curve25519: Move to third_party
curve25519 comes from boringssl as well, move it to that directory. See git log for which boringssl commit the implementation comes from, and changes that were applied. BRANCH=none BUG=chromium:884905 TEST=make buildall -j, which also include basic tests. Change-Id: I1dee4795009c1e2034a181f6083d1f9445c87d41 Signed-off-by: Nicolas Boichat <drinkcat@chromium.org> Reviewed-on: https://chromium-review.googlesource.com/c/chromiumos/platform/ec/+/1600946 Reviewed-by: Aseda Aboagye <aaboagye@chromium.org>
This commit is contained in:
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/* Copyright 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 "curve25519.h"
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#include "util.h"
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/*
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* fe means field element. Here the field is \Z/(2^255-19). An element t,
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* entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
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* t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
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* context.
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*/
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typedef int32_t fe[10];
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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 + BIT(24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
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carry1 = h1 + BIT(24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
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carry3 = h3 + BIT(24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
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carry5 = h5 + BIT(24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
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carry7 = h7 + BIT(24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
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carry0 = h0 + BIT(25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
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carry2 = h2 + BIT(25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
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carry4 = h4 + BIT(25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
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carry6 = h6 + BIT(25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
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carry8 = h8 + BIT(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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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) { 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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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;
|
||||
int64_t f4g1 = f4 * (int64_t) g1;
|
||||
int64_t f4g2 = f4 * (int64_t) g2;
|
||||
int64_t f4g3 = f4 * (int64_t) g3;
|
||||
int64_t f4g4 = f4 * (int64_t) g4;
|
||||
int64_t f4g5 = f4 * (int64_t) g5;
|
||||
int64_t f4g6_19 = f4 * (int64_t) g6_19;
|
||||
int64_t f4g7_19 = f4 * (int64_t) g7_19;
|
||||
int64_t f4g8_19 = f4 * (int64_t) g8_19;
|
||||
int64_t f4g9_19 = f4 * (int64_t) g9_19;
|
||||
int64_t f5g0 = f5 * (int64_t) g0;
|
||||
int64_t f5g1_2 = f5_2 * (int64_t) g1;
|
||||
int64_t f5g2 = f5 * (int64_t) g2;
|
||||
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 + BIT(25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
||||
carry4 = h4 + BIT(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 + BIT(24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
||||
carry5 = h5 + BIT(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 + BIT(25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
||||
carry6 = h6 + BIT(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 + BIT(24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
||||
carry7 = h7 + BIT(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 + BIT(25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||||
carry8 = h8 + BIT(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 + BIT(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 + BIT(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 + BIT(25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
||||
carry4 = h4 + BIT(25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||||
|
||||
carry1 = h1 + BIT(24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
||||
carry5 = h5 + BIT(24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
|
||||
|
||||
carry2 = h2 + BIT(25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
||||
carry6 = h6 + BIT(25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
|
||||
|
||||
carry3 = h3 + BIT(24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
||||
carry7 = h7 + BIT(24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
|
||||
|
||||
carry4 = h4 + BIT(25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||||
carry8 = h8 + BIT(25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
|
||||
|
||||
carry9 = h9 + BIT(24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
|
||||
|
||||
carry0 = h0 + BIT(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);
|
||||
}
|
||||
|
||||
/* 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) {
|
||||
unsigned i;
|
||||
b = 0-b;
|
||||
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 + BIT(24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
|
||||
carry1 = h1 + BIT(24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
||||
carry3 = h3 + BIT(24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
||||
carry5 = h5 + BIT(24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
|
||||
carry7 = h7 + BIT(24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
|
||||
|
||||
carry0 = h0 + BIT(25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
||||
carry2 = h2 + BIT(25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
||||
carry4 = h4 + BIT(25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||||
carry6 = h6 + BIT(25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
|
||||
carry8 = h8 + BIT(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;
|
||||
}
|
||||
|
||||
void x25519_scalar_mult(uint8_t out[32],
|
||||
const uint8_t scalar[32],
|
||||
const uint8_t point[32]) {
|
||||
fe x1, x2, z2, x3, z3, tmp0, tmp1;
|
||||
unsigned swap;
|
||||
int pos;
|
||||
|
||||
uint8_t e[32];
|
||||
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);
|
||||
|
||||
swap = 0;
|
||||
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);
|
||||
}
|
|
@ -0,0 +1 @@
|
|||
../third_party/boringssl/common/curve25519-generic.c
|
|
@ -1,65 +0,0 @@
|
|||
/* Copyright 2015, Google Inc.
|
||||
*
|
||||
* Permission to use, copy, modify, and/or distribute this software for any
|
||||
* purpose with or without fee is hereby granted, provided that the above
|
||||
* copyright notice and this permission notice appear in all copies.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
|
||||
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
|
||||
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
|
||||
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
|
||||
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
|
||||
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
|
||||
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
|
||||
|
||||
/* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
|
||||
* 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as
|
||||
* public domain but this file has the ISC license just to keep licencing
|
||||
* simple.
|
||||
*
|
||||
* The field functions are shared by Ed25519 and X25519 where possible. */
|
||||
|
||||
#include "common.h"
|
||||
#include "curve25519.h"
|
||||
#include "trng.h"
|
||||
#include "util.h"
|
||||
#define CRYPTO_memcmp safe_memcmp
|
||||
|
||||
#ifdef CONFIG_RNG
|
||||
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);
|
||||
}
|
||||
#endif
|
||||
|
||||
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;
|
||||
}
|
||||
|
||||
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);
|
||||
}
|
|
@ -0,0 +1 @@
|
|||
../third_party/boringssl/common/curve25519.c
|
|
@ -1,70 +0,0 @@
|
|||
/* Copyright 2017 The Chromium OS Authors. All rights reserved.
|
||||
* Use of this source code is governed by a BSD-style license that can be
|
||||
* found in the LICENSE file.
|
||||
*/
|
||||
|
||||
#ifndef __CROS_EC_CURVE25519_H
|
||||
#define __CROS_EC_CURVE25519_H
|
||||
|
||||
#include <stdint.h>
|
||||
|
||||
/* Curve25519.
|
||||
*
|
||||
* Curve25519 is an elliptic curve. See https://tools.ietf.org/html/rfc7748.
|
||||
*/
|
||||
|
||||
|
||||
/* X25519.
|
||||
*
|
||||
* X25519 is the Diffie-Hellman primitive built from curve25519. It is
|
||||
* sometimes referred to as “curve25519”, but “X25519” is a more precise
|
||||
* name.
