-/* ====================================================================
- * Copyright (c) 2016 The OpenSSL Project. All rights reserved.
+/*
+ * Copyright 2016 The OpenSSL Project Authors. All Rights Reserved.
*
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in
- * the documentation and/or other materials provided with the
- * distribution.
- *
- * 3. All advertising materials mentioning features or use of this
- * software must display the following acknowledgment:
- * "This product includes software developed by the OpenSSL Project
- * for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
- *
- * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
- * endorse or promote products derived from this software without
- * prior written permission. For written permission, please contact
- * licensing@OpenSSL.org.
- *
- * 5. Products derived from this software may not be called "OpenSSL"
- * nor may "OpenSSL" appear in their names without prior written
- * permission of the OpenSSL Project.
- *
- * 6. Redistributions of any form whatsoever must retain the following
- * acknowledgment:
- * "This product includes software developed by the OpenSSL Project
- * for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
- *
- * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
- * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
- * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
- * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
- * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
- * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
- * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
- * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
- * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
- * OF THE POSSIBILITY OF SUCH DAMAGE.
- * ====================================================================
+ * Licensed under the OpenSSL license (the "License"). You may not use
+ * this file except in compliance with the License. You can obtain a copy
+ * in the file LICENSE in the source distribution or at
+ * https://www.openssl.org/source/license.html
*/
/* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
* context. */
typedef int32_t fe[10];
+static const int64_t kBottom25Bits = 0x1ffffffLL;
+static const int64_t kBottom26Bits = 0x3ffffffLL;
+static const int64_t kTop39Bits = 0xfffffffffe000000LL;
+static const int64_t kTop38Bits = 0xfffffffffc000000LL;
+
static uint64_t load_3(const uint8_t *in) {
uint64_t result;
result = (uint64_t)in[0];
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;
+ 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 + (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;
+ 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;
int32_t h8 = h[8];
int32_t h9 = h[9];
int32_t q;
- int32_t carry0;
- int32_t carry1;
- int32_t carry2;
- int32_t carry3;
- int32_t carry4;
- int32_t carry5;
- int32_t carry6;
- int32_t carry7;
- int32_t carry8;
- int32_t carry9;
q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
q = (h0 + q) >> 26;
h0 += 19 * q;
/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
- carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
- carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
- carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
- carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
- carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
- carry9 = h9 >> 25; h9 -= carry9 << 25;
+ h1 += h0 >> 26; h0 &= kBottom26Bits;
+ h2 += h1 >> 25; h1 &= kBottom25Bits;
+ h3 += h2 >> 26; h2 &= kBottom26Bits;
+ h4 += h3 >> 25; h3 &= kBottom25Bits;
+ h5 += h4 >> 26; h4 &= kBottom26Bits;
+ h6 += h5 >> 25; h5 &= kBottom25Bits;
+ h7 += h6 >> 26; h6 &= kBottom26Bits;
+ h8 += h7 >> 25; h7 &= kBottom25Bits;
+ h9 += h8 >> 26; h8 &= kBottom26Bits;
+ h9 &= kBottom25Bits;
/* h10 = carry9 */
/* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
s[0] = h0 >> 0;
s[1] = h0 >> 8;
s[2] = h0 >> 16;
- s[3] = (h0 >> 24) | (h1 << 2);
+ s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2);
s[4] = h1 >> 6;
s[5] = h1 >> 14;
- s[6] = (h1 >> 22) | (h2 << 3);
+ s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3);
s[7] = h2 >> 5;
s[8] = h2 >> 13;
- s[9] = (h2 >> 21) | (h3 << 5);
+ s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5);
s[10] = h3 >> 3;
s[11] = h3 >> 11;
- s[12] = (h3 >> 19) | (h4 << 6);
+ s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6);
s[13] = h4 >> 2;
s[14] = h4 >> 10;
s[15] = h4 >> 18;
s[16] = h5 >> 0;
s[17] = h5 >> 8;
s[18] = h5 >> 16;
- s[19] = (h5 >> 24) | (h6 << 1);
+ s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1);
s[20] = h6 >> 7;
s[21] = h6 >> 15;
- s[22] = (h6 >> 23) | (h7 << 3);
+ s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3);
s[23] = h7 >> 5;
s[24] = h7 >> 13;
- s[25] = (h7 >> 21) | (h8 << 4);
+ s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4);
s[26] = h8 >> 4;
s[27] = h8 >> 12;
- s[28] = (h8 >> 20) | (h9 << 6);
+ s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6);
s[29] = h9 >> 2;
s[30] = h9 >> 10;
s[31] = h9 >> 18;
* |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;
+ 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 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+ 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 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+ 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 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+ 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 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+ 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 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+ 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 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+ 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 */
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;
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
- carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+ carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+ carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
- carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+ carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+ carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
- carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+ carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+ carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+ carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
- carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+ carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
h[0] = h0;
h[1] = h1;
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);
- for (i = 1; i < 1; ++i) {
- fe_sq(t0, t0);
- }
+
+ /* t1 = t0 ** (2 ** 2) = z ** 8 */
fe_sq(t1, t0);
- for (i = 1; i < 2; ++i) {
- fe_sq(t1, t1);
- }
+ 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);
- for (i = 1; i < 1; ++i) {
- fe_sq(t2, t2);
- }
+
+ /* 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);
- fe_sq(t2, t2);
- for (i = 1; i < 10; ++i) {
+
+ /* 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);
}
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;
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
- carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+ carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+ carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
- carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+ carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+ carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
- carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+ carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+ carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
- carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+ carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+ carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
- carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+ carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
- carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+ carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
h[0] = h0;
h[1] = h1;
return y;
}
-static void cmov(ge_precomp *t, ge_precomp *u, uint8_t b) {
+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);
}
-#if defined(OPENSSL_SMALL)
-
-/* This block of code replaces the standard base-point table with a much smaller
- * one. The standard table is 30,720 bytes while this one is just 960.
