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wolfssl/wolfcrypt/src/sp_c32.c
T
Sean Parkinson cc880e39ae Add deterministic ECDSA sig gen. Fix corner cases for add point. 
In verify, two points are added and they may either be the same point
(different z) or result in infinity.
If they are the same point then a double needs to be performed instead.
Detection of infinity added.
Calculation of wc_ecc_sig_size fixed to handle wehn there are more bits
in the order than in the modulus.
2019-11-14 12:49:45 +10:00

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/* sp.c
*
* Copyright (C) 2006-2019 wolfSSL Inc.
*
* This file is part of wolfSSL.
*
* wolfSSL is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* wolfSSL is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335, USA
*/
/* Implementation by Sean Parkinson. */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <wolfssl/wolfcrypt/settings.h>
#include <wolfssl/wolfcrypt/error-crypt.h>
#include <wolfssl/wolfcrypt/cpuid.h>
#ifdef NO_INLINE
#include <wolfssl/wolfcrypt/misc.h>
#else
#define WOLFSSL_MISC_INCLUDED
#include <wolfcrypt/src/misc.c>
#endif
#if defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH) || \
defined(WOLFSSL_HAVE_SP_ECC)
#ifdef RSA_LOW_MEM
#ifndef SP_RSA_PRIVATE_EXP_D
#define SP_RSA_PRIVATE_EXP_D
#endif
#ifndef WOLFSSL_SP_SMALL
#define WOLFSSL_SP_SMALL
#endif
#endif
#include <wolfssl/wolfcrypt/sp.h>
#ifndef WOLFSSL_SP_ASM
#if SP_WORD_SIZE == 32
#if (defined(WOLFSSL_SP_CACHE_RESISTANT) || defined(WOLFSSL_SP_SMALL)) && (defined(WOLFSSL_HAVE_SP_ECC) || !defined(WOLFSSL_RSA_PUBLIC_ONLY))
/* Mask for address to obfuscate which of the two address will be used. */
static const size_t addr_mask[2] = { 0, (size_t)-1 };
#endif
#if defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH)
#ifndef WOLFSSL_SP_NO_2048
/* Read big endian unsigned byte array into r.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a Byte array.
* n Number of bytes in array to read.
*/
static void sp_2048_from_bin(sp_digit* r, int size, const byte* a, int n)
{
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = n-1; i >= 0; i--) {
r[j] |= (((sp_digit)a[i]) << s);
if (s >= 15U) {
r[j] &= 0x7fffff;
s = 23U - s;
if (j + 1 >= size) {
break;
}
r[++j] = (sp_digit)a[i] >> s;
s = 8U - s;
}
else {
s += 8U;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
}
/* Convert an mp_int to an array of sp_digit.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a A multi-precision integer.
*/
static void sp_2048_from_mp(sp_digit* r, int size, const mp_int* a)
{
#if DIGIT_BIT == 23
int j;
XMEMCPY(r, a->dp, sizeof(sp_digit) * a->used);
for (j = a->used; j < size; j++) {
r[j] = 0;
}
#elif DIGIT_BIT > 23
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i] << s);
r[j] &= 0x7fffff;
s = 23U - s;
if (j + 1 >= size) {
break;
}
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
while ((s + 23U) <= (word32)DIGIT_BIT) {
s += 23U;
r[j] &= 0x7fffff;
if (j + 1 >= size) {
break;
}
if (s < (word32)DIGIT_BIT) {
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
}
else {
r[++j] = 0L;
}
}
s = (word32)DIGIT_BIT - s;
}
for (j++; j < size; j++) {
r[j] = 0;
}
#else
int i, j = 0, s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i]) << s;
if (s + DIGIT_BIT >= 23) {
r[j] &= 0x7fffff;
if (j + 1 >= size) {
break;
}
s = 23 - s;
if (s == DIGIT_BIT) {
r[++j] = 0;
s = 0;
}
else {
r[++j] = a->dp[i] >> s;
s = DIGIT_BIT - s;
}
}
else {
s += DIGIT_BIT;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
#endif
}
/* Write r as big endian to byte array.
* Fixed length number of bytes written: 256
*
* r A single precision integer.
* a Byte array.
*/
static void sp_2048_to_bin(sp_digit* r, byte* a)
{
int i, j, s = 0, b;
for (i=0; i<89; i++) {
r[i+1] += r[i] >> 23;
r[i] &= 0x7fffff;
}
j = 2048 / 8 - 1;
a[j] = 0;
for (i=0; i<90 && j>=0; i++) {
b = 0;
/* lint allow cast of mismatch sp_digit and int */
a[j--] |= (byte)(r[i] << s); b += 8 - s; /*lint !e9033*/
if (j < 0) {
break;
}
while (b < 23) {
a[j--] = r[i] >> b; b += 8;
if (j < 0) {
break;
}
}
s = 8 - (b - 23);
if (j >= 0) {
a[j] = 0;
}
if (s != 0) {
j++;
}
}
}
#ifndef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_2048_mul_15(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int64_t t0 = ((int64_t)a[ 0]) * b[ 0];
int64_t t1 = ((int64_t)a[ 0]) * b[ 1]
+ ((int64_t)a[ 1]) * b[ 0];
int64_t t2 = ((int64_t)a[ 0]) * b[ 2]
+ ((int64_t)a[ 1]) * b[ 1]
+ ((int64_t)a[ 2]) * b[ 0];
int64_t t3 = ((int64_t)a[ 0]) * b[ 3]
+ ((int64_t)a[ 1]) * b[ 2]
+ ((int64_t)a[ 2]) * b[ 1]
+ ((int64_t)a[ 3]) * b[ 0];
int64_t t4 = ((int64_t)a[ 0]) * b[ 4]
+ ((int64_t)a[ 1]) * b[ 3]
+ ((int64_t)a[ 2]) * b[ 2]
+ ((int64_t)a[ 3]) * b[ 1]
+ ((int64_t)a[ 4]) * b[ 0];
int64_t t5 = ((int64_t)a[ 0]) * b[ 5]
+ ((int64_t)a[ 1]) * b[ 4]
+ ((int64_t)a[ 2]) * b[ 3]
+ ((int64_t)a[ 3]) * b[ 2]
+ ((int64_t)a[ 4]) * b[ 1]
+ ((int64_t)a[ 5]) * b[ 0];
int64_t t6 = ((int64_t)a[ 0]) * b[ 6]
+ ((int64_t)a[ 1]) * b[ 5]
+ ((int64_t)a[ 2]) * b[ 4]
+ ((int64_t)a[ 3]) * b[ 3]
+ ((int64_t)a[ 4]) * b[ 2]
+ ((int64_t)a[ 5]) * b[ 1]
+ ((int64_t)a[ 6]) * b[ 0];
int64_t t7 = ((int64_t)a[ 0]) * b[ 7]
+ ((int64_t)a[ 1]) * b[ 6]
+ ((int64_t)a[ 2]) * b[ 5]
+ ((int64_t)a[ 3]) * b[ 4]
+ ((int64_t)a[ 4]) * b[ 3]
+ ((int64_t)a[ 5]) * b[ 2]
+ ((int64_t)a[ 6]) * b[ 1]
+ ((int64_t)a[ 7]) * b[ 0];
int64_t t8 = ((int64_t)a[ 0]) * b[ 8]
+ ((int64_t)a[ 1]) * b[ 7]
+ ((int64_t)a[ 2]) * b[ 6]
+ ((int64_t)a[ 3]) * b[ 5]
+ ((int64_t)a[ 4]) * b[ 4]
+ ((int64_t)a[ 5]) * b[ 3]
+ ((int64_t)a[ 6]) * b[ 2]
+ ((int64_t)a[ 7]) * b[ 1]
+ ((int64_t)a[ 8]) * b[ 0];
int64_t t9 = ((int64_t)a[ 0]) * b[ 9]
+ ((int64_t)a[ 1]) * b[ 8]
+ ((int64_t)a[ 2]) * b[ 7]
+ ((int64_t)a[ 3]) * b[ 6]
+ ((int64_t)a[ 4]) * b[ 5]
+ ((int64_t)a[ 5]) * b[ 4]
+ ((int64_t)a[ 6]) * b[ 3]
+ ((int64_t)a[ 7]) * b[ 2]
+ ((int64_t)a[ 8]) * b[ 1]
+ ((int64_t)a[ 9]) * b[ 0];
int64_t t10 = ((int64_t)a[ 0]) * b[10]
+ ((int64_t)a[ 1]) * b[ 9]
+ ((int64_t)a[ 2]) * b[ 8]
+ ((int64_t)a[ 3]) * b[ 7]
+ ((int64_t)a[ 4]) * b[ 6]
+ ((int64_t)a[ 5]) * b[ 5]
+ ((int64_t)a[ 6]) * b[ 4]
+ ((int64_t)a[ 7]) * b[ 3]
+ ((int64_t)a[ 8]) * b[ 2]
+ ((int64_t)a[ 9]) * b[ 1]
+ ((int64_t)a[10]) * b[ 0];
int64_t t11 = ((int64_t)a[ 0]) * b[11]
+ ((int64_t)a[ 1]) * b[10]
+ ((int64_t)a[ 2]) * b[ 9]
+ ((int64_t)a[ 3]) * b[ 8]
+ ((int64_t)a[ 4]) * b[ 7]
+ ((int64_t)a[ 5]) * b[ 6]
+ ((int64_t)a[ 6]) * b[ 5]
+ ((int64_t)a[ 7]) * b[ 4]
+ ((int64_t)a[ 8]) * b[ 3]
+ ((int64_t)a[ 9]) * b[ 2]
+ ((int64_t)a[10]) * b[ 1]
+ ((int64_t)a[11]) * b[ 0];
int64_t t12 = ((int64_t)a[ 0]) * b[12]
+ ((int64_t)a[ 1]) * b[11]
+ ((int64_t)a[ 2]) * b[10]
+ ((int64_t)a[ 3]) * b[ 9]
+ ((int64_t)a[ 4]) * b[ 8]
+ ((int64_t)a[ 5]) * b[ 7]
+ ((int64_t)a[ 6]) * b[ 6]
+ ((int64_t)a[ 7]) * b[ 5]
+ ((int64_t)a[ 8]) * b[ 4]
+ ((int64_t)a[ 9]) * b[ 3]
+ ((int64_t)a[10]) * b[ 2]
+ ((int64_t)a[11]) * b[ 1]
+ ((int64_t)a[12]) * b[ 0];
int64_t t13 = ((int64_t)a[ 0]) * b[13]
+ ((int64_t)a[ 1]) * b[12]
+ ((int64_t)a[ 2]) * b[11]
+ ((int64_t)a[ 3]) * b[10]
+ ((int64_t)a[ 4]) * b[ 9]
+ ((int64_t)a[ 5]) * b[ 8]
+ ((int64_t)a[ 6]) * b[ 7]
+ ((int64_t)a[ 7]) * b[ 6]
+ ((int64_t)a[ 8]) * b[ 5]
+ ((int64_t)a[ 9]) * b[ 4]
+ ((int64_t)a[10]) * b[ 3]
+ ((int64_t)a[11]) * b[ 2]
+ ((int64_t)a[12]) * b[ 1]
+ ((int64_t)a[13]) * b[ 0];
int64_t t14 = ((int64_t)a[ 0]) * b[14]
+ ((int64_t)a[ 1]) * b[13]
+ ((int64_t)a[ 2]) * b[12]
+ ((int64_t)a[ 3]) * b[11]
+ ((int64_t)a[ 4]) * b[10]
+ ((int64_t)a[ 5]) * b[ 9]
+ ((int64_t)a[ 6]) * b[ 8]
+ ((int64_t)a[ 7]) * b[ 7]
+ ((int64_t)a[ 8]) * b[ 6]
+ ((int64_t)a[ 9]) * b[ 5]
+ ((int64_t)a[10]) * b[ 4]
+ ((int64_t)a[11]) * b[ 3]
+ ((int64_t)a[12]) * b[ 2]
+ ((int64_t)a[13]) * b[ 1]
+ ((int64_t)a[14]) * b[ 0];
int64_t t15 = ((int64_t)a[ 1]) * b[14]
+ ((int64_t)a[ 2]) * b[13]
+ ((int64_t)a[ 3]) * b[12]
+ ((int64_t)a[ 4]) * b[11]
+ ((int64_t)a[ 5]) * b[10]
+ ((int64_t)a[ 6]) * b[ 9]
+ ((int64_t)a[ 7]) * b[ 8]
+ ((int64_t)a[ 8]) * b[ 7]
+ ((int64_t)a[ 9]) * b[ 6]
+ ((int64_t)a[10]) * b[ 5]
+ ((int64_t)a[11]) * b[ 4]
+ ((int64_t)a[12]) * b[ 3]
+ ((int64_t)a[13]) * b[ 2]
+ ((int64_t)a[14]) * b[ 1];
int64_t t16 = ((int64_t)a[ 2]) * b[14]
+ ((int64_t)a[ 3]) * b[13]
+ ((int64_t)a[ 4]) * b[12]
+ ((int64_t)a[ 5]) * b[11]
+ ((int64_t)a[ 6]) * b[10]
+ ((int64_t)a[ 7]) * b[ 9]
+ ((int64_t)a[ 8]) * b[ 8]
+ ((int64_t)a[ 9]) * b[ 7]
+ ((int64_t)a[10]) * b[ 6]
+ ((int64_t)a[11]) * b[ 5]
+ ((int64_t)a[12]) * b[ 4]
+ ((int64_t)a[13]) * b[ 3]
+ ((int64_t)a[14]) * b[ 2];
int64_t t17 = ((int64_t)a[ 3]) * b[14]
+ ((int64_t)a[ 4]) * b[13]
+ ((int64_t)a[ 5]) * b[12]
+ ((int64_t)a[ 6]) * b[11]
+ ((int64_t)a[ 7]) * b[10]
+ ((int64_t)a[ 8]) * b[ 9]
+ ((int64_t)a[ 9]) * b[ 8]
+ ((int64_t)a[10]) * b[ 7]
+ ((int64_t)a[11]) * b[ 6]
+ ((int64_t)a[12]) * b[ 5]
+ ((int64_t)a[13]) * b[ 4]
+ ((int64_t)a[14]) * b[ 3];
int64_t t18 = ((int64_t)a[ 4]) * b[14]
+ ((int64_t)a[ 5]) * b[13]
+ ((int64_t)a[ 6]) * b[12]
+ ((int64_t)a[ 7]) * b[11]
+ ((int64_t)a[ 8]) * b[10]
+ ((int64_t)a[ 9]) * b[ 9]
+ ((int64_t)a[10]) * b[ 8]
+ ((int64_t)a[11]) * b[ 7]
+ ((int64_t)a[12]) * b[ 6]
+ ((int64_t)a[13]) * b[ 5]
+ ((int64_t)a[14]) * b[ 4];
int64_t t19 = ((int64_t)a[ 5]) * b[14]
+ ((int64_t)a[ 6]) * b[13]
+ ((int64_t)a[ 7]) * b[12]
+ ((int64_t)a[ 8]) * b[11]
+ ((int64_t)a[ 9]) * b[10]
+ ((int64_t)a[10]) * b[ 9]
+ ((int64_t)a[11]) * b[ 8]
+ ((int64_t)a[12]) * b[ 7]
+ ((int64_t)a[13]) * b[ 6]
+ ((int64_t)a[14]) * b[ 5];
int64_t t20 = ((int64_t)a[ 6]) * b[14]
+ ((int64_t)a[ 7]) * b[13]
+ ((int64_t)a[ 8]) * b[12]
+ ((int64_t)a[ 9]) * b[11]
+ ((int64_t)a[10]) * b[10]
+ ((int64_t)a[11]) * b[ 9]
+ ((int64_t)a[12]) * b[ 8]
+ ((int64_t)a[13]) * b[ 7]
+ ((int64_t)a[14]) * b[ 6];
int64_t t21 = ((int64_t)a[ 7]) * b[14]
+ ((int64_t)a[ 8]) * b[13]
+ ((int64_t)a[ 9]) * b[12]
+ ((int64_t)a[10]) * b[11]
+ ((int64_t)a[11]) * b[10]
+ ((int64_t)a[12]) * b[ 9]
+ ((int64_t)a[13]) * b[ 8]
+ ((int64_t)a[14]) * b[ 7];
int64_t t22 = ((int64_t)a[ 8]) * b[14]
+ ((int64_t)a[ 9]) * b[13]
+ ((int64_t)a[10]) * b[12]
+ ((int64_t)a[11]) * b[11]
+ ((int64_t)a[12]) * b[10]
+ ((int64_t)a[13]) * b[ 9]
+ ((int64_t)a[14]) * b[ 8];
int64_t t23 = ((int64_t)a[ 9]) * b[14]
+ ((int64_t)a[10]) * b[13]
+ ((int64_t)a[11]) * b[12]
+ ((int64_t)a[12]) * b[11]
+ ((int64_t)a[13]) * b[10]
+ ((int64_t)a[14]) * b[ 9];
int64_t t24 = ((int64_t)a[10]) * b[14]
+ ((int64_t)a[11]) * b[13]
+ ((int64_t)a[12]) * b[12]
+ ((int64_t)a[13]) * b[11]
+ ((int64_t)a[14]) * b[10];
int64_t t25 = ((int64_t)a[11]) * b[14]
+ ((int64_t)a[12]) * b[13]
+ ((int64_t)a[13]) * b[12]
+ ((int64_t)a[14]) * b[11];
int64_t t26 = ((int64_t)a[12]) * b[14]
+ ((int64_t)a[13]) * b[13]
+ ((int64_t)a[14]) * b[12];
int64_t t27 = ((int64_t)a[13]) * b[14]
+ ((int64_t)a[14]) * b[13];
int64_t t28 = ((int64_t)a[14]) * b[14];
t1 += t0 >> 23; r[ 0] = t0 & 0x7fffff;
t2 += t1 >> 23; r[ 1] = t1 & 0x7fffff;
t3 += t2 >> 23; r[ 2] = t2 & 0x7fffff;
t4 += t3 >> 23; r[ 3] = t3 & 0x7fffff;
t5 += t4 >> 23; r[ 4] = t4 & 0x7fffff;
t6 += t5 >> 23; r[ 5] = t5 & 0x7fffff;
t7 += t6 >> 23; r[ 6] = t6 & 0x7fffff;
t8 += t7 >> 23; r[ 7] = t7 & 0x7fffff;
t9 += t8 >> 23; r[ 8] = t8 & 0x7fffff;
t10 += t9 >> 23; r[ 9] = t9 & 0x7fffff;
t11 += t10 >> 23; r[10] = t10 & 0x7fffff;
t12 += t11 >> 23; r[11] = t11 & 0x7fffff;
t13 += t12 >> 23; r[12] = t12 & 0x7fffff;
t14 += t13 >> 23; r[13] = t13 & 0x7fffff;
t15 += t14 >> 23; r[14] = t14 & 0x7fffff;
t16 += t15 >> 23; r[15] = t15 & 0x7fffff;
t17 += t16 >> 23; r[16] = t16 & 0x7fffff;
t18 += t17 >> 23; r[17] = t17 & 0x7fffff;
t19 += t18 >> 23; r[18] = t18 & 0x7fffff;
t20 += t19 >> 23; r[19] = t19 & 0x7fffff;
t21 += t20 >> 23; r[20] = t20 & 0x7fffff;
t22 += t21 >> 23; r[21] = t21 & 0x7fffff;
t23 += t22 >> 23; r[22] = t22 & 0x7fffff;
t24 += t23 >> 23; r[23] = t23 & 0x7fffff;
t25 += t24 >> 23; r[24] = t24 & 0x7fffff;
t26 += t25 >> 23; r[25] = t25 & 0x7fffff;
t27 += t26 >> 23; r[26] = t26 & 0x7fffff;
t28 += t27 >> 23; r[27] = t27 & 0x7fffff;
r[29] = (sp_digit)(t28 >> 23);
r[28] = t28 & 0x7fffff;
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_2048_sqr_15(sp_digit* r, const sp_digit* a)
{
int64_t t0 = ((int64_t)a[ 0]) * a[ 0];
int64_t t1 = (((int64_t)a[ 0]) * a[ 1]) * 2;
int64_t t2 = (((int64_t)a[ 0]) * a[ 2]) * 2
+ ((int64_t)a[ 1]) * a[ 1];
int64_t t3 = (((int64_t)a[ 0]) * a[ 3]
+ ((int64_t)a[ 1]) * a[ 2]) * 2;
int64_t t4 = (((int64_t)a[ 0]) * a[ 4]
+ ((int64_t)a[ 1]) * a[ 3]) * 2
+ ((int64_t)a[ 2]) * a[ 2];
int64_t t5 = (((int64_t)a[ 0]) * a[ 5]
+ ((int64_t)a[ 1]) * a[ 4]
+ ((int64_t)a[ 2]) * a[ 3]) * 2;
int64_t t6 = (((int64_t)a[ 0]) * a[ 6]
+ ((int64_t)a[ 1]) * a[ 5]
+ ((int64_t)a[ 2]) * a[ 4]) * 2
+ ((int64_t)a[ 3]) * a[ 3];
int64_t t7 = (((int64_t)a[ 0]) * a[ 7]
+ ((int64_t)a[ 1]) * a[ 6]
+ ((int64_t)a[ 2]) * a[ 5]
+ ((int64_t)a[ 3]) * a[ 4]) * 2;
int64_t t8 = (((int64_t)a[ 0]) * a[ 8]
+ ((int64_t)a[ 1]) * a[ 7]
+ ((int64_t)a[ 2]) * a[ 6]
+ ((int64_t)a[ 3]) * a[ 5]) * 2
+ ((int64_t)a[ 4]) * a[ 4];
int64_t t9 = (((int64_t)a[ 0]) * a[ 9]
+ ((int64_t)a[ 1]) * a[ 8]
+ ((int64_t)a[ 2]) * a[ 7]
+ ((int64_t)a[ 3]) * a[ 6]
+ ((int64_t)a[ 4]) * a[ 5]) * 2;
int64_t t10 = (((int64_t)a[ 0]) * a[10]
+ ((int64_t)a[ 1]) * a[ 9]
+ ((int64_t)a[ 2]) * a[ 8]
+ ((int64_t)a[ 3]) * a[ 7]
+ ((int64_t)a[ 4]) * a[ 6]) * 2
+ ((int64_t)a[ 5]) * a[ 5];
int64_t t11 = (((int64_t)a[ 0]) * a[11]
+ ((int64_t)a[ 1]) * a[10]
+ ((int64_t)a[ 2]) * a[ 9]
+ ((int64_t)a[ 3]) * a[ 8]
+ ((int64_t)a[ 4]) * a[ 7]
+ ((int64_t)a[ 5]) * a[ 6]) * 2;
int64_t t12 = (((int64_t)a[ 0]) * a[12]
+ ((int64_t)a[ 1]) * a[11]
+ ((int64_t)a[ 2]) * a[10]
+ ((int64_t)a[ 3]) * a[ 9]
+ ((int64_t)a[ 4]) * a[ 8]
+ ((int64_t)a[ 5]) * a[ 7]) * 2
+ ((int64_t)a[ 6]) * a[ 6];
int64_t t13 = (((int64_t)a[ 0]) * a[13]
+ ((int64_t)a[ 1]) * a[12]
+ ((int64_t)a[ 2]) * a[11]
+ ((int64_t)a[ 3]) * a[10]
+ ((int64_t)a[ 4]) * a[ 9]
+ ((int64_t)a[ 5]) * a[ 8]
+ ((int64_t)a[ 6]) * a[ 7]) * 2;
int64_t t14 = (((int64_t)a[ 0]) * a[14]
+ ((int64_t)a[ 1]) * a[13]
+ ((int64_t)a[ 2]) * a[12]
+ ((int64_t)a[ 3]) * a[11]
+ ((int64_t)a[ 4]) * a[10]
+ ((int64_t)a[ 5]) * a[ 9]
+ ((int64_t)a[ 6]) * a[ 8]) * 2
+ ((int64_t)a[ 7]) * a[ 7];
int64_t t15 = (((int64_t)a[ 1]) * a[14]
+ ((int64_t)a[ 2]) * a[13]
+ ((int64_t)a[ 3]) * a[12]
+ ((int64_t)a[ 4]) * a[11]
+ ((int64_t)a[ 5]) * a[10]
+ ((int64_t)a[ 6]) * a[ 9]
+ ((int64_t)a[ 7]) * a[ 8]) * 2;
int64_t t16 = (((int64_t)a[ 2]) * a[14]
+ ((int64_t)a[ 3]) * a[13]
+ ((int64_t)a[ 4]) * a[12]
+ ((int64_t)a[ 5]) * a[11]
+ ((int64_t)a[ 6]) * a[10]
+ ((int64_t)a[ 7]) * a[ 9]) * 2
+ ((int64_t)a[ 8]) * a[ 8];
int64_t t17 = (((int64_t)a[ 3]) * a[14]
+ ((int64_t)a[ 4]) * a[13]
+ ((int64_t)a[ 5]) * a[12]
+ ((int64_t)a[ 6]) * a[11]
+ ((int64_t)a[ 7]) * a[10]
+ ((int64_t)a[ 8]) * a[ 9]) * 2;
int64_t t18 = (((int64_t)a[ 4]) * a[14]
+ ((int64_t)a[ 5]) * a[13]
+ ((int64_t)a[ 6]) * a[12]
+ ((int64_t)a[ 7]) * a[11]
+ ((int64_t)a[ 8]) * a[10]) * 2
+ ((int64_t)a[ 9]) * a[ 9];
int64_t t19 = (((int64_t)a[ 5]) * a[14]
+ ((int64_t)a[ 6]) * a[13]
+ ((int64_t)a[ 7]) * a[12]
+ ((int64_t)a[ 8]) * a[11]
+ ((int64_t)a[ 9]) * a[10]) * 2;
int64_t t20 = (((int64_t)a[ 6]) * a[14]
+ ((int64_t)a[ 7]) * a[13]
+ ((int64_t)a[ 8]) * a[12]
+ ((int64_t)a[ 9]) * a[11]) * 2
+ ((int64_t)a[10]) * a[10];
int64_t t21 = (((int64_t)a[ 7]) * a[14]
+ ((int64_t)a[ 8]) * a[13]
+ ((int64_t)a[ 9]) * a[12]
+ ((int64_t)a[10]) * a[11]) * 2;
int64_t t22 = (((int64_t)a[ 8]) * a[14]
+ ((int64_t)a[ 9]) * a[13]
+ ((int64_t)a[10]) * a[12]) * 2
+ ((int64_t)a[11]) * a[11];
int64_t t23 = (((int64_t)a[ 9]) * a[14]
+ ((int64_t)a[10]) * a[13]
+ ((int64_t)a[11]) * a[12]) * 2;
int64_t t24 = (((int64_t)a[10]) * a[14]
+ ((int64_t)a[11]) * a[13]) * 2
+ ((int64_t)a[12]) * a[12];
int64_t t25 = (((int64_t)a[11]) * a[14]
+ ((int64_t)a[12]) * a[13]) * 2;
int64_t t26 = (((int64_t)a[12]) * a[14]) * 2
+ ((int64_t)a[13]) * a[13];
int64_t t27 = (((int64_t)a[13]) * a[14]) * 2;
int64_t t28 = ((int64_t)a[14]) * a[14];
t1 += t0 >> 23; r[ 0] = t0 & 0x7fffff;
t2 += t1 >> 23; r[ 1] = t1 & 0x7fffff;
t3 += t2 >> 23; r[ 2] = t2 & 0x7fffff;
t4 += t3 >> 23; r[ 3] = t3 & 0x7fffff;
t5 += t4 >> 23; r[ 4] = t4 & 0x7fffff;
t6 += t5 >> 23; r[ 5] = t5 & 0x7fffff;
t7 += t6 >> 23; r[ 6] = t6 & 0x7fffff;
t8 += t7 >> 23; r[ 7] = t7 & 0x7fffff;
t9 += t8 >> 23; r[ 8] = t8 & 0x7fffff;
t10 += t9 >> 23; r[ 9] = t9 & 0x7fffff;
t11 += t10 >> 23; r[10] = t10 & 0x7fffff;
t12 += t11 >> 23; r[11] = t11 & 0x7fffff;
t13 += t12 >> 23; r[12] = t12 & 0x7fffff;
t14 += t13 >> 23; r[13] = t13 & 0x7fffff;
t15 += t14 >> 23; r[14] = t14 & 0x7fffff;
t16 += t15 >> 23; r[15] = t15 & 0x7fffff;
t17 += t16 >> 23; r[16] = t16 & 0x7fffff;
t18 += t17 >> 23; r[17] = t17 & 0x7fffff;
t19 += t18 >> 23; r[18] = t18 & 0x7fffff;
t20 += t19 >> 23; r[19] = t19 & 0x7fffff;
t21 += t20 >> 23; r[20] = t20 & 0x7fffff;
t22 += t21 >> 23; r[21] = t21 & 0x7fffff;
t23 += t22 >> 23; r[22] = t22 & 0x7fffff;
t24 += t23 >> 23; r[23] = t23 & 0x7fffff;
t25 += t24 >> 23; r[24] = t24 & 0x7fffff;
t26 += t25 >> 23; r[25] = t25 & 0x7fffff;
t27 += t26 >> 23; r[26] = t26 & 0x7fffff;
t28 += t27 >> 23; r[27] = t27 & 0x7fffff;
r[29] = (sp_digit)(t28 >> 23);
r[28] = t28 & 0x7fffff;
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_15(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
r[ 0] = a[ 0] + b[ 0];
r[ 1] = a[ 1] + b[ 1];
r[ 2] = a[ 2] + b[ 2];
r[ 3] = a[ 3] + b[ 3];
r[ 4] = a[ 4] + b[ 4];
r[ 5] = a[ 5] + b[ 5];
r[ 6] = a[ 6] + b[ 6];
r[ 7] = a[ 7] + b[ 7];
r[ 8] = a[ 8] + b[ 8];
r[ 9] = a[ 9] + b[ 9];
r[10] = a[10] + b[10];
r[11] = a[11] + b[11];
r[12] = a[12] + b[12];
r[13] = a[13] + b[13];
r[14] = a[14] + b[14];
return 0;
}
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_sub_30(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 24; i += 8) {
r[i + 0] = a[i + 0] - b[i + 0];
r[i + 1] = a[i + 1] - b[i + 1];
r[i + 2] = a[i + 2] - b[i + 2];
r[i + 3] = a[i + 3] - b[i + 3];
r[i + 4] = a[i + 4] - b[i + 4];
r[i + 5] = a[i + 5] - b[i + 5];
r[i + 6] = a[i + 6] - b[i + 6];
r[i + 7] = a[i + 7] - b[i + 7];
}
r[24] = a[24] - b[24];
r[25] = a[25] - b[25];
r[26] = a[26] - b[26];
r[27] = a[27] - b[27];
r[28] = a[28] - b[28];
r[29] = a[29] - b[29];
return 0;
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_30(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 24; i += 8) {
r[i + 0] = a[i + 0] + b[i + 0];
r[i + 1] = a[i + 1] + b[i + 1];
r[i + 2] = a[i + 2] + b[i + 2];
r[i + 3] = a[i + 3] + b[i + 3];
r[i + 4] = a[i + 4] + b[i + 4];
r[i + 5] = a[i + 5] + b[i + 5];
r[i + 6] = a[i + 6] + b[i + 6];
r[i + 7] = a[i + 7] + b[i + 7];
}
r[24] = a[24] + b[24];
r[25] = a[25] + b[25];
r[26] = a[26] + b[26];
r[27] = a[27] + b[27];
r[28] = a[28] + b[28];
r[29] = a[29] + b[29];
return 0;
}
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_2048_mul_45(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
sp_digit p0[30];
sp_digit p1[30];
sp_digit p2[30];
sp_digit p3[30];
sp_digit p4[30];
sp_digit p5[30];
sp_digit t0[30];
sp_digit t1[30];
sp_digit t2[30];
sp_digit a0[15];
sp_digit a1[15];
sp_digit a2[15];
sp_digit b0[15];
sp_digit b1[15];
sp_digit b2[15];
(void)sp_2048_add_15(a0, a, &a[15]);
(void)sp_2048_add_15(b0, b, &b[15]);
(void)sp_2048_add_15(a1, &a[15], &a[30]);
(void)sp_2048_add_15(b1, &b[15], &b[30]);
(void)sp_2048_add_15(a2, a0, &a[30]);
(void)sp_2048_add_15(b2, b0, &b[30]);
sp_2048_mul_15(p0, a, b);
sp_2048_mul_15(p2, &a[15], &b[15]);
sp_2048_mul_15(p4, &a[30], &b[30]);
sp_2048_mul_15(p1, a0, b0);
sp_2048_mul_15(p3, a1, b1);
sp_2048_mul_15(p5, a2, b2);
XMEMSET(r, 0, sizeof(*r)*2U*45U);
(void)sp_2048_sub_30(t0, p3, p2);
(void)sp_2048_sub_30(t1, p1, p2);
(void)sp_2048_sub_30(t2, p5, t0);
(void)sp_2048_sub_30(t2, t2, t1);
(void)sp_2048_sub_30(t0, t0, p4);
(void)sp_2048_sub_30(t1, t1, p0);
(void)sp_2048_add_30(r, r, p0);
(void)sp_2048_add_30(&r[15], &r[15], t1);
(void)sp_2048_add_30(&r[30], &r[30], t2);
(void)sp_2048_add_30(&r[45], &r[45], t0);
(void)sp_2048_add_30(&r[60], &r[60], p4);
}
/* Square a into r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_2048_sqr_45(sp_digit* r, const sp_digit* a)
{
sp_digit p0[30];
sp_digit p1[30];
sp_digit p2[30];
sp_digit p3[30];
sp_digit p4[30];
sp_digit p5[30];
sp_digit t0[30];
sp_digit t1[30];
sp_digit t2[30];
sp_digit a0[15];
sp_digit a1[15];
sp_digit a2[15];
(void)sp_2048_add_15(a0, a, &a[15]);
(void)sp_2048_add_15(a1, &a[15], &a[30]);
(void)sp_2048_add_15(a2, a0, &a[30]);
sp_2048_sqr_15(p0, a);
sp_2048_sqr_15(p2, &a[15]);
sp_2048_sqr_15(p4, &a[30]);
sp_2048_sqr_15(p1, a0);
sp_2048_sqr_15(p3, a1);
sp_2048_sqr_15(p5, a2);
XMEMSET(r, 0, sizeof(*r)*2U*45U);
(void)sp_2048_sub_30(t0, p3, p2);
(void)sp_2048_sub_30(t1, p1, p2);
(void)sp_2048_sub_30(t2, p5, t0);
(void)sp_2048_sub_30(t2, t2, t1);
(void)sp_2048_sub_30(t0, t0, p4);
(void)sp_2048_sub_30(t1, t1, p0);
(void)sp_2048_add_30(r, r, p0);
(void)sp_2048_add_30(&r[15], &r[15], t1);
(void)sp_2048_add_30(&r[30], &r[30], t2);
(void)sp_2048_add_30(&r[45], &r[45], t0);
(void)sp_2048_add_30(&r[60], &r[60], p4);
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_45(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 40; i += 8) {
r[i + 0] = a[i + 0] + b[i + 0];
r[i + 1] = a[i + 1] + b[i + 1];
r[i + 2] = a[i + 2] + b[i + 2];
r[i + 3] = a[i + 3] + b[i + 3];
r[i + 4] = a[i + 4] + b[i + 4];
r[i + 5] = a[i + 5] + b[i + 5];
r[i + 6] = a[i + 6] + b[i + 6];
r[i + 7] = a[i + 7] + b[i + 7];
}
r[40] = a[40] + b[40];
r[41] = a[41] + b[41];
r[42] = a[42] + b[42];
r[43] = a[43] + b[43];
r[44] = a[44] + b[44];
return 0;
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 88; i += 8) {
r[i + 0] = a[i + 0] + b[i + 0];
r[i + 1] = a[i + 1] + b[i + 1];
r[i + 2] = a[i + 2] + b[i + 2];
r[i + 3] = a[i + 3] + b[i + 3];
r[i + 4] = a[i + 4] + b[i + 4];
r[i + 5] = a[i + 5] + b[i + 5];
r[i + 6] = a[i + 6] + b[i + 6];
r[i + 7] = a[i + 7] + b[i + 7];
}
r[88] = a[88] + b[88];
r[89] = a[89] + b[89];
return 0;
}
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_sub_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 88; i += 8) {
r[i + 0] = a[i + 0] - b[i + 0];
r[i + 1] = a[i + 1] - b[i + 1];
r[i + 2] = a[i + 2] - b[i + 2];
r[i + 3] = a[i + 3] - b[i + 3];
r[i + 4] = a[i + 4] - b[i + 4];
r[i + 5] = a[i + 5] - b[i + 5];
r[i + 6] = a[i + 6] - b[i + 6];
r[i + 7] = a[i + 7] - b[i + 7];
}
r[88] = a[88] - b[88];
r[89] = a[89] - b[89];
return 0;
}
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_2048_mul_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
sp_digit* z0 = r;
sp_digit z1[90];
sp_digit* a1 = z1;
sp_digit b1[45];
sp_digit* z2 = r + 90;
(void)sp_2048_add_45(a1, a, &a[45]);
(void)sp_2048_add_45(b1, b, &b[45]);
sp_2048_mul_45(z2, &a[45], &b[45]);
sp_2048_mul_45(z0, a, b);
sp_2048_mul_45(z1, a1, b1);
(void)sp_2048_sub_90(z1, z1, z2);
(void)sp_2048_sub_90(z1, z1, z0);
(void)sp_2048_add_90(r + 45, r + 45, z1);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_2048_sqr_90(sp_digit* r, const sp_digit* a)
{
sp_digit* z0 = r;
sp_digit z1[90];
sp_digit* a1 = z1;
sp_digit* z2 = r + 90;
(void)sp_2048_add_45(a1, a, &a[45]);
sp_2048_sqr_45(z2, &a[45]);
sp_2048_sqr_45(z0, a);
sp_2048_sqr_45(z1, a1);
(void)sp_2048_sub_90(z1, z1, z2);
(void)sp_2048_sub_90(z1, z1, z0);
(void)sp_2048_add_90(r + 45, r + 45, z1);
}
#endif /* !WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 90; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_sub_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 90; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_2048_mul_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[89]) * b[89];
r[179] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 177; k >= 0; k--) {
for (i = 89; i >= 0; i--) {
j = k - i;
if (j >= 90) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * b[j];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_2048_sqr_90(sp_digit* r, const sp_digit* a)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[89]) * a[89];
r[179] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 177; k >= 0; k--) {
for (i = 89; i >= 0; i--) {
j = k - i;
if (j >= 90 || i <= j) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * a[j] * 2;
}
if (i == j) {
c += ((int64_t)a[i]) * a[i];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
#endif /* WOLFSSL_SP_SMALL */
#if (defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH)) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)
#ifdef WOLFSSL_SP_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_45(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 45; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_sub_45(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 45; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#else
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_sub_45(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 40; i += 8) {
r[i + 0] = a[i + 0] - b[i + 0];
r[i + 1] = a[i + 1] - b[i + 1];
r[i + 2] = a[i + 2] - b[i + 2];
r[i + 3] = a[i + 3] - b[i + 3];
r[i + 4] = a[i + 4] - b[i + 4];
r[i + 5] = a[i + 5] - b[i + 5];
r[i + 6] = a[i + 6] - b[i + 6];
r[i + 7] = a[i + 7] - b[i + 7];
}
r[40] = a[40] - b[40];
r[41] = a[41] - b[41];
r[42] = a[42] - b[42];
r[43] = a[43] - b[43];
r[44] = a[44] - b[44];
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_2048_mul_45(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[44]) * b[44];
r[89] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 87; k >= 0; k--) {
for (i = 44; i >= 0; i--) {
j = k - i;
if (j >= 45) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * b[j];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_2048_sqr_45(sp_digit* r, const sp_digit* a)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[44]) * a[44];
r[89] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 87; k >= 0; k--) {
for (i = 44; i >= 0; i--) {
j = k - i;
if (j >= 45 || i <= j) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * a[j] * 2;
}
if (i == j) {
c += ((int64_t)a[i]) * a[i];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
#endif /* WOLFSSL_SP_SMALL */
#endif /* (WOLFSSL_HAVE_SP_RSA || WOLFSSL_HAVE_SP_DH) && !WOLFSSL_RSA_PUBLIC_ONLY */
/* Caclulate the bottom digit of -1/a mod 2^n.
*
* a A single precision number.
* rho Bottom word of inverse.
*/
static void sp_2048_mont_setup(const sp_digit* a, sp_digit* rho)
{
sp_digit x, b;
b = a[0];
x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
x *= 2 - b * x; /* here x*a==1 mod 2**8 */
x *= 2 - b * x; /* here x*a==1 mod 2**16 */
x *= 2 - b * x; /* here x*a==1 mod 2**32 */
x &= 0x7fffff;
/* rho = -1/m mod b */
*rho = (1L << 23) - x;
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_2048_mul_d_90(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 90; i++) {
t += tb * a[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[90] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x7fffff;
for (i = 0; i < 88; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[89];
r[89] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
r[90] = (sp_digit)(t[1] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
#if (defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH)) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)
/* r = 2^n mod m where n is the number of bits to reduce by.
* Given m must be 2048 bits, just need to subtract.
*
* r A single precision number.
* m A signle precision number.
*/
static void sp_2048_mont_norm_45(sp_digit* r, const sp_digit* m)
{
/* Set r = 2^n - 1. */
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<44; i++) {
r[i] = 0x7fffff;
}
#else
int i;
for (i = 0; i < 40; i += 8) {
r[i + 0] = 0x7fffff;
r[i + 1] = 0x7fffff;
r[i + 2] = 0x7fffff;
r[i + 3] = 0x7fffff;
r[i + 4] = 0x7fffff;
r[i + 5] = 0x7fffff;
r[i + 6] = 0x7fffff;
r[i + 7] = 0x7fffff;
}
r[40] = 0x7fffff;
r[41] = 0x7fffff;
r[42] = 0x7fffff;
r[43] = 0x7fffff;
#endif
r[44] = 0xfffL;
/* r = (2^n - 1) mod n */
(void)sp_2048_sub_45(r, r, m);
/* Add one so r = 2^n mod m */
r[0] += 1;
}
/* Compare a with b in constant time.
*
* a A single precision integer.
* b A single precision integer.
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_2048_cmp_45(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=44; i>=0; i--) {
r |= (a[i] - b[i]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#else
int i;
r |= (a[44] - b[44]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[43] - b[43]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[42] - b[42]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[41] - b[41]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[40] - b[40]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
for (i = 32; i >= 0; i -= 8) {
r |= (a[i + 7] - b[i + 7]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 6] - b[i + 6]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 5] - b[i + 5]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 4] - b[i + 4]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 3] - b[i + 3]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 2] - b[i + 2]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 1] - b[i + 1]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 0] - b[i + 0]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#endif /* WOLFSSL_SP_SMALL */
return r;
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*
* r A single precision number representing condition subtract result.
* a A single precision number to subtract from.
* b A single precision number to subtract.
* m Mask value to apply.
*/
static void sp_2048_cond_sub_45(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 45; i++) {
r[i] = a[i] - (b[i] & m);
}
#else
int i;
for (i = 0; i < 40; i += 8) {
r[i + 0] = a[i + 0] - (b[i + 0] & m);
r[i + 1] = a[i + 1] - (b[i + 1] & m);
r[i + 2] = a[i + 2] - (b[i + 2] & m);
r[i + 3] = a[i + 3] - (b[i + 3] & m);
r[i + 4] = a[i + 4] - (b[i + 4] & m);
r[i + 5] = a[i + 5] - (b[i + 5] & m);
r[i + 6] = a[i + 6] - (b[i + 6] & m);
r[i + 7] = a[i + 7] - (b[i + 7] & m);
}
r[40] = a[40] - (b[40] & m);
r[41] = a[41] - (b[41] & m);
r[42] = a[42] - (b[42] & m);
r[43] = a[43] - (b[43] & m);
r[44] = a[44] - (b[44] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Mul a by scalar b and add into r. (r += a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_2048_mul_add_45(sp_digit* r, const sp_digit* a,
const sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 45; i++) {
t += (tb * a[i]) + r[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[45] += t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] += t[0] & 0x7fffff;
for (i = 0; i < 40; i += 8) {
t[1] = tb * a[i+1];
r[i+1] += (t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] += (t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] += (t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] += (t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] += (t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] += (t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] += (t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] += (t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[41]; r[41] += (t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[42]; r[42] += (t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[43]; r[43] += (t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[44]; r[44] += (t[3] >> 23) + (t[4] & 0x7fffff);
r[45] += t[4] >> 23;
#endif /* WOLFSSL_SP_SMALL */
}
/* Normalize the values in each word to 23.
*
* a Array of sp_digit to normalize.
*/
static void sp_2048_norm_45(sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 44; i++) {
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
#else
int i;
for (i = 0; i < 40; i += 8) {
a[i+1] += a[i+0] >> 23; a[i+0] &= 0x7fffff;
a[i+2] += a[i+1] >> 23; a[i+1] &= 0x7fffff;
a[i+3] += a[i+2] >> 23; a[i+2] &= 0x7fffff;
a[i+4] += a[i+3] >> 23; a[i+3] &= 0x7fffff;
a[i+5] += a[i+4] >> 23; a[i+4] &= 0x7fffff;
a[i+6] += a[i+5] >> 23; a[i+5] &= 0x7fffff;
a[i+7] += a[i+6] >> 23; a[i+6] &= 0x7fffff;
a[i+8] += a[i+7] >> 23; a[i+7] &= 0x7fffff;
a[i+9] += a[i+8] >> 23; a[i+8] &= 0x7fffff;
}
a[40+1] += a[40] >> 23;
a[40] &= 0x7fffff;
a[41+1] += a[41] >> 23;
a[41] &= 0x7fffff;
a[42+1] += a[42] >> 23;
a[42] &= 0x7fffff;
a[43+1] += a[43] >> 23;
a[43] &= 0x7fffff;
#endif
}
/* Shift the result in the high 1024 bits down to the bottom.
*
* r A single precision number.
* a A single precision number.
*/
static void sp_2048_mont_shift_45(sp_digit* r, const sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
int64_t n = a[44] >> 12;
n += ((int64_t)a[45]) << 11;
for (i = 0; i < 44; i++) {
r[i] = n & 0x7fffff;
n >>= 23;
n += ((int64_t)a[46 + i]) << 11;
}
r[44] = (sp_digit)n;
#else
int i;
int64_t n = a[44] >> 12;
n += ((int64_t)a[45]) << 11;
for (i = 0; i < 40; i += 8) {
r[i + 0] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 46]) << 11;
r[i + 1] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 47]) << 11;
r[i + 2] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 48]) << 11;
r[i + 3] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 49]) << 11;
r[i + 4] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 50]) << 11;
r[i + 5] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 51]) << 11;
r[i + 6] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 52]) << 11;
r[i + 7] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 53]) << 11;
}
r[40] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[86]) << 11;
r[41] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[87]) << 11;
r[42] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[88]) << 11;
r[43] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[89]) << 11;
r[44] = (sp_digit)n;
#endif /* WOLFSSL_SP_SMALL */
XMEMSET(&r[45], 0, sizeof(*r) * 45U);
}
/* Reduce the number back to 2048 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_2048_mont_reduce_45(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
for (i=0; i<44; i++) {
mu = (a[i] * mp) & 0x7fffff;
sp_2048_mul_add_45(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = (a[i] * mp) & 0xfffL;
sp_2048_mul_add_45(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
sp_2048_mont_shift_45(a, a);
sp_2048_cond_sub_45(a, a, m, 0 - (((a[44] >> 12) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_2048_norm_45(a);
}
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_2048_mont_mul_45(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m, sp_digit mp)
{
sp_2048_mul_45(r, a, b);
sp_2048_mont_reduce_45(r, m, mp);
}
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_2048_mont_sqr_45(sp_digit* r, const sp_digit* a, const sp_digit* m,
sp_digit mp)
{
sp_2048_sqr_45(r, a);
sp_2048_mont_reduce_45(r, m, mp);
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_2048_mul_d_45(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 45; i++) {
t += tb * a[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[45] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x7fffff;
for (i = 0; i < 40; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[41];
r[41] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[42];
r[42] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[43];
r[43] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[44];
r[44] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
r[45] = (sp_digit)(t[4] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
/* Conditionally add a and b using the mask m.
* m is -1 to add and 0 when not.
*
* r A single precision number representing conditional add result.
* a A single precision number to add with.
* b A single precision number to add.
* m Mask value to apply.
*/
static void sp_2048_cond_add_45(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 45; i++) {
r[i] = a[i] + (b[i] & m);
}
#else
int i;
for (i = 0; i < 40; i += 8) {
r[i + 0] = a[i + 0] + (b[i + 0] & m);
r[i + 1] = a[i + 1] + (b[i + 1] & m);
r[i + 2] = a[i + 2] + (b[i + 2] & m);
r[i + 3] = a[i + 3] + (b[i + 3] & m);
r[i + 4] = a[i + 4] + (b[i + 4] & m);
r[i + 5] = a[i + 5] + (b[i + 5] & m);
r[i + 6] = a[i + 6] + (b[i + 6] & m);
r[i + 7] = a[i + 7] + (b[i + 7] & m);
}
r[40] = a[40] + (b[40] & m);
r[41] = a[41] + (b[41] & m);
r[42] = a[42] + (b[42] & m);
r[43] = a[43] + (b[43] & m);
r[44] = a[44] + (b[44] & m);
#endif /* WOLFSSL_SP_SMALL */
}
#ifdef WOLFSSL_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_45(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 45; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif
SP_NOINLINE static void sp_2048_rshift_45(sp_digit* r, sp_digit* a, byte n)
{
int i;
#ifdef WOLFSSL_SP_SMALL
for (i=0; i<44; i++) {
r[i] = ((a[i] >> n) | (a[i + 1] << (23 - n))) & 0x7fffff;
}
#else
for (i=0; i<40; i += 8) {
r[i+0] = ((a[i+0] >> n) | (a[i+1] << (23 - n))) & 0x7fffff;
r[i+1] = ((a[i+1] >> n) | (a[i+2] << (23 - n))) & 0x7fffff;
r[i+2] = ((a[i+2] >> n) | (a[i+3] << (23 - n))) & 0x7fffff;
r[i+3] = ((a[i+3] >> n) | (a[i+4] << (23 - n))) & 0x7fffff;
r[i+4] = ((a[i+4] >> n) | (a[i+5] << (23 - n))) & 0x7fffff;
r[i+5] = ((a[i+5] >> n) | (a[i+6] << (23 - n))) & 0x7fffff;
r[i+6] = ((a[i+6] >> n) | (a[i+7] << (23 - n))) & 0x7fffff;
r[i+7] = ((a[i+7] >> n) | (a[i+8] << (23 - n))) & 0x7fffff;
}
r[40] = ((a[40] >> n) | (a[41] << (23 - n))) & 0x7fffff;
r[41] = ((a[41] >> n) | (a[42] << (23 - n))) & 0x7fffff;
r[42] = ((a[42] >> n) | (a[43] << (23 - n))) & 0x7fffff;
r[43] = ((a[43] >> n) | (a[44] << (23 - n))) & 0x7fffff;
#endif
r[44] = a[44] >> n;
}
#ifdef WOLFSSL_SP_DIV_32
static WC_INLINE sp_digit sp_2048_div_word_45(sp_digit d1, sp_digit d0,
sp_digit dv)
{
sp_digit d, r, t;
/* All 23 bits from d1 and top 8 bits from d0. */
d = (d1 << 8) | (d0 >> 15);
r = d / dv;
d -= r * dv;
/* Up to 9 bits in r */
/* Next 8 bits from d0. */
r <<= 8;
d <<= 8;
d |= (d0 >> 7) & ((1 << 8) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 17 bits in r */
/* Remaining 7 bits from d0. */
r <<= 7;
d <<= 7;
d |= d0 & ((1 << 7) - 1);
t = d / dv;
r += t;
return r;
}
#endif /* WOLFSSL_SP_DIV_32 */
/* Divide d in a and put remainder into r (m*d + r = a)
* m is not calculated as it is not needed at this time.
*
* a Nmber to be divided.
* d Number to divide with.
* m Multiplier result.
