8185e649f8
- Remove OPENSSL_X25519_X86_64 which never worked, because we don't have the assembly. - Also remove OPENSSL_SMALL (which should have been OPENSSL_SMALL_FOOTPRINT) which isn't a priority at the moment. Reviewed-by: Rich Salz <rsalz@openssl.org>
3408 lines
140 KiB
C
3408 lines
140 KiB
C
/* ====================================================================
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* Copyright (c) 2016 The OpenSSL Project. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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*
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* 3. All advertising materials mentioning features or use of this
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* software must display the following acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
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*
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* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
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* endorse or promote products derived from this software without
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* prior written permission. For written permission, please contact
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* licensing@OpenSSL.org.
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*
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* 5. Products derived from this software may not be called "OpenSSL"
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* nor may "OpenSSL" appear in their names without prior written
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* permission of the OpenSSL Project.
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*
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* 6. Redistributions of any form whatsoever must retain the following
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* acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
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*
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* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
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* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
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* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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* OF THE POSSIBILITY OF SUCH DAMAGE.
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* ====================================================================
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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 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 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
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carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
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carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
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carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
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carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
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carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
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carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
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carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
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carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
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carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
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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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int32_t carry0;
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int32_t carry1;
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int32_t carry2;
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int32_t carry3;
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int32_t carry4;
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int32_t carry5;
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int32_t carry6;
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int32_t carry7;
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int32_t carry8;
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int32_t carry9;
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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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carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
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carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
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carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
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carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
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carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
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carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
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carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
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carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
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carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
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carry9 = h9 >> 25; h9 -= carry9 << 25;
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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) | (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) | (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) | (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) | (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) | (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) | (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) | (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) | (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;
|
|
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 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
|
|
carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
|
|
/* |h0| <= 2^25 */
|
|
/* |h4| <= 2^25 */
|
|
/* |h1| <= 1.71*2^59 */
|
|
/* |h5| <= 1.71*2^59 */
|
|
|
|
carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
|
|
carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
|
|
/* |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 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
|
|
carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
|
|
/* |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 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
|
|
carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
|
|
/* |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 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
|
|
carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
|
|
/* |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 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
|
|
/* |h9| <= 2^24; from now on fits into int32 unchanged */
|
|
/* |h0| <= 1.1*2^39 */
|
|
|
|
carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
|
|
/* |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 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
|
|
carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
|
|
|
|
carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
|
|
carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
|
|
|
|
carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
|
|
carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
|
|
|
|
carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
|
|
carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
|
|
|
|
carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
|
|
carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
|
|
|
|
carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
|
|
|
|
carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
|
|
|
|
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);
|
|
for (i = 1; i < 1; ++i) {
|
|
fe_sq(t0, t0);
|
|
}
|
|
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);
|
|
for (i = 1; i < 1; ++i) {
|
|
fe_sq(t2, t2);
|
|
}
|
|
fe_mul(t1, t1, t2);
|
|
fe_sq(t2, t1);
|
|
for (i = 1; i < 5; ++i) {
|
|
fe_sq(t2, t2);
|
|
}
|
|
fe_mul(t1, t2, t1);
|
|
fe_sq(t2, t1);
|
|
for (i = 1; i < 10; ++i) {
|
|
fe_sq(t2, t2);
|
|
}
|
|
fe_mul(t2, t2, t1);
|
|
fe_sq(t3, t2);
|
|
for (i = 1; i < 20; ++i) {
|
|
fe_sq(t3, t3);
|
|
}
|
|
fe_mul(t2, t3, t2);
|
|
fe_sq(t2, t2);
|
|
for (i = 1; i < 10; ++i) {
|
|
fe_sq(t2, t2);
|
|
}
|
|
fe_mul(t1, t2, t1);
|
|
fe_sq(t2, t1);
|
|
for (i = 1; i < 50; ++i) {
|
|
fe_sq(t2, t2);
|
|
}
|
|
fe_mul(t2, t2, t1);
|
|
fe_sq(t3, t2);
|
|
for (i = 1; i < 100; ++i) {
|
|
fe_sq(t3, t3);
|
|
}
|
|
fe_mul(t2, t3, t2);
|
|
fe_sq(t2, t2);
|
|
for (i = 1; i < 50; ++i) {
|
|
fe_sq(t2, t2);
|
|
}
|
|
fe_mul(t1, t2, t1);
|
|
fe_sq(t1, t1);
|
|
for (i = 1; i < 5; ++i) {
|
|
fe_sq(t1, t1);
|
|
}
|
|
fe_mul(out, t1, t0);
|
|
}
|
|
|
|
/* h = -f
|
|
*
|
|
* Preconditions:
|
|
* |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|
|
*
|
|
* Postconditions:
|
|
* |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
|
|
static void fe_neg(fe h, const fe f) {
|
|
unsigned i;
|
|
for (i = 0; i < 10; i++) {
|
|
h[i] = -f[i];
|
|
}
|
|
}
|
|
|
|
/* Replace (f,g) with (g,g) if b == 1;
|
|
* replace (f,g) with (f,g) if b == 0.
