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wolfssl/wolfcrypt/src/sp_int.c

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/* sp_int.c
*
* Copyright (C) 2006-2020 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>
#ifdef NO_INLINE
#include <wolfssl/wolfcrypt/misc.h>
#else
#define WOLFSSL_MISC_INCLUDED
#include <wolfcrypt/src/misc.c>
#endif
/* SP Build Options:
* WOLFSSL_HAVE_SP_RSA: Enable SP RSA support
* WOLFSSL_HAVE_SP_DH: Enable SP DH support
* WOLFSSL_HAVE_SP_ECC: Enable SP ECC support
* WOLFSSL_SP_MATH: Use only single precision math and algorithms it supports (no fastmath tfm.c or normal integer.c)
* WOLFSSL_SP_SMALL: Use smaller version of code and avoid large stack variables
* WOLFSSL_SP_NO_MALLOC: Always use stack, no heap XMALLOC/XFREE allowed
* WOLFSSL_SP_NO_2048: Disable RSA/DH 2048-bit support
* WOLFSSL_SP_NO_3072: Disable RSA/DH 3072-bit support
* WOLFSSL_SP_4096: Enable RSA/RH 4096-bit support
* WOLFSSL_SP_384 Enable ECC 384-bit SECP384R1 support
* WOLFSSL_SP_NO_256 Disable ECC 256-bit SECP256R1 support
* WOLFSSL_SP_CACHE_RESISTANT Enable cache resistantant code
* WOLFSSL_SP_ASM Enable assembly speedups (detect platform)
* WOLFSSL_SP_X86_64_ASM Enable Intel x86 assembly speedups like AVX/AVX2
* WOLFSSL_SP_ARM32_ASM Enable Aarch32 assembly speedups
* WOLFSSL_SP_ARM64_ASM Enable Aarch64 assembly speedups
* WOLFSSL_SP_ARM_CORTEX_M_ASM Enable Cortex-M assembly speedups
* WOLFSSL_SP_ARM_THUMB_ASM Enable ARM Thumb assembly speedups (used with -mthumb)
* SP_WORD_SIZE Force 32 or 64 bit mode
*/
#ifdef WOLFSSL_SP_MATH
#include <wolfssl/wolfcrypt/sp_int.h>
#if defined(WOLFSSL_HAVE_SP_DH) || defined(WOLFSSL_HAVE_SP_RSA)
WOLFSSL_LOCAL int sp_ModExp_1024(sp_int* base, sp_int* exp, sp_int* mod,
sp_int* res);
WOLFSSL_LOCAL int sp_ModExp_1536(sp_int* base, sp_int* exp, sp_int* mod,
sp_int* res);
WOLFSSL_LOCAL int sp_ModExp_2048(sp_int* base, sp_int* exp, sp_int* mod,
sp_int* res);
WOLFSSL_LOCAL int sp_ModExp_3072(sp_int* base, sp_int* exp, sp_int* mod,
sp_int* res);
WOLFSSL_LOCAL int sp_ModExp_4096(sp_int* base, sp_int* exp, sp_int* mod,
sp_int* res);
#endif
int sp_get_digit_count(sp_int *a)
{
int ret;
if (!a)
ret = 0;
else
ret = a->used;
return ret;
}
/* Initialize the big number to be zero.
*
* a SP integer.
* returns MP_OKAY always.
*/
int sp_init(sp_int* a)
{
a->used = 0;
a->size = SP_INT_DIGITS;
return MP_OKAY;
}
#if !defined(WOLFSSL_RSA_PUBLIC_ONLY) || (!defined(NO_DH) || defined(HAVE_ECC))
/* Initialize up to six big numbers to be zero.
*
* a SP integer.
* b SP integer.
* c SP integer.
* d SP integer.
* e SP integer.
* f SP integer.
* returns MP_OKAY always.
*/
int sp_init_multi(sp_int* a, sp_int* b, sp_int* c, sp_int* d, sp_int* e,
sp_int* f)
{
if (a != NULL) {
a->used = 0;
a->size = SP_INT_DIGITS;
}
if (b != NULL) {
b->used = 0;
b->size = SP_INT_DIGITS;
}
if (c != NULL) {
c->used = 0;
c->size = SP_INT_DIGITS;
}
if (d != NULL) {
d->used = 0;
d->size = SP_INT_DIGITS;
}
if (e != NULL) {
e->used = 0;
e->size = SP_INT_DIGITS;
}
if (f != NULL) {
f->used = 0;
f->size = SP_INT_DIGITS;
}
return MP_OKAY;
}
#endif
/* Clear the data from the big number and set to zero.
*
* a SP integer.
*/
void sp_clear(sp_int* a)
{
if (a != NULL) {
int i;
for (i=0; i<a->used; i++)
a->dp[i] = 0;
a->used = 0;
}
}
/* Calculate the number of 8-bit values required to represent the big number.
*
* a SP integer.
* returns the count.
*/
int sp_unsigned_bin_size(sp_int* a)
{
int size = sp_count_bits(a);
return (size + 7) / 8;
}
/* Convert a number as an array of bytes in big-endian format to a big number.
*
* a SP integer.
* in Array of bytes.
* inSz Number of data bytes in array.
* returns BAD_FUNC_ARG when the number is too big to fit in an SP and
MP_OKAY otherwise.
*/
int sp_read_unsigned_bin(sp_int* a, const byte* in, int inSz)
{
int err = MP_OKAY;
int i, j = 0, k;
if (inSz > SP_INT_DIGITS * (int)sizeof(a->dp[0])) {
err = MP_VAL;
}
if (err == MP_OKAY) {
for (i = inSz-1; i >= (SP_WORD_SIZE/8); i -= (SP_WORD_SIZE/8), j++) {
a->dp[j] = (((sp_int_digit)in[i-0]) << (0*8))
| (((sp_int_digit)in[i-1]) << (1*8))
| (((sp_int_digit)in[i-2]) << (2*8))
| (((sp_int_digit)in[i-3]) << (3*8));
#if SP_WORD_SIZE == 64
a->dp[j] |= (((sp_int_digit)in[i-4]) << (4*8))
| (((sp_int_digit)in[i-5]) << (5*8))
| (((sp_int_digit)in[i-6]) << (6*8))
| (((sp_int_digit)in[i-7]) << (7*8));
#endif
}
if (i >= 0) {
a->dp[j] = 0;
for (k = 0; k <= i; k++) {
a->dp[j] <<= 8;
a->dp[j] |= in[k];
}
}
a->used = j + 1;
}
sp_clamp(a);
return err;
}
#ifdef HAVE_ECC
/* Convert a number as string in big-endian format to a big number.
* Only supports base-16 (hexadecimal).
* Negative values not supported.
*
* a SP integer.
* in NUL terminated string.
* radix Number of values in a digit.
* returns BAD_FUNC_ARG when radix not supported or value is negative, MP_VAL
* when a character is not valid and MP_OKAY otherwise.