* r Remainder from the division.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_2048_div_45(const sp_digit* a, const sp_digit* d, sp_digit* m,
sp_digit* r)
{
int i;
#ifndef WOLFSSL_SP_DIV_32
int64_t d1;
#endif
sp_digit dv, r1;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_digit* td;
#else
sp_digit t1d[90 + 1], t2d[45 + 1], sdd[45 + 1];
#endif
sp_digit* t1;
sp_digit* t2;
sp_digit* sd;
int err = MP_OKAY;
(void)m;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * (4 * 45 + 3), NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
t1 = td;
t2 = td + 90 + 1;
sd = t2 + 45 + 1;
#else
t1 = t1d;
t2 = t2d;
sd = sdd;
#endif
sp_2048_mul_d_45(sd, d, 1 << 11);
sp_2048_mul_d_90(t1, a, 1 << 11);
dv = sd[44];
for (i=45; i>=0; i--) {
t1[45 + i] += t1[45 + i - 1] >> 23;
t1[45 + i - 1] &= 0x7fffff;
#ifndef WOLFSSL_SP_DIV_32
d1 = t1[45 + i];
d1 <<= 23;
d1 += t1[45 + i - 1];
r1 = (sp_digit)(d1 / dv);
#else
r1 = sp_2048_div_word_45(t1[45 + i], t1[45 + i - 1], dv);
#endif
sp_2048_mul_d_45(t2, sd, r1);
(void)sp_2048_sub_45(&t1[i], &t1[i], t2);
t1[45 + i] -= t2[45];
t1[45 + i] += t1[45 + i - 1] >> 23;
t1[45 + i - 1] &= 0x7fffff;
r1 = (((-t1[45 + i]) << 23) - t1[45 + i - 1]) / dv;
r1 -= t1[45 + i];
sp_2048_mul_d_45(t2, sd, r1);
(void)sp_2048_add_45(&t1[i], &t1[i], t2);
t1[45 + i] += t1[45 + i - 1] >> 23;
t1[45 + i - 1] &= 0x7fffff;
}
t1[45 - 1] += t1[45 - 2] >> 23;
t1[45 - 2] &= 0x7fffff;
d1 = t1[45 - 1];
r1 = (sp_digit)(d1 / dv);
sp_2048_mul_d_45(t2, sd, r1);
sp_2048_sub_45(t1, t1, t2);
XMEMCPY(r, t1, sizeof(*r) * 2U * 45U);
for (i=0; i<43; i++) {
r[i+1] += r[i] >> 23;
r[i] &= 0x7fffff;
}
sp_2048_cond_add_45(r, r, sd, 0 - ((r[44] < 0) ?
(sp_digit)1 : (sp_digit)0));
sp_2048_norm_45(r);
sp_2048_rshift_45(r, r, 11);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
/* Reduce a modulo m into r. (r = a mod m)
*
* r A single precision number that is the reduced result.
* a A single precision number that is to be reduced.
* m A single precision number that is the modulus to reduce with.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_2048_mod_45(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
return sp_2048_div_45(a, m, NULL, r);
}
/* Modular exponentiate a to the e mod m. (r = a^e mod m)
*
* r A single precision number that is the result of the operation.
* a A single precision number being exponentiated.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_2048_mod_exp_45(sp_digit* r, const sp_digit* a, const sp_digit* e, int bits,
const sp_digit* m, int reduceA)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* td;
sp_digit* t[3];
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 45 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
if (err == MP_OKAY) {
XMEMSET(td, 0, sizeof(*td) * 3U * 45U * 2U);
norm = t[0] = td;
t[1] = &td[45 * 2];
t[2] = &td[2 * 45 * 2];
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_45(norm, m);
if (reduceA != 0) {
err = sp_2048_mod_45(t[1], a, m);
}
else {
XMEMCPY(t[1], a, sizeof(sp_digit) * 45U);
}
}
if (err == MP_OKAY) {
sp_2048_mul_45(t[1], t[1], norm);
err = sp_2048_mod_45(t[1], t[1], m);
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_2048_mont_mul_45(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])),
sizeof(*t[2]) * 45 * 2);
sp_2048_mont_sqr_45(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2],
sizeof(*t[2]) * 45 * 2);
}
sp_2048_mont_reduce_45(t[0], m, mp);
n = sp_2048_cmp_45(t[0], m);
sp_2048_cond_sub_45(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(*r) * 45 * 2);
}
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
return err;
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[3][90];
#else
sp_digit* td;
sp_digit* t[3];
#endif
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 45 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
t[0] = td;
t[1] = &td[45 * 2];
t[2] = &td[2 * 45 * 2];
#endif
norm = t[0];
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_45(norm, m);
if (reduceA != 0) {
err = sp_2048_mod_45(t[1], a, m);
if (err == MP_OKAY) {
sp_2048_mul_45(t[1], t[1], norm);
err = sp_2048_mod_45(t[1], t[1], m);
}
}
else {
sp_2048_mul_45(t[1], a, norm);
err = sp_2048_mod_45(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_2048_mont_mul_45(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), sizeof(t[2]));
sp_2048_mont_sqr_45(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2], sizeof(t[2]));
}
sp_2048_mont_reduce_45(t[0], m, mp);
n = sp_2048_cmp_45(t[0], m);
sp_2048_cond_sub_45(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(t[0]));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[32][90];
#else
sp_digit* t[32];
sp_digit* td;
#endif
sp_digit* norm;
sp_digit rt[90];
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 32 * 90, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
for (i=0; i<32; i++)
t[i] = td + i * 90;
#endif
norm = t[0];
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_45(norm, m);
if (reduceA != 0) {
err = sp_2048_mod_45(t[1], a, m);
if (err == MP_OKAY) {
sp_2048_mul_45(t[1], t[1], norm);
err = sp_2048_mod_45(t[1], t[1], m);
}
}
else {
sp_2048_mul_45(t[1], a, norm);
err = sp_2048_mod_45(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
sp_2048_mont_sqr_45(t[ 2], t[ 1], m, mp);
sp_2048_mont_mul_45(t[ 3], t[ 2], t[ 1], m, mp);
sp_2048_mont_sqr_45(t[ 4], t[ 2], m, mp);
sp_2048_mont_mul_45(t[ 5], t[ 3], t[ 2], m, mp);
sp_2048_mont_sqr_45(t[ 6], t[ 3], m, mp);
sp_2048_mont_mul_45(t[ 7], t[ 4], t[ 3], m, mp);
sp_2048_mont_sqr_45(t[ 8], t[ 4], m, mp);
sp_2048_mont_mul_45(t[ 9], t[ 5], t[ 4], m, mp);
sp_2048_mont_sqr_45(t[10], t[ 5], m, mp);
sp_2048_mont_mul_45(t[11], t[ 6], t[ 5], m, mp);
sp_2048_mont_sqr_45(t[12], t[ 6], m, mp);
sp_2048_mont_mul_45(t[13], t[ 7], t[ 6], m, mp);
sp_2048_mont_sqr_45(t[14], t[ 7], m, mp);
sp_2048_mont_mul_45(t[15], t[ 8], t[ 7], m, mp);
sp_2048_mont_sqr_45(t[16], t[ 8], m, mp);
sp_2048_mont_mul_45(t[17], t[ 9], t[ 8], m, mp);
sp_2048_mont_sqr_45(t[18], t[ 9], m, mp);
sp_2048_mont_mul_45(t[19], t[10], t[ 9], m, mp);
sp_2048_mont_sqr_45(t[20], t[10], m, mp);
sp_2048_mont_mul_45(t[21], t[11], t[10], m, mp);
sp_2048_mont_sqr_45(t[22], t[11], m, mp);
sp_2048_mont_mul_45(t[23], t[12], t[11], m, mp);
sp_2048_mont_sqr_45(t[24], t[12], m, mp);
sp_2048_mont_mul_45(t[25], t[13], t[12], m, mp);
sp_2048_mont_sqr_45(t[26], t[13], m, mp);
sp_2048_mont_mul_45(t[27], t[14], t[13], m, mp);
sp_2048_mont_sqr_45(t[28], t[14], m, mp);
sp_2048_mont_mul_45(t[29], t[15], t[14], m, mp);
sp_2048_mont_sqr_45(t[30], t[15], m, mp);
sp_2048_mont_mul_45(t[31], t[16], t[15], m, mp);
bits = ((bits + 4) / 5) * 5;
i = ((bits + 22) / 23) - 1;
c = bits % 23;
if (c == 0) {
c = 23;
}
if (i < 45) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
XMEMCPY(rt, t[y], sizeof(rt));
for (; i>=0 || c>=5; ) {
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
sp_2048_mont_sqr_45(rt, rt, m, mp);
sp_2048_mont_sqr_45(rt, rt, m, mp);
sp_2048_mont_sqr_45(rt, rt, m, mp);
sp_2048_mont_sqr_45(rt, rt, m, mp);
sp_2048_mont_sqr_45(rt, rt, m, mp);
sp_2048_mont_mul_45(rt, rt, t[y], m, mp);
}
sp_2048_mont_reduce_45(rt, m, mp);
n = sp_2048_cmp_45(rt, m);
sp_2048_cond_sub_45(rt, rt, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, rt, sizeof(rt));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#endif
}
#endif /* (WOLFSSL_HAVE_SP_RSA || WOLFSSL_HAVE_SP_DH) && !WOLFSSL_RSA_PUBLIC_ONLY */
/* r = 2^n mod m where n is the number of bits to reduce by.
* Given m must be 2048 bits, just need to subtract.
*
* r A single precision number.
* m A signle precision number.
*/
static void sp_2048_mont_norm_90(sp_digit* r, const sp_digit* m)
{
/* Set r = 2^n - 1. */
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<89; i++) {
r[i] = 0x7fffff;
}
#else
int i;
for (i = 0; i < 88; i += 8) {
r[i + 0] = 0x7fffff;
r[i + 1] = 0x7fffff;
r[i + 2] = 0x7fffff;
r[i + 3] = 0x7fffff;
r[i + 4] = 0x7fffff;
r[i + 5] = 0x7fffff;
r[i + 6] = 0x7fffff;
r[i + 7] = 0x7fffff;
}
r[88] = 0x7fffff;
#endif
r[89] = 0x1L;
/* r = (2^n - 1) mod n */
(void)sp_2048_sub_90(r, r, m);
/* Add one so r = 2^n mod m */
r[0] += 1;
}
/* Compare a with b in constant time.
*
* a A single precision integer.
* b A single precision integer.
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_2048_cmp_90(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=89; i>=0; i--) {
r |= (a[i] - b[i]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#else
int i;
r |= (a[89] - b[89]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[88] - b[88]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
for (i = 80; i >= 0; i -= 8) {
r |= (a[i + 7] - b[i + 7]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 6] - b[i + 6]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 5] - b[i + 5]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 4] - b[i + 4]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 3] - b[i + 3]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 2] - b[i + 2]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 1] - b[i + 1]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 0] - b[i + 0]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#endif /* WOLFSSL_SP_SMALL */
return r;
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*
* r A single precision number representing condition subtract result.
* a A single precision number to subtract from.
* b A single precision number to subtract.
* m Mask value to apply.
*/
static void sp_2048_cond_sub_90(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 90; i++) {
r[i] = a[i] - (b[i] & m);
}
#else
int i;
for (i = 0; i < 88; i += 8) {
r[i + 0] = a[i + 0] - (b[i + 0] & m);
r[i + 1] = a[i + 1] - (b[i + 1] & m);
r[i + 2] = a[i + 2] - (b[i + 2] & m);
r[i + 3] = a[i + 3] - (b[i + 3] & m);
r[i + 4] = a[i + 4] - (b[i + 4] & m);
r[i + 5] = a[i + 5] - (b[i + 5] & m);
r[i + 6] = a[i + 6] - (b[i + 6] & m);
r[i + 7] = a[i + 7] - (b[i + 7] & m);
}
r[88] = a[88] - (b[88] & m);
r[89] = a[89] - (b[89] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Mul a by scalar b and add into r. (r += a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_2048_mul_add_90(sp_digit* r, const sp_digit* a,
const sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 90; i++) {
t += (tb * a[i]) + r[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[90] += t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] += t[0] & 0x7fffff;
for (i = 0; i < 88; i += 8) {
t[1] = tb * a[i+1];
r[i+1] += (t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] += (t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] += (t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] += (t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] += (t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] += (t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] += (t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] += (t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[89]; r[89] += (t[0] >> 23) + (t[1] & 0x7fffff);
r[90] += t[1] >> 23;
#endif /* WOLFSSL_SP_SMALL */
}
/* Normalize the values in each word to 23.
*
* a Array of sp_digit to normalize.
*/
static void sp_2048_norm_90(sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 89; i++) {
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
#else
int i;
for (i = 0; i < 88; i += 8) {
a[i+1] += a[i+0] >> 23; a[i+0] &= 0x7fffff;
a[i+2] += a[i+1] >> 23; a[i+1] &= 0x7fffff;
a[i+3] += a[i+2] >> 23; a[i+2] &= 0x7fffff;
a[i+4] += a[i+3] >> 23; a[i+3] &= 0x7fffff;
a[i+5] += a[i+4] >> 23; a[i+4] &= 0x7fffff;
a[i+6] += a[i+5] >> 23; a[i+5] &= 0x7fffff;
a[i+7] += a[i+6] >> 23; a[i+6] &= 0x7fffff;
a[i+8] += a[i+7] >> 23; a[i+7] &= 0x7fffff;
a[i+9] += a[i+8] >> 23; a[i+8] &= 0x7fffff;
}
a[88+1] += a[88] >> 23;
a[88] &= 0x7fffff;
#endif
}
/* Shift the result in the high 2048 bits down to the bottom.
*
* r A single precision number.
* a A single precision number.
*/
static void sp_2048_mont_shift_90(sp_digit* r, const sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
int64_t n = a[89] >> 1;
n += ((int64_t)a[90]) << 22;
for (i = 0; i < 89; i++) {
r[i] = n & 0x7fffff;
n >>= 23;
n += ((int64_t)a[91 + i]) << 22;
}
r[89] = (sp_digit)n;
#else
int i;
int64_t n = a[89] >> 1;
n += ((int64_t)a[90]) << 22;
for (i = 0; i < 88; i += 8) {
r[i + 0] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 91]) << 22;
r[i + 1] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 92]) << 22;
r[i + 2] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 93]) << 22;
r[i + 3] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 94]) << 22;
r[i + 4] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 95]) << 22;
r[i + 5] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 96]) << 22;
r[i + 6] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 97]) << 22;
r[i + 7] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 98]) << 22;
}
r[88] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[179]) << 22;
r[89] = (sp_digit)n;
#endif /* WOLFSSL_SP_SMALL */
XMEMSET(&r[90], 0, sizeof(*r) * 90U);
}
/* Reduce the number back to 2048 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_2048_mont_reduce_90(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
#ifdef WOLFSSL_SP_DH
if (mp != 1) {
for (i=0; i<89; i++) {
mu = (a[i] * mp) & 0x7fffff;
sp_2048_mul_add_90(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = (a[i] * mp) & 0x1L;
sp_2048_mul_add_90(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
else {
for (i=0; i<89; i++) {
mu = a[i] & 0x7fffff;
sp_2048_mul_add_90(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = a[i] & 0x1L;
sp_2048_mul_add_90(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
#else
for (i=0; i<89; i++) {
mu = (a[i] * mp) & 0x7fffff;
sp_2048_mul_add_90(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = (a[i] * mp) & 0x1L;
sp_2048_mul_add_90(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
#endif
sp_2048_mont_shift_90(a, a);
sp_2048_cond_sub_90(a, a, m, 0 - (((a[89] >> 1) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_2048_norm_90(a);
}
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_2048_mont_mul_90(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m, sp_digit mp)
{
sp_2048_mul_90(r, a, b);
sp_2048_mont_reduce_90(r, m, mp);
}
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_2048_mont_sqr_90(sp_digit* r, const sp_digit* a, const sp_digit* m,
sp_digit mp)
{
sp_2048_sqr_90(r, a);
sp_2048_mont_reduce_90(r, m, mp);
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_2048_mul_d_180(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 180; i++) {
t += tb * a[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[180] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x7fffff;
for (i = 0; i < 176; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[177];
r[177] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[178];
r[178] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[179];
r[179] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
r[180] = (sp_digit)(t[3] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
/* Conditionally add a and b using the mask m.
* m is -1 to add and 0 when not.
*
* r A single precision number representing conditional add result.
* a A single precision number to add with.
* b A single precision number to add.
* m Mask value to apply.
*/
static void sp_2048_cond_add_90(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 90; i++) {
r[i] = a[i] + (b[i] & m);
}
#else
int i;
for (i = 0; i < 88; i += 8) {
r[i + 0] = a[i + 0] + (b[i + 0] & m);
r[i + 1] = a[i + 1] + (b[i + 1] & m);
r[i + 2] = a[i + 2] + (b[i + 2] & m);
r[i + 3] = a[i + 3] + (b[i + 3] & m);
r[i + 4] = a[i + 4] + (b[i + 4] & m);
r[i + 5] = a[i + 5] + (b[i + 5] & m);
r[i + 6] = a[i + 6] + (b[i + 6] & m);
r[i + 7] = a[i + 7] + (b[i + 7] & m);
}
r[88] = a[88] + (b[88] & m);
r[89] = a[89] + (b[89] & m);
#endif /* WOLFSSL_SP_SMALL */
}
#ifdef WOLFSSL_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_sub_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 90; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#endif
#ifdef WOLFSSL_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 90; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif
SP_NOINLINE static void sp_2048_rshift_90(sp_digit* r, sp_digit* a, byte n)
{
int i;
#ifdef WOLFSSL_SP_SMALL
for (i=0; i<89; i++) {
r[i] = ((a[i] >> n) | (a[i + 1] << (23 - n))) & 0x7fffff;
}
#else
for (i=0; i<88; i += 8) {
r[i+0] = ((a[i+0] >> n) | (a[i+1] << (23 - n))) & 0x7fffff;
r[i+1] = ((a[i+1] >> n) | (a[i+2] << (23 - n))) & 0x7fffff;
r[i+2] = ((a[i+2] >> n) | (a[i+3] << (23 - n))) & 0x7fffff;
r[i+3] = ((a[i+3] >> n) | (a[i+4] << (23 - n))) & 0x7fffff;
r[i+4] = ((a[i+4] >> n) | (a[i+5] << (23 - n))) & 0x7fffff;
r[i+5] = ((a[i+5] >> n) | (a[i+6] << (23 - n))) & 0x7fffff;
r[i+6] = ((a[i+6] >> n) | (a[i+7] << (23 - n))) & 0x7fffff;
r[i+7] = ((a[i+7] >> n) | (a[i+8] << (23 - n))) & 0x7fffff;
}
r[88] = ((a[88] >> n) | (a[89] << (23 - n))) & 0x7fffff;
#endif
r[89] = a[89] >> n;
}
#ifdef WOLFSSL_SP_DIV_32
static WC_INLINE sp_digit sp_2048_div_word_90(sp_digit d1, sp_digit d0,
sp_digit dv)
{
sp_digit d, r, t;
/* All 23 bits from d1 and top 8 bits from d0. */
d = (d1 << 8) | (d0 >> 15);
r = d / dv;
d -= r * dv;
/* Up to 9 bits in r */
/* Next 8 bits from d0. */
r <<= 8;
d <<= 8;
d |= (d0 >> 7) & ((1 << 8) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 17 bits in r */
/* Remaining 7 bits from d0. */
r <<= 7;
d <<= 7;
d |= d0 & ((1 << 7) - 1);
t = d / dv;
r += t;
return r;
}
#endif /* WOLFSSL_SP_DIV_32 */
/* Divide d in a and put remainder into r (m*d + r = a)
* m is not calculated as it is not needed at this time.
*
* a Nmber to be divided.
* d Number to divide with.
* m Multiplier result.
* r Remainder from the division.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_2048_div_90(const sp_digit* a, const sp_digit* d, sp_digit* m,
sp_digit* r)
{
int i;
#ifndef WOLFSSL_SP_DIV_32
int64_t d1;
#endif
sp_digit dv, r1;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_digit* td;
#else
sp_digit t1d[180 + 1], t2d[90 + 1], sdd[90 + 1];
#endif
sp_digit* t1;
sp_digit* t2;
sp_digit* sd;
int err = MP_OKAY;
(void)m;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * (4 * 90 + 3), NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
t1 = td;
t2 = td + 180 + 1;
sd = t2 + 90 + 1;
#else
t1 = t1d;
t2 = t2d;
sd = sdd;
#endif
sp_2048_mul_d_90(sd, d, 1 << 22);
sp_2048_mul_d_180(t1, a, 1 << 22);
dv = sd[89];
for (i=90; i>=0; i--) {
t1[90 + i] += t1[90 + i - 1] >> 23;
t1[90 + i - 1] &= 0x7fffff;
#ifndef WOLFSSL_SP_DIV_32
d1 = t1[90 + i];
d1 <<= 23;
d1 += t1[90 + i - 1];
r1 = (sp_digit)(d1 / dv);
#else
r1 = sp_2048_div_word_90(t1[90 + i], t1[90 + i - 1], dv);
#endif
sp_2048_mul_d_90(t2, sd, r1);
(void)sp_2048_sub_90(&t1[i], &t1[i], t2);
t1[90 + i] -= t2[90];
t1[90 + i] += t1[90 + i - 1] >> 23;
t1[90 + i - 1] &= 0x7fffff;
r1 = (((-t1[90 + i]) << 23) - t1[90 + i - 1]) / dv;
r1 -= t1[90 + i];
sp_2048_mul_d_90(t2, sd, r1);
(void)sp_2048_add_90(&t1[i], &t1[i], t2);
t1[90 + i] += t1[90 + i - 1] >> 23;
t1[90 + i - 1] &= 0x7fffff;
}
t1[90 - 1] += t1[90 - 2] >> 23;
t1[90 - 2] &= 0x7fffff;
d1 = t1[90 - 1];
r1 = (sp_digit)(d1 / dv);
sp_2048_mul_d_90(t2, sd, r1);
sp_2048_sub_90(t1, t1, t2);
XMEMCPY(r, t1, sizeof(*r) * 2U * 90U);
for (i=0; i<88; i++) {
r[i+1] += r[i] >> 23;
r[i] &= 0x7fffff;
}
sp_2048_cond_add_90(r, r, sd, 0 - ((r[89] < 0) ?
(sp_digit)1 : (sp_digit)0));
sp_2048_norm_90(r);
sp_2048_rshift_90(r, r, 22);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
/* Reduce a modulo m into r. (r = a mod m)
*
* r A single precision number that is the reduced result.
* a A single precision number that is to be reduced.
* m A single precision number that is the modulus to reduce with.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_2048_mod_90(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
return sp_2048_div_90(a, m, NULL, r);
}
#if (defined(WOLFSSL_HAVE_SP_RSA) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)) || \
defined(WOLFSSL_HAVE_SP_DH)
/* Modular exponentiate a to the e mod m. (r = a^e mod m)
*
* r A single precision number that is the result of the operation.
* a A single precision number being exponentiated.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_2048_mod_exp_90(sp_digit* r, const sp_digit* a, const sp_digit* e, int bits,
const sp_digit* m, int reduceA)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* td;
sp_digit* t[3];
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 90 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
if (err == MP_OKAY) {
XMEMSET(td, 0, sizeof(*td) * 3U * 90U * 2U);
norm = t[0] = td;
t[1] = &td[90 * 2];
t[2] = &td[2 * 90 * 2];
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_90(norm, m);
if (reduceA != 0) {
err = sp_2048_mod_90(t[1], a, m);
}
else {
XMEMCPY(t[1], a, sizeof(sp_digit) * 90U);
}
}
if (err == MP_OKAY) {
sp_2048_mul_90(t[1], t[1], norm);
err = sp_2048_mod_90(t[1], t[1], m);
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_2048_mont_mul_90(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])),
sizeof(*t[2]) * 90 * 2);
sp_2048_mont_sqr_90(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2],
sizeof(*t[2]) * 90 * 2);
}
sp_2048_mont_reduce_90(t[0], m, mp);
n = sp_2048_cmp_90(t[0], m);
sp_2048_cond_sub_90(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(*r) * 90 * 2);
}
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
return err;
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[3][180];
#else
sp_digit* td;
sp_digit* t[3];
#endif
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 90 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
t[0] = td;
t[1] = &td[90 * 2];
t[2] = &td[2 * 90 * 2];
#endif
norm = t[0];
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_90(norm, m);
if (reduceA != 0) {
err = sp_2048_mod_90(t[1], a, m);
if (err == MP_OKAY) {
sp_2048_mul_90(t[1], t[1], norm);
err = sp_2048_mod_90(t[1], t[1], m);
}
}
else {
sp_2048_mul_90(t[1], a, norm);
err = sp_2048_mod_90(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_2048_mont_mul_90(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), sizeof(t[2]));
sp_2048_mont_sqr_90(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2], sizeof(t[2]));
}
sp_2048_mont_reduce_90(t[0], m, mp);
n = sp_2048_cmp_90(t[0], m);
sp_2048_cond_sub_90(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(t[0]));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[32][180];
#else
sp_digit* t[32];
sp_digit* td;
#endif
sp_digit* norm;
sp_digit rt[180];
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 32 * 180, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
for (i=0; i<32; i++)
t[i] = td + i * 180;
#endif
norm = t[0];
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_90(norm, m);
if (reduceA != 0) {
err = sp_2048_mod_90(t[1], a, m);
if (err == MP_OKAY) {
sp_2048_mul_90(t[1], t[1], norm);
err = sp_2048_mod_90(t[1], t[1], m);
}
}
else {
sp_2048_mul_90(t[1], a, norm);
err = sp_2048_mod_90(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
sp_2048_mont_sqr_90(t[ 2], t[ 1], m, mp);
sp_2048_mont_mul_90(t[ 3], t[ 2], t[ 1], m, mp);
sp_2048_mont_sqr_90(t[ 4], t[ 2], m, mp);
sp_2048_mont_mul_90(t[ 5], t[ 3], t[ 2], m, mp);
sp_2048_mont_sqr_90(t[ 6], t[ 3], m, mp);
sp_2048_mont_mul_90(t[ 7], t[ 4], t[ 3], m, mp);
sp_2048_mont_sqr_90(t[ 8], t[ 4], m, mp);
sp_2048_mont_mul_90(t[ 9], t[ 5], t[ 4], m, mp);
sp_2048_mont_sqr_90(t[10], t[ 5], m, mp);
sp_2048_mont_mul_90(t[11], t[ 6], t[ 5], m, mp);
sp_2048_mont_sqr_90(t[12], t[ 6], m, mp);
sp_2048_mont_mul_90(t[13], t[ 7], t[ 6], m, mp);
sp_2048_mont_sqr_90(t[14], t[ 7], m, mp);
sp_2048_mont_mul_90(t[15], t[ 8], t[ 7], m, mp);
sp_2048_mont_sqr_90(t[16], t[ 8], m, mp);
sp_2048_mont_mul_90(t[17], t[ 9], t[ 8], m, mp);
sp_2048_mont_sqr_90(t[18], t[ 9], m, mp);
sp_2048_mont_mul_90(t[19], t[10], t[ 9], m, mp);
sp_2048_mont_sqr_90(t[20], t[10], m, mp);
sp_2048_mont_mul_90(t[21], t[11], t[10], m, mp);
sp_2048_mont_sqr_90(t[22], t[11], m, mp);
sp_2048_mont_mul_90(t[23], t[12], t[11], m, mp);
sp_2048_mont_sqr_90(t[24], t[12], m, mp);
sp_2048_mont_mul_90(t[25], t[13], t[12], m, mp);
sp_2048_mont_sqr_90(t[26], t[13], m, mp);
sp_2048_mont_mul_90(t[27], t[14], t[13], m, mp);
sp_2048_mont_sqr_90(t[28], t[14], m, mp);
sp_2048_mont_mul_90(t[29], t[15], t[14], m, mp);
sp_2048_mont_sqr_90(t[30], t[15], m, mp);
sp_2048_mont_mul_90(t[31], t[16], t[15], m, mp);
bits = ((bits + 4) / 5) * 5;
i = ((bits + 22) / 23) - 1;
c = bits % 23;
if (c == 0) {
c = 23;
}
if (i < 90) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
XMEMCPY(rt, t[y], sizeof(rt));
for (; i>=0 || c>=5; ) {
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
sp_2048_mont_sqr_90(rt, rt, m, mp);
sp_2048_mont_sqr_90(rt, rt, m, mp);
sp_2048_mont_sqr_90(rt, rt, m, mp);
sp_2048_mont_sqr_90(rt, rt, m, mp);
sp_2048_mont_sqr_90(rt, rt, m, mp);
sp_2048_mont_mul_90(rt, rt, t[y], m, mp);
}
sp_2048_mont_reduce_90(rt, m, mp);
n = sp_2048_cmp_90(rt, m);
sp_2048_cond_sub_90(rt, rt, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, rt, sizeof(rt));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#endif
}
#endif /* (WOLFSSL_HAVE_SP_RSA && !WOLFSSL_RSA_PUBLIC_ONLY) || */
/* WOLFSSL_HAVE_SP_DH */
#if defined(WOLFSSL_HAVE_SP_RSA) && !defined(SP_RSA_PRIVATE_EXP_D) && \
!defined(RSA_LOW_MEM) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)
/* AND m into each word of a and store in r.
*
* r A single precision integer.
* a A single precision integer.
* m Mask to AND against each digit.
*/
static void sp_2048_mask_45(sp_digit* r, const sp_digit* a, sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<45; i++) {
r[i] = a[i] & m;
}
#else
int i;
for (i = 0; i < 40; i += 8) {
r[i+0] = a[i+0] & m;
r[i+1] = a[i+1] & m;
r[i+2] = a[i+2] & m;
r[i+3] = a[i+3] & m;
r[i+4] = a[i+4] & m;
r[i+5] = a[i+5] & m;
r[i+6] = a[i+6] & m;
r[i+7] = a[i+7] & m;
}
r[40] = a[40] & m;
r[41] = a[41] & m;
r[42] = a[42] & m;
r[43] = a[43] & m;
r[44] = a[44] & m;
#endif
}
#endif
#ifdef WOLFSSL_HAVE_SP_RSA
/* RSA public key operation.
*
* in Array of bytes representing the number to exponentiate, base.
* inLen Number of bytes in base.
* em Public exponent.
* mm Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 256 bytes long.
* outLen Number of bytes in result.
* returns 0 on success, MP_TO_E when the outLen is too small, MP_READ_E when
* an array is too long and MEMORY_E when dynamic memory allocation fails.
*/
int sp_RsaPublic_2048(const byte* in, word32 inLen, mp_int* em, mp_int* mm,
byte* out, word32* outLen)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* d = NULL;
sp_digit* a;
sp_digit* m;
sp_digit* r;
sp_digit* norm;
sp_digit e[1] = {0};
sp_digit mp;
int i;
int err = MP_OKAY;
if (*outLen < 256U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(em) > 23) {
err = MP_READ_E;
}
if (inLen > 256U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 90 * 5, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
a = d;
r = a + 90 * 2;
m = r + 90 * 2;
norm = r;
sp_2048_from_bin(a, 90, in, inLen);
#if DIGIT_BIT >= 23
e[0] = (sp_digit)em->dp[0];
#else
e[0] = (sp_digit)em->dp[0];
if (em->used > 1) {
e[0] |= ((sp_digit)em->dp[1]) << DIGIT_BIT;
}
#endif
if (e[0] == 0) {
err = MP_EXPTMOD_E;
}
}
if (err == MP_OKAY) {
sp_2048_from_mp(m, 90, mm);
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_90(norm, m);
}
if (err == MP_OKAY) {
sp_2048_mul_90(a, a, norm);
err = sp_2048_mod_90(a, a, m);
}
if (err == MP_OKAY) {
for (i=22; i>=0; i--) {
if ((e[0] >> i) != 0) {
break;
}
}
XMEMCPY(r, a, sizeof(sp_digit) * 90 * 2);
for (i--; i>=0; i--) {
sp_2048_mont_sqr_90(r, r, m, mp);
if (((e[0] >> i) & 1) == 1) {
sp_2048_mont_mul_90(r, r, a, m, mp);
}
}
sp_2048_mont_reduce_90(r, m, mp);
mp = sp_2048_cmp_90(r, m);
sp_2048_cond_sub_90(r, r, m, ((mp < 0) ?
(sp_digit)1 : (sp_digit)0)- 1);
sp_2048_to_bin(r, out);
*outLen = 256;
}
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_digit ad[180], md[90], rd[180];
#else
sp_digit* d = NULL;
#endif
sp_digit* a;
sp_digit* m;
sp_digit* r;
sp_digit e[1] = {0};
int err = MP_OKAY;
if (*outLen < 256U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(em) > 23) {
err = MP_READ_E;
}
if (inLen > 256U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 2048) {
err = MP_READ_E;
}
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 90 * 5, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = d;
r = a + 90 * 2;
m = r + 90 * 2;
}
#else
a = ad;
m = md;
r = rd;
#endif
if (err == MP_OKAY) {
sp_2048_from_bin(a, 90, in, inLen);
#if DIGIT_BIT >= 23
e[0] = (sp_digit)em->dp[0];
#else
e[0] = (sp_digit)em->dp[0];
if (em->used > 1) {
e[0] |= ((sp_digit)em->dp[1]) << DIGIT_BIT;
}
#endif
if (e[0] == 0) {
err = MP_EXPTMOD_E;
}
}
if (err == MP_OKAY) {
sp_2048_from_mp(m, 90, mm);
if (e[0] == 0x3) {
sp_2048_sqr_90(r, a);
err = sp_2048_mod_90(r, r, m);
if (err == MP_OKAY) {
sp_2048_mul_90(r, a, r);
err = sp_2048_mod_90(r, r, m);
}
}
else {
sp_digit* norm = r;
int i;
sp_digit mp;
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_90(norm, m);
sp_2048_mul_90(a, a, norm);
err = sp_2048_mod_90(a, a, m);
if (err == MP_OKAY) {
for (i=22; i>=0; i--) {
if ((e[0] >> i) != 0) {
break;
}
}
XMEMCPY(r, a, sizeof(sp_digit) * 180U);
for (i--; i>=0; i--) {
sp_2048_mont_sqr_90(r, r, m, mp);
if (((e[0] >> i) & 1) == 1) {
sp_2048_mont_mul_90(r, r, a, m, mp);
}
}
sp_2048_mont_reduce_90(r, m, mp);
mp = sp_2048_cmp_90(r, m);
sp_2048_cond_sub_90(r, r, m, ((mp < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
}
}
if (err == MP_OKAY) {
sp_2048_to_bin(r, out);
*outLen = 256;
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
#endif
return err;
#endif /* WOLFSSL_SP_SMALL */
}
#ifndef WOLFSSL_RSA_PUBLIC_ONLY
/* RSA private key operation.
*
* in Array of bytes representing the number to exponentiate, base.
* inLen Number of bytes in base.
* dm Private exponent.
* pm First prime.
* qm Second prime.
* dpm First prime's CRT exponent.
* dqm Second prime's CRT exponent.
* qim Inverse of second prime mod p.
* mm Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 256 bytes long.
* outLen Number of bytes in result.
* returns 0 on success, MP_TO_E when the outLen is too small, MP_READ_E when
* an array is too long and MEMORY_E when dynamic memory allocation fails.
*/
int sp_RsaPrivate_2048(const byte* in, word32 inLen, mp_int* dm,
mp_int* pm, mp_int* qm, mp_int* dpm, mp_int* dqm, mp_int* qim, mp_int* mm,
byte* out, word32* outLen)
{
#if defined(SP_RSA_PRIVATE_EXP_D) || defined(RSA_LOW_MEM)
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_digit* a;
sp_digit* d = NULL;
sp_digit* m;
sp_digit* r;
int err = MP_OKAY;
(void)pm;
(void)qm;
(void)dpm;
(void)dqm;
(void)qim;
if (*outLen < 256U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(dm) > 2048) {
err = MP_READ_E;
}
if (inLen > 256) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 90 * 4, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = d + 90;
m = a + 90;
r = a;
sp_2048_from_bin(a, 90, in, inLen);
sp_2048_from_mp(d, 90, dm);
sp_2048_from_mp(m, 90, mm);
err = sp_2048_mod_exp_90(r, a, d, 2048, m, 0);
}
if (err == MP_OKAY) {
sp_2048_to_bin(r, out);
*outLen = 256;
}
if (d != NULL) {
XMEMSET(d, 0, sizeof(sp_digit) * 90);
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
sp_digit a[180], d[90], m[90];
sp_digit* r = a;
int err = MP_OKAY;
(void)pm;
(void)qm;
(void)dpm;
(void)dqm;
(void)qim;
if (*outLen < 256U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(dm) > 2048) {
err = MP_READ_E;
}
if (inLen > 256U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
sp_2048_from_bin(a, 90, in, inLen);
sp_2048_from_mp(d, 90, dm);
sp_2048_from_mp(m, 90, mm);
err = sp_2048_mod_exp_90(r, a, d, 2048, m, 0);
}
if (err == MP_OKAY) {
sp_2048_to_bin(r, out);
*outLen = 256;
}
XMEMSET(d, 0, sizeof(sp_digit) * 90);
return err;
#endif /* WOLFSSL_SP_SMALL || defined(WOLFSSL_SMALL_STACK) */
#else
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_digit* t = NULL;
sp_digit* a;
sp_digit* p;
sp_digit* q;
sp_digit* dp;
sp_digit* dq;
sp_digit* qi;
sp_digit* tmp;
sp_digit* tmpa;
sp_digit* tmpb;
sp_digit* r;
int err = MP_OKAY;
(void)dm;
(void)mm;
if (*outLen < 256U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (inLen > 256) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
t = (sp_digit*)XMALLOC(sizeof(sp_digit) * 45 * 11, NULL,
DYNAMIC_TYPE_RSA);
if (t == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = t;
p = a + 90 * 2;
q = p + 45;
qi = dq = dp = q + 45;
tmpa = qi + 45;
tmpb = tmpa + 90;
tmp = t;
r = tmp + 90;
sp_2048_from_bin(a, 90, in, inLen);
sp_2048_from_mp(p, 45, pm);
sp_2048_from_mp(q, 45, qm);
sp_2048_from_mp(dp, 45, dpm);
err = sp_2048_mod_exp_45(tmpa, a, dp, 1024, p, 1);
}
if (err == MP_OKAY) {
sp_2048_from_mp(dq, 45, dqm);
err = sp_2048_mod_exp_45(tmpb, a, dq, 1024, q, 1);
}
if (err == MP_OKAY) {
(void)sp_2048_sub_45(tmpa, tmpa, tmpb);
sp_2048_mask_45(tmp, p, 0 - ((sp_int_digit)tmpa[44] >> 31));
(void)sp_2048_add_45(tmpa, tmpa, tmp);
sp_2048_from_mp(qi, 45, qim);
sp_2048_mul_45(tmpa, tmpa, qi);
err = sp_2048_mod_45(tmpa, tmpa, p);
}
if (err == MP_OKAY) {
sp_2048_mul_45(tmpa, q, tmpa);
(void)sp_2048_add_90(r, tmpb, tmpa);
sp_2048_norm_90(r);
sp_2048_to_bin(r, out);
*outLen = 256;
}
if (t != NULL) {
XMEMSET(t, 0, sizeof(sp_digit) * 45 * 11);
XFREE(t, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
sp_digit a[90 * 2];
sp_digit p[45], q[45], dp[45], dq[45], qi[45];
sp_digit tmp[90], tmpa[90], tmpb[90];
sp_digit* r = a;
int err = MP_OKAY;
(void)dm;
(void)mm;
if (*outLen < 256U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (inLen > 256U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
sp_2048_from_bin(a, 90, in, inLen);
sp_2048_from_mp(p, 45, pm);
sp_2048_from_mp(q, 45, qm);
sp_2048_from_mp(dp, 45, dpm);
sp_2048_from_mp(dq, 45, dqm);
sp_2048_from_mp(qi, 45, qim);
err = sp_2048_mod_exp_45(tmpa, a, dp, 1024, p, 1);
}
if (err == MP_OKAY) {
err = sp_2048_mod_exp_45(tmpb, a, dq, 1024, q, 1);
}
if (err == MP_OKAY) {
(void)sp_2048_sub_45(tmpa, tmpa, tmpb);
sp_2048_mask_45(tmp, p, 0 - ((sp_int_digit)tmpa[44] >> 31));
(void)sp_2048_add_45(tmpa, tmpa, tmp);
sp_2048_mul_45(tmpa, tmpa, qi);
err = sp_2048_mod_45(tmpa, tmpa, p);
}
if (err == MP_OKAY) {
sp_2048_mul_45(tmpa, tmpa, q);
(void)sp_2048_add_90(r, tmpb, tmpa);
sp_2048_norm_90(r);
sp_2048_to_bin(r, out);
*outLen = 256;
}
XMEMSET(tmpa, 0, sizeof(tmpa));
XMEMSET(tmpb, 0, sizeof(tmpb));
XMEMSET(p, 0, sizeof(p));
XMEMSET(q, 0, sizeof(q));
XMEMSET(dp, 0, sizeof(dp));
XMEMSET(dq, 0, sizeof(dq));
XMEMSET(qi, 0, sizeof(qi));
return err;
#endif /* WOLFSSL_SP_SMALL || defined(WOLFSSL_SMALL_STACK) */
#endif /* SP_RSA_PRIVATE_EXP_D || RSA_LOW_MEM */
}
#endif /* !WOLFSSL_RSA_PUBLIC_ONLY */
#endif /* WOLFSSL_HAVE_SP_RSA */
#if defined(WOLFSSL_HAVE_SP_DH) || (defined(WOLFSSL_HAVE_SP_RSA) && \
!defined(WOLFSSL_RSA_PUBLIC_ONLY))
/* Convert an array of sp_digit to an mp_int.
*
* a A single precision integer.
* r A multi-precision integer.
*/
static int sp_2048_to_mp(const sp_digit* a, mp_int* r)
{
int err;
err = mp_grow(r, (2048 + DIGIT_BIT - 1) / DIGIT_BIT);
if (err == MP_OKAY) { /*lint !e774 case where err is always MP_OKAY*/
#if DIGIT_BIT == 23
XMEMCPY(r->dp, a, sizeof(sp_digit) * 90);
r->used = 90;
mp_clamp(r);
#elif DIGIT_BIT < 23
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 90; i++) {
r->dp[j] |= a[i] << s;
r->dp[j] &= (1L << DIGIT_BIT) - 1;
s = DIGIT_BIT - s;
r->dp[++j] = a[i] >> s;
while (s + DIGIT_BIT <= 23) {
s += DIGIT_BIT;
r->dp[j++] &= (1L << DIGIT_BIT) - 1;
if (s == SP_WORD_SIZE) {
r->dp[j] = 0;
}
else {
r->dp[j] = a[i] >> s;
}
}
s = 23 - s;
}
r->used = (2048 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#else
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 90; i++) {
r->dp[j] |= ((mp_digit)a[i]) << s;
if (s + 23 >= DIGIT_BIT) {
#if DIGIT_BIT != 32 && DIGIT_BIT != 64
r->dp[j] &= (1L << DIGIT_BIT) - 1;
#endif
s = DIGIT_BIT - s;
r->dp[++j] = a[i] >> s;
s = 23 - s;
}
else {
s += 23;
}
}
r->used = (2048 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#endif
}
return err;
}
/* Perform the modular exponentiation for Diffie-Hellman.
*
* base Base. MP integer.
* exp Exponent. MP integer.
* mod Modulus. MP integer.
* res Result. MP integer.
* returs 0 on success, MP_READ_E if there are too many bytes in an array
* and MEMORY_E if memory allocation fails.
*/
int sp_ModExp_2048(mp_int* base, mp_int* exp, mp_int* mod, mp_int* res)
{
#ifdef WOLFSSL_SP_SMALL
int err = MP_OKAY;
sp_digit* d = NULL;
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 2048) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 90 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
b = d;
e = b + 90 * 2;
m = e + 90;
r = b;
sp_2048_from_mp(b, 90, base);
sp_2048_from_mp(e, 90, exp);
sp_2048_from_mp(m, 90, mod);
err = sp_2048_mod_exp_90(r, b, e, mp_count_bits(exp), m, 0);
}
if (err == MP_OKAY) {
err = sp_2048_to_mp(r, res);
}
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 90U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit bd[180], ed[90], md[90];
#else
sp_digit* d = NULL;
#endif
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int err = MP_OKAY;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 2048) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 2048) {
err = MP_READ_E;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 90 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
b = d;
e = b + 90 * 2;
m = e + 90;
r = b;
}
#else
r = b = bd;
e = ed;
m = md;
#endif
if (err == MP_OKAY) {
sp_2048_from_mp(b, 90, base);
sp_2048_from_mp(e, 90, exp);
sp_2048_from_mp(m, 90, mod);
err = sp_2048_mod_exp_90(r, b, e, expBits, m, 0);
}
if (err == MP_OKAY) {
err = sp_2048_to_mp(r, res);
}
XMEMSET(e, 0, sizeof(sp_digit) * 90U);
#ifdef WOLFSSL_SMALL_STACK
if (d != NULL)
XFREE(d, NULL, DYNAMIC_TYPE_DH);
#endif
return err;
#endif
}
#ifdef WOLFSSL_HAVE_SP_DH
#ifdef HAVE_FFDHE_2048
SP_NOINLINE static void sp_2048_lshift_90(sp_digit* r, sp_digit* a, byte n)
{
#ifdef WOLFSSL_SP_SMALL
int i;
r[90] = a[89] >> (23 - n);
for (i=89; i>0; i--) {
r[i] = ((a[i] << n) | (a[i-1] >> (23 - n))) & 0x7fffff;
}
#else
sp_int_digit s, t;
s = (sp_int_digit)a[89];
r[90] = s >> (23U - n);
s = (sp_int_digit)(a[89]); t = (sp_int_digit)(a[88]);
r[89] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[88]); t = (sp_int_digit)(a[87]);
r[88] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[87]); t = (sp_int_digit)(a[86]);
r[87] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[86]); t = (sp_int_digit)(a[85]);
r[86] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[85]); t = (sp_int_digit)(a[84]);
r[85] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[84]); t = (sp_int_digit)(a[83]);
r[84] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[83]); t = (sp_int_digit)(a[82]);
r[83] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[82]); t = (sp_int_digit)(a[81]);
r[82] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[81]); t = (sp_int_digit)(a[80]);
r[81] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[80]); t = (sp_int_digit)(a[79]);
r[80] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[79]); t = (sp_int_digit)(a[78]);
r[79] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[78]); t = (sp_int_digit)(a[77]);
r[78] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[77]); t = (sp_int_digit)(a[76]);
r[77] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[76]); t = (sp_int_digit)(a[75]);
r[76] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[75]); t = (sp_int_digit)(a[74]);
r[75] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[74]); t = (sp_int_digit)(a[73]);
r[74] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[73]); t = (sp_int_digit)(a[72]);
r[73] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[72]); t = (sp_int_digit)(a[71]);
r[72] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[71]); t = (sp_int_digit)(a[70]);
r[71] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[70]); t = (sp_int_digit)(a[69]);
r[70] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[69]); t = (sp_int_digit)(a[68]);
r[69] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[68]); t = (sp_int_digit)(a[67]);
r[68] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[67]); t = (sp_int_digit)(a[66]);
r[67] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[66]); t = (sp_int_digit)(a[65]);
r[66] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[65]); t = (sp_int_digit)(a[64]);
r[65] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[64]); t = (sp_int_digit)(a[63]);
r[64] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[63]); t = (sp_int_digit)(a[62]);
r[63] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[62]); t = (sp_int_digit)(a[61]);
r[62] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[61]); t = (sp_int_digit)(a[60]);
r[61] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[60]); t = (sp_int_digit)(a[59]);
r[60] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[59]); t = (sp_int_digit)(a[58]);
r[59] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[58]); t = (sp_int_digit)(a[57]);
r[58] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[57]); t = (sp_int_digit)(a[56]);
r[57] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[56]); t = (sp_int_digit)(a[55]);
r[56] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[55]); t = (sp_int_digit)(a[54]);
r[55] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[54]); t = (sp_int_digit)(a[53]);
r[54] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[53]); t = (sp_int_digit)(a[52]);
r[53] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[52]); t = (sp_int_digit)(a[51]);
r[52] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[51]); t = (sp_int_digit)(a[50]);
r[51] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[50]); t = (sp_int_digit)(a[49]);
r[50] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[49]); t = (sp_int_digit)(a[48]);
r[49] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[48]); t = (sp_int_digit)(a[47]);
r[48] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[47]); t = (sp_int_digit)(a[46]);
r[47] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[46]); t = (sp_int_digit)(a[45]);
r[46] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[45]); t = (sp_int_digit)(a[44]);
r[45] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[44]); t = (sp_int_digit)(a[43]);
r[44] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[43]); t = (sp_int_digit)(a[42]);
r[43] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[42]); t = (sp_int_digit)(a[41]);
r[42] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[41]); t = (sp_int_digit)(a[40]);
r[41] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[40]); t = (sp_int_digit)(a[39]);
r[40] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[39]); t = (sp_int_digit)(a[38]);
r[39] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[38]); t = (sp_int_digit)(a[37]);
r[38] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[37]); t = (sp_int_digit)(a[36]);
r[37] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[36]); t = (sp_int_digit)(a[35]);
r[36] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[35]); t = (sp_int_digit)(a[34]);
r[35] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[34]); t = (sp_int_digit)(a[33]);
r[34] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[33]); t = (sp_int_digit)(a[32]);
r[33] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[32]); t = (sp_int_digit)(a[31]);
r[32] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[31]); t = (sp_int_digit)(a[30]);
r[31] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[30]); t = (sp_int_digit)(a[29]);
r[30] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[29]); t = (sp_int_digit)(a[28]);
r[29] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[28]); t = (sp_int_digit)(a[27]);
r[28] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[27]); t = (sp_int_digit)(a[26]);
r[27] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[26]); t = (sp_int_digit)(a[25]);
r[26] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[25]); t = (sp_int_digit)(a[24]);
r[25] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[24]); t = (sp_int_digit)(a[23]);
r[24] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[23]); t = (sp_int_digit)(a[22]);
r[23] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[22]); t = (sp_int_digit)(a[21]);
r[22] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[21]); t = (sp_int_digit)(a[20]);
r[21] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[20]); t = (sp_int_digit)(a[19]);
r[20] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[19]); t = (sp_int_digit)(a[18]);
r[19] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[18]); t = (sp_int_digit)(a[17]);
r[18] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[17]); t = (sp_int_digit)(a[16]);
r[17] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[16]); t = (sp_int_digit)(a[15]);
r[16] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[15]); t = (sp_int_digit)(a[14]);
r[15] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[14]); t = (sp_int_digit)(a[13]);
r[14] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[13]); t = (sp_int_digit)(a[12]);
r[13] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[12]); t = (sp_int_digit)(a[11]);
r[12] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[11]); t = (sp_int_digit)(a[10]);
r[11] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[10]); t = (sp_int_digit)(a[9]);
r[10] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[9]); t = (sp_int_digit)(a[8]);
r[9] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[8]); t = (sp_int_digit)(a[7]);
r[8] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[7]); t = (sp_int_digit)(a[6]);
r[7] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[6]); t = (sp_int_digit)(a[5]);
r[6] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[5]); t = (sp_int_digit)(a[4]);
r[5] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[4]); t = (sp_int_digit)(a[3]);
r[4] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[3]); t = (sp_int_digit)(a[2]);
r[3] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[2]); t = (sp_int_digit)(a[1]);
r[2] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[1]); t = (sp_int_digit)(a[0]);
r[1] = ((s << n) | (t >> (23U - n))) & ;
#endif
r[0] = (a[0] << n) & 0x7fffff;
}
/* Modular exponentiate 2 to the e mod m. (r = 2^e mod m)
*
* r A single precision number that is the result of the operation.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_2048_mod_exp_2_90(sp_digit* r, const sp_digit* e, int bits, const sp_digit* m)
{
#ifndef WOLFSSL_SMALL_STACK
sp_digit nd[180];
sp_digit td[91];
#else
sp_digit* td;
#endif
sp_digit* norm;
sp_digit* tmp;
sp_digit mp = 1;
sp_digit n, o;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 271, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
norm = td;
tmp = td + 180;
#else
norm = nd;
tmp = td;
#endif
XMEMSET(td, 0, sizeof(td));
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_90(norm, m);
bits = ((bits + 3) / 4) * 4;
i = ((bits + 22) / 23) - 1;
c = bits % 23;
if (c == 0) {
c = 23;
}
if (i < 90) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 4) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 28) & 0xf;
n <<= 4;
c -= 4;
sp_2048_lshift_90(r, norm, y);
for (; i>=0 || c>=4; ) {
if (c < 4) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 28) & 0xf;
n <<= 4;
c -= 4;
sp_2048_mont_sqr_90(r, r, m, mp);
sp_2048_mont_sqr_90(r, r, m, mp);
sp_2048_mont_sqr_90(r, r, m, mp);
sp_2048_mont_sqr_90(r, r, m, mp);
sp_2048_lshift_90(r, r, y);
sp_2048_mul_d_90(tmp, norm, (r[90] << 22) + (r[89] >> 1));
r[90] = 0;
r[89] &= 0x1L;
(void)sp_2048_add_90(r, r, tmp);
sp_2048_norm_90(r);
o = sp_2048_cmp_90(r, m);
sp_2048_cond_sub_90(r, r, m, ((o < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
sp_2048_mont_reduce_90(r, m, mp);
n = sp_2048_cmp_90(r, m);
sp_2048_cond_sub_90(r, r, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
#endif /* HAVE_FFDHE_2048 */
/* Perform the modular exponentiation for Diffie-Hellman.
*
* base Base.
* exp Array of bytes that is the exponent.
* expLen Length of data, in bytes, in exponent.
* mod Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 256 bytes long.
* outLen Length, in bytes, of exponentiation result.
* returs 0 on success, MP_READ_E if there are too many bytes in an array
* and MEMORY_E if memory allocation fails.
