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3395 lines
138 KiB
C
3395 lines
138 KiB
C
/*
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* Copyright 2016 The OpenSSL Project Authors. All Rights Reserved.
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*
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* Licensed under the OpenSSL license (the "License"). You may not use
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* this file except in compliance with the License. You can obtain a copy
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* in the file LICENSE in the source distribution or at
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* https://www.openssl.org/source/license.html
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*/
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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).
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*
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* The field functions are shared by Ed25519 and X25519 where possible. */
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#include <string.h>
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#include "ec_lcl.h"
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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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typedef int32_t fe[10];
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static const int64_t kBottom25Bits = 0x1ffffffLL;
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static const int64_t kBottom26Bits = 0x3ffffffLL;
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static const int64_t kTop39Bits = 0xfffffffffe000000LL;
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static const int64_t kTop38Bits = 0xfffffffffc000000LL;
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static uint64_t load_3(const uint8_t *in) {
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uint64_t result;
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result = (uint64_t)in[0];
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result |= ((uint64_t)in[1]) << 8;
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result |= ((uint64_t)in[2]) << 16;
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return result;
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}
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static uint64_t load_4(const uint8_t *in) {
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uint64_t result;
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result = (uint64_t)in[0];
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result |= ((uint64_t)in[1]) << 8;
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result |= ((uint64_t)in[2]) << 16;
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result |= ((uint64_t)in[3]) << 24;
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return result;
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}
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static void fe_frombytes(fe h, const uint8_t *s) {
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/* Ignores top bit of h. */
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int64_t h0 = load_4(s);
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int64_t h1 = load_3(s + 4) << 6;
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int64_t h2 = load_3(s + 7) << 5;
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int64_t h3 = load_3(s + 10) << 3;
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int64_t h4 = load_3(s + 13) << 2;
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int64_t h5 = load_4(s + 16);
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int64_t h6 = load_3(s + 20) << 7;
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int64_t h7 = load_3(s + 23) << 5;
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int64_t h8 = load_3(s + 26) << 4;
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int64_t h9 = (load_3(s + 29) & 8388607) << 2;
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int64_t carry0;
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int64_t carry1;
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int64_t carry2;
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int64_t carry3;
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int64_t carry4;
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int64_t carry5;
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int64_t carry6;
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int64_t carry7;
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int64_t carry8;
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int64_t carry9;
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carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
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carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
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carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
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carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
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carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
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carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
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carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
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carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
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carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
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carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
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h[0] = h0;
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h[1] = h1;
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h[2] = h2;
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h[3] = h3;
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h[4] = h4;
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h[5] = h5;
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h[6] = h6;
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h[7] = h7;
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h[8] = h8;
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h[9] = h9;
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}
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/* Preconditions:
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* |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
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*
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* Write p=2^255-19; q=floor(h/p).
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* Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
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*
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* Proof:
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* Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
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* Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
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*
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* Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
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* Then 0<y<1.
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*
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* Write r=h-pq.
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* Have 0<=r<=p-1=2^255-20.
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* Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
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*
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* Write x=r+19(2^-255)r+y.
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* Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
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*
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* Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
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* so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */
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static void fe_tobytes(uint8_t *s, const fe h) {
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int32_t h0 = h[0];
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int32_t h1 = h[1];
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int32_t h2 = h[2];
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int32_t h3 = h[3];
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int32_t h4 = h[4];
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int32_t h5 = h[5];
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int32_t h6 = h[6];
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int32_t h7 = h[7];
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int32_t h8 = h[8];
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int32_t h9 = h[9];
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int32_t q;
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q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
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q = (h0 + q) >> 26;
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q = (h1 + q) >> 25;
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q = (h2 + q) >> 26;
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q = (h3 + q) >> 25;
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q = (h4 + q) >> 26;
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q = (h5 + q) >> 25;
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q = (h6 + q) >> 26;
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q = (h7 + q) >> 25;
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q = (h8 + q) >> 26;
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q = (h9 + q) >> 25;
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/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
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h0 += 19 * q;
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/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
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h1 += h0 >> 26; h0 &= kBottom26Bits;
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h2 += h1 >> 25; h1 &= kBottom25Bits;
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h3 += h2 >> 26; h2 &= kBottom26Bits;
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h4 += h3 >> 25; h3 &= kBottom25Bits;
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h5 += h4 >> 26; h4 &= kBottom26Bits;
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h6 += h5 >> 25; h5 &= kBottom25Bits;
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h7 += h6 >> 26; h6 &= kBottom26Bits;
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h8 += h7 >> 25; h7 &= kBottom25Bits;
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h9 += h8 >> 26; h8 &= kBottom26Bits;
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h9 &= kBottom25Bits;
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/* h10 = carry9 */
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/* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
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* Have h0+...+2^230 h9 between 0 and 2^255-1;
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* evidently 2^255 h10-2^255 q = 0.