*/
int sp_read_radix(sp_int* a, const char* in, int radix)
{
int err = MP_OKAY;
int i, j = 0, k = 0;
char ch;
if ((radix != 16) || (*in == '-')) {
err = BAD_FUNC_ARG;
}
while (*in == '0') {
in++;
}
if (err == MP_OKAY) {
a->dp[0] = 0;
for (i = (int)(XSTRLEN(in) - 1); i >= 0; i--) {
ch = in[i];
if (ch >= '0' && ch <= '9')
ch -= '0';
else if (ch >= 'A' && ch <= 'F')
ch -= 'A' - 10;
else if (ch >= 'a' && ch <= 'f')
ch -= 'a' - 10;
else {
err = MP_VAL;
break;
}
a->dp[k] |= ((sp_int_digit)ch) << j;
j += 4;
if (k >= SP_INT_DIGITS - 1) {
err = MP_VAL;
break;
}
if (j == DIGIT_BIT)
a->dp[++k] = 0;
j &= SP_WORD_SIZE - 1;
}
}
if (err == MP_OKAY) {
a->used = k + 1;
if (a->dp[k] == 0)
a->used--;
for (k++; k < a->size; k++)
a->dp[k] = 0;
sp_clamp(a);
}
return err;
}
#endif
/* Compare two big numbers.
*
* a SP integer.
* b SP integer.
* returns MP_GT if a is greater than b, MP_LT if a is less than b and MP_EQ
* when a equals b.
*/
int sp_cmp(sp_int* a, sp_int* b)
{
int ret = MP_EQ;
int i;
if (a->used > b->used)
ret = MP_GT;
else if (a->used < b->used)
ret = MP_LT;
else {
for (i = a->used - 1; i >= 0; i--) {
if (a->dp[i] > b->dp[i]) {
ret = MP_GT;
break;
}
else if (a->dp[i] < b->dp[i]) {
ret = MP_LT;
break;
}
}
}
return ret;
}
/* Count the number of bits in the big number.
*
* a SP integer.
* returns the number of bits.
*/
int sp_count_bits(sp_int* a)
{
int r = 0;
sp_int_digit d;
r = a->used - 1;
while (r >= 0 && a->dp[r] == 0)
r--;
if (r < 0)
r = 0;
else {
d = a->dp[r];
r *= SP_WORD_SIZE;
if (d >= (1L << (SP_WORD_SIZE / 2))) {
r += SP_WORD_SIZE;
while ((d & (1UL << (SP_WORD_SIZE - 1))) == 0) {
r--;
d <<= 1;
}
}
else {
while (d != 0) {
r++;
d >>= 1;
}
}
}
return r;
}
/* Determine if the most significant byte of the encoded big number as the top
* bit set.
*
* a SP integer.
* returns 1 when the top bit is set and 0 otherwise.
*/
int sp_leading_bit(sp_int* a)
{
int bit = 0;
sp_int_digit d;
if (a->used > 0) {
d = a->dp[a->used - 1];
while (d > (sp_int_digit)0xff)
d >>= 8;
bit = (int)(d >> 7);
}
return bit;
}
#if !defined(NO_DH) || defined(HAVE_ECC) || defined(WC_RSA_BLINDING) || \
!defined(WOLFSSL_RSA_VERIFY_ONLY)
/* Convert the big number to an array of bytes in big-endian format.
* The array must be large enough for encoded number - use mp_unsigned_bin_size
* to calculate the number of bytes required.
*
* a SP integer.
* out Array to put encoding into.
* returns MP_OKAY always.
*/
int sp_to_unsigned_bin(sp_int* a, byte* out)
{
int i, j, b;
sp_int_digit d;
j = sp_unsigned_bin_size(a) - 1;
for (i=0; j>=0; i++) {
d = a->dp[i];
for (b = 0; b < SP_WORD_SIZE / 8; b++) {
out[j] = d;
if (--j < 0) {
break;
}
d >>= 8;
}
}
return MP_OKAY;
}
#endif
/* Convert the big number to an array of bytes in big-endian format.
* The array must be large enough for encoded number - use mp_unsigned_bin_size
* to calculate the number of bytes required.
* Front-pads the output array with zeros make number the size of the array.
*
* a SP integer.
* out Array to put encoding into.
* outSz Size of the array.
* returns MP_OKAY always.
*/
int sp_to_unsigned_bin_len(sp_int* a, byte* out, int outSz)
{
int i, j, b;
j = outSz - 1;
for (i=0; j>=0; i++) {
for (b = 0; b < SP_WORD_SIZE; b += 8) {
out[j--] = a->dp[i] >> b;
if (j < 0)
break;
}
}
return MP_OKAY;
}
#if !defined(WOLFSSL_RSA_PUBLIC_ONLY) || (!defined(NO_DH) || defined(HAVE_ECC))
/* Ensure the data in the big number is zeroed.
*
* a SP integer.
*/
void sp_forcezero(sp_int* a)
{
ForceZero(a->dp, a->used * sizeof(sp_int_digit));
a->used = 0;
}
#endif
#if !defined(WOLFSSL_RSA_VERIFY_ONLY) || (!defined(NO_DH) || defined(HAVE_ECC))
/* Copy value of big number a into r.
*
* a SP integer.
* r SP integer.
* returns MP_OKAY always.
*/
int sp_copy(sp_int* a, sp_int* r)
{
if (a != r) {
XMEMCPY(r->dp, a->dp, a->used * sizeof(sp_int_digit));
r->used = a->used;
}
return MP_OKAY;
}
/* creates "a" then copies b into it */
int sp_init_copy (sp_int * a, sp_int * b)
{
int err;
if ((err = sp_init(a)) == MP_OKAY) {
if((err = sp_copy (b, a)) != MP_OKAY) {
sp_clear(a);
}
}
return err;
}
#endif
/* Set the big number to be the value of the digit.
*
* a SP integer.
* d Digit to be set.
* returns MP_OKAY always.
*/
int sp_set(sp_int* a, sp_int_digit d)
{
if (d == 0) {
a->dp[0] = d;
a->used = 0;
}
else {
a->dp[0] = d;
a->used = 1;
}
return MP_OKAY;
}
/* Recalculate the number of digits used.
*
* a SP integer.
*/
void sp_clamp(sp_int* a)
{
int i;
for (i = a->used - 1; i >= 0 && a->dp[i] == 0; i--) {
}
a->used = i + 1;
}
#if defined(WOLFSSL_RSA_VERIFY_ONLY) || (!defined(NO_DH) || defined(HAVE_ECC))
/* Grow big number to be able to hold l digits.
* This function does nothing as the number of digits is fixed.
*
* a SP integer.
* l Number of digits.
* returns MP_MEM if the number of digits requested is more than available and
* MP_OKAY otherwise.
*/
int sp_grow(sp_int* a, int l)
{
int err = MP_OKAY;
if (l > a->size)
err = MP_MEM;
return err;
}
#endif
#if !defined(WOLFSSL_RSA_VERIFY_ONLY) || (!defined(NO_DH) || defined(HAVE_ECC))
/* Sub a one digit number from the big number.
*
* a SP integer.
* d Digit to subtract.
* r SP integer - result.
* returns MP_OKAY always.
*/
int sp_sub_d(sp_int* a, sp_int_digit d, sp_int* r)
{
int i = 0;
sp_int_digit t;
r->used = a->used;
t = a->dp[0] - d;
if (t > a->dp[0]) {
for (++i; i < a->used; i++) {
r->dp[i] = a->dp[i] - 1;
if (r->dp[i] != (sp_int_digit)-1)
break;
}
}
r->dp[0] = t;
if (r != a) {
for (++i; i < a->used; i++)
r->dp[i] = a->dp[i];
}
sp_clamp(r);
return MP_OKAY;
}
#endif
/* Compare a one digit number with a big number.
