mars_nwe/mars-matrixssl
1
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity
Files
ee35b936b3965ffc854acc7613b4e44c94640a73
mars-matrixssl/crypto/math/pstm.c
Janne Johansson 97f62f766d MatrixSSL 3.8.7 changed files.
2016-11-28 09:48:14 +02:00

2505 lines
57 KiB
C
Raw Blame History

/**
* @file pstm.c
* @version $Format:%h%d$
*
* Multiprecision number implementation.
*/
/*
* Copyright (c) 2013-2016 INSIDE Secure Corporation
* Copyright (c) PeerSec Networks, 2002-2011
* All Rights Reserved
*
* The latest version of this code is available at http://www.matrixssl.org
*
* This software is open source; 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.
*
* This General Public License does NOT permit incorporating this software
* into proprietary programs. If you are unable to comply with the GPL, a
* commercial license for this software may be purchased from INSIDE at
* http://www.insidesecure.com/
*
* This program is distributed in 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
* http://www.gnu.org/copyleft/gpl.html
*/
/******************************************************************************/
/* This pstm mathematics library is
based on libraries by Tom St Denis. */
#include "../cryptoApi.h"
#include <ctype.h> /* toupper() */
#if defined(USE_MATRIX_RSA) || defined(USE_MATRIX_ECC) || defined(USE_MATRIX_DH) || defined(USE_CL_RSA) || defined(USE_CL_DH) || defined(USE_QUICK_ASSIST_RSA) || defined(USE_QUICK_ASSIST_ECC)
static int32_t pstm_mul_2d(const pstm_int *a, int16_t b, pstm_int *c);
/******************************************************************************/
/**
Initialize a pstm_int and allocate working memory for a given initial size.
@param[in] pool Memory pool to use for allocation.
@param[in,out] a Allocated pstm_int to initialize.
@param[in] size Number of digits to pre-allocate for integer. Typically
a digit is 32 or 64 bits.
@return < 0 on failure, >=0 on success.
*/
int32_t pstm_init_size(psPool_t *pool, pstm_int *a, uint16_t size)
{
uint16_t x;
if (size > PSTM_MAX_SIZE) {
return PSTM_MEM;
}
a->dp = psMalloc(pool, sizeof(pstm_digit) * size);
if (a->dp == NULL) {
return PSTM_MEM;
}
a->pool = pool; /* Pool to use when growing or shrinking digits */
a->used = 0; /* Zero of the digits are currently used */
a->alloc = size; /* How many digits are pre-allocated */
a->sign = PSTM_ZPOS; /* Number is positive */
/* zero the digits */
for (x = 0; x < size; x++) {
a->dp[x] = 0;
}
return PSTM_OKAY;
}
/******************************************************************************/
/*
Init a new pstm_int with a default size.
*/
int32_t pstm_init(psPool_t *pool, pstm_int *a)
{
return pstm_init_size(pool, a, (MIN_RSA_BITS / DIGIT_BIT) * 3);
}
/******************************************************************************/
/**
Grow a pstm_int to the give size in digits.
@param[in,out] a Allocated and initialized pstm_int to grow.
@param[in] size Number of digits to grow to. This is not the the number
of digits to grow _by_. 'size' <= current size is ignored, so this
api cannot be used to shrink the integer.
*/
int32_t pstm_grow(pstm_int * a, uint16_t size)
{
uint16_t i;
pstm_digit *tmp;
if (size > PSTM_MAX_SIZE) {
return PSTM_MEM;
}
/* If the alloc size is smaller alloc more ram. */
if (a->alloc < size) {
/*
Reallocate the array a->dp
We store the return in a temporary variable in case the operation
failed we don't want to overwrite the dp member of a.
*/
tmp = psRealloc(a->dp, sizeof (pstm_digit) * size, a->pool);
if (tmp == NULL) {
/* reallocation failed but "a" is still valid [can be freed] */
return PSTM_MEM;
}
/* reallocation succeeded so set a->dp */
a->dp = tmp;
i = a->alloc;
a->alloc = size;
/* zero excess digits */
for (; i < a->alloc; i++) {
a->dp[i] = 0;
}
}
return PSTM_OKAY;
}
/******************************************************************************/
/*
copy, b = a (b must be pre-allocated)
*/
int32_t pstm_copy(const pstm_int * a, pstm_int * b)
{
int32_t res, n;
/* If dst == src do nothing */
if (a == b) {
return PSTM_OKAY;
}
/* Grow dest */
if (b->alloc < a->used) {
if ((res = pstm_grow(b, a->used)) != PSTM_OKAY) {
return res;
}
}
/* Zero b and copy the parameters over */
{
/* pointer aliases */
register pstm_digit *tmpa, *tmpb;
/* source */
tmpa = a->dp;
/* destination */
tmpb = b->dp;
/* copy all the digits */
for (n = 0; n < a->used; n++) {
*tmpb++ = *tmpa++;
}
/* clear high digits */
for (; n < b->used; n++) {
*tmpb++ = 0;
}
}
/* copy used count and sign */
b->used = a->used;
b->sign = a->sign;
return PSTM_OKAY;
}
/******************************************************************************/
/**
b = |a|.