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* Goal: Output h0+...+2^230 h9. */
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s[0] = h0 >> 0;
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s[1] = h0 >> 8;
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s[2] = h0 >> 16;
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s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2);
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s[4] = h1 >> 6;
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s[5] = h1 >> 14;
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s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3);
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s[7] = h2 >> 5;
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s[8] = h2 >> 13;
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s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5);
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s[10] = h3 >> 3;
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s[11] = h3 >> 11;
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s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6);
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s[13] = h4 >> 2;
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s[14] = h4 >> 10;
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s[15] = h4 >> 18;
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s[16] = h5 >> 0;
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s[17] = h5 >> 8;
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s[18] = h5 >> 16;
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s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1);
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s[20] = h6 >> 7;
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s[21] = h6 >> 15;
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s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3);
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s[23] = h7 >> 5;
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s[24] = h7 >> 13;
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s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4);
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s[26] = h8 >> 4;
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s[27] = h8 >> 12;
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s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6);
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s[29] = h9 >> 2;
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s[30] = h9 >> 10;
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s[31] = h9 >> 18;
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}
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/* h = f */
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static void fe_copy(fe h, const fe f) {
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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;
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int64_t f4g1 = f4 * (int64_t) g1;
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int64_t f4g2 = f4 * (int64_t) g2;
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int64_t f4g3 = f4 * (int64_t) g3;
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int64_t f4g4 = f4 * (int64_t) g4;
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int64_t f4g5 = f4 * (int64_t) g5;
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int64_t f4g6_19 = f4 * (int64_t) g6_19;
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int64_t f4g7_19 = f4 * (int64_t) g7_19;
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int64_t f4g8_19 = f4 * (int64_t) g8_19;
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int64_t f4g9_19 = f4 * (int64_t) g9_19;
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int64_t f5g0 = f5 * (int64_t) g0;
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int64_t f5g1_2 = f5_2 * (int64_t) g1;
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int64_t f5g2 = f5 * (int64_t) g2;
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int64_t f5g3_2 = f5_2 * (int64_t) g3;
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int64_t f5g4 = f5 * (int64_t) g4;
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int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
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int64_t f5g6_19 = f5 * (int64_t) g6_19;
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int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
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int64_t f5g8_19 = f5 * (int64_t) g8_19;
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int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
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int64_t f6g0 = f6 * (int64_t) g0;
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int64_t f6g1 = f6 * (int64_t) g1;
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int64_t f6g2 = f6 * (int64_t) g2;
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int64_t f6g3 = f6 * (int64_t) g3;
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int64_t f6g4_19 = f6 * (int64_t) g4_19;
|
|
int64_t f6g5_19 = f6 * (int64_t) g5_19;
|
|
int64_t f6g6_19 = f6 * (int64_t) g6_19;
|
|
int64_t f6g7_19 = f6 * (int64_t) g7_19;
|
|
int64_t f6g8_19 = f6 * (int64_t) g8_19;
|
|
int64_t f6g9_19 = f6 * (int64_t) g9_19;
|
|
int64_t f7g0 = f7 * (int64_t) g0;
|
|
int64_t f7g1_2 = f7_2 * (int64_t) g1;
|
|
int64_t f7g2 = f7 * (int64_t) g2;
|
|
int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
|
|
int64_t f7g4_19 = f7 * (int64_t) g4_19;
|
|
int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
|
|
int64_t f7g6_19 = f7 * (int64_t) g6_19;
|
|
int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
|
|
int64_t f7g8_19 = f7 * (int64_t) g8_19;
|
|
int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
|
|
int64_t f8g0 = f8 * (int64_t) g0;
|
|
int64_t f8g1 = f8 * (int64_t) g1;
|
|
int64_t f8g2_19 = f8 * (int64_t) g2_19;
|
|
int64_t f8g3_19 = f8 * (int64_t) g3_19;
|
|
int64_t f8g4_19 = f8 * (int64_t) g4_19;
|
|
int64_t f8g5_19 = f8 * (int64_t) g5_19;
|
|
int64_t f8g6_19 = f8 * (int64_t) g6_19;
|
|
int64_t f8g7_19 = f8 * (int64_t) g7_19;
|
|
int64_t f8g8_19 = f8 * (int64_t) g8_19;
|
|
int64_t f8g9_19 = f8 * (int64_t) g9_19;
|
|
int64_t f9g0 = f9 * (int64_t) g0;
|
|
int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
|
|
int64_t f9g2_19 = f9 * (int64_t) g2_19;
|
|
int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
|
|
int64_t f9g4_19 = f9 * (int64_t) g4_19;
|
|
int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
|
|
int64_t f9g6_19 = f9 * (int64_t) g6_19;
|
|
int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
|
|
int64_t f9g8_19 = f9 * (int64_t) g8_19;
|
|
int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
|
|
int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
|
|
int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
|
|
int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
|
|
int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
|
|
int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
|
|
int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
|
|
int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
|
|
int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
|
|
int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
|
|
int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
|
|
int64_t carry0;
|
|
int64_t carry1;
|
|
int64_t carry2;
|
|
int64_t carry3;
|
|
int64_t carry4;
|
|
int64_t carry5;
|
|
int64_t carry6;
|
|
int64_t carry7;
|
|
int64_t carry8;
|
|
int64_t carry9;
|
|
|
|
/* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
|
|
* i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
|
|
* |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
|
|
* i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
|
|
|
|
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
|
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
|
/* |h0| <= 2^25 */
|
|
/* |h4| <= 2^25 */
|
|
/* |h1| <= 1.71*2^59 */
|
|
/* |h5| <= 1.71*2^59 */
|
|
|
|
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
|
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
|
|
/* |h1| <= 2^24; from now on fits into int32 */
|
|
/* |h5| <= 2^24; from now on fits into int32 */
|
|
/* |h2| <= 1.41*2^60 */
|
|
/* |h6| <= 1.41*2^60 */
|
|
|
|
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
|
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
|
|
/* |h2| <= 2^25; from now on fits into int32 unchanged */
|
|
/* |h6| <= 2^25; from now on fits into int32 unchanged */
|
|
/* |h3| <= 1.71*2^59 */
|
|
/* |h7| <= 1.71*2^59 */
|
|
|
|
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
|
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
|
|
/* |h3| <= 2^24; from now on fits into int32 unchanged */
|
|
/* |h7| <= 2^24; from now on fits into int32 unchanged */
|
|
/* |h4| <= 1.72*2^34 */
|
|
/* |h8| <= 1.41*2^60 */
|
|
|
|
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
|
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
|
|
/* |h4| <= 2^25; from now on fits into int32 unchanged */
|
|
/* |h8| <= 2^25; from now on fits into int32 unchanged */
|
|
/* |h5| <= 1.01*2^24 */
|
|
/* |h9| <= 1.71*2^59 */
|
|
|
|
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
|
|
/* |h9| <= 2^24; from now on fits into int32 unchanged */
|
|
/* |h0| <= 1.1*2^39 */
|
|
|
|
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
|
/* |h0| <= 2^25; from now on fits into int32 unchanged */
|
|
/* |h1| <= 1.01*2^24 */
|
|
|
|
h[0] = h0;
|
|
h[1] = h1;
|
|
h[2] = h2;
|
|
h[3] = h3;
|
|
h[4] = h4;
|
|
h[5] = h5;
|
|
h[6] = h6;
|
|
h[7] = h7;
|
|
h[8] = h8;
|
|
h[9] = h9;
|
|
}
|
|
|
|
/* h = f * f
|
|
* Can overlap h with f.