*
* a SP integer.
* d Digit to compare with.
* returns MP_GT if a is greater than d, MP_LT if a is less than d and MP_EQ
* when a equals d.
*/
int sp_cmp_d(sp_int *a, sp_int_digit d)
{
int ret = MP_EQ;
/* special case for zero*/
if (a->used == 0) {
if (d == 0)
ret = MP_EQ;
else
ret = MP_LT;
}
else if (a->used > 1)
ret = MP_GT;
else {
/* compare the only digit of a to d */
if (a->dp[0] > d)
ret = MP_GT;
else if (a->dp[0] < d)
ret = MP_LT;
}
return ret;
}
#if !defined(NO_DH) || defined(HAVE_ECC) || !defined(WOLFSSL_RSA_VERIFY_ONLY)
/* Left shift the number by number of bits.
* Bits may be larger than the word size.
*
* a SP integer.
* n Number of bits to shift.
* returns MP_OKAY always.
*/
static int sp_lshb(sp_int* a, int n)
{
int i;
if (n >= SP_WORD_SIZE) {
sp_lshd(a, n / SP_WORD_SIZE);
n %= SP_WORD_SIZE;
}
if (n != 0) {
a->dp[a->used] = 0;
for (i = a->used - 1; i >= 0; i--) {
a->dp[i+1] |= a->dp[i] >> (SP_WORD_SIZE - n);
a->dp[i] = a->dp[i] << n;
}
if (a->dp[a->used] != 0)
a->used++;
}
return MP_OKAY;
}
/* Subtract two large numbers into result: r = a - b
* a must be greater than b.
*
* a SP integer.
* b SP integer.
* r SP integer.
* returns MP_OKAY always.
*/
int sp_sub(sp_int* a, sp_int* b, sp_int* r)
{
int i;
sp_int_digit c = 0;
sp_int_digit t;
for (i = 0; i < a->used && i < b->used; i++) {
t = a->dp[i] - b->dp[i] - c;
if (c == 0)
c = t > a->dp[i];
else
c = t >= a->dp[i];
r->dp[i] = t;
}
for (; i < a->used; i++) {
r->dp[i] = a->dp[i] - c;
c &= (r->dp[i] == (sp_int_digit)-1);
}
r->used = i;
sp_clamp(r);
return MP_OKAY;
}
/* Shift a right by n bits into r: r = a >> n
*
* a SP integer operand.
* n Number of bits to shift.
* r SP integer result.
*/
void sp_rshb(sp_int* a, int n, sp_int* r)
{
int i;
int j;
for (i = n / SP_WORD_SIZE, j = 0; i < a->used-1; i++, j++)
r->dp[i] = (a->dp[j] >> n) | (a->dp[j+1] << (SP_WORD_SIZE - n));
r->dp[i] = a->dp[j] >> n;
r->used = j + 1;
sp_clamp(r);
}
/* Multiply a by digit n and put result into r shifting up o digits.
* r = (a * n) << (o * SP_WORD_SIZE)
*
* a SP integer to be multiplied.
* n Number to multiply by.
* r SP integer result.
* o Number of digits to move result up by.
*/
static void _sp_mul_d(sp_int* a, sp_int_digit n, sp_int* r, int o)
{
int i;
sp_int_word t = 0;
for (i = 0; i < o; i++)
r->dp[i] = 0;
for (i = 0; i < a->used; i++) {
t += (sp_int_word)n * a->dp[i];
r->dp[i + o] = (sp_int_digit)t;
t >>= SP_WORD_SIZE;
}
r->dp[i+o] = (sp_int_digit)t;
r->used = i+o+1;
sp_clamp(r);
}
/* Divide a by d and return the quotient in r and the remainder in rem.
* r = a / d; rem = a % d
*
* a SP integer to be divided.
* d SP integer to divide by.
* r SP integer of quotient.
* rem SP integer of remainder.
* returns MP_VAL when d is 0, MP_MEM when dynamic memory allocation fails and
* MP_OKAY otherwise.
*/
static int sp_div(sp_int* a, sp_int* d, sp_int* r, sp_int* rem)
{
int err = MP_OKAY;
int ret;
int done = 0;
int i;
int s;
#ifndef WOLFSSL_SP_DIV_32
sp_int_word w = 0;
#endif
sp_int_digit dt;
sp_int_digit t;
#ifdef WOLFSSL_SMALL_STACK
sp_int* sa = NULL;
sp_int* sd;
sp_int* tr;
sp_int* trial;
#else
sp_int sa[1];
sp_int sd[1];
sp_int tr[1];
sp_int trial[1];
#endif
if (sp_iszero(d))
err = MP_VAL;
ret = sp_cmp(a, d);
if (ret == MP_LT) {
if (rem != NULL) {
sp_copy(a, rem);
}
if (r != NULL) {
sp_set(r, 0);
}
done = 1;
}
else if (ret == MP_EQ) {
if (rem != NULL) {
sp_set(rem, 0);
}
if (r != NULL) {
sp_set(r, 1);
}
done = 1;
}
else if (sp_count_bits(a) == sp_count_bits(d)) {
/* a is greater than d but same bit length */
if (rem != NULL) {
sp_sub(a, d, rem);
}
if (r != NULL) {
sp_set(r, 1);
}
done = 1;
}
#ifdef WOLFSSL_SMALL_STACK
if (!done && err == MP_OKAY) {
sa = (sp_int*)XMALLOC(sizeof(sp_int) * 4, NULL, DYNAMIC_TYPE_BIGINT);
if (sa == NULL) {
err = MP_MEM;
}
}
#endif
if (!done && err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
sd = &sa[1];
tr = &sa[2];
trial = &sa[3];
#endif
sp_init(sa);
sp_init(sd);
sp_init(tr);
sp_init(trial);
s = sp_count_bits(d);
s = SP_WORD_SIZE - (s % SP_WORD_SIZE);
sp_copy(a, sa);
if (s != SP_WORD_SIZE) {
sp_lshb(sa, s);
sp_copy(d, sd);
sp_lshb(sd, s);
d = sd;
}
tr->used = sa->used - d->used + 1;
sp_clear(tr);
tr->used = sa->used - d->used + 1;
dt = d->dp[d->used-1];
#ifndef WOLFSSL_SP_DIV_32
for (i = sa->used - 1; i >= d->used; ) {
if (sa->dp[i] > dt) {
t = (sp_int_digit)-1;
}
else {
w = ((sp_int_word)sa->dp[i] << SP_WORD_SIZE) | sa->dp[i-1];
w /= dt;
if (w > (sp_int_digit)-1) {
t = (sp_int_digit)-1;
}
else {
t = (sp_int_digit)w;
}
}
if (t > 0) {
_sp_mul_d(d, t, trial, i - d->used);
while (sp_cmp(trial, sa) == MP_GT) {
t--;
_sp_mul_d(d, t, trial, i - d->used);
}
sp_sub(sa, trial, sa);
tr->dp[i - d->used] += t;
if (tr->dp[i - d->used] < t)
tr->dp[i + 1 - d->used]++;
}
i = sa->used - 1;
}
#else
{
sp_int_digit div = (dt >> (SP_WORD_SIZE / 2)) + 1;
for (i = sa->used - 1; i >= d->used; ) {
t = sa->dp[i] / div;
if ((t > 0) && (t << (SP_WORD_SIZE / 2) == 0))
t = (sp_int_digit)-1;
t <<= SP_WORD_SIZE / 2;
if (t == 0) {
t = sa->dp[i] << (SP_WORD_SIZE / 2);
t += sa->dp[i-1] >> (SP_WORD_SIZE / 2);
t /= div;
}
if (t > 0) {
_sp_mul_d(d, t, trial, i - d->used);
while (sp_cmp(trial, sa) == MP_GT) {
t--;
_sp_mul_d(d, t, trial, i - d->used);
}
sp_sub(sa, trial, sa);
tr->dp[i - d->used] += t;
if (tr->dp[i - d->used] < t)
tr->dp[i + 1 - d->used]++;
}
i = sa->used - 1;
}
while (sp_cmp(sa, d) != MP_LT) {
sp_sub(sa, d, sa);
sp_add_d(tr, 1, tr);
}
}
#endif
sp_clamp(tr);
if (rem != NULL) {
if (s != SP_WORD_SIZE)
sp_rshb(sa, s, sa);
sp_copy(sa, rem);
}
if (r != NULL)
sp_copy(tr, r);
}
#ifdef WOLFSSL_SMALL_STACK
if (sa != NULL)
XFREE(sa, NULL, DYNAMIC_TYPE_BIGINT);
#endif
return err;
}
#ifndef FREESCALE_LTC_TFM
/* Calculate the remainder of dividing a by m: r = a mod m.