Copy 'a' to 'b' and make positive.
*/
int32_t pstm_abs(const pstm_int *a, pstm_int *b)
{
if (pstm_copy(a, b) != PSTM_OKAY) {
return PSTM_MEM;
}
b->sign = 0;
return PSTM_OKAY;
}
/******************************************************************************/
/**
Trim unused digits.
This is used to ensure that leading zero digits are trimed and the
leading "used" digit will be non-zero. Typically very fast. Also fixes
the sign if there are no more leading digits
*/
void pstm_clamp(pstm_int *a)
{
/* decrease used while the most significant digit is zero. */
while (a->used > 0 && a->dp[a->used - 1] == 0) {
--(a->used);
}
/* reset the sign flag if used == 0 */
if (a->used == 0) {
a->sign = PSTM_ZPOS;
}
}
/******************************************************************************/
/**
Clear a big integer, and free associated working memory.
*/
void pstm_clear(pstm_int *a)
{
int32 i;
/* only do anything if a hasn't been freed previously */
if (a != NULL && a->dp != NULL) {
/* first zero the digits */
for (i = 0; i < a->used; i++) {
a->dp[i] = 0;
}
psFree (a->dp, a->pool);
/* reset members to make debugging easier */
a->dp = NULL;
a->alloc = a->used = 0;
a->sign = PSTM_ZPOS;
}
}
/******************************************************************************/
/**
Clears mp0 - mp7, stopping at the first NULL mp value.
@example pstm_clear_multi(a, b, c, d, NULL, NULL, NULL, NULL);
*/
void pstm_clear_multi(pstm_int *mp0, pstm_int *mp1, pstm_int *mp2,
pstm_int *mp3, pstm_int *mp4, pstm_int *mp5,
pstm_int *mp6, pstm_int *mp7)
{
if (mp0) {
pstm_clear(mp0);
if (mp1) {
pstm_clear(mp1);
if (mp2) {
pstm_clear(mp2);
if (mp3) {
pstm_clear(mp3);
if (mp4) {
pstm_clear(mp4);
if (mp5) {
pstm_clear(mp5);
if (mp6) {
pstm_clear(mp6);
if (mp7) {
pstm_clear(mp7);
}
}
}
}
}
}
}
}
}
/******************************************************************************/
/**
Set to zero.
*/
void pstm_zero(pstm_int * a)
{
uint16_t n;
pstm_digit *tmp;
a->sign = PSTM_ZPOS;
a->used = 0;
tmp = a->dp;
for (n = 0; n < a->alloc; n++) {
*tmp++ = 0;
}
}
/******************************************************************************/
/*
Compare maginitude of two ints (unsigned).
*/
int32_t pstm_cmp_mag(const pstm_int *a, const pstm_int *b)
{
uint16_t n;
const pstm_digit *tmpa, *tmpb;
/* compare based on # of non-zero digits */
if (a->used > b->used) {
return PSTM_GT;
} else if (a->used < b->used) {
return PSTM_LT;
}
/* alias for a */
tmpa = a->dp + (a->used - 1);
/* alias for b */
tmpb = b->dp + (a->used - 1);
/* compare based on digits */
for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
if (*tmpa > *tmpb) {
return PSTM_GT;
} else if (*tmpa < *tmpb) {
return PSTM_LT;
}
}
return PSTM_EQ;
}
/******************************************************************************/
/*
Compare two ints (signed)
*/
int32_t pstm_cmp(const pstm_int *a, const pstm_int *b)
{
/* compare based on sign */
if (a->sign != b->sign) {
if (a->sign == PSTM_NEG) {
return PSTM_LT;
} else {
return PSTM_GT;
}
}
/* compare digits */
if (a->sign == PSTM_NEG) {
/* if negative compare opposite direction */
return pstm_cmp_mag(b, a);
} else {
return pstm_cmp_mag(a, b);
}
}
/******************************************************************************/
/*
compare against a single digit
*/
int32_t pstm_cmp_d(const pstm_int *a, pstm_digit b)
{
/* compare based on sign */
if ((b && a->used == 0) || a->sign == PSTM_NEG) {
return PSTM_LT;
}
/* compare based on magnitude */
if (a->used > 1) {
return PSTM_GT;
}
/* compare the only digit of a to b */
if (a->dp[0] > b) {
return PSTM_GT;
} else if (a->dp[0] < b) {
return PSTM_LT;
} else {
return PSTM_EQ;
}
}
/******************************************************************************/
/*
pstm_ints can be initialized more precisely when they will populated
using pstm_read_unsigned_bin since the length of the byte stream is known
*/
int32_t pstm_init_for_read_unsigned_bin(psPool_t *pool, pstm_int *a, uint16_t len)
{
uint16_t size;
/*
Need to set this based on how many words max it will take to store the bin.