|
|
*
|
|
* Preconditions:
|
|
* |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
|
|
*
|
|
* Postconditions:
|
|
* |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
|
|
*
|
|
* See fe_mul.c for discussion of implementation strategy. */
|
|
static void fe_sq(fe h, const fe f) {
|
|
int32_t f0 = f[0];
|
|
int32_t f1 = f[1];
|
|
int32_t f2 = f[2];
|
|
int32_t f3 = f[3];
|
|
int32_t f4 = f[4];
|
|
int32_t f5 = f[5];
|
|
int32_t f6 = f[6];
|
|
int32_t f7 = f[7];
|
|
int32_t f8 = f[8];
|
|
int32_t f9 = f[9];
|
|
int32_t f0_2 = 2 * f0;
|
|
int32_t f1_2 = 2 * f1;
|
|
int32_t f2_2 = 2 * f2;
|
|
int32_t f3_2 = 2 * f3;
|
|
int32_t f4_2 = 2 * f4;
|
|
int32_t f5_2 = 2 * f5;
|
|
int32_t f6_2 = 2 * f6;
|
|
int32_t f7_2 = 2 * f7;
|
|
int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
|
|
int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
|
|
int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
|
|
int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
|
|
int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
|
|
int64_t f0f0 = f0 * (int64_t) f0;
|
|
int64_t f0f1_2 = f0_2 * (int64_t) f1;
|
|
int64_t f0f2_2 = f0_2 * (int64_t) f2;
|
|
int64_t f0f3_2 = f0_2 * (int64_t) f3;
|
|
int64_t f0f4_2 = f0_2 * (int64_t) f4;
|
|
int64_t f0f5_2 = f0_2 * (int64_t) f5;
|
|
int64_t f0f6_2 = f0_2 * (int64_t) f6;
|
|
int64_t f0f7_2 = f0_2 * (int64_t) f7;
|
|
int64_t f0f8_2 = f0_2 * (int64_t) f8;
|
|
int64_t f0f9_2 = f0_2 * (int64_t) f9;
|
|
int64_t f1f1_2 = f1_2 * (int64_t) f1;
|
|
int64_t f1f2_2 = f1_2 * (int64_t) f2;
|
|
int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
|
|
int64_t f1f4_2 = f1_2 * (int64_t) f4;
|
|
int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
|
|
int64_t f1f6_2 = f1_2 * (int64_t) f6;
|
|
int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
|
|
int64_t f1f8_2 = f1_2 * (int64_t) f8;
|
|
int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
|
|
int64_t f2f2 = f2 * (int64_t) f2;
|
|
int64_t f2f3_2 = f2_2 * (int64_t) f3;
|
|
int64_t f2f4_2 = f2_2 * (int64_t) f4;
|
|
int64_t f2f5_2 = f2_2 * (int64_t) f5;
|
|
int64_t f2f6_2 = f2_2 * (int64_t) f6;
|
|
int64_t f2f7_2 = f2_2 * (int64_t) f7;
|
|
int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
|
|
int64_t f2f9_38 = f2 * (int64_t) f9_38;
|
|
int64_t f3f3_2 = f3_2 * (int64_t) f3;
|
|
int64_t f3f4_2 = f3_2 * (int64_t) f4;
|
|
int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
|
|
int64_t f3f6_2 = f3_2 * (int64_t) f6;
|
|
int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
|
|
int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
|
|
int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
|
|
int64_t f4f4 = f4 * (int64_t) f4;
|
|
int64_t f4f5_2 = f4_2 * (int64_t) f5;
|
|
int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
|
|
int64_t f4f7_38 = f4 * (int64_t) f7_38;
|
|
int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
|
|
int64_t f4f9_38 = f4 * (int64_t) f9_38;
|
|
int64_t f5f5_38 = f5 * (int64_t) f5_38;
|
|
int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
|
|
int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
|
|
int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
|
|
int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
|
|
int64_t f6f6_19 = f6 * (int64_t) f6_19;
|
|
int64_t f6f7_38 = f6 * (int64_t) f7_38;
|
|
int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
|
|
int64_t f6f9_38 = f6 * (int64_t) f9_38;
|
|
int64_t f7f7_38 = f7 * (int64_t) f7_38;
|
|
int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
|
|
int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
|
|
int64_t f8f8_19 = f8 * (int64_t) f8_19;
|
|
int64_t f8f9_38 = f8 * (int64_t) f9_38;
|
|
int64_t f9f9_38 = f9 * (int64_t) f9_38;
|
|
int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
|
|
int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
|
|
int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
|
|
int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
|
|
int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
|
|
int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
|
|
int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
|
|
int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
|
|
int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
|
|
int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
|
|
int64_t carry0;
|
|
int64_t carry1;
|
|
int64_t carry2;
|
|
int64_t carry3;
|
|
int64_t carry4;
|
|
int64_t carry5;
|
|
int64_t carry6;
|
|
int64_t carry7;
|
|
int64_t carry8;
|
|
int64_t carry9;
|
|
|
|
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
|
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
|
|
|
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
|
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
|
|
|
|
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
|
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
|
|
|
|
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
|
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
|
|
|
|
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
|
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
|
|
|
|
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
|
|
|
|