|
||||
* See http://cr.yp.to/ecdh.html and https://tools.ietf.org/html/rfc7748.
|
||||
*/
|
||||
|
||||
#define X25519_PRIVATE_KEY_LEN 32
|
||||
#define X25519_PUBLIC_VALUE_LEN 32
|
||||
|
||||
/**
|
||||
* Generate a public/private key pair.
|
||||
* @param out_public_value generated public key.
|
||||
* @param out_private_value generated private key.
|
||||
*/
|
||||
void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]);
|
||||
|
||||
/**
|
||||
* Diffie-Hellman function.
|
||||
* @param out_shared_key
|
||||
* @param private_key
|
||||
* @param out_public_value
|
||||
* @return one on success and zero on error.
|
||||
*
|
||||
* X25519() writes a shared key to @out_shared_key that is calculated from the
|
||||
* given private key and the peer's public value.
|
||||
*
|
||||
* Don't use the shared key directly, rather use a KDF and also include the two
|
||||
* public values as inputs.
|
||||
*/
|
||||
int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
|
||||
const uint8_t peers_public_value[32]);
|
||||
|
||||
/**
|
||||
* Compute the matching public key.
|
||||
* @param out_public_value computed public key.
|
||||
* @param private_key private key to use.
|
||||
*
|
||||
* X25519_public_from_private() calculates a Diffie-Hellman public value from
|
||||
* the given private key and writes it to @out_public_value.
|
||||
*/
|
||||
void X25519_public_from_private(uint8_t out_public_value[32],
|
||||
const uint8_t private_key[32]);
|
||||
|
||||
/*
|
||||
* Low-level x25519 function, defined by either the generic or cortex-m0
|
||||
* implementation. Must not be called directly.
|
||||
*/
|
||||
void x25519_scalar_mult(uint8_t out[32],
|
||||
const uint8_t scalar[32],
|
||||
const uint8_t point[32]);
|
||||
|
||||
#endif /* __CROS_EC_CURVE25519_H */
|
|
@ -0,0 +1 @@
|
|||
../third_party/boringssl/include/curve25519.h
|
197
test/x25519.c
197
test/x25519.c
|
@ -1,197 +0,0 @@
|
|||
/* Copyright (c) 2015, Google Inc.
|
||||
*
|
||||
* Permission to use, copy, modify, and/or distribute this software for any
|
||||
* purpose with or without fee is hereby granted, provided that the above
|
||||
* copyright notice and this permission notice appear in all copies.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
|
||||
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
|
||||
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
|
||||
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
|
||||
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
|
||||
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
|
||||
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
|
||||
|
||||
#include "console.h"
|
||||
#include "common.h"
|
||||
#include "curve25519.h"
|
||||
#include "test_util.h"
|
||||
#include "timer.h"
|
||||
#include "util.h"
|
||||
#include "watchdog.h"
|
||||
|
||||
/*
|
||||
* Define this to test 1 million iterations of x25519 (takes up to
|
||||
* a few minutes on host, up to a few days on microcontroller).
|
||||
*/
|
||||
#undef TEST_X25519_1M_ITERATIONS
|
||||
|
||||
static int test_x25519(void)
|
||||
{
|
||||
/* Taken from https://tools.ietf.org/html/rfc7748#section-5.2 */
|
||||
static const uint8_t scalar1[32] = {
|
||||
0xa5, 0x46, 0xe3, 0x6b, 0xf0, 0x52, 0x7c, 0x9d,
|
||||
0x3b, 0x16, 0x15, 0x4b, 0x82, 0x46, 0x5e, 0xdd,
|
||||
0x62, 0x14, 0x4c, 0x0a, 0xc1, 0xfc, 0x5a, 0x18,
|
||||
0x50, 0x6a, 0x22, 0x44, 0xba, 0x44, 0x9a, 0xc4,
|
||||
};
|
||||
static const uint8_t point1[32] = {
|
||||
0xe6, 0xdb, 0x68, 0x67, 0x58, 0x30, 0x30, 0xdb,
|
||||
0x35, 0x94, 0xc1, 0xa4, 0x24, 0xb1, 0x5f, 0x7c,
|
||||
0x72, 0x66, 0x24, 0xec, 0x26, 0xb3, 0x35, 0x3b,
|
||||
0x10, 0xa9, 0x03, 0xa6, 0xd0, 0xab, 0x1c, 0x4c,
|
||||
};
|
||||
static const uint8_t expected1[32] = {
|
||||
0xc3, 0xda, 0x55, 0x37, 0x9d, 0xe9, 0xc6, 0x90,
|
||||
0x8e, 0x94, 0xea, 0x4d, 0xf2, 0x8d, 0x08, 0x4f,
|
||||
0x32, 0xec, 0xcf, 0x03, 0x49, 0x1c, 0x71, 0xf7,
|
||||
0x54, 0xb4, 0x07, 0x55, 0x77, 0xa2, 0x85, 0x52,
|
||||
};
|
||||
static const uint8_t scalar2[32] = {
|
||||
0x4b, 0x66, 0xe9, 0xd4, 0xd1, 0xb4, 0x67, 0x3c,
|
||||
0x5a, 0xd2, 0x26, 0x91, 0x95, 0x7d, 0x6a, 0xf5,
|
||||
0xc1, 0x1b, 0x64, 0x21, 0xe0, 0xea, 0x01, 0xd4,
|
||||
0x2c, 0xa4, 0x16, 0x9e, 0x79, 0x18, 0xba, 0x0d,
|
||||
};
|
||||
static const uint8_t point2[32] = {
|
||||
0xe5, 0x21, 0x0f, 0x12, 0x78, 0x68, 0x11, 0xd3,
|
||||
0xf4, 0xb7, 0x95, 0x9d, 0x05, 0x38, 0xae, 0x2c,
|
||||
0x31, 0xdb, 0xe7, 0x10, 0x6f, 0xc0, 0x3c, 0x3e,
|
||||
0xfc, 0x4c, 0xd5, 0x49, 0xc7, 0x15, 0xa4, 0x93,
|
||||
};
|
||||
static const uint8_t expected2[32] = {
|
||||
0x95, 0xcb, 0xde, 0x94, 0x76, 0xe8, 0x90, 0x7d,
|
||||
0x7a, 0xad, 0xe4, 0x5c, 0xb4, 0xb8, 0x73, 0xf8,