|
|
*
|
|
* Preconditions: b in {0,1}. */
|
|
static void fe_cmov(fe f, const fe g, unsigned b) {
|
|
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 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
|
|
carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
|
|
|
|
carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
|
|
carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
|
|
|
|
carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
|
|
carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
|
|
|
|
carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
|
|
carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
|
|
|
|
carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
|
|
carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
|
|
|
|
carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
|
|
|
|
carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
|
|
|
|
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},
|
|
{-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
|
|
-15616551, 11189268, -26829678, -5319081},
|
|
{26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
|
|
-3128826, -9541118, -15472047, -4166697},
|
|
},
|
|
{
|
|
{15636291, -9688557, 24204773, -7912398, 616977, -16685262,
|
|
27787600, -14772189, 28944400, -1550024},
|
|
{16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
|
|
16354577, -11775962, 7689662, 11199574},
|
|
{30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
|
|
7512774, 10017326, -17749093, -9920357},
|
|
},
|
|
{
|
|
{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
|
|
-28926210, 15006023, 3284568, -6276540},
|
|
{23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
|
|
7464579, 9656445, 13059162, 10374397},
|
|
{7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
|
|
-3839045, -641708, -101325},
|
|
},
|
|
{
|
|
{10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
|
|
32867885, 14515107, -15438304, 10819380},
|
|
{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
|
|
12483688, -12668491, 5581306},
|
|
{19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
|
|
28542350, 13850243, -23678021, -15815942},
|
|
},
|
|
{
|
|
{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
|
|
-19188627, -15224819, -9818940, -12085777},
|
|
{-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
|
|
-15689887, 1762328, 14866737},
|
|
{-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
|
|
-28236412, 3959421, 27914454, 4383652},
|
|
},
|
|
{
|
|
{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
|
|
5230134, -23952439, -15175766},
|
|
{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
|
|
20654025, 16520125, 30598449, 7715701},
|
|
{28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
|
|
-31400660, 1370708, 29794553, -1409300},
|
|
},
|
|
{
|
|
{14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
|
|
30290735, 10876454, -33154098, 2381726},
|
|
{-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
|
|
-6236617, 3696005, -32300832, 15351955},
|
|
{27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
|
|
-32961401, -2970515, 29551813, 10109425},
|
|
},
|
|
},
|
|
{
|
|
{
|
|
{-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
|
|
-2378284, -1627556, 10092783, -4764171},
|
|
{27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
|
|
-32508754, 12005538, -17810127, 12803510},
|
|
{17228999, -15661624, -1233527, 300140, -1224870, -11714777,
|
|
30364213, -9038194, 18016357, 4397660},
|
|
},
|
|
{
|
|
{-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
|
|
-26619106, 14544525, -17477504, 982639},
|
|
{29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
|
|
-4120128, -21047696, 9934963},
|
|
{5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
|
|
