:
|
||
* |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
|
||
static int fe_isnegative(const fe f) {
|
||
uint8_t s[32];
|
||
fe_tobytes(s, f);
|
||
return s[0] & 1;
|
||
}
|
||
|
||
/* h = 2 * f * f
|
||
* Can overlap h with f.
|
||
*
|
||
* Preconditions:
|
||
* |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
|
||
*
|
||
* Postconditions:
|
||
* |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
|
||
*
|
||
* See fe_mul.c for discussion of implementation strategy. */
|
||
static void fe_sq2(fe h, const fe f) {
|
||
int32_t f0 = f[0];
|
||
int32_t f1 = f[1];
|
||
int32_t f2 = f[2];
|
||
int32_t f3 = f[3];
|
||
int32_t f4 = f[4];
|
||
int32_t f5 = f[5];
|
||
int32_t f6 = f[6];
|
||
int32_t f7 = f[7];
|
||
int32_t f8 = f[8];
|
||
int32_t f9 = f[9];
|
||
int32_t f0_2 = 2 * f0;
|
||
int32_t f1_2 = 2 * f1;
|
||
int32_t f2_2 = 2 * f2;
|
||
int32_t f3_2 = 2 * f3;
|
||
int32_t f4_2 = 2 * f4;
|
||
int32_t f5_2 = 2 * f5;
|
||
int32_t f6_2 = 2 * f6;
|
||
int32_t f7_2 = 2 * f7;
|
||
int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
|
||
int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
|
||
int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
|
||
int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
|
||
int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
|
||
int64_t f0f0 = f0 * (int64_t) f0;
|
||
int64_t f0f1_2 = f0_2 * (int64_t) f1;
|
||
int64_t f0f2_2 = f0_2 * (int64_t) f2;
|
||
int64_t f0f3_2 = f0_2 * (int64_t) f3;
|
||
int64_t f0f4_2 = f0_2 * (int64_t) f4;
|
||
int64_t f0f5_2 = f0_2 * (int64_t) f5;
|
||
int64_t f0f6_2 = f0_2 * (int64_t) f6;
|
||
int64_t f0f7_2 = f0_2 * (int64_t) f7;
|
||
int64_t f0f8_2 = f0_2 * (int64_t) f8;
|
||
int64_t f0f9_2 = f0_2 * (int64_t) f9;
|
||
int64_t f1f1_2 = f1_2 * (int64_t) f1;
|
||
int64_t f1f2_2 = f1_2 * (int64_t) f2;
|
||
int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
|
||
int64_t f1f4_2 = f1_2 * (int64_t) f4;
|
||
int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
|
||
int64_t f1f6_2 = f1_2 * (int64_t) f6;
|
||
int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
|
||
int64_t f1f8_2 = f1_2 * (int64_t) f8;
|
||
int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
|
||
int64_t f2f2 = f2 * (int64_t) f2;
|
||
int64_t f2f3_2 = f2_2 * (int64_t) f3;
|
||
int64_t f2f4_2 = f2_2 * (int64_t) f4;
|
||
int64_t f2f5_2 = f2_2 * (int64_t) f5;
|
||
int64_t f2f6_2 = f2_2 * (int64_t) f6;
|
||
int64_t f2f7_2 = f2_2 * (int64_t) f7;
|
||
int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
|
||
int64_t f2f9_38 = f2 * (int64_t) f9_38;
|
||
int64_t f3f3_2 = f3_2 * (int64_t) f3;
|
||
int64_t f3f4_2 = f3_2 * (int64_t) f4;
|
||
int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
|
||
int64_t f3f6_2 = f3_2 * (int64_t) f6;
|
||
int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
|
||
int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
|
||
int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
|
||
int64_t f4f4 = f4 * (int64_t) f4;
|
||
int64_t f4f5_2 = f4_2 * (int64_t) f5;
|
||
int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
|
||
int64_t f4f7_38 = f4 * (int64_t) f7_38;
|
||
int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
|
||
int64_t f4f9_38 = f4 * (int64_t) f9_38;
|
||
int64_t f5f5_38 = f5 * (int64_t) f5_38;
|
||
int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
|
||
int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
|
||
int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
|
||
int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
|
||
int64_t f6f6_19 = f6 * (int64_t) f6_19;
|
||
int64_t f6f7_38 = f6 * (int64_t) f7_38;
|
||
int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
|
||
int64_t f6f9_38 = f6 * (int64_t) f9_38;
|
||
int64_t f7f7_38 = f7 * (int64_t) f7_38;
|
||
int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
|
||
int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
|
||
int64_t f8f8_19 = f8 * (int64_t) f8_19;
|
||
int64_t f8f9_38 = f8 * (int64_t) f9_38;
|
||
int64_t f9f9_38 = f9 * (int64_t) f9_38;
|
||
int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
|
||
int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
|
||
int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
|
||
int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
|
||
int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
|
||
int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
|
||
int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
|
||
int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
|
||
int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
|
||
int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
|
||
int64_t carry0;
|
||
int64_t carry1;
|
||
int64_t carry2;
|
||
int64_t carry3;
|
||
int64_t carry4;
|
||
int64_t carry5;
|
||
int64_t carry6;
|
||
int64_t carry7;
|
||
int64_t carry8;
|
||
int64_t carry9;
|
||
|
||
h0 += h0;
|
||
h1 += h1;
|
||
h2 += h2;
|
||
h3 += h3;
|
||
h4 += h4;
|
||
h5 += h5;
|
||
h6 += h6;
|
||
h7 += h7;
|
||
h8 += h8;
|
||
h9 += h9;
|
||
|
||
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
||
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||
|
||
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
||
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
|
||
|
||
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
||
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
|
||
|
||
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
||
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
|
||
|
||
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
|
||
|
||
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
|
||
|
||
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
||
|
||
h[0] = h0;
|
||
h[1] = h1;
|
||
h[2] = h2;
|
||
h[3] = h3;
|
||
h[4] = h4;
|
||
h[5] = h5;
|
||
h[6] = h6;
|
||
h[7] = h7;
|
||
h[8] = h8;
|
||
h[9] = h9;
|
||
}
|
||
|
||
static void fe_pow22523(fe out, const fe z) {
|
||
fe t0;
|
||
fe t1;
|
||
fe t2;
|
||
int i;
|
||
|
||
fe_sq(t0, z);
|
||
fe_sq(t1, t0);
|
||
for (i = 1; i < 2; ++i) {
|
||
fe_sq(t1, t1);
|
||
}
|
||
fe_mul(t1, z, t1);
|
||
fe_mul(t0, t0, t1);
|
||
fe_sq(t0, t0);
|
||
fe_mul(t0, t1, t0);
|
||
fe_sq(t1, t0);
|
||
for (i = 1; i < 5; ++i) {
|
||
fe_sq(t1, t1);
|
||
}
|
||
fe_mul(t0, t1, t0);
|
||
fe_sq(t1, t0);
|
||
for (i = 1; i < 10; ++i) {
|
||
fe_sq(t1, t1);
|
||
}
|
||
fe_mul(t1, t1, t0);
|
||
fe_sq(t2, t1);
|
||
for (i = 1; i < 20; ++i) {
|
||
fe_sq(t2, t2);
|
||
}
|
||
fe_mul(t1, t2, t1);
|
||
fe_sq(t1, t1);
|
||
for (i = 1; i < 10; ++i) {
|
||
fe_sq(t1, t1);
|
||
}
|
||
fe_mul(t0, t1, t0);
|
||
fe_sq(t1, t0);
|
||
for (i = 1; i < 50; ++i) {
|
||
fe_sq(t1, t1);
|
||
}
|
||
fe_mul(t1, t1, t0);
|
||
fe_sq(t2, t1);
|
||
for (i = 1; i < 100; ++i) {
|
||
fe_sq(t2, t2);
|
||
}
|
||
fe_mul(t1, t2, t1);
|
||
fe_sq(t1, t1);
|
||
for (i = 1; i < 50; ++i) {
|
||
fe_sq(t1, t1);
|
||
}
|
||
fe_mul(t0, t1, t0);
|
||
fe_sq(t0, t0);
|
||
for (i = 1; i < 2; ++i) {
|
||
fe_sq(t0, t0);
|
||
}
|
||
fe_mul(out, t0, z);
|
||
}
|
||
|
||
void x25519_ge_tobytes(uint8_t *s, const ge_p2 *h) {
|
||
fe recip;
|
||
fe x;
|
||
fe y;
|
||
|
||
fe_invert(recip, h->Z);
|
||
fe_mul(x, h->X, recip);
|
||
fe_mul(y, h->Y, recip);
|
||
fe_tobytes(s, y);
|
||
s[31] ^= fe_isnegative(x) << 7;
|
||
}
|
||
|
||
static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) {
|
||
fe recip;
|
||
fe x;
|
||
fe y;
|
||
|
||
fe_invert(recip, h->Z);
|
||
fe_mul(x, h->X, recip);
|
||
fe_mul(y, h->Y, recip);
|
||
fe_tobytes(s, y);
|
||
s[31] ^= fe_isnegative(x) << 7;
|
||
}
|
||
|
||
static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729,
|
||
-8787816, -6275908, -3247719, -18696448, -12055116};
|
||
|
||
static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472,
|
||
-272473, -25146209, -2005654, 326686, 11406482};
|
||
|
||
int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) {
|
||
fe u;
|
||
fe v;
|
||
fe v3;
|
||
fe vxx;
|
||
fe check;
|
||
|
||
fe_frombytes(h->Y, s);
|
||
fe_1(h->Z);
|
||
fe_sq(u, h->Y);
|
||
fe_mul(v, u, d);
|
||
fe_sub(u, u, h->Z); /* u = y^2-1 */
|
||
fe_add(v, v, h->Z); /* v = dy^2+1 */
|
||
|
||
fe_sq(v3, v);
|
||
fe_mul(v3, v3, v); /* v3 = v^3 */
|
||
fe_sq(h->X, v3);
|
||
fe_mul(h->X, h->X, v);
|
||
fe_mul(h->X, h->X, u); /* x = uv^7 */
|
||
|
||
fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
|
||
fe_mul(h->X, h->X, v3);
|
||
fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
|
||
|
||
fe_sq(vxx, h->X);
|
||
fe_mul(vxx, vxx, v);
|
||
fe_sub(check, vxx, u); /* vx^2-u */
|
||
if (fe_isnonzero(check)) {
|
||
fe_add(check, vxx, u); /* vx^2+u */
|
||
if (fe_isnonzero(check)) {
|
||
return -1;
|
||
}
|
||
fe_mul(h->X, h->X, sqrtm1);
|
||
}
|
||
|
||
if (fe_isnegative(h->X) != (s[31] >> 7)) {
|
||
fe_neg(h->X, h->X);
|
||
}
|
||
|
||
fe_mul(h->T, h->X, h->Y);
|
||
return 0;
|
||
}
|
||
|
||
static void ge_p2_0(ge_p2 *h) {
|
||
fe_0(h->X);
|
||
fe_1(h->Y);
|
||
fe_1(h->Z);
|
||
}
|
||
|
||
static void ge_p3_0(ge_p3 *h) {
|
||
fe_0(h->X);
|
||
fe_1(h->Y);
|
||
fe_1(h->Z);
|
||
fe_0(h->T);
|
||
}
|
||
|
||
static void ge_cached_0(ge_cached *h) {
|
||
fe_1(h->YplusX);
|
||
fe_1(h->YminusX);
|
||
fe_1(h->Z);
|
||
fe_0(h->T2d);
|
||
}
|
||
|
||
static void ge_precomp_0(ge_precomp *h) {
|
||
fe_1(h->yplusx);
|
||
fe_1(h->yminusx);
|
||
fe_0(h->xy2d);
|
||
}
|
||
|
||
/* r = p */
|
||
static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
|
||
fe_copy(r->X, p->X);
|
||
fe_copy(r->Y, p->Y);
|
||
fe_copy(r->Z, p->Z);
|
||
}
|
||
|
||
static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458,
|
||
15978800, -12551817, -6495438, 29715968, 9444199};
|
||
|
||
/* r = p */
|
||
void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
|
||
fe_add(r->YplusX, p->Y, p->X);
|
||
fe_sub(r->YminusX, p->Y, p->X);
|
||
fe_copy(r->Z, p->Z);
|
||
fe_mul(r->T2d, p->T, d2);
|
||
}
|
||
|
||
/* r = p */
|
||
void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
|
||
fe_mul(r->X, p->X, p->T);
|
||
fe_mul(r->Y, p->Y, p->Z);
|
||
fe_mul(r->Z, p->Z, p->T);
|
||
}
|
||
|
||
/* r = p */
|
||
void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
|
||
fe_mul(r->X, p->X, p->T);
|
||
fe_mul(r->Y, p->Y, p->Z);
|
||
fe_mul(r->Z, p->Z, p->T);
|
||
fe_mul(r->T, p->X, p->Y);
|
||
}
|
||
|
||
/* r = p */
|
||
static void ge_p1p1_to_cached(ge_cached *r, const ge_p1p1 *p) {
|
||
ge_p3 t;
|
||
x25519_ge_p1p1_to_p3(&t, p);
|
||
x25519_ge_p3_to_cached(r, &t);
|
||
}
|
||
|
||
/* r = 2 * p */
|
||
static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
|
||
fe t0;
|
||
|
||
fe_sq(r->X, p->X);
|
||
fe_sq(r->Z, p->Y);
|
||
fe_sq2(r->T, p->Z);
|
||
fe_add(r->Y, p->X, p->Y);
|
||
fe_sq(t0, r->Y);
|
||
fe_add(r->Y, r->Z, r->X);
|
||
fe_sub(r->Z, r->Z, r->X);
|
||
fe_sub(r->X, t0, r->Y);
|
||
fe_sub(r->T, r->T, r->Z);
|
||
}
|
||
|
||
/* r = 2 * p */
|
||
static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
|
||
ge_p2 q;
|
||
ge_p3_to_p2(&q, p);
|
||
ge_p2_dbl(r, &q);
|
||
}
|
||
|
||
/* r = p + q */
|
||
static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
|
||
fe t0;
|
||
|
||
fe_add(r->X, p->Y, p->X);
|
||
fe_sub(r->Y, p->Y, p->X);
|
||
fe_mul(r->Z, r->X, q->yplusx);
|
||
fe_mul(r->Y, r->Y, q->yminusx);
|
||
fe_mul(r->T, q->xy2d, p->T);
|
||
fe_add(t0, p->Z, p->Z);
|
||
fe_sub(r->X, r->Z, r->Y);
|
||
fe_add(r->Y, r->Z, r->Y);
|
||
fe_add(r->Z, t0, r->T);
|
||
fe_sub(r->T, t0, r->T);
|
||
}
|
||
|
||
/* r = p - q */
|
||
static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
|
||
fe t0;
|
||
|
||
fe_add(r->X, p->Y, p->X);
|
||
fe_sub(r->Y, p->Y, p->X);
|
||
fe_mul(r->Z, r->X, q->yminusx);
|
||
fe_mul(r->Y, r->Y, q->yplusx);
|
||
fe_mul(r->T, q->xy2d, p->T);
|
||
fe_add(t0, p->Z, p->Z);
|
||
fe_sub(r->X, r->Z, r->Y);
|
||
fe_add(r->Y, r->Z, r->Y);
|
||
fe_sub(r->Z, t0, r->T);
|
||
fe_add(r->T, t0, r->T);
|
||
}
|
||
|
||
/* r = p + q */
|
||
void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
|
||
fe t0;
|
||
|
||
fe_add(r->X, p->Y, p->X);
|
||
fe_sub(r->Y, p->Y, p->X);
|
||
fe_mul(r->Z, r->X, q->YplusX);
|
||
fe_mul(r->Y, r->Y, q->YminusX);
|
||
fe_mul(r->T, q->T2d, p->T);
|
||
fe_mul(r->X, p->Z, q->Z);
|
||
fe_add(t0, r->X, r->X);
|
||
fe_sub(r->X, r->Z, r->Y);
|
||
fe_add(r->Y, r->Z, r->Y);
|
||
fe_add(r->Z, t0, r->T);
|
||
fe_sub(r->T, t0, r->T);
|
||
}
|
||
|
||
/* r = p - q */
|
||