*/
int sp_DhExp_2048(mp_int* base, const byte* exp, word32 expLen,
mp_int* mod, byte* out, word32* outLen)
{
#ifdef WOLFSSL_SP_SMALL
int err = MP_OKAY;
sp_digit* d = NULL;
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
word32 i;
if (mp_count_bits(base) > 2048) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expLen > 256) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 90 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
b = d;
e = b + 90 * 2;
m = e + 90;
r = b;
sp_2048_from_mp(b, 90, base);
sp_2048_from_bin(e, 90, exp, expLen);
sp_2048_from_mp(m, 90, mod);
#ifdef HAVE_FFDHE_2048
if (base->used == 1 && base->dp[0] == 2 &&
((m[89] << 15) | (m[88] >> 8)) == 0xffffL) {
err = sp_2048_mod_exp_2_90(r, e, expLen * 8, m);
}
else
#endif
err = sp_2048_mod_exp_90(r, b, e, expLen * 8, m, 0);
}
if (err == MP_OKAY) {
sp_2048_to_bin(r, out);
*outLen = 256;
for (i=0; i<256 && out[i] == 0; i++) {
}
*outLen -= i;
XMEMMOVE(out, out + i, *outLen);
}
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 90U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit bd[180], ed[90], md[90];
#else
sp_digit* d = NULL;
#endif
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
word32 i;
int err = MP_OKAY;
if (mp_count_bits(base) > 2048) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expLen > 256U) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 2048) {
err = MP_READ_E;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 90 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
b = d;
e = b + 90 * 2;
m = e + 90;
r = b;
}
#else
r = b = bd;
e = ed;
m = md;
#endif
if (err == MP_OKAY) {
sp_2048_from_mp(b, 90, base);
sp_2048_from_bin(e, 90, exp, expLen);
sp_2048_from_mp(m, 90, mod);
#ifdef HAVE_FFDHE_2048
if (base->used == 1 && base->dp[0] == 2U &&
((m[89] << 15) | (m[88] >> 8)) == 0xffffL) {
err = sp_2048_mod_exp_2_90(r, e, expLen * 8U, m);
}
else {
#endif
err = sp_2048_mod_exp_90(r, b, e, expLen * 8U, m, 0);
#ifdef HAVE_FFDHE_2048
}
#endif
}
if (err == MP_OKAY) {
sp_2048_to_bin(r, out);
*outLen = 256;
for (i=0; i<256U && out[i] == 0U; i++) {
}
*outLen -= i;
XMEMMOVE(out, out + i, *outLen);
}
XMEMSET(e, 0, sizeof(sp_digit) * 90U);
#ifdef WOLFSSL_SMALL_STACK
if (d != NULL)
XFREE(d, NULL, DYNAMIC_TYPE_DH);
#endif
return err;
#endif
}
#endif /* WOLFSSL_HAVE_SP_DH */
/* Perform the modular exponentiation for Diffie-Hellman.
*
* base Base. MP integer.
* exp Exponent. MP integer.
* mod Modulus. MP integer.
* res Result. MP integer.
* returs 0 on success, MP_READ_E if there are too many bytes in an array
* and MEMORY_E if memory allocation fails.
*/
int sp_ModExp_1024(mp_int* base, mp_int* exp, mp_int* mod, mp_int* res)
{
#ifdef WOLFSSL_SP_SMALL
int err = MP_OKAY;
sp_digit* d = NULL;
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 1024) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 1024) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 1024) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 45 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
b = d;
e = b + 45 * 2;
m = e + 45;
r = b;
sp_2048_from_mp(b, 45, base);
sp_2048_from_mp(e, 45, exp);
sp_2048_from_mp(m, 45, mod);
err = sp_2048_mod_exp_45(r, b, e, mp_count_bits(exp), m, 0);
}
if (err == MP_OKAY) {
XMEMSET(r + 45, 0, sizeof(*r) * 45U);
err = sp_2048_to_mp(r, res);
}
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 45U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit bd[90], ed[45], md[45];
#else
sp_digit* d = NULL;
#endif
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int err = MP_OKAY;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 1024) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 1024) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 1024) {
err = MP_READ_E;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 45 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
b = d;
e = b + 45 * 2;
m = e + 45;
r = b;
}
#else
r = b = bd;
e = ed;
m = md;
#endif
if (err == MP_OKAY) {
sp_2048_from_mp(b, 45, base);
sp_2048_from_mp(e, 45, exp);
sp_2048_from_mp(m, 45, mod);
err = sp_2048_mod_exp_45(r, b, e, expBits, m, 0);
}
if (err == MP_OKAY) {
XMEMSET(r + 45, 0, sizeof(*r) * 45U);
err = sp_2048_to_mp(r, res);
}
XMEMSET(e, 0, sizeof(sp_digit) * 45U);
#ifdef WOLFSSL_SMALL_STACK
if (d != NULL)
XFREE(d, NULL, DYNAMIC_TYPE_DH);
#endif
return err;
#endif
}
#endif /* WOLFSSL_HAVE_SP_DH || (WOLFSSL_HAVE_SP_RSA && !WOLFSSL_RSA_PUBLIC_ONLY) */
#endif /* !WOLFSSL_SP_NO_2048 */
#ifndef WOLFSSL_SP_NO_3072
/* Read big endian unsigned byte array into r.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a Byte array.
* n Number of bytes in array to read.
*/
static void sp_3072_from_bin(sp_digit* r, int size, const byte* a, int n)
{
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = n-1; i >= 0; i--) {
r[j] |= (((sp_digit)a[i]) << s);
if (s >= 15U) {
r[j] &= 0x7fffff;
s = 23U - s;
if (j + 1 >= size) {
break;
}
r[++j] = (sp_digit)a[i] >> s;
s = 8U - s;
}
else {
s += 8U;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
}
/* Convert an mp_int to an array of sp_digit.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a A multi-precision integer.
*/
static void sp_3072_from_mp(sp_digit* r, int size, const mp_int* a)
{
#if DIGIT_BIT == 23
int j;
XMEMCPY(r, a->dp, sizeof(sp_digit) * a->used);
for (j = a->used; j < size; j++) {
r[j] = 0;
}
#elif DIGIT_BIT > 23
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i] << s);
r[j] &= 0x7fffff;
s = 23U - s;
if (j + 1 >= size) {
break;
}
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
while ((s + 23U) <= (word32)DIGIT_BIT) {
s += 23U;
r[j] &= 0x7fffff;
if (j + 1 >= size) {
break;
}
if (s < (word32)DIGIT_BIT) {
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
}
else {
r[++j] = 0L;
}
}
s = (word32)DIGIT_BIT - s;
}
for (j++; j < size; j++) {
r[j] = 0;
}
#else
int i, j = 0, s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i]) << s;
if (s + DIGIT_BIT >= 23) {
r[j] &= 0x7fffff;
if (j + 1 >= size) {
break;
}
s = 23 - s;
if (s == DIGIT_BIT) {
r[++j] = 0;
s = 0;
}
else {
r[++j] = a->dp[i] >> s;
s = DIGIT_BIT - s;
}
}
else {
s += DIGIT_BIT;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
#endif
}
/* Write r as big endian to byte array.
* Fixed length number of bytes written: 384
*
* r A single precision integer.
* a Byte array.
*/
static void sp_3072_to_bin(sp_digit* r, byte* a)
{
int i, j, s = 0, b;
for (i=0; i<133; i++) {
r[i+1] += r[i] >> 23;
r[i] &= 0x7fffff;
}
j = 3072 / 8 - 1;
a[j] = 0;
for (i=0; i<134 && j>=0; i++) {
b = 0;
/* lint allow cast of mismatch sp_digit and int */
a[j--] |= (byte)(r[i] << s); b += 8 - s; /*lint !e9033*/
if (j < 0) {
break;
}
while (b < 23) {
a[j--] = r[i] >> b; b += 8;
if (j < 0) {
break;
}
}
s = 8 - (b - 23);
if (j >= 0) {
a[j] = 0;
}
if (s != 0) {
j++;
}
}
}
#ifndef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_3072_mul_67(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j;
int64_t t[134];
XMEMSET(t, 0, sizeof(t));
for (i=0; i<67; i++) {
for (j=0; j<67; j++) {
t[i+j] += ((int64_t)a[i]) * b[j];
}
}
for (i=0; i<133; i++) {
r[i] = t[i] & 0x7fffff;
t[i+1] += t[i] >> 23;
}
r[133] = (sp_digit)t[133];
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_3072_sqr_67(sp_digit* r, const sp_digit* a)
{
int i, j;
int64_t t[134];
XMEMSET(t, 0, sizeof(t));
for (i=0; i<67; i++) {
for (j=0; j<i; j++) {
t[i+j] += (((int64_t)a[i]) * a[j]) * 2;
}
t[i+i] += ((int64_t)a[i]) * a[i];
}
for (i=0; i<133; i++) {
r[i] = t[i] & 0x7fffff;
t[i+1] += t[i] >> 23;
}
r[133] = (sp_digit)t[133];
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_add_67(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 64; i += 8) {
r[i + 0] = a[i + 0] + b[i + 0];
r[i + 1] = a[i + 1] + b[i + 1];
r[i + 2] = a[i + 2] + b[i + 2];
r[i + 3] = a[i + 3] + b[i + 3];
r[i + 4] = a[i + 4] + b[i + 4];
r[i + 5] = a[i + 5] + b[i + 5];
r[i + 6] = a[i + 6] + b[i + 6];
r[i + 7] = a[i + 7] + b[i + 7];
}
r[64] = a[64] + b[64];
r[65] = a[65] + b[65];
r[66] = a[66] + b[66];
return 0;
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_add_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 128; i += 8) {
r[i + 0] = a[i + 0] + b[i + 0];
r[i + 1] = a[i + 1] + b[i + 1];
r[i + 2] = a[i + 2] + b[i + 2];
r[i + 3] = a[i + 3] + b[i + 3];
r[i + 4] = a[i + 4] + b[i + 4];
r[i + 5] = a[i + 5] + b[i + 5];
r[i + 6] = a[i + 6] + b[i + 6];
r[i + 7] = a[i + 7] + b[i + 7];
}
r[128] = a[128] + b[128];
r[129] = a[129] + b[129];
r[130] = a[130] + b[130];
r[131] = a[131] + b[131];
r[132] = a[132] + b[132];
r[133] = a[133] + b[133];
return 0;
}
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_sub_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 128; i += 8) {
r[i + 0] = a[i + 0] - b[i + 0];
r[i + 1] = a[i + 1] - b[i + 1];
r[i + 2] = a[i + 2] - b[i + 2];
r[i + 3] = a[i + 3] - b[i + 3];
r[i + 4] = a[i + 4] - b[i + 4];
r[i + 5] = a[i + 5] - b[i + 5];
r[i + 6] = a[i + 6] - b[i + 6];
r[i + 7] = a[i + 7] - b[i + 7];
}
r[128] = a[128] - b[128];
r[129] = a[129] - b[129];
r[130] = a[130] - b[130];
r[131] = a[131] - b[131];
r[132] = a[132] - b[132];
r[133] = a[133] - b[133];
return 0;
}
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_3072_mul_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
sp_digit* z0 = r;
sp_digit z1[134];
sp_digit* a1 = z1;
sp_digit b1[67];
sp_digit* z2 = r + 134;
(void)sp_3072_add_67(a1, a, &a[67]);
(void)sp_3072_add_67(b1, b, &b[67]);
sp_3072_mul_67(z2, &a[67], &b[67]);
sp_3072_mul_67(z0, a, b);
sp_3072_mul_67(z1, a1, b1);
(void)sp_3072_sub_134(z1, z1, z2);
(void)sp_3072_sub_134(z1, z1, z0);
(void)sp_3072_add_134(r + 67, r + 67, z1);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_3072_sqr_134(sp_digit* r, const sp_digit* a)
{
sp_digit* z0 = r;
sp_digit z1[134];
sp_digit* a1 = z1;
sp_digit* z2 = r + 134;
(void)sp_3072_add_67(a1, a, &a[67]);
sp_3072_sqr_67(z2, &a[67]);
sp_3072_sqr_67(z0, a);
sp_3072_sqr_67(z1, a1);
(void)sp_3072_sub_134(z1, z1, z2);
(void)sp_3072_sub_134(z1, z1, z0);
(void)sp_3072_add_134(r + 67, r + 67, z1);
}
#endif /* !WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_add_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 134; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_sub_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 134; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_3072_mul_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[133]) * b[133];
r[267] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 265; k >= 0; k--) {
for (i = 133; i >= 0; i--) {
j = k - i;
if (j >= 134) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * b[j];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_3072_sqr_134(sp_digit* r, const sp_digit* a)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[133]) * a[133];
r[267] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 265; k >= 0; k--) {
for (i = 133; i >= 0; i--) {
j = k - i;
if (j >= 134 || i <= j) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * a[j] * 2;
}
if (i == j) {
c += ((int64_t)a[i]) * a[i];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
#endif /* WOLFSSL_SP_SMALL */
#if (defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH)) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)
#ifdef WOLFSSL_SP_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_add_67(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 67; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_sub_67(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 67; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#else
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_sub_67(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 64; i += 8) {
r[i + 0] = a[i + 0] - b[i + 0];
r[i + 1] = a[i + 1] - b[i + 1];
r[i + 2] = a[i + 2] - b[i + 2];
r[i + 3] = a[i + 3] - b[i + 3];
r[i + 4] = a[i + 4] - b[i + 4];
r[i + 5] = a[i + 5] - b[i + 5];
r[i + 6] = a[i + 6] - b[i + 6];
r[i + 7] = a[i + 7] - b[i + 7];
}
r[64] = a[64] - b[64];
r[65] = a[65] - b[65];
r[66] = a[66] - b[66];
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_3072_mul_67(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[66]) * b[66];
r[133] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 131; k >= 0; k--) {
for (i = 66; i >= 0; i--) {
j = k - i;
if (j >= 67) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * b[j];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_3072_sqr_67(sp_digit* r, const sp_digit* a)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[66]) * a[66];
r[133] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 131; k >= 0; k--) {
for (i = 66; i >= 0; i--) {
j = k - i;
if (j >= 67 || i <= j) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * a[j] * 2;
}
if (i == j) {
c += ((int64_t)a[i]) * a[i];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
#endif /* WOLFSSL_SP_SMALL */
#endif /* (WOLFSSL_HAVE_SP_RSA || WOLFSSL_HAVE_SP_DH) && !WOLFSSL_RSA_PUBLIC_ONLY */
/* Caclulate the bottom digit of -1/a mod 2^n.
*
* a A single precision number.
* rho Bottom word of inverse.
*/
static void sp_3072_mont_setup(const sp_digit* a, sp_digit* rho)
{
sp_digit x, b;
b = a[0];
x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
x *= 2 - b * x; /* here x*a==1 mod 2**8 */
x *= 2 - b * x; /* here x*a==1 mod 2**16 */
x *= 2 - b * x; /* here x*a==1 mod 2**32 */
x &= 0x7fffff;
/* rho = -1/m mod b */
*rho = (1L << 23) - x;
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_3072_mul_d_134(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 134; i++) {
t += tb * a[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[134] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x7fffff;
for (i = 0; i < 128; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[129];
r[129] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[130];
r[130] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[131];
r[131] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[132];
r[132] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[133];
r[133] = (sp_digit)(t[4] >> 23) + (t[5] & 0x7fffff);
r[134] = (sp_digit)(t[5] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
#if (defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH)) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)
/* r = 2^n mod m where n is the number of bits to reduce by.
* Given m must be 3072 bits, just need to subtract.
*
* r A single precision number.
* m A signle precision number.
*/
static void sp_3072_mont_norm_67(sp_digit* r, const sp_digit* m)
{
/* Set r = 2^n - 1. */
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<66; i++) {
r[i] = 0x7fffff;
}
#else
int i;
for (i = 0; i < 64; i += 8) {
r[i + 0] = 0x7fffff;
r[i + 1] = 0x7fffff;
r[i + 2] = 0x7fffff;
r[i + 3] = 0x7fffff;
r[i + 4] = 0x7fffff;
r[i + 5] = 0x7fffff;
r[i + 6] = 0x7fffff;
r[i + 7] = 0x7fffff;
}
r[64] = 0x7fffff;
r[65] = 0x7fffff;
#endif
r[66] = 0x3ffffL;
/* r = (2^n - 1) mod n */
(void)sp_3072_sub_67(r, r, m);
/* Add one so r = 2^n mod m */
r[0] += 1;
}
/* Compare a with b in constant time.
*
* a A single precision integer.
* b A single precision integer.
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_3072_cmp_67(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=66; i>=0; i--) {
r |= (a[i] - b[i]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#else
int i;
r |= (a[66] - b[66]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[65] - b[65]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[64] - b[64]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
for (i = 56; i >= 0; i -= 8) {
r |= (a[i + 7] - b[i + 7]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 6] - b[i + 6]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 5] - b[i + 5]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 4] - b[i + 4]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 3] - b[i + 3]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 2] - b[i + 2]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 1] - b[i + 1]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 0] - b[i + 0]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#endif /* WOLFSSL_SP_SMALL */
return r;
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*
* r A single precision number representing condition subtract result.
* a A single precision number to subtract from.
* b A single precision number to subtract.
* m Mask value to apply.
*/
static void sp_3072_cond_sub_67(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 67; i++) {
r[i] = a[i] - (b[i] & m);
}
#else
int i;
for (i = 0; i < 64; i += 8) {
r[i + 0] = a[i + 0] - (b[i + 0] & m);
r[i + 1] = a[i + 1] - (b[i + 1] & m);
r[i + 2] = a[i + 2] - (b[i + 2] & m);
r[i + 3] = a[i + 3] - (b[i + 3] & m);
r[i + 4] = a[i + 4] - (b[i + 4] & m);
r[i + 5] = a[i + 5] - (b[i + 5] & m);
r[i + 6] = a[i + 6] - (b[i + 6] & m);
r[i + 7] = a[i + 7] - (b[i + 7] & m);
}
r[64] = a[64] - (b[64] & m);
r[65] = a[65] - (b[65] & m);
r[66] = a[66] - (b[66] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Mul a by scalar b and add into r. (r += a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_3072_mul_add_67(sp_digit* r, const sp_digit* a,
const sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 67; i++) {
t += (tb * a[i]) + r[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[67] += t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] += t[0] & 0x7fffff;
for (i = 0; i < 64; i += 8) {
t[1] = tb * a[i+1];
r[i+1] += (t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] += (t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] += (t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] += (t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] += (t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] += (t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] += (t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] += (t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[65]; r[65] += (t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[66]; r[66] += (t[1] >> 23) + (t[2] & 0x7fffff);
r[67] += t[2] >> 23;
#endif /* WOLFSSL_SP_SMALL */
}
/* Normalize the values in each word to 23.
*
* a Array of sp_digit to normalize.
*/
static void sp_3072_norm_67(sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 66; i++) {
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
#else
int i;
for (i = 0; i < 64; i += 8) {
a[i+1] += a[i+0] >> 23; a[i+0] &= 0x7fffff;
a[i+2] += a[i+1] >> 23; a[i+1] &= 0x7fffff;
a[i+3] += a[i+2] >> 23; a[i+2] &= 0x7fffff;
a[i+4] += a[i+3] >> 23; a[i+3] &= 0x7fffff;
a[i+5] += a[i+4] >> 23; a[i+4] &= 0x7fffff;
a[i+6] += a[i+5] >> 23; a[i+5] &= 0x7fffff;
a[i+7] += a[i+6] >> 23; a[i+6] &= 0x7fffff;
a[i+8] += a[i+7] >> 23; a[i+7] &= 0x7fffff;
a[i+9] += a[i+8] >> 23; a[i+8] &= 0x7fffff;
}
a[64+1] += a[64] >> 23;
a[64] &= 0x7fffff;
a[65+1] += a[65] >> 23;
a[65] &= 0x7fffff;
#endif
}
/* Shift the result in the high 1536 bits down to the bottom.
*
* r A single precision number.
* a A single precision number.
*/
static void sp_3072_mont_shift_67(sp_digit* r, const sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
sp_digit n, s;
s = a[67];
n = a[66] >> 18;
for (i = 0; i < 66; i++) {
n += (s & 0x7fffff) << 5;
r[i] = n & 0x7fffff;
n >>= 23;
s = a[68 + i] + (s >> 23);
}
n += s << 5;
r[66] = n;
#else
sp_digit n, s;
int i;
s = a[67]; n = a[66] >> 18;
for (i = 0; i < 64; i += 8) {
n += (s & 0x7fffff) << 5; r[i+0] = n & 0x7fffff;
n >>= 23; s = a[i+68] + (s >> 23);
n += (s & 0x7fffff) << 5; r[i+1] = n & 0x7fffff;
n >>= 23; s = a[i+69] + (s >> 23);
n += (s & 0x7fffff) << 5; r[i+2] = n & 0x7fffff;
n >>= 23; s = a[i+70] + (s >> 23);
n += (s & 0x7fffff) << 5; r[i+3] = n & 0x7fffff;
n >>= 23; s = a[i+71] + (s >> 23);
n += (s & 0x7fffff) << 5; r[i+4] = n & 0x7fffff;
n >>= 23; s = a[i+72] + (s >> 23);
n += (s & 0x7fffff) << 5; r[i+5] = n & 0x7fffff;
n >>= 23; s = a[i+73] + (s >> 23);
n += (s & 0x7fffff) << 5; r[i+6] = n & 0x7fffff;
n >>= 23; s = a[i+74] + (s >> 23);
n += (s & 0x7fffff) << 5; r[i+7] = n & 0x7fffff;
n >>= 23; s = a[i+75] + (s >> 23);
}
n += (s & 0x7fffff) << 5; r[64] = n & 0x7fffff;
n >>= 23; s = a[132] + (s >> 23);
n += (s & 0x7fffff) << 5; r[65] = n & 0x7fffff;
n >>= 23; s = a[133] + (s >> 23);
n += s << 5; r[66] = n;
#endif /* WOLFSSL_SP_SMALL */
XMEMSET(&r[67], 0, sizeof(*r) * 67U);
}
/* Reduce the number back to 3072 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_3072_mont_reduce_67(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
for (i=0; i<66; i++) {
mu = (a[i] * mp) & 0x7fffff;
sp_3072_mul_add_67(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = (a[i] * mp) & 0x3ffffL;
sp_3072_mul_add_67(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
sp_3072_mont_shift_67(a, a);
sp_3072_cond_sub_67(a, a, m, 0 - (((a[66] >> 18) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_3072_norm_67(a);
}
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_3072_mont_mul_67(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m, sp_digit mp)
{
sp_3072_mul_67(r, a, b);
sp_3072_mont_reduce_67(r, m, mp);
}
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_3072_mont_sqr_67(sp_digit* r, const sp_digit* a, const sp_digit* m,
sp_digit mp)
{
sp_3072_sqr_67(r, a);
sp_3072_mont_reduce_67(r, m, mp);
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_3072_mul_d_67(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 67; i++) {
t += tb * a[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[67] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x7fffff;
for (i = 0; i < 64; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[65];
r[65] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[66];
r[66] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
r[67] = (sp_digit)(t[2] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
/* Conditionally add a and b using the mask m.
* m is -1 to add and 0 when not.
*
* r A single precision number representing conditional add result.
* a A single precision number to add with.
* b A single precision number to add.
* m Mask value to apply.
*/
static void sp_3072_cond_add_67(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 67; i++) {
r[i] = a[i] + (b[i] & m);
}
#else
int i;
for (i = 0; i < 64; i += 8) {
r[i + 0] = a[i + 0] + (b[i + 0] & m);
r[i + 1] = a[i + 1] + (b[i + 1] & m);
r[i + 2] = a[i + 2] + (b[i + 2] & m);
r[i + 3] = a[i + 3] + (b[i + 3] & m);
r[i + 4] = a[i + 4] + (b[i + 4] & m);
r[i + 5] = a[i + 5] + (b[i + 5] & m);
r[i + 6] = a[i + 6] + (b[i + 6] & m);
r[i + 7] = a[i + 7] + (b[i + 7] & m);
}
r[64] = a[64] + (b[64] & m);
r[65] = a[65] + (b[65] & m);
r[66] = a[66] + (b[66] & m);
#endif /* WOLFSSL_SP_SMALL */
}
#ifdef WOLFSSL_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_add_67(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 67; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif
#ifdef WOLFSSL_SP_DIV_32
static WC_INLINE sp_digit sp_3072_div_word_67(sp_digit d1, sp_digit d0,
sp_digit dv)
{
sp_digit d, r, t;
/* All 23 bits from d1 and top 8 bits from d0. */
d = (d1 << 8) | (d0 >> 15);
r = d / dv;
d -= r * dv;
/* Up to 9 bits in r */
/* Next 8 bits from d0. */
r <<= 8;
d <<= 8;
d |= (d0 >> 7) & ((1 << 8) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 17 bits in r */
/* Remaining 7 bits from d0. */
r <<= 7;
d <<= 7;
d |= d0 & ((1 << 7) - 1);
t = d / dv;
r += t;
return r;
}
#endif /* WOLFSSL_SP_DIV_32 */
/* Divide d in a and put remainder into r (m*d + r = a)
* m is not calculated as it is not needed at this time.
*
* a Number to be divided.
* d Number to divide with.
* m Multiplier result.
* r Remainder from the division.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_3072_div_67(const sp_digit* a, const sp_digit* d, sp_digit* m,
sp_digit* r)
{
int i;
#ifndef WOLFSSL_SP_DIV_32
int64_t d1;
#endif
sp_digit dv, r1;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_digit* td;
#else
sp_digit t1d[134], t2d[67 + 1];
#endif
sp_digit* t1;
sp_digit* t2;
int err = MP_OKAY;
(void)m;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * (3 * 67 + 1), NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
t1 = td;
t2 = td + 2 * 67;
#else
t1 = t1d;
t2 = t2d;
#endif
dv = d[66];
XMEMCPY(t1, a, sizeof(*t1) * 2U * 67U);
for (i=66; i>=0; i--) {
t1[67 + i] += t1[67 + i - 1] >> 23;
t1[67 + i - 1] &= 0x7fffff;
#ifndef WOLFSSL_SP_DIV_32
d1 = t1[67 + i];
d1 <<= 23;
d1 += t1[67 + i - 1];
r1 = (sp_digit)(d1 / dv);
#else
r1 = sp_3072_div_word_67(t1[67 + i], t1[67 + i - 1], dv);
#endif
sp_3072_mul_d_67(t2, d, r1);
(void)sp_3072_sub_67(&t1[i], &t1[i], t2);
t1[67 + i] -= t2[67];
t1[67 + i] += t1[67 + i - 1] >> 23;
t1[67 + i - 1] &= 0x7fffff;
r1 = (((-t1[67 + i]) << 23) - t1[67 + i - 1]) / dv;
r1++;
sp_3072_mul_d_67(t2, d, r1);
(void)sp_3072_add_67(&t1[i], &t1[i], t2);
t1[67 + i] += t1[67 + i - 1] >> 23;
t1[67 + i - 1] &= 0x7fffff;
}
t1[67 - 1] += t1[67 - 2] >> 23;
t1[67 - 2] &= 0x7fffff;
d1 = t1[67 - 1];
r1 = (sp_digit)(d1 / dv);
sp_3072_mul_d_67(t2, d, r1);
(void)sp_3072_sub_67(t1, t1, t2);
XMEMCPY(r, t1, sizeof(*r) * 2U * 67U);
for (i=0; i<65; i++) {
r[i+1] += r[i] >> 23;
r[i] &= 0x7fffff;
}
sp_3072_cond_add_67(r, r, d, 0 - ((r[66] < 0) ?
(sp_digit)1 : (sp_digit)0));
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
/* Reduce a modulo m into r. (r = a mod m)
*
* r A single precision number that is the reduced result.
* a A single precision number that is to be reduced.
* m A single precision number that is the modulus to reduce with.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_3072_mod_67(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
return sp_3072_div_67(a, m, NULL, r);
}
/* Modular exponentiate a to the e mod m. (r = a^e mod m)
*
* r A single precision number that is the result of the operation.
* a A single precision number being exponentiated.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_3072_mod_exp_67(sp_digit* r, const sp_digit* a, const sp_digit* e, int bits,
const sp_digit* m, int reduceA)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* td;
sp_digit* t[3];
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 67 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
if (err == MP_OKAY) {
XMEMSET(td, 0, sizeof(*td) * 3U * 67U * 2U);
norm = t[0] = td;
t[1] = &td[67 * 2];
t[2] = &td[2 * 67 * 2];
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_67(norm, m);
if (reduceA != 0) {
err = sp_3072_mod_67(t[1], a, m);
}
else {
XMEMCPY(t[1], a, sizeof(sp_digit) * 67U);
}
}
if (err == MP_OKAY) {
sp_3072_mul_67(t[1], t[1], norm);
err = sp_3072_mod_67(t[1], t[1], m);
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_3072_mont_mul_67(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])),
sizeof(*t[2]) * 67 * 2);
sp_3072_mont_sqr_67(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2],
sizeof(*t[2]) * 67 * 2);
}
sp_3072_mont_reduce_67(t[0], m, mp);
n = sp_3072_cmp_67(t[0], m);
sp_3072_cond_sub_67(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(*r) * 67 * 2);
}
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
return err;
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[3][134];
#else
sp_digit* td;
sp_digit* t[3];
#endif
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 67 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
t[0] = td;
t[1] = &td[67 * 2];
t[2] = &td[2 * 67 * 2];
#endif
norm = t[0];
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_67(norm, m);
if (reduceA != 0) {
err = sp_3072_mod_67(t[1], a, m);
if (err == MP_OKAY) {
sp_3072_mul_67(t[1], t[1], norm);
err = sp_3072_mod_67(t[1], t[1], m);
}
}
else {
sp_3072_mul_67(t[1], a, norm);
err = sp_3072_mod_67(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_3072_mont_mul_67(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), sizeof(t[2]));
sp_3072_mont_sqr_67(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2], sizeof(t[2]));
}
sp_3072_mont_reduce_67(t[0], m, mp);
n = sp_3072_cmp_67(t[0], m);
sp_3072_cond_sub_67(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(t[0]));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[32][134];
#else
sp_digit* t[32];
sp_digit* td;
#endif
sp_digit* norm;
sp_digit rt[134];
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 32 * 134, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
for (i=0; i<32; i++)
t[i] = td + i * 134;
#endif
norm = t[0];
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_67(norm, m);
if (reduceA != 0) {
err = sp_3072_mod_67(t[1], a, m);
if (err == MP_OKAY) {
sp_3072_mul_67(t[1], t[1], norm);
err = sp_3072_mod_67(t[1], t[1], m);
}
}
else {
sp_3072_mul_67(t[1], a, norm);
err = sp_3072_mod_67(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
sp_3072_mont_sqr_67(t[ 2], t[ 1], m, mp);
sp_3072_mont_mul_67(t[ 3], t[ 2], t[ 1], m, mp);
sp_3072_mont_sqr_67(t[ 4], t[ 2], m, mp);
sp_3072_mont_mul_67(t[ 5], t[ 3], t[ 2], m, mp);
sp_3072_mont_sqr_67(t[ 6], t[ 3], m, mp);
sp_3072_mont_mul_67(t[ 7], t[ 4], t[ 3], m, mp);
sp_3072_mont_sqr_67(t[ 8], t[ 4], m, mp);
sp_3072_mont_mul_67(t[ 9], t[ 5], t[ 4], m, mp);
sp_3072_mont_sqr_67(t[10], t[ 5], m, mp);
sp_3072_mont_mul_67(t[11], t[ 6], t[ 5], m, mp);
sp_3072_mont_sqr_67(t[12], t[ 6], m, mp);
sp_3072_mont_mul_67(t[13], t[ 7], t[ 6], m, mp);
sp_3072_mont_sqr_67(t[14], t[ 7], m, mp);
sp_3072_mont_mul_67(t[15], t[ 8], t[ 7], m, mp);
sp_3072_mont_sqr_67(t[16], t[ 8], m, mp);
sp_3072_mont_mul_67(t[17], t[ 9], t[ 8], m, mp);
sp_3072_mont_sqr_67(t[18], t[ 9], m, mp);
sp_3072_mont_mul_67(t[19], t[10], t[ 9], m, mp);
sp_3072_mont_sqr_67(t[20], t[10], m, mp);
sp_3072_mont_mul_67(t[21], t[11], t[10], m, mp);
sp_3072_mont_sqr_67(t[22], t[11], m, mp);
sp_3072_mont_mul_67(t[23], t[12], t[11], m, mp);
sp_3072_mont_sqr_67(t[24], t[12], m, mp);
sp_3072_mont_mul_67(t[25], t[13], t[12], m, mp);
sp_3072_mont_sqr_67(t[26], t[13], m, mp);
sp_3072_mont_mul_67(t[27], t[14], t[13], m, mp);
sp_3072_mont_sqr_67(t[28], t[14], m, mp);
sp_3072_mont_mul_67(t[29], t[15], t[14], m, mp);
sp_3072_mont_sqr_67(t[30], t[15], m, mp);
sp_3072_mont_mul_67(t[31], t[16], t[15], m, mp);
bits = ((bits + 4) / 5) * 5;
i = ((bits + 22) / 23) - 1;
c = bits % 23;
if (c == 0) {
c = 23;
}
if (i < 67) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
XMEMCPY(rt, t[y], sizeof(rt));
for (; i>=0 || c>=5; ) {
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
sp_3072_mont_sqr_67(rt, rt, m, mp);
sp_3072_mont_sqr_67(rt, rt, m, mp);
sp_3072_mont_sqr_67(rt, rt, m, mp);
sp_3072_mont_sqr_67(rt, rt, m, mp);
sp_3072_mont_sqr_67(rt, rt, m, mp);
sp_3072_mont_mul_67(rt, rt, t[y], m, mp);
}
sp_3072_mont_reduce_67(rt, m, mp);
n = sp_3072_cmp_67(rt, m);
sp_3072_cond_sub_67(rt, rt, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, rt, sizeof(rt));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#endif
}
#endif /* (WOLFSSL_HAVE_SP_RSA || WOLFSSL_HAVE_SP_DH) && !WOLFSSL_RSA_PUBLIC_ONLY */
/* r = 2^n mod m where n is the number of bits to reduce by.
* Given m must be 3072 bits, just need to subtract.
*
* r A single precision number.
* m A signle precision number.
*/
static void sp_3072_mont_norm_134(sp_digit* r, const sp_digit* m)
{
/* Set r = 2^n - 1. */
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<133; i++) {
r[i] = 0x7fffff;
}
#else
int i;
for (i = 0; i < 128; i += 8) {
r[i + 0] = 0x7fffff;
r[i + 1] = 0x7fffff;
r[i + 2] = 0x7fffff;
r[i + 3] = 0x7fffff;
r[i + 4] = 0x7fffff;
r[i + 5] = 0x7fffff;
r[i + 6] = 0x7fffff;
r[i + 7] = 0x7fffff;
}
r[128] = 0x7fffff;
r[129] = 0x7fffff;
r[130] = 0x7fffff;
r[131] = 0x7fffff;
r[132] = 0x7fffff;
#endif
r[133] = 0x1fffL;
/* r = (2^n - 1) mod n */
(void)sp_3072_sub_134(r, r, m);
/* Add one so r = 2^n mod m */
r[0] += 1;
}
/* Compare a with b in constant time.
*
* a A single precision integer.
* b A single precision integer.
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_3072_cmp_134(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=133; i>=0; i--) {
r |= (a[i] - b[i]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#else
int i;
r |= (a[133] - b[133]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[132] - b[132]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[131] - b[131]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[130] - b[130]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[129] - b[129]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[128] - b[128]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
for (i = 120; i >= 0; i -= 8) {
r |= (a[i + 7] - b[i + 7]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 6] - b[i + 6]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 5] - b[i + 5]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 4] - b[i + 4]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 3] - b[i + 3]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 2] - b[i + 2]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 1] - b[i + 1]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 0] - b[i + 0]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#endif /* WOLFSSL_SP_SMALL */
return r;
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*
* r A single precision number representing condition subtract result.
* a A single precision number to subtract from.
* b A single precision number to subtract.
* m Mask value to apply.
*/
static void sp_3072_cond_sub_134(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 134; i++) {
r[i] = a[i] - (b[i] & m);
}
#else
int i;
for (i = 0; i < 128; i += 8) {
r[i + 0] = a[i + 0] - (b[i + 0] & m);
r[i + 1] = a[i + 1] - (b[i + 1] & m);
r[i + 2] = a[i + 2] - (b[i + 2] & m);
r[i + 3] = a[i + 3] - (b[i + 3] & m);
r[i + 4] = a[i + 4] - (b[i + 4] & m);
r[i + 5] = a[i + 5] - (b[i + 5] & m);
r[i + 6] = a[i + 6] - (b[i + 6] & m);
r[i + 7] = a[i + 7] - (b[i + 7] & m);
}
r[128] = a[128] - (b[128] & m);
r[129] = a[129] - (b[129] & m);
r[130] = a[130] - (b[130] & m);
r[131] = a[131] - (b[131] & m);
r[132] = a[132] - (b[132] & m);
r[133] = a[133] - (b[133] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Mul a by scalar b and add into r. (r += a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_3072_mul_add_134(sp_digit* r, const sp_digit* a,
const sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 134; i++) {
t += (tb * a[i]) + r[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[134] += t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] += t[0] & 0x7fffff;
for (i = 0; i < 128; i += 8) {
t[1] = tb * a[i+1];
r[i+1] += (t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] += (t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] += (t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] += (t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] += (t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] += (t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] += (t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] += (t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[129]; r[129] += (t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[130]; r[130] += (t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[131]; r[131] += (t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[132]; r[132] += (t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[133]; r[133] += (t[4] >> 23) + (t[5] & 0x7fffff);
r[134] += t[5] >> 23;
#endif /* WOLFSSL_SP_SMALL */
}
/* Normalize the values in each word to 23.
*
* a Array of sp_digit to normalize.
*/
static void sp_3072_norm_134(sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 133; i++) {
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
#else
int i;
for (i = 0; i < 128; i += 8) {
a[i+1] += a[i+0] >> 23; a[i+0] &= 0x7fffff;
a[i+2] += a[i+1] >> 23; a[i+1] &= 0x7fffff;
a[i+3] += a[i+2] >> 23; a[i+2] &= 0x7fffff;
a[i+4] += a[i+3] >> 23; a[i+3] &= 0x7fffff;
a[i+5] += a[i+4] >> 23; a[i+4] &= 0x7fffff;
a[i+6] += a[i+5] >> 23; a[i+5] &= 0x7fffff;
a[i+7] += a[i+6] >> 23; a[i+6] &= 0x7fffff;
a[i+8] += a[i+7] >> 23; a[i+7] &= 0x7fffff;
a[i+9] += a[i+8] >> 23; a[i+8] &= 0x7fffff;
}
a[128+1] += a[128] >> 23;
a[128] &= 0x7fffff;
a[129+1] += a[129] >> 23;
a[129] &= 0x7fffff;
a[130+1] += a[130] >> 23;
a[130] &= 0x7fffff;
a[131+1] += a[131] >> 23;
a[131] &= 0x7fffff;
a[132+1] += a[132] >> 23;
a[132] &= 0x7fffff;
#endif
}
/* Shift the result in the high 3072 bits down to the bottom.
*
* r A single precision number.
* a A single precision number.
*/
static void sp_3072_mont_shift_134(sp_digit* r, const sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
int64_t n = a[133] >> 13;
n += ((int64_t)a[134]) << 10;
for (i = 0; i < 133; i++) {
r[i] = n & 0x7fffff;
n >>= 23;
n += ((int64_t)a[135 + i]) << 10;
}
r[133] = (sp_digit)n;
#else
int i;
int64_t n = a[133] >> 13;
n += ((int64_t)a[134]) << 10;
for (i = 0; i < 128; i += 8) {
r[i + 0] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 135]) << 10;
r[i + 1] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 136]) << 10;
r[i + 2] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 137]) << 10;
r[i + 3] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 138]) << 10;
r[i + 4] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 139]) << 10;
r[i + 5] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 140]) << 10;
r[i + 6] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 141]) << 10;
r[i + 7] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 142]) << 10;
}
r[128] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[263]) << 10;
r[129] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[264]) << 10;
r[130] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[265]) << 10;
r[131] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[266]) << 10;
r[132] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[267]) << 10;
r[133] = (sp_digit)n;
#endif /* WOLFSSL_SP_SMALL */
XMEMSET(&r[134], 0, sizeof(*r) * 134U);
}
/* Reduce the number back to 3072 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_3072_mont_reduce_134(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
#ifdef WOLFSSL_SP_DH
if (mp != 1) {
for (i=0; i<133; i++) {
mu = (a[i] * mp) & 0x7fffff;
sp_3072_mul_add_134(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = (a[i] * mp) & 0x1fffL;
sp_3072_mul_add_134(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
else {
for (i=0; i<133; i++) {
mu = a[i] & 0x7fffff;
sp_3072_mul_add_134(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = a[i] & 0x1fffL;
sp_3072_mul_add_134(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
#else
for (i=0; i<133; i++) {
mu = (a[i] * mp) & 0x7fffff;
sp_3072_mul_add_134(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = (a[i] * mp) & 0x1fffL;
sp_3072_mul_add_134(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
#endif
sp_3072_mont_shift_134(a, a);
sp_3072_cond_sub_134(a, a, m, 0 - (((a[133] >> 13) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_3072_norm_134(a);
}
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_3072_mont_mul_134(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m, sp_digit mp)
{
sp_3072_mul_134(r, a, b);
sp_3072_mont_reduce_134(r, m, mp);
}
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_3072_mont_sqr_134(sp_digit* r, const sp_digit* a, const sp_digit* m,
sp_digit mp)
{
sp_3072_sqr_134(r, a);
sp_3072_mont_reduce_134(r, m, mp);
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_3072_mul_d_268(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 268; i++) {
t += tb * a[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[268] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x7fffff;
for (i = 0; i < 264; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[265];
r[265] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[266];
r[266] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[267];
r[267] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
r[268] = (sp_digit)(t[3] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
/* Conditionally add a and b using the mask m.
* m is -1 to add and 0 when not.
*
* r A single precision number representing conditional add result.
* a A single precision number to add with.
* b A single precision number to add.
* m Mask value to apply.
*/
static void sp_3072_cond_add_134(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 134; i++) {
r[i] = a[i] + (b[i] & m);
}
#else
int i;
for (i = 0; i < 128; i += 8) {
r[i + 0] = a[i + 0] + (b[i + 0] & m);
r[i + 1] = a[i + 1] + (b[i + 1] & m);
r[i + 2] = a[i + 2] + (b[i + 2] & m);
r[i + 3] = a[i + 3] + (b[i + 3] & m);
r[i + 4] = a[i + 4] + (b[i + 4] & m);
r[i + 5] = a[i + 5] + (b[i + 5] & m);
r[i + 6] = a[i + 6] + (b[i + 6] & m);
r[i + 7] = a[i + 7] + (b[i + 7] & m);
}
r[128] = a[128] + (b[128] & m);
r[129] = a[129] + (b[129] & m);
r[130] = a[130] + (b[130] & m);
r[131] = a[131] + (b[131] & m);
r[132] = a[132] + (b[132] & m);
r[133] = a[133] + (b[133] & m);
#endif /* WOLFSSL_SP_SMALL */
}
#ifdef WOLFSSL_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_sub_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 134; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#endif
#ifdef WOLFSSL_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_add_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 134; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif
SP_NOINLINE static void sp_3072_rshift_134(sp_digit* r, sp_digit* a, byte n)
{
int i;
#ifdef WOLFSSL_SP_SMALL
for (i=0; i<133; i++) {
r[i] = ((a[i] >> n) | (a[i + 1] << (23 - n))) & 0x7fffff;
}
#else
for (i=0; i<128; i += 8) {
r[i+0] = ((a[i+0] >> n) | (a[i+1] << (23 - n))) & 0x7fffff;
r[i+1] = ((a[i+1] >> n) | (a[i+2] << (23 - n))) & 0x7fffff;
r[i+2] = ((a[i+2] >> n) | (a[i+3] << (23 - n))) & 0x7fffff;
r[i+3] = ((a[i+3] >> n) | (a[i+4] << (23 - n))) & 0x7fffff;
r[i+4] = ((a[i+4] >> n) | (a[i+5] << (23 - n))) & 0x7fffff;
r[i+5] = ((a[i+5] >> n) | (a[i+6] << (23 - n))) & 0x7fffff;
r[i+6] = ((a[i+6] >> n) | (a[i+7] << (23 - n))) & 0x7fffff;
r[i+7] = ((a[i+7] >> n) | (a[i+8] << (23 - n))) & 0x7fffff;
}
r[128] = ((a[128] >> n) | (a[129] << (23 - n))) & 0x7fffff;
r[129] = ((a[129] >> n) | (a[130] << (23 - n))) & 0x7fffff;
r[130] = ((a[130] >> n) | (a[131] << (23 - n))) & 0x7fffff;
r[131] = ((a[131] >> n) | (a[132] << (23 - n))) & 0x7fffff;
r[132] = ((a[132] >> n) | (a[133] << (23 - n))) & 0x7fffff;
#endif
r[133] = a[133] >> n;
}
#ifdef WOLFSSL_SP_DIV_32
static WC_INLINE sp_digit sp_3072_div_word_134(sp_digit d1, sp_digit d0,
sp_digit dv)
{
sp_digit d, r, t;
/* All 23 bits from d1 and top 8 bits from d0. */
d = (d1 << 8) | (d0 >> 15);
r = d / dv;
d -= r * dv;
/* Up to 9 bits in r */
/* Next 8 bits from d0. */
r <<= 8;
d <<= 8;
d |= (d0 >> 7) & ((1 << 8) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 17 bits in r */
/* Remaining 7 bits from d0. */
r <<= 7;
d <<= 7;
d |= d0 & ((1 << 7) - 1);
t = d / dv;
r += t;
return r;
}
#endif /* WOLFSSL_SP_DIV_32 */
/* Divide d in a and put remainder into r (m*d + r = a)
* m is not calculated as it is not needed at this time.
*
* a Nmber to be divided.
* d Number to divide with.
* m Multiplier result.
* r Remainder from the division.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_3072_div_134(const sp_digit* a, const sp_digit* d, sp_digit* m,
sp_digit* r)
{
int i;
#ifndef WOLFSSL_SP_DIV_32
int64_t d1;
#endif
sp_digit dv, r1;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_digit* td;
#else
sp_digit t1d[268 + 1], t2d[134 + 1], sdd[134 + 1];
#endif
sp_digit* t1;
sp_digit* t2;
sp_digit* sd;
int err = MP_OKAY;
(void)m;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * (4 * 134 + 3), NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
t1 = td;
t2 = td + 268 + 1;
sd = t2 + 134 + 1;
#else
t1 = t1d;
t2 = t2d;
sd = sdd;
#endif
sp_3072_mul_d_134(sd, d, 1 << 10);
sp_3072_mul_d_268(t1, a, 1 << 10);
dv = sd[133];
for (i=134; i>=0; i--) {
t1[134 + i] += t1[134 + i - 1] >> 23;
t1[134 + i - 1] &= 0x7fffff;
#ifndef WOLFSSL_SP_DIV_32
d1 = t1[134 + i];
d1 <<= 23;
d1 += t1[134 + i - 1];
r1 = (sp_digit)(d1 / dv);
#else
r1 = sp_3072_div_word_134(t1[134 + i], t1[134 + i - 1], dv);
#endif
sp_3072_mul_d_134(t2, sd, r1);
(void)sp_3072_sub_134(&t1[i], &t1[i], t2);
t1[134 + i] -= t2[134];
t1[134 + i] += t1[134 + i - 1] >> 23;
t1[134 + i - 1] &= 0x7fffff;
r1 = (((-t1[134 + i]) << 23) - t1[134 + i - 1]) / dv;
r1 -= t1[134 + i];
sp_3072_mul_d_134(t2, sd, r1);
(void)sp_3072_add_134(&t1[i], &t1[i], t2);
t1[134 + i] += t1[134 + i - 1] >> 23;
t1[134 + i - 1] &= 0x7fffff;
}
t1[134 - 1] += t1[134 - 2] >> 23;
t1[134 - 2] &= 0x7fffff;
d1 = t1[134 - 1];
r1 = (sp_digit)(d1 / dv);
sp_3072_mul_d_134(t2, sd, r1);
sp_3072_sub_134(t1, t1, t2);
XMEMCPY(r, t1, sizeof(*r) * 2U * 134U);
for (i=0; i<132; i++) {
r[i+1] += r[i] >> 23;
r[i] &= 0x7fffff;
}
sp_3072_cond_add_134(r, r, sd, 0 - ((r[133] < 0) ?
(sp_digit)1 : (sp_digit)0));
sp_3072_norm_134(r);
sp_3072_rshift_134(r, r, 10);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
/* Reduce a modulo m into r. (r = a mod m)
*
* r A single precision number that is the reduced result.
* a A single precision number that is to be reduced.
* m A single precision number that is the modulus to reduce with.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_3072_mod_134(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
return sp_3072_div_134(a, m, NULL, r);
}
#if (defined(WOLFSSL_HAVE_SP_RSA) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)) || \
defined(WOLFSSL_HAVE_SP_DH)
/* Modular exponentiate a to the e mod m. (r = a^e mod m)
*
* r A single precision number that is the result of the operation.
* a A single precision number being exponentiated.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_3072_mod_exp_134(sp_digit* r, const sp_digit* a, const sp_digit* e, int bits,
const sp_digit* m, int reduceA)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* td;
sp_digit* t[3];
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 134 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
if (err == MP_OKAY) {
XMEMSET(td, 0, sizeof(*td) * 3U * 134U * 2U);
norm = t[0] = td;
t[1] = &td[134 * 2];
t[2] = &td[2 * 134 * 2];
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_134(norm, m);
if (reduceA != 0) {
err = sp_3072_mod_134(t[1], a, m);
}
else {
XMEMCPY(t[1], a, sizeof(sp_digit) * 134U);
}
}
if (err == MP_OKAY) {
sp_3072_mul_134(t[1], t[1], norm);
err = sp_3072_mod_134(t[1], t[1], m);
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_3072_mont_mul_134(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])),
sizeof(*t[2]) * 134 * 2);
sp_3072_mont_sqr_134(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2],
sizeof(*t[2]) * 134 * 2);
}
sp_3072_mont_reduce_134(t[0], m, mp);
n = sp_3072_cmp_134(t[0], m);
sp_3072_cond_sub_134(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(*r) * 134 * 2);
}
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
return err;
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[3][268];
#else
sp_digit* td;
sp_digit* t[3];
#endif
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 134 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
t[0] = td;
t[1] = &td[134 * 2];
t[2] = &td[2 * 134 * 2];
#endif
norm = t[0];
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_134(norm, m);
if (reduceA != 0) {
err = sp_3072_mod_134(t[1], a, m);
if (err == MP_OKAY) {
sp_3072_mul_134(t[1], t[1], norm);
err = sp_3072_mod_134(t[1], t[1], m);
}
}
else {
sp_3072_mul_134(t[1], a, norm);
err = sp_3072_mod_134(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_3072_mont_mul_134(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), sizeof(t[2]));
sp_3072_mont_sqr_134(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2], sizeof(t[2]));
}
sp_3072_mont_reduce_134(t[0], m, mp);
n = sp_3072_cmp_134(t[0], m);
sp_3072_cond_sub_134(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(t[0]));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[32][268];
#else
sp_digit* t[32];
sp_digit* td;
#endif
sp_digit* norm;
sp_digit rt[268];
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 32 * 268, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
for (i=0; i<32; i++)
t[i] = td + i * 268;
#endif
norm = t[0];
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_134(norm, m);
if (reduceA != 0) {
err = sp_3072_mod_134(t[1], a, m);
if (err == MP_OKAY) {
sp_3072_mul_134(t[1], t[1], norm);
err = sp_3072_mod_134(t[1], t[1], m);
}
}
else {
sp_3072_mul_134(t[1], a, norm);
err = sp_3072_mod_134(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
sp_3072_mont_sqr_134(t[ 2], t[ 1], m, mp);
sp_3072_mont_mul_134(t[ 3], t[ 2], t[ 1], m, mp);
sp_3072_mont_sqr_134(t[ 4], t[ 2], m, mp);
sp_3072_mont_mul_134(t[ 5], t[ 3], t[ 2], m, mp);
sp_3072_mont_sqr_134(t[ 6], t[ 3], m, mp);
sp_3072_mont_mul_134(t[ 7], t[ 4], t[ 3], m, mp);
sp_3072_mont_sqr_134(t[ 8], t[ 4], m, mp);
sp_3072_mont_mul_134(t[ 9], t[ 5], t[ 4], m, mp);
sp_3072_mont_sqr_134(t[10], t[ 5], m, mp);
sp_3072_mont_mul_134(t[11], t[ 6], t[ 5], m, mp);
sp_3072_mont_sqr_134(t[12], t[ 6], m, mp);
sp_3072_mont_mul_134(t[13], t[ 7], t[ 6], m, mp);
sp_3072_mont_sqr_134(t[14], t[ 7], m, mp);
sp_3072_mont_mul_134(t[15], t[ 8], t[ 7], m, mp);
sp_3072_mont_sqr_134(t[16], t[ 8], m, mp);
sp_3072_mont_mul_134(t[17], t[ 9], t[ 8], m, mp);
sp_3072_mont_sqr_134(t[18], t[ 9], m, mp);
sp_3072_mont_mul_134(t[19], t[10], t[ 9], m, mp);
sp_3072_mont_sqr_134(t[20], t[10], m, mp);
sp_3072_mont_mul_134(t[21], t[11], t[10], m, mp);
sp_3072_mont_sqr_134(t[22], t[11], m, mp);
sp_3072_mont_mul_134(t[23], t[12], t[11], m, mp);
sp_3072_mont_sqr_134(t[24], t[12], m, mp);
sp_3072_mont_mul_134(t[25], t[13], t[12], m, mp);
sp_3072_mont_sqr_134(t[26], t[13], m, mp);
sp_3072_mont_mul_134(t[27], t[14], t[13], m, mp);
sp_3072_mont_sqr_134(t[28], t[14], m, mp);
sp_3072_mont_mul_134(t[29], t[15], t[14], m, mp);
sp_3072_mont_sqr_134(t[30], t[15], m, mp);
sp_3072_mont_mul_134(t[31], t[16], t[15], m, mp);
bits = ((bits + 4) / 5) * 5;
i = ((bits + 22) / 23) - 1;
c = bits % 23;
if (c == 0) {
c = 23;
}
if (i < 134) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
XMEMCPY(rt, t[y], sizeof(rt));
for (; i>=0 || c>=5; ) {
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
sp_3072_mont_sqr_134(rt, rt, m, mp);
sp_3072_mont_sqr_134(rt, rt, m, mp);
sp_3072_mont_sqr_134(rt, rt, m, mp);
sp_3072_mont_sqr_134(rt, rt, m, mp);
sp_3072_mont_sqr_134(rt, rt, m, mp);
sp_3072_mont_mul_134(rt, rt, t[y], m, mp);
}
sp_3072_mont_reduce_134(rt, m, mp);
n = sp_3072_cmp_134(rt, m);
sp_3072_cond_sub_134(rt, rt, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, rt, sizeof(rt));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#endif
}
#endif /* (WOLFSSL_HAVE_SP_RSA && !WOLFSSL_RSA_PUBLIC_ONLY) || */
/* WOLFSSL_HAVE_SP_DH */
#if defined(WOLFSSL_HAVE_SP_RSA) && !defined(SP_RSA_PRIVATE_EXP_D) && \
!defined(RSA_LOW_MEM) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)
/* AND m into each word of a and store in r.