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
|
|
|
h[0] = h0;
|
|
h[1] = h1;
|
|
h[2] = h2;
|
|
h[3] = h3;
|
|
h[4] = h4;
|
|
h[5] = h5;
|
|
h[6] = h6;
|
|
h[7] = h7;
|
|
h[8] = h8;
|
|
h[9] = h9;
|
|
}
|
|
|
|
static void fe_invert(fe out, const fe z) {
|
|
fe t0;
|
|
fe t1;
|
|
fe t2;
|
|
fe t3;
|
|
int i;
|
|
|
|
/*
|
|
* Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
|
|
* 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
|
|
*/
|
|
|
|
/* t0 = z ** 2 */
|
|
fe_sq(t0, z);
|
|
|
|
/* t1 = t0 ** (2 ** 2) = z ** 8 */
|
|
fe_sq(t1, t0);
|
|
fe_sq(t1, t1);
|
|
|
|
/* t1 = z * t1 = z ** 9 */
|
|
fe_mul(t1, z, t1);
|
|
/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
|
|
fe_mul(t0, t0, t1);
|
|
|
|
/* t2 = t0 ** 2 = z ** 22 */
|
|
fe_sq(t2, t0);
|
|
|
|
/* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
|
|
fe_mul(t1, t1, t2);
|
|
|
|
/* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
|
|
fe_sq(t2, t1);
|
|
for (i = 1; i < 5; ++i) {
|
|
fe_sq(t2, t2);
|
|
}
|
|
|
|
/* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
|
|
fe_mul(t1, t2, t1);
|
|
|
|
/* Continuing similarly... */
|
|
|
|
/* t2 = z ** (2 ** 20 - 1) */
|
|
fe_sq(t2, t1);
|
|
for (i = 1; i < 10; ++i) {
|
|
fe_sq(t2, t2);
|
|
}
|
|
fe_mul(t2, t2, t1);
|
|
|
|
/* t2 = z ** (2 ** 40 - 1) */
|
|
fe_sq(t3, t2);
|
|
for (i = 1; i < 20; ++i) {
|
|
fe_sq(t3, t3);
|
|
}
|
|
fe_mul(t2, t3, t2);
|
|
|
|
/* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
|
|
for (i = 0; i < 10; ++i) {
|
|
fe_sq(t2, t2);
|
|
}
|
|
/* t1 = z ** (2 ** 50 - 1) */
|
|
fe_mul(t1, t2, t1);
|
|
|
|
/* t2 = z ** (2 ** 100 - 1) */
|
|
fe_sq(t2, t1);
|
|
for (i = 1; i < 50; ++i) {
|
|
fe_sq(t2, t2);
|
|
}
|
|
fe_mul(t2, t2, t1);
|
|
|
|
/* t2 = z ** (2 ** 200 - 1) */
|
|
fe_sq(t3, t2);
|
|
for (i = 1; i < 100; ++i) {
|
|
fe_sq(t3, t3);
|
|
}
|
|
fe_mul(t2, t3, t2);
|
|
|
|
/* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
|
|
fe_sq(t2, t2);
|
|
for (i = 1; i < 50; ++i) {
|
|
fe_sq(t2, t2);
|
|
}
|
|
|
|
/* t1 = z ** (2 ** 250 - 1) */
|
|
fe_mul(t1, t2, t1);
|
|
|
|
/* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
|
|
fe_sq(t1, t1);
|
|
for (i = 1; i < 5; ++i) {
|
|
fe_sq(t1, t1);
|
|
}
|
|
|
|
/* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
|
|
fe_mul(out, t1, t0);
|
|
}
|
|
|
|
/* h = -f
|
|
*
|
|
* Preconditions:
|
|
* |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|
|
*
|
|
* Postconditions:
|
|
* |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
|
|
static void fe_neg(fe h, const fe f) {
|
|
unsigned i;
|
|
for (i = 0; i < 10; i++) {
|
|
h[i] = -f[i];
|
|
}
|
|
}
|
|
|
|
/* Replace (f,g) with (g,g) if b == 1;
|
|
* replace (f,g) with (f,g) if b == 0.
|
|
*
|
|
* Preconditions: b in {0,1}. */
|
|
static void fe_cmov(fe f, const fe g, unsigned b) {
|
|
size_t i;
|
|
b = 0-b;
|
|
for (i = 0; i < 10; i++) {
|
|
int32_t x = f[i] ^ g[i];
|
|
x &= b;
|
|
f[i] ^= x;
|
|
}
|
|
}
|
|
|
|
/* h = 2 * f * f
|
|
* Can overlap h with f.
|
|
*
|
|
* Preconditions:
|
|
* |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
|
|
*
|
|
* Postconditions:
|
|
* |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
|
|
*
|
|
* See fe_mul.c for discussion of implementation strategy. */
|
|
static void fe_sq2(fe h, const fe f) {
|
|
int32_t f0 = f[0];
|
|
int32_t f1 = f[1];
|
|
int32_t f2 = f[2];
|
|
int32_t f3 = f[3];
|
|
int32_t f4 = f[4];
|
|
int32_t f5 = f[5];
|
|
int32_t f6 = f[6];
|
|
int32_t f7 = f[7];
|
|
int32_t f8 = f[8];
|
|
int32_t f9 = f[9];
|
|
int32_t f0_2 = 2 * f0;
|
|
int32_t f1_2 = 2 * f1;
|
|
int32_t f2_2 = 2 * f2;
|
|
int32_t f3_2 = 2 * f3;
|
|
int32_t f4_2 = 2 * f4;
|
|
int32_t f5_2 = 2 * f5;
|
|
int32_t f6_2 = 2 * f6;
|
|
int32_t f7_2 = 2 * f7;
|
|
int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
|
|
int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
|
|
int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
|
|
int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
|
|
int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
|
|
int64_t f0f0 = f0 * (int64_t) f0;
|
|
int64_t f0f1_2 = f0_2 * (int64_t) f1;
|
|
int64_t f0f2_2 = f0_2 * (int64_t) f2;
|
|
int64_t f0f3_2 = f0_2 * (int64_t) f3;
|
|
int64_t f0f4_2 = f0_2 * (int64_t) f4;
|
|
int64_t f0f5_2 = f0_2 * (int64_t) f5;
|
|
int64_t f0f6_2 = f0_2 * (int64_t) f6;
|
|
int64_t f0f7_2 = f0_2 * (int64_t) f7;
|
|
int64_t f0f8_2 = f0_2 * (int64_t) f8;
|
|
int64_t f0f9_2 = f0_2 * (int64_t) f9;
|
|
int64_t f1f1_2 = f1_2 * (int64_t) f1;
|
|
int64_t f1f2_2 = f1_2 * (int64_t) f2;
|
|
int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
|
|
int64_t f1f4_2 = f1_2 * (int64_t) f4;
|
|
int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
|
|
int64_t f1f6_2 = f1_2 * (int64_t) f6;
|
|
int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
|
|
int64_t f1f8_2 = f1_2 * (int64_t) f8;
|
|
int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
|
|
int64_t f2f2 = f2 * (int64_t) f2;
|
|
int64_t f2f3_2 = f2_2 * (int64_t) f3;
|
|
int64_t f2f4_2 = f2_2 * (int64_t) f4;
|
|
int64_t f2f5_2 = f2_2 * (int64_t) f5;
|
|
int64_t f2f6_2 = f2_2 * (int64_t) f6;
|
|
int64_t f2f7_2 = f2_2 * (int64_t) f7;
|
|
int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