void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
|
||
fe t0;
|
||
|
||
fe_add(r->X, p->Y, p->X);
|
||
fe_sub(r->Y, p->Y, p->X);
|
||
fe_mul(r->Z, r->X, q->YminusX);
|
||
fe_mul(r->Y, r->Y, q->YplusX);
|
||
fe_mul(r->T, q->T2d, p->T);
|
||
fe_mul(r->X, p->Z, q->Z);
|
||
fe_add(t0, r->X, r->X);
|
||
fe_sub(r->X, r->Z, r->Y);
|
||
fe_add(r->Y, r->Z, r->Y);
|
||
fe_sub(r->Z, t0, r->T);
|
||
fe_add(r->T, t0, r->T);
|
||
}
|
||
|
||
static uint8_t equal(signed char b, signed char c) {
|
||
uint8_t ub = b;
|
||
uint8_t uc = c;
|
||
uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
|
||
uint32_t y = x; /* 0: yes; 1..255: no */
|
||
y -= 1; /* 4294967295: yes; 0..254: no */
|
||
y >>= 31; /* 1: yes; 0: no */
|
||
return y;
|
||
}
|
||
|
||
static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) {
|
||
fe_cmov(t->yplusx, u->yplusx, b);
|
||
fe_cmov(t->yminusx, u->yminusx, b);
|
||
fe_cmov(t->xy2d, u->xy2d, b);
|
||
}
|
||
|
||
void x25519_ge_scalarmult_small_precomp(
|
||
ge_p3 *h, const uint8_t a[32], const uint8_t precomp_table[15 * 2 * 32]) {
|
||
/* precomp_table is first expanded into matching |ge_precomp|
|
||
* elements. */
|
||
ge_precomp multiples[15];
|
||
|
||
unsigned i;
|
||
for (i = 0; i < 15; i++) {
|
||
const uint8_t *bytes = &precomp_table[i*(2 * 32)];
|
||
fe x, y;
|
||
fe_frombytes(x, bytes);
|
||
fe_frombytes(y, bytes + 32);
|
||
|
||
ge_precomp *out = &multiples[i];
|
||
fe_add(out->yplusx, y, x);
|
||
fe_sub(out->yminusx, y, x);
|
||
fe_mul(out->xy2d, x, y);
|
||
fe_mul(out->xy2d, out->xy2d, d2);
|
||
}
|
||
|
||
/* See the comment above |k25519SmallPrecomp| about the structure of the
|
||
* precomputed elements. This loop does 64 additions and 64 doublings to
|
||
* calculate the result. */
|
||
ge_p3_0(h);
|
||
|
||
for (i = 63; i < 64; i--) {
|
||
unsigned j;
|
||
signed char index = 0;
|
||
|
||
for (j = 0; j < 4; j++) {
|
||
const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7));
|
||
index |= (bit << j);
|
||
}
|
||
|
||
ge_precomp e;
|
||
ge_precomp_0(&e);
|
||
|
||
for (j = 1; j < 16; j++) {
|
||
cmov(&e, &multiples[j-1], equal(index, j));
|
||
}
|
||
|
||
ge_cached cached;
|
||
ge_p1p1 r;
|
||
x25519_ge_p3_to_cached(&cached, h);
|
||
x25519_ge_add(&r, h, &cached);
|
||
x25519_ge_p1p1_to_p3(h, &r);
|
||
|
||
ge_madd(&r, h, &e);
|
||
x25519_ge_p1p1_to_p3(h, &r);
|
||
}
|
||
}
|
||
|
||
#if defined(OPENSSL_SMALL)
|
||
|
||
/* This block of code replaces the standard base-point table with a much smaller
|
||
* one. The standard table is 30,720 bytes while this one is just 960.
|
||
*
|
||
* This table contains 15 pairs of group elements, (x, y), where each field
|
||
* element is serialised with |fe_tobytes|. If |i| is the index of the group
|
||
* element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀
|
||
* is the most significant bit). The value of the group element is then:
|
||
* (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator. */
|
||
static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = {
|
||
0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95,
|
||
0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0,
|
||
0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66,
|
||
0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
|
||
0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
|
||
0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e,
|
||
0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4,
|
||
0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62,
|
||
0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba,
|
||
0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd,
|
||
0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61,
|
||
0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c,
|
||
0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c,
|
||
0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5,
|
||
0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3,
|
||
0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18,
|
||
0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2,
|
||
0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95,
|
||
0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b,
|
||
0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90,
|
||
0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52,
|
||
0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb,
|
||
0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c,
|
||
0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e,
|
||
0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e,
|
||
0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a,
|
||
0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43,
|
||
0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53,
|
||
0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8,
|
||
0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89,
|
||
0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef,
|
||
0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60,
|
||
0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a,
|
||
0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8,
|
||
0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54,
|
||
0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b,
|
||
0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd,
|
||
0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb,
|
||
0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c,
|
||
0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b,
|
||
0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63,
|
||
0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a,
|
||
0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07,
|
||
0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa,
|
||
0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a,
|
||
0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84,
|
||
0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc,
|
||
0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42,
|
||
0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0,
|
||
0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0,
|
||
0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a,
|
||
0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5,
|
||
0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c,
|
||
0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27,
|
||
0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31,
|
||
0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c,
|
||
0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87,
|
||
0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0,
|
||
0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23,
|
||
0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2,
|
||
0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87,
|
||
0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d,
|
||
0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b,
|
||
0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d,
|
||
0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6,
|
||
0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84,
|
||
0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04,
|
||
0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19,
|
||
0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b,
|
||
0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a,
|
||
0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea,
|
||
0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30,
|
||
0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7,
|
||
0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa,
|
||
0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5,
|
||
0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71,
|
||
0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab,
|
||
0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb,
|
||
0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c,
|
||
0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25,
|
||
};
|
||
|
||
void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) {
|
||
x25519_ge_scalarmult_small_precomp(h, a, k25519SmallPrecomp);
|
||
}
|
||
|
||
#else
|
||
|
||
/* k25519Precomp[i][j] = (j+1)*256^i*B */
|
||
static const ge_precomp k25519Precomp[32][8] = {
|
||
{
|
||
{
|
||
{25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
|
||
27544626, -11754271, -6079156, 2047605},
|
||
{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
|
||
5043384, 19500929, -15469378},
|
||
{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
|
||
29287919, 11864899, -24514362, -4438546},
|
||
},
|
||
{
|
||
{-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
|
||
-11717903, -3814571, -358445, -10211303},
|
||
{-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
|
||
-15616551, 11189268, -26829678, -5319081},
|
||
{26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
|
||
-3128826, -9541118, -15472047, -4166697},
|
||
},
|
||
{
|
||
{15636291, -9688557, 24204773, -7912398, 616977, -16685262,
|
||
27787600, -14772189, 28944400, -1550024},
|
||
{16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
|
||
16354577, -11775962, 7689662, 11199574},
|
||
{30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
|
||
7512774, 10017326, -17749093, -9920357},
|
||
},
|
||
{
|
||
{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
|
||
-28926210, 15006023, 3284568, -6276540},
|
||
{23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
|
||
7464579, 9656445, 13059162, 10374397},
|
||
{7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
|
||
-3839045, -641708, -101325},
|
||
},
|
||
{
|
||
{10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
|
||
32867885, 14515107, -15438304, 10819380},
|
||
{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
|
||
12483688, -12668491, 5581306},
|
||
{19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
|
||
28542350, 13850243, -23678021, -15815942},
|
||
},
|
||
{
|
||
{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
|
||
-19188627, -15224819, -9818940, -12085777},
|
||
{-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
|
||
-15689887, 1762328, 14866737},
|
||
{-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
|
||
-28236412, 3959421, 27914454, 4383652},
|
||
},
|
||
{
|
||
{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
|
||
5230134, -23952439, -15175766},
|
||
{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
|
||
20654025, 16520125, 30598449, 7715701},
|
||
{28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
|
||
-31400660, 1370708, 29794553, -1409300},
|
||
},
|
||
{
|
||
{14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
|
||
30290735, 10876454, -33154098, 2381726},
|
||
{-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
|
||
-6236617, 3696005, -32300832, 15351955},
|
||
{27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
|
||
-32961401, -2970515, 29551813, 10109425},
|
||
},
|
||
},
|
||
{
|
||
{
|
||
{-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
|
||
-2378284, -1627556, 10092783, -4764171},
|
||
{27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
|
||
-32508754, 12005538, -17810127, 12803510},
|
||
{17228999, -15661624, -1233527, 300140, -1224870, -11714777,
|
||
30364213, -9038194, 18016357, 4397660},
|
||
},
|
||
{
|
||
{-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
|
||
-26619106, 14544525, -17477504, 982639},
|
||
{29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
|
||
-4120128, -21047696, 9934963},
|
||
{5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
|
||
-14747930, 4559895, -30123922, -10897950},
|
||
},
|
||
{
|
||
{-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
|
||
24191034, 4541697, -13338309, 5500568},
|
||
{12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
|
||
-17430592, 12264343, 10874051, 13524335},
|
||
{25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
|
||
5080568, -22528059, 5376628},
|
||
},
|
||
{
|
||
{-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
|
||
-22321305, -9447443, 4535768, 1569007},
|
||
{-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
|
||
-30494562, 3044290, 31848280, 12543772},
|
||
{-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
|
||
-27377195, -2062731, 7718482, 14474653},