*
* a SP integer.
* m SP integer.
* r SP integer.
* returns MP_VAL when m is 0 and MP_OKAY otherwise.
*/
int sp_mod(sp_int* a, sp_int* m, sp_int* r)
{
return sp_div(a, m, NULL, r);
}
#endif
#endif
/* Clear all data in the big number and sets value to zero.
*
* a SP integer.
*/
void sp_zero(sp_int* a)
{
XMEMSET(a->dp, 0, a->size * sizeof(*a->dp));
a->used = 0;
}
/* Add a one digit number to the big number.
*
* a SP integer.
* d Digit to add.
* r SP integer - result.
* returns MP_OKAY always.
*/
int sp_add_d(sp_int* a, sp_int_digit d, sp_int* r)
{
int i = 0;
r->used = a->used;
if (a->used == 0) {
r->used = 1;
}
r->dp[0] = a->dp[0] + d;
if (r->dp[i] < a->dp[i]) {
for (; i < a->used; i++) {
r->dp[i] = a->dp[i] + 1;
if (r->dp[i] != 0)
break;
}
if (i == a->used) {
r->used++;
r->dp[i] = 1;
}
}
for (; i < a->used; i++)
r->dp[i] = a->dp[i];
return MP_OKAY;
}
#if !defined(NO_DH) || defined(HAVE_ECC) || defined(WC_RSA_BLINDING) || \
!defined(WOLFSSL_RSA_VERIFY_ONLY)
/* Left shift the big number by a number of digits.
* WIll chop off digits overflowing maximum size.
*
* a SP integer.
* s Number of digits to shift.
* returns MP_OKAY always.
*/
int sp_lshd(sp_int* a, int s)
{
if (a->used + s > a->size)
a->used = a->size - s;
XMEMMOVE(a->dp + s, a->dp, a->used * sizeof(sp_int_digit));
a->used += s;
XMEMSET(a->dp, 0, s * sizeof(sp_int_digit));
sp_clamp(a);
return MP_OKAY;
}
#endif
#if !defined(NO_PWDBASED) || defined(WOLFSSL_KEY_GEN) || !defined(NO_DH)
/* Add two large numbers into result: r = a + b
*
* a SP integer.
* b SP integer.
* r SP integer.
* returns MP_OKAY always.
*/
int sp_add(sp_int* a, sp_int* b, sp_int* r)
{
int i;
sp_int_digit c = 0;
sp_int_digit t;
for (i = 0; i < a->used && i < b->used; i++) {
t = a->dp[i] + b->dp[i] + c;
if (c == 0)
c = t < a->dp[i];
else
c = t <= a->dp[i];
r->dp[i] = t;
}
for (; i < a->used; i++) {
r->dp[i] = a->dp[i] + c;
c = (a->dp[i] != 0) && (r->dp[i] == 0);
}
for (; i < b->used; i++) {
r->dp[i] = b->dp[i] + c;
c = (b->dp[i] != 0) && (r->dp[i] == 0);
}
r->dp[i] = c;
r->used = (int)(i + c);
return MP_OKAY;
}
#endif /* !NO_PWDBASED || WOLFSSL_KEY_GEN || !NO_DH */
#ifndef NO_RSA
/* Set a number into the big number.
*
* a SP integer.
* b Value to set.
* returns MP_OKAY always.
*/
int sp_set_int(sp_int* a, unsigned long b)
{
if (b == 0) {
a->used = 0;
a->dp[0] = 0;
}
else {
a->used = 1;
a->dp[0] = (sp_int_digit)b;
}
return MP_OKAY;
}
#endif /* !NO_RSA */
#ifdef WC_MP_TO_RADIX
/* Hex string characters. */
static const char sp_hex_char[16] = {
'0', '1', '2', '3', '4', '5', '6', '7',
'8', '9', 'a', 'b', 'c', 'd', 'e', 'f'
};
/* Put the hex string version, big-endian, of a in str.
*
* a SP integer.
* str Hex string is stored here.
* returns MP_OKAY always.
*/
int sp_tohex(sp_int* a, char* str)
{
int i, j;
/* quick out if its zero */
if (sp_iszero(a) == MP_YES) {
*str++ = '0';
*str = '\0';
}
else {
i = a->used - 1;
for (j = SP_WORD_SIZE - 4; j >= 0; j -= 4) {
if (((a->dp[i] >> j) & 0xf) != 0)
break;
}
for (; j >= 0; j -= 4)
*(str++) = sp_hex_char[(a->dp[i] >> j) & 0xf];
for (--i; i >= 0; i--) {
for (j = SP_WORD_SIZE - 4; j >= 0; j -= 4)
*(str++) = sp_hex_char[(a->dp[i] >> j) & 0xf];
}
*str = '\0';
}
return MP_OKAY;
}
#endif /* WC_MP_TO_RADIX */
#if defined(WOLFSSL_KEY_GEN) || !defined(NO_DH) && !defined(WC_NO_RNG)
/* Set a bit of a: a |= 1 << i
* The field 'used' is updated in a.
*
* a SP integer to modify.
* i Index of bit to set.
* returns MP_OKAY always.
*/
int sp_set_bit(sp_int* a, int i)
{
int ret = MP_OKAY;
if ((a == NULL) || (i / SP_WORD_SIZE >= SP_INT_DIGITS)) {
ret = BAD_FUNC_ARG;
}
else {
a->dp[i/SP_WORD_SIZE] |= (sp_int_digit)1 << (i % SP_WORD_SIZE);
if (a->used <= i / SP_WORD_SIZE)
a->used = (i / SP_WORD_SIZE) + 1;
}
return ret;
}
/* Exponentiate 2 to the power of e: a = 2^e
* This is done by setting the 'e'th bit.