-14747930, 4559895, -30123922, -10897950},
|
|
},
|
|
{
|
|
{-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
|
|
24191034, 4541697, -13338309, 5500568},
|
|
{12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
|
|
-17430592, 12264343, 10874051, 13524335},
|
|
{25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
|
|
5080568, -22528059, 5376628},
|
|
},
|
|
{
|
|
{-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
|
|
-22321305, -9447443, 4535768, 1569007},
|
|
{-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
|
|
-30494562, 3044290, 31848280, 12543772},
|
|
{-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
|
|
-27377195, -2062731, 7718482, 14474653},
|
|
},
|
|
{
|
|
{2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
|
|
-7236665, 24316168, -5253567},
|
|
{13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
|
|
33040651, -13424532, -20729456, 8321686},
|
|
{21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
|
|
23845965, -11874838, -9984458, 608372},
|
|
},
|
|
{
|
|
{-13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
|
|
1123968, -6780577, 27229399, 23887},
|
|
{-23244140, -294205, -11744728, 14712571, -29465699, -2029617,
|
|
12797024, -6440308, -1633405, 16678954},
|
|
{-29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
|
|
-1508144, -4795045, -17169265, 4904953},
|
|
},
|
|
{
|
|
{24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
|
|
5169211, 16191880, 2128236, -4326833},
|
|
{-16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
|
|
-29806336, 916033, -6882542, -2986532},
|
|
{-22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
|
|
285431, 2763829, 15736322, 4143876},
|
|
},
|
|
{
|
|
{2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
|
|
-14594663, 23527084, -16458268},
|
|
{33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
|
|
-32625340, 4087881, -15188911, -14416214},
|
|
{1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
|
|
4357868, -4774191, -16323038},
|
|
},
|
|
},
|
|
{
|
|
{
|
|
{6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
|
|
23365147, -3949732, 7390890, 2759800},
|
|
{4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
|
|
-4264057, 1244380, -12919645},
|
|
{-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
|
|
9208236, 15886429, 16489664},
|
|
},
|
|
{
|
|
{1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
|
|
-13693198, 398369, -30606455, -712933},
|
|
{-25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
|
|
13348553, 12076947, -30836462, 5113182},
|
|
{-17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
|
|
-30341101, -7336386, 13847711, 5387222},
|
|
},
|
|
{
|
|
{-18582163, -3416217, 17824843, -2340966, 22744343, -10442611,
|
|
8763061, 3617786, -19600662, 10370991},
|
|
{20246567, -14369378, 22358229, -543712, 18507283, -10413996,
|
|
14554437, -8746092, 32232924, 16763880},
|
|
{9648505, 10094563, 26416693, 14745928, -30374318, -6472621,
|
|
11094161, 15689506, 3140038, -16510092},
|
|
},
|
|
{
|
|
{-16160072, 5472695, 31895588, 4744994, 8823515, 10365685,
|
|
-27224800, 9448613, -28774454, 366295},
|
|
{19153450, 11523972, -11096490, -6503142, -24647631, 5420647,
|
|
28344573, 8041113, 719605, 11671788},
|
|
{8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
|
|
-15266516, 27000813, -10195553},
|
|
},
|
|
{
|
|
{-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
|
|
5336097, 6750977, -14521026},
|
|
{11836410, -3979488, 26297894, 16080799, 23455045, 15735944,
|
|
1695823, -8819122, 8169720, 16220347},
|
|
{-18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
|
|
-11144307, -2627664, -5990708, -14166033},
|
|
},
|
|
{
|
|
{-23308498, -10968312, 15213228, -10081214, -30853605, -11050004,
|
|
27884329, 2847284, 2655861, 1738395},