|
||
},
|
||
{
|
||
{2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
|
||
-7236665, 24316168, -5253567},
|
||
{13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
|
||
33040651, -13424532, -20729456, 8321686},
|
||
{21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
|
||
23845965, -11874838, -9984458, 608372},
|
||
},
|
||
{
|
||
{-13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
|
||
1123968, -6780577, 27229399, 23887},
|
||
{-23244140, -294205, -11744728, 14712571, -29465699, -2029617,
|
||
12797024, -6440308, -1633405, 16678954},
|
||
{-29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
|
||
-1508144, -4795045, -17169265, 4904953},
|
||
},
|
||
{
|
||
{24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
|
||
5169211, 16191880, 2128236, -4326833},
|
||
{-16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
|
||
-29806336, 916033, -6882542, -2986532},
|
||
{-22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
|
||
285431, 2763829, 15736322, 4143876},
|
||
},
|
||
{
|
||
{2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
|
||
-14594663, 23527084, -16458268},
|
||
{33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
|
||
-32625340, 4087881, -15188911, -14416214},
|
||
{1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
|
||
4357868, -4774191, -16323038},
|
||
},
|
||
},
|
||
{
|
||
{
|
||
{6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
|
||
23365147, -3949732, 7390890, 2759800},
|
||
{4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
|
||
-4264057, 1244380, -12919645},
|
||
{-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
|
||
9208236, 15886429, 16489664},
|
||
},
|
||
{
|
||
{1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
|
||
-13693198, 398369, -30606455, -712933},
|
||
{-25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
|
||
13348553, 12076947, -30836462, 5113182},
|
||
{-17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
|
||
-30341101, -7336386, 13847711, 5387222},
|
||
},
|
||
{
|
||
{-18582163, -3416217, 17824843, -2340966, 22744343, -10442611,
|
||
8763061, 3617786, -19600662, 10370991},
|
||
{20246567, -14369378, 22358229, -543712, 18507283, -10413996,
|
||
14554437, -8746092, 32232924, 16763880},
|
||
{9648505, 10094563, 26416693, 14745928, -30374318, -6472621,
|
||
11094161, 15689506, 3140038, -16510092},
|
||
},
|
||
{
|
||
{-16160072, 5472695, 31895588, 4744994, 8823515, 10365685,
|
||
-27224800, 9448613, -28774454, 366295},
|
||
{19153450, 11523972, -11096490, -6503142, -24647631, 5420647,
|
||
28344573, 8041113, 719605, 11671788},
|
||
{8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
|
||
-15266516, 27000813, -10195553},
|
||
},
|
||
{
|
||
{-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
|
||
5336097, 6750977, -14521026},
|
||
{11836410, -3979488, 26297894, 16080799, 23455045, 15735944,
|
||
1695823, -8819122, 8169720, 16220347},
|
||
{-18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
|
||
-11144307, -2627664, -5990708, -14166033},
|
||
},
|
||
{
|
||
{-23308498, -10968312, 15213228, -10081214, -30853605, -11050004,
|
||
27884329, 2847284, 2655861, 1738395},
|
||
{-27537433, -14253021, -25336301, -8002780, -9370762, 8129821,
|
||
21651608, -3239336, -19087449, -11005278},
|
||
{1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
|
||
5821408, 10478196, 8544890},
|
||
},
|
||
{
|
||
{32173121, -16129311, 24896207, 3921497, 22579056, -3410854,
|
||
19270449, 12217473, 17789017, -3395995},
|
||
{-30552961, -2228401, -15578829, -10147201, 13243889, 517024,
|
||
15479401, -3853233, 30460520, 1052596},
|
||
{-11614875, 13323618, 32618793, 8175907, -15230173, 12596687,
|
||
27491595, -4612359, 3179268, -9478891},
|
||
},
|
||
{
|
||
{31947069, -14366651, -4640583, -15339921, -15125977, -6039709,
|
||
-14756777, -16411740, 19072640, -9511060},
|
||
{11685058, 11822410, 3158003, -13952594, 33402194, -4165066,
|
||
5977896, -5215017, 473099, 5040608},
|
||
{-20290863, 8198642, -27410132, 11602123, 1290375, -2799760,
|
||
28326862, 1721092, -19558642, -3131606},
|
||
},
|
||
},
|
||
{
|
||
{
|
||
{7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
|
||
8076149, -27868496, 11538389},
|
||
{-19935666, 3899861, 18283497, -6801568, -15728660, -11249211,
|
||
8754525, 7446702, -5676054, 5797016},
|
||
{-11295600, -3793569, -15782110, -7964573, 12708869, -8456199,
|
||
2014099, -9050574, -2369172, -5877341},
|
||
},
|
||
{
|
||
{-22472376, -11568741, -27682020, 1146375, 18956691, 16640559,
|
||
1192730, -3714199, 15123619, 10811505},
|
||
{14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363,
|
||
15776356, -28886779, -11974553},
|
||
{-28241164, -8072475, -4978962, -5315317, 29416931, 1847569,
|
||
-20654173, -16484855, 4714547, -9600655},
|
||
},
|
||
{
|
||
{15200332, 8368572, 19679101, 15970074, -31872674, 1959451,
|
||
24611599, -4543832, -11745876, 12340220},
|
||
{12876937, -10480056, 33134381, 6590940, -6307776, 14872440,
|
||
9613953, 8241152, 15370987, 9608631},
|
||
{-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868,
|
||
15866074, -28210621, -8814099},
|
||
},
|
||
{
|
||
{26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233,
|
||
858697, 20571223, 8420556},
|
||
{14620715, 13067227, -15447274, 8264467, 14106269, 15080814,
|
||
33531827, 12516406, -21574435, -12476749},
|
||
{236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519,
|
||
7256740, 8791136, 15069930},
|
||
},
|
||
{
|
||
{1276410, -9371918, 22949635, -16322807, -23493039, -5702186,
|
||
14711875, 4874229, -30663140, -2331391},
|
||
{5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175,
|
||
-7912378, -33069337, 9234253},
|
||
{20590503, -9018988, 31529744, -7352666, -2706834, 10650548,
|
||
31559055, -11609587, 18979186, 13396066},
|
||
},
|
||
{
|
||
{24474287, 4968103, 22267082, 4407354, 24063882, -8325180,
|
||
-18816887, 13594782, 33514650, 7021958},
|
||
{-11566906, -6565505, -21365085, 15928892, -26158305, 4315421,
|
||
-25948728, -3916677, -21480480, 12868082},
|
||
{-28635013, 13504661, 19988037, -2132761, 21078225, 6443208,
|
||
-21446107, 2244500, -12455797, -8089383},
|
||
},
|
||
{
|
||
{-30595528, 13793479, -5852820, 319136, -25723172, -6263899,
|
||
33086546, 8957937, -15233648, 5540521},
|
||
{-11630176, -11503902, -8119500, -7643073, 2620056, 1022908,
|
||
-23710744, -1568984, -16128528, -14962807},
|
||
{23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819,
|
||
892185, -11513277, -15205948},
|
||
},
|
||
{
|
||
{9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819,
|
||
4763127, -19179614, 5867134},
|
||
{-32765025, 1927590, 31726409, -4753295, 23962434, -16019500,
|
||
27846559, 5931263, -29749703, -16108455},
|
||
{27461885, -2977536, 22380810, 1815854, -23033753, -3031938,
|
||
7283490, -15148073, -19526700, 7734629},
|
||
},
|
||
},
|
||
{
|
||
{
|
||
{-8010264, -9590817, -11120403, 6196038, 29344158, -13430885,
|
||
7585295, -3176626, 18549497, 15302069},
|
||
{-32658337, -6171222, -7672793, -11051681, 6258878, 13504381,
|
||
10458790, -6418461, -8872242, 8424746},
|
||
{24687205, 8613276, -30667046, -3233545, 1863892, -1830544,
|
||
19206234, 7134917, -11284482, -828919},
|
||
},
|
||
{
|
||
{11334899, -9218022, 8025293, 12707519, 17523892, -10476071,
|
||
10243738, -14685461, -5066034, 16498837},
|
||
{8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925,
|
||
-14124238, 6536641, 10543906},
|
||
{-28946384, 15479763, -17466835, 568876, -1497683, 11223454,
|
||
-2669190, -16625574, -27235709, 8876771},
|
||
},
|
||
{
|
||
{-25742899, -12566864, -15649966, -846607, -33026686, -796288,
|
||
-33481822, 15824474, -604426, -9039817},
|
||
{10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697,
|
||
-4890037, 1657394, 3084098},
|
||
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|
||
{-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107,
|
||
-8570186, -9689599, -3031667},
|
||
{25008904, -10771599, -4305031, -9638010, 16265036, 15721635,
|
||
683793, -11823784, 15723479, -15163481},
|
||
{-9660625, 12374379, -27006999, -7026148, -7724114, -12314514,
|
||
11879682, 5400171, 519526, -1235876},
|
||
},
|
||
{
|
||
{22258397, -16332233, -7869817, 14613016, -22520255, -2950923,
|
||
-20353881, 7315967, 16648397, 7605640},
|
||
{-8081308, -8464597, -8223311, 9719710, 19259459, -15348212,
|
||
23994942, -5281555, -9468848, 4763278},
|
||
{-21699244, 9220969, -15730624, 1084137, -25476107, -2852390,
|
||
31088447, -7764523, -11356529, 728112},
|
||
},
|
||
{
|
||
{26047220, -11751471, -6900323, -16521798, 24092068, 9158119,
|
||
-4273545, -12555558, -29365436, -5498272},
|
||
{17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007,
|
||
12327945, 10750447, 10014012},
|
||
{-10312768, 3936952, 9156313, -8897683, 16498692, -994647,
|
||
-27481051, -666732, 3424691, 7540221},
|
||
},
|
||
{
|
||
{30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422,
|
||
-16317219, -9244265, 15258046},
|
||
{13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406,
|
||
2711395, 1062915, -5136345},
|
||
{-19240248, -11254599, -29509029, -7499965, -5835763, 13005411,
|
||
-6066489, 12194497, 32960380, 1459310},
|
||
},
|
||
},
|
||
{
|
||
{
|
||
{19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197,
|
||
-6101885, 18638003, -11174937},
|
||
{31395534, 15098109, 26581030, 8030562, -16527914, -5007134,
|
||
9012486, -7584354, -6643087, -5442636},
|
||
{-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222,
|
||
9677543, -32294889, -6456008},
|
||
},
|
||
{
|
||
{-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579,
|
||
-7839692, -7852844, -8138429},
|
||
{-15236356, -15433509, 7766470, 746860, 26346930, -10221762,
|
||
-27333451, 10754588, -9431476, 5203576},
|
||
{31834314, 14135496, -770007, 5159118, 20917671, -16768096,
|
||
-7467973, -7337524, 31809243, 7347066},
|
||
},
|
||
{
|
||
{-9606723, -11874240, 20414459, 13033986, 13716524, -11691881,
|
||
19797970, -12211255, 15192876, -2087490},
|
||
{-12663563, -2181719, 1168162, -3804809, 26747877, -14138091,
|
||
10609330, 12694420, 33473243, -13382104},
|
||
{33184999, 11180355, 15832085, -11385430, -1633671, 225884,
|
||
15089336, -11023903, -6135662, 14480053},
|
||
},
|
||
{
|
||
{31308717, -5619998, 31030840, -1897099, 15674547, -6582883,
|
||
5496208, 13685227, 27595050, 8737275},
|
||
{-20318852, -15150239, 10933843, -16178022, 8335352, -7546022,
|
||
-31008351, -12610604, 26498114, 66511},
|
||
{22644454, -8761729, -16671776, 4884562, -3105614, -13559366,
|
||
30540766, -4286747, -13327787, -7515095},
|
||
},
|
||
{
|
||
{-28017847, 9834845, 18617207, -2681312, -3401956, -13307506,
|
||
8205540, 13585437, -17127465, 15115439},
|
||
{23711543, -672915, 31206561, -8362711, 6164647, -9709987,
|
||
-33535882, -1426096, 8236921, 16492939},
|
||
{-23910559, -13515526, -26299483, -4503841, 25005590, -7687270,
|
||
19574902, 10071562, 6708380, -6222424},
|
||
},
|
||
{
|
||
{2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017,
|
||
9328700, 29955601, -11678310},
|
||
{3096359, 9271816, -21620864, -15521844, -14847996, -7592937,
|
||
-25892142, -12635595, -9917575, 6216608},
|
||
{-32615849, 338663, -25195611, 2510422, -29213566, -13820213,
|
||
24822830, -6146567, -26767480, 7525079},
|
||
},
|
||
{
|
||
{-23066649, -13985623, 16133487, -7896178, -3389565, 778788,
|
||
-910336, -2782495, -19386633, 11994101},
|
||
{21691500, -13624626, -641331, -14367021, 3285881, -3483596,
|
||
-25064666, 9718258, -7477437, 13381418},
|
||
{18445390, -4202236, 14979846, 11622458, -1727110, -3582980,
|
||
23111648, -6375247, 28535282, 15779576},
|
||
},
|
||
{
|
||
{30098053, 3089662, -9234387, 16662135, -21306940, 11308411,
|
||
-14068454, 12021730, 9955285, -16303356},
|
||
{9734894, -14576830, -7473633, -9138735, 2060392, 11313496,
|
||
-18426029, 9924399, 20194861, 13380996},
|
||
{-26378102, -7965207, -22167821, 15789297, -18055342, -6168792,
|
||
-1984914, 15707771, 26342023, 10146099},
|
||
},
|
||
},
|
||
{
|
||
{
|
||
{-26016874, -219943, 21339191, -41388, 19745256, -2878700,
|
||
-29637280, 2227040, 21612326, -545728},
|
||
{-13077387, 1184228, 23562814, -5970442, -20351244, -6348714,
|
||
25764461, 12243797, -20856566, 11649658},
|
||
{-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944,
|
||
6114064, 33514190, 2333242},