|
||||
0x8b, 0x59, 0x5a, 0x68, 0x79, 0x9f, 0xa1, 0x52,
|
||||
0xe6, 0xf8, 0xf7, 0x64, 0x7a, 0xac, 0x79, 0x57,
|
||||
};
|
||||
uint8_t out[32];
|
||||
|
||||
X25519(out, scalar1, point1);
|
||||
|
||||
if (memcmp(expected1, out, sizeof(out)) != 0) {
|
||||
ccprintf("X25519 test one failed.\n");
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
X25519(out, scalar2, point2);
|
||||
|
||||
if (memcmp(expected2, out, sizeof(out)) != 0) {
|
||||
ccprintf("X25519 test two failed.\n");
|
||||
return 0;
|
||||
}
|
||||
|
||||
return 1;
|
||||
}
|
||||
|
||||
static int test_x25519_small_order(void)
|
||||
{
|
||||
static const uint8_t kSmallOrderPoint[32] = {
|
||||
0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae,
|
||||
0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a,
|
||||
0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd,
|
||||
0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8,
|
||||
};
|
||||
uint8_t out[32], private_key[32];
|
||||
|
||||
memset(private_key, 0x11, sizeof(private_key));
|
||||
|
||||
if (X25519(out, private_key, kSmallOrderPoint)) {
|
||||
ccprintf("X25519 returned success with a small-order input.\n");
|
||||
return 0;
|
||||
}
|
||||
|
||||
return 1;
|
||||
}
|
||||
|
||||
static int test_x25519_iterated(void)
|
||||
{
|
||||
/* Taken from https://tools.ietf.org/html/rfc7748#section-5.2 */
|
||||
static const uint8_t expected_1K[32] = {
|
||||
0x68, 0x4c, 0xf5, 0x9b, 0xa8, 0x33, 0x09, 0x55,
|
||||
0x28, 0x00, 0xef, 0x56, 0x6f, 0x2f, 0x4d, 0x3c,
|
||||
0x1c, 0x38, 0x87, 0xc4, 0x93, 0x60, 0xe3, 0x87,
|
||||
0x5f, 0x2e, 0xb9, 0x4d, 0x99, 0x53, 0x2c, 0x51,
|
||||
};
|
||||
#ifdef TEST_X25519_1M_ITERATIONS
|
||||
static const uint8_t expected_1M[32] = {
|
||||
0x7c, 0x39, 0x11, 0xe0, 0xab, 0x25, 0x86, 0xfd,
|
||||
0x86, 0x44, 0x97, 0x29, 0x7e, 0x57, 0x5e, 0x6f,
|
||||
0x3b, 0xc6, 0x01, 0xc0, 0x88, 0x3c, 0x30, 0xdf,
|
||||
0x5f, 0x4d, 0xd2, 0xd2, 0x4f, 0x66, 0x54, 0x24
|
||||
};
|
||||
#endif
|
||||
uint8_t scalar[32] = {9}, point[32] = {9}, out[32];
|
||||
unsigned i;
|
||||
|
||||
for (i = 0; i < 1000; i++) {
|
||||
watchdog_reload();
|
||||
X25519(out, scalar, point);
|
||||
memcpy(point, scalar, sizeof(point));
|
||||
memcpy(scalar, out, sizeof(scalar));
|
||||
}
|
||||
|
||||
if (memcmp(expected_1K, scalar, sizeof(expected_1K)) != 0) {
|
||||
ccprintf("1,000 iterations X25519 test failed\n");
|
||||
return 0;
|
||||
}
|
||||
|
||||
#ifdef TEST_X25519_1M_ITERATIONS
|
||||
for (; i < 1000000; i++) {
|
||||
watchdog_reload();
|
||||
X25519(out, scalar, point);
|
||||
memcpy(point, scalar, sizeof(point));
|
||||
memcpy(scalar, out, sizeof(scalar));
|
||||
if ((i % 10000) == 0)
|
||||
ccprints("%d", i);
|
||||
}
|
||||
|
||||
if (memcmp(expected_1M, scalar, sizeof(expected_1M)) != 0) {
|
||||
ccprintf("1,000,000 iterations X25519 test failed\n");
|
||||
return 0;
|
||||
}
|
||||
#endif
|
||||
|
||||
return 1;
|
||||
}
|
||||
|
||||
static void test_x25519_speed(void)
|
||||
{
|
||||
static const uint8_t scalar1[32] = {
|
||||
0xa5, 0x46, 0xe3, 0x6b, 0xf0, 0x52, 0x7c, 0x9d,
|
||||
0x3b, 0x16, 0x15, 0x4b, 0x82, 0x46, 0x5e, 0xdd,
|
||||
0x62, 0x14, 0x4c, 0x0a, 0xc1, 0xfc, 0x5a, 0x18,
|
||||
0x50, 0x6a, 0x22, 0x44, 0xba, 0x44, 0x9a, 0xc4,
|
||||
};
|
||||
static const uint8_t point1[32] = {
|
||||
0xe6, 0xdb, 0x68, 0x67, 0x58, 0x30, 0x30, 0xdb,
|
||||
0x35, 0x94, 0xc1, 0xa4, 0x24, 0xb1, 0x5f, 0x7c,
|
||||
0x72, 0x66, 0x24, 0xec, 0x26, 0xb3, 0x35, 0x3b,
|
||||
0x10, 0xa9, 0x03, 0xa6, 0xd0, 0xab, 0x1c, 0x4c,
|
||||
};
|
||||
uint8_t out[32];
|
||||
timestamp_t t0, t1;
|
||||
|
||||
X25519(out, scalar1, point1);
|
||||
t0 = get_time();
|
||||
X25519(out, scalar1, point1);
|
||||
t1 = get_time();
|
||||
ccprintf("X25519 duration %lld us\n", (long long)(t1.val - t0.val));
|
||||
}
|
||||
|
||||
void run_test(void)
|
||||
{
|
||||
watchdog_reload();
|
||||
/* do not check speed, just as a benchmark */
|
||||
test_x25519_speed();
|
||||
|
||||
watchdog_reload();
|
||||
if (!test_x25519() || !test_x25519_iterated() ||
|
||||
!test_x25519_small_order()) {
|
||||
test_fail();
|
||||
return;
|
||||
}
|
||||
|
||||
test_pass();
|
||||
}
|
|
@ -0,0 +1 @@
|
|||
../third_party/boringssl/test/x25519.c
|
|
@ -8,6 +8,8 @@ third_party {
|
|||
value: "https://boringssl.googlesource.com/boringssl/"
|
||||
}
|
||||
version: "859679518d3433cdd0dd6cf534bd7bdb2a32dd60"
|
||||
# TODO(crbug.com/884905): Refresh curve25519 to latest boringssl
|
||||
# version_curve25519: "c034e2d3ce16df5f89134515bc113eb4f3a28e0e"
|
||||
last_upgrade_date { year: 2018 month: 07 day: 05 }
|
||||
license_type: NOTICE
|
||||
local_modifications: "Adapted code to work with EC codebase."