|
|
{-27537433, -14253021, -25336301, -8002780, -9370762, 8129821,
|
|
21651608, -3239336, -19087449, -11005278},
|
|
{1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
|
|
5821408, 10478196, 8544890},
|
|
},
|
|
{
|
|
{32173121, -16129311, 24896207, 3921497, 22579056, -3410854,
|
|
19270449, 12217473, 17789017, -3395995},
|
|
{-30552961, -2228401, -15578829, -10147201, 13243889, 517024,
|
|
15479401, -3853233, 30460520, 1052596},
|
|
{-11614875, 13323618, 32618793, 8175907, -15230173, 12596687,
|
|
27491595, -4612359, 3179268, -9478891},
|
|
},
|
|
{
|
|
{31947069, -14366651, -4640583, -15339921, -15125977, -6039709,
|
|
-14756777, -16411740, 19072640, -9511060},
|
|
{11685058, 11822410, 3158003, -13952594, 33402194, -4165066,
|
|
5977896, -5215017, 473099, 5040608},
|
|
{-20290863, 8198642, -27410132, 11602123, 1290375, -2799760,
|
|
28326862, 1721092, -19558642, -3131606},
|
|
},
|
|
},
|
|
{
|
|
{
|
|
{7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
|
|
8076149, -27868496, 11538389},
|
|
{-19935666, 3899861, 18283497, -6801568, -15728660, -11249211,
|
|
8754525, 7446702, -5676054, 5797016},
|
|
{-11295600, -3793569, -15782110, -7964573, 12708869, -8456199,
|
|
2014099, -9050574, -2369172, -5877341},
|
|
},
|
|
{
|
|
{-22472376, -11568741, -27682020, 1146375, 18956691, 16640559,
|
|
1192730, -3714199, 15123619, 10811505},
|
|
{14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363,
|
|
15776356, -28886779, -11974553},
|
|
{-28241164, -8072475, -4978962, -5315317, 29416931, 1847569,
|
|
-20654173, -16484855, 4714547, -9600655},
|
|
},
|
|
{
|
|
{15200332, 8368572, 19679101, 15970074, -31872674, 1959451,
|
|
24611599, -4543832, -11745876, 12340220},
|
|
{12876937, -10480056, 33134381, 6590940, -6307776, 14872440,
|
|
9613953, 8241152, 15370987, 9608631},
|
|
{-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868,
|
|
15866074, -28210621, -8814099},
|
|
},
|
|
{
|
|
{26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233,
|
|
858697, 20571223, 8420556},
|
|
{14620715, 13067227, -15447274, 8264467, 14106269, 15080814,
|
|
33531827, 12516406, -21574435, -12476749},
|
|
{236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519,
|
|
7256740, 8791136, 15069930},
|
|
},
|
|
{
|
|
{1276410, -9371918, 22949635, -16322807, -23493039, -5702186,
|
|
14711875, 4874229, -30663140, -2331391},
|
|
{5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175,
|
|
-7912378, -33069337, 9234253},
|
|
{20590503, -9018988, 31529744, -7352666, -2706834, 10650548,
|
|
31559055, -11609587, 18979186, 13396066},
|
|
},
|
|
{
|
|
{24474287, 4968103, 22267082, 4407354, 24063882, -8325180,
|
|
-18816887, 13594782, 33514650, 7021958},
|
|
{-11566906, -6565505, -21365085, 15928892, -26158305, 4315421,
|
|
-25948728, -3916677, -21480480, 12868082},
|
|
{-28635013, 13504661, 19988037, -2132761, 21078225, 6443208,
|
|
-21446107, 2244500, -12455797, -8089383},
|
|
},
|
|
{
|
|
{-30595528, 13793479, -5852820, 319136, -25723172, -6263899,
|
|
33086546, 8957937, -15233648, 5540521},
|
|
{-11630176, -11503902, -8119500, -7643073, 2620056, 1022908,
|
|
-23710744, -1568984, -16128528, -14962807},
|
|
{23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819,
|
|
892185, -11513277, -15205948},
|
|
},
|
|
{
|
|
{9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819,
|
|
4763127, -19179614, 5867134},
|
|
{-32765025, 1927590, 31726409, -4753295, 23962434, -16019500,
|
|
27846559, 5931263, -29749703, -16108455},
|
|
{27461885, -2977536, 22380810, 1815854, -23033753, -3031938,
|
|
7283490, -15148073, -19526700, 7734629},
|
|
},
|
|
},
|
|
{
|
|
{
|
|
{-8010264, -9590817, -11120403, 6196038, 29344158, -13430885,
|
|
7585295, -3176626, 18549497, 15302069},
|
|
{-32658337, -6171222, -7672793, -11051681, 6258878, 13504381,