|
||
},
|
||
{
|
||
{-21433588, -12421821, 8119782, 7219913, -21830522, -9016134,
|
||
-6679750, -12670638, 24350578, -13450001},
|
||
{-4116307, -11271533, -23886186, 4843615, -30088339, 690623,
|
||
-31536088, -10406836, 8317860, 12352766},
|
||
{18200138, -14475911, -33087759, -2696619, -23702521, -9102511,
|
||
-23552096, -2287550, 20712163, 6719373},
|
||
},
|
||
{
|
||
{26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530,
|
||
-3763210, 26224235, -3297458},
|
||
{-17168938, -14854097, -3395676, -16369877, -19954045, 14050420,
|
||
21728352, 9493610, 18620611, -16428628},
|
||
{-13323321, 13325349, 11432106, 5964811, 18609221, 6062965,
|
||
-5269471, -9725556, -30701573, -16479657},
|
||
},
|
||
{
|
||
{-23860538, -11233159, 26961357, 1640861, -32413112, -16737940,
|
||
12248509, -5240639, 13735342, 1934062},
|
||
{25089769, 6742589, 17081145, -13406266, 21909293, -16067981,
|
||
-15136294, -3765346, -21277997, 5473616},
|
||
{31883677, -7961101, 1083432, -11572403, 22828471, 13290673,
|
||
-7125085, 12469656, 29111212, -5451014},
|
||
},
|
||
{
|
||
{24244947, -15050407, -26262976, 2791540, -14997599, 16666678,
|
||
24367466, 6388839, -10295587, 452383},
|
||
{-25640782, -3417841, 5217916, 16224624, 19987036, -4082269,
|
||
-24236251, -5915248, 15766062, 8407814},
|
||
{-20406999, 13990231, 15495425, 16395525, 5377168, 15166495,
|
||
-8917023, -4388953, -8067909, 2276718},
|
||
},
|
||
{
|
||
{30157918, 12924066, -17712050, 9245753, 19895028, 3368142,
|
||
-23827587, 5096219, 22740376, -7303417},
|
||
{2041139, -14256350, 7783687, 13876377, -25946985, -13352459,
|
||
24051124, 13742383, -15637599, 13295222},
|
||
{33338237, -8505733, 12532113, 7977527, 9106186, -1715251,
|
||
-17720195, -4612972, -4451357, -14669444},
|
||
},
|
||
{
|
||
{-20045281, 5454097, -14346548, 6447146, 28862071, 1883651,
|
||
-2469266, -4141880, 7770569, 9620597},
|
||
{23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528,
|
||
-1694323, -33502340, -14767970},
|
||
{1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801,
|
||
1220118, 30494170, -11440799},
|
||
},
|
||
{
|
||
{-5037580, -13028295, -2970559, -3061767, 15640974, -6701666,
|
||
-26739026, 926050, -1684339, -13333647},
|
||
{13908495, -3549272, 30919928, -6273825, -21521863, 7989039,
|
||
9021034, 9078865, 3353509, 4033511},
|
||
{-29663431, -15113610, 32259991, -344482, 24295849, -12912123,
|
||
23161163, 8839127, 27485041, 7356032},
|
||
},
|
||
},
|
||
{
|
||
{
|
||
{9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
|
||
2625015, 28431036, -16771834},
|
||
{-23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
|
||
-22545972, 14150565, 15970762, 4099461},
|
||
{29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
|
||
13617293, -9937143, 11465739, 8317062},
|
||
},
|
||
{
|
||
{-25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
|
||
14898637, 3848455, 20969334, -5157516},
|
||
{-20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
|
||
-21610826, -3649888, 11177095, 14989547},
|
||
{-24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
|
||
13515641, 2581286, -28487508, 9930240},
|
||
},
|
||
{
|
||
{-17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
|
||
18345767, -13403753, 16291481, -5314038},
|
||
{-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
|
||
6957617, 4368891, 9788741},
|
||
{16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
|
||
-21722536, -8613148, 16250552, -11111103},
|
||
},
|
||
{
|
||
{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
|
||
10604807, -30190403, 4782747},
|
||
{-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
|
||
-9981571, 4383045, 22546403, 437323},
|
||
{31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
|
||
27343084, 2786261, -30633590, -14097016},
|
||
},
|
||
{
|
||
{-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
|
||
-19690631, 2355319, -19284671, -6114373},
|
||
{15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
|
||
18952177, 15496498, -29380133, 11754228},
|
||
{-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
|
||
7141596, 11724556, 22761615, -10134141},
|
||
},
|
||
{
|
||
{16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
|
||
-28741185, -12227393, 32851222, 11717399},
|
||
{11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
|
||
31474879, 3483633, -1193175, -4030831},
|
||
{-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
|
||
33142652, 6546660, -19985279, -3948376},
|
||
},
|
||
{
|
||
{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
|
||
-8537131, -12833048, -30772034, -15486313},
|
||
{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
|
||
-31135347, -16049879, 10928917, 3011958},
|
||
{-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
|
||
-30831056, -12805180, 18008031, 10258577},
|
||
},
|
||
{
|
||
{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
|
||
-1853465, 1367120, 25127874, 6671743},
|
||
{29701166, -14373934, -10878120, 9279288, -17568, 13127210,
|
||
21382910, 11042292, 25838796, 4642684},
|
||
{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
|
||
30468147, -13900640, 18423289, 4177476},
|
||
},
|
||
},
|
||
};
|
||
|
||
static uint8_t negative(signed char b) {
|
||
uint32_t x = b;
|
||
x >>= 31; /* 1: yes; 0: no */
|
||
return x;
|
||
}
|
||
|
||
static void table_select(ge_precomp *t, int pos, signed char b) {
|
||
ge_precomp minust;
|
||
uint8_t bnegative = negative(b);
|
||
uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
|
||
|
||
ge_precomp_0(t);
|
||
cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
|
||
cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
|
||
cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
|
||
cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
|
||
cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
|
||
cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
|
||
cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
|
||
cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
|
||
fe_copy(minust.yplusx, t->yminusx);
|
||
fe_copy(minust.yminusx, t->yplusx);
|
||
fe_neg(minust.xy2d, t->xy2d);
|
||
cmov(t, &minust, bnegative);
|
||
}
|
||
|
||
/* h = a * B
|
||
* where a = a[0]+256*a[1]+...+256^31 a[31]
|
||
* B is the Ed25519 base point (x,4/5) with x positive.
|
||
*
|
||
* Preconditions:
|
||
* a[31] <= 127 */
|
||
void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t *a) {
|
||
signed char e[64];
|
||
signed char carry;
|
||
ge_p1p1 r;
|
||
ge_p2 s;
|
||
ge_precomp t;
|
||
int i;
|
||
|
||
for (i = 0; i < 32; ++i) {
|
||
e[2 * i + 0] = (a[i] >> 0) & 15;
|
||
e[2 * i + 1] = (a[i] >> 4) & 15;
|
||
}
|
||
/* each e[i] is between 0 and 15 */
|
||
/* e[63] is between 0 and 7 */
|
||
|
||
carry = 0;
|
||
for (i = 0; i < 63; ++i) {
|
||
e[i] += carry;
|
||
carry = e[i] + 8;
|
||
carry >>= 4;
|
||
e[i] -= carry << 4;
|
||
}
|
||
e[63] += carry;
|
||
/* each e[i] is between -8 and 8 */
|
||
|
||
ge_p3_0(h);
|
||
for (i = 1; i < 64; i += 2) {
|
||
table_select(&t, i / 2, e[i]);
|
||
ge_madd(&r, h, &t);
|
||
x25519_ge_p1p1_to_p3(h, &r);
|
||
}
|
||
|
||
ge_p3_dbl(&r, h);
|
||
x25519_ge_p1p1_to_p2(&s, &r);
|
||
ge_p2_dbl(&r, &s);
|
||
x25519_ge_p1p1_to_p2(&s, &r);
|
||
ge_p2_dbl(&r, &s);
|
||
x25519_ge_p1p1_to_p2(&s, &r);
|
||
ge_p2_dbl(&r, &s);
|
||
x25519_ge_p1p1_to_p3(h, &r);
|
||
|
||
for (i = 0; i < 64; i += 2) {
|
||
table_select(&t, i / 2, e[i]);
|
||
ge_madd(&r, h, &t);
|
||
x25519_ge_p1p1_to_p3(h, &r);
|
||
}
|
||
}
|
||
|
||
#endif
|
||
|
||
static void cmov_cached(ge_cached *t, ge_cached *u, uint8_t b) {
|
||
fe_cmov(t->YplusX, u->YplusX, b);
|
||
fe_cmov(t->YminusX, u->YminusX, b);
|
||
fe_cmov(t->Z, u->Z, b);
|
||
fe_cmov(t->T2d, u->T2d, b);
|
||
}
|
||
|
||
/* r = scalar * A.
|
||
* where a = a[0]+256*a[1]+...+256^31 a[31]. */
|
||
void x25519_ge_scalarmult(ge_p2 *r, const uint8_t *scalar, const ge_p3 *A) {
|
||
ge_p2 Ai_p2[8];
|
||
ge_cached Ai[16];
|
||
ge_p1p1 t;
|
||
|
||
ge_cached_0(&Ai[0]);
|
||
x25519_ge_p3_to_cached(&Ai[1], A);
|
||
ge_p3_to_p2(&Ai_p2[1], A);
|
||
|
||
unsigned i;
|
||
for (i = 2; i < 16; i += 2) {
|
||
ge_p2_dbl(&t, &Ai_p2[i / 2]);
|
||
ge_p1p1_to_cached(&Ai[i], &t);
|
||
if (i < 8) {
|
||
x25519_ge_p1p1_to_p2(&Ai_p2[i], &t);
|
||
}
|
||
x25519_ge_add(&t, A, &Ai[i]);
|
||
ge_p1p1_to_cached(&Ai[i + 1], &t);
|
||
if (i < 7) {
|
||
x25519_ge_p1p1_to_p2(&Ai_p2[i + 1], &t);
|
||
}
|
||
}
|
||
|
||
ge_p2_0(r);
|
||
ge_p3 u;
|
||
|
||
for (i = 0; i < 256; i += 4) {
|
||
ge_p2_dbl(&t, r);
|
||
x25519_ge_p1p1_to_p2(r, &t);
|
||
ge_p2_dbl(&t, r);
|
||
x25519_ge_p1p1_to_p2(r, &t);
|
||
ge_p2_dbl(&t, r);
|
||
x25519_ge_p1p1_to_p2(r, &t);
|
||
ge_p2_dbl(&t, r);
|
||
x25519_ge_p1p1_to_p3(&u, &t);
|
||
|
||
uint8_t index = scalar[31 - i/8];
|
||
index >>= 4 - (i & 4);
|
||
index &= 0xf;
|
||
|
||
unsigned j;
|
||
ge_cached selected;
|
||
ge_cached_0(&selected);
|
||
for (j = 0; j < 16; j++) {
|
||
cmov_cached(&selected, &Ai[j], equal(j, index));
|
||
}
|
||
|
||
x25519_ge_add(&t, &u, &selected);
|
||
x25519_ge_p1p1_to_p2(r, &t);
|
||
}
|
||
}
|
||
|
||
static void slide(signed char *r, const uint8_t *a) {
|
||
int i;
|
||
int b;
|
||
int k;
|
||
|
||
for (i = 0; i < 256; ++i) {
|
||
r[i] = 1 & (a[i >> 3] >> (i & 7));
|
||
}
|
||
|
||
for (i = 0; i < 256; ++i) {
|
||
if (r[i]) {
|
||
for (b = 1; b <= 6 && i + b < 256; ++b) {
|
||
if (r[i + b]) {
|
||
if (r[i] + (r[i + b] << b) <= 15) {
|
||
r[i] += r[i + b] << b;
|
||
r[i + b] = 0;
|
||
} else if (r[i] - (r[i + b] << b) >= -15) {
|
||
r[i] -= r[i + b] << b;
|
||
for (k = i + b; k < 256; ++k) {
|
||
if (!r[k]) {
|
||
r[k] = 1;
|
||
break;
|
||
}
|
||
r[k] = 0;
|
||
}
|
||
} else {
|
||
break;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
static const ge_precomp Bi[8] = {
|
||
{
|
||
{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
|
||
-11754271, -6079156, 2047605},
|
||
{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
|
||
5043384, 19500929, -15469378},
|
||
{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
|
||
11864899, -24514362, -4438546},
|
||
},
|
||
{
|
||
{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
|
||
-14772189, 28944400, -1550024},
|
||
{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
|
||
-11775962, 7689662, 11199574},
|
||
{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
|
||
10017326, -17749093, -9920357},
|
||
},
|
||
{
|
||
{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
|
||
14515107, -15438304, 10819380},
|
||
{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
|
||
12483688, -12668491, 5581306},
|
||
{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
|
||
13850243, -23678021, -15815942},
|
||
},
|
||
{
|
||
{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
|
||
5230134, -23952439, -15175766},
|
||
{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
|
||
16520125, 30598449, 7715701},
|
||
{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
|
||
1370708, 29794553, -1409300},
|
||
},
|
||
{
|
||
{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
|
||
-1361450, -13062696, 13821877},
|
||
{-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
|
||
-7212327, 18853322, -14220951},
|
||
{4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
|
||
-10431137, 2207753, -3209784},
|
||
},
|
||
{
|
||
{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
|
||
-663000, -31111463, -16132436},
|
||
{25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
|
||
15725684, 171356, 6466918},
|
||
{23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
|
||
-14088058, -30714912, 16193877},
|
||
},
|
||
{
|
||
{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
|
||
4729455, -18074513, 9256800},
|
||
{-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
|
||
9761698, -19827198, 630305},
|
||
{-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
|
||
-15960994, -2449256, -14291300},
|
||
},
|
||
{
|
||
{-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
|
||
15033784, 25105118, -7894876},
|
||
{-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
|
||
1573892, -2625887, 2198790, -15804619},
|
||
{-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
|
||
-16236442, -32461234, -12290683},
|
||
},
|
||
};
|
||
|
||
/* r = a * A + b * B
|
||
* where a = a[0]+256*a[1]+...+256^31 a[31].