|
||||
|
|
|
@ -0,0 +1,821 @@
|
|||
/* Copyright 2015, Google Inc.
|
||||
*
|
||||
* Permission to use, copy, modify, and/or distribute this software for any
|
||||
* purpose with or without fee is hereby granted, provided that the above
|
||||
* copyright notice and this permission notice appear in all copies.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
|
||||
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
|
||||
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
|
||||
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
|
||||
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
|
||||
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
|
||||
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
|
||||
|
||||
/* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
|
||||
* 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as
|
||||
* public domain but this file has the ISC license just to keep licencing
|
||||
* simple.
|
||||
*
|
||||
* The field functions are shared by Ed25519 and X25519 where possible. */
|
||||
|
||||
#include "curve25519.h"
|
||||
#include "util.h"
|
||||
|
||||
/*
|
||||
* fe means field element. Here the field is \Z/(2^255-19). An element t,
|
||||
* entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
|
||||
* t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
|
||||
* context.
|
||||
*/
|
||||
typedef int32_t fe[10];
|
||||
|
||||
static const int64_t kBottom25Bits = INT64_C(0x1ffffff);
|
||||
static const int64_t kBottom26Bits = INT64_C(0x3ffffff);
|
||||
static const int64_t kTop39Bits = INT64_C(0xfffffffffe000000);
|
||||
static const int64_t kTop38Bits = INT64_C(0xfffffffffc000000);
|
||||
|
||||
static uint64_t load_3(const uint8_t *in) {
|
||||
uint64_t result;
|
||||
result = (uint64_t)in[0];
|
||||
result |= ((uint64_t)in[1]) << 8;
|
||||
result |= ((uint64_t)in[2]) << 16;
|
||||
return result;
|
||||
}
|
||||
|
||||
static uint64_t load_4(const uint8_t *in) {
|
||||
uint64_t result;
|
||||
result = (uint64_t)in[0];
|
||||
result |= ((uint64_t)in[1]) << 8;
|
||||
result |= ((uint64_t)in[2]) << 16;
|
||||
result |= ((uint64_t)in[3]) << 24;
|
||||
return result;
|
||||
}
|
||||
|
||||
static void fe_frombytes(fe h, const uint8_t *s) {
|
||||
/* Ignores top bit of h. */
|
||||
int64_t h0 = load_4(s);
|
||||
int64_t h1 = load_3(s + 4) << 6;
|
||||
int64_t h2 = load_3(s + 7) << 5;
|
||||
int64_t h3 = load_3(s + 10) << 3;
|
||||
int64_t h4 = load_3(s + 13) << 2;
|
||||
int64_t h5 = load_4(s + 16);
|
||||
int64_t h6 = load_3(s + 20) << 7;
|
||||
int64_t h7 = load_3(s + 23) << 5;
|
||||
int64_t h8 = load_3(s + 26) << 4;
|
||||
int64_t h9 = (load_3(s + 29) & 8388607) << 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;
|
||||
|
||||
carry9 = h9 + BIT(24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
|
||||
carry1 = h1 + BIT(24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
||||
carry3 = h3 + BIT(24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
||||
carry5 = h5 + BIT(24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
|
||||
carry7 = h7 + BIT(24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
|
||||
|
||||
carry0 = h0 + BIT(25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
||||
carry2 = h2 + BIT(25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
||||
carry4 = h4 + BIT(25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||||
carry6 = h6 + BIT(25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
|
||||
carry8 = h8 + BIT(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;
|
||||
}
|
||||
|
||||
/* Preconditions:
|
||||
* |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
|
||||
*
|
||||
* Write p=2^255-19; q=floor(h/p).
|
||||
* Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
|
||||
*
|
||||
* Proof:
|
||||
* Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
|
||||
* Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
|
||||
*
|
||||
* Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
|
||||
* Then 0<y<1.
|
||||
*
|
||||
* Write r=h-pq.
|
||||
* Have 0<=r<=p-1=2^255-20.
|
||||
* Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
|
||||
*
|
||||
* Write x=r+19(2^-255)r+y.
|
||||
* Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
|
||||
*
|
||||
* Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
|
||||
* so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */
|
||||
static void fe_tobytes(uint8_t *s, const fe h) {
|
||||
int32_t h0 = h[0];
|
||||
int32_t h1 = h[1];
|
||||
int32_t h2 = h[2];
|
||||
int32_t h3 = h[3];
|
||||
int32_t h4 = h[4];
|
||||
int32_t h5 = h[5];
|
||||
int32_t h6 = h[6];
|
||||
int32_t h7 = h[7];
|
||||
int32_t h8 = h[8];
|
||||
int32_t h9 = h[9];
|
||||
int32_t q;
|
||||
|
||||
q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
|
||||
q = (h0 + q) >> 26;
|
||||
q = (h1 + q) >> 25;
|
||||
q = (h2 + q) >> 26;
|
||||
q = (h3 + q) >> 25;
|
||||
q = (h4 + q) >> 26;
|
||||
q = (h5 + q) >> 25;
|
||||
q = (h6 + q) >> 26;
|
||||
q = (h7 + q) >> 25;
|
||||
q = (h8 + q) >> 26;
|
||||
q = (h9 + q) >> 25;
|
||||
|
||||
/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
|
||||
h0 += 19 * q;
|
||||
/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
|
||||
|
||||
h1 += h0 >> 26; h0 &= kBottom26Bits;
|
||||
h2 += h1 >> 25; h1 &= kBottom25Bits;
|
||||
h3 += h2 >> 26; h2 &= kBottom26Bits;
|
||||
h4 += h3 >> 25; h3 &= kBottom25Bits;
|
||||
h5 += h4 >> 26; h4 &= kBottom26Bits;
|
||||
h6 += h5 >> 25; h5 &= kBottom25Bits;
|
||||
h7 += h6 >> 26; h6 &= kBottom26Bits;
|
||||
h8 += h7 >> 25; h7 &= kBottom25Bits;
|
||||
h9 += h8 >> 26; h8 &= kBottom26Bits;
|
||||
h9 &= kBottom25Bits;
|
||||
/* h10 = carry9 */
|
||||
|
||||
/* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
|
||||
* Have h0+...+2^230 h9 between 0 and 2^255-1;
|
||||
* evidently 2^255 h10-2^255 q = 0.