The magic + 2:
1 to round up for the remainder of this integer math
1 for the initial carry of '1' bits that fall between DIGIT_BIT and 8
*/
size = (((len / sizeof(pstm_digit)) * (sizeof(pstm_digit) * CHAR_BIT))
/ DIGIT_BIT) + 2;
return pstm_init_size(pool, a, size);
}
/******************************************************************************/
/**
Reads a unsigned char array into pstm_int format.
@param[in,out] a The allocated and initialized pstm_int
@param[in] b Pointer to a byte array of length 'c'.
@param[in] c Length in bytes of 'b'.
@pre User should have called pstm_init_for_read_unsigned_bin first.
@note There is some grow logic here if the default pstm_init was used but we
don't really want to hit it.
*/
int32_t pstm_read_unsigned_bin(pstm_int *a, const unsigned char *buf, uint16_t len)
{
/* zero the int */
pstm_zero (a);
/*
If we know the endianness of this architecture, and we're using
32-bit pstm_digits, we can optimize this
TODO Can optimize 64 bit case as well.
*/
#if (defined(ENDIAN_LITTLE) || defined(ENDIAN_BIG)) && !defined(PSTM_64BIT)
/* But not for both simultaneously */
#if defined(ENDIAN_LITTLE) && defined(ENDIAN_BIG)
#error Both ENDIAN_LITTLE and ENDIAN_BIG defined.
#endif
{
unsigned char *pd;
int16_t slen;
if ((unsigned)len > (PSTM_MAX_SIZE * sizeof(pstm_digit))) {
uint16_t excess = len - (PSTM_MAX_SIZE * sizeof(pstm_digit));
len -= excess;
buf += excess;
}
a->used = (len + sizeof(pstm_digit) - 1) / sizeof(pstm_digit);
if (a->alloc < a->used) {
if (pstm_grow(a, a->used) != PSTM_OKAY) {
return PSTM_MEM;
}
}
pd = (unsigned char *)a->dp;
/* read the bytes in */
/* these loops need len to go negative */
slen = (int16_t)len;
#ifdef ENDIAN_BIG
{
/* Use Duff's device to unroll the loop. */
uint16_t idx = (slen - 1) & ~3;
switch (slen % 4) {
case 0: do { pd[idx+0] = *buf++;
case 3: pd[idx+1] = *buf++;
case 2: pd[idx+2] = *buf++;
case 1: pd[idx+3] = *buf++;
idx -= 4;
} while ((slen -= 4) > 0);
}
}
#else
for (slen -= 1; slen >= 0; slen -= 1) {
pd[slen] = *buf++;
}
#endif
}
#else
/* Big enough based on the len? */
a->used = (((len / sizeof(pstm_digit)) * (sizeof(pstm_digit) * CHAR_BIT))
/ DIGIT_BIT) + 2;
if (a->alloc < a->used) {
if (pstm_grow(a, a->used) != PSTM_OKAY) {
return PSTM_MEM;
}
}
/* read the bytes in */
for (; len > 0; len--) {
if (pstm_mul_2d (a, 8, a) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
a->dp[0] |= *buf++;
a->used += 1;
}
#endif
pstm_clamp (a);
return PS_SUCCESS;
}
/******************************************************************************/
/**
Read a pstm_int from an ASN.1 formatted buffer.