|
||
* and b = b[0]+256*b[1]+...+256^31 b[31].
|
||
* B is the Ed25519 base point (x,4/5) with x positive. */
|
||
static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
|
||
const ge_p3 *A, const uint8_t *b) {
|
||
signed char aslide[256];
|
||
signed char bslide[256];
|
||
ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
|
||
ge_p1p1 t;
|
||
ge_p3 u;
|
||
ge_p3 A2;
|
||
int i;
|
||
|
||
slide(aslide, a);
|
||
slide(bslide, b);
|
||
|
||
x25519_ge_p3_to_cached(&Ai[0], A);
|
||
ge_p3_dbl(&t, A);
|
||
x25519_ge_p1p1_to_p3(&A2, &t);
|
||
x25519_ge_add(&t, &A2, &Ai[0]);
|
||
x25519_ge_p1p1_to_p3(&u, &t);
|
||
x25519_ge_p3_to_cached(&Ai[1], &u);
|
||
x25519_ge_add(&t, &A2, &Ai[1]);
|
||
x25519_ge_p1p1_to_p3(&u, &t);
|
||
x25519_ge_p3_to_cached(&Ai[2], &u);
|
||
x25519_ge_add(&t, &A2, &Ai[2]);
|
||
x25519_ge_p1p1_to_p3(&u, &t);
|
||
x25519_ge_p3_to_cached(&Ai[3], &u);
|
||
x25519_ge_add(&t, &A2, &Ai[3]);
|
||
x25519_ge_p1p1_to_p3(&u, &t);
|
||
x25519_ge_p3_to_cached(&Ai[4], &u);
|
||
x25519_ge_add(&t, &A2, &Ai[4]);
|
||
x25519_ge_p1p1_to_p3(&u, &t);
|
||
x25519_ge_p3_to_cached(&Ai[5], &u);
|
||
x25519_ge_add(&t, &A2, &Ai[5]);
|
||
x25519_ge_p1p1_to_p3(&u, &t);
|
||
x25519_ge_p3_to_cached(&Ai[6], &u);
|
||
x25519_ge_add(&t, &A2, &Ai[6]);
|
||
x25519_ge_p1p1_to_p3(&u, &t);
|
||
x25519_ge_p3_to_cached(&Ai[7], &u);
|
||
|
||
ge_p2_0(r);
|
||
|
||
for (i = 255; i >= 0; --i) {
|
||
if (aslide[i] || bslide[i]) {
|
||
break;
|
||
}
|
||
}
|
||
|
||
for (; i >= 0; --i) {
|
||
ge_p2_dbl(&t, r);
|
||
|
||
if (aslide[i] > 0) {
|
||
x25519_ge_p1p1_to_p3(&u, &t);
|
||
x25519_ge_add(&t, &u, &Ai[aslide[i] / 2]);
|
||
} else if (aslide[i] < 0) {
|
||
x25519_ge_p1p1_to_p3(&u, &t);
|
||
x25519_ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
|
||
}
|
||
|
||
if (bslide[i] > 0) {
|
||
x25519_ge_p1p1_to_p3(&u, &t);
|
||
ge_madd(&t, &u, &Bi[bslide[i] / 2]);
|
||
} else if (bslide[i] < 0) {
|
||
x25519_ge_p1p1_to_p3(&u, &t);
|
||
ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
|
||
}
|
||
|
||
x25519_ge_p1p1_to_p2(r, &t);
|
||
}
|
||
}
|
||
|
||
/* The set of scalars is \Z/l
|
||
* where l = 2^252 + 27742317777372353535851937790883648493. */
|
||
|
||
/* Input:
|
||
* s[0]+256*s[1]+...+256^63*s[63] = s
|
||
*
|
||
* Output:
|
||
* s[0]+256*s[1]+...+256^31*s[31] = s mod l
|
||
* where l = 2^252 + 27742317777372353535851937790883648493.
|
||
* Overwrites s in place. */
|
||
void x25519_sc_reduce(uint8_t *s) {
|
||
int64_t s0 = 2097151 & load_3(s);
|
||
int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
|
||
int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
|
||
int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
|
||
int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
|
||
int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
|
||
int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
|
||
int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
|
||
int64_t s8 = 2097151 & load_3(s + 21);
|
||
int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
|
||
int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
|
||
int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
|
||
int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
|
||
int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
|
||
int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
|
||
int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
|
||
int64_t s16 = 2097151 & load_3(s + 42);
|
||
int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
|
||
int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
|
||
int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
|
||
int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
|
||
int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
|
||
int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
|
||
int64_t s23 = (load_4(s + 60) >> 3);
|
||
int64_t carry0;
|
||
int64_t carry1;
|
||
int64_t carry2;
|
||
int64_t carry3;
|
||
int64_t carry4;
|
||
int64_t carry5;
|
||
int64_t carry6;
|
||
int64_t carry7;
|
||
int64_t carry8;
|
||
int64_t carry9;
|
||
int64_t carry10;
|
||
int64_t carry11;
|
||
int64_t carry12;
|
||
int64_t carry13;
|
||
int64_t carry14;
|
||
int64_t carry15;
|
||
int64_t carry16;
|
||
|
||
s11 += s23 * 666643;
|
||
s12 += s23 * 470296;
|
||
s13 += s23 * 654183;
|
||
s14 -= s23 * 997805;
|
||
s15 += s23 * 136657;
|
||
s16 -= s23 * 683901;
|
||
s23 = 0;
|
||
|
||
s10 += s22 * 666643;
|
||
s11 += s22 * 470296;
|
||
s12 += s22 * 654183;
|
||
s13 -= s22 * 997805;
|
||
s14 += s22 * 136657;
|
||
s15 -= s22 * 683901;
|
||
s22 = 0;
|
||
|
||
s9 += s21 * 666643;
|
||
s10 += s21 * 470296;
|
||
s11 += s21 * 654183;
|
||
s12 -= s21 * 997805;
|
||
s13 += s21 * 136657;
|
||
s14 -= s21 * 683901;
|
||
s21 = 0;
|
||
|
||
s8 += s20 * 666643;
|
||
s9 += s20 * 470296;
|
||
s10 += s20 * 654183;
|
||
s11 -= s20 * 997805;
|
||
s12 += s20 * 136657;
|
||
s13 -= s20 * 683901;
|
||
s20 = 0;
|
||
|
||
s7 += s19 * 666643;
|
||
s8 += s19 * 470296;
|
||
s9 += s19 * 654183;
|
||
s10 -= s19 * 997805;
|
||
s11 += s19 * 136657;
|
||
s12 -= s19 * 683901;
|
||
s19 = 0;
|
||
|
||
s6 += s18 * 666643;
|
||
s7 += s18 * 470296;
|
||
s8 += s18 * 654183;
|
||
s9 -= s18 * 997805;
|
||
s10 += s18 * 136657;
|
||
s11 -= s18 * 683901;
|
||
s18 = 0;
|
||
|
||
carry6 = (s6 + (1 << 20)) >> 21;
|
||
s7 += carry6;
|
||
s6 -= carry6 << 21;
|
||
carry8 = (s8 + (1 << 20)) >> 21;
|
||
s9 += carry8;
|
||
s8 -= carry8 << 21;
|
||
carry10 = (s10 + (1 << 20)) >> 21;
|
||
s11 += carry10;
|
||
s10 -= carry10 << 21;
|
||
carry12 = (s12 + (1 << 20)) >> 21;
|
||
s13 += carry12;
|
||
s12 -= carry12 << 21;
|
||
carry14 = (s14 + (1 << 20)) >> 21;
|
||
s15 += carry14;
|
||
s14 -= carry14 << 21;
|
||
carry16 = (s16 + (1 << 20)) >> 21;
|
||
s17 += carry16;
|
||
s16 -= carry16 << 21;
|
||
|
||
carry7 = (s7 + (1 << 20)) >> 21;
|
||
s8 += carry7;
|
||
s7 -= carry7 << 21;
|
||
carry9 = (s9 + (1 << 20)) >> 21;
|
||
s10 += carry9;
|
||
s9 -= carry9 << 21;
|
||
carry11 = (s11 + (1 << 20)) >> 21;
|
||
s12 += carry11;
|
||
s11 -= carry11 << 21;
|
||
carry13 = (s13 + (1 << 20)) >> 21;
|
||
s14 += carry13;
|
||
s13 -= carry13 << 21;
|
||
carry15 = (s15 + (1 << 20)) >> 21;
|
||
s16 += carry15;
|
||
s15 -= carry15 << 21;
|
||
|
||
s5 += s17 * 666643;
|
||
s6 += s17 * 470296;
|
||
s7 += s17 * 654183;
|
||
s8 -= s17 * 997805;
|
||
s9 += s17 * 136657;
|
||
s10 -= s17 * 683901;
|
||
s17 = 0;
|
||
|
||
s4 += s16 * 666643;
|
||
s5 += s16 * 470296;
|
||
s6 += s16 * 654183;
|
||
s7 -= s16 * 997805;
|
||
s8 += s16 * 136657;
|
||
s9 -= s16 * 683901;
|
||
s16 = 0;
|
||
|
||
s3 += s15 * 666643;
|
||
s4 += s15 * 470296;
|
||
s5 += s15 * 654183;
|
||
s6 -= s15 * 997805;
|
||
s7 += s15 * 136657;
|
||
s8 -= s15 * 683901;
|
||
s15 = 0;
|
||
|
||
s2 += s14 * 666643;
|
||
s3 += s14 * 470296;
|
||
s4 += s14 * 654183;
|
||
s5 -= s14 * 997805;
|
||
s6 += s14 * 136657;
|
||
s7 -= s14 * 683901;
|
||
s14 = 0;
|
||
|
||
s1 += s13 * 666643;
|
||
s2 += s13 * 470296;
|
||
s3 += s13 * 654183;
|
||
s4 -= s13 * 997805;
|
||
s5 += s13 * 136657;
|
||
s6 -= s13 * 683901;
|
||
s13 = 0;
|
||
|
||
s0 += s12 * 666643;
|
||
s1 += s12 * 470296;
|
||
s2 += s12 * 654183;
|
||
s3 -= s12 * 997805;
|
||
s4 += s12 * 136657;
|
||
s5 -= s12 * 683901;
|
||
s12 = 0;
|
||
|
||
carry0 = (s0 + (1 << 20)) >> 21;
|
||
s1 += carry0;
|
||
s0 -= carry0 << 21;
|
||
carry2 = (s2 + (1 << 20)) >> 21;
|
||
s3 += carry2;
|
||
s2 -= carry2 << 21;
|
||
carry4 = (s4 + (1 << 20)) >> 21;
|
||
s5 += carry4;
|
||
s4 -= carry4 << 21;
|
||
carry6 = (s6 + (1 << 20)) >> 21;
|
||
s7 += carry6;
|
||
s6 -= carry6 << 21;
|
||
carry8 = (s8 + (1 << 20)) >> 21;
|
||
s9 += carry8;
|
||
s8 -= carry8 << 21;
|
||
carry10 = (s10 + (1 << 20)) >> 21;
|
||
s11 += carry10;
|
||
s10 -= carry10 << 21;
|
||
|
||
carry1 = (s1 + (1 << 20)) >> 21;
|
||
s2 += carry1;
|
||
s1 -= carry1 << 21;
|
||
carry3 = (s3 + (1 << 20)) >> 21;
|
||
s4 += carry3;
|
||
s3 -= carry3 << 21;
|
||
carry5 = (s5 + (1 << 20)) >> 21;
|
||
s6 += carry5;
|
||
s5 -= carry5 << 21;
|
||
carry7 = (s7 + (1 << 20)) >> 21;
|
||
s8 += carry7;
|
||
s7 -= carry7 << 21;
|
||
carry9 = (s9 + (1 << 20)) >> 21;
|
||
s10 += carry9;
|
||
s9 -= carry9 << 21;
|
||
carry11 = (s11 + (1 << 20)) >> 21;
|
||
s12 += carry11;
|
||
s11 -= carry11 << 21;
|
||
|
||
s0 += s12 * 666643;
|
||
s1 += s12 * 470296;
|
||
s2 += s12 * 654183;
|
||
s3 -= s12 * 997805;
|
||
s4 += s12 * 136657;
|
||
s5 -= s12 * 683901;
|
||
s12 = 0;
|
||
|
||
carry0 = s0 >> 21;
|
||
s1 += carry0;
|
||
s0 -= carry0 << 21;
|
||
carry1 = s1 >> 21;
|
||
s2 += carry1;
|
||
s1 -= carry1 << 21;
|
||
carry2 = s2 >> 21;
|
||
s3 += carry2;
|
||