*
* r A single precision integer.
* a A single precision integer.
* m Mask to AND against each digit.
*/
static void sp_3072_mask_67(sp_digit* r, const sp_digit* a, sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<67; i++) {
r[i] = a[i] & m;
}
#else
int i;
for (i = 0; i < 64; i += 8) {
r[i+0] = a[i+0] & m;
r[i+1] = a[i+1] & m;
r[i+2] = a[i+2] & m;
r[i+3] = a[i+3] & m;
r[i+4] = a[i+4] & m;
r[i+5] = a[i+5] & m;
r[i+6] = a[i+6] & m;
r[i+7] = a[i+7] & m;
}
r[64] = a[64] & m;
r[65] = a[65] & m;
r[66] = a[66] & m;
#endif
}
#endif
#ifdef WOLFSSL_HAVE_SP_RSA
/* RSA public key operation.
*
* in Array of bytes representing the number to exponentiate, base.
* inLen Number of bytes in base.
* em Public exponent.
* mm Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 384 bytes long.
* outLen Number of bytes in result.
* returns 0 on success, MP_TO_E when the outLen is too small, MP_READ_E when
* an array is too long and MEMORY_E when dynamic memory allocation fails.
*/
int sp_RsaPublic_3072(const byte* in, word32 inLen, mp_int* em, mp_int* mm,
byte* out, word32* outLen)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* d = NULL;
sp_digit* a;
sp_digit* m;
sp_digit* r;
sp_digit* norm;
sp_digit e[1] = {0};
sp_digit mp;
int i;
int err = MP_OKAY;
if (*outLen < 384U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(em) > 23) {
err = MP_READ_E;
}
if (inLen > 384U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 134 * 5, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
a = d;
r = a + 134 * 2;
m = r + 134 * 2;
norm = r;
sp_3072_from_bin(a, 134, in, inLen);
#if DIGIT_BIT >= 23
e[0] = (sp_digit)em->dp[0];
#else
e[0] = (sp_digit)em->dp[0];
if (em->used > 1) {
e[0] |= ((sp_digit)em->dp[1]) << DIGIT_BIT;
}
#endif
if (e[0] == 0) {
err = MP_EXPTMOD_E;
}
}
if (err == MP_OKAY) {
sp_3072_from_mp(m, 134, mm);
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_134(norm, m);
}
if (err == MP_OKAY) {
sp_3072_mul_134(a, a, norm);
err = sp_3072_mod_134(a, a, m);
}
if (err == MP_OKAY) {
for (i=22; i>=0; i--) {
if ((e[0] >> i) != 0) {
break;
}
}
XMEMCPY(r, a, sizeof(sp_digit) * 134 * 2);
for (i--; i>=0; i--) {
sp_3072_mont_sqr_134(r, r, m, mp);
if (((e[0] >> i) & 1) == 1) {
sp_3072_mont_mul_134(r, r, a, m, mp);
}
}
sp_3072_mont_reduce_134(r, m, mp);
mp = sp_3072_cmp_134(r, m);
sp_3072_cond_sub_134(r, r, m, ((mp < 0) ?
(sp_digit)1 : (sp_digit)0)- 1);
sp_3072_to_bin(r, out);
*outLen = 384;
}
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_digit ad[268], md[134], rd[268];
#else
sp_digit* d = NULL;
#endif
sp_digit* a;
sp_digit* m;
sp_digit* r;
sp_digit e[1] = {0};
int err = MP_OKAY;
if (*outLen < 384U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(em) > 23) {
err = MP_READ_E;
}
if (inLen > 384U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 3072) {
err = MP_READ_E;
}
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 134 * 5, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = d;
r = a + 134 * 2;
m = r + 134 * 2;
}
#else
a = ad;
m = md;
r = rd;
#endif
if (err == MP_OKAY) {
sp_3072_from_bin(a, 134, in, inLen);
#if DIGIT_BIT >= 23
e[0] = (sp_digit)em->dp[0];
#else
e[0] = (sp_digit)em->dp[0];
if (em->used > 1) {
e[0] |= ((sp_digit)em->dp[1]) << DIGIT_BIT;
}
#endif
if (e[0] == 0) {
err = MP_EXPTMOD_E;
}
}
if (err == MP_OKAY) {
sp_3072_from_mp(m, 134, mm);
if (e[0] == 0x3) {
sp_3072_sqr_134(r, a);
err = sp_3072_mod_134(r, r, m);
if (err == MP_OKAY) {
sp_3072_mul_134(r, a, r);
err = sp_3072_mod_134(r, r, m);
}
}
else {
sp_digit* norm = r;
int i;
sp_digit mp;
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_134(norm, m);
sp_3072_mul_134(a, a, norm);
err = sp_3072_mod_134(a, a, m);
if (err == MP_OKAY) {
for (i=22; i>=0; i--) {
if ((e[0] >> i) != 0) {
break;
}
}
XMEMCPY(r, a, sizeof(sp_digit) * 268U);
for (i--; i>=0; i--) {
sp_3072_mont_sqr_134(r, r, m, mp);
if (((e[0] >> i) & 1) == 1) {
sp_3072_mont_mul_134(r, r, a, m, mp);
}
}
sp_3072_mont_reduce_134(r, m, mp);
mp = sp_3072_cmp_134(r, m);
sp_3072_cond_sub_134(r, r, m, ((mp < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
}
}
if (err == MP_OKAY) {
sp_3072_to_bin(r, out);
*outLen = 384;
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
#endif
return err;
#endif /* WOLFSSL_SP_SMALL */
}
#ifndef WOLFSSL_RSA_PUBLIC_ONLY
/* RSA private key operation.
*
* in Array of bytes representing the number to exponentiate, base.
* inLen Number of bytes in base.
* dm Private exponent.
* pm First prime.
* qm Second prime.
* dpm First prime's CRT exponent.
* dqm Second prime's CRT exponent.
* qim Inverse of second prime mod p.
* mm Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 384 bytes long.
* outLen Number of bytes in result.
* returns 0 on success, MP_TO_E when the outLen is too small, MP_READ_E when
* an array is too long and MEMORY_E when dynamic memory allocation fails.
*/
int sp_RsaPrivate_3072(const byte* in, word32 inLen, mp_int* dm,
mp_int* pm, mp_int* qm, mp_int* dpm, mp_int* dqm, mp_int* qim, mp_int* mm,
byte* out, word32* outLen)
{
#if defined(SP_RSA_PRIVATE_EXP_D) || defined(RSA_LOW_MEM)
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_digit* a;
sp_digit* d = NULL;
sp_digit* m;
sp_digit* r;
int err = MP_OKAY;
(void)pm;
(void)qm;
(void)dpm;
(void)dqm;
(void)qim;
if (*outLen < 384U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(dm) > 3072) {
err = MP_READ_E;
}
if (inLen > 384) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 134 * 4, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = d + 134;
m = a + 134;
r = a;
sp_3072_from_bin(a, 134, in, inLen);
sp_3072_from_mp(d, 134, dm);
sp_3072_from_mp(m, 134, mm);
err = sp_3072_mod_exp_134(r, a, d, 3072, m, 0);
}
if (err == MP_OKAY) {
sp_3072_to_bin(r, out);
*outLen = 384;
}
if (d != NULL) {
XMEMSET(d, 0, sizeof(sp_digit) * 134);
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
sp_digit a[268], d[134], m[134];
sp_digit* r = a;
int err = MP_OKAY;
(void)pm;
(void)qm;
(void)dpm;
(void)dqm;
(void)qim;
if (*outLen < 384U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(dm) > 3072) {
err = MP_READ_E;
}
if (inLen > 384U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
sp_3072_from_bin(a, 134, in, inLen);
sp_3072_from_mp(d, 134, dm);
sp_3072_from_mp(m, 134, mm);
err = sp_3072_mod_exp_134(r, a, d, 3072, m, 0);
}
if (err == MP_OKAY) {
sp_3072_to_bin(r, out);
*outLen = 384;
}
XMEMSET(d, 0, sizeof(sp_digit) * 134);
return err;
#endif /* WOLFSSL_SP_SMALL || defined(WOLFSSL_SMALL_STACK) */
#else
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_digit* t = NULL;
sp_digit* a;
sp_digit* p;
sp_digit* q;
sp_digit* dp;
sp_digit* dq;
sp_digit* qi;
sp_digit* tmp;
sp_digit* tmpa;
sp_digit* tmpb;
sp_digit* r;
int err = MP_OKAY;
(void)dm;
(void)mm;
if (*outLen < 384U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (inLen > 384) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
t = (sp_digit*)XMALLOC(sizeof(sp_digit) * 67 * 11, NULL,
DYNAMIC_TYPE_RSA);
if (t == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = t;
p = a + 134 * 2;
q = p + 67;
qi = dq = dp = q + 67;
tmpa = qi + 67;
tmpb = tmpa + 134;
tmp = t;
r = tmp + 134;
sp_3072_from_bin(a, 134, in, inLen);
sp_3072_from_mp(p, 67, pm);
sp_3072_from_mp(q, 67, qm);
sp_3072_from_mp(dp, 67, dpm);
err = sp_3072_mod_exp_67(tmpa, a, dp, 1536, p, 1);
}
if (err == MP_OKAY) {
sp_3072_from_mp(dq, 67, dqm);
err = sp_3072_mod_exp_67(tmpb, a, dq, 1536, q, 1);
}
if (err == MP_OKAY) {
(void)sp_3072_sub_67(tmpa, tmpa, tmpb);
sp_3072_mask_67(tmp, p, 0 - ((sp_int_digit)tmpa[66] >> 31));
(void)sp_3072_add_67(tmpa, tmpa, tmp);
sp_3072_from_mp(qi, 67, qim);
sp_3072_mul_67(tmpa, tmpa, qi);
err = sp_3072_mod_67(tmpa, tmpa, p);
}
if (err == MP_OKAY) {
sp_3072_mul_67(tmpa, q, tmpa);
(void)sp_3072_add_134(r, tmpb, tmpa);
sp_3072_norm_134(r);
sp_3072_to_bin(r, out);
*outLen = 384;
}
if (t != NULL) {
XMEMSET(t, 0, sizeof(sp_digit) * 67 * 11);
XFREE(t, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
sp_digit a[134 * 2];
sp_digit p[67], q[67], dp[67], dq[67], qi[67];
sp_digit tmp[134], tmpa[134], tmpb[134];
sp_digit* r = a;
int err = MP_OKAY;
(void)dm;
(void)mm;
if (*outLen < 384U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (inLen > 384U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
sp_3072_from_bin(a, 134, in, inLen);
sp_3072_from_mp(p, 67, pm);
sp_3072_from_mp(q, 67, qm);
sp_3072_from_mp(dp, 67, dpm);
sp_3072_from_mp(dq, 67, dqm);
sp_3072_from_mp(qi, 67, qim);
err = sp_3072_mod_exp_67(tmpa, a, dp, 1536, p, 1);
}
if (err == MP_OKAY) {
err = sp_3072_mod_exp_67(tmpb, a, dq, 1536, q, 1);
}
if (err == MP_OKAY) {
(void)sp_3072_sub_67(tmpa, tmpa, tmpb);
sp_3072_mask_67(tmp, p, 0 - ((sp_int_digit)tmpa[66] >> 31));
(void)sp_3072_add_67(tmpa, tmpa, tmp);
sp_3072_mul_67(tmpa, tmpa, qi);
err = sp_3072_mod_67(tmpa, tmpa, p);
}
if (err == MP_OKAY) {
sp_3072_mul_67(tmpa, tmpa, q);
(void)sp_3072_add_134(r, tmpb, tmpa);
sp_3072_norm_134(r);
sp_3072_to_bin(r, out);
*outLen = 384;
}
XMEMSET(tmpa, 0, sizeof(tmpa));
XMEMSET(tmpb, 0, sizeof(tmpb));
XMEMSET(p, 0, sizeof(p));
XMEMSET(q, 0, sizeof(q));
XMEMSET(dp, 0, sizeof(dp));
XMEMSET(dq, 0, sizeof(dq));
XMEMSET(qi, 0, sizeof(qi));
return err;
#endif /* WOLFSSL_SP_SMALL || defined(WOLFSSL_SMALL_STACK) */
#endif /* SP_RSA_PRIVATE_EXP_D || RSA_LOW_MEM */
}
#endif /* !WOLFSSL_RSA_PUBLIC_ONLY */
#endif /* WOLFSSL_HAVE_SP_RSA */
#if defined(WOLFSSL_HAVE_SP_DH) || (defined(WOLFSSL_HAVE_SP_RSA) && \
!defined(WOLFSSL_RSA_PUBLIC_ONLY))
/* Convert an array of sp_digit to an mp_int.
*
* a A single precision integer.
* r A multi-precision integer.
*/
static int sp_3072_to_mp(const sp_digit* a, mp_int* r)
{
int err;
err = mp_grow(r, (3072 + DIGIT_BIT - 1) / DIGIT_BIT);
if (err == MP_OKAY) { /*lint !e774 case where err is always MP_OKAY*/
#if DIGIT_BIT == 23
XMEMCPY(r->dp, a, sizeof(sp_digit) * 134);
r->used = 134;
mp_clamp(r);
#elif DIGIT_BIT < 23
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 134; i++) {
r->dp[j] |= a[i] << s;
r->dp[j] &= (1L << DIGIT_BIT) - 1;
s = DIGIT_BIT - s;
r->dp[++j] = a[i] >> s;
while (s + DIGIT_BIT <= 23) {
s += DIGIT_BIT;
r->dp[j++] &= (1L << DIGIT_BIT) - 1;
if (s == SP_WORD_SIZE) {
r->dp[j] = 0;
}
else {
r->dp[j] = a[i] >> s;
}
}
s = 23 - s;
}
r->used = (3072 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#else
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 134; i++) {
r->dp[j] |= ((mp_digit)a[i]) << s;
if (s + 23 >= DIGIT_BIT) {
#if DIGIT_BIT != 32 && DIGIT_BIT != 64
r->dp[j] &= (1L << DIGIT_BIT) - 1;
#endif
s = DIGIT_BIT - s;
r->dp[++j] = a[i] >> s;
s = 23 - s;
}
else {
s += 23;
}
}
r->used = (3072 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#endif
}
return err;
}
/* Perform the modular exponentiation for Diffie-Hellman.
*
* base Base. MP integer.
* exp Exponent. MP integer.
* mod Modulus. MP integer.
* res Result. MP integer.
* returs 0 on success, MP_READ_E if there are too many bytes in an array
* and MEMORY_E if memory allocation fails.
*/
int sp_ModExp_3072(mp_int* base, mp_int* exp, mp_int* mod, mp_int* res)
{
#ifdef WOLFSSL_SP_SMALL
int err = MP_OKAY;
sp_digit* d = NULL;
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 3072) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 134 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
b = d;
e = b + 134 * 2;
m = e + 134;
r = b;
sp_3072_from_mp(b, 134, base);
sp_3072_from_mp(e, 134, exp);
sp_3072_from_mp(m, 134, mod);
err = sp_3072_mod_exp_134(r, b, e, mp_count_bits(exp), m, 0);
}
if (err == MP_OKAY) {
err = sp_3072_to_mp(r, res);
}
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 134U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit bd[268], ed[134], md[134];
#else
sp_digit* d = NULL;
#endif
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int err = MP_OKAY;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 3072) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 3072) {
err = MP_READ_E;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 134 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
b = d;
e = b + 134 * 2;
m = e + 134;
r = b;
}
#else
r = b = bd;
e = ed;
m = md;
#endif
if (err == MP_OKAY) {
sp_3072_from_mp(b, 134, base);
sp_3072_from_mp(e, 134, exp);
sp_3072_from_mp(m, 134, mod);
err = sp_3072_mod_exp_134(r, b, e, expBits, m, 0);
}
if (err == MP_OKAY) {
err = sp_3072_to_mp(r, res);
}
XMEMSET(e, 0, sizeof(sp_digit) * 134U);
#ifdef WOLFSSL_SMALL_STACK
if (d != NULL)
XFREE(d, NULL, DYNAMIC_TYPE_DH);
#endif
return err;
#endif
}
#ifdef WOLFSSL_HAVE_SP_DH
#ifdef HAVE_FFDHE_3072
SP_NOINLINE static void sp_3072_lshift_134(sp_digit* r, sp_digit* a, byte n)
{
#ifdef WOLFSSL_SP_SMALL
int i;
r[134] = a[133] >> (23 - n);
for (i=133; i>0; i--) {
r[i] = ((a[i] << n) | (a[i-1] >> (23 - n))) & 0x7fffff;
}
#else
sp_int_digit s, t;
s = (sp_int_digit)a[133];
r[134] = s >> (23U - n);
s = (sp_int_digit)(a[133]); t = (sp_int_digit)(a[132]);
r[133] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[132]); t = (sp_int_digit)(a[131]);
r[132] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[131]); t = (sp_int_digit)(a[130]);
r[131] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[130]); t = (sp_int_digit)(a[129]);
r[130] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[129]); t = (sp_int_digit)(a[128]);
r[129] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[128]); t = (sp_int_digit)(a[127]);
r[128] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[127]); t = (sp_int_digit)(a[126]);
r[127] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[126]); t = (sp_int_digit)(a[125]);
r[126] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[125]); t = (sp_int_digit)(a[124]);
r[125] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[124]); t = (sp_int_digit)(a[123]);
r[124] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[123]); t = (sp_int_digit)(a[122]);
r[123] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[122]); t = (sp_int_digit)(a[121]);
r[122] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[121]); t = (sp_int_digit)(a[120]);
r[121] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[120]); t = (sp_int_digit)(a[119]);
r[120] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[119]); t = (sp_int_digit)(a[118]);
r[119] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[118]); t = (sp_int_digit)(a[117]);
r[118] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[117]); t = (sp_int_digit)(a[116]);
r[117] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[116]); t = (sp_int_digit)(a[115]);
r[116] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[115]); t = (sp_int_digit)(a[114]);
r[115] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[114]); t = (sp_int_digit)(a[113]);
r[114] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[113]); t = (sp_int_digit)(a[112]);
r[113] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[112]); t = (sp_int_digit)(a[111]);
r[112] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[111]); t = (sp_int_digit)(a[110]);
r[111] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[110]); t = (sp_int_digit)(a[109]);
r[110] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[109]); t = (sp_int_digit)(a[108]);
r[109] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[108]); t = (sp_int_digit)(a[107]);
r[108] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[107]); t = (sp_int_digit)(a[106]);
r[107] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[106]); t = (sp_int_digit)(a[105]);
r[106] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[105]); t = (sp_int_digit)(a[104]);
r[105] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[104]); t = (sp_int_digit)(a[103]);
r[104] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[103]); t = (sp_int_digit)(a[102]);
r[103] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[102]); t = (sp_int_digit)(a[101]);
r[102] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[101]); t = (sp_int_digit)(a[100]);
r[101] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[100]); t = (sp_int_digit)(a[99]);
r[100] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[99]); t = (sp_int_digit)(a[98]);
r[99] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[98]); t = (sp_int_digit)(a[97]);
r[98] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[97]); t = (sp_int_digit)(a[96]);
r[97] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[96]); t = (sp_int_digit)(a[95]);
r[96] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[95]); t = (sp_int_digit)(a[94]);
r[95] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[94]); t = (sp_int_digit)(a[93]);
r[94] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[93]); t = (sp_int_digit)(a[92]);
r[93] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[92]); t = (sp_int_digit)(a[91]);
r[92] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[91]); t = (sp_int_digit)(a[90]);
r[91] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[90]); t = (sp_int_digit)(a[89]);
r[90] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[89]); t = (sp_int_digit)(a[88]);
r[89] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[88]); t = (sp_int_digit)(a[87]);
r[88] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[87]); t = (sp_int_digit)(a[86]);
r[87] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[86]); t = (sp_int_digit)(a[85]);
r[86] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[85]); t = (sp_int_digit)(a[84]);
r[85] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[84]); t = (sp_int_digit)(a[83]);
r[84] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[83]); t = (sp_int_digit)(a[82]);
r[83] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[82]); t = (sp_int_digit)(a[81]);
r[82] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[81]); t = (sp_int_digit)(a[80]);
r[81] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[80]); t = (sp_int_digit)(a[79]);
r[80] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[79]); t = (sp_int_digit)(a[78]);
r[79] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[78]); t = (sp_int_digit)(a[77]);
r[78] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[77]); t = (sp_int_digit)(a[76]);
r[77] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[76]); t = (sp_int_digit)(a[75]);
r[76] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[75]); t = (sp_int_digit)(a[74]);
r[75] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[74]); t = (sp_int_digit)(a[73]);
r[74] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[73]); t = (sp_int_digit)(a[72]);
r[73] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[72]); t = (sp_int_digit)(a[71]);
r[72] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[71]); t = (sp_int_digit)(a[70]);
r[71] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[70]); t = (sp_int_digit)(a[69]);
r[70] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[69]); t = (sp_int_digit)(a[68]);
r[69] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[68]); t = (sp_int_digit)(a[67]);
r[68] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[67]); t = (sp_int_digit)(a[66]);
r[67] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[66]); t = (sp_int_digit)(a[65]);
r[66] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[65]); t = (sp_int_digit)(a[64]);
r[65] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[64]); t = (sp_int_digit)(a[63]);
r[64] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[63]); t = (sp_int_digit)(a[62]);
r[63] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[62]); t = (sp_int_digit)(a[61]);
r[62] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[61]); t = (sp_int_digit)(a[60]);
r[61] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[60]); t = (sp_int_digit)(a[59]);
r[60] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[59]); t = (sp_int_digit)(a[58]);
r[59] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[58]); t = (sp_int_digit)(a[57]);
r[58] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[57]); t = (sp_int_digit)(a[56]);
r[57] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[56]); t = (sp_int_digit)(a[55]);
r[56] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[55]); t = (sp_int_digit)(a[54]);
r[55] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[54]); t = (sp_int_digit)(a[53]);
r[54] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[53]); t = (sp_int_digit)(a[52]);
r[53] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[52]); t = (sp_int_digit)(a[51]);
r[52] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[51]); t = (sp_int_digit)(a[50]);
r[51] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[50]); t = (sp_int_digit)(a[49]);
r[50] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[49]); t = (sp_int_digit)(a[48]);
r[49] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[48]); t = (sp_int_digit)(a[47]);
r[48] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[47]); t = (sp_int_digit)(a[46]);
r[47] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[46]); t = (sp_int_digit)(a[45]);
r[46] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[45]); t = (sp_int_digit)(a[44]);
r[45] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[44]); t = (sp_int_digit)(a[43]);
r[44] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[43]); t = (sp_int_digit)(a[42]);
r[43] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[42]); t = (sp_int_digit)(a[41]);
r[42] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[41]); t = (sp_int_digit)(a[40]);
r[41] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[40]); t = (sp_int_digit)(a[39]);
r[40] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[39]); t = (sp_int_digit)(a[38]);
r[39] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[38]); t = (sp_int_digit)(a[37]);
r[38] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[37]); t = (sp_int_digit)(a[36]);
r[37] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[36]); t = (sp_int_digit)(a[35]);
r[36] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[35]); t = (sp_int_digit)(a[34]);
r[35] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[34]); t = (sp_int_digit)(a[33]);
r[34] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[33]); t = (sp_int_digit)(a[32]);
r[33] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[32]); t = (sp_int_digit)(a[31]);
r[32] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[31]); t = (sp_int_digit)(a[30]);
r[31] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[30]); t = (sp_int_digit)(a[29]);
r[30] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[29]); t = (sp_int_digit)(a[28]);
r[29] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[28]); t = (sp_int_digit)(a[27]);
r[28] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[27]); t = (sp_int_digit)(a[26]);
r[27] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[26]); t = (sp_int_digit)(a[25]);
r[26] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[25]); t = (sp_int_digit)(a[24]);
r[25] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[24]); t = (sp_int_digit)(a[23]);
r[24] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[23]); t = (sp_int_digit)(a[22]);
r[23] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[22]); t = (sp_int_digit)(a[21]);
r[22] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[21]); t = (sp_int_digit)(a[20]);
r[21] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[20]); t = (sp_int_digit)(a[19]);
r[20] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[19]); t = (sp_int_digit)(a[18]);
r[19] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[18]); t = (sp_int_digit)(a[17]);
r[18] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[17]); t = (sp_int_digit)(a[16]);
r[17] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[16]); t = (sp_int_digit)(a[15]);
r[16] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[15]); t = (sp_int_digit)(a[14]);
r[15] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[14]); t = (sp_int_digit)(a[13]);
r[14] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[13]); t = (sp_int_digit)(a[12]);
r[13] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[12]); t = (sp_int_digit)(a[11]);
r[12] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[11]); t = (sp_int_digit)(a[10]);
r[11] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[10]); t = (sp_int_digit)(a[9]);
r[10] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[9]); t = (sp_int_digit)(a[8]);
r[9] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[8]); t = (sp_int_digit)(a[7]);
r[8] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[7]); t = (sp_int_digit)(a[6]);
r[7] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[6]); t = (sp_int_digit)(a[5]);
r[6] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[5]); t = (sp_int_digit)(a[4]);
r[5] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[4]); t = (sp_int_digit)(a[3]);
r[4] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[3]); t = (sp_int_digit)(a[2]);
r[3] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[2]); t = (sp_int_digit)(a[1]);
r[2] = ((s << n) | (t >> (23U - n))) & ;
s = (sp_int_digit)(a[1]); t = (sp_int_digit)(a[0]);
r[1] = ((s << n) | (t >> (23U - n))) & ;
#endif
r[0] = (a[0] << n) & 0x7fffff;
}
/* Modular exponentiate 2 to the e mod m. (r = 2^e mod m)
*
* r A single precision number that is the result of the operation.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_3072_mod_exp_2_134(sp_digit* r, const sp_digit* e, int bits, const sp_digit* m)
{
#ifndef WOLFSSL_SMALL_STACK
sp_digit nd[268];
sp_digit td[135];
#else
sp_digit* td;
#endif
sp_digit* norm;
sp_digit* tmp;
sp_digit mp = 1;
sp_digit n, o;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 403, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
norm = td;
tmp = td + 268;
#else
norm = nd;
tmp = td;
#endif
XMEMSET(td, 0, sizeof(td));
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_134(norm, m);
bits = ((bits + 3) / 4) * 4;
i = ((bits + 22) / 23) - 1;
c = bits % 23;
if (c == 0) {
c = 23;
}
if (i < 134) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 4) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 28) & 0xf;
n <<= 4;
c -= 4;
sp_3072_lshift_134(r, norm, y);
for (; i>=0 || c>=4; ) {
if (c < 4) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 28) & 0xf;
n <<= 4;
c -= 4;
sp_3072_mont_sqr_134(r, r, m, mp);
sp_3072_mont_sqr_134(r, r, m, mp);
sp_3072_mont_sqr_134(r, r, m, mp);
sp_3072_mont_sqr_134(r, r, m, mp);
sp_3072_lshift_134(r, r, y);
sp_3072_mul_d_134(tmp, norm, (r[134] << 10) + (r[133] >> 13));
r[134] = 0;
r[133] &= 0x1fffL;
(void)sp_3072_add_134(r, r, tmp);
sp_3072_norm_134(r);
o = sp_3072_cmp_134(r, m);
sp_3072_cond_sub_134(r, r, m, ((o < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
sp_3072_mont_reduce_134(r, m, mp);
n = sp_3072_cmp_134(r, m);
sp_3072_cond_sub_134(r, r, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
#endif /* HAVE_FFDHE_3072 */
/* Perform the modular exponentiation for Diffie-Hellman.
*
* base Base.
* exp Array of bytes that is the exponent.
* expLen Length of data, in bytes, in exponent.
* mod Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 384 bytes long.
* outLen Length, in bytes, of exponentiation result.
* returs 0 on success, MP_READ_E if there are too many bytes in an array
* and MEMORY_E if memory allocation fails.
*/
int sp_DhExp_3072(mp_int* base, const byte* exp, word32 expLen,
mp_int* mod, byte* out, word32* outLen)
{
#ifdef WOLFSSL_SP_SMALL
int err = MP_OKAY;
sp_digit* d = NULL;
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
word32 i;
if (mp_count_bits(base) > 3072) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expLen > 384) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 134 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
b = d;
e = b + 134 * 2;
m = e + 134;
r = b;
sp_3072_from_mp(b, 134, base);
sp_3072_from_bin(e, 134, exp, expLen);
sp_3072_from_mp(m, 134, mod);
#ifdef HAVE_FFDHE_3072
if (base->used == 1 && base->dp[0] == 2 &&
((m[133] << 3) | (m[132] >> 20)) == 0xffffL) {
err = sp_3072_mod_exp_2_134(r, e, expLen * 8, m);
}
else
#endif
err = sp_3072_mod_exp_134(r, b, e, expLen * 8, m, 0);
}
if (err == MP_OKAY) {
sp_3072_to_bin(r, out);
*outLen = 384;
for (i=0; i<384 && out[i] == 0; i++) {
}
*outLen -= i;
XMEMMOVE(out, out + i, *outLen);
}
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 134U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit bd[268], ed[134], md[134];
#else
sp_digit* d = NULL;
#endif
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
word32 i;
int err = MP_OKAY;
if (mp_count_bits(base) > 3072) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expLen > 384U) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 3072) {
err = MP_READ_E;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 134 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
b = d;
e = b + 134 * 2;
m = e + 134;
r = b;
}
#else
r = b = bd;
e = ed;
m = md;
#endif
if (err == MP_OKAY) {
sp_3072_from_mp(b, 134, base);
sp_3072_from_bin(e, 134, exp, expLen);
sp_3072_from_mp(m, 134, mod);
#ifdef HAVE_FFDHE_3072
if (base->used == 1 && base->dp[0] == 2U &&
((m[133] << 3) | (m[132] >> 20)) == 0xffffL) {
err = sp_3072_mod_exp_2_134(r, e, expLen * 8U, m);
}
else {
#endif
err = sp_3072_mod_exp_134(r, b, e, expLen * 8U, m, 0);
#ifdef HAVE_FFDHE_3072
}
#endif
}
if (err == MP_OKAY) {
sp_3072_to_bin(r, out);
*outLen = 384;
for (i=0; i<384U && out[i] == 0U; i++) {
}
*outLen -= i;
XMEMMOVE(out, out + i, *outLen);
}
XMEMSET(e, 0, sizeof(sp_digit) * 134U);
#ifdef WOLFSSL_SMALL_STACK
if (d != NULL)
XFREE(d, NULL, DYNAMIC_TYPE_DH);
#endif
return err;
#endif
}
#endif /* WOLFSSL_HAVE_SP_DH */
/* Perform the modular exponentiation for Diffie-Hellman.
*
* base Base. MP integer.
* exp Exponent. MP integer.
* mod Modulus. MP integer.
* res Result. MP integer.
* returs 0 on success, MP_READ_E if there are too many bytes in an array
* and MEMORY_E if memory allocation fails.
*/
int sp_ModExp_1536(mp_int* base, mp_int* exp, mp_int* mod, mp_int* res)
{
#ifdef WOLFSSL_SP_SMALL
int err = MP_OKAY;
sp_digit* d = NULL;
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 1536) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 1536) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 1536) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 67 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
b = d;
e = b + 67 * 2;
m = e + 67;
r = b;
sp_3072_from_mp(b, 67, base);
sp_3072_from_mp(e, 67, exp);
sp_3072_from_mp(m, 67, mod);
err = sp_3072_mod_exp_67(r, b, e, mp_count_bits(exp), m, 0);
}
if (err == MP_OKAY) {
XMEMSET(r + 67, 0, sizeof(*r) * 67U);
err = sp_3072_to_mp(r, res);
}
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 67U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit bd[134], ed[67], md[67];
#else
sp_digit* d = NULL;
#endif
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int err = MP_OKAY;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 1536) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 1536) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 1536) {
err = MP_READ_E;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 67 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
b = d;
e = b + 67 * 2;
m = e + 67;
r = b;
}
#else
r = b = bd;
e = ed;
m = md;
#endif
if (err == MP_OKAY) {
sp_3072_from_mp(b, 67, base);
sp_3072_from_mp(e, 67, exp);
sp_3072_from_mp(m, 67, mod);
err = sp_3072_mod_exp_67(r, b, e, expBits, m, 0);
}
if (err == MP_OKAY) {
XMEMSET(r + 67, 0, sizeof(*r) * 67U);
err = sp_3072_to_mp(r, res);
}
XMEMSET(e, 0, sizeof(sp_digit) * 67U);
#ifdef WOLFSSL_SMALL_STACK
if (d != NULL)
XFREE(d, NULL, DYNAMIC_TYPE_DH);
#endif
return err;
#endif
}
#endif /* WOLFSSL_HAVE_SP_DH || (WOLFSSL_HAVE_SP_RSA && !WOLFSSL_RSA_PUBLIC_ONLY) */
#endif /* !WOLFSSL_SP_NO_3072 */
#endif /* WOLFSSL_HAVE_SP_RSA || WOLFSSL_HAVE_SP_DH */
#ifdef WOLFSSL_HAVE_SP_ECC
#ifndef WOLFSSL_SP_NO_256
/* Point structure to use. */
typedef struct sp_point {
sp_digit x[2 * 10];
sp_digit y[2 * 10];
sp_digit z[2 * 10];
int infinity;
} sp_point;
/* The modulus (prime) of the curve P256. */
static const sp_digit p256_mod[10] = {
0x3ffffff,0x3ffffff,0x3ffffff,0x003ffff,0x0000000,0x0000000,0x0000000,
0x0000400,0x3ff0000,0x03fffff
};
/* The Montogmery normalizer for modulus of the curve P256. */
static const sp_digit p256_norm_mod[10] = {
0x0000001,0x0000000,0x0000000,0x3fc0000,0x3ffffff,0x3ffffff,0x3ffffff,
0x3fffbff,0x000ffff,0x0000000
};
/* The Montogmery multiplier for modulus of the curve P256. */
static const sp_digit p256_mp_mod = 0x000001;
#if defined(WOLFSSL_VALIDATE_ECC_KEYGEN) || defined(HAVE_ECC_SIGN) || \
defined(HAVE_ECC_VERIFY)
/* The order of the curve P256. */
static const sp_digit p256_order[10] = {
0x0632551,0x272b0bf,0x1e84f3b,0x2b69c5e,0x3bce6fa,0x3ffffff,0x3ffffff,
0x00003ff,0x3ff0000,0x03fffff
};
#endif
/* The order of the curve P256 minus 2. */
static const sp_digit p256_order2[10] = {
0x063254f,0x272b0bf,0x1e84f3b,0x2b69c5e,0x3bce6fa,0x3ffffff,0x3ffffff,
0x00003ff,0x3ff0000,0x03fffff
};
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
/* The Montogmery normalizer for order of the curve P256. */
static const sp_digit p256_norm_order[10] = {
0x39cdaaf,0x18d4f40,0x217b0c4,0x14963a1,0x0431905,0x0000000,0x0000000,
0x3fffc00,0x000ffff,0x0000000
};
#endif
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
/* The Montogmery multiplier for order of the curve P256. */
static const sp_digit p256_mp_order = 0x200bc4f;
#endif
/* The base point of curve P256. */
static const sp_point p256_base = {
/* X ordinate */
{
0x098c296,0x04e5176,0x33a0f4a,0x204b7ac,0x277037d,0x0e9103c,0x3ce6e56,
0x1091fe2,0x1f2e12c,0x01ac5f4, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
},
/* Y ordinate */
{
0x3bf51f5,0x1901a0d,0x1ececbb,0x15dacc5,0x22bce33,0x303e785,0x27eb4a7,
0x1fe6e3b,0x2e2fe1a,0x013f8d0, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
},
/* Z ordinate */
{
0x0000001,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,
0x0000000,0x0000000,0x0000000, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
},
/* infinity */
0
};
#if defined(HAVE_ECC_CHECK_KEY) || defined(HAVE_COMP_KEY)
static const sp_digit p256_b[10] = {
0x3d2604b,0x38f0f89,0x30f63bc,0x2c3314e,0x0651d06,0x1a621af,0x2bbd557,
0x24f9ecf,0x1d8aa3a,0x016b18d
};
#endif
static int sp_ecc_point_new_ex(void* heap, sp_point* sp, sp_point** p)
{
int ret = MP_OKAY;
(void)heap;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
(void)sp;
*p = (sp_point*)XMALLOC(sizeof(sp_point), heap, DYNAMIC_TYPE_ECC);
#else
*p = sp;
#endif
if (p == NULL) {
ret = MEMORY_E;
}
return ret;
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
/* Allocate memory for point and return error. */
#define sp_ecc_point_new(heap, sp, p) sp_ecc_point_new_ex((heap), NULL, &(p))
#else
/* Set pointer to data and return no error. */
#define sp_ecc_point_new(heap, sp, p) sp_ecc_point_new_ex((heap), &(sp), &(p))
#endif
static void sp_ecc_point_free(sp_point* p, int clear, void* heap)
{
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
/* If valid pointer then clear point data if requested and free data. */
if (p != NULL) {
if (clear != 0) {
XMEMSET(p, 0, sizeof(*p));
}
XFREE(p, heap, DYNAMIC_TYPE_ECC);
}
#else
/* Clear point data if requested. */
if (clear != 0) {
XMEMSET(p, 0, sizeof(*p));
}
#endif
(void)heap;
}
/* Multiply a number by Montogmery normalizer mod modulus (prime).
*
* r The resulting Montgomery form number.
* a The number to convert.
* m The modulus (prime).
* returns MEMORY_E when memory allocation fails and MP_OKAY otherwise.
*/
static int sp_256_mod_mul_norm_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
int64_t* td;
#else
int64_t td[8];
int64_t a32d[8];
#endif
int64_t* t;
int64_t* a32;
int64_t o;
int err = MP_OKAY;
(void)m;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
td = (int64_t*)XMALLOC(sizeof(int64_t) * 2 * 8, NULL, DYNAMIC_TYPE_ECC);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
t = td;
a32 = td + 8;
#else
t = td;
a32 = a32d;
#endif
a32[0] = a[0];
a32[0] |= a[1] << 26U;
a32[0] &= 0xffffffffL;
a32[1] = (sp_digit)(a[1] >> 6);
a32[1] |= a[2] << 20U;
a32[1] &= 0xffffffffL;
a32[2] = (sp_digit)(a[2] >> 12);
a32[2] |= a[3] << 14U;
a32[2] &= 0xffffffffL;
a32[3] = (sp_digit)(a[3] >> 18);
a32[3] |= a[4] << 8U;
a32[3] &= 0xffffffffL;
a32[4] = (sp_digit)(a[4] >> 24);
a32[4] |= a[5] << 2U;
a32[4] |= a[6] << 28U;
a32[4] &= 0xffffffffL;
a32[5] = (sp_digit)(a[6] >> 4);
a32[5] |= a[7] << 22U;
a32[5] &= 0xffffffffL;
a32[6] = (sp_digit)(a[7] >> 10);
a32[6] |= a[8] << 16U;
a32[6] &= 0xffffffffL;
a32[7] = (sp_digit)(a[8] >> 16);
a32[7] |= a[9] << 10U;
a32[7] &= 0xffffffffL;
/* 1 1 0 -1 -1 -1 -1 0 */
t[0] = 0 + a32[0] + a32[1] - a32[3] - a32[4] - a32[5] - a32[6];
/* 0 1 1 0 -1 -1 -1 -1 */
t[1] = 0 + a32[1] + a32[2] - a32[4] - a32[5] - a32[6] - a32[7];
/* 0 0 1 1 0 -1 -1 -1 */
t[2] = 0 + a32[2] + a32[3] - a32[5] - a32[6] - a32[7];
/* -1 -1 0 2 2 1 0 -1 */
t[3] = 0 - a32[0] - a32[1] + 2 * a32[3] + 2 * a32[4] + a32[5] - a32[7];
/* 0 -1 -1 0 2 2 1 0 */
t[4] = 0 - a32[1] - a32[2] + 2 * a32[4] + 2 * a32[5] + a32[6];
/* 0 0 -1 -1 0 2 2 1 */
t[5] = 0 - a32[2] - a32[3] + 2 * a32[5] + 2 * a32[6] + a32[7];
/* -1 -1 0 0 0 1 3 2 */
t[6] = 0 - a32[0] - a32[1] + a32[5] + 3 * a32[6] + 2 * a32[7];
/* 1 0 -1 -1 -1 -1 0 3 */
t[7] = 0 + a32[0] - a32[2] - a32[3] - a32[4] - a32[5] + 3 * a32[7];
t[1] += t[0] >> 32U; t[0] &= 0xffffffffL;
t[2] += t[1] >> 32U; t[1] &= 0xffffffffL;
t[3] += t[2] >> 32U; t[2] &= 0xffffffffL;
t[4] += t[3] >> 32U; t[3] &= 0xffffffffL;
t[5] += t[4] >> 32U; t[4] &= 0xffffffffL;
t[6] += t[5] >> 32U; t[5] &= 0xffffffffL;
t[7] += t[6] >> 32U; t[6] &= 0xffffffffL;
o = t[7] >> 32U; t[7] &= 0xffffffffL;
t[0] += o;
t[3] -= o;
t[6] -= o;
t[7] += o;
t[1] += t[0] >> 32U; t[0] &= 0xffffffffL;
t[2] += t[1] >> 32U; t[1] &= 0xffffffffL;
t[3] += t[2] >> 32U; t[2] &= 0xffffffffL;
t[4] += t[3] >> 32U; t[3] &= 0xffffffffL;
t[5] += t[4] >> 32U; t[4] &= 0xffffffffL;
t[6] += t[5] >> 32U; t[5] &= 0xffffffffL;
t[7] += t[6] >> 32U; t[6] &= 0xffffffffL;
r[0] = (sp_digit)(t[0]) & 0x3ffffffL;
r[1] = (sp_digit)(t[0] >> 26U);
r[1] |= t[1] << 6U;
r[1] &= 0x3ffffffL;
r[2] = (sp_digit)(t[1] >> 20U);
r[2] |= t[2] << 12U;
r[2] &= 0x3ffffffL;
r[3] = (sp_digit)(t[2] >> 14U);
r[3] |= t[3] << 18U;
r[3] &= 0x3ffffffL;
r[4] = (sp_digit)(t[3] >> 8U);
r[4] |= t[4] << 24U;
r[4] &= 0x3ffffffL;
r[5] = (sp_digit)(t[4] >> 2U) & 0x3ffffffL;
r[6] = (sp_digit)(t[4] >> 28U);
r[6] |= t[5] << 4U;
r[6] &= 0x3ffffffL;
r[7] = (sp_digit)(t[5] >> 22U);
r[7] |= t[6] << 10U;
r[7] &= 0x3ffffffL;
r[8] = (sp_digit)(t[6] >> 16U);
r[8] |= t[7] << 16U;
r[8] &= 0x3ffffffL;
r[9] = (sp_digit)(t[7] >> 10U);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_ECC);
}
#endif
return err;
}
/* Convert an mp_int to an array of sp_digit.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a A multi-precision integer.
*/
static void sp_256_from_mp(sp_digit* r, int size, const mp_int* a)
{
#if DIGIT_BIT == 26
int j;
XMEMCPY(r, a->dp, sizeof(sp_digit) * a->used);
for (j = a->used; j < size; j++) {
r[j] = 0;
}
#elif DIGIT_BIT > 26
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i] << s);
r[j] &= 0x3ffffff;
s = 26U - s;
if (j + 1 >= size) {
break;
}
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
while ((s + 26U) <= (word32)DIGIT_BIT) {
s += 26U;
r[j] &= 0x3ffffff;
if (j + 1 >= size) {
break;
}
if (s < (word32)DIGIT_BIT) {
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
}
else {
r[++j] = 0L;
}
}
s = (word32)DIGIT_BIT - s;
}
for (j++; j < size; j++) {
r[j] = 0;
}
#else
int i, j = 0, s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i]) << s;
if (s + DIGIT_BIT >= 26) {
r[j] &= 0x3ffffff;
if (j + 1 >= size) {
break;
}
s = 26 - s;
if (s == DIGIT_BIT) {
r[++j] = 0;
s = 0;
}
else {
r[++j] = a->dp[i] >> s;
s = DIGIT_BIT - s;
}
}
else {
s += DIGIT_BIT;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
#endif
}
/* Convert a point of type ecc_point to type sp_point.
*
* p Point of type sp_point (result).
* pm Point of type ecc_point.
*/
static void sp_256_point_from_ecc_point_10(sp_point* p, const ecc_point* pm)
{
XMEMSET(p->x, 0, sizeof(p->x));
XMEMSET(p->y, 0, sizeof(p->y));
XMEMSET(p->z, 0, sizeof(p->z));
sp_256_from_mp(p->x, 10, pm->x);
sp_256_from_mp(p->y, 10, pm->y);
sp_256_from_mp(p->z, 10, pm->z);
p->infinity = 0;
}
/* Convert an array of sp_digit to an mp_int.
*
* a A single precision integer.
* r A multi-precision integer.
*/
static int sp_256_to_mp(const sp_digit* a, mp_int* r)
{
int err;
err = mp_grow(r, (256 + DIGIT_BIT - 1) / DIGIT_BIT);
if (err == MP_OKAY) { /*lint !e774 case where err is always MP_OKAY*/
#if DIGIT_BIT == 26
XMEMCPY(r->dp, a, sizeof(sp_digit) * 10);
r->used = 10;
mp_clamp(r);
#elif DIGIT_BIT < 26
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 10; i++) {
r->dp[j] |= a[i] << s;
r->dp[j] &= (1L << DIGIT_BIT) - 1;
s = DIGIT_BIT - s;
r->dp[++j] = a[i] >> s;
while (s + DIGIT_BIT <= 26) {
s += DIGIT_BIT;
r->dp[j++] &= (1L << DIGIT_BIT) - 1;
if (s == SP_WORD_SIZE) {
r->dp[j] = 0;
}
else {
r->dp[j] = a[i] >> s;
}
}
s = 26 - s;
}
r->used = (256 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#else
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 10; i++) {
r->dp[j] |= ((mp_digit)a[i]) << s;
if (s + 26 >= DIGIT_BIT) {
#if DIGIT_BIT != 32 && DIGIT_BIT != 64
r->dp[j] &= (1L << DIGIT_BIT) - 1;
#endif
s = DIGIT_BIT - s;
r->dp[++j] = a[i] >> s;
s = 26 - s;
}
else {
s += 26;
}
}
r->used = (256 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#endif
}
return err;
}
/* Convert a point of type sp_point to type ecc_point.
*
* p Point of type sp_point.
* pm Point of type ecc_point (result).
* returns MEMORY_E when allocation of memory in ecc_point fails otherwise
* MP_OKAY.
*/
static int sp_256_point_to_ecc_point_10(const sp_point* p, ecc_point* pm)
{
int err;
err = sp_256_to_mp(p->x, pm->x);
if (err == MP_OKAY) {
err = sp_256_to_mp(p->y, pm->y);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->z, pm->z);
}
return err;
}
/* Compare a with b in constant time.
*
* a A single precision integer.
* b A single precision integer.
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_256_cmp_10(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=9; i>=0; i--) {
r |= (a[i] - b[i]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#else
r |= (a[ 9] - b[ 9]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 8] - b[ 8]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 7] - b[ 7]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 6] - b[ 6]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 5] - b[ 5]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 4] - b[ 4]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 3] - b[ 3]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 2] - b[ 2]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 1] - b[ 1]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 0] - b[ 0]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
#endif /* WOLFSSL_SP_SMALL */
return r;
}
/* Normalize the values in each word to 26.
*
* a Array of sp_digit to normalize.
*/
static void sp_256_norm_10(sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 9; i++) {
a[i+1] += a[i] >> 26;
a[i] &= 0x3ffffff;
}
#else
a[1] += a[0] >> 26; a[0] &= 0x3ffffff;
a[2] += a[1] >> 26; a[1] &= 0x3ffffff;
a[3] += a[2] >> 26; a[2] &= 0x3ffffff;
a[4] += a[3] >> 26; a[3] &= 0x3ffffff;
a[5] += a[4] >> 26; a[4] &= 0x3ffffff;
a[6] += a[5] >> 26; a[5] &= 0x3ffffff;
a[7] += a[6] >> 26; a[6] &= 0x3ffffff;
a[8] += a[7] >> 26; a[7] &= 0x3ffffff;
a[9] += a[8] >> 26; a[8] &= 0x3ffffff;
#endif
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*
* r A single precision number representing condition subtract result.
* a A single precision number to subtract from.
* b A single precision number to subtract.
* m Mask value to apply.
*/
static void sp_256_cond_sub_10(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 10; i++) {
r[i] = a[i] - (b[i] & m);
}
#else
r[ 0] = a[ 0] - (b[ 0] & m);
r[ 1] = a[ 1] - (b[ 1] & m);
r[ 2] = a[ 2] - (b[ 2] & m);
r[ 3] = a[ 3] - (b[ 3] & m);
r[ 4] = a[ 4] - (b[ 4] & m);
r[ 5] = a[ 5] - (b[ 5] & m);
r[ 6] = a[ 6] - (b[ 6] & m);
r[ 7] = a[ 7] - (b[ 7] & m);
r[ 8] = a[ 8] - (b[ 8] & m);
r[ 9] = a[ 9] - (b[ 9] & m);
#endif /* WOLFSSL_SP_SMALL */
}
#define sp_256_mont_reduce_order_10 sp_256_mont_reduce_10
/* Mul a by scalar b and add into r. (r += a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_256_mul_add_10(sp_digit* r, const sp_digit* a,
const sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 10; i++) {
t += (tb * a[i]) + r[i];
r[i] = t & 0x3ffffff;
t >>= 26;
}
r[10] += t;
#else
int64_t tb = b;
int64_t t[10];
t[ 0] = tb * a[ 0];
t[ 1] = tb * a[ 1];
t[ 2] = tb * a[ 2];
t[ 3] = tb * a[ 3];
t[ 4] = tb * a[ 4];
t[ 5] = tb * a[ 5];
t[ 6] = tb * a[ 6];
t[ 7] = tb * a[ 7];
t[ 8] = tb * a[ 8];
t[ 9] = tb * a[ 9];
r[ 0] += (t[ 0] & 0x3ffffff);
r[ 1] += (t[ 0] >> 26) + (t[ 1] & 0x3ffffff);
r[ 2] += (t[ 1] >> 26) + (t[ 2] & 0x3ffffff);
r[ 3] += (t[ 2] >> 26) + (t[ 3] & 0x3ffffff);
r[ 4] += (t[ 3] >> 26) + (t[ 4] & 0x3ffffff);
r[ 5] += (t[ 4] >> 26) + (t[ 5] & 0x3ffffff);
r[ 6] += (t[ 5] >> 26) + (t[ 6] & 0x3ffffff);
r[ 7] += (t[ 6] >> 26) + (t[ 7] & 0x3ffffff);
r[ 8] += (t[ 7] >> 26) + (t[ 8] & 0x3ffffff);
r[ 9] += (t[ 8] >> 26) + (t[ 9] & 0x3ffffff);
r[10] += t[ 9] >> 26;
#endif /* WOLFSSL_SP_SMALL */
}
/* Shift the result in the high 256 bits down to the bottom.
*
* r A single precision number.
* a A single precision number.