*
* a SP integer.
* e Exponent.
* returns MP_OKAY always.
*/
int sp_2expt(sp_int* a, int e)
{
sp_zero(a);
return sp_set_bit(a, e);
}
/* Generate a random prime for RSA only.
*
* r SP integer
* len Number of bytes to prime.
* rng Random number generator.
* heap Unused
* returns MP_OKAY on success and MP_VAL when length is not supported or random
* number genrator fails.
*/
int sp_rand_prime(sp_int* r, int len, WC_RNG* rng, void* heap)
{
static const int USE_BBS = 1;
int err = 0, type;
int isPrime = MP_NO;
(void)heap;
/* get type */
if (len < 0) {
type = USE_BBS;
len = -len;
}
else {
type = 0;
}
#if defined(WOLFSSL_HAVE_SP_DH) && defined(WOLFSSL_KEY_GEN)
if (len == 32) {
}
else
#endif
/* Generate RSA primes that are half the modulus length. */
#ifndef WOLFSSL_SP_NO_3072
if (len != 128 && len != 192)
#else
if (len != 128)
#endif
{
err = MP_VAL;
}
r->used = len / (SP_WORD_SIZE / 8);
/* Assume the candidate is probably prime and then test until
* it is proven composite. */
while (err == 0 && isPrime == MP_NO) {
#ifdef SHOW_GEN
printf(".");
fflush(stdout);
#endif
/* generate value */
err = wc_RNG_GenerateBlock(rng, (byte*)r->dp, len);
if (err != 0) {
err = MP_VAL;
break;
}
/* munge bits */
((byte*)r->dp)[len-1] |= 0x80 | 0x40;
r->dp[0] |= 0x01 | ((type & USE_BBS) ? 0x02 : 0x00);
/* test */
/* Running Miller-Rabin up to 3 times gives us a 2^{-80} chance
* of a 1024-bit candidate being a false positive, when it is our
* prime candidate. (Note 4.49 of Handbook of Applied Cryptography.)
* Using 8 because we've always used 8 */
sp_prime_is_prime_ex(r, 8, &isPrime, rng);
}
return err;
}
/* Multiply a by b and store in r: r = a * b
*
* a SP integer to multiply.
* b SP integer to multiply.
* r SP integer result.
* returns MP_OKAY always.
*/
int sp_mul(sp_int* a, sp_int* b, sp_int* r)
{
int err = MP_OKAY;
int i;
#ifdef WOLFSSL_SMALL_STACK
sp_int* t = NULL;
sp_int* tr;
#else
sp_int t[1];
sp_int tr[1];
#endif
if (a->used + b->used > SP_INT_DIGITS)
err = MP_VAL;
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
t = (sp_int*)XMALLOC(sizeof(sp_int) * 2, NULL, DYNAMIC_TYPE_BIGINT);
if (t == NULL)
err = MP_MEM;
else
tr = &t[1];
}
#endif
if (err == MP_OKAY) {
sp_init(t);
sp_init(tr);
for (i = 0; i < b->used; i++) {
_sp_mul_d(a, b->dp[i], t, i);
sp_add(tr, t, tr);
}
sp_copy(tr, r);
}
#ifdef WOLFSSL_SMALL_STACK
if (t != NULL)
XFREE(t, NULL, DYNAMIC_TYPE_BIGINT);
#endif
return err;
}
/* Square a mod m and store in r: r = (a * a) mod m
*
* a SP integer to square.
* m SP integer modulus.
* r SP integer result.
* returns MP_VAL when m is 0, MP_MEM when dynamic memory allocation fails,
* BAD_FUNC_ARG when a is to big and MP_OKAY otherwise.
*/
static int sp_sqrmod(sp_int* a, sp_int* m, sp_int* r)
{
int err = MP_OKAY;
if (a->used * 2 > SP_INT_DIGITS)
err = MP_VAL;
if (err == MP_OKAY)
err = sp_mul(a, a, r);
if (err == MP_OKAY)
err = sp_mod(r, m, r);
return err;
}
#if defined(WOLFSSL_HAVE_SP_DH) || defined(WOLFSSL_KEY_GEN)
/* Multiply a by b mod m and store in r: r = (a * b) mod m
*
* a SP integer to multiply.
* b SP integer to multiply.
* m SP integer modulus.
* r SP integer result.
* returns MP_VAL when m is 0, MP_MEM when dynamic memory allocation fails and
* MP_OKAY otherwise.
*/
int sp_mulmod(sp_int* a, sp_int* b, sp_int* m, sp_int* r)
{
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
sp_int* t = NULL;
#else
sp_int t[1];
#endif
if (a->used + b->used > SP_INT_DIGITS)
err = MP_VAL;
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
t = (sp_int*)XMALLOC(sizeof(sp_int), NULL, DYNAMIC_TYPE_BIGINT);
if (t == NULL) {
err = MP_MEM;
}
}
#endif
if (err == MP_OKAY) {
err = sp_mul(a, b, t);
}
if (err == MP_OKAY) {
err = sp_mod(t, m, r);
}
#ifdef WOLFSSL_SMALL_STACK
if (t != NULL)
XFREE(t, NULL, DYNAMIC_TYPE_BIGINT);
#endif
return err;
}
#endif
/* Calculate a modulo the digit d into r: r = a mod d
*
* a SP integer to square.
* d SP integer digit, modulus.
* r SP integer digit, result.
* returns MP_VAL when d is 0 and MP_OKAY otherwise.
*/
static int sp_mod_d(sp_int* a, const sp_int_digit d, sp_int_digit* r)
{
int err = MP_OKAY;
int i;
sp_int_word w = 0;
sp_int_digit t;
if (d == 0)
err = MP_VAL;
if (err == MP_OKAY) {
for (i = a->used - 1; i >= 0; i--) {
w = (w << SP_WORD_SIZE) | a->dp[i];
t = (sp_int_digit)(w / d);
w -= (sp_int_word)t * d;
}
*r = (sp_int_digit)w;
}
return err;
}
/* Calculates the Greatest Common Denominator (GCD) of a and b into r.
*
* a SP integer operand.
* b SP integer operand.
* r SP integer result.
* returns MP_MEM when dynamic memory allocation fails and MP_OKAY otherwise.
*/
int sp_gcd(sp_int* a, sp_int* b, sp_int* r)
{
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
sp_int* u = NULL;
sp_int* v;
sp_int* t;
#else
sp_int u[1], v[1], t[1];
#endif
if (sp_iszero(a))
sp_copy(b, r);
else if (sp_iszero(b))
sp_copy(a, r);
else {
#ifdef WOLFSSL_SMALL_STACK
u = (sp_int*)XMALLOC(sizeof(sp_int) * 3, NULL, DYNAMIC_TYPE_BIGINT);
if (u == NULL)
err = MP_MEM;
else {
v = &u[1];
t = &u[2];
}
#endif
if (err == MP_OKAY) {
sp_init(u);
sp_init(v);
sp_init(t);
if (sp_cmp(a, b) != MP_LT) {
sp_copy(b, u);
/* First iteration - u = a, v = b */
if (b->used == 1) {
err = sp_mod_d(a, b->dp[0], &v->dp[0]);
if (err == MP_OKAY)
v->used = (v->dp[0] != 0);
}
else
err = sp_mod(a, b, v);
}
else {
sp_copy(a, u);
/* First iteration - u = b, v = a */
if (a->used == 1) {
err = sp_mod_d(b, a->dp[0], &v->dp[0]);
if (err == MP_OKAY)
v->used = (v->dp[0] != 0);
}
else
err = sp_mod(b, a, v);
}
}
if (err == MP_OKAY) {
while (!sp_iszero(v)) {
if (v->used == 1) {
sp_mod_d(u, v->dp[0], &t->dp[0]);
t->used = (t->dp[0] != 0);
}
else
sp_mod(u, v, t);
sp_copy(v, u);
sp_copy(t, v);
}
sp_copy(u, r);
}
}
#ifdef WOLFSSL_SMALL_STACK
if (u != NULL)
XFREE(u, NULL, DYNAMIC_TYPE_BIGINT);
#endif
return err;
}
/* Divides a by 2 and stores in r: r = a >> 1
*
* a SP integer to divide.