s2 -= carry2 << 21;
|
||
carry3 = s3 >> 21;
|
||
s4 += carry3;
|
||
s3 -= carry3 << 21;
|
||
carry4 = s4 >> 21;
|
||
s5 += carry4;
|
||
s4 -= carry4 << 21;
|
||
carry5 = s5 >> 21;
|
||
s6 += carry5;
|
||
s5 -= carry5 << 21;
|
||
carry6 = s6 >> 21;
|
||
s7 += carry6;
|
||
s6 -= carry6 << 21;
|
||
carry7 = s7 >> 21;
|
||
s8 += carry7;
|
||
s7 -= carry7 << 21;
|
||
carry8 = s8 >> 21;
|
||
s9 += carry8;
|
||
s8 -= carry8 << 21;
|
||
carry9 = s9 >> 21;
|
||
s10 += carry9;
|
||
s9 -= carry9 << 21;
|
||
carry10 = s10 >> 21;
|
||
s11 += carry10;
|
||
s10 -= carry10 << 21;
|
||
carry11 = s11 >> 21;
|
||
s12 += carry11;
|
||
s11 -= carry11 << 21;
|
||
|
||
s0 += s12 * 666643;
|
||
s1 += s12 * 470296;
|
||
s2 += s12 * 654183;
|
||
s3 -= s12 * 997805;
|
||
s4 += s12 * 136657;
|
||
s5 -= s12 * 683901;
|
||
s12 = 0;
|
||
|
||
carry0 = s0 >> 21;
|
||
s1 += carry0;
|
||
s0 -= carry0 << 21;
|
||
carry1 = s1 >> 21;
|
||
s2 += carry1;
|
||
s1 -= carry1 << 21;
|
||
carry2 = s2 >> 21;
|
||
s3 += carry2;
|
||
s2 -= carry2 << 21;
|
||
carry3 = s3 >> 21;
|
||
s4 += carry3;
|
||
s3 -= carry3 << 21;
|
||
carry4 = s4 >> 21;
|
||
s5 += carry4;
|
||
s4 -= carry4 << 21;
|
||
carry5 = s5 >> 21;
|
||
s6 += carry5;
|
||
s5 -= carry5 << 21;
|
||
carry6 = s6 >> 21;
|
||
s7 += carry6;
|
||
s6 -= carry6 << 21;
|
||
carry7 = s7 >> 21;
|
||
s8 += carry7;
|
||
s7 -= carry7 << 21;
|
||
carry8 = s8 >> 21;
|
||
s9 += carry8;
|
||
s8 -= carry8 << 21;
|
||
carry9 = s9 >> 21;
|
||
s10 += carry9;
|
||
s9 -= carry9 << 21;
|
||
carry10 = s10 >> 21;
|
||
s11 += carry10;
|
||
s10 -= carry10 << 21;
|
||
|
||
s[0] = s0 >> 0;
|
||
s[1] = s0 >> 8;
|
||
s[2] = (s0 >> 16) | (s1 << 5);
|
||
s[3] = s1 >> 3;
|
||
s[4] = s1 >> 11;
|
||
s[5] = (s1 >> 19) | (s2 << 2);
|
||
s[6] = s2 >> 6;
|
||
s[7] = (s2 >> 14) | (s3 << 7);
|
||
s[8] = s3 >> 1;
|
||
s[9] = s3 >> 9;
|
||
s[10] = (s3 >> 17) | (s4 << 4);
|
||
s[11] = s4 >> 4;
|
||
s[12] = s4 >> 12;
|
||
s[13] = (s4 >> 20) | (s5 << 1);
|
||
s[14] = s5 >> 7;
|
||
s[15] = (s5 >> 15) | (s6 << 6);
|
||
s[16] = s6 >> 2;
|
||
s[17] = s6 >> 10;
|
||
s[18] = (s6 >> 18) | (s7 << 3);
|
||
s[19] = s7 >> 5;
|
||
s[20] = s7 >> 13;
|
||
s[21] = s8 >> 0;
|
||
s[22] = s8 >> 8;
|
||
s[23] = (s8 >> 16) | (s9 << 5);
|
||
s[24] = s9 >> 3;
|
||
s[25] = s9 >> 11;
|
||
s[26] = (s9 >> 19) | (s10 << 2);
|
||
s[27] = s10 >> 6;
|
||
s[28] = (s10 >> 14) | (s11 << 7);
|
||
s[29] = s11 >> 1;
|
||
s[30] = s11 >> 9;
|
||
s[31] = s11 >> 17;
|
||
}
|
||
|
||
/* Input:
|
||
* a[0]+256*a[1]+...+256^31*a[31] = a
|
||
* b[0]+256*b[1]+...+256^31*b[31] = b
|
||
* c[0]+256*c[1]+...+256^31*c[31] = c
|
||
*
|
||
* Output:
|
||
* s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
|
||
* where l = 2^252 + 27742317777372353535851937790883648493. */
|
||
static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
|
||
const uint8_t *c) {
|
||
int64_t a0 = 2097151 & load_3(a);
|
||
int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
|
||
int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
|
||
int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
|
||
int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
|
||
int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
|
||
int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
|
||
int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
|
||
int64_t a8 = 2097151 & load_3(a + 21);
|
||
int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
|
||
int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
|
||
int64_t a11 = (load_4(a + 28) >> 7);
|
||
int64_t b0 = 2097151 & load_3(b);
|
||
int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
|
||
int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
|
||
int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
|
||
int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
|
||
int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
|
||
int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
|
||
int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
|
||
int64_t b8 = 2097151 & load_3(b + 21);
|
||
int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
|
||
int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
|
||
int64_t b11 = (load_4(b + 28) >> 7);
|
||
int64_t c0 = 2097151 & load_3(c);
|
||
int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
|
||
int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
|
||
int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
|
||
int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
|
||
int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
|
||
int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
|
||
int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
|
||
int64_t c8 = 2097151 & load_3(c + 21);
|
||
int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
|
||
int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
|
||
int64_t c11 = (load_4(c + 28) >> 7);
|
||
int64_t s0;
|
||
int64_t s1;
|
||
int64_t s2;
|
||
int64_t s3;
|
||
int64_t s4;
|
||
int64_t s5;
|
||
int64_t s6;
|
||
int64_t s7;
|
||
int64_t s8;
|
||
int64_t s9;
|
||
int64_t s10;
|
||
int64_t s11;
|
||
int64_t s12;
|
||
int64_t s13;
|
||
int64_t s14;
|
||
int64_t s15;
|
||
int64_t s16;
|
||
int64_t s17;
|
||
int64_t s18;
|
||
int64_t s19;
|
||
int64_t s20;
|
||
int64_t s21;
|
||
int64_t s22;
|
||
int64_t s23;
|
||
int64_t carry0;
|
||
int64_t carry1;
|
||
int64_t carry2;
|
||
int64_t carry3;
|
||
int64_t carry4;
|
||
int64_t carry5;
|
||
int64_t carry6;
|
||
int64_t carry7;
|
||
int64_t carry8;
|
||
int64_t carry9;
|
||
int64_t carry10;
|
||
int64_t carry11;
|
||
int64_t carry12;
|
||
int64_t carry13;
|
||
int64_t carry14;
|
||
int64_t carry15;
|
||
int64_t carry16;
|
||
int64_t carry17;
|
||
int64_t carry18;
|
||
int64_t carry19;
|
||
int64_t carry20;
|
||
int64_t carry21;
|
||
int64_t carry22;
|
||
|
||
s0 = c0 + a0 * b0;
|
||
s1 = c1 + a0 * b1 + a1 * b0;
|
||
s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
|
||
s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
|
||
s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
|
||
s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
|
||
s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
|
||
s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
|
||
a6 * b1 + a7 * b0;
|
||
s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
|
||
a6 * b2 + a7 * b1 + a8 * b0;
|
||
s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
|
||
a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
|
||
s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
|
||
a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
|
||
s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
|
||
a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
|
||
s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 +
|
||
a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
|
||
s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 +
|
||
a9 * b4 + a10 * b3 + a11 * b2;
|
||
s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 +
|
||
a10 * b4 + a11 * b3;
|
||
s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 +
|
||
a11 * b4;
|
||
s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
|
||
s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
|
||
s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
|
||
s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
|
||
s20 = a9 * b11 + a10 * b10 + a11 * b9;
|
||
s21 = a10 * b11 + a11 * b10;
|
||
s22 = a11 * b11;
|
||
s23 = 0;
|
||
|
||
carry0 = (s0 + (1 << 20)) >> 21;
|
||
s1 += carry0;
|
||
s0 -= carry0 << 21;
|
||
carry2 = (s2 + (1 << 20)) >> 21;
|
||
s3 += carry2;
|
||
s2 -= carry2 << 21;
|
||
carry4 = (s4 + (1 << 20)) >> 21;
|
||
s5 += carry4;
|
||
s4 -= carry4 << 21;
|
||
carry6 = (s6 + (1 << 20)) >> 21;
|
||
s7 += carry6;
|
||
s6 -= carry6 << 21;
|
||
carry8 = (s8 + (1 << 20)) >> 21;
|
||
s9 += carry8;
|
||
s8 -= carry8 << 21;
|
||
carry10 = (s10 + (1 << 20)) >> 21;
|
||
s11 += carry10;
|
||
s10 -= carry10 << 21;
|
||
carry12 = (s12 + (1 << 20)) >> 21;
|
||
s13 += carry12;
|
||
s12 -= carry12 << 21;
|
||
carry14 = (s14 + (1 << 20)) >> 21;
|
||
s15 += carry14;
|
||
s14 -= carry14 << 21;
|
||
carry16 = (s16 + (1 << 20)) >> 21;
|
||
s17 += carry16;
|
||
s16 -= carry16 << 21;
|
||
carry18 = (s18 + (1 << 20)) >> 21;
|
||
s19 += carry18;
|
||
s18 -= carry18 << 21;
|
||
carry20 = (s20 + (1 << 20)) >> 21;
|
||
s21 += carry20;
|
||
s20 -= carry20 << 21;
|
||
carry22 = (s22 + (1 << 20)) >> 21;
|
||
s23 += carry22;
|
||
s22 -= carry22 << 21;
|
||
|
||
carry1 = (s1 + (1 << 20)) >> 21;
|
||
s2 += carry1;
|
||
s1 -= carry1 << 21;
|
||
carry3 = (s3 + (1 << 20)) >> 21;
|
||