*/
static void sp_256_mont_shift_10(sp_digit* r, const sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
sp_digit n, s;
s = a[10];
n = a[9] >> 22;
for (i = 0; i < 9; i++) {
n += (s & 0x3ffffff) << 4;
r[i] = n & 0x3ffffff;
n >>= 26;
s = a[11 + i] + (s >> 26);
}
n += s << 4;
r[9] = n;
#else
sp_digit n, s;
s = a[10]; n = a[9] >> 22;
n += (s & 0x3ffffff) << 4; r[ 0] = n & 0x3ffffff;
n >>= 26; s = a[11] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 1] = n & 0x3ffffff;
n >>= 26; s = a[12] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 2] = n & 0x3ffffff;
n >>= 26; s = a[13] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 3] = n & 0x3ffffff;
n >>= 26; s = a[14] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 4] = n & 0x3ffffff;
n >>= 26; s = a[15] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 5] = n & 0x3ffffff;
n >>= 26; s = a[16] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 6] = n & 0x3ffffff;
n >>= 26; s = a[17] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 7] = n & 0x3ffffff;
n >>= 26; s = a[18] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 8] = n & 0x3ffffff;
n >>= 26; s = a[19] + (s >> 26);
n += s << 4; r[ 9] = n;
#endif /* WOLFSSL_SP_SMALL */
XMEMSET(&r[10], 0, sizeof(*r) * 10U);
}
/* Reduce the number back to 256 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_256_mont_reduce_10(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
if (mp != 1) {
for (i=0; i<9; i++) {
mu = (a[i] * mp) & 0x3ffffff;
sp_256_mul_add_10(a+i, m, mu);
a[i+1] += a[i] >> 26;
}
mu = (a[i] * mp) & 0x3fffffL;
sp_256_mul_add_10(a+i, m, mu);
a[i+1] += a[i] >> 26;
a[i] &= 0x3ffffff;
}
else {
for (i=0; i<9; i++) {
mu = a[i] & 0x3ffffff;
sp_256_mul_add_10(a+i, p256_mod, mu);
a[i+1] += a[i] >> 26;
}
mu = a[i] & 0x3fffffL;
sp_256_mul_add_10(a+i, p256_mod, mu);
a[i+1] += a[i] >> 26;
a[i] &= 0x3ffffff;
}
sp_256_mont_shift_10(a, a);
sp_256_cond_sub_10(a, a, m, 0 - (((a[9] >> 22) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_10(a);
}
#ifdef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_256_mul_10(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[9]) * b[9];
r[19] = (sp_digit)(c >> 26);
c = (c & 0x3ffffff) << 26;
for (k = 17; k >= 0; k--) {
for (i = 9; i >= 0; i--) {
j = k - i;
if (j >= 10) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * b[j];
}
r[k + 2] += c >> 52;
r[k + 1] = (c >> 26) & 0x3ffffff;
c = (c & 0x3ffffff) << 26;
}
r[0] = (sp_digit)(c >> 26);
}
#else
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_256_mul_10(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int64_t t0 = ((int64_t)a[ 0]) * b[ 0];
int64_t t1 = ((int64_t)a[ 0]) * b[ 1]
+ ((int64_t)a[ 1]) * b[ 0];
int64_t t2 = ((int64_t)a[ 0]) * b[ 2]
+ ((int64_t)a[ 1]) * b[ 1]
+ ((int64_t)a[ 2]) * b[ 0];
int64_t t3 = ((int64_t)a[ 0]) * b[ 3]
+ ((int64_t)a[ 1]) * b[ 2]
+ ((int64_t)a[ 2]) * b[ 1]
+ ((int64_t)a[ 3]) * b[ 0];
int64_t t4 = ((int64_t)a[ 0]) * b[ 4]
+ ((int64_t)a[ 1]) * b[ 3]
+ ((int64_t)a[ 2]) * b[ 2]
+ ((int64_t)a[ 3]) * b[ 1]
+ ((int64_t)a[ 4]) * b[ 0];
int64_t t5 = ((int64_t)a[ 0]) * b[ 5]
+ ((int64_t)a[ 1]) * b[ 4]
+ ((int64_t)a[ 2]) * b[ 3]
+ ((int64_t)a[ 3]) * b[ 2]
+ ((int64_t)a[ 4]) * b[ 1]
+ ((int64_t)a[ 5]) * b[ 0];
int64_t t6 = ((int64_t)a[ 0]) * b[ 6]
+ ((int64_t)a[ 1]) * b[ 5]
+ ((int64_t)a[ 2]) * b[ 4]
+ ((int64_t)a[ 3]) * b[ 3]
+ ((int64_t)a[ 4]) * b[ 2]
+ ((int64_t)a[ 5]) * b[ 1]
+ ((int64_t)a[ 6]) * b[ 0];
int64_t t7 = ((int64_t)a[ 0]) * b[ 7]
+ ((int64_t)a[ 1]) * b[ 6]
+ ((int64_t)a[ 2]) * b[ 5]
+ ((int64_t)a[ 3]) * b[ 4]
+ ((int64_t)a[ 4]) * b[ 3]
+ ((int64_t)a[ 5]) * b[ 2]
+ ((int64_t)a[ 6]) * b[ 1]
+ ((int64_t)a[ 7]) * b[ 0];
int64_t t8 = ((int64_t)a[ 0]) * b[ 8]
+ ((int64_t)a[ 1]) * b[ 7]
+ ((int64_t)a[ 2]) * b[ 6]
+ ((int64_t)a[ 3]) * b[ 5]
+ ((int64_t)a[ 4]) * b[ 4]
+ ((int64_t)a[ 5]) * b[ 3]
+ ((int64_t)a[ 6]) * b[ 2]
+ ((int64_t)a[ 7]) * b[ 1]
+ ((int64_t)a[ 8]) * b[ 0];
int64_t t9 = ((int64_t)a[ 0]) * b[ 9]
+ ((int64_t)a[ 1]) * b[ 8]
+ ((int64_t)a[ 2]) * b[ 7]
+ ((int64_t)a[ 3]) * b[ 6]
+ ((int64_t)a[ 4]) * b[ 5]
+ ((int64_t)a[ 5]) * b[ 4]
+ ((int64_t)a[ 6]) * b[ 3]
+ ((int64_t)a[ 7]) * b[ 2]
+ ((int64_t)a[ 8]) * b[ 1]
+ ((int64_t)a[ 9]) * b[ 0];
int64_t t10 = ((int64_t)a[ 1]) * b[ 9]
+ ((int64_t)a[ 2]) * b[ 8]
+ ((int64_t)a[ 3]) * b[ 7]
+ ((int64_t)a[ 4]) * b[ 6]
+ ((int64_t)a[ 5]) * b[ 5]
+ ((int64_t)a[ 6]) * b[ 4]
+ ((int64_t)a[ 7]) * b[ 3]
+ ((int64_t)a[ 8]) * b[ 2]
+ ((int64_t)a[ 9]) * b[ 1];
int64_t t11 = ((int64_t)a[ 2]) * b[ 9]
+ ((int64_t)a[ 3]) * b[ 8]
+ ((int64_t)a[ 4]) * b[ 7]
+ ((int64_t)a[ 5]) * b[ 6]
+ ((int64_t)a[ 6]) * b[ 5]
+ ((int64_t)a[ 7]) * b[ 4]
+ ((int64_t)a[ 8]) * b[ 3]
+ ((int64_t)a[ 9]) * b[ 2];
int64_t t12 = ((int64_t)a[ 3]) * b[ 9]
+ ((int64_t)a[ 4]) * b[ 8]
+ ((int64_t)a[ 5]) * b[ 7]
+ ((int64_t)a[ 6]) * b[ 6]
+ ((int64_t)a[ 7]) * b[ 5]
+ ((int64_t)a[ 8]) * b[ 4]
+ ((int64_t)a[ 9]) * b[ 3];
int64_t t13 = ((int64_t)a[ 4]) * b[ 9]
+ ((int64_t)a[ 5]) * b[ 8]
+ ((int64_t)a[ 6]) * b[ 7]
+ ((int64_t)a[ 7]) * b[ 6]
+ ((int64_t)a[ 8]) * b[ 5]
+ ((int64_t)a[ 9]) * b[ 4];
int64_t t14 = ((int64_t)a[ 5]) * b[ 9]
+ ((int64_t)a[ 6]) * b[ 8]
+ ((int64_t)a[ 7]) * b[ 7]
+ ((int64_t)a[ 8]) * b[ 6]
+ ((int64_t)a[ 9]) * b[ 5];
int64_t t15 = ((int64_t)a[ 6]) * b[ 9]
+ ((int64_t)a[ 7]) * b[ 8]
+ ((int64_t)a[ 8]) * b[ 7]
+ ((int64_t)a[ 9]) * b[ 6];
int64_t t16 = ((int64_t)a[ 7]) * b[ 9]
+ ((int64_t)a[ 8]) * b[ 8]
+ ((int64_t)a[ 9]) * b[ 7];
int64_t t17 = ((int64_t)a[ 8]) * b[ 9]
+ ((int64_t)a[ 9]) * b[ 8];
int64_t t18 = ((int64_t)a[ 9]) * b[ 9];
t1 += t0 >> 26; r[ 0] = t0 & 0x3ffffff;
t2 += t1 >> 26; r[ 1] = t1 & 0x3ffffff;
t3 += t2 >> 26; r[ 2] = t2 & 0x3ffffff;
t4 += t3 >> 26; r[ 3] = t3 & 0x3ffffff;
t5 += t4 >> 26; r[ 4] = t4 & 0x3ffffff;
t6 += t5 >> 26; r[ 5] = t5 & 0x3ffffff;
t7 += t6 >> 26; r[ 6] = t6 & 0x3ffffff;
t8 += t7 >> 26; r[ 7] = t7 & 0x3ffffff;
t9 += t8 >> 26; r[ 8] = t8 & 0x3ffffff;
t10 += t9 >> 26; r[ 9] = t9 & 0x3ffffff;
t11 += t10 >> 26; r[10] = t10 & 0x3ffffff;
t12 += t11 >> 26; r[11] = t11 & 0x3ffffff;
t13 += t12 >> 26; r[12] = t12 & 0x3ffffff;
t14 += t13 >> 26; r[13] = t13 & 0x3ffffff;
t15 += t14 >> 26; r[14] = t14 & 0x3ffffff;
t16 += t15 >> 26; r[15] = t15 & 0x3ffffff;
t17 += t16 >> 26; r[16] = t16 & 0x3ffffff;
t18 += t17 >> 26; r[17] = t17 & 0x3ffffff;
r[19] = (sp_digit)(t18 >> 26);
r[18] = t18 & 0x3ffffff;
}
#endif /* WOLFSSL_SP_SMALL */
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_256_mont_mul_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m, sp_digit mp)
{
sp_256_mul_10(r, a, b);
sp_256_mont_reduce_10(r, m, mp);
}
#ifdef WOLFSSL_SP_SMALL
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_256_sqr_10(sp_digit* r, const sp_digit* a)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[9]) * a[9];
r[19] = (sp_digit)(c >> 26);
c = (c & 0x3ffffff) << 26;
for (k = 17; k >= 0; k--) {
for (i = 9; i >= 0; i--) {
j = k - i;
if (j >= 10 || i <= j) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * a[j] * 2;
}
if (i == j) {
c += ((int64_t)a[i]) * a[i];
}
r[k + 2] += c >> 52;
r[k + 1] = (c >> 26) & 0x3ffffff;
c = (c & 0x3ffffff) << 26;
}
r[0] = (sp_digit)(c >> 26);
}
#else
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_256_sqr_10(sp_digit* r, const sp_digit* a)
{
int64_t t0 = ((int64_t)a[ 0]) * a[ 0];
int64_t t1 = (((int64_t)a[ 0]) * a[ 1]) * 2;
int64_t t2 = (((int64_t)a[ 0]) * a[ 2]) * 2
+ ((int64_t)a[ 1]) * a[ 1];
int64_t t3 = (((int64_t)a[ 0]) * a[ 3]
+ ((int64_t)a[ 1]) * a[ 2]) * 2;
int64_t t4 = (((int64_t)a[ 0]) * a[ 4]
+ ((int64_t)a[ 1]) * a[ 3]) * 2
+ ((int64_t)a[ 2]) * a[ 2];
int64_t t5 = (((int64_t)a[ 0]) * a[ 5]
+ ((int64_t)a[ 1]) * a[ 4]
+ ((int64_t)a[ 2]) * a[ 3]) * 2;
int64_t t6 = (((int64_t)a[ 0]) * a[ 6]
+ ((int64_t)a[ 1]) * a[ 5]
+ ((int64_t)a[ 2]) * a[ 4]) * 2
+ ((int64_t)a[ 3]) * a[ 3];
int64_t t7 = (((int64_t)a[ 0]) * a[ 7]
+ ((int64_t)a[ 1]) * a[ 6]
+ ((int64_t)a[ 2]) * a[ 5]
+ ((int64_t)a[ 3]) * a[ 4]) * 2;
int64_t t8 = (((int64_t)a[ 0]) * a[ 8]
+ ((int64_t)a[ 1]) * a[ 7]
+ ((int64_t)a[ 2]) * a[ 6]
+ ((int64_t)a[ 3]) * a[ 5]) * 2
+ ((int64_t)a[ 4]) * a[ 4];
int64_t t9 = (((int64_t)a[ 0]) * a[ 9]
+ ((int64_t)a[ 1]) * a[ 8]
+ ((int64_t)a[ 2]) * a[ 7]
+ ((int64_t)a[ 3]) * a[ 6]
+ ((int64_t)a[ 4]) * a[ 5]) * 2;
int64_t t10 = (((int64_t)a[ 1]) * a[ 9]
+ ((int64_t)a[ 2]) * a[ 8]
+ ((int64_t)a[ 3]) * a[ 7]
+ ((int64_t)a[ 4]) * a[ 6]) * 2
+ ((int64_t)a[ 5]) * a[ 5];
int64_t t11 = (((int64_t)a[ 2]) * a[ 9]
+ ((int64_t)a[ 3]) * a[ 8]
+ ((int64_t)a[ 4]) * a[ 7]
+ ((int64_t)a[ 5]) * a[ 6]) * 2;
int64_t t12 = (((int64_t)a[ 3]) * a[ 9]
+ ((int64_t)a[ 4]) * a[ 8]
+ ((int64_t)a[ 5]) * a[ 7]) * 2
+ ((int64_t)a[ 6]) * a[ 6];
int64_t t13 = (((int64_t)a[ 4]) * a[ 9]
+ ((int64_t)a[ 5]) * a[ 8]
+ ((int64_t)a[ 6]) * a[ 7]) * 2;
int64_t t14 = (((int64_t)a[ 5]) * a[ 9]
+ ((int64_t)a[ 6]) * a[ 8]) * 2
+ ((int64_t)a[ 7]) * a[ 7];
int64_t t15 = (((int64_t)a[ 6]) * a[ 9]
+ ((int64_t)a[ 7]) * a[ 8]) * 2;
int64_t t16 = (((int64_t)a[ 7]) * a[ 9]) * 2
+ ((int64_t)a[ 8]) * a[ 8];
int64_t t17 = (((int64_t)a[ 8]) * a[ 9]) * 2;
int64_t t18 = ((int64_t)a[ 9]) * a[ 9];
t1 += t0 >> 26; r[ 0] = t0 & 0x3ffffff;
t2 += t1 >> 26; r[ 1] = t1 & 0x3ffffff;
t3 += t2 >> 26; r[ 2] = t2 & 0x3ffffff;
t4 += t3 >> 26; r[ 3] = t3 & 0x3ffffff;
t5 += t4 >> 26; r[ 4] = t4 & 0x3ffffff;
t6 += t5 >> 26; r[ 5] = t5 & 0x3ffffff;
t7 += t6 >> 26; r[ 6] = t6 & 0x3ffffff;
t8 += t7 >> 26; r[ 7] = t7 & 0x3ffffff;
t9 += t8 >> 26; r[ 8] = t8 & 0x3ffffff;
t10 += t9 >> 26; r[ 9] = t9 & 0x3ffffff;
t11 += t10 >> 26; r[10] = t10 & 0x3ffffff;
t12 += t11 >> 26; r[11] = t11 & 0x3ffffff;
t13 += t12 >> 26; r[12] = t12 & 0x3ffffff;
t14 += t13 >> 26; r[13] = t13 & 0x3ffffff;
t15 += t14 >> 26; r[14] = t14 & 0x3ffffff;
t16 += t15 >> 26; r[15] = t15 & 0x3ffffff;
t17 += t16 >> 26; r[16] = t16 & 0x3ffffff;
t18 += t17 >> 26; r[17] = t17 & 0x3ffffff;
r[19] = (sp_digit)(t18 >> 26);
r[18] = t18 & 0x3ffffff;
}
#endif /* WOLFSSL_SP_SMALL */
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_256_mont_sqr_10(sp_digit* r, const sp_digit* a, const sp_digit* m,
sp_digit mp)
{
sp_256_sqr_10(r, a);
sp_256_mont_reduce_10(r, m, mp);
}
#if !defined(WOLFSSL_SP_SMALL) || defined(HAVE_COMP_KEY)
/* Square the Montgomery form number a number of times. (r = a ^ n mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* n Number of times to square.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_256_mont_sqr_n_10(sp_digit* r, const sp_digit* a, int n,
const sp_digit* m, sp_digit mp)
{
sp_256_mont_sqr_10(r, a, m, mp);
for (; n > 1; n--) {
sp_256_mont_sqr_10(r, r, m, mp);
}
}
#endif /* !WOLFSSL_SP_SMALL || HAVE_COMP_KEY */
#ifdef WOLFSSL_SP_SMALL
/* Mod-2 for the P256 curve. */
static const uint32_t p256_mod_2[8] = {
0xfffffffdU,0xffffffffU,0xffffffffU,0x00000000U,0x00000000U,0x00000000U,
0x00000001U,0xffffffffU
};
#endif /* !WOLFSSL_SP_SMALL */
/* Invert the number, in Montgomery form, modulo the modulus (prime) of the
* P256 curve. (r = 1 / a mod m)
*
* r Inverse result.
* a Number to invert.
* td Temporary data.
*/
static void sp_256_mont_inv_10(sp_digit* r, const sp_digit* a, sp_digit* td)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* t = td;
int i;
XMEMCPY(t, a, sizeof(sp_digit) * 10);
for (i=254; i>=0; i--) {
sp_256_mont_sqr_10(t, t, p256_mod, p256_mp_mod);
if (p256_mod_2[i / 32] & ((sp_digit)1 << (i % 32)))
sp_256_mont_mul_10(t, t, a, p256_mod, p256_mp_mod);
}
XMEMCPY(r, t, sizeof(sp_digit) * 10);
#else
sp_digit* t = td;
sp_digit* t2 = td + 2 * 10;
sp_digit* t3 = td + 4 * 10;
/* t = a^2 */
sp_256_mont_sqr_10(t, a, p256_mod, p256_mp_mod);
/* t = a^3 = t * a */
sp_256_mont_mul_10(t, t, a, p256_mod, p256_mp_mod);
/* t2= a^c = t ^ 2 ^ 2 */
sp_256_mont_sqr_n_10(t2, t, 2, p256_mod, p256_mp_mod);
/* t3= a^d = t2 * a */
sp_256_mont_mul_10(t3, t2, a, p256_mod, p256_mp_mod);
/* t = a^f = t2 * t */
sp_256_mont_mul_10(t, t2, t, p256_mod, p256_mp_mod);
/* t2= a^f0 = t ^ 2 ^ 4 */
sp_256_mont_sqr_n_10(t2, t, 4, p256_mod, p256_mp_mod);
/* t3= a^fd = t2 * t3 */
sp_256_mont_mul_10(t3, t2, t3, p256_mod, p256_mp_mod);
/* t = a^ff = t2 * t */
sp_256_mont_mul_10(t, t2, t, p256_mod, p256_mp_mod);
/* t2= a^ff00 = t ^ 2 ^ 8 */
sp_256_mont_sqr_n_10(t2, t, 8, p256_mod, p256_mp_mod);
/* t3= a^fffd = t2 * t3 */
sp_256_mont_mul_10(t3, t2, t3, p256_mod, p256_mp_mod);
/* t = a^ffff = t2 * t */
sp_256_mont_mul_10(t, t2, t, p256_mod, p256_mp_mod);
/* t2= a^ffff0000 = t ^ 2 ^ 16 */
sp_256_mont_sqr_n_10(t2, t, 16, p256_mod, p256_mp_mod);
/* t3= a^fffffffd = t2 * t3 */
sp_256_mont_mul_10(t3, t2, t3, p256_mod, p256_mp_mod);
/* t = a^ffffffff = t2 * t */
sp_256_mont_mul_10(t, t2, t, p256_mod, p256_mp_mod);
/* t = a^ffffffff00000000 = t ^ 2 ^ 32 */
sp_256_mont_sqr_n_10(t2, t, 32, p256_mod, p256_mp_mod);
/* t2= a^ffffffffffffffff = t2 * t */
sp_256_mont_mul_10(t, t2, t, p256_mod, p256_mp_mod);
/* t2= a^ffffffff00000001 = t2 * a */
sp_256_mont_mul_10(t2, t2, a, p256_mod, p256_mp_mod);
/* t2= a^ffffffff000000010000000000000000000000000000000000000000
* = t2 ^ 2 ^ 160 */
sp_256_mont_sqr_n_10(t2, t2, 160, p256_mod, p256_mp_mod);
/* t2= a^ffffffff00000001000000000000000000000000ffffffffffffffff
* = t2 * t */
sp_256_mont_mul_10(t2, t2, t, p256_mod, p256_mp_mod);
/* t2= a^ffffffff00000001000000000000000000000000ffffffffffffffff00000000
* = t2 ^ 2 ^ 32 */
sp_256_mont_sqr_n_10(t2, t2, 32, p256_mod, p256_mp_mod);
/* r = a^ffffffff00000001000000000000000000000000fffffffffffffffffffffffd
* = t2 * t3 */
sp_256_mont_mul_10(r, t2, t3, p256_mod, p256_mp_mod);
#endif /* WOLFSSL_SP_SMALL */
}
/* Map the Montgomery form projective co-ordinate point to an affine point.
*
* r Resulting affine co-ordinate point.
* p Montgomery form projective co-ordinate point.
* t Temporary ordinate data.
*/
static void sp_256_map_10(sp_point* r, const sp_point* p, sp_digit* t)
{
sp_digit* t1 = t;
sp_digit* t2 = t + 2*10;
int32_t n;
sp_256_mont_inv_10(t1, p->z, t + 2*10);
sp_256_mont_sqr_10(t2, t1, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t1, t2, t1, p256_mod, p256_mp_mod);
/* x /= z^2 */
sp_256_mont_mul_10(r->x, p->x, t2, p256_mod, p256_mp_mod);
XMEMSET(r->x + 10, 0, sizeof(r->x) / 2U);
sp_256_mont_reduce_10(r->x, p256_mod, p256_mp_mod);
/* Reduce x to less than modulus */
n = sp_256_cmp_10(r->x, p256_mod);
sp_256_cond_sub_10(r->x, r->x, p256_mod, 0 - ((n >= 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_10(r->x);
/* y /= z^3 */
sp_256_mont_mul_10(r->y, p->y, t1, p256_mod, p256_mp_mod);
XMEMSET(r->y + 10, 0, sizeof(r->y) / 2U);
sp_256_mont_reduce_10(r->y, p256_mod, p256_mp_mod);
/* Reduce y to less than modulus */
n = sp_256_cmp_10(r->y, p256_mod);
sp_256_cond_sub_10(r->y, r->y, p256_mod, 0 - ((n >= 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_10(r->y);
XMEMSET(r->z, 0, sizeof(r->z));
r->z[0] = 1;
}
#ifdef WOLFSSL_SP_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_256_add_10(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 10; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#else
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_256_add_10(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
r[ 0] = a[ 0] + b[ 0];
r[ 1] = a[ 1] + b[ 1];
r[ 2] = a[ 2] + b[ 2];
r[ 3] = a[ 3] + b[ 3];
r[ 4] = a[ 4] + b[ 4];
r[ 5] = a[ 5] + b[ 5];
r[ 6] = a[ 6] + b[ 6];
r[ 7] = a[ 7] + b[ 7];
r[ 8] = a[ 8] + b[ 8];
r[ 9] = a[ 9] + b[ 9];
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
/* Add two Montgomery form numbers (r = a + b % m).
*
* r Result of addition.
* a First number to add in Montogmery form.
* b Second number to add in Montogmery form.
* m Modulus (prime).
*/
static void sp_256_mont_add_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m)
{
(void)sp_256_add_10(r, a, b);
sp_256_norm_10(r);
sp_256_cond_sub_10(r, r, m, 0 - (((r[9] >> 22) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_10(r);
}
/* Double a Montgomery form number (r = a + a % m).
*
* r Result of doubling.
* a Number to double in Montogmery form.
* m Modulus (prime).
*/
static void sp_256_mont_dbl_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
(void)sp_256_add_10(r, a, a);
sp_256_norm_10(r);
sp_256_cond_sub_10(r, r, m, 0 - (((r[9] >> 22) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_10(r);
}
/* Triple a Montgomery form number (r = a + a + a % m).
*
* r Result of Tripling.
* a Number to triple in Montogmery form.
* m Modulus (prime).
*/
static void sp_256_mont_tpl_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
(void)sp_256_add_10(r, a, a);
sp_256_norm_10(r);
sp_256_cond_sub_10(r, r, m, 0 - (((r[9] >> 22) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_10(r);
(void)sp_256_add_10(r, r, a);
sp_256_norm_10(r);
sp_256_cond_sub_10(r, r, m, 0 - (((r[9] >> 22) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_10(r);
}
#ifdef WOLFSSL_SP_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_256_sub_10(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 10; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#else
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_256_sub_10(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
r[ 0] = a[ 0] - b[ 0];
r[ 1] = a[ 1] - b[ 1];
r[ 2] = a[ 2] - b[ 2];
r[ 3] = a[ 3] - b[ 3];
r[ 4] = a[ 4] - b[ 4];
r[ 5] = a[ 5] - b[ 5];
r[ 6] = a[ 6] - b[ 6];
r[ 7] = a[ 7] - b[ 7];
r[ 8] = a[ 8] - b[ 8];
r[ 9] = a[ 9] - b[ 9];
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
/* Conditionally add a and b using the mask m.
* m is -1 to add and 0 when not.
*
* r A single precision number representing conditional add result.
* a A single precision number to add with.
* b A single precision number to add.
* m Mask value to apply.
*/
static void sp_256_cond_add_10(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 10; i++) {
r[i] = a[i] + (b[i] & m);
}
#else
r[ 0] = a[ 0] + (b[ 0] & m);
r[ 1] = a[ 1] + (b[ 1] & m);
r[ 2] = a[ 2] + (b[ 2] & m);
r[ 3] = a[ 3] + (b[ 3] & m);
r[ 4] = a[ 4] + (b[ 4] & m);
r[ 5] = a[ 5] + (b[ 5] & m);
r[ 6] = a[ 6] + (b[ 6] & m);
r[ 7] = a[ 7] + (b[ 7] & m);
r[ 8] = a[ 8] + (b[ 8] & m);
r[ 9] = a[ 9] + (b[ 9] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Subtract two Montgomery form numbers (r = a - b % m).
*
* r Result of subtration.
* a Number to subtract from in Montogmery form.
* b Number to subtract with in Montogmery form.
* m Modulus (prime).
*/
static void sp_256_mont_sub_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m)
{
(void)sp_256_sub_10(r, a, b);
sp_256_cond_add_10(r, r, m, r[9] >> 22);
sp_256_norm_10(r);
}
/* Shift number left one bit.
* Bottom bit is lost.
*
* r Result of shift.
* a Number to shift.
*/
SP_NOINLINE static void sp_256_rshift1_10(sp_digit* r, sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<9; i++) {
r[i] = ((a[i] >> 1) | (a[i + 1] << 25)) & 0x3ffffff;
}
#else
r[0] = ((a[0] >> 1) | (a[1] << 25)) & 0x3ffffff;
r[1] = ((a[1] >> 1) | (a[2] << 25)) & 0x3ffffff;
r[2] = ((a[2] >> 1) | (a[3] << 25)) & 0x3ffffff;
r[3] = ((a[3] >> 1) | (a[4] << 25)) & 0x3ffffff;
r[4] = ((a[4] >> 1) | (a[5] << 25)) & 0x3ffffff;
r[5] = ((a[5] >> 1) | (a[6] << 25)) & 0x3ffffff;
r[6] = ((a[6] >> 1) | (a[7] << 25)) & 0x3ffffff;
r[7] = ((a[7] >> 1) | (a[8] << 25)) & 0x3ffffff;
r[8] = ((a[8] >> 1) | (a[9] << 25)) & 0x3ffffff;
#endif
r[9] = a[9] >> 1;
}
/* Divide the number by 2 mod the modulus (prime). (r = a / 2 % m)
*
* r Result of division by 2.
* a Number to divide.
* m Modulus (prime).
*/
static void sp_256_div2_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
sp_256_cond_add_10(r, a, m, 0 - (a[0] & 1));
sp_256_norm_10(r);
sp_256_rshift1_10(r, r);
}
/* Double the Montgomery form projective point p.
*
* r Result of doubling point.
* p Point to double.
* t Temporary ordinate data.
*/
static void sp_256_proj_point_dbl_10(sp_point* r, const sp_point* p, sp_digit* t)
{
sp_point* rp[2];
sp_digit* t1 = t;
sp_digit* t2 = t + 2*10;
sp_digit* x;
sp_digit* y;
sp_digit* z;
int i;
/* When infinity don't double point passed in - constant time. */
rp[0] = r;
/*lint allow cast to different type of pointer*/
rp[1] = (sp_point*)t; /*lint !e9087 !e740*/
XMEMSET(rp[1], 0, sizeof(sp_point));
x = rp[p->infinity]->x;
y = rp[p->infinity]->y;
z = rp[p->infinity]->z;
/* Put point to double into result - good for infinty. */
if (r != p) {
for (i=0; i<10; i++) {
r->x[i] = p->x[i];
}
for (i=0; i<10; i++) {
r->y[i] = p->y[i];
}
for (i=0; i<10; i++) {
r->z[i] = p->z[i];
}
r->infinity = p->infinity;
}
/* T1 = Z * Z */
sp_256_mont_sqr_10(t1, z, p256_mod, p256_mp_mod);
/* Z = Y * Z */
sp_256_mont_mul_10(z, y, z, p256_mod, p256_mp_mod);
/* Z = 2Z */
sp_256_mont_dbl_10(z, z, p256_mod);
/* T2 = X - T1 */
sp_256_mont_sub_10(t2, x, t1, p256_mod);
/* T1 = X + T1 */
sp_256_mont_add_10(t1, x, t1, p256_mod);
/* T2 = T1 * T2 */
sp_256_mont_mul_10(t2, t1, t2, p256_mod, p256_mp_mod);
/* T1 = 3T2 */
sp_256_mont_tpl_10(t1, t2, p256_mod);
/* Y = 2Y */
sp_256_mont_dbl_10(y, y, p256_mod);
/* Y = Y * Y */
sp_256_mont_sqr_10(y, y, p256_mod, p256_mp_mod);
/* T2 = Y * Y */
sp_256_mont_sqr_10(t2, y, p256_mod, p256_mp_mod);
/* T2 = T2/2 */
sp_256_div2_10(t2, t2, p256_mod);
/* Y = Y * X */
sp_256_mont_mul_10(y, y, x, p256_mod, p256_mp_mod);
/* X = T1 * T1 */
sp_256_mont_mul_10(x, t1, t1, p256_mod, p256_mp_mod);
/* X = X - Y */
sp_256_mont_sub_10(x, x, y, p256_mod);
/* X = X - Y */
sp_256_mont_sub_10(x, x, y, p256_mod);
/* Y = Y - X */
sp_256_mont_sub_10(y, y, x, p256_mod);
/* Y = Y * T1 */
sp_256_mont_mul_10(y, y, t1, p256_mod, p256_mp_mod);
/* Y = Y - T2 */
sp_256_mont_sub_10(y, y, t2, p256_mod);
}
/* Compare two numbers to determine if they are equal.
* Constant time implementation.
*
* a First number to compare.
* b Second number to compare.
* returns 1 when equal and 0 otherwise.
*/
static int sp_256_cmp_equal_10(const sp_digit* a, const sp_digit* b)
{
return ((a[0] ^ b[0]) | (a[1] ^ b[1]) | (a[2] ^ b[2]) | (a[3] ^ b[3]) |
(a[4] ^ b[4]) | (a[5] ^ b[5]) | (a[6] ^ b[6]) | (a[7] ^ b[7]) |
(a[8] ^ b[8]) | (a[9] ^ b[9])) == 0;
}
/* Add two Montgomery form projective points.
*
* r Result of addition.
* p Frist point to add.
* q Second point to add.
* t Temporary ordinate data.
*/
static void sp_256_proj_point_add_10(sp_point* r, const sp_point* p, const sp_point* q,
sp_digit* t)
{
const sp_point* ap[2];
sp_point* rp[2];
sp_digit* t1 = t;
sp_digit* t2 = t + 2*10;
sp_digit* t3 = t + 4*10;
sp_digit* t4 = t + 6*10;
sp_digit* t5 = t + 8*10;
sp_digit* x;
sp_digit* y;
sp_digit* z;
int i;
/* Ensure only the first point is the same as the result. */
if (q == r) {
const sp_point* a = p;
p = q;
q = a;
}
/* Check double */
(void)sp_256_sub_10(t1, p256_mod, q->y);
sp_256_norm_10(t1);
if ((sp_256_cmp_equal_10(p->x, q->x) & sp_256_cmp_equal_10(p->z, q->z) &
(sp_256_cmp_equal_10(p->y, q->y) | sp_256_cmp_equal_10(p->y, t1))) != 0) {
sp_256_proj_point_dbl_10(r, p, t);
}
else {
rp[0] = r;
/*lint allow cast to different type of pointer*/
rp[1] = (sp_point*)t; /*lint !e9087 !e740*/
XMEMSET(rp[1], 0, sizeof(sp_point));
x = rp[p->infinity | q->infinity]->x;
y = rp[p->infinity | q->infinity]->y;
z = rp[p->infinity | q->infinity]->z;
ap[0] = p;
ap[1] = q;
for (i=0; i<10; i++) {
r->x[i] = ap[p->infinity]->x[i];
}
for (i=0; i<10; i++) {
r->y[i] = ap[p->infinity]->y[i];
}
for (i=0; i<10; i++) {
r->z[i] = ap[p->infinity]->z[i];
}
r->infinity = ap[p->infinity]->infinity;
/* U1 = X1*Z2^2 */
sp_256_mont_sqr_10(t1, q->z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t3, t1, q->z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t1, t1, x, p256_mod, p256_mp_mod);
/* U2 = X2*Z1^2 */
sp_256_mont_sqr_10(t2, z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t4, t2, z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t2, t2, q->x, p256_mod, p256_mp_mod);
/* S1 = Y1*Z2^3 */
sp_256_mont_mul_10(t3, t3, y, p256_mod, p256_mp_mod);
/* S2 = Y2*Z1^3 */
sp_256_mont_mul_10(t4, t4, q->y, p256_mod, p256_mp_mod);
/* H = U2 - U1 */
sp_256_mont_sub_10(t2, t2, t1, p256_mod);
/* R = S2 - S1 */
sp_256_mont_sub_10(t4, t4, t3, p256_mod);
/* Z3 = H*Z1*Z2 */
sp_256_mont_mul_10(z, z, q->z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(z, z, t2, p256_mod, p256_mp_mod);
/* X3 = R^2 - H^3 - 2*U1*H^2 */
sp_256_mont_sqr_10(x, t4, p256_mod, p256_mp_mod);
sp_256_mont_sqr_10(t5, t2, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(y, t1, t5, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t5, t5, t2, p256_mod, p256_mp_mod);
sp_256_mont_sub_10(x, x, t5, p256_mod);
sp_256_mont_dbl_10(t1, y, p256_mod);
sp_256_mont_sub_10(x, x, t1, p256_mod);
/* Y3 = R*(U1*H^2 - X3) - S1*H^3 */
sp_256_mont_sub_10(y, y, x, p256_mod);
sp_256_mont_mul_10(y, y, t4, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t5, t5, t3, p256_mod, p256_mp_mod);
sp_256_mont_sub_10(y, y, t5, p256_mod);
}
}
#ifdef WOLFSSL_SP_SMALL
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine co-ordinates.
*
* r Resulting point.
* g Point to multiply.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_10(sp_point* r, const sp_point* g, const sp_digit* k,
int map, void* heap)
{
sp_point* td;
sp_point* t[3];
sp_digit* tmp;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
(void)heap;
td = (sp_point*)XMALLOC(sizeof(sp_point) * 3, heap, DYNAMIC_TYPE_ECC);
if (td == NULL)
err = MEMORY_E;
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, heap,
DYNAMIC_TYPE_ECC);
if (tmp == NULL)
err = MEMORY_E;
if (err == MP_OKAY) {
XMEMSET(td, 0, sizeof(*td) * 3);
t[0] = &td[0];
t[1] = &td[1];
t[2] = &td[2];
/* t[0] = {0, 0, 1} * norm */
t[0]->infinity = 1;
/* t[1] = {g->x, g->y, g->z} * norm */
err = sp_256_mod_mul_norm_10(t[1]->x, g->x, p256_mod);
}
if (err == MP_OKAY)
err = sp_256_mod_mul_norm_10(t[1]->y, g->y, p256_mod);
if (err == MP_OKAY)
err = sp_256_mod_mul_norm_10(t[1]->z, g->z, p256_mod);
if (err == MP_OKAY) {
i = 9;
c = 22;
n = k[i--] << (26 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1)
break;
n = k[i--];
c = 26;
}
y = (n >> 25) & 1;
n <<= 1;
sp_256_proj_point_add_10(t[y^1], t[0], t[1], tmp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])),
sizeof(sp_point));
sp_256_proj_point_dbl_10(t[2], t[2], tmp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2],
sizeof(sp_point));
}
if (map != 0) {
sp_256_map_10(r, t[0], tmp);
}
else {
XMEMCPY(r, t[0], sizeof(sp_point));
}
}
if (tmp != NULL) {
XMEMSET(tmp, 0, sizeof(sp_digit) * 2 * 10 * 5);
XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
}
if (td != NULL) {
XMEMSET(td, 0, sizeof(sp_point) * 3);
XFREE(td, NULL, DYNAMIC_TYPE_ECC);
}
return err;
}
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine co-ordinates.
*
* r Resulting point.
* g Point to multiply.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_10(sp_point* r, const sp_point* g, const sp_digit* k,
int map, void* heap)
{
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_point td[3];
sp_digit tmpd[2 * 10 * 5];
#endif
sp_point* t;
sp_digit* tmp;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
(void)heap;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_point td[3];
t = (sp_point*)XMALLOC(sizeof(*td) * 3, heap, DYNAMIC_TYPE_ECC);
if (t == NULL)
err = MEMORY_E;
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, heap,
DYNAMIC_TYPE_ECC);
if (tmp == NULL)
err = MEMORY_E;
#else
t = td;
tmp = tmpd;
#endif
if (err == MP_OKAY) {
t[0] = &td[0];
t[1] = &td[1];
t[2] = &td[2];
/* t[0] = {0, 0, 1} * norm */
XMEMSET(&t[0], 0, sizeof(t[0]));
t[0].infinity = 1;
/* t[1] = {g->x, g->y, g->z} * norm */
err = sp_256_mod_mul_norm_10(t[1].x, g->x, p256_mod);
}
if (err == MP_OKAY)
err = sp_256_mod_mul_norm_10(t[1].y, g->y, p256_mod);
if (err == MP_OKAY)
err = sp_256_mod_mul_norm_10(t[1].z, g->z, p256_mod);
if (err == MP_OKAY) {
i = 9;
c = 22;
n = k[i--] << (26 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1)
break;
n = k[i--];
c = 26;
}
y = (n >> 25) & 1;
n <<= 1;
sp_256_proj_point_add_10(&t[y^1], &t[0], &t[1], tmp);
XMEMCPY(&t[2], (void*)(((size_t)&t[0] & addr_mask[y^1]) +
((size_t)&t[1] & addr_mask[y])), sizeof(t[2]));
sp_256_proj_point_dbl_10(&t[2], &t[2], tmp);
XMEMCPY((void*)(((size_t)&t[0] & addr_mask[y^1]) +
((size_t)&t[1] & addr_mask[y])), &t[2], sizeof(t[2]));
}
if (map != 0) {
sp_256_map_10(r, &t[0], tmp);
}
else {
XMEMCPY(r, &t[0], sizeof(sp_point));
}
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (tmp != NULL) {
XMEMSET(tmp, 0, sizeof(sp_digit) * 2 * 10 * 5);
XFREE(tmp, heap, DYNAMIC_TYPE_ECC);
}
if (t != NULL) {
XMEMSET(t, 0, sizeof(sp_point) * 3);
XFREE(t, heap, DYNAMIC_TYPE_ECC);
}
#else
ForceZero(tmpd, sizeof(tmpd));
ForceZero(td, sizeof(td));
#endif
return err;
}
#else
/* A table entry for pre-computed points. */
typedef struct sp_table_entry {
sp_digit x[10];
sp_digit y[10];
} sp_table_entry;
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine co-ordinates.
*
* r Resulting point.
* g Point to multiply.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_fast_10(sp_point* r, const sp_point* g, const sp_digit* k,
int map, void* heap)
{
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_point td[16];
sp_point rtd;
sp_digit tmpd[2 * 10 * 5];
#endif
sp_point* t;
sp_point* rt;
sp_digit* tmp;
sp_digit n;
int i;
int c, y;
int err;
(void)heap;
err = sp_ecc_point_new(heap, rtd, rt);
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
t = (sp_point*)XMALLOC(sizeof(sp_point) * 16, heap, DYNAMIC_TYPE_ECC);
if (t == NULL)
err = MEMORY_E;
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, heap,
DYNAMIC_TYPE_ECC);
if (tmp == NULL)
err = MEMORY_E;
#else
t = td;
tmp = tmpd;
#endif
if (err == MP_OKAY) {
/* t[0] = {0, 0, 1} * norm */
XMEMSET(&t[0], 0, sizeof(t[0]));
t[0].infinity = 1;
/* t[1] = {g->x, g->y, g->z} * norm */
(void)sp_256_mod_mul_norm_10(t[1].x, g->x, p256_mod);
(void)sp_256_mod_mul_norm_10(t[1].y, g->y, p256_mod);
(void)sp_256_mod_mul_norm_10(t[1].z, g->z, p256_mod);
t[1].infinity = 0;
sp_256_proj_point_dbl_10(&t[ 2], &t[ 1], tmp);
t[ 2].infinity = 0;
sp_256_proj_point_add_10(&t[ 3], &t[ 2], &t[ 1], tmp);
t[ 3].infinity = 0;
sp_256_proj_point_dbl_10(&t[ 4], &t[ 2], tmp);
t[ 4].infinity = 0;
sp_256_proj_point_add_10(&t[ 5], &t[ 3], &t[ 2], tmp);
t[ 5].infinity = 0;
sp_256_proj_point_dbl_10(&t[ 6], &t[ 3], tmp);
t[ 6].infinity = 0;
sp_256_proj_point_add_10(&t[ 7], &t[ 4], &t[ 3], tmp);
t[ 7].infinity = 0;
sp_256_proj_point_dbl_10(&t[ 8], &t[ 4], tmp);
t[ 8].infinity = 0;
sp_256_proj_point_add_10(&t[ 9], &t[ 5], &t[ 4], tmp);
t[ 9].infinity = 0;
sp_256_proj_point_dbl_10(&t[10], &t[ 5], tmp);
t[10].infinity = 0;
sp_256_proj_point_add_10(&t[11], &t[ 6], &t[ 5], tmp);
t[11].infinity = 0;
sp_256_proj_point_dbl_10(&t[12], &t[ 6], tmp);
t[12].infinity = 0;
sp_256_proj_point_add_10(&t[13], &t[ 7], &t[ 6], tmp);
t[13].infinity = 0;
sp_256_proj_point_dbl_10(&t[14], &t[ 7], tmp);
t[14].infinity = 0;
sp_256_proj_point_add_10(&t[15], &t[ 8], &t[ 7], tmp);
t[15].infinity = 0;
i = 8;
n = k[i+1] << 6;
c = 18;
y = n >> 24;
XMEMCPY(rt, &t[y], sizeof(sp_point));
n <<= 8;
for (; i>=0 || c>=4; ) {
if (c < 4) {
n |= k[i--] << (6 - c);
c += 26;
}
y = (n >> 28) & 0xf;
n <<= 4;
c -= 4;
sp_256_proj_point_dbl_10(rt, rt, tmp);
sp_256_proj_point_dbl_10(rt, rt, tmp);
sp_256_proj_point_dbl_10(rt, rt, tmp);
sp_256_proj_point_dbl_10(rt, rt, tmp);
sp_256_proj_point_add_10(rt, rt, &t[y], tmp);
}
if (map != 0) {
sp_256_map_10(r, rt, tmp);
}
else {
XMEMCPY(r, rt, sizeof(sp_point));
}
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (tmp != NULL) {
XMEMSET(tmp, 0, sizeof(sp_digit) * 2 * 10 * 5);
XFREE(tmp, heap, DYNAMIC_TYPE_ECC);
}
if (t != NULL) {
XMEMSET(t, 0, sizeof(sp_point) * 16);
XFREE(t, heap, DYNAMIC_TYPE_ECC);
}
#else
ForceZero(tmpd, sizeof(tmpd));
ForceZero(td, sizeof(td));
#endif
sp_ecc_point_free(rt, 1, heap);
return err;
}
#ifdef FP_ECC
/* Double the Montgomery form projective point p a number of times.
*
* r Result of repeated doubling of point.
* p Point to double.
* n Number of times to double
* t Temporary ordinate data.
*/
static void sp_256_proj_point_dbl_n_10(sp_point* r, const sp_point* p, int n,
sp_digit* t)
{
sp_point* rp[2];
sp_digit* w = t;
sp_digit* a = t + 2*10;
sp_digit* b = t + 4*10;
sp_digit* t1 = t + 6*10;
sp_digit* t2 = t + 8*10;
sp_digit* x;
sp_digit* y;
sp_digit* z;
int i;
rp[0] = r;
/*lint allow cast to different type of pointer*/
rp[1] = (sp_point*)t; /*lint !e9087 !e740*/
XMEMSET(rp[1], 0, sizeof(sp_point));
x = rp[p->infinity]->x;
y = rp[p->infinity]->y;
z = rp[p->infinity]->z;
if (r != p) {
for (i=0; i<10; i++) {
r->x[i] = p->x[i];
}
for (i=0; i<10; i++) {
r->y[i] = p->y[i];
}
for (i=0; i<10; i++) {
r->z[i] = p->z[i];
}
r->infinity = p->infinity;
}
/* Y = 2*Y */
sp_256_mont_dbl_10(y, y, p256_mod);
/* W = Z^4 */
sp_256_mont_sqr_10(w, z, p256_mod, p256_mp_mod);
sp_256_mont_sqr_10(w, w, p256_mod, p256_mp_mod);
while (n-- > 0) {
/* A = 3*(X^2 - W) */
sp_256_mont_sqr_10(t1, x, p256_mod, p256_mp_mod);
sp_256_mont_sub_10(t1, t1, w, p256_mod);
sp_256_mont_tpl_10(a, t1, p256_mod);
/* B = X*Y^2 */
sp_256_mont_sqr_10(t2, y, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(b, t2, x, p256_mod, p256_mp_mod);
/* X = A^2 - 2B */
sp_256_mont_sqr_10(x, a, p256_mod, p256_mp_mod);
sp_256_mont_dbl_10(t1, b, p256_mod);
sp_256_mont_sub_10(x, x, t1, p256_mod);
/* Z = Z*Y */
sp_256_mont_mul_10(z, z, y, p256_mod, p256_mp_mod);
/* t2 = Y^4 */
sp_256_mont_sqr_10(t2, t2, p256_mod, p256_mp_mod);
if (n != 0) {
/* W = W*Y^4 */
sp_256_mont_mul_10(w, w, t2, p256_mod, p256_mp_mod);
}
/* y = 2*A*(B - X) - Y^4 */
sp_256_mont_sub_10(y, b, x, p256_mod);
sp_256_mont_mul_10(y, y, a, p256_mod, p256_mp_mod);
sp_256_mont_dbl_10(y, y, p256_mod);
sp_256_mont_sub_10(y, y, t2, p256_mod);
}
/* Y = Y/2 */
sp_256_div2_10(y, y, p256_mod);
}
#endif /* FP_ECC */
/* Add two Montgomery form projective points. The second point has a q value of
* one.
* Only the first point can be the same pointer as the result point.
*
* r Result of addition.
* p Frist point to add.
* q Second point to add.
* t Temporary ordinate data.
*/
static void sp_256_proj_point_add_qz1_10(sp_point* r, const sp_point* p,
const sp_point* q, sp_digit* t)
{
const sp_point* ap[2];
sp_point* rp[2];
sp_digit* t1 = t;
sp_digit* t2 = t + 2*10;
sp_digit* t3 = t + 4*10;
sp_digit* t4 = t + 6*10;
sp_digit* t5 = t + 8*10;
sp_digit* x;
sp_digit* y;
sp_digit* z;
int i;
/* Check double */
(void)sp_256_sub_10(t1, p256_mod, q->y);
sp_256_norm_10(t1);
if ((sp_256_cmp_equal_10(p->x, q->x) & sp_256_cmp_equal_10(p->z, q->z) &
(sp_256_cmp_equal_10(p->y, q->y) | sp_256_cmp_equal_10(p->y, t1))) != 0) {
sp_256_proj_point_dbl_10(r, p, t);
}
else {
rp[0] = r;
/*lint allow cast to different type of pointer*/
rp[1] = (sp_point*)t; /*lint !e9087 !e740*/
XMEMSET(rp[1], 0, sizeof(sp_point));
x = rp[p->infinity | q->infinity]->x;
y = rp[p->infinity | q->infinity]->y;
z = rp[p->infinity | q->infinity]->z;
ap[0] = p;
ap[1] = q;
for (i=0; i<10; i++) {
r->x[i] = ap[p->infinity]->x[i];
}
for (i=0; i<10; i++) {
r->y[i] = ap[p->infinity]->y[i];
}
for (i=0; i<10; i++) {
r->z[i] = ap[p->infinity]->z[i];
}
r->infinity = ap[p->infinity]->infinity;
/* U2 = X2*Z1^2 */
sp_256_mont_sqr_10(t2, z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t4, t2, z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t2, t2, q->x, p256_mod, p256_mp_mod);
/* S2 = Y2*Z1^3 */
sp_256_mont_mul_10(t4, t4, q->y, p256_mod, p256_mp_mod);
/* H = U2 - X1 */
sp_256_mont_sub_10(t2, t2, x, p256_mod);
/* R = S2 - Y1 */
sp_256_mont_sub_10(t4, t4, y, p256_mod);
/* Z3 = H*Z1 */
sp_256_mont_mul_10(z, z, t2, p256_mod, p256_mp_mod);
/* X3 = R^2 - H^3 - 2*X1*H^2 */
sp_256_mont_sqr_10(t1, t4, p256_mod, p256_mp_mod);
sp_256_mont_sqr_10(t5, t2, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t3, x, t5, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t5, t5, t2, p256_mod, p256_mp_mod);
sp_256_mont_sub_10(x, t1, t5, p256_mod);
sp_256_mont_dbl_10(t1, t3, p256_mod);
sp_256_mont_sub_10(x, x, t1, p256_mod);
/* Y3 = R*(X1*H^2 - X3) - Y1*H^3 */
sp_256_mont_sub_10(t3, t3, x, p256_mod);
sp_256_mont_mul_10(t3, t3, t4, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t5, t5, y, p256_mod, p256_mp_mod);
sp_256_mont_sub_10(y, t3, t5, p256_mod);
}
}
#ifdef FP_ECC
/* Convert the projective point to affine.
* Ordinates are in Montgomery form.
*
* a Point to convert.
* t Temprorary data.
*/
static void sp_256_proj_to_affine_10(sp_point* a, sp_digit* t)
{
sp_digit* t1 = t;
sp_digit* t2 = t + 2 * 10;
sp_digit* tmp = t + 4 * 10;
sp_256_mont_inv_10(t1, a->z, tmp);
sp_256_mont_sqr_10(t2, t1, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t1, t2, t1, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(a->x, a->x, t2, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(a->y, a->y, t1, p256_mod, p256_mp_mod);
XMEMCPY(a->z, p256_norm_mod, sizeof(p256_norm_mod));
}
/* Generate the pre-computed table of points for the base point.
*
* a The base point.
* table Place to store generated point data.
* tmp Temprorary data.
* heap Heap to use for allocation.