* r SP integer result.
* returns MP_OKAY always.
*/
static int sp_div_2(sp_int* a, sp_int* r)
{
int i;
for (i = 0; i < a->used-1; i++)
r->dp[i] = (a->dp[i] >> 1) | (a->dp[i+1] << (SP_WORD_SIZE - 1));
r->dp[i] = a->dp[i] >> 1;
r->used = i + 1;
sp_clamp(r);
return MP_OKAY;
}
/* Calculates the multiplicative inverse in the field.
*
* a SP integer to invert.
* m SP integer that is the modulus of the field.
* r SP integer result.
* returns MP_VAL when a or m is 0, MP_MEM when dynamic memory allocation fails
* and MP_OKAY otherwise.
*/
int sp_invmod(sp_int* a, sp_int* m, sp_int* r)
{
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
sp_int* u = NULL;
sp_int* v;
sp_int* b;
sp_int* c;
#else
sp_int u[1], v[1], b[1], c[1];
#endif
#ifdef WOLFSSL_SMALL_STACK
u = (sp_int*)XMALLOC(sizeof(sp_int) * 4, NULL, DYNAMIC_TYPE_BIGINT);
if (u == NULL) {
err = MP_MEM;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
v = &u[1];
b = &u[2];
c = &u[3];
#endif
sp_init(v);
if (sp_cmp(a, m) != MP_LT) {
err = sp_mod(a, m, v);
a = v;
}
}
/* 0 != n*m + 1 (+ve m), r*a mod 0 is always 0 (never 1) */
if ((err == MP_OKAY) && (sp_iszero(a) || sp_iszero(m))) {
err = MP_VAL;
}
/* r*2*x != n*2*y + 1 */
if ((err == MP_OKAY) && sp_iseven(a) && sp_iseven(m)) {
err = MP_VAL;
}
/* 1*1 = 0*m + 1 */
if ((err == MP_OKAY) && sp_isone(a)) {
sp_set(r, 1);
}
else if (err != MP_OKAY) {
}
else if (sp_iseven(m)) {
/* a^-1 mod m = m + (1 - m*(m^-1 % a)) / a
* = m - (m*(m^-1 % a) - 1) / a
*/
err = sp_invmod(m, a, r);
if (err == MP_OKAY) {
err = sp_mul(r, m, r);
}
if (err == MP_OKAY) {
sp_sub_d(r, 1, r);
sp_div(r, a, r, NULL);
sp_sub(m, r, r);
}
}
else {
if (err == MP_OKAY) {
sp_init(u);
sp_init(b);
sp_init(c);
sp_copy(m, u);
sp_copy(a, v);
sp_zero(b);
sp_set(c, 1);
while (!sp_isone(v) && !sp_iszero(u)) {
if (sp_iseven(u)) {
sp_div_2(u, u);
if (sp_isodd(b)) {
sp_add(b, m, b);
}
sp_div_2(b, b);
}
else if (sp_iseven(v)) {
sp_div_2(v, v);
if (sp_isodd(c)) {
sp_add(c, m, c);
}
sp_div_2(c, c);
}
else if (sp_cmp(u, v) != MP_LT) {
sp_sub(u, v, u);
if (sp_cmp(b, c) == MP_LT) {
sp_add(b, m, b);
}
sp_sub(b, c, b);
}
else {
sp_sub(v, u, v);
if (sp_cmp(c, b) == MP_LT) {
sp_add(c, m, c);
}
sp_sub(c, b, c);
}
}
if (sp_iszero(u)) {
err = MP_VAL;
}
else {
sp_copy(c, r);
}
}
}
#ifdef WOLFSSL_SMALL_STACK
if (u != NULL) {
XFREE(u, NULL, DYNAMIC_TYPE_BIGINT);
}
#endif
return err;
}
/* Calculates the Lowest Common Multiple (LCM) of a and b and stores in r.
*
* a SP integer operand.
* b SP integer operand.
* r SP integer result.
* returns MP_MEM when dynamic memory allocation fails and MP_OKAY otherwise.
*/
int sp_lcm(sp_int* a, sp_int* b, sp_int* r)
{
int err = MP_OKAY;
#ifndef WOLFSSL_SMALL_STACK
sp_int t[2];
#else
sp_int *t = NULL;
#endif
#ifdef WOLFSSL_SMALL_STACK
t = (sp_int*)XMALLOC(sizeof(sp_int) * 2, NULL, DYNAMIC_TYPE_BIGINT);
if (t == NULL) {
err = MP_MEM;
}
#endif
if (err == MP_OKAY) {
sp_init(&t[0]);
sp_init(&t[1]);
err = sp_gcd(a, b, &t[0]);
if (err == MP_OKAY) {
if (sp_cmp(a, b) == MP_GT) {
err = sp_div(a, &t[0], &t[1], NULL);
if (err == MP_OKAY)
err = sp_mul(b, &t[1], r);
}
else {
err = sp_div(b, &t[0], &t[1], NULL);
if (err == MP_OKAY)
err = sp_mul(a, &t[1], r);
}
}
}
#ifdef WOLFSSL_SMALL_STACK
if (t != NULL)
XFREE(t, NULL, DYNAMIC_TYPE_BIGINT);
#endif
return err;
}
/* Exponentiates b to the power of e modulo m into r: r = b ^ e mod m
*
* b SP integer base.
* e SP integer exponent.
* m SP integer modulus.
* r SP integer result.
* returns MP_VAL when m is not 1024, 2048, 1536 or 3072 bits and otherwise
* MP_OKAY.