|
||||
* Goal: Output h0+...+2^230 h9. */
|
||||
|
||||
s[0] = h0 >> 0;
|
||||
s[1] = h0 >> 8;
|
||||
s[2] = h0 >> 16;
|
||||
s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2);
|
||||
s[4] = h1 >> 6;
|
||||
s[5] = h1 >> 14;
|
||||
s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3);
|
||||
s[7] = h2 >> 5;
|
||||
s[8] = h2 >> 13;
|
||||
s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5);
|
||||
s[10] = h3 >> 3;
|
||||
s[11] = h3 >> 11;
|
||||
s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6);
|
||||
s[13] = h4 >> 2;
|
||||
s[14] = h4 >> 10;
|
||||
s[15] = h4 >> 18;
|
||||
s[16] = h5 >> 0;
|
||||
s[17] = h5 >> 8;
|
||||
s[18] = h5 >> 16;
|
||||
s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1);
|
||||
s[20] = h6 >> 7;
|
||||
s[21] = h6 >> 15;
|
||||
s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3);
|
||||
s[23] = h7 >> 5;
|
||||
s[24] = h7 >> 13;
|
||||
s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4);
|
||||
s[26] = h8 >> 4;
|
||||
s[27] = h8 >> 12;
|
||||
s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6);
|
||||
s[29] = h9 >> 2;
|
||||
s[30] = h9 >> 10;
|
||||
s[31] = h9 >> 18;
|
||||
}
|
||||
|
||||
/* h = f */
|
||||
static void fe_copy(fe h, const fe f) {
|
||||
memmove(h, f, sizeof(int32_t) * 10);
|
||||
}
|
||||
|
||||
/* h = 0 */
|
||||
static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); }
|
||||
|
||||
/* h = 1 */
|
||||
static void fe_1(fe h) {
|
||||
memset(h, 0, sizeof(int32_t) * 10);
|
||||
h[0] = 1;
|
||||
}
|
||||
|
||||
/* h = f + g
|
||||
* Can overlap h with f or g.
|
||||
*
|
||||
* Preconditions:
|
||||
* |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|
||||
* |g| 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*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
|
||||
static void fe_add(fe h, const fe f, const fe g) {
|
||||
unsigned i;
|
||||
for (i = 0; i < 10; i++) {
|
||||
h[i] = f[i] + g[i];
|
||||
}
|
||||
}
|
||||
|
||||
/* h = f - g
|
||||
* Can overlap h with f or g.
|
||||
*
|
||||
* Preconditions:
|
||||
* |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|
||||
* |g| 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*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
|
||||
static void fe_sub(fe h, const fe f, const fe g) {
|
||||
unsigned i;
|
||||
for (i = 0; i < 10; i++) {
|
||||
h[i] = f[i] - g[i];
|
||||
}
|
||||
}
|
||||
|
||||
/* h = f * g
|
||||
* Can overlap h with f or g.
|
||||
*
|
||||
* Preconditions:
|
||||
* |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
|
||||
* |g| 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.
|
||||
*
|
||||
* Notes on implementation strategy:
|
||||
*
|
||||
* Using schoolbook multiplication.
|
||||
* Karatsuba would save a little in some cost models.
|
||||
*
|
||||
* Most multiplications by 2 and 19 are 32-bit precomputations;
|
||||
* cheaper than 64-bit postcomputations.
|
||||
*
|
||||
* There is one remaining multiplication by 19 in the carry chain;
|
||||
* one *19 precomputation can be merged into this,
|
||||
* but the resulting data flow is considerably less clean.
|
||||
*
|
||||
* There are 12 carries below.
|
||||
* 10 of them are 2-way parallelizable and vectorizable.
|
||||
* Can get away with 11 carries, but then data flow is much deeper.
|
||||
*
|
||||
* With tighter constraints on inputs can squeeze carries into int32. */
|
||||
static void fe_mul(fe h, const fe f, const fe g) {
|
||||
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 g0 = g[0];
|
||||
int32_t g1 = g[1];
|
||||
int32_t g2 = g[2];
|
||||
int32_t g3 = g[3];
|
||||
int32_t g4 = g[4];
|
||||
int32_t g5 = g[5];
|
||||
int32_t g6 = g[6];
|
||||
int32_t g7 = g[7];
|
||||
int32_t g8 = g[8];
|
||||
int32_t g9 = g[9];
|
||||
int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
|
||||
int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
|
||||
int32_t g3_19 = 19 * g3;
|
||||
int32_t g4_19 = 19 * g4;
|
||||
int32_t g5_19 = 19 * g5;
|
||||
int32_t g6_19 = 19 * g6;
|
||||
int32_t g7_19 = 19 * g7;
|
||||
int32_t g8_19 = 19 * g8;
|
||||
int32_t g9_19 = 19 * g9;
|
||||
int32_t f1_2 = 2 * f1;
|
||||
int32_t f3_2 = 2 * f3;
|
||||
int32_t f5_2 = 2 * f5;
|
||||
int32_t f7_2 = 2 * f7;
|
||||
int32_t f9_2 = 2 * f9;
|
||||
int64_t f0g0 = f0 * (int64_t) g0;
|
||||
int64_t f0g1 = f0 * (int64_t) g1;
|
||||
int64_t f0g2 = f0 * (int64_t) g2;
|
||||
int64_t f0g3 = f0 * (int64_t) g3;
|
||||
int64_t f0g4 = f0 * (int64_t) g4;
|
||||
int64_t f0g5 = f0 * (int64_t) g5;
|
||||
int64_t f0g6 = f0 * (int64_t) g6;
|
||||
int64_t f0g7 = f0 * (int64_t) g7;
|
||||
int64_t f0g8 = f0 * (int64_t) g8;
|
||||
int64_t f0g9 = f0 * (int64_t) g9;
|
||||
int64_t f1g0 = f1 * (int64_t) g0;
|
||||
int64_t f1g1_2 = f1_2 * (int64_t) g1;
|
||||
int64_t f1g2 = f1 * (int64_t) g2;
|
||||
int64_t f1g3_2 = f1_2 * (int64_t) g3;
|
||||
int64_t f1g4 = f1 * (int64_t) g4;
|
||||
int64_t f1g5_2 = f1_2 * (int64_t) g5;
|
||||
int64_t f1g6 = f1 * (int64_t) g6;
|
||||
int64_t f1g7_2 = f1_2 * (int64_t) g7;
|
||||
int64_t f1g8 = f1 * (int64_t) g8;
|
||||
int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
|
||||
int64_t f2g0 = f2 * (int64_t) g0;
|
||||
int64_t f2g1 = f2 * (int64_t) g1;
|
||||
int64_t f2g2 = f2 * (int64_t) g2;
|
||||
int64_t f2g3 = f2 * (int64_t) g3;
|
||||
int64_t f2g4 = f2 * (int64_t) g4;
|
||||
int64_t f2g5 = f2 * (int64_t) g5;
|
||||
int64_t f2g6 = f2 * (int64_t) g6;
|
||||
int64_t f2g7 = f2 * (int64_t) g7;
|
||||
int64_t f2g8_19 = f2 * (int64_t) g8_19;
|
||||
int64_t f2g9_19 = f2 * (int64_t) g9_19;
|
||||
int64_t f3g0 = f3 * (int64_t) g0;
|
||||
int64_t f3g1_2 = f3_2 * (int64_t) g1;
|
||||
int64_t f3g2 = f3 * (int64_t) g2;
|
||||
int64_t f3g3_2 = f3_2 * (int64_t) g3;
|
||||
int64_t f3g4 = f3 * (int64_t) g4;
|
||||
int64_t f3g5_2 = f3_2 * (int64_t) g5;
|
||||
int64_t f3g6 = f3 * (int64_t) g6;