|
|
int64_t f2f9_38 = f2 * (int64_t) f9_38;
|
|
int64_t f3f3_2 = f3_2 * (int64_t) f3;
|
|
int64_t f3f4_2 = f3_2 * (int64_t) f4;
|
|
int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
|
|
int64_t f3f6_2 = f3_2 * (int64_t) f6;
|
|
int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
|
|
int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
|
|
int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
|
|
int64_t f4f4 = f4 * (int64_t) f4;
|
|
int64_t f4f5_2 = f4_2 * (int64_t) f5;
|
|
int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
|
|
int64_t f4f7_38 = f4 * (int64_t) f7_38;
|
|
int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
|
|
int64_t f4f9_38 = f4 * (int64_t) f9_38;
|
|
int64_t f5f5_38 = f5 * (int64_t) f5_38;
|
|
int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
|
|
int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
|
|
int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
|
|
int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
|
|
int64_t f6f6_19 = f6 * (int64_t) f6_19;
|
|
int64_t f6f7_38 = f6 * (int64_t) f7_38;
|
|
int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
|
|
int64_t f6f9_38 = f6 * (int64_t) f9_38;
|
|
int64_t f7f7_38 = f7 * (int64_t) f7_38;
|
|
int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
|
|
int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
|
|
int64_t f8f8_19 = f8 * (int64_t) f8_19;
|
|
int64_t f8f9_38 = f8 * (int64_t) f9_38;
|
|
int64_t f9f9_38 = f9 * (int64_t) f9_38;
|
|
int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
|
|
int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
|
|
int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
|
|
int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
|
|
int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
|
|
int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
|
|
int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
|
|
int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
|
|
int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
|
|
int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
|
|
int64_t carry0;
|
|
int64_t carry1;
|
|
int64_t carry2;
|
|
int64_t carry3;
|
|
int64_t carry4;
|
|
int64_t carry5;
|
|
int64_t carry6;
|
|
int64_t carry7;
|
|
int64_t carry8;
|
|
int64_t carry9;
|
|
|
|
h0 += h0;
|
|
h1 += h1;
|
|
h2 += h2;
|
|
h3 += h3;
|
|
h4 += h4;
|
|
h5 += h5;
|
|
h6 += h6;
|
|
h7 += h7;
|
|
h8 += h8;
|
|
h9 += h9;
|
|
|
|
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
|
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
|
|
|
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
|
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
|
|
|
|
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
|
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
|
|
|
|
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
|
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
|
|
|
|
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
|
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
|
|
|
|
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
|
|
|
|
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
|
|
|
h[0] = h0;
|
|
h[1] = h1;
|
|
h[2] = h2;
|
|
h[3] = h3;
|
|
h[4] = h4;
|
|
h[5] = h5;
|
|
h[6] = h6;
|
|
h[7] = h7;
|
|
h[8] = h8;
|
|
h[9] = h9;
|
|
}
|
|
|
|
/* ge means group element.
|
|
|
|
* Here the group is the set of pairs (x,y) of field elements (see fe.h)
|
|
* satisfying -x^2 + y^2 = 1 + d x^2y^2
|
|
* where d = -121665/121666.
|
|
*
|
|
* Representations:
|
|
* ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
|
|
* ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
|
|
* ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
|
|
* ge_precomp (Duif): (y+x,y-x,2dxy) */
|
|
|
|
typedef struct {
|
|
fe X;
|
|
fe Y;
|
|
fe Z;
|
|
} ge_p2;
|
|
|
|
typedef struct {
|
|
fe X;
|
|
fe Y;
|
|
fe Z;
|
|
fe T;
|
|
} ge_p3;
|
|
|
|
typedef struct {
|
|
fe X;
|
|
fe Y;
|
|
fe Z;
|
|
fe T;
|
|
} ge_p1p1;
|
|
|
|
typedef struct {
|
|
fe yplusx;
|
|
fe yminusx;
|
|
fe xy2d;
|
|
} ge_precomp;
|
|
|
|
typedef struct {
|
|
fe YplusX;
|
|
fe YminusX;
|
|
fe Z;
|
|
fe T2d;
|
|
} ge_cached;
|
|
|
|
static void ge_p3_0(ge_p3 *h) {
|
|
fe_0(h->X);
|
|
fe_1(h->Y);
|
|
fe_1(h->Z);
|
|
fe_0(h->T);
|
|
}
|
|
|
|
static void ge_precomp_0(ge_precomp *h) {
|
|
fe_1(h->yplusx);
|
|
fe_1(h->yminusx);
|
|
fe_0(h->xy2d);
|
|
}
|
|
|
|
/* r = p */
|
|
static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
|
|
fe_copy(r->X, p->X);
|
|
fe_copy(r->Y, p->Y);
|
|
fe_copy(r->Z, p->Z);
|
|
}
|
|
|
|
/* r = p */
|
|
static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
|
|
fe_mul(r->X, p->X, p->T);
|
|
fe_mul(r->Y, p->Y, p->Z);
|
|
fe_mul(r->Z, p->Z, p->T);
|
|
}
|
|
|
|
/* r = p */
|
|
static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
|
|
fe_mul(r->X, p->X, p->T);
|
|
fe_mul(r->Y, p->Y, p->Z);
|
|
fe_mul(r->Z, p->Z, p->T);
|
|
fe_mul(r->T, p->X, p->Y);
|
|
}
|
|
|
|
/* r = 2 * p */
|
|
static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
|
|
fe t0;
|
|
|
|
fe_sq(r->X, p->X);
|
|
fe_sq(r->Z, p->Y);
|
|
fe_sq2(r->T, p->Z);
|
|
fe_add(r->Y, p->X, p->Y);
|
|
fe_sq(t0, r->Y);