s4 += carry3;
|
||
s3 -= carry3 << 21;
|
||
carry5 = (s5 + (1 << 20)) >> 21;
|
||
s6 += carry5;
|
||
s5 -= carry5 << 21;
|
||
carry7 = (s7 + (1 << 20)) >> 21;
|
||
s8 += carry7;
|
||
s7 -= carry7 << 21;
|
||
carry9 = (s9 + (1 << 20)) >> 21;
|
||
s10 += carry9;
|
||
s9 -= carry9 << 21;
|
||
carry11 = (s11 + (1 << 20)) >> 21;
|
||
s12 += carry11;
|
||
s11 -= carry11 << 21;
|
||
carry13 = (s13 + (1 << 20)) >> 21;
|
||
s14 += carry13;
|
||
s13 -= carry13 << 21;
|
||
carry15 = (s15 + (1 << 20)) >> 21;
|
||
s16 += carry15;
|
||
s15 -= carry15 << 21;
|
||
carry17 = (s17 + (1 << 20)) >> 21;
|
||
s18 += carry17;
|
||
s17 -= carry17 << 21;
|
||
carry19 = (s19 + (1 << 20)) >> 21;
|
||
s20 += carry19;
|
||
s19 -= carry19 << 21;
|
||
carry21 = (s21 + (1 << 20)) >> 21;
|
||
s22 += carry21;
|
||
s21 -= carry21 << 21;
|
||
|
||
s11 += s23 * 666643;
|
||
s12 += s23 * 470296;
|
||
s13 += s23 * 654183;
|
||
s14 -= s23 * 997805;
|
||
s15 += s23 * 136657;
|
||
s16 -= s23 * 683901;
|
||
s23 = 0;
|
||
|
||
s10 += s22 * 666643;
|
||
s11 += s22 * 470296;
|
||
s12 += s22 * 654183;
|
||
s13 -= s22 * 997805;
|
||
s14 += s22 * 136657;
|
||
s15 -= s22 * 683901;
|
||
s22 = 0;
|
||
|
||
s9 += s21 * 666643;
|
||
s10 += s21 * 470296;
|
||
s11 += s21 * 654183;
|
||
s12 -= s21 * 997805;
|
||
s13 += s21 * 136657;
|
||
s14 -= s21 * 683901;
|
||
s21 = 0;
|
||
|
||
s8 += s20 * 666643;
|
||
s9 += s20 * 470296;
|
||
s10 += s20 * 654183;
|
||
s11 -= s20 * 997805;
|
||
s12 += s20 * 136657;
|
||
s13 -= s20 * 683901;
|
||
s20 = 0;
|
||
|
||
s7 += s19 * 666643;
|
||
s8 += s19 * 470296;
|
||
s9 += s19 * 654183;
|
||
s10 -= s19 * 997805;
|
||
s11 += s19 * 136657;
|
||
s12 -= s19 * 683901;
|
||
s19 = 0;
|
||
|
||
s6 += s18 * 666643;
|
||
s7 += s18 * 470296;
|
||
s8 += s18 * 654183;
|
||
s9 -= s18 * 997805;
|
||
s10 += s18 * 136657;
|
||
s11 -= s18 * 683901;
|
||
s18 = 0;
|
||
|
||
carry6 = (s6 + (1 << 20)) >> 21;
|
||
s7 += carry6;
|
||
s6 -= carry6 << 21;
|
||
carry8 = (s8 + (1 << 20)) >> 21;
|
||
s9 += carry8;
|
||
s8 -= carry8 << 21;
|
||
carry10 = (s10 + (1 << 20)) >> 21;
|
||
s11 += carry10;
|
||
s10 -= carry10 << 21;
|
||
carry12 = (s12 + (1 << 20)) >> 21;
|
||
s13 += carry12;
|
||
s12 -= carry12 << 21;
|
||
carry14 = (s14 + (1 << 20)) >> 21;
|
||
s15 += carry14;
|
||
s14 -= carry14 << 21;
|
||
carry16 = (s16 + (1 << 20)) >> 21;
|
||
s17 += carry16;
|
||
s16 -= carry16 << 21;
|
||
|
||
carry7 = (s7 + (1 << 20)) >> 21;
|
||
s8 += carry7;
|
||
s7 -= carry7 << 21;
|
||
carry9 = (s9 + (1 << 20)) >> 21;
|
||
s10 += carry9;
|
||
s9 -= carry9 << 21;
|
||
carry11 = (s11 + (1 << 20)) >> 21;
|
||
s12 += carry11;
|
||
s11 -= carry11 << 21;
|
||
carry13 = (s13 + (1 << 20)) >> 21;
|
||
s14 += carry13;
|
||
s13 -= carry13 << 21;
|
||
carry15 = (s15 + (1 << 20)) >> 21;
|
||
s16 += carry15;
|
||
s15 -= carry15 << 21;
|
||
|
||
s5 += s17 * 666643;
|
||
s6 += s17 * 470296;
|
||
s7 += s17 * 654183;
|
||
s8 -= s17 * 997805;
|
||
s9 += s17 * 136657;
|
||
s10 -= s17 * 683901;
|
||
s17 = 0;
|
||
|
||
s4 += s16 * 666643;
|
||
s5 += s16 * 470296;
|
||
s6 += s16 * 654183;
|
||
s7 -= s16 * 997805;
|
||
s8 += s16 * 136657;
|
||
s9 -= s16 * 683901;
|
||
s16 = 0;
|
||
|
||
s3 += s15 * 666643;
|
||
s4 += s15 * 470296;
|
||
s5 += s15 * 654183;
|
||
s6 -= s15 * 997805;
|
||
s7 += s15 * 136657;
|
||
s8 -= s15 * 683901;
|
||
s15 = 0;
|
||
|
||
s2 += s14 * 666643;
|
||
s3 += s14 * 470296;
|
||
s4 += s14 * 654183;
|
||
s5 -= s14 * 997805;
|
||
s6 += s14 * 136657;
|
||
s7 -= s14 * 683901;
|
||
s14 = 0;
|
||
|
||
s1 += s13 * 666643;
|
||
s2 += s13 * 470296;
|
||
s3 += s13 * 654183;
|
||
s4 -= s13 * 997805;
|
||
s5 += s13 * 136657;
|
||
s6 -= s13 * 683901;
|
||
s13 = 0;
|
||
|
||
s0 += s12 * 666643;
|
||
s1 += s12 * 470296;
|
||
s2 += s12 * 654183;
|
||
s3 -= s12 * 997805;
|
||
s4 += s12 * 136657;
|
||
s5 -= s12 * 683901;
|
||
s12 = 0;
|
||
|
||
carry0 = (s0 + (1 << 20)) >> 21;
|
||
s1 += carry0;
|
||
s0 -= carry0 << 21;
|
||
carry2 = (s2 + (1 << 20)) >> 21;
|
||
s3 += carry2;
|
||
s2 -= carry2 << 21;
|
||
carry4 = (s4 + (1 << 20)) >> 21;
|
||
s5 += carry4;
|
||
s4 -= carry4 << 21;
|
||
carry6 = (s6 + (1 << 20)) >> 21;
|
||
s7 += carry6;
|
||
s6 -= carry6 << 21;
|
||
carry8 = (s8 + (1 << 20)) >> 21;
|
||
s9 += carry8;
|
||
s8 -= carry8 << 21;
|
||
carry10 = (s10 + (1 << 20)) >> 21;
|
||
s11 += carry10;
|
||
s10 -= carry10 << 21;
|
||
|
||
carry1 = (s1 + (1 << 20)) >> 21;
|
||
s2 += carry1;
|
||
s1 -= carry1 << 21;
|
||
carry3 = (s3 + (1 << 20)) >> 21;
|
||
s4 += carry3;
|
||
s3 -= carry3 << 21;
|
||
carry5 = (s5 + (1 << 20)) >> 21;
|
||
s6 += carry5;
|
||
s5 -= carry5 << 21;
|
||
carry7 = (s7 + (1 << 20)) >> 21;
|
||
s8 += carry7;
|
||
s7 -= carry7 << 21;
|
||
carry9 = (s9 + (1 << 20)) >> 21;
|
||
s10 += carry9;
|
||
s9 -= carry9 << 21;
|
||
carry11 = (s11 + (1 << 20)) >> 21;
|
||
s12 += carry11;
|
||
s11 -= carry11 << 21;
|
||
|
||
s0 += s12 * 666643;
|
||
s1 += s12 * 470296;
|
||
s2 += s12 * 654183;
|
||
s3 -= s12 * 997805;
|
||
s4 += s12 * 136657;
|
||
s5 -= s12 * 683901;
|
||
s12 = 0;
|
||
|
||
carry0 = s0 >> 21;
|
||
s1 += carry0;
|
||
s0 -= carry0 << 21;
|
||
carry1 = s1 >> 21;
|
||
s2 += carry1;
|
||
s1 -= carry1 << 21;
|
||
carry2 = s2 >> 21;
|
||
s3 += carry2;
|
||
s2 -= carry2 << 21;
|
||
carry3 = s3 >> 21;
|
||
s4 += carry3;
|
||
s3 -= carry3 << 21;
|
||
carry4 = s4 >> 21;
|
||
s5 += carry4;
|
||
s4 -= carry4 << 21;
|
||
carry5 = s5 >> 21;
|
||
s6 += carry5;
|
||
s5 -= carry5 << 21;
|
||
carry6 = s6 >> 21;
|
||
s7 += carry6;
|
||
s6 -= carry6 << 21;
|
||
carry7 = s7 >> 21;
|
||
s8 += carry7;
|
||
s7 -= carry7 << 21;
|
||
carry8 = s8 >> 21;
|
||
s9 += carry8;
|
||
s8 -= carry8 << 21;
|
||
carry9 = s9 >> 21;
|
||
s10 += carry9;
|
||
s9 -= carry9 << 21;
|
||
carry10 = s10 >> 21;
|
||
s11 += carry10;
|
||
s10 -= carry10 << 21;
|
||
carry11 = s11 >> 21;
|
||
s12 += carry11;
|
||
s11 -= carry11 << 21;
|
||
|
||
s0 += s12 * 666643;
|
||
s1 += s12 * 470296;
|
||
s2 += s12 * 654183;
|
||
s3 -= s12 * 997805;
|
||
s4 += s12 * 136657;
|
||
s5 -= s12 * 683901;
|
||
s12 = 0;
|
||
|
||
carry0 = s0 >> 21;
|
||
s1 += carry0;
|
||
s0 -= carry0 << 21;
|
||
carry1 = s1 >> 21;
|
||
s2 += carry1;
|
||
s1 -= carry1 << 21;
|
||
carry2 = s2 >> 21;
|
||
s3 += carry2;
|
||
s2 -= carry2 << 21;
|
||
carry3 = s3 >> 21;
|
||
s4 += carry3;
|
||
s3 -= carry3 << 21;
|
||
carry4 = s4 >> 21;
|
||
s5 += carry4;
|
||
s4 -= carry4 << 21;
|
||
carry5 = s5 >> 21;
|
||
s6 += carry5;
|
||
s5 -= carry5 << 21;
|
||
carry6 = s6 >> 21;
|
||
s7 += carry6;
|
||
s6 -= carry6 << 21;
|
||
carry7 = s7 >> 21;
|
||
s8 += carry7;
|
||
s7 -= carry7 << 21;
|
||
carry8 = s8 >> 21;
|
||
s9 += carry8;
|
||
s8 -= carry8 << 21;
|
||
carry9 = s9 >> 21;
|
||
s10 += carry9;
|
||
s9 -= carry9 << 21;
|
||
carry10 = s10 >> 21;
|
||
s11 += carry10;
|
||
s10 -= carry10 << 21;
|
||
|
||
s[0] = s0 >> 0;
|
||
s[1] = s0 >> 8;
|
||
s[2] = (s0 >> 16) | (s1 << 5);
|
||
s[3] = s1 >> 3;
|
||
s[4] = s1 >> 11;
|
||
s[5] = (s1 >> 19) | (s2 << 2);
|
||
s[6] = s2 >> 6;
|
||
s[7] = (s2 >> 14) | (s3 << 7);
|
||
s[8] = s3 >> 1;
|
||
s[9] = s3 >> 9;
|
||
s[10] = (s3 >> 17) | (s4 << 4);
|
||
s[11] = s4 >> 4;
|
||
s[12] = s4 >> 12;
|
||
s[13] = (s4 >> 20) | (s5 << 1);
|
||
s[14] = s5 >> 7;
|
||
s[15] = (s5 >> 15) | (s6 << 6);
|
||
s[16] = s6 >> 2;
|
||
s[17] = s6 >> 10;
|
||
s[18] = (s6 >> 18) | (s7 << 3);
|
||
s[19] = s7 >> 5;
|
||
s[20] = s7 >> 13;
|
||
s[21] = s8 >> 0;
|
||
s[22] = s8 >> 8;
|
||
s[23] = (s8 >> 16) | (s9 << 5);
|
||
s[24] = s9 >> 3;
|
||
s[25] = s9 >> 11;
|
||
s[26] = (s9 >> 19) | (s10 << 2);
|
||
s[27] = s10 >> 6;
|
||
s[28] = (s10 >> 14) | (s11 << 7);
|
||
s[29] = s11 >> 1;
|
||
s[30] = s11 >> 9;
|
||
s[31] = s11 >> 17;
|
||
}
|
||
|
||
void ED25519_keypair(uint8_t out_public_key[32], uint8_t out_private_key[64]) {
|
||
uint8_t seed[32];
|
||
RAND_bytes(seed, 32);
|
||
ED25519_keypair_from_seed(out_public_key, out_private_key, seed);
|
||
}
|
||
|
||
int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
|
||
const uint8_t private_key[64]) {
|
||
uint8_t az[SHA512_DIGEST_LENGTH];
|
||
SHA512(private_key, 32, az);
|
||
|
||
az[0] &= 248;
|
||
az[31] &= 63;
|
||
az[31] |= 64;
|
||
|
||
SHA512_CTX hash_ctx;
|
||
SHA512_Init(&hash_ctx);
|
||
SHA512_Update(&hash_ctx, az + 32, 32);
|
||
SHA512_Update(&hash_ctx, message, message_len);
|
||
uint8_t nonce[SHA512_DIGEST_LENGTH];
|
||
SHA512_Final(nonce, &hash_ctx);
|
||
|
||
x25519_sc_reduce(nonce);
|
||
ge_p3 R;
|
||
x25519_ge_scalarmult_base(&R, nonce);
|
||
ge_p3_tobytes(out_sig, &R);
|
||
|
||
SHA512_Init(&hash_ctx);
|
||
SHA512_Update(&hash_ctx, out_sig, 32);
|
||
SHA512_Update(&hash_ctx, private_key + 32, 32);
|
||