|
||||
int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
|
||||
int64_t f3g8_19 = f3 * (int64_t) g8_19;
|
||||
int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
|
||||
int64_t f4g0 = f4 * (int64_t) g0;
|
||||
int64_t f4g1 = f4 * (int64_t) g1;
|
||||
int64_t f4g2 = f4 * (int64_t) g2;
|
||||
int64_t f4g3 = f4 * (int64_t) g3;
|
||||
int64_t f4g4 = f4 * (int64_t) g4;
|
||||
int64_t f4g5 = f4 * (int64_t) g5;
|
||||
int64_t f4g6_19 = f4 * (int64_t) g6_19;
|
||||
int64_t f4g7_19 = f4 * (int64_t) g7_19;
|
||||
int64_t f4g8_19 = f4 * (int64_t) g8_19;
|
||||
int64_t f4g9_19 = f4 * (int64_t) g9_19;
|
||||
int64_t f5g0 = f5 * (int64_t) g0;
|
||||
int64_t f5g1_2 = f5_2 * (int64_t) g1;
|
||||
int64_t f5g2 = f5 * (int64_t) g2;
|
||||
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 + BIT(25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
||||
carry4 = h4 + BIT(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 + BIT(24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
||||
carry5 = h5 + BIT(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 + BIT(25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
||||
carry6 = h6 + BIT(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 + BIT(24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
||||
carry7 = h7 + BIT(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 + BIT(25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||||
carry8 = h8 + BIT(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 + BIT(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 + BIT(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 + BIT(25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
||||
carry4 = h4 + BIT(25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||||
|
||||
carry1 = h1 + BIT(24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
||||
carry5 = h5 + BIT(24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
|
||||
|
||||
carry2 = h2 + BIT(25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
||||
carry6 = h6 + BIT(25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
|
||||
|
||||
carry3 = h3 + BIT(24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
||||
carry7 = h7 + BIT(24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
|
||||
|
||||
carry4 = h4 + BIT(25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||||
carry8 = h8 + BIT(25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
|
||||
|
||||
carry9 = h9 + BIT(24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
|
||||
|
||||
carry0 = h0 + BIT(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);
|
||||
}
|
||||
|
||||
/* 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) {
|
||||
unsigned i;
|
||||
b = 0-b;
|
||||
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 + BIT(24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
|
||||
carry1 = h1 + BIT(24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
||||
carry3 = h3 + BIT(24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
||||
carry5 = h5 + BIT(24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
|
||||
carry7 = h7 + BIT(24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
|
||||
|
||||
carry0 = h0 + BIT(25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
||||
carry2 = h2 + BIT(25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
||||
carry4 = h4 + BIT(25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
||||
carry6 = h6 + BIT(25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
|
||||
carry8 = h8 + BIT(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;
|
||||
}
|
||||
|
||||
void x25519_scalar_mult(uint8_t out[32],
|
||||
const uint8_t scalar[32],
|
||||
const uint8_t point[32]) {
|
||||
fe x1, x2, z2, x3, z3, tmp0, tmp1;
|
||||
unsigned swap;
|
||||
int pos;
|
||||
|
||||
uint8_t e[32];
|
||||
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);
|
||||
|
||||
swap = 0;
|
||||
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);
|
||||
}
|
|
@ -0,0 +1,65 @@
|
|||
/* Copyright 2015, Google Inc.
|
||||
*
|
||||
* Permission to use, copy, modify, and/or distribute this software for any
|
||||
* purpose with or without fee is hereby granted, provided that the above
|
||||
* copyright notice and this permission notice appear in all copies.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
|
||||
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
|
||||
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
|
||||
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
|
||||
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
|
||||
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
|
||||
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
|
||||
|
||||
/* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
|
||||
* 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as
|
||||
* public domain but this file has the ISC license just to keep licencing
|
||||
* simple.
|
||||
*
|
||||
* The field functions are shared by Ed25519 and X25519 where possible. */
|
||||
|
||||
#include "common.h"
|
||||
#include "curve25519.h"
|
||||
#include "trng.h"
|
||||
#include "util.h"
|
||||
#define CRYPTO_memcmp safe_memcmp
|
||||
|
||||
#ifdef CONFIG_RNG
|
||||
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);
|
||||
}
|
||||
#endif
|
||||
|
||||
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;
|
||||
}
|
||||
|
||||
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);
|
||||
}
|
|
@ -0,0 +1,70 @@
|
|||
/* Copyright 2017 The Chromium OS Authors. All rights reserved.
|
||||
* Use of this source code is governed by a BSD-style license that can be
|
||||
* found in the LICENSE file.
|
||||
*/
|
||||
|
||||
#ifndef __CROS_EC_CURVE25519_H
|
||||
#define __CROS_EC_CURVE25519_H
|
||||
|
||||
#include <stdint.h>
|
||||
|
||||
/* Curve25519.