|
|
10458790, -6418461, -8872242, 8424746},
|
|
{24687205, 8613276, -30667046, -3233545, 1863892, -1830544,
|
|
19206234, 7134917, -11284482, -828919},
|
|
},
|
|
{
|
|
{11334899, -9218022, 8025293, 12707519, 17523892, -10476071,
|
|
10243738, -14685461, -5066034, 16498837},
|
|
{8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925,
|
|
-14124238, 6536641, 10543906},
|
|
{-28946384, 15479763, -17466835, 568876, -1497683, 11223454,
|
|
-2669190, -16625574, -27235709, 8876771},
|
|
},
|
|
{
|
|
{-25742899, -12566864, -15649966, -846607, -33026686, -796288,
|
|
-33481822, 15824474, -604426, -9039817},
|
|
{10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697,
|
|
-4890037, 1657394, 3084098},
|
|
{10477963, -7470260, 12119566, -13250805, 29016247, -5365589,
|
|
31280319, 14396151, -30233575, 15272409},
|
|
},
|
|
{
|
|
{-12288309, 3169463, 28813183, 16658753, 25116432, -5630466,
|
|
-25173957, -12636138, -25014757, 1950504},
|
|
{-26180358, 9489187, 11053416, -14746161, -31053720, 5825630,
|
|
-8384306, -8767532, 15341279, 8373727},
|
|
{28685821, 7759505, -14378516, -12002860, -31971820, 4079242,
|
|
298136, -10232602, -2878207, 15190420},
|
|
},
|
|
{
|
|
{-32932876, 13806336, -14337485, -15794431, -24004620, 10940928,
|
|
8669718, 2742393, -26033313, -6875003},
|
|
{-1580388, -11729417, -25979658, -11445023, -17411874, -10912854,
|
|
9291594, -16247779, -12154742, 6048605},
|
|
{-30305315, 14843444, 1539301, 11864366, 20201677, 1900163,
|
|
13934231, 5128323, 11213262, 9168384},
|
|
},
|
|
{
|
|
{-26280513, 11007847, 19408960, -940758, -18592965, -4328580,
|
|
-5088060, -11105150, 20470157, -16398701},
|
|
{-23136053, 9282192, 14855179, -15390078, -7362815, -14408560,
|
|
-22783952, 14461608, 14042978, 5230683},
|
|
{29969567, -2741594, -16711867, -8552442, 9175486, -2468974,
|
|
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-16317219, -9244265, 15258046},
|
|
{13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406,
|
|
2711395, 1062915, -5136345},
|
|
{-19240248, -11254599, -29509029, -7499965, -5835763, 13005411,
|
|
-6066489, 12194497, 32960380, 1459310},
|
|
},
|
|
},
|
|
{
|
|
{
|
|
{19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197,
|
|
-6101885, 18638003, -11174937},
|
|
{31395534, 15098109, 26581030, 8030562, -16527914, -5007134,
|
|
9012486, -7584354, -6643087, -5442636},
|
|
{-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222,
|
|
9677543, -32294889, -6456008},
|
|
},
|
|
{
|
|
{-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579,
|
|
-7839692, -7852844, -8138429},
|
|
{-15236356, -15433509, 7766470, 746860, 26346930, -10221762,
|
|
-27333451, 10754588, -9431476, 5203576},
|
|
{31834314, 14135496, -770007, 5159118, 20917671, -16768096,
|
|
-7467973, -7337524, 31809243, 7347066},
|
|
},
|
|
{
|
|
{-9606723, -11874240, 20414459, 13033986, 13716524, -11691881,
|
|
19797970, -12211255, 15192876, -2087490},
|
|
{-12663563, -2181719, 1168162, -3804809, 26747877, -14138091,
|
|
10609330, 12694420, 33473243, -13382104},
|
|
{33184999, 11180355, 15832085, -11385430, -1633671, 225884,
|
|
15089336, -11023903, -6135662, 14480053},
|
|
},
|
|
{
|
|
{31308717, -5619998, 31030840, -1897099, 15674547, -6582883,
|
|
5496208, 13685227, 27595050, 8737275},
|
|
{-20318852, -15150239, 10933843, -16178022, 8335352, -7546022,
|
|
-31008351, -12610604, 26498114, 66511},
|
|
{22644454, -8761729, -16671776, 4884562, -3105614, -13559366,
|
|
30540766, -4286747, -13327787, -7515095},
|
|
},
|
|
{
|
|
{-28017847, 9834845, 18617207, -2681312, -3401956, -13307506,
|
|
8205540, 13585437, -17127465, 15115439},
|
|
{23711543, -672915, 31206561, -8362711, 6164647, -9709987,
|
|
-33535882, -1426096, 8236921, 16492939},
|
|