*/
int sp_exptmod(sp_int* b, sp_int* e, sp_int* m, sp_int* r)
{
int err = MP_OKAY;
int done = 0;
int mBits = sp_count_bits(m);
int bBits = sp_count_bits(b);
int eBits = sp_count_bits(e);
if (sp_iszero(m)) {
err = MP_VAL;
}
else if (sp_isone(m)) {
sp_set(r, 0);
done = 1;
}
else if (sp_iszero(e)) {
sp_set(r, 1);
done = 1;
}
else if (sp_iszero(b)) {
sp_set(r, 0);
done = 1;
}
else if (m->used * 2 > SP_INT_DIGITS) {
err = BAD_FUNC_ARG;
}
if (!done && (err == MP_OKAY)) {
#ifndef WOLFSSL_SP_NO_2048
if ((mBits == 1024) && sp_isodd(m) && (bBits <= 1024) &&
(eBits <= 1024)) {
err = sp_ModExp_1024(b, e, m, r);
done = 1;
}
else if ((mBits == 2048) && sp_isodd(m) && (bBits <= 2048) &&
(eBits <= 2048)) {
err = sp_ModExp_2048(b, e, m, r);
done = 1;
}
else
#endif
#ifndef WOLFSSL_SP_NO_3072
if ((mBits == 1536) && sp_isodd(m) && (bBits <= 1536) &&
(eBits <= 1536)) {
err = sp_ModExp_1536(b, e, m, r);
done = 1;
}
else if ((mBits == 3072) && sp_isodd(m) && (bBits <= 3072) &&
(eBits <= 3072)) {
err = sp_ModExp_3072(b, e, m, r);
done = 1;
}
else
#endif
#ifdef WOLFSSL_SP_4096
if ((mBits == 4096) && sp_isodd(m) && (bBits <= 4096) &&
(eBits <= 4096)) {
err = sp_ModExp_4096(b, e, m, r);
done = 1;
}
else
#endif
{
}
}
#if defined(WOLFSSL_HAVE_SP_DH) && defined(WOLFSSL_KEY_GEN)
if (!done && (err == MP_OKAY)) {
int i;
#ifdef WOLFSSL_SMALL_STACK
sp_int* t = NULL;
#else
sp_int t[1];
#endif
#ifdef WOLFSSL_SMALL_STACK
if (!done && (err == MP_OKAY)) {
t = (sp_int*)XMALLOC(sizeof(sp_int), NULL, DYNAMIC_TYPE_BIGINT);
if (t == NULL) {
err = MP_MEM;
}
}
#endif
if (!done && (err == MP_OKAY)) {
sp_init(t);
if (sp_cmp(b, m) != MP_LT) {
err = sp_mod(b, m, t);
if (err == MP_OKAY && sp_iszero(t)) {
sp_set(r, 0);
done = 1;
}
}
else {
sp_copy(b, t);
}
if (!done && (err == MP_OKAY)) {
for (i = eBits-2; err == MP_OKAY && i >= 0; i--) {
err = sp_sqrmod(t, m, t);
if (err == MP_OKAY && (e->dp[i / SP_WORD_SIZE] >>
(i % SP_WORD_SIZE)) & 1) {
err = sp_mulmod(t, b, m, t);
}
}
}
}
if (!done && (err == MP_OKAY)) {
sp_copy(t, r);
}
#ifdef WOLFSSL_SMALL_STACK
if (t != NULL) {
XFREE(t, NULL, DYNAMIC_TYPE_BIGINT);
}
#endif
}
#else
if (!done && (err == MP_OKAY)) {
err = MP_VAL;
}
#endif
(void)mBits;
(void)bBits;
(void)eBits;
return err;
}
/* Number of entries in array of number of least significant zero bits. */
#define SP_LNZ_CNT 16
/* Number of bits the array checks. */
#define SP_LNZ_BITS 4
/* Mask to apply to check with array. */
#define SP_LNZ_MASK 0xf
/* Number of least significant zero bits in first SP_LNZ_CNT numbers. */
static const int lnz[SP_LNZ_CNT] = {
4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
};
/* Count the number of least significant zero bits.
*
* a Number to check
* returns the count of least significant zero bits.
*/
static int sp_cnt_lsb(sp_int* a)
{
int i, j;
int cnt = 0;
int bc = 0;
if (!sp_iszero(a)) {
for (i = 0; i < a->used && a->dp[i] == 0; i++, cnt += SP_WORD_SIZE) {
}
for (j = 0; j < SP_WORD_SIZE; j += SP_LNZ_BITS) {
bc = lnz[(a->dp[i] >> j) & SP_LNZ_MASK];
if (bc != 4) {
bc += cnt + j;
break;
}
}
}
return bc;
}
/* Miller-Rabin test of "a" to the base of "b" as described in
* HAC pp. 139 Algorithm 4.24
*
* Sets result to 0 if definitely composite or 1 if probably prime.
* Randomly the chance of error is no more than 1/4 and often
* very much lower.
*
* a SP integer to check.
* b SP integer small prime.
* result Whether a is likely prime: MP_YES or MP_NO.
* n1 SP integer operand.
* y SP integer operand.
* r SP integer operand.
* returns MP_VAL when a is not 1024, 2048, 1536 or 3072 and MP_OKAY otherwise.
*/
static int sp_prime_miller_rabin_ex(sp_int * a, sp_int * b, int *result,
sp_int *n1, sp_int *y, sp_int *r)
{
int s, j;
int err = MP_OKAY;
/* default */
*result = MP_NO;
/* ensure b > 1 */
if (sp_cmp_d(b, 1) == MP_GT) {
/* get n1 = a - 1 */
sp_copy(a, n1);
sp_sub_d(n1, 1, n1);
/* set 2**s * r = n1 */
sp_copy(n1, r);
/* count the number of least significant bits
* which are zero
*/
s = sp_cnt_lsb(r);
/* now divide n - 1 by 2**s */
sp_rshb(r, s, r);
/* compute y = b**r mod a */
sp_zero(y);
err = sp_exptmod(b, r, a, y);
if (err == MP_OKAY) {
/* probably prime until shown otherwise */
*result = MP_YES;
/* if y != 1 and y != n1 do */
if (sp_cmp_d(y, 1) != MP_EQ && sp_cmp(y, n1) != MP_EQ) {
j = 1;
/* while j <= s-1 and y != n1 */
while ((j <= (s - 1)) && sp_cmp(y, n1) != MP_EQ) {
sp_sqrmod(y, a, y);
/* if y == 1 then composite */
if (sp_cmp_d(y, 1) == MP_EQ) {
*result = MP_NO;
break;
}
++j;
}
/* if y != n1 then composite */
if (*result == MP_YES && sp_cmp(y, n1) != MP_EQ)
*result = MP_NO;
}
}
}
return err;
}
/* Miller-Rabin test of "a" to the base of "b" as described in
* HAC pp. 139 Algorithm 4.24
*
* Sets result to 0 if definitely composite or 1 if probably prime.
* Randomly the chance of error is no more than 1/4 and often
* very much lower.
*
* a SP integer to check.
* b SP integer small prime.
* result Whether a is likely prime: MP_YES or MP_NO.
* returns MP_MEM when dynamic memory allocation fails, MP_VAL when a is not
* 1024, 2048, 1536 or 3072 and MP_OKAY otherwise.
*/
static int sp_prime_miller_rabin(sp_int * a, sp_int * b, int *result)
{
int err = MP_OKAY;
#ifndef WOLFSSL_SMALL_STACK
sp_int n1[1], y[1], r[1];
#else
sp_int *n1 = NULL, *y, *r;
#endif
#ifdef WOLFSSL_SMALL_STACK
n1 = (sp_int*)XMALLOC(sizeof(sp_int) * 3, NULL, DYNAMIC_TYPE_BIGINT);
if (n1 == NULL)
err = MP_MEM;
else {
y = &n1[1];
r = &n1[2];
}
#endif
if (err == MP_OKAY) {
sp_init(n1);
sp_init(y);
sp_init(r);
err = sp_prime_miller_rabin_ex(a, b, result, n1, y, r);
sp_clear(n1);
sp_clear(y);
sp_clear(r);
}
#ifdef WOLFSSL_SMALL_STACK
if (n1 != NULL)
XFREE(n1, NULL, DYNAMIC_TYPE_BIGINT);
#endif
return err;
}
/* Number of pre-computed primes. First n primes. */
#define SP_PRIME_SIZE 256
/* a few primes */
static const sp_int_digit primes[SP_PRIME_SIZE] = {
0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, 0x0083,
0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
};
/* Check whether a is prime.