|
||||
*
|
||||
* Curve25519 is an elliptic curve. See https://tools.ietf.org/html/rfc7748.
|
||||
*/
|
||||
|
||||
|
||||
/* X25519.
|
||||
*
|
||||
* X25519 is the Diffie-Hellman primitive built from curve25519. It is
|
||||
* sometimes referred to as “curve25519”, but “X25519” is a more precise
|
||||
* name.
|
||||
* See http://cr.yp.to/ecdh.html and https://tools.ietf.org/html/rfc7748.
|
||||
*/
|
||||
|
||||
#define X25519_PRIVATE_KEY_LEN 32
|
||||
#define X25519_PUBLIC_VALUE_LEN 32
|
||||
|
||||
/**
|
||||
* Generate a public/private key pair.
|
||||
* @param out_public_value generated public key.
|
||||
* @param out_private_value generated private key.
|
||||
*/
|
||||
void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]);
|
||||
|
||||
/**
|
||||
* Diffie-Hellman function.
|
||||
* @param out_shared_key
|
||||
* @param private_key
|
||||
* @param out_public_value
|
||||
* @return one on success and zero on error.
|
||||
*
|
||||
* X25519() writes a shared key to @out_shared_key that is calculated from the
|
||||
* given private key and the peer's public value.
|
||||
*
|
||||
* Don't use the shared key directly, rather use a KDF and also include the two
|
||||
* public values as inputs.
|
||||
*/
|
||||
int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
|
||||
const uint8_t peers_public_value[32]);
|
||||
|
||||
/**
|
||||
* Compute the matching public key.
|
||||
* @param out_public_value computed public key.
|
||||
* @param private_key private key to use.
|
||||
*
|
||||
* X25519_public_from_private() calculates a Diffie-Hellman public value from
|
||||
* the given private key and writes it to @out_public_value.
|
||||
*/
|
||||
void X25519_public_from_private(uint8_t out_public_value[32],
|
||||
const uint8_t private_key[32]);
|
||||
|
||||
/*
|
||||
* Low-level x25519 function, defined by either the generic or cortex-m0
|
||||
* implementation. Must not be called directly.
|
||||
*/
|
||||
void x25519_scalar_mult(uint8_t out[32],
|
||||
const uint8_t scalar[32],
|
||||
const uint8_t point[32]);
|
||||
|
||||
#endif /* __CROS_EC_CURVE25519_H */
|
|
@ -0,0 +1,197 @@
|
|||
/* Copyright (c) 2015, Google Inc.
|
||||
*
|
||||
* Permission to use, copy, modify, and/or distribute this software for any
|
||||
* purpose with or without fee is hereby granted, provided that the above
|
||||
* copyright notice and this permission notice appear in all copies.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
|
||||
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
|
||||
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
|
||||
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
|
||||
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
|
||||
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
|
||||
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
|
||||
|
||||
#include "console.h"
|
||||
#include "common.h"
|
||||
#include "curve25519.h"
|
||||
#include "test_util.h"
|
||||
#include "timer.h"
|
||||
#include "util.h"
|
||||
#include "watchdog.h"
|
||||
|
||||
/*
|
||||
* Define this to test 1 million iterations of x25519 (takes up to
|
||||
* a few minutes on host, up to a few days on microcontroller).
|
||||
*/
|
||||
#undef TEST_X25519_1M_ITERATIONS
|
||||
|
||||
static int test_x25519(void)
|
||||
{
|
||||
/* Taken from https://tools.ietf.org/html/rfc7748#section-5.2 */
|
||||
static const uint8_t scalar1[32] = {
|
||||
0xa5, 0x46, 0xe3, 0x6b, 0xf0, 0x52, 0x7c, 0x9d,
|
||||
0x3b, 0x16, 0x15, 0x4b, 0x82, 0x46, 0x5e, 0xdd,
|
||||
0x62, 0x14, 0x4c, 0x0a, 0xc1, 0xfc, 0x5a, 0x18,
|
||||
0x50, 0x6a, 0x22, 0x44, 0xba, 0x44, 0x9a, 0xc4,
|
||||
};
|
||||
static const uint8_t point1[32] = {
|
||||
0xe6, 0xdb, 0x68, 0x67, 0x58, 0x30, 0x30, 0xdb,
|
||||
0x35, 0x94, 0xc1, 0xa4, 0x24, 0xb1, 0x5f, 0x7c,
|
||||
0x72, 0x66, 0x24, 0xec, 0x26, 0xb3, 0x35, 0x3b,
|
||||
0x10, 0xa9, 0x03, 0xa6, 0xd0, 0xab, 0x1c, 0x4c,
|
||||
};
|
||||
static const uint8_t expected1[32] = {
|
||||
0xc3, 0xda, 0x55, 0x37, 0x9d, 0xe9, 0xc6, 0x90,
|
||||
0x8e, 0x94, 0xea, 0x4d, 0xf2, 0x8d, 0x08, 0x4f,
|
||||
0x32, 0xec, 0xcf, 0x03, 0x49, 0x1c, 0x71, 0xf7,
|
||||
0x54, 0xb4, 0x07, 0x55, 0x77, 0xa2, 0x85, 0x52,
|
||||
};
|
||||
static const uint8_t scalar2[32] = {
|
||||
0x4b, 0x66, 0xe9, 0xd4, 0xd1, 0xb4, 0x67, 0x3c,
|
||||
0x5a, 0xd2, 0x26, 0x91, 0x95, 0x7d, 0x6a, 0xf5,
|
||||
0xc1, 0x1b, 0x64, 0x21, 0xe0, 0xea, 0x01, 0xd4,
|
||||
0x2c, 0xa4, 0x16, 0x9e, 0x79, 0x18, 0xba, 0x0d,
|
||||
};
|
||||
static const uint8_t point2[32] = {
|
||||