*/
static int sp_256_gen_stripe_table_10(const sp_point* a,
sp_table_entry* table, sp_digit* tmp, void* heap)
{
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_point td, s1d, s2d;
#endif
sp_point* t;
sp_point* s1 = NULL;
sp_point* s2 = NULL;
int i, j;
int err;
(void)heap;
err = sp_ecc_point_new(heap, td, t);
if (err == MP_OKAY) {
err = sp_ecc_point_new(heap, s1d, s1);
}
if (err == MP_OKAY) {
err = sp_ecc_point_new(heap, s2d, s2);
}
if (err == MP_OKAY) {
err = sp_256_mod_mul_norm_10(t->x, a->x, p256_mod);
}
if (err == MP_OKAY) {
err = sp_256_mod_mul_norm_10(t->y, a->y, p256_mod);
}
if (err == MP_OKAY) {
err = sp_256_mod_mul_norm_10(t->z, a->z, p256_mod);
}
if (err == MP_OKAY) {
t->infinity = 0;
sp_256_proj_to_affine_10(t, tmp);
XMEMCPY(s1->z, p256_norm_mod, sizeof(p256_norm_mod));
s1->infinity = 0;
XMEMCPY(s2->z, p256_norm_mod, sizeof(p256_norm_mod));
s2->infinity = 0;
/* table[0] = {0, 0, infinity} */
XMEMSET(&table[0], 0, sizeof(sp_table_entry));
/* table[1] = Affine version of 'a' in Montgomery form */
XMEMCPY(table[1].x, t->x, sizeof(table->x));
XMEMCPY(table[1].y, t->y, sizeof(table->y));
for (i=1; i<8; i++) {
sp_256_proj_point_dbl_n_10(t, t, 32, tmp);
sp_256_proj_to_affine_10(t, tmp);
XMEMCPY(table[1<<i].x, t->x, sizeof(table->x));
XMEMCPY(table[1<<i].y, t->y, sizeof(table->y));
}
for (i=1; i<8; i++) {
XMEMCPY(s1->x, table[1<<i].x, sizeof(table->x));
XMEMCPY(s1->y, table[1<<i].y, sizeof(table->y));
for (j=(1<<i)+1; j<(1<<(i+1)); j++) {
XMEMCPY(s2->x, table[j-(1<<i)].x, sizeof(table->x));
XMEMCPY(s2->y, table[j-(1<<i)].y, sizeof(table->y));
sp_256_proj_point_add_qz1_10(t, s1, s2, tmp);
sp_256_proj_to_affine_10(t, tmp);
XMEMCPY(table[j].x, t->x, sizeof(table->x));
XMEMCPY(table[j].y, t->y, sizeof(table->y));
}
}
}
sp_ecc_point_free(s2, 0, heap);
sp_ecc_point_free(s1, 0, heap);
sp_ecc_point_free( t, 0, heap);
return err;
}
#endif /* FP_ECC */
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine co-ordinates.
*
* r Resulting point.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_stripe_10(sp_point* r, const sp_point* g,
const sp_table_entry* table, const sp_digit* k, int map, void* heap)
{
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_point rtd;
sp_point pd;
sp_digit td[2 * 10 * 5];
#endif
sp_point* rt;
sp_point* p = NULL;
sp_digit* t;
int i, j;
int y, x;
int err;
(void)g;
(void)heap;
err = sp_ecc_point_new(heap, rtd, rt);
if (err == MP_OKAY) {
err = sp_ecc_point_new(heap, pd, p);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
t = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, heap,
DYNAMIC_TYPE_ECC);
if (t == NULL) {
err = MEMORY_E;
}
#else
t = td;
#endif
if (err == MP_OKAY) {
XMEMCPY(p->z, p256_norm_mod, sizeof(p256_norm_mod));
XMEMCPY(rt->z, p256_norm_mod, sizeof(p256_norm_mod));
y = 0;
for (j=0,x=31; j<8; j++,x+=32) {
y |= ((k[x / 26] >> (x % 26)) & 1) << j;
}
XMEMCPY(rt->x, table[y].x, sizeof(table[y].x));
XMEMCPY(rt->y, table[y].y, sizeof(table[y].y));
rt->infinity = !y;
for (i=30; i>=0; i--) {
y = 0;
for (j=0,x=i; j<8; j++,x+=32) {
y |= ((k[x / 26] >> (x % 26)) & 1) << j;
}
sp_256_proj_point_dbl_10(rt, rt, t);
XMEMCPY(p->x, table[y].x, sizeof(table[y].x));
XMEMCPY(p->y, table[y].y, sizeof(table[y].y));
p->infinity = !y;
sp_256_proj_point_add_qz1_10(rt, rt, p, t);
}
if (map != 0) {
sp_256_map_10(r, rt, t);
}
else {
XMEMCPY(r, rt, sizeof(sp_point));
}
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (t != NULL) {
XFREE(t, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_ecc_point_free(p, 0, heap);
sp_ecc_point_free(rt, 0, heap);
return err;
}
#ifdef FP_ECC
#ifndef FP_ENTRIES
#define FP_ENTRIES 16
#endif
typedef struct sp_cache_t {
sp_digit x[10];
sp_digit y[10];
sp_table_entry table[256];
uint32_t cnt;
int set;
} sp_cache_t;
static THREAD_LS_T sp_cache_t sp_cache[FP_ENTRIES];
static THREAD_LS_T int sp_cache_last = -1;
static THREAD_LS_T int sp_cache_inited = 0;
#ifndef HAVE_THREAD_LS
static volatile int initCacheMutex = 0;
static wolfSSL_Mutex sp_cache_lock;
#endif
static void sp_ecc_get_cache(const sp_point* g, sp_cache_t** cache)
{
int i, j;
uint32_t least;
if (sp_cache_inited == 0) {
for (i=0; i<FP_ENTRIES; i++) {
sp_cache[i].set = 0;
}
sp_cache_inited = 1;
}
/* Compare point with those in cache. */
for (i=0; i<FP_ENTRIES; i++) {
if (!sp_cache[i].set)
continue;
if (sp_256_cmp_equal_10(g->x, sp_cache[i].x) &
sp_256_cmp_equal_10(g->y, sp_cache[i].y)) {
sp_cache[i].cnt++;
break;
}
}
/* No match. */
if (i == FP_ENTRIES) {
/* Find empty entry. */
i = (sp_cache_last + 1) % FP_ENTRIES;
for (; i != sp_cache_last; i=(i+1)%FP_ENTRIES) {
if (!sp_cache[i].set) {
break;
}
}
/* Evict least used. */
if (i == sp_cache_last) {
least = sp_cache[0].cnt;
for (j=1; j<FP_ENTRIES; j++) {
if (sp_cache[j].cnt < least) {
i = j;
least = sp_cache[i].cnt;
}
}
}
XMEMCPY(sp_cache[i].x, g->x, sizeof(sp_cache[i].x));
XMEMCPY(sp_cache[i].y, g->y, sizeof(sp_cache[i].y));
sp_cache[i].set = 1;
sp_cache[i].cnt = 1;
}
*cache = &sp_cache[i];
sp_cache_last = i;
}
#endif /* FP_ECC */
/* Multiply the base point of P256 by the scalar and return the result.
* If map is true then convert result to affine co-ordinates.
*
* r Resulting point.
* g Point to multiply.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_10(sp_point* r, const sp_point* g, const sp_digit* k,
int map, void* heap)
{
#ifndef FP_ECC
return sp_256_ecc_mulmod_fast_10(r, g, k, map, heap);
#else
sp_digit tmp[2 * 10 * 5];
sp_cache_t* cache;
int err = MP_OKAY;
#ifndef HAVE_THREAD_LS
if (initCacheMutex == 0) {
wc_InitMutex(&sp_cache_lock);
initCacheMutex = 1;
}
if (wc_LockMutex(&sp_cache_lock) != 0)
err = BAD_MUTEX_E;
#endif /* HAVE_THREAD_LS */
if (err == MP_OKAY) {
sp_ecc_get_cache(g, &cache);
if (cache->cnt == 2)
sp_256_gen_stripe_table_10(g, cache->table, tmp, heap);
#ifndef HAVE_THREAD_LS
wc_UnLockMutex(&sp_cache_lock);
#endif /* HAVE_THREAD_LS */
if (cache->cnt < 2) {
err = sp_256_ecc_mulmod_fast_10(r, g, k, map, heap);
}
else {
err = sp_256_ecc_mulmod_stripe_10(r, g, cache->table, k,
map, heap);
}
}
return err;
#endif
}
#endif
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine co-ordinates.
*
* km Scalar to multiply by.
* p Point to multiply.
* r Resulting point.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
int sp_ecc_mulmod_256(mp_int* km, ecc_point* gm, ecc_point* r, int map,
void* heap)
{
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_point p;
sp_digit kd[10];
#endif
sp_point* point;
sp_digit* k = NULL;
int err = MP_OKAY;
err = sp_ecc_point_new(heap, p, point);
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (err == MP_OKAY) {
k = (sp_digit*)XMALLOC(sizeof(sp_digit) * 10, heap,
DYNAMIC_TYPE_ECC);
if (k == NULL)
err = MEMORY_E;
}
#else
k = kd;
#endif
if (err == MP_OKAY) {
sp_256_from_mp(k, 10, km);
sp_256_point_from_ecc_point_10(point, gm);
err = sp_256_ecc_mulmod_10(point, point, k, map, heap);
}
if (err == MP_OKAY) {
err = sp_256_point_to_ecc_point_10(point, r);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (k != NULL) {
XFREE(k, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_ecc_point_free(point, 0, heap);
return err;
}
#ifdef WOLFSSL_SP_SMALL
/* Multiply the base point of P256 by the scalar and return the result.
* If map is true then convert result to affine co-ordinates.
*
* r Resulting point.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_base_10(sp_point* r, const sp_digit* k,
int map, void* heap)
{
/* No pre-computed values. */
return sp_256_ecc_mulmod_10(r, &p256_base, k, map, heap);
}
#else
static const sp_table_entry p256_table[256] = {
/* 0 */
{ { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 },
{ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
/* 1 */
{ { 0x0a9143c,0x1cc3506,0x360179e,0x3f17fb6,0x075ba95,0x1d88944,
0x3b732b7,0x15719e7,0x376a537,0x0062417 },
{ 0x295560a,0x094d5f3,0x245cddf,0x392e867,0x18b4ab8,0x3487cc9,
0x288688d,0x176174b,0x3182588,0x0215c7f } },
/* 2 */
{ { 0x147519a,0x2218090,0x32f0202,0x2b09acd,0x0d0981e,0x1e17af2,
0x14a7caa,0x163a6a7,0x10ddbdf,0x03654f1 },
{ 0x1590f8f,0x0d8733f,0x09179d6,0x1ad139b,0x372e962,0x0bad933,
0x1961102,0x223cdff,0x37e9eb2,0x0218fae } },
/* 3 */
{ { 0x0db6485,0x1ad88d7,0x2f97785,0x288bc28,0x3808f0e,0x3df8c02,
0x28d9544,0x20280f9,0x055b5ff,0x00001d8 },
{ 0x38d2010,0x13ae6e0,0x308a763,0x2ecc90d,0x254014f,0x10a9981,
0x247d398,0x0fb8383,0x3613437,0x020c21d } },
/* 4 */
{ { 0x2a0d2bb,0x08bf145,0x34994f9,0x1b06988,0x30d5cc1,0x1f18b22,
0x01cf3a5,0x199fe49,0x161fd1b,0x00bd79a },
{ 0x1a01797,0x171c2fd,0x21925c1,0x1358255,0x23d20b4,0x1c7f6d4,
0x111b370,0x03dec12,0x1168d6f,0x03d923e } },
/* 5 */
{ { 0x137bbbc,0x19a11f8,0x0bec9e5,0x27a29a8,0x3e43446,0x275cd18,
0x0427617,0x00056c7,0x285133d,0x016af80 },
{ 0x04c7dab,0x2a0df30,0x0c0792a,0x1310c98,0x3573d9f,0x239b30d,
0x1315627,0x1ce0c32,0x25b6b6f,0x0252edc } },
/* 6 */
{ { 0x20f141c,0x26d23dc,0x3c74bbf,0x334b7d6,0x06199b3,0x0441171,
0x3f61294,0x313bf70,0x3cb2f7d,0x03375ae },
{ 0x2f436fd,0x19c02fa,0x26becca,0x1b6e64c,0x26f647f,0x053c948,
0x0fa7920,0x397d830,0x2bd4bda,0x028d86f } },
/* 7 */
{ { 0x17c13c7,0x2895616,0x03e128a,0x17d42df,0x1c38d63,0x0f02747,
0x039aecf,0x0a4b01c,0x209c4b5,0x02e84b2 },
{ 0x1f91dfd,0x023e916,0x07fb9e4,0x19b3ba8,0x13af43b,0x35e02ca,
0x0eb0899,0x3bd2c7b,0x19d701f,0x014faee } },
/* 8 */
{ { 0x0e63d34,0x1fb8c6c,0x0fab4fe,0x1caa795,0x0f46005,0x179ed69,
0x093334d,0x120c701,0x39206d5,0x021627e },
{ 0x183553a,0x03d7319,0x09e5aa7,0x12b8959,0x2087909,0x0011194,
0x1045071,0x0713f32,0x16d0254,0x03aec1a } },
/* 9 */
{ { 0x01647c5,0x1b2856b,0x1799461,0x11f133d,0x0b8127d,0x1937eeb,
0x266aa37,0x1f68f71,0x0cbd1b2,0x03aca08 },
{ 0x287e008,0x1be361a,0x38f3940,0x276488d,0x2d87dfa,0x0333b2c,
0x2d2e428,0x368755b,0x09b55a7,0x007ca0a } },
/* 10 */
{ { 0x389da99,0x2a8300e,0x0022abb,0x27ae0a1,0x0a6f2d7,0x207017a,
0x047862b,0x1358c9e,0x35905e5,0x00cde92 },
{ 0x1f7794a,0x1d40348,0x3f613c6,0x2ddf5b5,0x0207005,0x133f5ba,
0x1a37810,0x3ef5829,0x0d5f4c2,0x0035978 } },
/* 11 */
{ { 0x1275d38,0x026efad,0x2358d9d,0x1142f82,0x14268a7,0x1cfac99,
0x362ff49,0x288cbc1,0x24252f4,0x0308f68 },
{ 0x394520c,0x06e13c2,0x178e5da,0x18ec16f,0x1096667,0x134a7a8,
0x0dcb869,0x33fc4e9,0x38cc790,0x006778e } },
/* 12 */
{ { 0x2c5fe04,0x29c5b09,0x1bdb183,0x02ceee8,0x03b28de,0x132dc4b,
0x32c586a,0x32ff5d0,0x3d491fc,0x038d372 },
{ 0x2a58403,0x2351aea,0x3a53b40,0x21a0ba5,0x39a6974,0x1aaaa2b,
0x3901273,0x03dfe78,0x3447b4e,0x039d907 } },
/* 13 */
{ { 0x364ba59,0x14e5077,0x02fc7d7,0x3b02c09,0x1d33f10,0x0560616,
0x06dfc6a,0x15efd3c,0x357052a,0x01284b7 },
{ 0x039dbd0,0x18ce3e5,0x3e1fbfa,0x352f794,0x0d3c24b,0x07c6cc5,
0x1e4ffa2,0x3a91bf5,0x293bb5b,0x01abd6a } },
/* 14 */
{ { 0x0c91999,0x02da644,0x0491da1,0x100a960,0x00a24b4,0x2330824,
0x0094b4b,0x1004cf8,0x35a66a4,0x017f8d1 },
{ 0x13e7b4b,0x232af7e,0x391ab0f,0x069f08f,0x3292b50,0x3479898,
0x2889aec,0x2a4590b,0x308ecfe,0x02d5138 } },
/* 15 */
{ { 0x2ddfdce,0x231ba45,0x39e6647,0x19be245,0x12c3291,0x35399f8,
0x0d6e764,0x3082d3a,0x2bda6b0,0x0382dac },
{ 0x37efb57,0x04b7cae,0x00070d3,0x379e431,0x01aac0d,0x1e6f251,
0x0336ad6,0x0ddd3e4,0x3de25a6,0x01c7008 } },
/* 16 */
{ { 0x3e20925,0x230912f,0x286762a,0x30e3f73,0x391c19a,0x34e1c18,
0x16a5d5d,0x093d96a,0x3d421d3,0x0187561 },
{ 0x37173ea,0x19ce8a8,0x0b65e87,0x0214dde,0x2238480,0x16ead0f,
0x38441e0,0x3bef843,0x2124621,0x03e847f } },
/* 17 */
{ { 0x0b19ffd,0x247cacb,0x3c231c8,0x16ec648,0x201ba8d,0x2b172a3,
0x103d678,0x2fb72db,0x04c1f13,0x0161bac },
{ 0x3e8ed09,0x171b949,0x2de20c3,0x0f06067,0x21e81a3,0x1b194be,
0x0fd6c05,0x13c449e,0x0087086,0x006756b } },
/* 18 */
{ { 0x09a4e1f,0x27d604c,0x00741e9,0x06fa49c,0x0ab7de7,0x3f4a348,
0x25ef0be,0x158fc9a,0x33f7f9c,0x039f001 },
{ 0x2f59f76,0x3598e83,0x30501f6,0x15083f2,0x0669b3b,0x29980b5,
0x0c1f7a7,0x0f02b02,0x0fec65b,0x0382141 } },
/* 19 */
{ { 0x031b3ca,0x23da368,0x2d66f09,0x27b9b69,0x06d1cab,0x13c91ba,
0x3d81fa9,0x25ad16f,0x0825b09,0x01e3c06 },
{ 0x225787f,0x3bf790e,0x2c9bb7e,0x0347732,0x28016f8,0x0d6ff0d,
0x2a4877b,0x1d1e833,0x3b87e94,0x010e9dc } },
/* 20 */
{ { 0x2b533d5,0x1ddcd34,0x1dc0625,0x3da86f7,0x3673b8a,0x1e7b0a4,
0x3e7c9aa,0x19ac55d,0x251c3b2,0x02edb79 },
{ 0x25259b3,0x24c0ead,0x3480e7e,0x34f40e9,0x3d6a0af,0x2cf3f09,
0x2c83d19,0x2e66f16,0x19a5d18,0x0182d18 } },
/* 21 */
{ { 0x2e5aa1c,0x28e3846,0x3658bd6,0x0ad279c,0x1b8b765,0x397e1fb,
0x130014e,0x3ff342c,0x3b2aeeb,0x02743c9 },
{ 0x2730a55,0x0918c5e,0x083aca9,0x0bf76ef,0x19c955b,0x300669c,
0x01dfe0a,0x312341f,0x26d356e,0x0091295 } },
/* 22 */
{ { 0x2cf1f96,0x00e52ba,0x271c6db,0x2a40930,0x19f2122,0x0b2f4ee,
0x26ac1b8,0x3bda498,0x0873581,0x0117963 },
{ 0x38f9dbc,0x3d1e768,0x2040d3f,0x11ba222,0x3a8aaf1,0x1b82fb5,
0x1adfb24,0x2de9251,0x21cc1e4,0x0301038 } },
/* 23 */
{ { 0x38117b6,0x2bc001b,0x1433847,0x3fdce8d,0x3651969,0x3651d7a,
0x2b35761,0x1bb1d20,0x097682c,0x00737d7 },
{ 0x1f04839,0x1dd6d04,0x16987db,0x3d12378,0x17dbeac,0x1c2cc86,
0x121dd1b,0x3fcf6ca,0x1f8a92d,0x00119d5 } },
/* 24 */
{ { 0x0e8ffcd,0x2b174af,0x1a82cc8,0x22cbf98,0x30d53c4,0x080b5b1,
0x3161727,0x297cfdb,0x2113b83,0x0011b97 },
{ 0x0007f01,0x23fd936,0x3183e7b,0x0496bd0,0x07fb1ef,0x178680f,
0x1c5ea63,0x0016c11,0x2c3303d,0x01b8041 } },
/* 25 */
{ { 0x0dd73b1,0x1cd6122,0x10d948c,0x23e657b,0x3767070,0x15a8aad,
0x385ea8c,0x33c7ce0,0x0ede901,0x0110965 },
{ 0x2d4b65b,0x2a8b244,0x0c37f8f,0x0ee5b24,0x394c234,0x3a5e347,
0x26e4a15,0x39a3b4c,0x2514c2e,0x029e5be } },
/* 26 */
{ { 0x23addd7,0x3ed8120,0x13b3359,0x20f959a,0x09e2a61,0x32fcf20,
0x05b78e3,0x19ba7e2,0x1a9c697,0x0392b4b },
{ 0x2048a61,0x3dfd0a3,0x19a0357,0x233024b,0x3082d19,0x00fb63b,
0x3a1af4c,0x1450ff0,0x046c37b,0x0317a50 } },
/* 27 */
{ { 0x3e75f9e,0x294e30a,0x3a78476,0x3a32c48,0x36fd1a9,0x0427012,
0x1e4df0b,0x11d1f61,0x1afdb46,0x018ca0f },
{ 0x2f2df15,0x0a33dee,0x27f4ce7,0x1542b66,0x3e592c4,0x20d2f30,
0x3226ade,0x2a4e3ea,0x1ab1981,0x01a2f46 } },
/* 28 */
{ { 0x087d659,0x3ab5446,0x305ac08,0x3d2cd64,0x33374d5,0x3f9d3f8,
0x186981c,0x37f5a5a,0x2f53c6f,0x01254a4 },
{ 0x2cec896,0x1e32786,0x04844a8,0x043b16d,0x3d964b2,0x1935829,
0x16f7e26,0x1a0dd9a,0x30d2603,0x003b1d4 } },
/* 29 */
{ { 0x12687bb,0x04e816b,0x21fa2da,0x1abccb8,0x3a1f83b,0x375181e,
0x0f5ef51,0x0fc2ce4,0x3a66486,0x003d881 },
{ 0x3138233,0x1f8eec3,0x2718bd6,0x1b09caa,0x2dd66b9,0x1bb222b,
0x1004072,0x1b73e3b,0x07208ed,0x03fc36c } },
/* 30 */
{ { 0x095d553,0x3e84053,0x0a8a749,0x3f575a0,0x3a44052,0x3ced59b,
0x3b4317f,0x03a8c60,0x13c8874,0x00c4ed4 },
{ 0x0d11549,0x0b8ab02,0x221cb40,0x02ed37b,0x2071ee1,0x1fc8c83,
0x3987dd4,0x27e049a,0x0f986f1,0x00b4eaf } },
/* 31 */
{ { 0x15581a2,0x2214060,0x11af4c2,0x1598c88,0x19a0a6d,0x32acba6,
0x3a7a0f0,0x2337c66,0x210ded9,0x0300dbe },
{ 0x1fbd009,0x3822eb0,0x181629a,0x2401b45,0x30b68b1,0x2e78363,
0x2b32779,0x006530b,0x2c4b6d4,0x029aca8 } },
/* 32 */
{ { 0x13549cf,0x0f943db,0x265ed43,0x1bfeb35,0x06f3369,0x3847f2d,
0x1bfdacc,0x26181a5,0x252af7c,0x02043b8 },
{ 0x159bb2c,0x143f85c,0x357b654,0x2f9d62c,0x2f7dfbe,0x1a7fa9c,
0x057e74d,0x05d14ac,0x17a9273,0x035215c } },
/* 33 */
{ { 0x0cb5a98,0x106a2bc,0x10bf117,0x24c7cc4,0x3d3da8f,0x2ce0ab7,
0x14e2cba,0x1813866,0x1a72f9a,0x01a9811 },
{ 0x2b2411d,0x3034fe8,0x16e0170,0x0f9443a,0x0be0eb8,0x2196cf3,
0x0c9f738,0x15e40ef,0x0faf9e1,0x034f917 } },
/* 34 */
{ { 0x03f7669,0x3da6efa,0x3d6bce1,0x209ca1d,0x109f8ae,0x09109e3,
0x08ae543,0x3067255,0x1dee3c2,0x0081dd5 },
{ 0x3ef1945,0x358765b,0x28c387b,0x3bec4b4,0x218813c,0x0b7d92a,
0x3cd1d67,0x2c0367e,0x2e57154,0x0123717 } },
/* 35 */
{ { 0x3e5a199,0x1e42ffd,0x0bb7123,0x33e6273,0x1e0efb8,0x294671e,
0x3a2bfe0,0x3d11709,0x2eddff6,0x03cbec2 },
{ 0x0b5025f,0x0255d7c,0x1f2241c,0x35d03ea,0x0550543,0x202fef4,
0x23c8ad3,0x354963e,0x015db28,0x0284fa4 } },
/* 36 */
{ { 0x2b65cbc,0x1e8d428,0x0226f9f,0x1c8a919,0x10b04b9,0x08fc1e8,
0x1ce241e,0x149bc99,0x2b01497,0x00afc35 },
{ 0x3216fb7,0x1374fd2,0x226ad3d,0x19fef76,0x0f7d7b8,0x1c21417,
0x37b83f6,0x3a27eba,0x25a162f,0x010aa52 } },
/* 37 */
{ { 0x2adf191,0x1ab42fa,0x28d7584,0x2409689,0x20f8a48,0x253707d,
0x2030504,0x378f7a1,0x169c65e,0x00b0b76 },
{ 0x3849c17,0x085c764,0x10dd6d0,0x2e87689,0x1460488,0x30e9521,
0x10c7063,0x1b6f120,0x21f42c5,0x03d0dfe } },
/* 38 */
{ { 0x20f7dab,0x035c512,0x29ac6aa,0x24c5ddb,0x20f0497,0x17ce5e1,
0x00a050f,0x1eaa14b,0x3335470,0x02abd16 },
{ 0x18d364a,0x0df0cf0,0x316585e,0x018f925,0x0d40b9b,0x17b1511,
0x1716811,0x1caf3d0,0x10df4f2,0x0337d8c } },
/* 39 */
{ { 0x2a8b7ef,0x0f188e3,0x2287747,0x06216f0,0x008e935,0x2f6a38d,
0x1567722,0x0bfc906,0x0bada9e,0x03c3402 },
{ 0x014d3b1,0x099c749,0x2a76291,0x216c067,0x3b37549,0x14ef2f6,
0x21b96d4,0x1ee2d71,0x2f5ca88,0x016f570 } },
/* 40 */
{ { 0x09a3154,0x3d1a7bd,0x2e9aef0,0x255b8ac,0x03e85a5,0x2a492a7,
0x2aec1ea,0x11c6516,0x3c8a09e,0x02a84b7 },
{ 0x1f69f1d,0x09c89d3,0x1e7326f,0x0b28bfd,0x0e0e4c8,0x1ea7751,
0x18ce73b,0x2a406e7,0x273e48c,0x01b00db } },
/* 41 */
{ { 0x36e3138,0x2b84a83,0x345a5cf,0x00096b4,0x16966ef,0x159caf1,
0x13c64b4,0x2f89226,0x25896af,0x00a4bfd },
{ 0x2213402,0x1435117,0x09fed52,0x09d0e4b,0x0f6580e,0x2871cba,
0x3b397fd,0x1c9d825,0x090311b,0x0191383 } },
/* 42 */
{ { 0x07153f0,0x1087869,0x18c9e1e,0x1e64810,0x2b86c3b,0x0175d9c,
0x3dce877,0x269de4e,0x393cab7,0x03c96b9 },
{ 0x1869d0c,0x06528db,0x02641f3,0x209261b,0x29d55c8,0x25ba517,
0x3b5ea30,0x028f927,0x25313db,0x00e6e39 } },
/* 43 */
{ { 0x2fd2e59,0x150802d,0x098f377,0x19a4957,0x135e2c0,0x38a95ce,
0x1ab21a0,0x36c1b67,0x32f0f19,0x00e448b },
{ 0x3cad53c,0x3387800,0x17e3cfb,0x03f9970,0x3225b2c,0x2a84e1d,
0x3af1d29,0x3fe35ca,0x2f8ce80,0x0237a02 } },
/* 44 */
{ { 0x07bbb76,0x3aa3648,0x2758afb,0x1f085e0,0x1921c7e,0x3010dac,
0x22b74b1,0x230137e,0x1062e36,0x021c652 },
{ 0x3993df5,0x24a2ee8,0x126ab5f,0x2d7cecf,0x0639d75,0x16d5414,
0x1aa78a8,0x3f78404,0x26a5b74,0x03f0c57 } },
/* 45 */
{ { 0x0d6ecfa,0x3f506ba,0x3f86561,0x3d86bb1,0x15f8c44,0x2491d07,
0x052a7b4,0x2422261,0x3adee38,0x039b529 },
{ 0x193c75d,0x14bb451,0x1162605,0x293749c,0x370a70d,0x2e8b1f6,
0x2ede937,0x2b95f4a,0x39a9be2,0x00d77eb } },
/* 46 */
{ { 0x2736636,0x15bf36a,0x2b7e6b9,0x25eb8b2,0x209f51d,0x3cd2659,
0x10bf410,0x034afec,0x3d71c83,0x0076971 },
{ 0x0ce6825,0x07920cf,0x3c3b5c4,0x23fe55c,0x015ad11,0x08c0dae,
0x0552c7f,0x2e75a8a,0x0fddbf4,0x01c1df0 } },
/* 47 */
{ { 0x2b9661c,0x0ffe351,0x3d71bf6,0x1ac34b3,0x3a1dfd3,0x211fe3d,
0x33e140a,0x3f9100d,0x32ee50e,0x014ea18 },
{ 0x16d8051,0x1bfda1a,0x068a097,0x2571d3d,0x1daec0c,0x39389af,
0x194dc35,0x3f3058a,0x36d34e1,0x000a329 } },
/* 48 */
{ { 0x09877ee,0x351f73f,0x0002d11,0x0420074,0x2c8b362,0x130982d,
0x02c1175,0x3c11b40,0x0d86962,0x001305f },
{ 0x0daddf5,0x2f4252c,0x15c06d9,0x1d49339,0x1bea235,0x0b680ed,
0x3356e67,0x1d1d198,0x1e9fed9,0x03dee93 } },
/* 49 */
{ { 0x3e1263f,0x2fe8d3a,0x3ce6d0d,0x0d5c6b9,0x3557637,0x0a9bd48,
0x0405538,0x0710749,0x2005213,0x038c7e5 },
{ 0x26b6ec6,0x2e485ba,0x3c44d1b,0x0b9cf0b,0x037a1d1,0x27428a5,
0x0e7eac8,0x351ef04,0x259ce34,0x02a8e98 } },
/* 50 */
{ { 0x2f3dcd3,0x3e77d4d,0x3360fbc,0x1434afd,0x36ceded,0x3d413d6,
0x1710fad,0x36bb924,0x1627e79,0x008e637 },
{ 0x109569e,0x1c168db,0x3769cf4,0x2ed4527,0x0ea0619,0x17d80d3,
0x1c03773,0x18843fe,0x1b21c04,0x015c5fd } },
/* 51 */
{ { 0x1dd895e,0x08a7248,0x04519fe,0x001030a,0x18e5185,0x358dfb3,
0x13d2391,0x0a37be8,0x0560e3c,0x019828b },
{ 0x27fcbd0,0x2a22bb5,0x30969cc,0x1e03aa7,0x1c84724,0x0ba4ad3,
0x32f4817,0x0914cca,0x14c4f52,0x01893b9 } },
/* 52 */
{ { 0x097eccc,0x1273936,0x00aa095,0x364fe62,0x04d49d1,0x10e9f08,
0x3c24230,0x3ef01c8,0x2fb92bd,0x013ce4a },
{ 0x1e44fd9,0x27e3e9f,0x2156696,0x3915ecc,0x0b66cfb,0x1a3af0f,
0x2fa8033,0x0e6736c,0x177ccdb,0x0228f9e } },
/* 53 */
{ { 0x2c4b125,0x06207c1,0x0a8cdde,0x003db8f,0x1ae34e3,0x31e84fa,
0x2999de5,0x11013bd,0x02370c2,0x00e2234 },
{ 0x0f91081,0x200d591,0x1504762,0x1857c05,0x23d9fcf,0x0cb34db,
0x27edc86,0x08cd860,0x2471810,0x029798b } },
/* 54 */
{ { 0x3acd6c8,0x097b8cb,0x3c661a8,0x15152f2,0x1699c63,0x237e64c,
0x23edf79,0x16b7033,0x0e6466a,0x00b11da },
{ 0x0a64bc9,0x1bfe324,0x1f5cb34,0x08391de,0x0630a60,0x3017a21,
0x09d064b,0x14a8365,0x041f9e6,0x01ed799 } },
/* 55 */
{ { 0x128444a,0x2508b07,0x2a39216,0x362f84d,0x2e996c5,0x2c31ff3,
0x07afe5f,0x1d1288e,0x3cb0c8d,0x02e2bdc },
{ 0x38b86fd,0x3a0ea8c,0x1cff5fd,0x1629629,0x3fee3f1,0x02b250c,
0x2e8f6f2,0x0225727,0x15f7f3f,0x0280d8e } },
/* 56 */
{ { 0x10f7770,0x0f1aee8,0x0e248c7,0x20684a8,0x3a6f16d,0x06f0ae7,
0x0df6825,0x2d4cc40,0x301875f,0x012f8da },
{ 0x3b56dbb,0x1821ba7,0x24f8922,0x22c1f9e,0x0306fef,0x1b54bc8,
0x2ccc056,0x00303ba,0x2871bdc,0x0232f26 } },
/* 57 */
{ { 0x0dac4ab,0x0625730,0x3112e13,0x101c4bf,0x3a874a4,0x2873b95,
0x32ae7c6,0x0d7e18c,0x13e0c08,0x01139d5 },
{ 0x334002d,0x00fffdd,0x025c6d5,0x22c2cd1,0x19d35cb,0x3a1ce2d,
0x3702760,0x3f06257,0x03a5eb8,0x011c29a } },
/* 58 */
{ { 0x0513482,0x1d87724,0x276a81b,0x0a807a4,0x3028720,0x339cc20,
0x2441ee0,0x31bbf36,0x290c63d,0x0059041 },
{ 0x106a2ed,0x0d2819b,0x100bf50,0x114626c,0x1dd4d77,0x2e08632,
0x14ae72a,0x2ed3f64,0x1fd7abc,0x035cd1e } },
/* 59 */
{ { 0x2d4c6e5,0x3bec596,0x104d7ed,0x23d6c1b,0x0262cf0,0x15d72c5,
0x2d5bb18,0x199ac4b,0x1e30771,0x020591a },
{ 0x21e291e,0x2e75e55,0x1661d7a,0x08b0778,0x3eb9daf,0x0d78144,
0x1827eb1,0x0fe73d2,0x123f0dd,0x0028db7 } },
/* 60 */
{ { 0x1d5533c,0x34cb1d0,0x228f098,0x27a1a11,0x17c5f5a,0x0d26f44,
0x2228ade,0x2c460e6,0x3d6fdba,0x038cc77 },
{ 0x3cc6ed8,0x02ada1a,0x260e510,0x2f7bde8,0x37160c3,0x33a1435,
0x23d9a7b,0x0ce2641,0x02a492e,0x034ed1e } },
/* 61 */
{ { 0x3821f90,0x26dba3c,0x3aada14,0x3b59bad,0x292edd9,0x2804c45,
0x3669531,0x296f42e,0x35a4c86,0x01ca049 },
{ 0x3ff47e5,0x2163df4,0x2441503,0x2f18405,0x15e1616,0x37f66ec,
0x30f11a7,0x141658a,0x27ece14,0x00b018b } },
/* 62 */
{ { 0x159ac2e,0x3e65bc0,0x2713a76,0x0db2f6c,0x3281e77,0x2391811,
0x16d2880,0x1fbc4ab,0x1f92c4e,0x00a0a8d },
{ 0x0ce5cd2,0x152c7b0,0x02299c3,0x3244de7,0x2cf99ef,0x3a0b047,
0x2caf383,0x0aaf664,0x113554d,0x031c735 } },
/* 63 */
{ { 0x1b578f4,0x177a702,0x3a7a488,0x1638ebf,0x31884e2,0x2460bc7,
0x36b1b75,0x3ce8e3d,0x340cf47,0x03143d9 },
{ 0x34b68ea,0x12b7ccd,0x1fe2a9c,0x08da659,0x0a406f3,0x1694c14,
0x06a2228,0x16370be,0x3a72129,0x02e7b2c } },
/* 64 */
{ { 0x0f8b16a,0x21043bd,0x266a56f,0x3fb11ec,0x197241a,0x36721f0,
0x006b8e6,0x2ac6c29,0x202cd42,0x0200fcf },
{ 0x0dbec69,0x0c26a01,0x105f7f0,0x3dceeeb,0x3a83b85,0x363865f,
0x097273a,0x2b70718,0x00e5067,0x03025d1 } },
/* 65 */
{ { 0x379ab34,0x295bcb0,0x38d1846,0x22e1077,0x3a8ee06,0x1db1a3b,
0x3144591,0x07cc080,0x2d5915f,0x03c6bcc },
{ 0x175bd50,0x0dd4c57,0x27bc99c,0x2ebdcbd,0x3837cff,0x235dc8f,
0x13a4184,0x0722c18,0x130e2d4,0x008f43c } },
/* 66 */
{ { 0x01500d9,0x2adbb7d,0x2da8857,0x397f2fa,0x10d890a,0x25c9654,
0x3e86488,0x3eb754b,0x1d6c0a3,0x02c0a23 },
{ 0x10bcb08,0x083cc19,0x2e16853,0x04da575,0x271af63,0x2626a9d,
0x3520a7b,0x32348c7,0x24ff408,0x03ff4dc } },
/* 67 */
{ { 0x058e6cb,0x1a3992d,0x1d28539,0x080c5e9,0x2992dad,0x2a9d7d5,
0x14ae0b7,0x09b7ce0,0x34ad78c,0x03d5643 },
{ 0x30ba55a,0x092f4f3,0x0bae0fc,0x12831de,0x20fc472,0x20ed9d2,
0x29864f6,0x1288073,0x254f6f7,0x00635b6 } },
/* 68 */
{ { 0x1be5a2b,0x0f88975,0x33c6ed9,0x20d64d3,0x06fe799,0x0989bff,
0x1409262,0x085a90c,0x0d97990,0x0142eed },
{ 0x17ec63e,0x06471b9,0x0db2378,0x1006077,0x265422c,0x08db83d,
0x28099b0,0x1270d06,0x11801fe,0x00ac400 } },
/* 69 */
{ { 0x3391593,0x22d7166,0x30fcfc6,0x2896609,0x3c385f5,0x066b72e,
0x04f3aad,0x2b831c5,0x19983fb,0x0375562 },
{ 0x0b82ff4,0x222e39d,0x34c993b,0x101c79c,0x2d2e03c,0x0f00c8a,
0x3a9eaf4,0x1810669,0x151149d,0x039b931 } },
/* 70 */
{ { 0x29af288,0x1956ec7,0x293155f,0x193deb6,0x1647e1a,0x2ca0839,
0x297e4bc,0x15bfd0d,0x1b107ed,0x0147803 },
{ 0x31c327e,0x05a6e1d,0x02ad43d,0x02d2a5b,0x129cdb2,0x37ad1de,
0x3d51f53,0x245df01,0x2414982,0x0388bd0 } },
/* 71 */
{ { 0x35f1abb,0x17a3d18,0x0874cd4,0x2d5a14e,0x17edc0c,0x16a00d3,
0x072c1fb,0x1232725,0x33d52dc,0x03dc24d },
{ 0x0af30d6,0x259aeea,0x369c401,0x12bc4de,0x295bf5f,0x0d8711f,
0x26162a9,0x16c44e5,0x288e727,0x02f54b4 } },
/* 72 */
{ { 0x05fa877,0x1571ea7,0x3d48ab1,0x1c9f4e8,0x017dad6,0x0f46276,
0x343f9e7,0x1de990f,0x0e4c8aa,0x028343e },
{ 0x094f92d,0x3abf633,0x1b3a0bb,0x2f83137,0x0d818c8,0x20bae85,
0x0c65f8b,0x1a8008b,0x0c7946d,0x0295b1e } },
/* 73 */
{ { 0x1d09529,0x08e46c3,0x1fcf296,0x298f6b7,0x1803e0e,0x2d6fd20,
0x37351f5,0x0d9e8b1,0x1f8731a,0x0362fbf },
{ 0x00157f4,0x06750bf,0x2650ab9,0x35ffb23,0x2f51cae,0x0b522c2,
0x39cb400,0x191e337,0x0a5ce9f,0x021529a } },
/* 74 */
{ { 0x3506ea5,0x17d9ed8,0x0d66dc3,0x22693f8,0x19286c4,0x3a57353,
0x101d3bf,0x1aa54fc,0x20b9884,0x0172b3a },
{ 0x0eac44d,0x37d8327,0x1c3aa90,0x3d0d534,0x23db29a,0x3576eaf,
0x1d3de8a,0x3bea423,0x11235e4,0x039260b } },
/* 75 */
{ { 0x34cd55e,0x01288b0,0x1132231,0x2cc9a03,0x358695b,0x3e87650,
0x345afa1,0x01267ec,0x3f616b2,0x02011ad },
{ 0x0e7d098,0x0d6078e,0x0b70b53,0x237d1bc,0x0d7f61e,0x132de31,
0x1ea9ea4,0x2bd54c3,0x27b9082,0x03ac5f2 } },
/* 76 */
{ { 0x2a145b9,0x06d661d,0x31ec175,0x03f06f1,0x3a5cf6b,0x249c56e,
0x2035653,0x384c74f,0x0bafab5,0x0025ec0 },
{ 0x25f69e1,0x1b23a55,0x1199aa6,0x16ad6f9,0x077e8f7,0x293f661,
0x33ba11d,0x3327980,0x07bafdb,0x03e571d } },
/* 77 */
{ { 0x2bae45e,0x3c074ef,0x2955558,0x3c312f1,0x2a8ebe9,0x2f193f1,
0x3705b1d,0x360deba,0x01e566e,0x00d4498 },
{ 0x21161cd,0x1bc787e,0x2f87933,0x3553197,0x1328ab8,0x093c879,
0x17eee27,0x2adad1d,0x1236068,0x003be5c } },
/* 78 */
{ { 0x0ca4226,0x2633dd5,0x2c8e025,0x0e3e190,0x05eede1,0x1a385e4,
0x163f744,0x2f25522,0x1333b4f,0x03f05b6 },
{ 0x3c800ca,0x1becc79,0x2daabe9,0x0c499e2,0x1138063,0x3fcfa2d,
0x2244976,0x1e85cf5,0x2f1b95d,0x0053292 } },
/* 79 */
{ { 0x12f81d5,0x1dc6eaf,0x11967a4,0x1a407df,0x31a5f9d,0x2b67241,
0x18bef7c,0x08c7762,0x063f59c,0x01015ec },
{ 0x1c05c0a,0x360bfa2,0x1f85bff,0x1bc7703,0x3e4911c,0x0d685b6,
0x2fccaea,0x02c4cef,0x164f133,0x0070ed7 } },
/* 80 */
{ { 0x0ec21fe,0x052ffa0,0x3e825fe,0x1ab0956,0x3f6ce11,0x3d29759,
0x3c5a072,0x18ebe62,0x148db7e,0x03eb49c },
{ 0x1ab05b3,0x02dab0a,0x1ae690c,0x0f13894,0x137a9a8,0x0aab79f,
0x3dc875c,0x06a1029,0x1e39f0e,0x01dce1f } },
/* 81 */
{ { 0x16c0dd7,0x3b31269,0x2c741e9,0x3611821,0x2a5cffc,0x1416bb3,
0x3a1408f,0x311fa3d,0x1c0bef0,0x02cdee1 },
{ 0x00e6a8f,0x1adb933,0x0f23359,0x2fdace2,0x2fd6d4b,0x0e73bd3,
0x2453fac,0x0a356ae,0x2c8f9f6,0x02704d6 } },
/* 82 */
{ { 0x0e35743,0x28c80a1,0x0def32a,0x2c6168f,0x1320d6a,0x37c6606,
0x21b1761,0x2147ee0,0x21fc433,0x015c84d },
{ 0x1fc9168,0x36cda9c,0x003c1f0,0x1cd7971,0x15f98ba,0x1ef363d,
0x0ca87e3,0x046f7d9,0x3c9e6bb,0x0372eb0 } },
/* 83 */
{ { 0x118cbe2,0x3665a11,0x304ef01,0x062727a,0x3d242fc,0x11ffbaf,
0x3663c7e,0x1a189c9,0x09e2d62,0x02e3072 },
{ 0x0e1d569,0x162f772,0x0cd051a,0x322df62,0x3563809,0x047cc7a,
0x027fd9f,0x08b509b,0x3da2f94,0x01748ee } },
/* 84 */
{ { 0x1c8f8be,0x31ca525,0x22bf0a1,0x200efcd,0x02961c4,0x3d8f52b,
0x018403d,0x3a40279,0x1cb91ec,0x030427e },
{ 0x0945705,0x0257416,0x05c0c2d,0x25b77ae,0x3b9083d,0x2901126,
0x292b8d7,0x07b8611,0x04f2eee,0x026f0cd } },
/* 85 */
{ { 0x2913074,0x2b8d590,0x02b10d5,0x09d2295,0x255491b,0x0c41cca,
0x1ca665b,0x133051a,0x1525f1a,0x00a5647 },
{ 0x04f983f,0x3d6daee,0x04e1e76,0x1067d7e,0x1be7eef,0x02ea862,
0x00d4968,0x0ccb048,0x11f18ef,0x018dd95 } },
/* 86 */
{ { 0x22976cc,0x17c5395,0x2c38bda,0x3983bc4,0x222bca3,0x332a614,
0x3a30646,0x261eaef,0x1c808e2,0x02f6de7 },
{ 0x306a772,0x32d7272,0x2dcefd2,0x2abf94d,0x038f475,0x30ad76e,
0x23e0227,0x3052b0a,0x001add3,0x023ba18 } },
/* 87 */
{ { 0x0ade873,0x25a6069,0x248ccbe,0x13713ee,0x17ee9aa,0x28152e9,
0x2e28995,0x2a92cb3,0x17a6f77,0x024b947 },
{ 0x190a34d,0x2ebea1c,0x1ed1948,0x16fdaf4,0x0d698f7,0x32bc451,
0x0ee6e30,0x2aaab40,0x06f0a56,0x01460be } },
/* 88 */
{ { 0x24cc99c,0x1884b1e,0x1ca1fba,0x1a0f9b6,0x2ff609b,0x2b26316,
0x3b27cb5,0x29bc976,0x35d4073,0x024772a },
{ 0x3575a70,0x1b30f57,0x07fa01b,0x0e5be36,0x20cb361,0x26605cd,
0x1d4e8c8,0x13cac59,0x2db9797,0x005e833 } },
/* 89 */
{ { 0x36c8d3a,0x1878a81,0x124b388,0x0e4843e,0x1701aad,0x0ea0d76,
0x10eae41,0x37d0653,0x36c7f4c,0x00ba338 },
{ 0x37a862b,0x1cf6ac0,0x08fa912,0x2dd8393,0x101ba9b,0x0eebcb7,
0x2453883,0x1a3cfe5,0x2cb34f6,0x03d3331 } },
/* 90 */
{ { 0x1f79687,0x3d4973c,0x281544e,0x2564bbe,0x17c5954,0x171e34a,
0x231741a,0x3cf2784,0x0889a0d,0x02b036d },
{ 0x301747f,0x3f1c477,0x1f1386b,0x163bc5f,0x1592b93,0x332daed,
0x080e4f5,0x1d28b96,0x26194c9,0x0256992 } },
/* 91 */
{ { 0x15a4c93,0x07bf6b0,0x114172c,0x1ce0961,0x140269b,0x1b2c2eb,
0x0dfb1c1,0x019ddaa,0x0ba2921,0x008c795 },
{ 0x2e6d2dc,0x37e45e2,0x2918a70,0x0fce444,0x34d6aa6,0x396dc88,
0x27726b5,0x0c787d8,0x032d8a7,0x02ac2f8 } },
/* 92 */
{ { 0x1131f2d,0x2b43a63,0x3101097,0x38cec13,0x0637f09,0x17a69d2,
0x086196d,0x299e46b,0x0802cf6,0x03c6f32 },
{ 0x0daacb4,0x1a4503a,0x100925c,0x15583d9,0x23c4e40,0x1de4de9,
0x1cc8fc4,0x2c9c564,0x0695aeb,0x02145a5 } },
/* 93 */
{ { 0x1dcf593,0x17050fc,0x3e3bde3,0x0a6c062,0x178202b,0x2f7674f,
0x0dadc29,0x15763a7,0x1d2daad,0x023d9f6 },
{ 0x081ea5f,0x045959d,0x190c841,0x3a78d31,0x0e7d2dd,0x1414fea,
0x1d43f40,0x22d77ff,0x2b9c072,0x03e115c } },
/* 94 */
{ { 0x3af71c9,0x29e9c65,0x25655e1,0x111e9cd,0x3a14494,0x3875418,
0x34ae070,0x0b06686,0x310616b,0x03b7b89 },
{ 0x1734121,0x00d3d44,0x29f0b2f,0x1552897,0x31cac6e,0x1030bb3,
0x0148f3a,0x35fd237,0x29b44eb,0x027f49f } },
/* 95 */
{ { 0x2e2cb16,0x1d962bd,0x19b63cc,0x0b3f964,0x3e3eb7d,0x1a35560,
0x0c58161,0x3ce1d6a,0x3b6958f,0x029030b },
{ 0x2dcc158,0x3b1583f,0x30568c9,0x31957c8,0x27ad804,0x28c1f84,
0x3967049,0x37b3f64,0x3b87dc6,0x0266f26 } },
/* 96 */
{ { 0x27dafc6,0x2548764,0x0d1984a,0x1a57027,0x252c1fb,0x24d9b77,
0x1581a0f,0x1f99276,0x10ba16d,0x026af88 },
{ 0x0915220,0x2be1292,0x16c6480,0x1a93760,0x2fa7317,0x1a07296,
0x1539871,0x112c31f,0x25787f3,0x01e2070 } },
/* 97 */
{ { 0x0bcf3ff,0x266d478,0x34f6933,0x31449fd,0x00d02cb,0x340765a,
0x3465a2d,0x225023e,0x319a30e,0x00579b8 },
{ 0x20e05f4,0x35b834f,0x0404646,0x3710d62,0x3fad7bd,0x13e1434,
0x21c7d1c,0x1cb3af9,0x2cf1911,0x003957e } },
/* 98 */
{ { 0x0787564,0x36601be,0x1ce67e9,0x084c7a1,0x21a3317,0x2067a35,
0x0158cab,0x195ddac,0x1766fe9,0x035cf42 },
{ 0x2b7206e,0x20d0947,0x3b42424,0x03f1862,0x0a51929,0x38c2948,
0x0bb8595,0x2942d77,0x3748f15,0x0249428 } },
/* 99 */
{ { 0x2577410,0x3c23e2f,0x28c6caf,0x00d41de,0x0fd408a,0x30298e9,
0x363289e,0x2302fc7,0x082c1cc,0x01dd050 },
{ 0x30991cd,0x103e9ba,0x029605a,0x19927f7,0x0c1ca08,0x0c93f50,
0x28a3c7b,0x082e4e9,0x34d12eb,0x0232c13 } },
/* 100 */
{ { 0x106171c,0x0b4155a,0x0c3fb1c,0x336c090,0x19073e9,0x2241a10,
0x0e6b4fd,0x0ed476e,0x1ef4712,0x039390a },
{ 0x0ec36f4,0x3754f0e,0x2a270b8,0x007fd2d,0x0f9d2dc,0x1e6a692,
0x066e078,0x1954974,0x2ff3c6e,0x00def28 } },
/* 101 */
{ { 0x3562470,0x0b8f1f7,0x0ac94cd,0x28b0259,0x244f272,0x031e4ef,
0x2d5df98,0x2c8a9f1,0x2dc3002,0x016644f },
{ 0x350592a,0x0e6a0d5,0x1e027a1,0x2039e0f,0x399e01d,0x2817593,
0x0c0375e,0x3889b3e,0x24ab013,0x010de1b } },
/* 102 */
{ { 0x256b5a6,0x0ac3b67,0x28f9ff3,0x29b67f1,0x30750d9,0x25e11a9,
0x15e8455,0x279ebb0,0x298b7e7,0x0218e32 },
{ 0x2fc24b2,0x2b82582,0x28f22f5,0x2bd36b3,0x305398e,0x3b2e9e3,
0x365dd0a,0x29bc0ed,0x36a7b3a,0x007b374 } },
/* 103 */
{ { 0x05ff2f3,0x2b3589b,0x29785d3,0x300a1ce,0x0a2d516,0x0844355,
0x14c9fad,0x3ccb6b6,0x385d459,0x0361743 },
{ 0x0b11da3,0x002e344,0x18c49f7,0x0c29e0c,0x1d2c22c,0x08237b3,
0x2988f49,0x0f18955,0x1c3b4ed,0x02813c6 } },
/* 104 */
{ { 0x17f93bd,0x249323b,0x11f6087,0x174e4bd,0x3cb64ac,0x086dc6b,
0x2e330a8,0x142c1f2,0x2ea5c09,0x024acbb },
{ 0x1b6e235,0x3132521,0x00f085a,0x2a4a4db,0x1ab2ca4,0x0142224,
0x3aa6b3e,0x09db203,0x2215834,0x007b9e0 } },
/* 105 */
{ { 0x23e79f7,0x28b8039,0x1906a60,0x2cbce67,0x1f590e7,0x181f027,
0x21054a6,0x3854240,0x2d857a6,0x03cfcb3 },
{ 0x10d9b55,0x1443cfc,0x2648200,0x2b36190,0x09d2fcf,0x22f439f,
0x231aa7e,0x3884395,0x0543da3,0x003d5a9 } },
/* 106 */
{ { 0x043e0df,0x06ffe84,0x3e6d5b2,0x3327001,0x26c74b6,0x12a145e,
0x256ec0d,0x3898c69,0x3411969,0x02f63c5 },
{ 0x2b7494a,0x2eee1af,0x38388a9,0x1bd17ce,0x21567d4,0x13969e6,
0x3a12a7a,0x3e8277d,0x03530cc,0x00b4687 } },
/* 107 */
{ { 0x06508da,0x38e04d4,0x15a7192,0x312875e,0x3336180,0x2a6512c,
0x1b59497,0x2e91b37,0x25eb91f,0x02841e9 },
{ 0x394d639,0x0747143,0x37d7e6d,0x1d62962,0x08b4af3,0x34df287,
0x3c5584b,0x26bc869,0x20af87a,0x0060f5d } },
/* 108 */
{ { 0x1de59a4,0x1a5c443,0x2f8729d,0x01c3a2f,0x0f1ad8d,0x3cbaf9e,
0x1b49634,0x35d508a,0x39dc269,0x0075105 },
{ 0x390d30e,0x37033e0,0x110cb32,0x14c37a0,0x20a3b27,0x2f00ce6,
0x2f1dc52,0x34988c6,0x0c29606,0x01dc7e7 } },
/* 109 */
{ { 0x1040739,0x24f9de1,0x2939999,0x2e6009a,0x244539d,0x17e3f09,
0x00f6f2f,0x1c63b3d,0x2310362,0x019109e },
{ 0x1428aa8,0x3cb61e1,0x09a84f4,0x0ffafed,0x07b7adc,0x08f406b,
0x1b2c6df,0x035b480,0x3496ae9,0x012766d } },
/* 110 */
{ { 0x35d1099,0x2362f10,0x1a08cc7,0x13a3a34,0x12adbcd,0x32da290,
0x02e2a02,0x151140b,0x01b3f60,0x0240df6 },
{ 0x34c7b61,0x2eb09c1,0x172e7cd,0x2ad5eff,0x2fe2031,0x25b54d4,
0x0cec965,0x18e7187,0x26a7cc0,0x00230f7 } },
/* 111 */
{ { 0x2d552ab,0x374083d,0x01f120f,0x2601736,0x156baff,0x04d44a4,
0x3b7c3e9,0x1acbc1b,0x0424579,0x031a425 },
{ 0x1231bd1,0x0eba710,0x020517b,0x21d7316,0x21eac6e,0x275a848,
0x0837abf,0x0eb0082,0x302cafe,0x00fe8f6 } },