- *
- * This table contains 15 pairs of group elements, (x, y), where each field
- * element is serialised with |fe_tobytes|. If |i| is the index of the group
- * element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀
- * is the most significant bit). The value of the group element is then:
- * (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator. */
-static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = {
- 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95,
- 0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0,
- 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e,
- 0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4,
- 0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62,
- 0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba,
- 0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd,
- 0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61,
- 0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c,
- 0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c,
- 0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5,
- 0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3,
- 0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18,
- 0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2,
- 0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95,
- 0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b,
- 0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90,
- 0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52,
- 0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb,
- 0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c,
- 0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e,
- 0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e,
- 0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a,
- 0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43,
- 0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53,
- 0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8,
- 0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89,
- 0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef,
- 0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60,
- 0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a,
- 0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8,
- 0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54,
- 0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b,
- 0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd,
- 0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb,
- 0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c,
- 0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b,
- 0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63,
- 0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a,
- 0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07,
- 0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa,
- 0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a,
- 0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84,
- 0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc,
- 0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42,
- 0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0,
- 0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0,
- 0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a,
- 0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5,
- 0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c,
- 0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27,
- 0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31,
- 0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c,
- 0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87,
- 0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0,
- 0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23,
- 0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2,
- 0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87,
- 0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d,
- 0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b,
- 0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d,
- 0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6,
- 0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84,
- 0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04,
- 0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19,
- 0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b,
- 0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a,
- 0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea,
- 0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30,
- 0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7,
- 0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa,
- 0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5,
- 0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71,
- 0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab,
- 0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb,
- 0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c,
- 0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25,
-};
-
-static void ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) {
- /* k25519SmallPrecomp is first expanded into matching |ge_precomp|
- * elements. */
- ge_precomp multiples[15];
-
- unsigned i;
- for (i = 0; i < 15; i++) {
- const uint8_t *bytes = &k25519SmallPrecomp[i*(2 * 32)];
- fe x, y;
- fe_frombytes(x, bytes);
- fe_frombytes(y, bytes + 32);
-
- ge_precomp *out = &multiples[i];
- fe_add(out->yplusx, y, x);
- fe_sub(out->yminusx, y, x);
- fe_mul(out->xy2d, x, y);
- fe_mul(out->xy2d, out->xy2d, d2);
- }
-
- /* See the comment above |k25519SmallPrecomp| about the structure of the
- * precomputed elements. This loop does 64 additions and 64 doublings to
- * calculate the result. */
- ge_p3_0(h);
-
- for (i = 63; i < 64; i--) {
- unsigned j;
- signed char index = 0;
-
- for (j = 0; j < 4; j++) {
- const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7));
- index |= (bit << j);
- }
-
- ge_precomp e;
- ge_precomp_0(&e);
-
- for (j = 1; j < 16; j++) {
- cmov(&e, &multiples[j-1], equal(index, j));
- }
-
- ge_cached cached;
- ge_p1p1 r;
- ge_p3_to_cached(&cached, h);
- ge_add(&r, h, &cached);
- ge_p1p1_to_p3(h, &r);
-
- ge_madd(&r, h, &e);
- ge_p1p1_to_p3(h, &r);
- }
-}
-
-#else
-
/* k25519Precomp[i][j] = (j+1)*256^i*B */
static const ge_precomp k25519Precomp[32][8] = {
{
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);
+ uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
ge_precomp_0(t);
cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
}
}
-#endif
-
-#if defined(OPENSSL_X25519_X86_64)
-
-static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
- const uint8_t point[32]) {
- x25519_x86_64(out, scalar, point);
-}
-
-#else
-
/* Replace (f,g) with (g,f) if b == 1;
* replace (f,g) with (f,g) if b == 0.
*
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;
+ 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 + (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;
+ 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;
x25519_scalar_mult_generic(out, scalar, point);
}
-#endif /* OPENSSL_X25519_X86_64 */
-
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};
return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
}
-#if defined(OPENSSL_X25519_X86_64)
-
-/* When |OPENSSL_X25519_X86_64| is set, base point multiplication is done with
- * the Montgomery ladder because it's faster. Otherwise it's done using the
- * Ed25519 tables. */
-
-void X25519_public_from_private(uint8_t out_public_value[32],
- const uint8_t private_key[32]) {
- static const uint8_t kMongomeryBasePoint[32] = {9};
- x25519_scalar_mult(out_public_value, private_key, kMongomeryBasePoint);
-}
-
-#else
-
void X25519_public_from_private(uint8_t out_public_value[32],
const uint8_t private_key[32]) {
uint8_t e[32];
fe_mul(zplusy, zplusy, zminusy_inv);
fe_tobytes(out_public_value, zplusy);
}
-
-#endif /* OPENSSL_X25519_X86_64 */
projects / openssl.git / blobdiff