SHA512_Update(&hash_ctx, message, message_len);
|
||
uint8_t hram[SHA512_DIGEST_LENGTH];
|
||
SHA512_Final(hram, &hash_ctx);
|
||
|
||
x25519_sc_reduce(hram);
|
||
sc_muladd(out_sig + 32, hram, az, nonce);
|
||
|
||
return 1;
|
||
}
|
||
|
||
int ED25519_verify(const uint8_t *message, size_t message_len,
|
||
const uint8_t signature[64], const uint8_t public_key[32]) {
|
||
ge_p3 A;
|
||
if ((signature[63] & 224) != 0 ||
|
||
x25519_ge_frombytes_vartime(&A, public_key) != 0) {
|
||
return 0;
|
||
}
|
||
|
||
fe_neg(A.X, A.X);
|
||
fe_neg(A.T, A.T);
|
||
|
||
uint8_t pkcopy[32];
|
||
OPENSSL_memcpy(pkcopy, public_key, 32);
|
||
uint8_t rcopy[32];
|
||
OPENSSL_memcpy(rcopy, signature, 32);
|
||
uint8_t scopy[32];
|
||
OPENSSL_memcpy(scopy, signature + 32, 32);
|
||
|
||
SHA512_CTX hash_ctx;
|
||
SHA512_Init(&hash_ctx);
|
||
SHA512_Update(&hash_ctx, signature, 32);
|
||
SHA512_Update(&hash_ctx, public_key, 32);
|
||
SHA512_Update(&hash_ctx, message, message_len);
|
||
uint8_t h[SHA512_DIGEST_LENGTH];
|
||
SHA512_Final(h, &hash_ctx);
|
||
|
||
x25519_sc_reduce(h);
|
||
|
||
ge_p2 R;
|
||
ge_double_scalarmult_vartime(&R, h, &A, scopy);
|
||
|
||
uint8_t rcheck[32];
|
||
x25519_ge_tobytes(rcheck, &R);
|
||
|
||
return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;
|
||
}
|
||
|
||
void ED25519_keypair_from_seed(uint8_t out_public_key[32],
|
||
uint8_t out_private_key[64],
|
||
const uint8_t seed[32]) {
|
||
uint8_t az[SHA512_DIGEST_LENGTH];
|
||
SHA512(seed, 32, az);
|
||
|
||
az[0] &= 248;
|
||
az[31] &= 63;
|
||
az[31] |= 64;
|
||
|
||
ge_p3 A;
|
||
x25519_ge_scalarmult_base(&A, az);
|
||
ge_p3_tobytes(out_public_key, &A);
|
||
|
||
OPENSSL_memcpy(out_private_key, seed, 32);
|
||
OPENSSL_memcpy(out_private_key + 32, out_public_key, 32);
|
||
}
|
||
|
||
|
||
#if defined(BORINGSSL_X25519_X86_64)
|
||
|
||
static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
|
||
const uint8_t point[32]) {
|
||
x25519_x86_64(out, scalar, point);
|
||
}
|
||
|
||
#else
|
||
|
||
/* Replace (f,g) with (g,f) if b == 1;
|
||
* replace (f,g) with (f,g) if b == 0.
|
||
*
|
||
* Preconditions: b in {0,1}. */
|
||
static void fe_cswap(fe f, fe g, unsigned int b) {
|
||
b = 0-b;
|
||
unsigned i;
|
||
for (i = 0; i < 10; i++) {
|
||
int32_t x = f[i] ^ g[i];
|
||
x &= b;
|
||
f[i] ^= x;
|
||
g[i] ^= x;
|
||
}
|
||
}
|
||
|
||
/* h = f * 121666
|
||
* Can overlap h with f.
|
||
*
|
||
* Preconditions:
|
||
* |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
|
||
*
|
||
* Postconditions:
|
||
* |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
|
||
static void fe_mul121666(fe h, fe f) {
|
||
int32_t f0 = f[0];
|
||
int32_t f1 = f[1];
|
||
int32_t f2 = f[2];
|
||
int32_t f3 = f[3];
|
||
int32_t f4 = f[4];
|
||
int32_t f5 = f[5];
|
||
int32_t f6 = f[6];
|
||
int32_t f7 = f[7];
|
||
int32_t f8 = f[8];
|
||
int32_t f9 = f[9];
|
||
int64_t h0 = f0 * (int64_t) 121666;
|
||
int64_t h1 = f1 * (int64_t) 121666;
|
||
int64_t h2 = f2 * (int64_t) 121666;
|
||
int64_t h3 = f3 * (int64_t) 121666;
|
||
int64_t h4 = f4 * (int64_t) 121666;
|
||
int64_t h5 = f5 * (int64_t) 121666;
|
||
int64_t h6 = f6 * (int64_t) 121666;
|
||
int64_t h7 = f7 * (int64_t) 121666;
|
||
int64_t h8 = f8 * (int64_t) 121666;
|
||
int64_t h9 = f9 * (int64_t) 121666;
|
||
int64_t carry0;
|
||
int64_t carry1;
|
||
int64_t carry2;
|
||
int64_t carry3;
|
||
int64_t carry4;
|
||
int64_t carry5;
|
||
int64_t carry6;
|
||
int64_t carry7;
|
||
int64_t carry8;
|
||
int64_t carry9;
|
||
|
||
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
|
||
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
||
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
||
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
|
||
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
|
||
|
||
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
||
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
||
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
|
||
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
|
||
|
||
h[0] = h0;
|
||
h[1] = h1;
|
||
h[2] = h2;
|
||
h[3] = h3;
|
||
h[4] = h4;
|
||
h[5] = h5;
|
||
h[6] = h6;
|
||
h[7] = h7;
|
||
h[8] = h8;
|
||
h[9] = h9;
|
||
}
|
||
|
||
static void x25519_scalar_mult_generic(uint8_t out[32],
|
||
const uint8_t scalar[32],
|
||
const uint8_t point[32]) {
|
||
fe x1, x2, z2, x3, z3, tmp0, tmp1;
|
||
|
||
uint8_t e[32];
|
||
OPENSSL_memcpy(e, scalar, 32);
|
||
e[0] &= 248;
|
||
e[31] &= 127;
|
||
e[31] |= 64;
|
||
fe_frombytes(x1, point);
|
||
fe_1(x2);
|
||
fe_0(z2);
|
||
fe_copy(x3, x1);
|
||
fe_1(z3);
|
||
|
||
unsigned swap = 0;
|
||
int pos;
|
||
for (pos = 254; pos >= 0; --pos) {
|
||
unsigned b = 1 & (e[pos / 8] >> (pos & 7));
|
||
swap ^= b;
|
||
fe_cswap(x2, x3, swap);
|
||
fe_cswap(z2, z3, swap);
|
||
swap = b;
|
||
fe_sub(tmp0, x3, z3);
|
||
fe_sub(tmp1, x2, z2);
|
||
fe_add(x2, x2, z2);
|
||
fe_add(z2, x3, z3);
|
||
fe_mul(z3, tmp0, x2);
|
||
fe_mul(z2, z2, tmp1);
|
||
fe_sq(tmp0, tmp1);
|
||
fe_sq(tmp1, x2);
|
||
fe_add(x3, z3, z2);
|
||
fe_sub(z2, z3, z2);
|
||
fe_mul(x2, tmp1, tmp0);
|
||
fe_sub(tmp1, tmp1, tmp0);
|
||
fe_sq(z2, z2);
|
||
fe_mul121666(z3, tmp1);
|
||
fe_sq(x3, x3);
|
||
fe_add(tmp0, tmp0, z3);
|
||
fe_mul(z3, x1, z2);
|
||
fe_mul(z2, tmp1, tmp0);
|
||
}
|
||
fe_cswap(x2, x3, swap);
|
||
fe_cswap(z2, z3, swap);
|
||
|
||
fe_invert(z2, z2);
|
||
fe_mul(x2, x2, z2);
|
||
fe_tobytes(out, x2);
|
||
}
|
||
|
||
static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
|
||
const uint8_t point[32]) {
|
||
#if defined(BORINGSSL_X25519_NEON)
|
||
if (CRYPTO_is_NEON_capable()) {
|
||
x25519_NEON(out, scalar, point);
|
||
return;
|
||
}
|
||
#endif
|
||
|
||
x25519_scalar_mult_generic(out, scalar, point);
|
||
}
|
||
|
||
#endif /* BORINGSSL_X25519_X86_64 */
|
||
|
||
|
||
void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]) {
|
||
RAND_bytes(out_private_key, 32);
|
||
|
||
/* All X25519 implementations should decode scalars correctly (see
|
||
* https://tools.ietf.org/html/rfc7748#section-5). However, if an
|
||
* implementation doesn't then it might interoperate with random keys a
|
||
* fraction of the time because they'll, randomly, happen to be correctly
|
||
* formed.
|
||
*
|
||
* Thus we do the opposite of the masking here to make sure that our private
|
||
* keys are never correctly masked and so, hopefully, any incorrect
|
||
* implementations are deterministically broken.
|
||
*
|
||
* This does not affect security because, although we're throwing away
|
||
* entropy, a valid implementation of scalarmult should throw away the exact
|
||
* same bits anyway. */
|
||
out_private_key[0] |= 7;
|
||
out_private_key[31] &= 63;
|
||
out_private_key[31] |= 128;
|
||
|
||
X25519_public_from_private(out_public_value, out_private_key);
|
||
}
|
||
|
||
int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
|
||
const uint8_t peer_public_value[32]) {
|
||
static const uint8_t kZeros[32] = {0};
|
||
x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
|
||
/* The all-zero output results when the input is a point of small order. */
|
||
return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
|
||
}
|
||
|
||
#if defined(BORINGSSL_X25519_X86_64)
|
||
|
||
/* When |BORINGSSL_X25519_X86_64| is set, base point multiplication is done with
|
||
* the Montgomery ladder because it's faster. Otherwise it's done using the
|
||
* Ed25519 tables. */
|
||
|
||
void X25519_public_from_private(uint8_t out_public_value[32],
|
||
const uint8_t private_key[32]) {
|
||
static const uint8_t kMongomeryBasePoint[32] = {9};
|
||
x25519_scalar_mult(out_public_value, private_key, kMongomeryBasePoint);
|
||
}
|
||
|
||
#else
|
||
|
||
void X25519_public_from_private(uint8_t out_public_value[32],
|
||
const uint8_t private_key[32]) {
|
||
#if defined(BORINGSSL_X25519_NEON)
|
||
if (CRYPTO_is_NEON_capable()) {
|
||
static const uint8_t kMongomeryBasePoint[32] = {9};
|
||
x25519_NEON(out_public_value, private_key, kMongomeryBasePoint);
|
||
return;
|
||
}
|
||
#endif
|
||
|
||
uint8_t e[32];
|
||
OPENSSL_memcpy(e, private_key, 32);
|
||
e[0] &= 248;
|
||
e[31] &= 127;
|
||
e[31] |= 64;
|
||
|
||
ge_p3 A;
|
||
x25519_ge_scalarmult_base(&A, e);
|
||
|
||
/* We only need the u-coordinate of the curve25519 point. The map is
|
||
* u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */
|
||
fe zplusy, zminusy, zminusy_inv;
|
||
fe_add(zplusy, A.Z, A.Y);
|
||
fe_sub(zminusy, A.Z, A.Y);
|
||
fe_invert(zminusy_inv, zminusy);
|
||
fe_mul(zplusy, zplusy, zminusy_inv);
|
||
fe_tobytes(out_public_value, zplusy);
|
||
}
|
||
|
||
#endif /* BORINGSSL_X25519_X86_64 */
|