|
|
fe_add(r->Y, r->Z, r->X);
|
|
fe_sub(r->Z, r->Z, r->X);
|
|
fe_sub(r->X, t0, r->Y);
|
|
fe_sub(r->T, r->T, r->Z);
|
|
}
|
|
|
|
/* r = 2 * p */
|
|
static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
|
|
ge_p2 q;
|
|
ge_p3_to_p2(&q, p);
|
|
ge_p2_dbl(r, &q);
|
|
}
|
|
|
|
/* r = p + q */
|
|
static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
|
|
fe t0;
|
|
|
|
fe_add(r->X, p->Y, p->X);
|
|
fe_sub(r->Y, p->Y, p->X);
|
|
fe_mul(r->Z, r->X, q->yplusx);
|
|
fe_mul(r->Y, r->Y, q->yminusx);
|
|
fe_mul(r->T, q->xy2d, p->T);
|
|
fe_add(t0, p->Z, p->Z);
|
|
fe_sub(r->X, r->Z, r->Y);
|
|
fe_add(r->Y, r->Z, r->Y);
|
|
fe_add(r->Z, t0, r->T);
|
|
fe_sub(r->T, t0, r->T);
|
|
}
|
|
|
|
static uint8_t equal(signed char b, signed char c) {
|
|
uint8_t ub = b;
|
|
uint8_t uc = c;
|
|
uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
|
|
uint32_t y = x; /* 0: yes; 1..255: no */
|
|
y -= 1; /* 4294967295: yes; 0..254: no */
|
|
y >>= 31; /* 1: yes; 0: no */
|
|
return y;
|
|
}
|
|
|
|
static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) {
|
|
fe_cmov(t->yplusx, u->yplusx, b);
|
|
fe_cmov(t->yminusx, u->yminusx, b);
|
|
fe_cmov(t->xy2d, u->xy2d, b);
|
|
}
|
|
|
|
/* k25519Precomp[i][j] = (j+1)*256^i*B */
|
|
static const ge_precomp k25519Precomp[32][8] = {
|
|
{
|
|
{
|
|
{25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
|
|
27544626, -11754271, -6079156, 2047605},
|
|
{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
|
|
5043384, 19500929, -15469378},
|
|
{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
|
|
29287919, 11864899, -24514362, -4438546},
|
|
},
|
|
{
|
|
{-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
|
|
-11717903, -3814571, -358445, -10211303},
|
|
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|
|
-7467973, -7337524, 31809243, 7347066},
|
|
},
|
|
{
|
|
{-9606723, -11874240, 20414459, 13033986, 13716524, -11691881,
|
|
19797970, -12211255, 15192876, -2087490},
|
|
{-12663563, -2181719, 1168162, -3804809, 26747877, -14138091,
|
|
10609330, 12694420, 33473243, -13382104},
|
|
{33184999, 11180355, 15832085, -11385430, -1633671, 225884,
|
|
15089336, -11023903, -6135662, 14480053},
|
|
},
|
|
{
|
|
{31308717, -5619998, 31030840, -1897099, 15674547, -6582883,
|
|
5496208, 13685227, 27595050, 8737275},
|
|
{-20318852, -15150239, 10933843, -16178022, 8335352, -7546022,
|
|
-31008351, -12610604, 26498114, 66511},
|
|
{22644454, -8761729, -16671776, 4884562, -3105614, -13559366,
|
|
30540766, -4286747, -13327787, -7515095},
|
|
},
|
|
{
|
|
{-28017847, 9834845, 18617207, -2681312, -3401956, -13307506,
|
|
8205540, 13585437, -17127465, 15115439},
|
|
{23711543, -672915, 31206561, -8362711, 6164647, -9709987,
|
|
-33535882, -1426096, 8236921, 16492939},
|
|
{-23910559, -13515526, -26299483, -4503841, 25005590, -7687270,
|
|
19574902, 10071562, 6708380, -6222424},
|
|
},
|
|
{
|
|
{2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017,
|
|
9328700, 29955601, -11678310},
|
|
{3096359, 9271816, -21620864, -15521844, -14847996, -7592937,
|
|
-25892142, -12635595, -9917575, 6216608},
|
|
{-32615849, 338663, -25195611, 2510422, -29213566, -13820213,
|
|
24822830, -6146567, -26767480, 7525079},
|
|
},
|
|
{
|
|
{-23066649, -13985623, 16133487, -7896178, -3389565, 778788,
|
|
-910336, -2782495, -19386633, 11994101},
|
|
{21691500, -13624626, -641331, -14367021, 3285881, -3483596,
|
|
-25064666, 9718258, -7477437, 13381418},
|
|
{18445390, -4202236, 14979846, 11622458, -1727110, -3582980,
|
|
23111648, -6375247, 28535282, 15779576},
|
|
},
|
|
{
|
|
{30098053, 3089662, -9234387, 16662135, -21306940, 11308411,
|
|
-14068454, 12021730, 9955285, -16303356},
|
|
{9734894, -14576830, -7473633, -9138735, 2060392, 11313496,
|
|
-18426029, 9924399, 20194861, 13380996},
|
|
{-26378102, -7965207, -22167821, 15789297, -18055342, -6168792,
|
|
-1984914, 15707771, 26342023, 10146099},
|
|
},
|
|
},
|
|
{
|
|
{
|
|
{-26016874, -219943, 21339191, -41388, 19745256, -2878700,
|
|
-29637280, 2227040, 21612326, -545728},
|
|
{-13077387, 1184228, 23562814, -5970442, -20351244, -6348714,
|
|
25764461, 12243797, -20856566, 11649658},
|
|
{-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944,
|
|
6114064, 33514190, 2333242},
|
|
},
|
|
{
|
|
{-21433588, -12421821, 8119782, 7219913, -21830522, -9016134,
|
|
-6679750, -12670638, 24350578, -13450001},
|
|
{-4116307, -11271533, -23886186, 4843615, -30088339, 690623,
|
|
-31536088, -10406836, 8317860, 12352766},
|
|
{18200138, -14475911, -33087759, -2696619, -23702521, -9102511,
|
|
-23552096, -2287550, 20712163, 6719373},
|
|
},
|
|
{
|
|
{26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530,
|
|
-3763210, 26224235, -3297458},
|
|
{-17168938, -14854097, -3395676, -16369877, -19954045, 14050420,
|
|
21728352, 9493610, 18620611, -16428628},
|
|
{-13323321, 13325349, 11432106, 5964811, 18609221, 6062965,
|
|
-5269471, -9725556, -30701573, -16479657},
|
|
},
|
|
{
|
|
{-23860538, -11233159, 26961357, 1640861, -32413112, -16737940,
|
|
12248509, -5240639, 13735342, 1934062},
|
|
{25089769, 6742589, 17081145, -13406266, 21909293, -16067981,
|
|
-15136294, -3765346, -21277997, 5473616},
|
|