* Checks against a number of small primes and does t iterations of
* Miller-Rabin.
*
* a SP integer to check.
* t Number of iterations of Muller-Rabin to perform.
* result MP_YES when prime.
* MP_NO when not prime.
* returns MP_VAL when t is out of range, MP_MEM when dynamic memory allocation
* fails and otherwise MP_OKAY.
*/
int sp_prime_is_prime(sp_int *a, int t, int* result)
{
int err = MP_OKAY;
int i;
int haveRes = 0;
#ifndef WOLFSSL_SMALL_STACK
sp_int b[1];
#else
sp_int *b = NULL;
#endif
sp_int_digit d;
if (t <= 0 || t > SP_PRIME_SIZE) {
*result = MP_NO;
err = MP_VAL;
}
if (sp_isone(a)) {
*result = MP_NO;
return MP_OKAY;
}
if (err == MP_OKAY && a->used == 1) {
/* check against primes table */
for (i = 0; i < SP_PRIME_SIZE; i++) {
if (sp_cmp_d(a, primes[i]) == MP_EQ) {
*result = MP_YES;
haveRes = 1;
break;
}
}
}
if (err == MP_OKAY && !haveRes) {
/* do trial division */
for (i = 0; i < SP_PRIME_SIZE; i++) {
err = sp_mod_d(a, primes[i], &d);
if (err != MP_OKAY || d == 0) {
*result = MP_NO;
haveRes = 1;
break;
}
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY && !haveRes) {
b = (sp_int*)XMALLOC(sizeof(sp_int), NULL, DYNAMIC_TYPE_BIGINT);
if (b == NULL)
err = MP_MEM;
}
#endif
if (err == MP_OKAY && !haveRes) {
/* now do 't' miller rabins */
sp_init(b);
for (i = 0; i < t; i++) {
sp_set(b, primes[i]);
err = sp_prime_miller_rabin(a, b, result);
if (err != MP_OKAY || *result == MP_NO)
break;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (b != NULL)
XFREE(b, NULL, DYNAMIC_TYPE_BIGINT);
#endif
return err;
}
/* Check whether a is prime.
* Checks against a number of small primes and does t iterations of
* Miller-Rabin.
*
* a SP integer to check.
* t Number of iterations of Muller-Rabin to perform.
* result MP_YES when prime.
* MP_NO when not prime.
* rng Random number generator.
* returns MP_VAL when t is out of range, MP_MEM when dynamic memory allocation
* fails and otherwise MP_OKAY.
*/
int sp_prime_is_prime_ex(sp_int* a, int t, int* result, WC_RNG* rng)
{
int err = MP_OKAY;
int ret = MP_YES;
int haveRes = 0;
int i;
#ifndef WC_NO_RNG
#ifndef WOLFSSL_SMALL_STACK
sp_int b[1], c[1], n1[1], y[1], r[1];
#else
sp_int *b = NULL, *c = NULL, *n1 = NULL, *y = NULL, *r = NULL;
#endif
word32 baseSz;
#endif
if (a == NULL || result == NULL || rng == NULL)
err = MP_VAL;
if (sp_isone(a)) {
*result = MP_NO;
return MP_OKAY;
}
if (err == MP_OKAY && a->used == 1) {
/* check against primes table */
for (i = 0; i < SP_PRIME_SIZE; i++) {
if (sp_cmp_d(a, primes[i]) == MP_EQ) {
ret = MP_YES;
haveRes = 1;
break;
}
}
}
if (err == MP_OKAY && !haveRes) {
sp_int_digit d;
/* do trial division */
for (i = 0; i < SP_PRIME_SIZE; i++) {
err = sp_mod_d(a, primes[i], &d);
if (err != MP_OKAY || d == 0) {
ret = MP_NO;
haveRes = 1;
break;
}
}
}
#ifndef WC_NO_RNG
/* now do a miller rabin with up to t random numbers, this should
* give a (1/4)^t chance of a false prime. */
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY && !haveRes) {
b = (sp_int*)XMALLOC(sizeof(sp_int) * 5, NULL, DYNAMIC_TYPE_BIGINT);
if (b == NULL) {
err = MP_MEM;
}
else {
c = &b[1]; n1 = &b[2]; y= &b[3]; r = &b[4];
}
}
#endif
if (err == MP_OKAY && !haveRes) {
sp_init(b);
sp_init(c);
sp_init(n1);
sp_init(y);
sp_init(r);
err = sp_sub_d(a, 2, c);
}
if (err == MP_OKAY && !haveRes) {
baseSz = (sp_count_bits(a) + 7) / 8;
while (t > 0) {
err = wc_RNG_GenerateBlock(rng, (byte*)b->dp, baseSz);
if (err != MP_OKAY)
break;
b->used = a->used;
if (sp_cmp_d(b, 2) != MP_GT || sp_cmp(b, c) != MP_LT)
continue;
err = sp_prime_miller_rabin_ex(a, b, &ret, n1, y, r);
if (err != MP_OKAY || ret == MP_NO)
break;
t--;
}
sp_clear(n1);
sp_clear(y);
sp_clear(r);
sp_clear(b);
sp_clear(c);
}
#ifdef WOLFSSL_SMALL_STACK
if (b != NULL)
XFREE(b, NULL, DYNAMIC_TYPE_BIGINT);
#endif
#else
(void)t;
#endif /* !WC_NO_RNG */
*result = ret;
return err;
}
#ifndef NO_DH
int sp_exch(sp_int* a, sp_int* b)
{
int err = MP_OKAY;
#ifndef WOLFSSL_SMALL_STACK
sp_int t[1];
#else
sp_int *t = NULL;
#endif
#ifdef WOLFSSL_SMALL_STACK
t = (sp_int*)XMALLOC(sizeof(sp_int), NULL, DYNAMIC_TYPE_BIGINT);
if (t == NULL)
err = MP_MEM;
#endif
if (err == MP_OKAY) {
*t = *a;
*a = *b;
*b = *t;
}
#ifdef WOLFSSL_SMALL_STACK
if (t != NULL)
XFREE(t, NULL, DYNAMIC_TYPE_BIGINT);
#endif
return MP_OKAY;
}
#endif
#endif
#if defined(WOLFSSL_KEY_GEN) && !defined(NO_RSA)
/* Multiply a by digit n and put result into r. r = a * n
*
* a SP integer to be multiplied.
* n Number to multiply by.
* r SP integer result.
* returns MP_OKAY always.
*/
int sp_mul_d(sp_int* a, sp_int_digit n, sp_int* r)
{
_sp_mul_d(a, n, r, 0);
return MP_OKAY;
}
#endif
/* Returns the run time settings.
*
* returns the settings value.
*/
word32 CheckRunTimeSettings(void)
{
return CTC_SETTINGS;
}
#endif /* WOLFSSL_SP_MATH */
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