/* 112 */
{ { 0x1058880,0x28f9941,0x03f2d75,0x3bd90e5,0x17da365,0x2ac9249,
0x07861cf,0x023fd05,0x1b0fdb8,0x031712f },
{ 0x272b56b,0x04f8d2c,0x043a735,0x25446e4,0x1c8327e,0x221125a,
0x0ce37df,0x2dad7f6,0x39446c2,0x00b55b6 } },
/* 113 */
{ { 0x346ac6b,0x05e0bff,0x2425246,0x0981e8b,0x1d19f79,0x2692378,
0x3ea3c40,0x2e90beb,0x19de503,0x003d5af },
{ 0x05cda49,0x353b44d,0x299d137,0x3f205bc,0x2821158,0x3ad0d00,
0x06a54aa,0x2d7c79f,0x39d1173,0x01000ee } },
/* 114 */
{ { 0x0803387,0x3a06268,0x14043b8,0x3d4e72f,0x1ece115,0x0a1dfc8,
0x17208dd,0x0be790a,0x122a07f,0x014dd95 },
{ 0x0a4182d,0x202886a,0x1f79a49,0x1e8c867,0x0a2bbd0,0x28668b5,
0x0d0a2e1,0x115259d,0x3586c5d,0x01e815b } },
/* 115 */
{ { 0x18a2a47,0x2c95627,0x2773646,0x1230f7c,0x15b5829,0x2fc354e,
0x2c000ea,0x099d547,0x2f17a1a,0x01df520 },
{ 0x3853948,0x06f6561,0x3feeb8a,0x2f5b3ef,0x3a6f817,0x01a0791,
0x2ec0578,0x2c392ad,0x12b2b38,0x0104540 } },
/* 116 */
{ { 0x1e28ced,0x0fc3d1b,0x2c473c7,0x1826c4f,0x21d5da7,0x39718e4,
0x38ce9e6,0x0251986,0x172fbea,0x0337c11 },
{ 0x053c3b0,0x0f162db,0x043c1cb,0x04111ee,0x297fe3c,0x32e5e03,
0x2b8ae12,0x0c427ec,0x1da9738,0x03b9c0f } },
/* 117 */
{ { 0x357e43a,0x054503f,0x11b8345,0x34ec6e0,0x2d44660,0x3d0ae61,
0x3b5dff8,0x33884ac,0x09da162,0x00a82b6 },
{ 0x3c277ba,0x129a51a,0x027664e,0x1530507,0x0c788c9,0x2afd89d,
0x1aa64cc,0x1196450,0x367ac2b,0x0358b42 } },
/* 118 */
{ { 0x0054ac4,0x1761ecb,0x378839c,0x167c9f7,0x2570058,0x0604a35,
0x37cbf3b,0x0909bb7,0x3f2991c,0x02ce688 },
{ 0x0b16ae5,0x212857c,0x351b952,0x2c684db,0x30c6a05,0x09c01e0,
0x23c137f,0x1331475,0x092c067,0x0013b40 } },
/* 119 */
{ { 0x2e90393,0x0617466,0x24e61f4,0x0a528f5,0x03047b4,0x2153f05,
0x0001a69,0x30e1eb8,0x3c10177,0x0282a47 },
{ 0x22c831e,0x28fc06b,0x3e16ff0,0x208adc9,0x0bb76ae,0x28c1d6d,
0x12c8a15,0x031063c,0x1889ed2,0x002133e } },
/* 120 */
{ { 0x0a6becf,0x14277bf,0x3328d98,0x201f7fe,0x12fceae,0x1de3a2e,
0x0a15c44,0x3ddf976,0x1b273ab,0x0355e55 },
{ 0x1b5d4f1,0x369e78c,0x3a1c210,0x12cf3e9,0x3aa52f0,0x309f082,
0x112089d,0x107c753,0x24202d1,0x023853a } },
/* 121 */
{ { 0x2897042,0x140d17c,0x2c4aeed,0x07d0d00,0x18d0533,0x22f7ec8,
0x19c194c,0x3456323,0x2372aa4,0x0165f86 },
{ 0x30bd68c,0x1fb06b3,0x0945032,0x372ac09,0x06d4be0,0x27f8fa1,
0x1c8d7ac,0x137a96e,0x236199b,0x0328fc0 } },
/* 122 */
{ { 0x170bd20,0x2842d58,0x1de7592,0x3c5b4fd,0x20ea897,0x12cab78,
0x363ff14,0x01f928c,0x17e309c,0x02f79ff },
{ 0x0f5432c,0x2edb4ae,0x044b516,0x32f810d,0x2210dc1,0x23e56d6,
0x301e6ff,0x34660f6,0x10e0a7d,0x02d88eb } },
/* 123 */
{ { 0x0c7b65b,0x2f59d58,0x2289a75,0x2408e92,0x1ab8c55,0x1ec99e5,
0x220fd0d,0x04defe0,0x24658ec,0x035aa8b },
{ 0x138bb85,0x2f002d4,0x295c10a,0x08760ce,0x28c31d1,0x1c0a8cb,
0x0ff00b1,0x144eac9,0x2e02dcc,0x0044598 } },
/* 124 */
{ { 0x3b42b87,0x050057b,0x0dff781,0x1c06db1,0x1bd9f5d,0x1f5f04a,
0x2cccd7a,0x143e19b,0x1cb94b7,0x036cfb8 },
{ 0x34837cf,0x3cf6c3c,0x0d4fb26,0x22ee55e,0x1e7eed1,0x315995f,
0x2cdf937,0x1a96574,0x0425220,0x0221a99 } },
/* 125 */
{ { 0x1b569ea,0x0d33ed9,0x19c13c2,0x107dc84,0x2200111,0x0569867,
0x2dc85da,0x05ef22e,0x0eb018a,0x029c33d },
{ 0x04a6a65,0x3e5eba3,0x378f224,0x09c04d0,0x036e5cf,0x3df8258,
0x3a609e4,0x1eddef8,0x2abd174,0x02a91dc } },
/* 126 */
{ { 0x2a60cc0,0x1d84c5e,0x115f676,0x1840da0,0x2c79163,0x2f06ed6,
0x198bb4b,0x3e5d37b,0x1dc30fa,0x018469b },
{ 0x15ee47a,0x1e32f30,0x16a530e,0x2093836,0x02e8962,0x3767b62,
0x335adf3,0x27220db,0x2f81642,0x0173ffe } },
/* 127 */
{ { 0x37a99cd,0x1533fe6,0x05a1c0d,0x27610f1,0x17bf3b9,0x0b1ce78,
0x0a908f6,0x265300e,0x3237dc1,0x01b969a },
{ 0x3a5db77,0x2d15382,0x0d63ef8,0x1feb3d8,0x0b7b880,0x19820de,
0x11c0c67,0x2af3396,0x38d242d,0x0120688 } },
/* 128 */
{ { 0x1d0b34a,0x05ef00d,0x00a7e34,0x1ae0c9f,0x1440b38,0x300d8b4,
0x37262da,0x3e50e3e,0x14ce0cd,0x00b1044 },
{ 0x195a0b1,0x173bc6b,0x03622ba,0x2a19f55,0x1c09b37,0x07921b2,
0x16cdd20,0x24a5c9b,0x2bf42ff,0x00811de } },
/* 129 */
{ { 0x0d65dbf,0x145cf06,0x1ad82f7,0x038ce7b,0x077bf94,0x33c4007,
0x22d26bd,0x25ad9c0,0x09ac773,0x02b1990 },
{ 0x2261cc3,0x2ecdbf1,0x3e908b0,0x3246439,0x0213f7b,0x1179b04,
0x01cebaa,0x0be1595,0x175cc12,0x033a39a } },
/* 130 */
{ { 0x00a67d2,0x086d06f,0x248a0f1,0x0291134,0x362d476,0x166d1cd,
0x044f1d6,0x2d2a038,0x365250b,0x0023f78 },
{ 0x08bf287,0x3b0f6a1,0x1d6eace,0x20b4cda,0x2c2a621,0x0912520,
0x02dfdc9,0x1b35cd6,0x3d2565d,0x00bdf8b } },
/* 131 */
{ { 0x3770fa7,0x2e4b6f0,0x03f9ae4,0x170de41,0x1095e8d,0x1dd845c,
0x334e9d1,0x00ab953,0x12e9077,0x03196fa },
{ 0x2fd0a40,0x228c0fd,0x384b275,0x38ef339,0x3e7d822,0x3e5d9ef,
0x24f5854,0x0ece9eb,0x247d119,0x012ffe3 } },
/* 132 */
{ { 0x0ff1480,0x07487c0,0x1b16cd4,0x1f41d53,0x22ab8fb,0x2f83cfa,
0x01d2efb,0x259f6b2,0x2e65772,0x00f9392 },
{ 0x05303e6,0x23cdb4f,0x23977e1,0x12e4898,0x03bd999,0x0c930f0,
0x170e261,0x180a27b,0x2fd58ec,0x014e22b } },
/* 133 */
{ { 0x25d7713,0x0c5fad7,0x09daad1,0x3b9d779,0x109b985,0x1d3ec98,
0x35bc4fc,0x2f838cb,0x0d14f75,0x0173e42 },
{ 0x2657b12,0x10d4423,0x19e6760,0x296e5bb,0x2bfd421,0x25c3330,
0x29f51f8,0x0338838,0x24060f0,0x029a62e } },
/* 134 */
{ { 0x3748fec,0x2c5a1bb,0x2cf973d,0x289fa74,0x3e6e755,0x38997bf,
0x0b6544c,0x2b6358c,0x38a7aeb,0x02c50bb },
{ 0x3d5770a,0x06be7c5,0x012fad3,0x19cb2cd,0x266af3b,0x3ccd677,
0x160d1bd,0x141d5af,0x2965851,0x034625a } },
/* 135 */
{ { 0x3c41c08,0x255eacc,0x22e1ec5,0x2b151a3,0x087de94,0x311cbdb,
0x016b73a,0x368e462,0x20b7981,0x0099ec3 },
{ 0x262b988,0x1539763,0x21e76e5,0x15445b4,0x1d8ddc7,0x34a9be6,
0x10faf03,0x24e4d18,0x07aa111,0x02d538a } },
/* 136 */
{ { 0x38a876b,0x048ad45,0x04b40a0,0x3fc2144,0x251ff96,0x13ca7dd,
0x0b31ab1,0x3539814,0x28b5f87,0x0212aec },
{ 0x270790a,0x350e7e0,0x346bd5e,0x276178f,0x22d6cb5,0x3078884,
0x355c1b6,0x15901d7,0x3671765,0x03950db } },
/* 137 */
{ { 0x286e8d5,0x2409788,0x13be53f,0x2d21911,0x0353c95,0x10238e8,
0x32f5bde,0x3a67b60,0x28b5b9c,0x001013d },
{ 0x381e8e5,0x0cef7a9,0x2f5bcad,0x06058f0,0x33cdf50,0x04672a8,
0x1769600,0x31c055d,0x3df0ac1,0x00e9098 } },
/* 138 */
{ { 0x2eb596d,0x197b326,0x12b4c29,0x39c08f2,0x101ea03,0x3804e58,
0x04b4b62,0x28d9d1c,0x13f905e,0x0032a3f },
{ 0x11b2b61,0x08e9095,0x0d06925,0x270e43f,0x21eb7a8,0x0e4a98f,
0x31d2be0,0x030cf9f,0x2644ddb,0x025b728 } },
/* 139 */
{ { 0x07510af,0x2ed0e8e,0x2a01203,0x2a2a68d,0x0846fea,0x3e540de,
0x3a57702,0x1677348,0x2123aad,0x010d8f8 },
{ 0x0246a47,0x0e871d0,0x124dca4,0x34b9577,0x2b362b8,0x363ebe5,
0x3086045,0x26313e6,0x15cd8bb,0x0210384 } },
/* 140 */
{ { 0x023e8a7,0x0817884,0x3a0bf12,0x3376371,0x3c808a8,0x18e9777,
0x12a2721,0x35b538a,0x2bd30de,0x017835a },
{ 0x0fc0f64,0x1c8709f,0x2d8807a,0x0743957,0x242eec0,0x347e76c,
0x27bef91,0x289689a,0x0f42945,0x01f7a92 } },
/* 141 */
{ { 0x1060a81,0x3dbc739,0x1615abd,0x1cbe3e5,0x3e79f9c,0x1ab09a2,
0x136c540,0x05b473f,0x2beebfd,0x02af0a8 },
{ 0x3e2eac7,0x19be474,0x04668ac,0x18f4b74,0x36f10ba,0x0a0b4c6,
0x10e3770,0x3bf059e,0x3946c7e,0x013a8d4 } },
/* 142 */
{ { 0x266309d,0x28be354,0x1a3eed8,0x3020651,0x10a51c6,0x1e31770,
0x0af45a5,0x3ff0f3b,0x2891c94,0x00e9db9 },
{ 0x17b0d0f,0x33a291f,0x0a5f9aa,0x25a3d61,0x2963ace,0x39a5fef,
0x230c724,0x1919146,0x10a465e,0x02084a8 } },
/* 143 */
{ { 0x3ab8caa,0x31870f3,0x2390ef7,0x2103850,0x218eb8e,0x3a5ccf2,
0x1dff677,0x2c59334,0x371599c,0x02a9f2a },
{ 0x0837bd1,0x3249cef,0x35d702f,0x3430dab,0x1c06407,0x108f692,
0x221292f,0x05f0c5d,0x073fe06,0x01038e0 } },
/* 144 */
{ { 0x3bf9b7c,0x2020929,0x30d0f4f,0x080fef8,0x3365d23,0x1f3e738,
0x3e53209,0x1549afe,0x300b305,0x038d811 },
{ 0x0c6c2c7,0x2e6445b,0x3ee64dc,0x022e932,0x0726837,0x0deb67b,
0x1ed4346,0x3857f73,0x277a3de,0x01950b5 } },
/* 145 */
{ { 0x36c377a,0x0adb41e,0x08be3f3,0x11e40d1,0x36cb038,0x036a2bd,
0x3dd3a82,0x1bc875b,0x2ee09bb,0x02994d2 },
{ 0x035facf,0x05e0344,0x07e630a,0x0ce772d,0x335e55a,0x111fce4,
0x250fe1c,0x3bc89ba,0x32fdc9a,0x03cf2d9 } },
/* 146 */
{ { 0x355fd83,0x1c67f8e,0x1d10eb3,0x1b21d77,0x0e0d7a4,0x173a9e1,
0x2c9fa90,0x1c39cce,0x22eaae8,0x01f2bea },
{ 0x153b338,0x0534107,0x26c69b8,0x283be1f,0x3e0acc0,0x059cac3,
0x13d1081,0x148bbee,0x3c1b9bd,0x002aac4 } },
/* 147 */
{ { 0x2681297,0x3389e34,0x146addc,0x2c6d425,0x2cb350e,0x1986abc,
0x0431737,0x04ba4b7,0x2028470,0x012e469 },
{ 0x2f8ddcf,0x3c4255c,0x1af4dcf,0x07a6a44,0x208ebf6,0x0dc90c3,
0x34360ac,0x072ad23,0x0537232,0x01254d3 } },
/* 148 */
{ { 0x07b7e9d,0x3df5c7c,0x116f83d,0x28c4f35,0x3a478ef,0x3011fb8,
0x2f264b6,0x317b9e3,0x04fd65a,0x032bd1b },
{ 0x2aa8266,0x3431de4,0x04bba04,0x19a44da,0x0edf454,0x392c5ac,
0x265168a,0x1dc3d5b,0x25704c6,0x00533a7 } },
/* 149 */
{ { 0x25e8f91,0x1178fa5,0x2492994,0x2eb2c3c,0x0d3aca1,0x0322828,
0x1cc70f9,0x269c74c,0x0a53e4c,0x006edc2 },
{ 0x18bdd7a,0x2a79a55,0x26b1d5c,0x0200628,0x0734a05,0x3273c7b,
0x13aa714,0x0040ac2,0x2f2da30,0x03e7449 } },
/* 150 */
{ { 0x3f9563e,0x2f29eab,0x14a0749,0x3fad264,0x1dd077a,0x3d7c59c,
0x3a0311b,0x331a789,0x0b9729e,0x0201ebf },
{ 0x1b08b77,0x2a4cdf2,0x3e387f8,0x21510f1,0x286c3a7,0x1dbf62e,
0x3afa594,0x3363217,0x0d16568,0x01d46b7 } },
/* 151 */
{ { 0x0715c0d,0x28e2d04,0x17f78ae,0x1c63dda,0x1d113ea,0x0fefc1b,
0x1eab149,0x1d0fd99,0x0682537,0x00a7b11 },
{ 0x10bebbc,0x11c672d,0x14223d9,0x2ff9141,0x1399ee5,0x34b7b6c,
0x0d5b3a8,0x01df643,0x0e392a4,0x03fe4dc } },
/* 152 */
{ { 0x2b75b65,0x0b5a6f1,0x11c559a,0x3549999,0x24188f8,0x37a75f4,
0x29f33e3,0x34068a2,0x38ba2a9,0x025dd91 },
{ 0x29af2c7,0x0988b64,0x0923885,0x1b539a4,0x1334f5d,0x226947a,
0x2cc7e5a,0x20beb39,0x13fac2f,0x01d298c } },
/* 153 */
{ { 0x35f079c,0x137f76d,0x2fbbb2f,0x254638d,0x185b07c,0x1f34db7,
0x2cfcf0e,0x218f46d,0x2150ff4,0x02add6f },
{ 0x33fc9b7,0x0d9f005,0x0fd081b,0x0834965,0x2b90a74,0x102448d,
0x3dbf03c,0x167d857,0x02e0b44,0x013afab } },
/* 154 */
{ { 0x09f2c53,0x317f9d7,0x1411eb6,0x0463aba,0x0d25220,0x256b176,
0x087633f,0x2bff322,0x07b2c1b,0x037e662 },
{ 0x10aaecb,0x23bb4a1,0x2272bb7,0x06c075a,0x09d4918,0x0736f2b,
0x0dd511b,0x101625e,0x0a7779f,0x009ec10 } },
/* 155 */
{ { 0x33b2eb2,0x0176dfd,0x2118904,0x022386c,0x2e0df85,0x2588c9f,
0x1b71525,0x28fd540,0x137e4cf,0x02ce4f7 },
{ 0x3d75165,0x0c39ecf,0x3554a12,0x30af34c,0x2d66344,0x3ded408,
0x36f1be0,0x0d065b0,0x012d046,0x0025623 } },
/* 156 */
{ { 0x2601c3b,0x1824fc0,0x335fe08,0x3e33d70,0x0fb0252,0x252bfca,
0x1cf2808,0x1922e55,0x1a9db9f,0x020721e },
{ 0x2f56c51,0x39a1f31,0x218c040,0x1a4fc5d,0x3fed471,0x0164d4e,
0x388a419,0x06f1113,0x0f55fc1,0x03e8352 } },
/* 157 */
{ { 0x1608e4d,0x3872778,0x022cbc6,0x044d60a,0x3010dda,0x15fb0b5,
0x37ddc11,0x19f5bda,0x156b6a3,0x023a838 },
{ 0x383b3b4,0x1380bc8,0x353ca35,0x250fc07,0x169966b,0x3780f29,
0x36632b2,0x2d6b13f,0x124fa00,0x00fd6ae } },
/* 158 */
{ { 0x1739efb,0x2ec3656,0x2c0d337,0x3d39faf,0x1c751b0,0x04699f4,
0x252dd64,0x095b8b6,0x0872b74,0x022f1da },
{ 0x2d3d253,0x38edca0,0x379fa5b,0x287d635,0x3a9f679,0x059d9ee,
0x0ac168e,0x3cd3e87,0x19060fc,0x02ce1bc } },
/* 159 */
{ { 0x3edcfc2,0x0f04d4b,0x2f0d31f,0x1898be2,0x25396bf,0x15ca230,
0x02b4eae,0x2713668,0x0f71b06,0x0132d18 },
{ 0x38095ea,0x1ed34d6,0x3603ae6,0x165bf01,0x192bbf8,0x1852859,
0x075f66b,0x1488f85,0x10895ef,0x014b035 } },
/* 160 */
{ { 0x1339848,0x3084385,0x0c8d231,0x3a1c1de,0x0e87a28,0x255b85c,
0x1de6616,0x2702e74,0x1382bb0,0x012b0f2 },
{ 0x198987d,0x381545a,0x34d619b,0x312b827,0x18b2376,0x28fe4cf,
0x20b7651,0x017d077,0x0c7e397,0x00e0365 } },
/* 161 */
{ { 0x1542e75,0x0d56aa0,0x39b701a,0x287b806,0x396c724,0x0935c21,
0x3a29776,0x0debdac,0x171de26,0x00b38f8 },
{ 0x1d5bc1a,0x3fad27d,0x22b5cfe,0x1f89ddf,0x0a65560,0x144dd5b,
0x2aac2f9,0x139353f,0x0520b62,0x00b9b36 } },
/* 162 */
{ { 0x031c31d,0x16552e3,0x1a0c368,0x0016fc8,0x168533d,0x171e7b2,
0x17626e7,0x275502f,0x14742c6,0x03285dd },
{ 0x2d2dbb2,0x3b6bffd,0x1d18cc6,0x2f45d2a,0x0fd0d8c,0x2915e3a,
0x1e8793a,0x0b39a1d,0x3139cab,0x02a5da9 } },
/* 163 */
{ { 0x3fb353d,0x147c6e4,0x3a720a6,0x22d5ff3,0x1d75cab,0x06c54a0,
0x08cfa73,0x12666aa,0x3170a1f,0x021c829 },
{ 0x13e1b90,0x3a34dda,0x1fc38c3,0x02c5bdb,0x2d345dc,0x14aa1d0,
0x28d00ab,0x224f23a,0x329c769,0x025c67b } },
/* 164 */
{ { 0x0e35909,0x3bb6356,0x0116820,0x370cf77,0x29366d8,0x3881409,
0x3999d06,0x013075f,0x176e157,0x02941ca },
{ 0x0e70b2e,0x28dfab1,0x2a8a002,0x15da242,0x084dcf6,0x116ca97,
0x31bf186,0x1dc9735,0x09df7b7,0x0264e27 } },
/* 165 */
{ { 0x2da7a4b,0x3023c9e,0x1366238,0x00ff4e2,0x03abe9d,0x19bd44b,
0x272e897,0x20b91ad,0x2aa202c,0x02a2201 },
{ 0x380184e,0x08112b4,0x0b85660,0x31049aa,0x3a8cb78,0x36113c5,
0x1670c0a,0x373f9e7,0x3fb4738,0x00010ef } },
/* 166 */
{ { 0x2d5192e,0x26d770d,0x32af8d5,0x34d1642,0x1acf885,0x05805e0,
0x166d0a1,0x1219a0d,0x301ba6c,0x014bcfb },
{ 0x2dcb64d,0x19cca83,0x379f398,0x08e01a0,0x10a482c,0x0103cc2,
0x0be5fa7,0x1f9d45b,0x1899ef2,0x00ca5af } },
/* 167 */
{ { 0x14d81d7,0x2aea251,0x1b3c476,0x3bd47ae,0x29eade7,0x0715e61,
0x1a21cd8,0x1c7a586,0x2bfaee5,0x00ee43f },
{ 0x096f7cb,0x0c08f95,0x1bc4939,0x361fed4,0x255be41,0x26fad73,
0x31dd489,0x02c600f,0x29d9f81,0x01ba201 } },
/* 168 */
{ { 0x03ea1db,0x1eac46d,0x1292ce3,0x2a54967,0x20a7ff1,0x3e13c61,
0x1b02218,0x2b44e14,0x3eadefa,0x029c88a },
{ 0x30a9144,0x31e3b0a,0x19c5a2a,0x147cbe9,0x05a0240,0x051f38e,
0x11eca56,0x31a4247,0x123bc2a,0x02fa535 } },
/* 169 */
{ { 0x3226ce7,0x1251782,0x0b7072f,0x11e59fa,0x2b8afd7,0x169b18f,
0x2a46f18,0x31d9bb7,0x2fe9be8,0x01de0b7 },
{ 0x1b38626,0x34aa90f,0x3ad1760,0x21ddbd9,0x3460ae7,0x1126736,
0x1b86fc5,0x0b92cd0,0x167a289,0x000e0e1 } },
/* 170 */
{ { 0x1ec1a0f,0x36bbf5e,0x1c972d8,0x3f73ace,0x13bbcd6,0x23d86a5,
0x175ffc5,0x2d083d5,0x2c4adf7,0x036f661 },
{ 0x1f39eb7,0x2a20505,0x176c81a,0x3d6e636,0x16ee2fc,0x3cbdc5f,
0x25475dc,0x2ef4151,0x3c46860,0x0238934 } },
/* 171 */
{ { 0x2587390,0x3639526,0x0588749,0x13c32fb,0x212bb19,0x09660f1,
0x207da4b,0x2bf211b,0x1c4407b,0x01506a6 },
{ 0x24c8842,0x105a498,0x05ffdb2,0x0ab61b0,0x26044c1,0x3dff3d8,
0x1d14b44,0x0d74716,0x049f57d,0x030024b } },
/* 172 */
{ { 0x32e61ef,0x31d70f7,0x35cad3c,0x320b86c,0x07e8841,0x027ca7d,
0x2d30d19,0x2513718,0x2347286,0x01d7901 },
{ 0x3c237d0,0x107f16e,0x01c9e7d,0x3c3b13c,0x0c9537b,0x20af54d,
0x051a162,0x2161a47,0x258c784,0x016df2d } },
/* 173 */
{ { 0x228ead1,0x29c2122,0x07f6964,0x023f4ed,0x1802dc5,0x19f96ce,
0x24bfd17,0x25e866b,0x2ba8df0,0x01eb84f },
{ 0x2dd384e,0x05bbe3a,0x3f06fd2,0x366dacb,0x30361a2,0x2f36d7c,
0x0b98784,0x38ff481,0x074e2a8,0x01e1f60 } },
/* 174 */
{ { 0x17fbb1c,0x0975add,0x1debc5e,0x2cb2880,0x3e47bdd,0x3488cff,
0x15e9a36,0x2121129,0x0199ef2,0x017088a },
{ 0x0315250,0x352a162,0x17c1773,0x0ae09c2,0x321b21a,0x3bd74cf,
0x3c4ea1d,0x3cac2ad,0x3abbaf0,0x039174d } },
/* 175 */
{ { 0x0511c8a,0x3c78d0a,0x2cd3d2d,0x322f729,0x3ebb229,0x09f0e69,
0x0a71a76,0x2e74d5e,0x12284df,0x03b5ef0 },
{ 0x3dea561,0x0a9b7e4,0x0ed1cf2,0x237523c,0x05443f1,0x2eb48fa,
0x3861405,0x1b49f62,0x0c945ca,0x02ab25f } },
/* 176 */
{ { 0x16bd00a,0x13a9d28,0x3cc1eb5,0x2b7d702,0x2d839e9,0x3e6ff01,
0x2bb7f11,0x3713824,0x3b31163,0x00c63e5 },
{ 0x30d7138,0x0316fb0,0x0220ecc,0x08eaf0c,0x244e8df,0x0088d81,
0x37972fb,0x3fd34ae,0x2a19a84,0x03e907e } },
/* 177 */
{ { 0x2642269,0x0b65d29,0x03bd440,0x33a6ede,0x3c81814,0x2507982,
0x0d38e47,0x3a788e6,0x32c1d26,0x00e2eda },
{ 0x2577f87,0x392895a,0x3e1cc64,0x14f7047,0x08b52d2,0x08a01ca,
0x336abf6,0x00697fc,0x105ce76,0x0253742 } },
/* 178 */
{ { 0x293f92a,0x33df737,0x3315156,0x32e26d7,0x0a01333,0x26579d4,
0x004df9c,0x0aba409,0x067d25c,0x02481de },
{ 0x3f39d44,0x1c78042,0x13d7e24,0x0825aed,0x35f2c90,0x3270f63,
0x04b7b35,0x3ad4531,0x28bd29b,0x0207a10 } },
/* 179 */
{ { 0x077199f,0x270aeb1,0x0dd96dd,0x3b9ad7b,0x28cb8ee,0x3903f43,
0x37db3fe,0x292c62b,0x362dbbf,0x006e52a },
{ 0x247f143,0x0362cf3,0x216344f,0x3f18fd1,0x351e623,0x31664e0,
0x0f270fc,0x243bbc6,0x2280555,0x001a8e3 } },
/* 180 */
{ { 0x3355b49,0x2c04e6c,0x399b2e5,0x182d3af,0x020e265,0x09a7cf7,
0x0ffa6bd,0x353e302,0x02083d9,0x029ecdb },
{ 0x33e8830,0x0570e86,0x1c0b64d,0x386a27e,0x0d5fcea,0x0b45a4c,
0x2ee4a2e,0x0a8833f,0x2b4a282,0x02f9531 } },
/* 181 */
{ { 0x191167c,0x36cf7e3,0x225ed6c,0x1e79e99,0x0517c3f,0x11ab1fd,
0x05648f3,0x08aedc4,0x1abeae0,0x02fcc29 },
{ 0x3828a68,0x1e16fa4,0x30368e7,0x0c9fcfb,0x25161c3,0x24851ac,
0x1b5feb5,0x344eb84,0x0de2732,0x0347208 } },
/* 182 */
{ { 0x038b363,0x384d1e4,0x2519043,0x151ac17,0x158c11f,0x009b2b4,
0x257abe6,0x2368d3f,0x3ed68a1,0x02df45e },
{ 0x29c2559,0x2962478,0x3d8444c,0x1d96fff,0x04f7a03,0x1391a52,
0x0de4af7,0x3319126,0x15e6412,0x00e65ff } },
/* 183 */
{ { 0x3d61507,0x1d1a0a2,0x0d2af20,0x354d299,0x329e132,0x2a28578,
0x2ddfb08,0x04fa3ff,0x1293c6c,0x003bae2 },
{ 0x3e259f8,0x1a68fa9,0x3e67e9b,0x39b44f9,0x1ce1db7,0x347e9a1,
0x3318f6a,0x2dbbc9d,0x2f8c922,0x008a245 } },
/* 184 */
{ { 0x212ab5b,0x2b896c2,0x0136959,0x07e55ef,0x0cc1117,0x05b8ac3,
0x18429ed,0x025fa01,0x11d6e93,0x03b016b },
{ 0x03f3708,0x2e96fab,0x1d77157,0x0d4c2d6,0x131baf9,0x0608d39,
0x3552371,0x06cdd1e,0x1567ff1,0x01f4c50 } },
/* 185 */
{ { 0x2dfefab,0x270173d,0x37077bd,0x1a372cd,0x1be2f22,0x28e2ee5,
0x3ead973,0x35e8f94,0x2fc9bc1,0x03a7399 },
{ 0x36a02a1,0x2855d9b,0x00ed75a,0x37d8398,0x138c087,0x233706e,
0x147f346,0x01947e2,0x3017228,0x0365942 } },
/* 186 */
{ { 0x2057e60,0x2d31296,0x25e4504,0x2fa37bc,0x1cbccc3,0x1f0732f,
0x3532081,0x2de8a98,0x19a804e,0x005359a },
{ 0x31f411a,0x2a10576,0x369c2c8,0x02fe035,0x109fbaf,0x30bddeb,
0x1eef901,0x1662ad3,0x0410d43,0x01bd31a } },
/* 187 */
{ { 0x2c24a96,0x1b7d3a5,0x19a3872,0x217f2f6,0x2534dbc,0x2cab8c2,
0x066ef28,0x26aecf1,0x0fd6118,0x01310d4 },
{ 0x055b8da,0x1fdc5be,0x38a1296,0x25118f0,0x341a423,0x2ba4cd0,
0x3e1413e,0x062d70d,0x2425a31,0x029c9b4 } },
/* 188 */
{ { 0x08c1086,0x1acfba5,0x22e1dae,0x0f72f4e,0x3f1de50,0x0f408bc,
0x35ed3f0,0x3ce48fc,0x282cc6c,0x004d8e7 },
{ 0x1afaa86,0x24e3ef3,0x22589ac,0x3ec9952,0x1f45bc5,0x14144ca,
0x23b26e4,0x0d68c65,0x1e1c1a3,0x032a4d9 } },
/* 189 */
{ { 0x03b2d20,0x16b1d53,0x241b361,0x05e4138,0x1742a54,0x32741c7,
0x0521c4c,0x1ca96c2,0x034970b,0x02738a7 },
{ 0x13e0ad6,0x207dcdb,0x034c8cc,0x27bcbe1,0x18060da,0x33a18b6,
0x2d1d1a6,0x2be60d7,0x3d7ab42,0x012312a } },
/* 190 */
{ { 0x0c7485a,0x06c3310,0x0dbfd22,0x2ef949d,0x0ead455,0x098f4ba,
0x3c76989,0x0cf2d24,0x032f67b,0x01e005f },
{ 0x30cb5ee,0x0d5da64,0x0ed2b9d,0x2503102,0x1c0d14e,0x1cbc693,
0x37bf552,0x07013e2,0x054de5c,0x014f341 } },
/* 191 */
{ { 0x128ccac,0x1617e97,0x346ebcd,0x158016d,0x25f823e,0x34048ea,
0x39f0a1c,0x3ea3df1,0x1c1d3d7,0x03ba919 },
{ 0x151803b,0x01967c1,0x2f70781,0x27df39a,0x06c0b59,0x24a239c,
0x15a7702,0x2464d06,0x2a47ae6,0x006db90 } },
/* 192 */
{ { 0x27d04c3,0x024df3d,0x38112e8,0x38a27ba,0x01e312b,0x0965358,
0x35d8879,0x2f4f55a,0x214187f,0x0008936 },
{ 0x05fe36f,0x2ee18c3,0x1f5f87a,0x1813bd4,0x0580f3c,0x0ed0a7b,
0x0fb1bfb,0x3fcce59,0x2f042bf,0x01820e3 } },
/* 193 */
{ { 0x20bbe99,0x32cbc9f,0x39ee432,0x3cc12a8,0x37bda44,0x3ea4e40,
0x097c7a9,0x0590d7d,0x2022d33,0x018dbac },
{ 0x3ae00aa,0x3439864,0x2d2ffcf,0x3f8c6b9,0x0875a00,0x3e4e407,
0x3658a29,0x22eb3d0,0x2b63921,0x022113b } },
/* 194 */
{ { 0x33bae58,0x05c749a,0x1f3e114,0x1c45f8e,0x27db3df,0x06a3ab6,
0x37bc7f8,0x1e27b34,0x3dc51fb,0x009eea0 },
{ 0x3f54de5,0x3d0e7fe,0x1a71a7d,0x02ed7f8,0x0727703,0x2ca5e92,
0x2e8e35d,0x292ad0b,0x13487f3,0x02b6d8b } },
/* 195 */
{ { 0x175df2a,0x05a28a8,0x32e99b1,0x13d8630,0x2082aa0,0x11ac245,
0x24f2e71,0x322cb27,0x17675e7,0x02e643f },
{ 0x1f37313,0x2765ad3,0x0789082,0x1e742d0,0x11c2055,0x2021dc4,
0x09ae4a7,0x346359b,0x2f94d10,0x0205c1f } },
/* 196 */
{ { 0x3d6ff96,0x1f2ac80,0x336097d,0x3f03610,0x35b851b,0x010b6d2,
0x0823c4d,0x2a9709a,0x2ead5a8,0x00de4b6 },
{ 0x01afa0b,0x0621965,0x3671528,0x1050b60,0x3f3e9e7,0x2f93829,
0x0825275,0x006e85f,0x35e94b0,0x016af58 } },
/* 197 */
{ { 0x2c4927c,0x3ea1382,0x0f23727,0x0d69f23,0x3e38860,0x2b72837,
0x3cd5ea4,0x2d84292,0x321846a,0x016656f },
{ 0x29dfa33,0x3e182e0,0x018be90,0x2ba563f,0x2caafe2,0x218c0d9,
0x3baf447,0x1047a6c,0x0a2d483,0x01130cb } },
/* 198 */
{ { 0x00ed80c,0x2a5fc79,0x0a82a74,0x2c4c74b,0x15f938c,0x30b5ab6,
0x32124b7,0x295314f,0x2fb8082,0x007c858 },
{ 0x20b173e,0x19f315c,0x12f97e4,0x198217c,0x040e8a6,0x3275977,
0x2bc20e4,0x01f2633,0x02bc3e9,0x023c750 } },
/* 199 */
{ { 0x3c4058a,0x24be73e,0x16704f5,0x2d8a4bd,0x3b15e14,0x3076315,
0x1cfe37b,0x36fe715,0x343926e,0x02c6603 },
{ 0x2c76b09,0x0cf824c,0x3f7898c,0x274cec1,0x11df527,0x18eed18,
0x08ead48,0x23915bc,0x19b3744,0x00a0a2b } },
/* 200 */
{ { 0x0cf4ac5,0x1c8b131,0x0afb696,0x0ff7799,0x2f5ac1a,0x022420c,
0x11baa2e,0x2ce4015,0x1275a14,0x0125cfc },
{ 0x22eac5d,0x360cd4c,0x3568e59,0x3d42f66,0x35e07ee,0x09620e4,
0x36720fa,0x22b1eac,0x2d0db16,0x01b6b23 } },
/* 201 */
{ { 0x1a835ef,0x1516bbb,0x2d51f7b,0x3487443,0x14aa113,0x0dd06c2,
0x1a65e01,0x379300d,0x35920b9,0x012c8fb },
{ 0x04c7341,0x2eda00f,0x3c37e82,0x1b4fd62,0x0d45770,0x1478fba,
0x127863a,0x26939cd,0x134ddf4,0x01375c5 } },
/* 202 */
{ { 0x1476cd9,0x1119ca5,0x325bbf9,0x0bf8c69,0x0648d07,0x312d9f8,
0x01c8b8f,0x136ec51,0x0002f4a,0x03f4c5c },
{ 0x195d0e1,0x10ffd22,0x29aa1cb,0x3443bdc,0x276e695,0x05e6260,
0x15f9764,0x3cd9783,0x18c9569,0x0053eb1 } },
/* 203 */
{ { 0x312ae18,0x280197c,0x3fc9ad9,0x303f324,0x251958d,0x29f4a11,
0x2142408,0x3694366,0x25136ab,0x03b5f1d },
{ 0x1d4abbc,0x1c3c689,0x13ea462,0x3cfc684,0x39b5dd8,0x2d4654b,
0x09b0755,0x27d4f18,0x3f74d2e,0x03fbf2d } },
/* 204 */
{ { 0x2119185,0x2525eae,0x1ba4bd0,0x0c2ab11,0x1d54e8c,0x294845e,
0x2479dea,0x3602d24,0x17e87e0,0x0060069 },
{ 0x0afffb0,0x34fe37f,0x1240073,0x02eb895,0x06cf33c,0x2d7f7ef,
0x1d763b5,0x04191e0,0x11e1ead,0x027e3f0 } },
/* 205 */
{ { 0x269544c,0x0e85c57,0x3813158,0x19fc12d,0x20eaf85,0x1e2930c,
0x22a8fd2,0x1a6a478,0x09d3d3a,0x02a74e0 },
{ 0x1a2da3b,0x30b0b16,0x0847936,0x3d86257,0x138ccbc,0x0f5421a,
0x25244e6,0x23bdd79,0x1aee117,0x00c01ae } },
/* 206 */
{ { 0x1eead28,0x07cac32,0x1fbc0bb,0x17627d3,0x17eef63,0x0b3a24e,
0x0757fdb,0x3dd841d,0x3d745f8,0x002ae17 },
{ 0x25b4549,0x29f24cf,0x2f21ecd,0x1725e48,0x04be2bb,0x10ee010,
0x1a1274b,0x10b0898,0x27511e9,0x02c48b5 } },
/* 207 */
{ { 0x2a5ae7a,0x181ef99,0x0be33be,0x3e9dab7,0x101e703,0x3adb971,
0x1043014,0x2ebb2be,0x1c1097d,0x027d667 },
{ 0x3f250ed,0x16dc603,0x20dc6d7,0x1d0d268,0x38eb915,0x02c89e8,
0x1605a41,0x12de109,0x0e08a29,0x01f554a } },
/* 208 */
{ { 0x0c26def,0x163d988,0x2d1ef0f,0x3a960ac,0x1025585,0x0738e20,
0x27d79b0,0x05cc3ef,0x201303f,0x00a333a },
{ 0x1644ba5,0x2af345e,0x30b8d1d,0x3a01bff,0x31fc643,0x1acf85e,
0x0a76fc6,0x04efe98,0x348a1d0,0x03062eb } },
/* 209 */
{ { 0x1c4216d,0x18e3217,0x02ac34e,0x19c8185,0x200c010,0x17d4192,
0x13a1719,0x165af51,0x09db7a9,0x0277be0 },
{ 0x3ab8d2c,0x2190b99,0x22b641e,0x0cd88de,0x3b42404,0x1310862,
0x106a6d6,0x23395f5,0x0b06880,0x000d5fe } },
/* 210 */
{ { 0x0d2cc88,0x36f9913,0x339d8e9,0x237c2e3,0x0cc61c2,0x34c2832,
0x309874c,0x2621d28,0x2dd1b48,0x0392806 },
{ 0x17cd8f9,0x07bab3d,0x0c482ed,0x0faf565,0x31b767d,0x2f4bde1,
0x295c717,0x330c29c,0x179ce10,0x0119b5f } },
/* 211 */
{ { 0x1ada2c7,0x0c624a7,0x227d47d,0x30e3e6a,0x14fa0a6,0x0829678,
0x24fd288,0x2b46a43,0x122451e,0x0319ca9 },
{ 0x186b655,0x01f3217,0x0af1306,0x0efe6b5,0x2f0235d,0x1c45ca9,
0x2086805,0x1d44e66,0x0faf2a6,0x0178f59 } },
/* 212 */
{ { 0x33b4416,0x10431e6,0x2d99aa6,0x217aac9,0x0cd8fcf,0x2d95a9d,
0x3ff74ad,0x10bf17a,0x295eb8e,0x01b229e },
{ 0x02a63bd,0x182e9ec,0x004710c,0x00e2e3c,0x06b2f23,0x04b642c,
0x2c37383,0x32a4631,0x022ad82,0x00d22b9 } },
/* 213 */
{ { 0x0cda2fb,0x1d198d7,0x26d27f4,0x286381c,0x022acca,0x24ac7c8,
0x2df7824,0x0b4ba16,0x1e0d9ef,0x03041d3 },
{ 0x29a65b3,0x0f3912b,0x151bfcf,0x2b0175c,0x0fd71e4,0x39aa5e2,
0x311f50c,0x13ff351,0x3dbc9e5,0x03eeb7e } },
/* 214 */
{ { 0x0a99363,0x0fc7348,0x2775171,0x23db3c8,0x2b91565,0x134d66c,
0x0175cd2,0x1bf365a,0x2b48371,0x02dfe5d },
{ 0x16dbf74,0x2389357,0x2f36575,0x3f5c70e,0x38d23ba,0x090f7f8,
0x3477600,0x3201523,0x32ecafc,0x03d3506 } },
/* 215 */
{ { 0x1abd48d,0x073ca3f,0x38a451f,0x0d8cb01,0x1ce81be,0x05c51ba,
0x0e29741,0x03c41ab,0x0eae016,0x0060209 },
{ 0x2e58358,0x1da62d9,0x2358038,0x14b39b2,0x1635687,0x39079b1,
0x380e345,0x1b49608,0x23983cf,0x019f97d } },
/* 216 */
{ { 0x34899ef,0x332e373,0x04c0f89,0x3c27aed,0x1949015,0x09663b2,
0x2f9276b,0x07f1951,0x09a04c1,0x027fbde },
{ 0x3d2a071,0x19fb3d4,0x1b096d3,0x1fe9146,0x3b10e1a,0x0478bbb,
0x2b3fb06,0x1388329,0x181a99c,0x02f2030 } },
/* 217 */
{ { 0x1eb82e6,0x14dbe39,0x3920972,0x31fd5b2,0x21a484f,0x02d7697,
0x0e21715,0x37c431e,0x2629f8c,0x01249c3 },
{ 0x26b50ad,0x26deefa,0x0ffc1a3,0x30688e2,0x39a0284,0x041c65e,
0x03eb178,0x0bdfd50,0x2f96137,0x034bb94 } },
/* 218 */
{ { 0x0e0362a,0x334a162,0x194dd37,0x29e3e97,0x2442fa8,0x10d2949,
0x3836e5a,0x2dccebf,0x0bee5ab,0x037ed1e },
{ 0x33eede6,0x3c739d9,0x2f04a91,0x350ad6c,0x3a5390a,0x14c368b,
0x26f7bf5,0x11ce979,0x0b408df,0x0366850 } },
/* 219 */
{ { 0x28ea498,0x0886d5b,0x2e090e0,0x0a4d58f,0x2623478,0x0d74ab7,
0x2b83913,0x12c6b81,0x18d623f,0x01d8301 },
{ 0x198aa79,0x26d6330,0x3a7f0b8,0x34bc1ea,0x2f74890,0x378955a,
0x204110f,0x0102538,0x02d8f19,0x01c5066 } },
/* 220 */
{ { 0x14b0f45,0x2838cd3,0x14e16f0,0x0e0e4aa,0x2d9280b,0x0f18757,
0x3324c6b,0x1391ceb,0x1ce89d5,0x00ebe74 },
{ 0x0930371,0x3de6048,0x3097fd8,0x1308705,0x3eda266,0x3108c26,
0x1545dcd,0x1f7583a,0x1c37395,0x02c7e05 } },
/* 221 */
{ { 0x1fec44a,0x2a9e3a2,0x0caf84f,0x11cf2a9,0x0c8c2ae,0x06da989,
0x1c807dc,0x3c149a4,0x1141543,0x02906bb },
{ 0x15ffe04,0x0d4e65f,0x2e20424,0x37d896d,0x18bacb2,0x1e05ddd,
0x1660be8,0x183be17,0x1dd86fb,0x035ba70 } },
/* 222 */
{ { 0x2853264,0x0ba5fb1,0x0a0b3aa,0x2df88c1,0x2771533,0x23aba6f,
0x112bb7b,0x3e3086e,0x210ae9b,0x027271b },
{ 0x030b74c,0x0269678,0x1e90a23,0x135a98c,0x24ed749,0x126de7c,
0x344b23a,0x186da27,0x19640fa,0x0159af5 } },
/* 223 */
{ { 0x18061f3,0x3004630,0x3c70066,0x34df20f,0x1190b25,0x1c9cc91,
0x1fc8e02,0x0d17bc1,0x390f525,0x033cb1c },
{ 0x0eb30cf,0x2f3ad04,0x303aa09,0x2e835dd,0x1cfd2eb,0x143fc95,
0x02c43a1,0x025e7a1,0x3558aa2,0x000bd45 } },
/* 224 */
{ { 0x1db7d07,0x3bde52b,0x1500396,0x1089115,0x20b4fc7,0x1e2a8f3,
0x3f8eacc,0x365f7eb,0x1a5e8d4,0x0053a6b },
{ 0x37079e2,0x120284b,0x000edaa,0x33792c2,0x145baa3,0x20e055f,
0x365e2d7,0x26ba005,0x3ab8e9d,0x0282b53 } },
/* 225 */
{ { 0x2653618,0x2dd8852,0x2a5f0bf,0x0f0c7aa,0x2187281,0x1252757,
0x13e7374,0x3b47855,0x0b86e56,0x02f354c },
{ 0x2e9c47b,0x2fa14cc,0x19ab169,0x3fad401,0x0dc2776,0x24afeed,
0x3a97611,0x0d07736,0x3cf6979,0x02424a0 } },
/* 226 */
{ { 0x2e81a13,0x000c91d,0x123967b,0x265885c,0x29bee1a,0x0cb8675,
0x2d361bd,0x1526823,0x3c9ace1,0x00d7bad },
{ 0x24e5bdc,0x02b969f,0x2c6e128,0x34edb3b,0x12dcd2c,0x3899af0,
0x24224c6,0x3a1914b,0x0f4448a,0x026a2cb } },
/* 227 */
{ { 0x1d03b59,0x1c6fc82,0x32abf64,0x28ed96b,0x1c90e62,0x2f57bb2,
0x3ff168e,0x04de7fd,0x0f4d449,0x01af6d8 },
{ 0x255bc30,0x2bfaf22,0x3fe0dad,0x0584025,0x1c79ead,0x3078ef7,
0x2197414,0x022a50b,0x0fd94ba,0x0007b0f } },
/* 228 */
{ { 0x09485c2,0x09dfaf7,0x10c7ba6,0x1e48bec,0x248cc9a,0x028a362,
0x21d60f7,0x193d93d,0x1c04754,0x0346b2c },
{ 0x2f36612,0x240ac49,0x0d8bd26,0x13b8186,0x259c3a4,0x020d5fb,
0x38a8133,0x09b0937,0x39d4056,0x01f7341 } },
/* 229 */
{ { 0x05a4b48,0x1f534fc,0x07725ce,0x148dc8c,0x2adcd29,0x04aa456,
0x0f79718,0x066e346,0x189377d,0x002fd4d },
{ 0x068ea73,0x336569b,0x184d35e,0x32a08e9,0x3c7f3bb,0x11ce9c8,
0x3674c6f,0x21bf27e,0x0d9e166,0x034a2f9 } },
/* 230 */
{ { 0x0fa8e4b,0x2e6418e,0x18fc5d2,0x1ba24ff,0x0559f18,0x0dbedbf,
0x2de2aa4,0x22338e9,0x3aa510f,0x035d801 },
{ 0x23a4988,0x02aad94,0x02732d1,0x111d374,0x0b455cf,0x0d01c9e,
0x067082a,0x2ec05fd,0x368b303,0x03cad4b } },
/* 231 */
{ { 0x035b4ca,0x1fabea6,0x1cbc0d5,0x3f2ed9a,0x02d2232,0x1990c66,
0x2eb680c,0x3b4ea3b,0x18ecc5a,0x03636fa },
{ 0x1a02709,0x26f8ff1,0x1fa8cba,0x397d6e8,0x230be68,0x043aa14,
0x3d43cdf,0x25c17fa,0x3a3ee55,0x0380564 } },
/* 232 */
{ { 0x275a0a6,0x16bd43a,0x0033d3e,0x2b15e16,0x2512226,0x005d901,
0x26d50fd,0x3bc19bf,0x3b1aeb8,0x02bfb01 },
{ 0x0bb0a31,0x26559e0,0x1aae7fb,0x330dcc2,0x16f1af3,0x06afce2,
0x13a15a0,0x2ff7645,0x3546e2d,0x029c6e4 } },
/* 233 */
{ { 0x0f593d2,0x384b806,0x122bbf8,0x0a281e0,0x1d1a904,0x2e93cab,
0x0505db0,0x08f6454,0x05c6285,0x014e880 },
{ 0x3f2b935,0x22d8e79,0x161a07c,0x16b060a,0x02bff97,0x146328b,
0x3ceea77,0x238f61a,0x19b3d58,0x02fd1f4 } },
/* 234 */
{ { 0x17665d5,0x259e9f7,0x0de5672,0x15cbcbd,0x34e3030,0x035240f,
0x0005ae8,0x286d851,0x07f39c9,0x000070b },
{ 0x1efc6d6,0x2a0051a,0x2724143,0x2a9ef1e,0x0c810bd,0x1e05429,
0x25670ba,0x2e66d7d,0x0e786ff,0x03f6b7e } },
/* 235 */
{ { 0x3c00785,0x232e23f,0x2b67fd3,0x244ed23,0x077fa75,0x3cda3ef,
0x14d055b,0x0f25011,0x24d5aa4,0x00ea0e3 },
{ 0x297bb9a,0x198ca4f,0x14d9561,0x18d1076,0x39eb933,0x2b6caa0,
0x1591a60,0x0768d45,0x257873e,0x00f36e0 } },
/* 236 */
{ { 0x1e77eab,0x0502a5f,0x0109137,0x0350592,0x3f7e1c5,0x3ac7437,
0x2dcad2c,0x1fee9d8,0x089f1f5,0x0169833 },
{ 0x0d45673,0x0d8e090,0x065580b,0x065644f,0x11b82be,0x3592dd0,
0x3284b8d,0x23f0015,0x16fdbfd,0x0248bfd } },
/* 237 */
{ { 0x1a129a1,0x1977bb2,0x0e041b2,0x15f30a1,0x0a5b1ce,0x3afef8f,
0x380c46c,0x3358810,0x27df6c5,0x01ca466 },
{ 0x3b90f9a,0x3d14ea3,0x031b298,0x02e2390,0x2d719c0,0x25bc615,
0x2c0e777,0x0226b8c,0x3803624,0x0179e45 } },
/* 238 */
{ { 0x363cdfb,0x1bb155f,0x24fd5c1,0x1c7c72b,0x28e6a35,0x18165f2,
0x226bea5,0x0beaff3,0x371e24c,0x0138294 },
{ 0x1765357,0x29034e9,0x22b4276,0x11035ce,0x23c89af,0x074468c,
0x3370ae4,0x013bae3,0x018d566,0x03d7fde } },
/* 239 */
{ { 0x209df21,0x0f8ff86,0x0e47fbf,0x23b99ba,0x126d5d2,0x2722405,
0x16bd0a2,0x1799082,0x0e9533f,0x039077c },
{ 0x3ba9e3f,0x3f6902c,0x1895305,0x3ac9813,0x3f2340c,0x3c0d9f1,
0x26e1927,0x0557c21,0x16eac4f,0x023b75f } },
/* 240 */
{ { 0x3fc8ff3,0x0770382,0x342fc9a,0x0afa4db,0x314efd8,0x328e07b,
0x016f7cc,0x3ba599c,0x1caed8a,0x0050cb0 },
{ 0x0b23c26,0x2120a5c,0x3273ec6,0x1cc1cd6,0x2a64fe8,0x2bbc3d6,
0x09f6e5e,0x34b1b8e,0x00b5ac8,0x032bbd2 } },
/* 241 */
{ { 0x1315922,0x1725e1d,0x0ca5524,0x1c4c18f,0x3d82951,0x193bcb2,
0x0e60d0b,0x388dbcf,0x37e8efa,0x0342e85 },
{ 0x1b3af60,0x26ba3ec,0x220e53a,0x394f4b6,0x01a796a,0x3e7bbca,
0x163605d,0x2b85807,0x17c1c54,0x03cc725 } },
/* 242 */
{ { 0x1cc4597,0x1635492,0x2028c0f,0x2c2eb82,0x2dc5015,0x0d2a052,
0x05fc557,0x1f0ebbf,0x0cb96e1,0x0004d01 },
{ 0x1a824bf,0x3896172,0x2ed7b29,0x178007a,0x0d59318,0x07bda2b,
0x2ee6826,0x0f9b235,0x04b9193,0x01bcddf } },
/* 243 */
{ { 0x0333fd2,0x0eeb46a,0x15b89f9,0x00968aa,0x2a89302,0x2bdd6b3,
0x1e5037e,0x2541884,0x24ed2d0,0x01b6e8f },
{ 0x04399cd,0x3be6334,0x3adea48,0x1bb9adc,0x31811c6,0x05fb2bc,
0x360752c,0x3d29dcb,0x3423bec,0x03c4f3c } },
/* 244 */
{ { 0x119e2eb,0x2e7b02a,0x0f68cee,0x257d8b0,0x183a9a1,0x2ae88a6,
0x3a3bb67,0x2eb4f3e,0x1a9274b,0x0320fea },
{ 0x2fa1ce0,0x346c2d8,0x2fbf0d7,0x3d4d063,0x0e58b60,0x09c1bc1,
0x28ef9e5,0x09a0efe,0x0f45d70,0x02d275c } },
/* 245 */
{ { 0x2d5513b,0x31d443e,0x1e2d914,0x3b2c5d4,0x105f32e,0x27ee756,
0x050418d,0x3c73db6,0x1bb0c30,0x01673eb },
{ 0x1cb7fd6,0x1eb08d5,0x26a3e16,0x2e20810,0x0249367,0x029e219,
0x2ec58c9,0x12d9fab,0x362354a,0x016eafc } },
/* 246 */
{ { 0x2424865,0x260747b,0x177f37c,0x1e3cb95,0x08b0028,0x2783016,
0x2970f1b,0x323c1c0,0x2a79026,0x0186231 },
{ 0x0f244da,0x26866f4,0x087306f,0x173ec20,0x31ecced,0x3c84d8d,
0x070f9b9,0x2e764d5,0x075df50,0x0264ff9 } },
/* 247 */
{ { 0x32c3609,0x0c737e6,0x14ea68e,0x300b11b,0x184eb19,0x29dd440,
0x09ec1a9,0x185adeb,0x0664c80,0x0207dd9 },
{ 0x1fbe978,0x30a969d,0x33561d7,0x34fc60e,0x36743fe,0x00774af,
0x0d1f045,0x018360e,0x12a5fe9,0x01592a0 } },
/* 248 */
{ { 0x2817d1d,0x2993d3e,0x2e0f7a5,0x112faa0,0x255f968,0x355fe6a,
0x3f5a0fc,0x075b2d7,0x3cf00e5,0x0089afc },
{ 0x32833cf,0x06a7e4b,0x09a8d6d,0x1693d3e,0x320a0a3,0x3cfdfdd,
0x136c498,0x1e0d845,0x347ff25,0x01a1de7 } },
/* 249 */
{ { 0x3043d08,0x030705c,0x20fa79b,0x1d07f00,0x0a54467,0x29b49b4,
0x367e289,0x0b82f4d,0x0d1eb09,0x025ef2c },
{ 0x32ed3c3,0x1baaa3c,0x3c482ab,0x146ca06,0x3c8a4f1,0x3e85e3c,
0x1bf4f3b,0x1195534,0x3e80a78,0x02a1cbf } },
/* 250 */
{ { 0x32b2086,0x2de4d68,0x3486b1a,0x03a0583,0x2e1eb71,0x2dab9af,
0x10cd913,0x28daa6f,0x3fcb732,0x000a04a },
{ 0x3605318,0x3f5f2b3,0x2d1da63,0x143f7f5,0x1646e5d,0x040b586,
0x1683982,0x25abe87,0x0c9fe53,0x001ce47 } },
/* 251 */
{ { 0x380d02b,0x055fc22,0x3f7fc50,0x3458a1d,0x26b8333,0x23550ab,
0x0a1af87,0x0a821eb,0x2dc7e6d,0x00d574a },
{ 0x07386e1,0x3ccd68a,0x3275b41,0x253e390,0x2fd272a,0x1e6627a,
0x2ca2cde,0x0e9e4a1,0x1e37c2a,0x00f70ac } },
/* 252 */
{ { 0x0581352,0x2748701,0x02bed68,0x094dd9e,0x30a00c8,0x3fb5c07,
0x3bd5909,0x211ac80,0x1103ccd,0x0311e1a },
{ 0x0c768ed,0x29dc209,0x36575db,0x009a107,0x272feea,0x2b33383,
0x313ed56,0x134c9cc,0x168d5bb,0x033310a } },
/* 253 */
{ { 0x17620b9,0x143784f,0x256a94e,0x229664a,0x1d89a5c,0x1d521f2,
0x0076406,0x1c73f70,0x342aa48,0x03851fa },
{ 0x0f3ae46,0x2ad3bab,0x0fbe274,0x3ed40d4,0x2fd4936,0x232103a,
0x2afe474,0x25b8f7c,0x047080e,0x008e6b0 } },
/* 254 */
{ { 0x3fee8d4,0x347cd4a,0x0fec481,0x33fe9ec,0x0ce80b5,0x33a6bcf,
0x1c4c9e2,0x3967441,0x1a3f5f7,0x03157e8 },
{ 0x257c227,0x1bc53a0,0x200b318,0x0fcd0af,0x2c5b165,0x2a413ec,
0x2fc998a,0x2da6426,0x19cd4f4,0x0025336 } },
/* 255 */
{ { 0x303beba,0x2072135,0x32918a9,0x140cb3a,0x08631d1,0x0ef527b,
0x05f2c9e,0x2b4ce91,0x0b642ab,0x02e428c },
{ 0x0a5abf9,0x15013ed,0x3603b46,0x30dd76d,0x3004750,0x28d7627,
0x1a42ccc,0x093ddbe,0x39a1b79,0x00067e2 } },
};
/* Multiply the base point of P256 by the scalar and return the result.