{-23910559, -13515526, -26299483, -4503841, 25005590, -7687270,
|
|
19574902, 10071562, 6708380, -6222424},
|
|
},
|
|
{
|
|
{2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017,
|
|
9328700, 29955601, -11678310},
|
|
{3096359, 9271816, -21620864, -15521844, -14847996, -7592937,
|
|
-25892142, -12635595, -9917575, 6216608},
|
|
{-32615849, 338663, -25195611, 2510422, -29213566, -13820213,
|
|
24822830, -6146567, -26767480, 7525079},
|
|
},
|
|
{
|
|
{-23066649, -13985623, 16133487, -7896178, -3389565, 778788,
|
|
-910336, -2782495, -19386633, 11994101},
|
|
{21691500, -13624626, -641331, -14367021, 3285881, -3483596,
|
|
-25064666, 9718258, -7477437, 13381418},
|
|
{18445390, -4202236, 14979846, 11622458, -1727110, -3582980,
|
|
23111648, -6375247, 28535282, 15779576},
|
|
},
|
|
{
|
|
{30098053, 3089662, -9234387, 16662135, -21306940, 11308411,
|
|
-14068454, 12021730, 9955285, -16303356},
|
|
{9734894, -14576830, -7473633, -9138735, 2060392, 11313496,
|
|
-18426029, 9924399, 20194861, 13380996},
|
|
{-26378102, -7965207, -22167821, 15789297, -18055342, -6168792,
|
|
-1984914, 15707771, 26342023, 10146099},
|
|
},
|
|
},
|
|
{
|
|
{
|
|
{-26016874, -219943, 21339191, -41388, 19745256, -2878700,
|
|
-29637280, 2227040, 21612326, -545728},
|
|
{-13077387, 1184228, 23562814, -5970442, -20351244, -6348714,
|
|
25764461, 12243797, -20856566, 11649658},
|
|
{-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944,
|
|
6114064, 33514190, 2333242},
|
|
},
|
|
{
|
|
{-21433588, -12421821, 8119782, 7219913, -21830522, -9016134,
|
|
-6679750, -12670638, 24350578, -13450001},
|
|
{-4116307, -11271533, -23886186, 4843615, -30088339, 690623,
|
|
-31536088, -10406836, 8317860, 12352766},
|
|
{18200138, -14475911, -33087759, -2696619, -23702521, -9102511,
|
|
-23552096, -2287550, 20712163, 6719373},
|
|
},
|
|
{
|
|
{26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530,
|
|
-3763210, 26224235, -3297458},
|
|
{-17168938, -14854097, -3395676, -16369877, -19954045, 14050420,
|
|
21728352, 9493610, 18620611, -16428628},
|
|
{-13323321, 13325349, 11432106, 5964811, 18609221, 6062965,
|
|
-5269471, -9725556, -30701573, -16479657},
|
|
},
|
|
{
|
|
{-23860538, -11233159, 26961357, 1640861, -32413112, -16737940,
|
|
12248509, -5240639, 13735342, 1934062},
|
|
{25089769, 6742589, 17081145, -13406266, 21909293, -16067981,
|
|
-15136294, -3765346, -21277997, 5473616},
|
|
{31883677, -7961101, 1083432, -11572403, 22828471, 13290673,
|
|
-7125085, 12469656, 29111212, -5451014},
|
|
},
|
|
{
|
|
{24244947, -15050407, -26262976, 2791540, -14997599, 16666678,
|
|
24367466, 6388839, -10295587, 452383},
|
|
{-25640782, -3417841, 5217916, 16224624, 19987036, -4082269,
|
|
-24236251, -5915248, 15766062, 8407814},
|
|
{-20406999, 13990231, 15495425, 16395525, 5377168, 15166495,
|
|
-8917023, -4388953, -8067909, 2276718},
|
|
},
|
|
{
|
|
{30157918, 12924066, -17712050, 9245753, 19895028, 3368142,
|
|
-23827587, 5096219, 22740376, -7303417},
|
|
{2041139, -14256350, 7783687, 13876377, -25946985, -13352459,
|
|
24051124, 13742383, -15637599, 13295222},
|
|
{33338237, -8505733, 12532113, 7977527, 9106186, -1715251,
|
|
-17720195, -4612972, -4451357, -14669444},
|
|
},
|
|
{
|
|
{-20045281, 5454097, -14346548, 6447146, 28862071, 1883651,
|
|
-2469266, -4141880, 7770569, 9620597},
|
|
{23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528,
|
|
-1694323, -33502340, -14767970},
|
|
{1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801,
|
|
1220118, 30494170, -11440799},
|
|
},
|
|
{
|
|
{-5037580, -13028295, -2970559, -3061767, 15640974, -6701666,
|
|
-26739026, 926050, -1684339, -13333647},
|
|
{13908495, -3549272, 30919928, -6273825, -21521863, 7989039,
|
|
9021034, 9078865, 3353509, 4033511},
|
|