{31883677, -7961101, 1083432, -11572403, 22828471, 13290673,
|
|
-7125085, 12469656, 29111212, -5451014},
|
|
},
|
|
{
|
|
{24244947, -15050407, -26262976, 2791540, -14997599, 16666678,
|
|
24367466, 6388839, -10295587, 452383},
|
|
{-25640782, -3417841, 5217916, 16224624, 19987036, -4082269,
|
|
-24236251, -5915248, 15766062, 8407814},
|
|
{-20406999, 13990231, 15495425, 16395525, 5377168, 15166495,
|
|
-8917023, -4388953, -8067909, 2276718},
|
|
},
|
|
{
|
|
{30157918, 12924066, -17712050, 9245753, 19895028, 3368142,
|
|
-23827587, 5096219, 22740376, -7303417},
|
|
{2041139, -14256350, 7783687, 13876377, -25946985, -13352459,
|
|
24051124, 13742383, -15637599, 13295222},
|
|
{33338237, -8505733, 12532113, 7977527, 9106186, -1715251,
|
|
-17720195, -4612972, -4451357, -14669444},
|
|
},
|
|
{
|
|
{-20045281, 5454097, -14346548, 6447146, 28862071, 1883651,
|
|
-2469266, -4141880, 7770569, 9620597},
|
|
{23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528,
|
|
-1694323, -33502340, -14767970},
|
|
{1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801,
|
|
1220118, 30494170, -11440799},
|
|
},
|
|
{
|
|
{-5037580, -13028295, -2970559, -3061767, 15640974, -6701666,
|
|
-26739026, 926050, -1684339, -13333647},
|
|
{13908495, -3549272, 30919928, -6273825, -21521863, 7989039,
|
|
9021034, 9078865, 3353509, 4033511},
|
|
{-29663431, -15113610, 32259991, -344482, 24295849, -12912123,
|
|
23161163, 8839127, 27485041, 7356032},
|
|
},
|
|
},
|
|
{
|
|
{
|
|
{9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
|
|
2625015, 28431036, -16771834},
|
|
{-23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
|
|
-22545972, 14150565, 15970762, 4099461},
|
|
{29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
|
|
13617293, -9937143, 11465739, 8317062},
|
|
},
|
|
{
|
|
{-25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
|
|
14898637, 3848455, 20969334, -5157516},
|
|
{-20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
|
|
-21610826, -3649888, 11177095, 14989547},
|
|
{-24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
|
|
13515641, 2581286, -28487508, 9930240},
|
|
},
|
|
{
|
|
{-17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
|
|
18345767, -13403753, 16291481, -5314038},
|
|
{-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
|
|
6957617, 4368891, 9788741},
|
|
{16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
|
|
-21722536, -8613148, 16250552, -11111103},
|
|
},
|
|
{
|
|
{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
|
|
10604807, -30190403, 4782747},
|
|
{-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
|
|
-9981571, 4383045, 22546403, 437323},
|
|
{31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
|
|
27343084, 2786261, -30633590, -14097016},
|
|
},
|
|
{
|
|
{-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
|
|
-19690631, 2355319, -19284671, -6114373},
|
|
{15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
|
|
18952177, 15496498, -29380133, 11754228},
|
|
{-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
|
|
7141596, 11724556, 22761615, -10134141},
|
|
},
|
|
{
|
|
{16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
|
|
-28741185, -12227393, 32851222, 11717399},
|
|
{11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
|
|
31474879, 3483633, -1193175, -4030831},
|
|
{-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
|
|
33142652, 6546660, -19985279, -3948376},
|
|
},
|
|
{
|
|
{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
|
|
-8537131, -12833048, -30772034, -15486313},
|
|
{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
|
|
-31135347, -16049879, 10928917, 3011958},
|
|
{-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
|
|
-30831056, -12805180, 18008031, 10258577},
|
|
},
|
|
{
|
|
{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
|
|
-1853465, 1367120, 25127874, 6671743},
|
|
{29701166, -14373934, -10878120, 9279288, -17568, 13127210,
|
|
21382910, 11042292, 25838796, 4642684},
|
|
{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
|
|
30468147, -13900640, 18423289, 4177476},
|
|
},
|
|
},
|
|
};
|
|
|
|
static uint8_t negative(signed char b) {
|
|
uint32_t x = b;
|
|
x >>= 31; /* 1: yes; 0: no */
|
|
return x;
|
|
}
|
|
|
|
static void table_select(ge_precomp *t, int pos, signed char b) {
|
|
ge_precomp minust;
|
|
uint8_t bnegative = negative(b);
|
|
uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
|
|
|
|
ge_precomp_0(t);
|
|
cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
|
|
cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
|
|
cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
|
|
cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
|
|
cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
|
|
cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
|
|
cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
|
|
cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
|
|
fe_copy(minust.yplusx, t->yminusx);
|
|
fe_copy(minust.yminusx, t->yplusx);
|
|
fe_neg(minust.xy2d, t->xy2d);
|
|
cmov(t, &minust, bnegative);
|
|
}
|
|
|
|
/* h = a * B
|
|
* where a = a[0]+256*a[1]+...+256^31 a[31]
|
|
* B is the Ed25519 base point (x,4/5) with x positive.