* If map is true then convert result to affine co-ordinates.
*
* r Resulting point.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_base_10(sp_point* r, const sp_digit* k,
int map, void* heap)
{
return sp_256_ecc_mulmod_stripe_10(r, &p256_base, p256_table,
k, map, heap);
}
#endif
/* Multiply the base point of P256 by the scalar and return the result.
* If map is true then convert result to affine co-ordinates.
*
* km Scalar to multiply by.
* r Resulting point.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
int sp_ecc_mulmod_base_256(mp_int* km, ecc_point* r, int map, void* heap)
{
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_point p;
sp_digit kd[10];
#endif
sp_point* point;
sp_digit* k = NULL;
int err = MP_OKAY;
err = sp_ecc_point_new(heap, p, point);
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (err == MP_OKAY) {
k = (sp_digit*)XMALLOC(sizeof(sp_digit) * 10, heap,
DYNAMIC_TYPE_ECC);
if (k == NULL) {
err = MEMORY_E;
}
}
#else
k = kd;
#endif
if (err == MP_OKAY) {
sp_256_from_mp(k, 10, km);
err = sp_256_ecc_mulmod_base_10(point, k, map, heap);
}
if (err == MP_OKAY) {
err = sp_256_point_to_ecc_point_10(point, r);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (k != NULL) {
XFREE(k, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_ecc_point_free(point, 0, heap);
return err;
}
#if defined(WOLFSSL_VALIDATE_ECC_KEYGEN) || defined(HAVE_ECC_SIGN) || \
defined(HAVE_ECC_VERIFY)
/* Returns 1 if the number of zero.
* Implementation is constant time.
*
* a Number to check.
* returns 1 if the number is zero and 0 otherwise.
*/
static int sp_256_iszero_10(const sp_digit* a)
{
return (a[0] | a[1] | a[2] | a[3] | a[4] | a[5] | a[6] | a[7] |
a[8] | a[9]) == 0;
}
#endif /* WOLFSSL_VALIDATE_ECC_KEYGEN || HAVE_ECC_SIGN || HAVE_ECC_VERIFY */
/* Add 1 to a. (a = a + 1)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_256_add_one_10(sp_digit* a)
{
a[0]++;
sp_256_norm_10(a);
}
/* Read big endian unsigned byte array into r.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a Byte array.
* n Number of bytes in array to read.
*/
static void sp_256_from_bin(sp_digit* r, int size, const byte* a, int n)
{
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = n-1; i >= 0; i--) {
r[j] |= (((sp_digit)a[i]) << s);
if (s >= 18U) {
r[j] &= 0x3ffffff;
s = 26U - s;
if (j + 1 >= size) {
break;
}
r[++j] = (sp_digit)a[i] >> s;
s = 8U - s;
}
else {
s += 8U;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
}
/* Generates a scalar that is in the range 1..order-1.
*
* rng Random number generator.
* k Scalar value.
* returns RNG failures, MEMORY_E when memory allocation fails and
* MP_OKAY on success.
*/
static int sp_256_ecc_gen_k_10(WC_RNG* rng, sp_digit* k)
{
int err;
byte buf[32];
do {
err = wc_RNG_GenerateBlock(rng, buf, sizeof(buf));
if (err == 0) {
sp_256_from_bin(k, 10, buf, (int)sizeof(buf));
if (sp_256_cmp_10(k, p256_order2) < 0) {
sp_256_add_one_10(k);
break;
}
}
}
while (err == 0);
return err;
}
/* Makes a random EC key pair.
*
* rng Random number generator.
* priv Generated private value.
* pub Generated public point.
* heap Heap to use for allocation.
* returns ECC_INF_E when the point does not have the correct order, RNG
* failures, MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
int sp_ecc_make_key_256(WC_RNG* rng, mp_int* priv, ecc_point* pub, void* heap)
{
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_point p;
sp_digit kd[10];
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
sp_point inf;
#endif
#endif
sp_point* point;
sp_digit* k = NULL;
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
sp_point* infinity;
#endif
int err;
(void)heap;
err = sp_ecc_point_new(heap, p, point);
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
if (err == MP_OKAY) {
err = sp_ecc_point_new(heap, inf, infinity);
}
#endif
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (err == MP_OKAY) {
k = (sp_digit*)XMALLOC(sizeof(sp_digit) * 10, heap,
DYNAMIC_TYPE_ECC);
if (k == NULL) {
err = MEMORY_E;
}
}
#else
k = kd;
#endif
if (err == MP_OKAY) {
err = sp_256_ecc_gen_k_10(rng, k);
}
if (err == MP_OKAY) {
err = sp_256_ecc_mulmod_base_10(point, k, 1, NULL);
}
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
if (err == MP_OKAY) {
err = sp_256_ecc_mulmod_10(infinity, point, p256_order, 1, NULL);
}
if (err == MP_OKAY) {
if ((sp_256_iszero_10(point->x) == 0) || (sp_256_iszero_10(point->y) == 0)) {
err = ECC_INF_E;
}
}
#endif
if (err == MP_OKAY) {
err = sp_256_to_mp(k, priv);
}
if (err == MP_OKAY) {
err = sp_256_point_to_ecc_point_10(point, pub);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (k != NULL) {
XFREE(k, heap, DYNAMIC_TYPE_ECC);
}
#endif
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
sp_ecc_point_free(infinity, 1, heap);
#endif
sp_ecc_point_free(point, 1, heap);
return err;
}
#ifdef HAVE_ECC_DHE
/* Write r as big endian to byte array.
* Fixed length number of bytes written: 32
*
* r A single precision integer.
* a Byte array.
*/
static void sp_256_to_bin(sp_digit* r, byte* a)
{
int i, j, s = 0, b;
for (i=0; i<9; i++) {
r[i+1] += r[i] >> 26;
r[i] &= 0x3ffffff;
}
j = 256 / 8 - 1;
a[j] = 0;
for (i=0; i<10 && j>=0; i++) {
b = 0;
/* lint allow cast of mismatch sp_digit and int */
a[j--] |= (byte)(r[i] << s); b += 8 - s; /*lint !e9033*/
if (j < 0) {
break;
}
while (b < 26) {
a[j--] = r[i] >> b; b += 8;
if (j < 0) {
break;
}
}
s = 8 - (b - 26);
if (j >= 0) {
a[j] = 0;
}
if (s != 0) {
j++;
}
}
}
/* Multiply the point by the scalar and serialize the X ordinate.
* The number is 0 padded to maximum size on output.
*
* priv Scalar to multiply the point by.
* pub Point to multiply.
* out Buffer to hold X ordinate.
* outLen On entry, size of the buffer in bytes.
* On exit, length of data in buffer in bytes.
* heap Heap to use for allocation.
* returns BUFFER_E if the buffer is to small for output size,
* MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
int sp_ecc_secret_gen_256(mp_int* priv, ecc_point* pub, byte* out,
word32* outLen, void* heap)
{
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_point p;
sp_digit kd[10];
#endif
sp_point* point = NULL;
sp_digit* k = NULL;
int err = MP_OKAY;
if (*outLen < 32U) {
err = BUFFER_E;
}
if (err == MP_OKAY) {
err = sp_ecc_point_new(heap, p, point);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (err == MP_OKAY) {
k = (sp_digit*)XMALLOC(sizeof(sp_digit) * 10, heap,
DYNAMIC_TYPE_ECC);
if (k == NULL)
err = MEMORY_E;
}
#else
k = kd;
#endif
if (err == MP_OKAY) {
sp_256_from_mp(k, 10, priv);
sp_256_point_from_ecc_point_10(point, pub);
err = sp_256_ecc_mulmod_10(point, point, k, 1, heap);
}
if (err == MP_OKAY) {
sp_256_to_bin(point->x, out);
*outLen = 32;
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (k != NULL) {
XFREE(k, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_ecc_point_free(point, 0, heap);
return err;
}
#endif /* HAVE_ECC_DHE */
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
#endif
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_256_mul_d_10(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 10; i++) {
t += tb * a[i];
r[i] = t & 0x3ffffff;
t >>= 26;
}
r[10] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[10];
t[ 0] = tb * a[ 0];
t[ 1] = tb * a[ 1];
t[ 2] = tb * a[ 2];
t[ 3] = tb * a[ 3];
t[ 4] = tb * a[ 4];
t[ 5] = tb * a[ 5];
t[ 6] = tb * a[ 6];
t[ 7] = tb * a[ 7];
t[ 8] = tb * a[ 8];
t[ 9] = tb * a[ 9];
r[ 0] = (t[ 0] & 0x3ffffff);
r[ 1] = (sp_digit)(t[ 0] >> 26) + (t[ 1] & 0x3ffffff);
r[ 2] = (sp_digit)(t[ 1] >> 26) + (t[ 2] & 0x3ffffff);
r[ 3] = (sp_digit)(t[ 2] >> 26) + (t[ 3] & 0x3ffffff);
r[ 4] = (sp_digit)(t[ 3] >> 26) + (t[ 4] & 0x3ffffff);
r[ 5] = (sp_digit)(t[ 4] >> 26) + (t[ 5] & 0x3ffffff);
r[ 6] = (sp_digit)(t[ 5] >> 26) + (t[ 6] & 0x3ffffff);
r[ 7] = (sp_digit)(t[ 6] >> 26) + (t[ 7] & 0x3ffffff);
r[ 8] = (sp_digit)(t[ 7] >> 26) + (t[ 8] & 0x3ffffff);
r[ 9] = (sp_digit)(t[ 8] >> 26) + (t[ 9] & 0x3ffffff);
r[10] = (sp_digit)(t[ 9] >> 26);
#endif /* WOLFSSL_SP_SMALL */
}
#ifdef WOLFSSL_SP_DIV_32
static WC_INLINE sp_digit sp_256_div_word_10(sp_digit d1, sp_digit d0,
sp_digit dv)
{
sp_digit d, r, t, dv;
int64_t t0, t1;
/* dv has 14 bits. */
dv = (div >> 12) + 1;
/* All 26 bits from d1 and top 5 bits from d0. */
d = (d1 << 5) | (d0 >> 21);
r = d / dv;
d -= r * dv;
/* Up to 17 bits in r */
/* Next 9 bits from d0. */
d <<= 9;
r <<= 9;
d |= (d0 >> 12) & ((1 << 9) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 26 bits in r */
/* Handle rounding error with dv - top part */
t0 = ((int64_t)d1 << 26) + d0;
t1 = (int64_t)r * dv;
t1 = t0 - t1;
t = (sp_digit)(t1 >> 12) / dv;
r += t;
/* Handle rounding error with dv - bottom 32 bits */
t1 = (sp_digit)t0 - (r * dv);
t = (sp_digit)t1 / dv;
r += t;
return r;
}
#endif /* WOLFSSL_SP_DIV_32 */
/* Divide d in a and put remainder into r (m*d + r = a)
* m is not calculated as it is not needed at this time.
*
* a Number to be divided.
* d Number to divide with.
* m Multiplier result.
* r Remainder from the division.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_256_div_10(const sp_digit* a, const sp_digit* d, sp_digit* m,
sp_digit* r)
{
int i;
#ifndef WOLFSSL_SP_DIV_32
int64_t d1;
#endif
sp_digit dv, r1;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_digit* td;
#else
sp_digit t1d[20], t2d[10 + 1];
#endif
sp_digit* t1;
sp_digit* t2;
int err = MP_OKAY;
(void)m;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * (3 * 10 + 1), NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
t1 = td;
t2 = td + 2 * 10;
#else
t1 = t1d;
t2 = t2d;
#endif
dv = d[9];
XMEMCPY(t1, a, sizeof(*t1) * 2U * 10U);
for (i=9; i>=0; i--) {
t1[10 + i] += t1[10 + i - 1] >> 26;
t1[10 + i - 1] &= 0x3ffffff;
#ifndef WOLFSSL_SP_DIV_32
d1 = t1[10 + i];
d1 <<= 26;
d1 += t1[10 + i - 1];
r1 = (sp_digit)(d1 / dv);
#else
r1 = sp_256_div_word_10(t1[10 + i], t1[10 + i - 1], dv);
#endif
sp_256_mul_d_10(t2, d, r1);
(void)sp_256_sub_10(&t1[i], &t1[i], t2);
t1[10 + i] -= t2[10];
t1[10 + i] += t1[10 + i - 1] >> 26;
t1[10 + i - 1] &= 0x3ffffff;
r1 = (((-t1[10 + i]) << 26) - t1[10 + i - 1]) / dv;
r1++;
sp_256_mul_d_10(t2, d, r1);
(void)sp_256_add_10(&t1[i], &t1[i], t2);
t1[10 + i] += t1[10 + i - 1] >> 26;
t1[10 + i - 1] &= 0x3ffffff;
}
t1[10 - 1] += t1[10 - 2] >> 26;
t1[10 - 2] &= 0x3ffffff;
d1 = t1[10 - 1];
r1 = (sp_digit)(d1 / dv);
sp_256_mul_d_10(t2, d, r1);
(void)sp_256_sub_10(t1, t1, t2);
XMEMCPY(r, t1, sizeof(*r) * 2U * 10U);
for (i=0; i<8; i++) {
r[i+1] += r[i] >> 26;
r[i] &= 0x3ffffff;
}
sp_256_cond_add_10(r, r, d, 0 - ((r[9] < 0) ?
(sp_digit)1 : (sp_digit)0));
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
/* Reduce a modulo m into r. (r = a mod m)
*
* r A single precision number that is the reduced result.
* a A single precision number that is to be reduced.
* m A single precision number that is the modulus to reduce with.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_256_mod_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
return sp_256_div_10(a, m, NULL, r);
}
#endif
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
#ifdef WOLFSSL_SP_SMALL
/* Order-2 for the P256 curve. */
static const uint32_t p256_order_2[8] = {
0xfc63254fU,0xf3b9cac2U,0xa7179e84U,0xbce6faadU,0xffffffffU,0xffffffffU,
0x00000000U,0xffffffffU
};
#else
/* The low half of the order-2 of the P256 curve. */
static const uint32_t p256_order_low[4] = {
0xfc63254fU,0xf3b9cac2U,0xa7179e84U,0xbce6faadU
};
#endif /* WOLFSSL_SP_SMALL */
/* Multiply two number mod the order of P256 curve. (r = a * b mod order)
*
* r Result of the multiplication.
* a First operand of the multiplication.
* b Second operand of the multiplication.
*/
static void sp_256_mont_mul_order_10(sp_digit* r, const sp_digit* a, const sp_digit* b)
{
sp_256_mul_10(r, a, b);
sp_256_mont_reduce_order_10(r, p256_order, p256_mp_order);
}
/* Square number mod the order of P256 curve. (r = a * a mod order)
*
* r Result of the squaring.
* a Number to square.
*/
static void sp_256_mont_sqr_order_10(sp_digit* r, const sp_digit* a)
{
sp_256_sqr_10(r, a);
sp_256_mont_reduce_order_10(r, p256_order, p256_mp_order);
}
#ifndef WOLFSSL_SP_SMALL
/* Square number mod the order of P256 curve a number of times.
* (r = a ^ n mod order)
*
* r Result of the squaring.
* a Number to square.
*/
static void sp_256_mont_sqr_n_order_10(sp_digit* r, const sp_digit* a, int n)
{
int i;
sp_256_mont_sqr_order_10(r, a);
for (i=1; i<n; i++) {
sp_256_mont_sqr_order_10(r, r);
}
}
#endif /* !WOLFSSL_SP_SMALL */
/* Invert the number, in Montgomery form, modulo the order of the P256 curve.
* (r = 1 / a mod order)
*
* r Inverse result.
* a Number to invert.
* td Temporary data.
*/
static void sp_256_mont_inv_order_10(sp_digit* r, const sp_digit* a,
sp_digit* td)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* t = td;
int i;
XMEMCPY(t, a, sizeof(sp_digit) * 10);
for (i=254; i>=0; i--) {
sp_256_mont_sqr_order_10(t, t);
if ((p256_order_2[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
sp_256_mont_mul_order_10(t, t, a);
}
}
XMEMCPY(r, t, sizeof(sp_digit) * 10U);
#else
sp_digit* t = td;
sp_digit* t2 = td + 2 * 10;
sp_digit* t3 = td + 4 * 10;
int i;
/* t = a^2 */
sp_256_mont_sqr_order_10(t, a);
/* t = a^3 = t * a */
sp_256_mont_mul_order_10(t, t, a);
/* t2= a^c = t ^ 2 ^ 2 */
sp_256_mont_sqr_n_order_10(t2, t, 2);
/* t3= a^f = t2 * t */
sp_256_mont_mul_order_10(t3, t2, t);
/* t2= a^f0 = t3 ^ 2 ^ 4 */
sp_256_mont_sqr_n_order_10(t2, t3, 4);
/* t = a^ff = t2 * t3 */
sp_256_mont_mul_order_10(t, t2, t3);
/* t3= a^ff00 = t ^ 2 ^ 8 */
sp_256_mont_sqr_n_order_10(t2, t, 8);
/* t = a^ffff = t2 * t */
sp_256_mont_mul_order_10(t, t2, t);
/* t2= a^ffff0000 = t ^ 2 ^ 16 */
sp_256_mont_sqr_n_order_10(t2, t, 16);
/* t = a^ffffffff = t2 * t */
sp_256_mont_mul_order_10(t, t2, t);
/* t2= a^ffffffff0000000000000000 = t ^ 2 ^ 64 */
sp_256_mont_sqr_n_order_10(t2, t, 64);
/* t2= a^ffffffff00000000ffffffff = t2 * t */
sp_256_mont_mul_order_10(t2, t2, t);
/* t2= a^ffffffff00000000ffffffff00000000 = t2 ^ 2 ^ 32 */
sp_256_mont_sqr_n_order_10(t2, t2, 32);
/* t2= a^ffffffff00000000ffffffffffffffff = t2 * t */
sp_256_mont_mul_order_10(t2, t2, t);
/* t2= a^ffffffff00000000ffffffffffffffffbce6 */
for (i=127; i>=112; i--) {
sp_256_mont_sqr_order_10(t2, t2);
if (((sp_digit)p256_order_low[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
sp_256_mont_mul_order_10(t2, t2, a);
}
}
/* t2= a^ffffffff00000000ffffffffffffffffbce6f */
sp_256_mont_sqr_n_order_10(t2, t2, 4);
sp_256_mont_mul_order_10(t2, t2, t3);
/* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84 */
for (i=107; i>=64; i--) {
sp_256_mont_sqr_order_10(t2, t2);
if (((sp_digit)p256_order_low[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
sp_256_mont_mul_order_10(t2, t2, a);
}
}
/* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f */
sp_256_mont_sqr_n_order_10(t2, t2, 4);
sp_256_mont_mul_order_10(t2, t2, t3);
/* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2 */
for (i=59; i>=32; i--) {
sp_256_mont_sqr_order_10(t2, t2);
if (((sp_digit)p256_order_low[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
sp_256_mont_mul_order_10(t2, t2, a);
}
}
/* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2f */
sp_256_mont_sqr_n_order_10(t2, t2, 4);
sp_256_mont_mul_order_10(t2, t2, t3);
/* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc63254 */
for (i=27; i>=0; i--) {
sp_256_mont_sqr_order_10(t2, t2);
if (((sp_digit)p256_order_low[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
sp_256_mont_mul_order_10(t2, t2, a);
}
}
/* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632540 */
sp_256_mont_sqr_n_order_10(t2, t2, 4);
/* r = a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc63254f */
sp_256_mont_mul_order_10(r, t2, t3);
#endif /* WOLFSSL_SP_SMALL */
}
#endif /* HAVE_ECC_SIGN || HAVE_ECC_VERIFY */
#ifdef HAVE_ECC_SIGN
#ifndef SP_ECC_MAX_SIG_GEN
#define SP_ECC_MAX_SIG_GEN 64
#endif
/* Sign the hash using the private key.
* e = [hash, 256 bits] from binary
* r = (k.G)->x mod order
* s = (r * x + e) / k mod order
* The hash is truncated to the first 256 bits.
*
* hash Hash to sign.
* hashLen Length of the hash data.
* rng Random number generator.
* priv Private part of key - scalar.
* rm First part of result as an mp_int.
* sm Sirst part of result as an mp_int.
* heap Heap to use for allocation.
* returns RNG failures, MEMORY_E when memory allocation fails and
* MP_OKAY on success.
*/
int sp_ecc_sign_256(const byte* hash, word32 hashLen, WC_RNG* rng, mp_int* priv,
mp_int* rm, mp_int* sm, mp_int* km, void* heap)
{
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_digit* d = NULL;
#else
sp_digit ed[2*10];
sp_digit xd[2*10];
sp_digit kd[2*10];
sp_digit rd[2*10];
sp_digit td[3 * 2*10];
sp_point p;
#endif
sp_digit* e = NULL;
sp_digit* x = NULL;
sp_digit* k = NULL;
sp_digit* r = NULL;
sp_digit* tmp = NULL;
sp_point* point = NULL;
sp_digit carry;
sp_digit* s = NULL;
sp_digit* kInv = NULL;
int err = MP_OKAY;
int32_t c;
int i;
(void)heap;
err = sp_ecc_point_new(heap, p, point);
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 7 * 2 * 10, heap,
DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
}
#endif
if (err == MP_OKAY) {
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
e = d + 0 * 10;
x = d + 2 * 10;
k = d + 4 * 10;
r = d + 6 * 10;
tmp = d + 8 * 10;
#else
e = ed;
x = xd;
k = kd;
r = rd;
tmp = td;
#endif
s = e;
kInv = k;
if (hashLen > 32U) {
hashLen = 32U;
}
sp_256_from_bin(e, 10, hash, (int)hashLen);
}
for (i = SP_ECC_MAX_SIG_GEN; err == MP_OKAY && i > 0; i--) {
sp_256_from_mp(x, 10, priv);
/* New random point. */
if (km == NULL || mp_iszero(km)) {
err = sp_256_ecc_gen_k_10(rng, k);
}
else {
sp_256_from_mp(k, 10, km);
mp_zero(km);
}
if (err == MP_OKAY) {
err = sp_256_ecc_mulmod_base_10(point, k, 1, NULL);
}
if (err == MP_OKAY) {
/* r = point->x mod order */
XMEMCPY(r, point->x, sizeof(sp_digit) * 10U);
sp_256_norm_10(r);
c = sp_256_cmp_10(r, p256_order);
sp_256_cond_sub_10(r, r, p256_order, 0L - (sp_digit)(c >= 0));
sp_256_norm_10(r);
/* Conv k to Montgomery form (mod order) */
sp_256_mul_10(k, k, p256_norm_order);
err = sp_256_mod_10(k, k, p256_order);
}
if (err == MP_OKAY) {
sp_256_norm_10(k);
/* kInv = 1/k mod order */
sp_256_mont_inv_order_10(kInv, k, tmp);
sp_256_norm_10(kInv);
/* s = r * x + e */
sp_256_mul_10(x, x, r);
err = sp_256_mod_10(x, x, p256_order);
}
if (err == MP_OKAY) {
sp_256_norm_10(x);
carry = sp_256_add_10(s, e, x);
sp_256_cond_sub_10(s, s, p256_order, 0 - carry);
sp_256_norm_10(s);
c = sp_256_cmp_10(s, p256_order);
sp_256_cond_sub_10(s, s, p256_order, 0L - (sp_digit)(c >= 0));
sp_256_norm_10(s);
/* s = s * k^-1 mod order */
sp_256_mont_mul_order_10(s, s, kInv);
sp_256_norm_10(s);
/* Check that signature is usable. */
if (sp_256_iszero_10(s) == 0) {
break;
}
}
}
if (i == 0) {
err = RNG_FAILURE_E;
}
if (err == MP_OKAY) {
err = sp_256_to_mp(r, rm);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(s, sm);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (d != NULL) {
XMEMSET(d, 0, sizeof(sp_digit) * 8 * 10);
XFREE(d, heap, DYNAMIC_TYPE_ECC);
}
#else
XMEMSET(e, 0, sizeof(sp_digit) * 2U * 10U);
XMEMSET(x, 0, sizeof(sp_digit) * 2U * 10U);
XMEMSET(k, 0, sizeof(sp_digit) * 2U * 10U);
XMEMSET(r, 0, sizeof(sp_digit) * 2U * 10U);
XMEMSET(r, 0, sizeof(sp_digit) * 2U * 10U);
XMEMSET(tmp, 0, sizeof(sp_digit) * 3U * 2U * 10U);
#endif
sp_ecc_point_free(point, 1, heap);
return err;
}
#endif /* HAVE_ECC_SIGN */
#ifdef HAVE_ECC_VERIFY
/* Verify the signature values with the hash and public key.
* e = Truncate(hash, 256)
* u1 = e/s mod order
* u2 = r/s mod order
* r == (u1.G + u2.Q)->x mod order
* Optimization: Leave point in projective form.
* (x, y, 1) == (x' / z'*z', y' / z'*z'*z', z' / z')
* (r + n*order).z'.z' mod prime == (u1.G + u2.Q)->x'
* The hash is truncated to the first 256 bits.
*
* hash Hash to sign.
* hashLen Length of the hash data.
* rng Random number generator.
* priv Private part of key - scalar.
* rm First part of result as an mp_int.
* sm Sirst part of result as an mp_int.
* heap Heap to use for allocation.
* returns RNG failures, MEMORY_E when memory allocation fails and
* MP_OKAY on success.
*/
int sp_ecc_verify_256(const byte* hash, word32 hashLen, mp_int* pX,
mp_int* pY, mp_int* pZ, mp_int* r, mp_int* sm, int* res, void* heap)
{
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_digit* d = NULL;
#else
sp_digit u1d[2*10];
sp_digit u2d[2*10];
sp_digit sd[2*10];
sp_digit tmpd[2*10 * 5];
sp_point p1d;
sp_point p2d;
#endif
sp_digit* u1 = NULL;
sp_digit* u2 = NULL;
sp_digit* s = NULL;
sp_digit* tmp = NULL;
sp_point* p1;
sp_point* p2 = NULL;
sp_digit carry;
int32_t c;
int err;
err = sp_ecc_point_new(heap, p1d, p1);
if (err == MP_OKAY) {
err = sp_ecc_point_new(heap, p2d, p2);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 16 * 10, heap,
DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
}
#endif
if (err == MP_OKAY) {
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
u1 = d + 0 * 10;
u2 = d + 2 * 10;
s = d + 4 * 10;
tmp = d + 6 * 10;
#else
u1 = u1d;
u2 = u2d;
s = sd;
tmp = tmpd;
#endif
if (hashLen > 32U) {
hashLen = 32U;
}
sp_256_from_bin(u1, 10, hash, (int)hashLen);
sp_256_from_mp(u2, 10, r);
sp_256_from_mp(s, 10, sm);
sp_256_from_mp(p2->x, 10, pX);
sp_256_from_mp(p2->y, 10, pY);
sp_256_from_mp(p2->z, 10, pZ);
{
sp_256_mul_10(s, s, p256_norm_order);
}
err = sp_256_mod_10(s, s, p256_order);
}
if (err == MP_OKAY) {
sp_256_norm_10(s);
{
sp_256_mont_inv_order_10(s, s, tmp);
sp_256_mont_mul_order_10(u1, u1, s);
sp_256_mont_mul_order_10(u2, u2, s);
}
err = sp_256_ecc_mulmod_base_10(p1, u1, 0, heap);
}
if (err == MP_OKAY) {
err = sp_256_ecc_mulmod_10(p2, p2, u2, 0, heap);
}
if (err == MP_OKAY) {
{
sp_256_proj_point_add_10(p1, p1, p2, tmp);
if (sp_256_iszero_10(p1->z)) {
if (sp_256_iszero_10(p1->x) && sp_256_iszero_10(p1->y)) {
sp_256_proj_point_dbl_10(p1, p2, tmp);
}
else {
/* Y ordinate is not used from here - don't set. */
p1->x[0] = 0;
p1->x[1] = 0;
p1->x[2] = 0;
p1->x[3] = 0;
p1->x[4] = 0;
p1->x[5] = 0;
p1->x[6] = 0;
p1->x[7] = 0;
p1->x[8] = 0;
p1->x[9] = 0;
XMEMCPY(p1->z, p256_norm_mod, sizeof(p256_norm_mod));
}
}
}
/* (r + n*order).z'.z' mod prime == (u1.G + u2.Q)->x' */
/* Reload r and convert to Montgomery form. */
sp_256_from_mp(u2, 10, r);
err = sp_256_mod_mul_norm_10(u2, u2, p256_mod);
}
if (err == MP_OKAY) {
/* u1 = r.z'.z' mod prime */
sp_256_mont_sqr_10(p1->z, p1->z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(u1, u2, p1->z, p256_mod, p256_mp_mod);
*res = (int)(sp_256_cmp_10(p1->x, u1) == 0);
if (*res == 0) {
/* Reload r and add order. */
sp_256_from_mp(u2, 10, r);
carry = sp_256_add_10(u2, u2, p256_order);
/* Carry means result is greater than mod and is not valid. */
if (carry == 0) {
sp_256_norm_10(u2);
/* Compare with mod and if greater or equal then not valid. */
c = sp_256_cmp_10(u2, p256_mod);
if (c < 0) {
/* Convert to Montogomery form */
err = sp_256_mod_mul_norm_10(u2, u2, p256_mod);
if (err == MP_OKAY) {
/* u1 = (r + 1*order).z'.z' mod prime */
sp_256_mont_mul_10(u1, u2, p1->z, p256_mod,
p256_mp_mod);
*res = (int)(sp_256_cmp_10(p1->x, u1) == 0);
}
}
}
}
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (d != NULL)
XFREE(d, heap, DYNAMIC_TYPE_ECC);
#endif
sp_ecc_point_free(p1, 0, heap);
sp_ecc_point_free(p2, 0, heap);
return err;
}
#endif /* HAVE_ECC_VERIFY */
#ifdef HAVE_ECC_CHECK_KEY
/* Check that the x and y oridinates are a valid point on the curve.
*
* point EC point.
* heap Heap to use if dynamically allocating.
* returns MEMORY_E if dynamic memory allocation fails, MP_VAL if the point is
* not on the curve and MP_OKAY otherwise.
*/
static int sp_256_ecc_is_point_10(sp_point* point, void* heap)
{
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_digit* d = NULL;
#else
sp_digit t1d[2*10];
sp_digit t2d[2*10];
#endif
sp_digit* t1;
sp_digit* t2;
int err = MP_OKAY;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 10 * 4, heap, DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
t1 = d + 0 * 10;
t2 = d + 2 * 10;
#else
(void)heap;
t1 = t1d;
t2 = t2d;
#endif
sp_256_sqr_10(t1, point->y);
(void)sp_256_mod_10(t1, t1, p256_mod);
sp_256_sqr_10(t2, point->x);
(void)sp_256_mod_10(t2, t2, p256_mod);
sp_256_mul_10(t2, t2, point->x);
(void)sp_256_mod_10(t2, t2, p256_mod);
(void)sp_256_sub_10(t2, p256_mod, t2);
sp_256_mont_add_10(t1, t1, t2, p256_mod);
sp_256_mont_add_10(t1, t1, point->x, p256_mod);
sp_256_mont_add_10(t1, t1, point->x, p256_mod);
sp_256_mont_add_10(t1, t1, point->x, p256_mod);
if (sp_256_cmp_10(t1, p256_b) != 0) {
err = MP_VAL;
}
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (d != NULL) {
XFREE(d, heap, DYNAMIC_TYPE_ECC);
}
#endif
return err;
}
/* Check that the x and y oridinates are a valid point on the curve.
*
* pX X ordinate of EC point.
* pY Y ordinate of EC point.
* returns MEMORY_E if dynamic memory allocation fails, MP_VAL if the point is
* not on the curve and MP_OKAY otherwise.
*/
int sp_ecc_is_point_256(mp_int* pX, mp_int* pY)
{
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_point pubd;
#endif
sp_point* pub;
byte one[1] = { 1 };
int err;
err = sp_ecc_point_new(NULL, pubd, pub);
if (err == MP_OKAY) {
sp_256_from_mp(pub->x, 10, pX);
sp_256_from_mp(pub->y, 10, pY);
sp_256_from_bin(pub->z, 10, one, (int)sizeof(one));
err = sp_256_ecc_is_point_10(pub, NULL);
}
sp_ecc_point_free(pub, 0, NULL);
return err;
}
/* Check that the private scalar generates the EC point (px, py), the point is
* on the curve and the point has the correct order.
*
* pX X ordinate of EC point.
* pY Y ordinate of EC point.
* privm Private scalar that generates EC point.
* returns MEMORY_E if dynamic memory allocation fails, MP_VAL if the point is
* not on the curve, ECC_INF_E if the point does not have the correct order,
* ECC_PRIV_KEY_E when the private scalar doesn't generate the EC point and
* MP_OKAY otherwise.
*/
int sp_ecc_check_key_256(mp_int* pX, mp_int* pY, mp_int* privm, void* heap)
{
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_digit privd[10];
sp_point pubd;
sp_point pd;
#endif
sp_digit* priv = NULL;
sp_point* pub;
sp_point* p = NULL;
byte one[1] = { 1 };
int err;
err = sp_ecc_point_new(heap, pubd, pub);
if (err == MP_OKAY) {
err = sp_ecc_point_new(heap, pd, p);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (err == MP_OKAY) {
priv = (sp_digit*)XMALLOC(sizeof(sp_digit) * 10, heap,
DYNAMIC_TYPE_ECC);
if (priv == NULL) {
err = MEMORY_E;
}
}
#endif
if (err == MP_OKAY) {
#if !(defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK))
priv = privd;
#endif
sp_256_from_mp(pub->x, 10, pX);
sp_256_from_mp(pub->y, 10, pY);
sp_256_from_bin(pub->z, 10, one, (int)sizeof(one));
sp_256_from_mp(priv, 10, privm);
/* Check point at infinitiy. */
if ((sp_256_iszero_10(pub->x) != 0) &&
(sp_256_iszero_10(pub->y) != 0)) {
err = ECC_INF_E;
}
}
if (err == MP_OKAY) {
/* Check range of X and Y */
if (sp_256_cmp_10(pub->x, p256_mod) >= 0 ||
sp_256_cmp_10(pub->y, p256_mod) >= 0) {
err = ECC_OUT_OF_RANGE_E;
}
}
if (err == MP_OKAY) {
/* Check point is on curve */
err = sp_256_ecc_is_point_10(pub, heap);
}
if (err == MP_OKAY) {
/* Point * order = infinity */
err = sp_256_ecc_mulmod_10(p, pub, p256_order, 1, heap);
}
if (err == MP_OKAY) {
/* Check result is infinity */
if ((sp_256_iszero_10(p->x) == 0) ||
(sp_256_iszero_10(p->y) == 0)) {
err = ECC_INF_E;
}
}
if (err == MP_OKAY) {
/* Base * private = point */
err = sp_256_ecc_mulmod_base_10(p, priv, 1, heap);
}
if (err == MP_OKAY) {
/* Check result is public key */
if (sp_256_cmp_10(p->x, pub->x) != 0 ||
sp_256_cmp_10(p->y, pub->y) != 0) {
err = ECC_PRIV_KEY_E;
}
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (priv != NULL) {
XFREE(priv, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_ecc_point_free(p, 0, heap);
sp_ecc_point_free(pub, 0, heap);
return err;
}
#endif
#ifdef WOLFSSL_PUBLIC_ECC_ADD_DBL
/* Add two projective EC points together.
* (pX, pY, pZ) + (qX, qY, qZ) = (rX, rY, rZ)
*
* pX First EC point's X ordinate.
* pY First EC point's Y ordinate.
* pZ First EC point's Z ordinate.
* qX Second EC point's X ordinate.
* qY Second EC point's Y ordinate.
* qZ Second EC point's Z ordinate.
* rX Resultant EC point's X ordinate.
* rY Resultant EC point's Y ordinate.
* rZ Resultant EC point's Z ordinate.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
int sp_ecc_proj_add_point_256(mp_int* pX, mp_int* pY, mp_int* pZ,
mp_int* qX, mp_int* qY, mp_int* qZ,
mp_int* rX, mp_int* rY, mp_int* rZ)
{
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_digit tmpd[2 * 10 * 5];
sp_point pd;
sp_point qd;
#endif
sp_digit* tmp;
sp_point* p;
sp_point* q = NULL;
int err;
err = sp_ecc_point_new(NULL, pd, p);
if (err == MP_OKAY) {
err = sp_ecc_point_new(NULL, qd, q);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (err == MP_OKAY) {
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, NULL,
DYNAMIC_TYPE_ECC);
if (tmp == NULL) {
err = MEMORY_E;
}
}
#else
tmp = tmpd;
#endif
if (err == MP_OKAY) {
sp_256_from_mp(p->x, 10, pX);
sp_256_from_mp(p->y, 10, pY);
sp_256_from_mp(p->z, 10, pZ);
sp_256_from_mp(q->x, 10, qX);
sp_256_from_mp(q->y, 10, qY);
sp_256_from_mp(q->z, 10, qZ);
sp_256_proj_point_add_10(p, p, q, tmp);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->x, rX);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->y, rY);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->z, rZ);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (tmp != NULL) {
XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
}
#endif
sp_ecc_point_free(q, 0, NULL);
sp_ecc_point_free(p, 0, NULL);
return err;
}
/* Double a projective EC point.
* (pX, pY, pZ) + (pX, pY, pZ) = (rX, rY, rZ)
*
* pX EC point's X ordinate.
* pY EC point's Y ordinate.
* pZ EC point's Z ordinate.
* rX Resultant EC point's X ordinate.
* rY Resultant EC point's Y ordinate.
* rZ Resultant EC point's Z ordinate.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
int sp_ecc_proj_dbl_point_256(mp_int* pX, mp_int* pY, mp_int* pZ,
mp_int* rX, mp_int* rY, mp_int* rZ)
{
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_digit tmpd[2 * 10 * 2];
sp_point pd;
#endif
sp_digit* tmp;
sp_point* p;
int err;
err = sp_ecc_point_new(NULL, pd, p);
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (err == MP_OKAY) {
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 2, NULL,
DYNAMIC_TYPE_ECC);
if (tmp == NULL) {
err = MEMORY_E;
}
}
#else
tmp = tmpd;
#endif
if (err == MP_OKAY) {
sp_256_from_mp(p->x, 10, pX);
sp_256_from_mp(p->y, 10, pY);
sp_256_from_mp(p->z, 10, pZ);
sp_256_proj_point_dbl_10(p, p, tmp);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->x, rX);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->y, rY);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->z, rZ);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (tmp != NULL) {
XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
}
#endif
sp_ecc_point_free(p, 0, NULL);
return err;
}
/* Map a projective EC point to affine in place.
* pZ will be one.
*
* pX EC point's X ordinate.
* pY EC point's Y ordinate.
* pZ EC point's Z ordinate.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
int sp_ecc_map_256(mp_int* pX, mp_int* pY, mp_int* pZ)
{
#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
sp_digit tmpd[2 * 10 * 4];
sp_point pd;
#endif
sp_digit* tmp;
sp_point* p;
int err;
err = sp_ecc_point_new(NULL, pd, p);
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (err == MP_OKAY) {
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 4, NULL,
DYNAMIC_TYPE_ECC);
if (tmp == NULL) {
err = MEMORY_E;
}
}
#else
tmp = tmpd;
#endif
if (err == MP_OKAY) {
sp_256_from_mp(p->x, 10, pX);
sp_256_from_mp(p->y, 10, pY);
sp_256_from_mp(p->z, 10, pZ);
sp_256_map_10(p, p, tmp);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->x, pX);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->y, pY);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->z, pZ);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (tmp != NULL) {
XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
}
#endif
sp_ecc_point_free(p, 0, NULL);
return err;
}
#endif /* WOLFSSL_PUBLIC_ECC_ADD_DBL */
#ifdef HAVE_COMP_KEY
/* Find the square root of a number mod the prime of the curve.
*
* y The number to operate on and the result.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
static int sp_256_mont_sqrt_10(sp_digit* y)
{
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_digit* d;
#else
sp_digit t1d[2 * 10];
sp_digit t2d[2 * 10];
#endif
sp_digit* t1;
sp_digit* t2;
int err = MP_OKAY;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 4 * 10, NULL, DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
t1 = d + 0 * 10;
t2 = d + 2 * 10;
#else
t1 = t1d;
t2 = t2d;
#endif
{
/* t2 = y ^ 0x2 */
sp_256_mont_sqr_10(t2, y, p256_mod, p256_mp_mod);
/* t1 = y ^ 0x3 */
sp_256_mont_mul_10(t1, t2, y, p256_mod, p256_mp_mod);
/* t2 = y ^ 0xc */
sp_256_mont_sqr_n_10(t2, t1, 2, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xf */
sp_256_mont_mul_10(t1, t1, t2, p256_mod, p256_mp_mod);
/* t2 = y ^ 0xf0 */
sp_256_mont_sqr_n_10(t2, t1, 4, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xff */
sp_256_mont_mul_10(t1, t1, t2, p256_mod, p256_mp_mod);
/* t2 = y ^ 0xff00 */
sp_256_mont_sqr_n_10(t2, t1, 8, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xffff */
sp_256_mont_mul_10(t1, t1, t2, p256_mod, p256_mp_mod);
/* t2 = y ^ 0xffff0000 */
sp_256_mont_sqr_n_10(t2, t1, 16, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xffffffff */
sp_256_mont_mul_10(t1, t1, t2, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xffffffff00000000 */
sp_256_mont_sqr_n_10(t1, t1, 32, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xffffffff00000001 */
sp_256_mont_mul_10(t1, t1, y, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xffffffff00000001000000000000000000000000 */
sp_256_mont_sqr_n_10(t1, t1, 96, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xffffffff00000001000000000000000000000001 */
sp_256_mont_mul_10(t1, t1, y, p256_mod, p256_mp_mod);
sp_256_mont_sqr_n_10(y, t1, 94, p256_mod, p256_mp_mod);
}
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_ECC);
}
#endif
return err;
}
/* Uncompress the point given the X ordinate.
*
* xm X ordinate.
* odd Whether the Y ordinate is odd.
* ym Calculated Y ordinate.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
int sp_ecc_uncompress_256(mp_int* xm, int odd, mp_int* ym)
{
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
sp_digit* d;
#else
sp_digit xd[2 * 10];
sp_digit yd[2 * 10];
#endif
sp_digit* x = NULL;
sp_digit* y = NULL;
int err = MP_OKAY;
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 4 * 10, NULL, DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
x = d + 0 * 10;
y = d + 2 * 10;
#else
x = xd;
y = yd;
#endif
sp_256_from_mp(x, 10, xm);
err = sp_256_mod_mul_norm_10(x, x, p256_mod);
}
if (err == MP_OKAY) {
/* y = x^3 */
{
sp_256_mont_sqr_10(y, x, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(y, y, x, p256_mod, p256_mp_mod);
}
/* y = x^3 - 3x */
sp_256_mont_sub_10(y, y, x, p256_mod);
sp_256_mont_sub_10(y, y, x, p256_mod);
sp_256_mont_sub_10(y, y, x, p256_mod);
/* y = x^3 - 3x + b */
err = sp_256_mod_mul_norm_10(x, p256_b, p256_mod);
}
if (err == MP_OKAY) {
sp_256_mont_add_10(y, y, x, p256_mod);
/* y = sqrt(x^3 - 3x + b) */
err = sp_256_mont_sqrt_10(y);
}
if (err == MP_OKAY) {
XMEMSET(y + 10, 0, 10U * sizeof(sp_digit));
sp_256_mont_reduce_10(y, p256_mod, p256_mp_mod);
if ((((word32)y[0] ^ (word32)odd) & 1U) != 0U) {
sp_256_mont_sub_10(y, p256_mod, y, p256_mod);
}
err = sp_256_to_mp(y, ym);
}
#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_ECC);
}
#endif
return err;
}
#endif
#endif /* !WOLFSSL_SP_NO_256 */
#endif /* WOLFSSL_HAVE_SP_ECC */
#endif /* SP_WORD_SIZE == 32 */
#endif /* !WOLFSSL_SP_ASM */
#endif /* WOLFSSL_HAVE_SP_RSA || WOLFSSL_HAVE_SP_DH || WOLFSSL_HAVE_SP_ECC */
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