0xe5, 0x21, 0x0f, 0x12, 0x78, 0x68, 0x11, 0xd3,
|
||||
0xf4, 0xb7, 0x95, 0x9d, 0x05, 0x38, 0xae, 0x2c,
|
||||
0x31, 0xdb, 0xe7, 0x10, 0x6f, 0xc0, 0x3c, 0x3e,
|
||||
0xfc, 0x4c, 0xd5, 0x49, 0xc7, 0x15, 0xa4, 0x93,
|
||||
};
|
||||
static const uint8_t expected2[32] = {
|
||||
0x95, 0xcb, 0xde, 0x94, 0x76, 0xe8, 0x90, 0x7d,
|
||||
0x7a, 0xad, 0xe4, 0x5c, 0xb4, 0xb8, 0x73, 0xf8,
|
||||
0x8b, 0x59, 0x5a, 0x68, 0x79, 0x9f, 0xa1, 0x52,
|
||||
0xe6, 0xf8, 0xf7, 0x64, 0x7a, 0xac, 0x79, 0x57,
|
||||
};
|
||||
uint8_t out[32];
|
||||
|
||||
X25519(out, scalar1, point1);
|
||||
|
||||
if (memcmp(expected1, out, sizeof(out)) != 0) {
|
||||
ccprintf("X25519 test one failed.\n");
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
X25519(out, scalar2, point2);
|
||||
|
||||
if (memcmp(expected2, out, sizeof(out)) != 0) {
|
||||
ccprintf("X25519 test two failed.\n");
|
||||
return 0;
|
||||
}
|
||||
|
||||
return 1;
|
||||
}
|
||||
|
||||
static int test_x25519_small_order(void)
|
||||
{
|
||||
static const uint8_t kSmallOrderPoint[32] = {
|
||||
0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae,
|
||||
0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a,
|
||||
0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd,
|
||||
0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8,
|
||||
};
|
||||
uint8_t out[32], private_key[32];
|
||||
|
||||
memset(private_key, 0x11, sizeof(private_key));
|
||||
|
||||
if (X25519(out, private_key, kSmallOrderPoint)) {
|
||||
ccprintf("X25519 returned success with a small-order input.\n");
|
||||
return 0;
|
||||
}
|
||||
|
||||
return 1;
|
||||
}
|
||||
|
||||
static int test_x25519_iterated(void)
|
||||
{
|
||||
/* Taken from https://tools.ietf.org/html/rfc7748#section-5.2 */
|
||||
static const uint8_t expected_1K[32] = {
|
||||
0x68, 0x4c, 0xf5, 0x9b, 0xa8, 0x33, 0x09, 0x55,
|
||||
0x28, 0x00, 0xef, 0x56, 0x6f, 0x2f, 0x4d, 0x3c,
|
||||
0x1c, 0x38, 0x87, 0xc4, 0x93, 0x60, 0xe3, 0x87,
|
||||
0x5f, 0x2e, 0xb9, 0x4d, 0x99, 0x53, 0x2c, 0x51,
|
||||
};
|
||||
#ifdef TEST_X25519_1M_ITERATIONS
|
||||
static const uint8_t expected_1M[32] = {
|
||||
0x7c, 0x39, 0x11, 0xe0, 0xab, 0x25, 0x86, 0xfd,
|
||||
0x86, 0x44, 0x97, 0x29, 0x7e, 0x57, 0x5e, 0x6f,
|
||||
0x3b, 0xc6, 0x01, 0xc0, 0x88, 0x3c, 0x30, 0xdf,
|
||||
0x5f, 0x4d, 0xd2, 0xd2, 0x4f, 0x66, 0x54, 0x24
|
||||
};
|
||||
#endif
|
||||
uint8_t scalar[32] = {9}, point[32] = {9}, out[32];
|
||||
unsigned i;
|
||||
|
||||
for (i = 0; i < 1000; i++) {
|
||||
watchdog_reload();
|
||||
X25519(out, scalar, point);
|
||||
memcpy(point, scalar, sizeof(point));
|
||||
memcpy(scalar, out, sizeof(scalar));
|
||||
}
|
||||
|
||||
if (memcmp(expected_1K, scalar, sizeof(expected_1K)) != 0) {
|
||||
ccprintf("1,000 iterations X25519 test failed\n");
|
||||
return 0;
|
||||
}
|
||||
|
||||
#ifdef TEST_X25519_1M_ITERATIONS
|
||||
for (; i < 1000000; i++) {
|
||||
watchdog_reload();
|
||||
X25519(out, scalar, point);
|
||||
memcpy(point, scalar, sizeof(point));
|
||||
memcpy(scalar, out, sizeof(scalar));
|
||||
if ((i % 10000) == 0)
|
||||
ccprints("%d", i);
|
||||
}
|
||||
|
||||
if (memcmp(expected_1M, scalar, sizeof(expected_1M)) != 0) {
|
||||
ccprintf("1,000,000 iterations X25519 test failed\n");
|
||||
return 0;
|
||||
}
|
||||
#endif
|
||||
|
||||
return 1;
|
||||
}
|
||||
|
||||
static void test_x25519_speed(void)
|
||||
{
|
||||
static const uint8_t scalar1[32] = {
|
||||
0xa5, 0x46, 0xe3, 0x6b, 0xf0, 0x52, 0x7c, 0x9d,
|
||||
0x3b, 0x16, 0x15, 0x4b, 0x82, 0x46, 0x5e, 0xdd,
|
||||
0x62, 0x14, 0x4c, 0x0a, 0xc1, 0xfc, 0x5a, 0x18,
|
||||
0x50, 0x6a, 0x22, 0x44, 0xba, 0x44, 0x9a, 0xc4,
|
||||
};
|
||||
static const uint8_t point1[32] = {
|
||||
0xe6, 0xdb, 0x68, 0x67, 0x58, 0x30, 0x30, 0xdb,
|
||||
0x35, 0x94, 0xc1, 0xa4, 0x24, 0xb1, 0x5f, 0x7c,
|
||||
0x72, 0x66, 0x24, 0xec, 0x26, 0xb3, 0x35, 0x3b,
|
||||
0x10, 0xa9, 0x03, 0xa6, 0xd0, 0xab, 0x1c, 0x4c,
|
||||
};
|
||||
uint8_t out[32];
|
||||
timestamp_t t0, t1;
|
||||
|
||||
X25519(out, scalar1, point1);
|
||||
t0 = get_time();
|
||||
X25519(out, scalar1, point1);
|
||||
t1 = get_time();
|
||||
ccprintf("X25519 duration %lld us\n", (long long)(t1.val - t0.val));
|
||||
}
|
||||
|
||||
void run_test(void)
|
||||
{
|
||||
watchdog_reload();
|
||||
/* do not check speed, just as a benchmark */
|
||||
test_x25519_speed();
|
||||
|
||||
watchdog_reload();
|
||||
if (!test_x25519() || !test_x25519_iterated() ||
|
||||
!test_x25519_small_order()) {
|
||||
test_fail();
|
||||
return;
|
||||
}
|
||||
|
||||
test_pass();
|
||||
}
|
Loading…
Reference in New Issue