{-29663431, -15113610, 32259991, -344482, 24295849, -12912123,
|
|
23161163, 8839127, 27485041, 7356032},
|
|
},
|
|
},
|
|
{
|
|
{
|
|
{9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
|
|
2625015, 28431036, -16771834},
|
|
{-23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
|
|
-22545972, 14150565, 15970762, 4099461},
|
|
{29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
|
|
13617293, -9937143, 11465739, 8317062},
|
|
},
|
|
{
|
|
{-25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
|
|
14898637, 3848455, 20969334, -5157516},
|
|
{-20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
|
|
-21610826, -3649888, 11177095, 14989547},
|
|
{-24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
|
|
13515641, 2581286, -28487508, 9930240},
|
|
},
|
|
{
|
|
{-17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
|
|
18345767, -13403753, 16291481, -5314038},
|
|
{-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
|
|
6957617, 4368891, 9788741},
|
|
{16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
|
|
-21722536, -8613148, 16250552, -11111103},
|
|
},
|
|
{
|
|
{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
|
|
10604807, -30190403, 4782747},
|
|
{-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
|
|
-9981571, 4383045, 22546403, 437323},
|
|
{31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
|
|
27343084, 2786261, -30633590, -14097016},
|
|
},
|
|
{
|
|
{-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
|
|
-19690631, 2355319, -19284671, -6114373},
|
|
{15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
|
|
18952177, 15496498, -29380133, 11754228},
|
|
{-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
|
|
7141596, 11724556, 22761615, -10134141},
|
|
},
|
|
{
|
|
{16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
|
|
-28741185, -12227393, 32851222, 11717399},
|
|
{11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
|
|
31474879, 3483633, -1193175, -4030831},
|
|
{-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
|
|
33142652, 6546660, -19985279, -3948376},
|
|
},
|
|
{
|
|
{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
|
|
-8537131, -12833048, -30772034, -15486313},
|
|
{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
|
|
-31135347, -16049879, 10928917, 3011958},
|
|
{-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
|
|
-30831056, -12805180, 18008031, 10258577},
|
|
},
|
|
{
|
|
{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
|
|
-1853465, 1367120, 25127874, 6671743},
|
|
{29701166, -14373934, -10878120, 9279288, -17568, 13127210,
|
|
21382910, 11042292, 25838796, 4642684},
|
|
{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
|
|
30468147, -13900640, 18423289, 4177476},
|
|
},
|
|
},
|
|
};
|
|
|
|
static uint8_t negative(signed char b) {
|
|
uint32_t x = b;
|
|
x >>= 31; /* 1: yes; 0: no */
|
|
return x;
|
|
}
|
|
|
|
static void table_select(ge_precomp *t, int pos, signed char b) {
|
|
ge_precomp minust;
|
|
uint8_t bnegative = negative(b);
|
|
uint8_t babs = b - (((-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 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
|
|
carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
|
|
carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
|
|
carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
|
|
carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
|
|
|
|
carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
|
|
carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
|
|
carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
|
|
carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
|
|
carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
|
|
|
|
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);
|
|
}
|