|
|
*
|
|
* Preconditions:
|
|
* a[31] <= 127 */
|
|
static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) {
|
|
signed char e[64];
|
|
signed char carry;
|
|
ge_p1p1 r;
|
|
ge_p2 s;
|
|
ge_precomp t;
|
|
int i;
|
|
|
|
for (i = 0; i < 32; ++i) {
|
|
e[2 * i + 0] = (a[i] >> 0) & 15;
|
|
e[2 * i + 1] = (a[i] >> 4) & 15;
|
|
}
|
|
/* each e[i] is between 0 and 15 */
|
|
/* e[63] is between 0 and 7 */
|
|
|
|
carry = 0;
|
|
for (i = 0; i < 63; ++i) {
|
|
e[i] += carry;
|
|
carry = e[i] + 8;
|
|
carry >>= 4;
|
|
e[i] -= carry << 4;
|
|
}
|
|
e[63] += carry;
|
|
/* each e[i] is between -8 and 8 */
|
|
|
|
ge_p3_0(h);
|
|
for (i = 1; i < 64; i += 2) {
|
|
table_select(&t, i / 2, e[i]);
|
|
ge_madd(&r, h, &t);
|
|
ge_p1p1_to_p3(h, &r);
|
|
}
|
|
|
|
ge_p3_dbl(&r, h);
|
|
ge_p1p1_to_p2(&s, &r);
|
|
ge_p2_dbl(&r, &s);
|
|
ge_p1p1_to_p2(&s, &r);
|
|
ge_p2_dbl(&r, &s);
|
|
ge_p1p1_to_p2(&s, &r);
|
|
ge_p2_dbl(&r, &s);
|
|
ge_p1p1_to_p3(h, &r);
|
|
|
|
for (i = 0; i < 64; i += 2) {
|
|
table_select(&t, i / 2, e[i]);
|
|
ge_madd(&r, h, &t);
|
|
ge_p1p1_to_p3(h, &r);
|
|
}
|
|
}
|
|
|
|
/* 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) {
|
|
size_t 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 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
|
|
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
|
|
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
|
|
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
|
|
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
|
|
|
|
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
|
|
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
|
|
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
|
|
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
|
|
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
|
|
|
|
h[0] = h0;
|
|
h[1] = h1;
|
|
h[2] = h2;
|
|
h[3] = h3;
|
|
h[4] = h4;
|
|
h[5] = h5;
|
|
h[6] = h6;
|
|
h[7] = h7;
|
|
h[8] = h8;
|
|
h[9] = h9;
|
|
}
|
|
|
|
static void x25519_scalar_mult_generic(uint8_t out[32],
|
|
const uint8_t scalar[32],
|
|
const uint8_t point[32]) {
|
|
fe x1, x2, z2, x3, z3, tmp0, tmp1;
|
|
uint8_t e[32];
|
|
unsigned swap = 0;
|
|
int pos;
|
|
|
|
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);
|
|
|
|
for (pos = 254; pos >= 0; --pos) {
|
|
unsigned b = 1 & (e[pos / 8] >> (pos & 7));
|
|
swap ^= b;
|
|
fe_cswap(x2, x3, swap);
|
|
fe_cswap(z2, z3, swap);
|
|
swap = b;
|
|
fe_sub(tmp0, x3, z3);
|
|
fe_sub(tmp1, x2, z2);
|
|
fe_add(x2, x2, z2);
|
|
fe_add(z2, x3, z3);
|
|
fe_mul(z3, tmp0, x2);
|
|
fe_mul(z2, z2, tmp1);
|
|
fe_sq(tmp0, tmp1);
|
|
fe_sq(tmp1, x2);
|
|
fe_add(x3, z3, z2);
|
|
fe_sub(z2, z3, z2);
|
|
fe_mul(x2, tmp1, tmp0);
|
|
fe_sub(tmp1, tmp1, tmp0);
|
|
fe_sq(z2, z2);
|
|
fe_mul121666(z3, tmp1);
|
|
fe_sq(x3, x3);
|
|
fe_add(tmp0, tmp0, z3);
|
|
fe_mul(z3, x1, z2);
|
|
fe_mul(z2, tmp1, tmp0);
|
|
}
|
|
fe_cswap(x2, x3, swap);
|
|
fe_cswap(z2, z3, swap);
|
|
|
|
fe_invert(z2, z2);
|
|
fe_mul(x2, x2, z2);
|
|
fe_tobytes(out, x2);
|
|
}
|
|
|
|
static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
|
|
const uint8_t point[32]) {
|
|
x25519_scalar_mult_generic(out, scalar, point);
|
|
}
|
|
|
|
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]) {
|
|
uint8_t e[32];
|
|
ge_p3 A;
|
|
fe zplusy, zminusy, zminusy_inv;
|
|
|
|
memcpy(e, private_key, 32);
|
|
e[0] &= 248;
|
|
e[31] &= 127;
|
|
e[31] |= 64;
|
|
|
|
ge_scalarmult_base(&A, e);
|
|
|
|
/* We only need the u-coordinate of the curve25519 point. The map is
|
|
* u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */
|
|
fe_add(zplusy, A.Z, A.Y);
|
|
fe_sub(zminusy, A.Z, A.Y);
|
|
fe_invert(zminusy_inv, zminusy);
|
|
fe_mul(zplusy, zplusy, zminusy_inv);
|
|
fe_tobytes(out_public_value, zplusy);
|
|
}
|