*/
int32_t pstm_read_asn(psPool_t *pool, const unsigned char **pp, uint16_t len,
pstm_int *a)
{
const unsigned char *p = *pp;
uint16_t vlen;
if (len < 1 || *(p++) != ASN_INTEGER ||
getAsnLength(&p, len - 1, &vlen) < 0 || (len - 1) < vlen) {
return PS_PARSE_FAIL;
}
/* Make a smart size since we know the length */
if (pstm_init_for_read_unsigned_bin(pool, a, vlen) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
if (pstm_read_unsigned_bin(a, p, vlen) != 0) {
pstm_clear(a);
psTraceCrypto("pstm_read_asn failed\n");
return PS_PARSE_FAIL;
}
*pp = p + vlen;
return PS_SUCCESS;
}
#if defined USE_ECC || defined USE_DH || defined USE_CERT_GEN
/******************************************************************************/
/**
Add a digit to an int.
c = a + b;
@param[in] pool Memory pool
@param[in] a Big integer operand
@param[in] b Big digit operand
@param[out] c Big integer result
@return < 0 on failure
*/
int32_t pstm_add_d(psPool_t *pool, const pstm_int *a, pstm_digit b, pstm_int *c)
{
pstm_int tmp;
int32_t res;
if (pstm_init_size(pool, &tmp, sizeof(pstm_digit)) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
pstm_set(&tmp, b);
res = pstm_add(a, &tmp, c);
pstm_clear(&tmp);
return res;
}
#endif /* defined USE_ECC || defined USE_DH || defined USE_CERT_GEN */
#ifdef USE_ECC
/* chars used in radix (base) conversions */
const static unsigned char pstm_s_rmap[64] =
"0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
/**
Read in data to a big integer from a given radix (base).
Typically the radix is 16 to read in hex data.
To read in binary data, use pstm_read_unsigned_bin().
@param[in] pool Memory pool
@param[out] a Big integer to load data into.
@param[in] buf ASCII buffer containing 'len' bytes of data to read.
@param[in] len Number of bytes to read from 'buf'.
@param[in] radix Base of data in each byte of buf. Typically 16.
@return < 0 on failure
*/
int32_t pstm_read_radix(psPool_t *pool, pstm_int *a,
const char *buf, uint16_t len, uint8_t radix)
{
int32_t y, neg;
unsigned char ch;
/* make sure the radix is ok */
if (radix < 2 || radix > 64) {
return PS_ARG_FAIL;
}
/* if the leading digit is a minus set the sign to negative. */
if (*buf == '-') {
++buf; len--;
neg = PSTM_NEG;
} else {
neg = PSTM_ZPOS;
}
/* set the integer to the default of zero */
pstm_zero(a);
/* process each digit of the string */
while (len > 0) {
/*
if the radix < 36 the conversion is case insensitive this allows
numbers like 1AB and 1ab to represent the same value [e.g. in hex].
*/
ch = ((radix < 36) ?
(unsigned char)toupper((unsigned char)*buf) :
(unsigned char)*buf);
for (y = 0; y < 64; y++) {
if (ch == pstm_s_rmap[y]) {
break;
}
}
/*
if the char was found in the map and is less than the given
radix, add it to the number, otherwise exit the loop.
*/
if (y < radix) {
pstm_mul_d (a, (pstm_digit) radix, a);
pstm_add_d (pool, a, (pstm_digit) y, a);
} else {
break;
}
++buf; len--;
}
/* set the sign only if a != 0 */
if (pstm_iszero(a) != PS_TRUE) {
a->sign = neg;
}
return PS_SUCCESS;
}
#endif /* USE_ECC */
/******************************************************************************/
uint16_t pstm_count_bits(const pstm_int * a)
{
int16 r;
pstm_digit q;
if (a->used == 0) {
return 0;
}
/* get number of digits and add that */
r = (a->used - 1) * DIGIT_BIT;
/* take the last digit and count the bits in it */
q = a->dp[a->used - 1];
while (q > ((pstm_digit) 0)) {
++r;
q >>= ((pstm_digit) 1);
}
return r;
}
/******************************************************************************/
uint16_t pstm_unsigned_bin_size(const pstm_int *a)
{
uint16_t size = pstm_count_bits (a);
return (size / 8 + ((size & 7) != 0 ? 1 : 0));
}
/******************************************************************************/
/**
a = b, where b is a single digit.
*/
void pstm_set(pstm_int *a, pstm_digit b)
{
pstm_zero(a);
a->dp[0] = b;
a->used = a->dp[0] ? 1 : 0;
}
/******************************************************************************/
/**
Right shift 'a' by 'b' digits.
@note This is not a bit shift.
*/
void pstm_rshd(pstm_int *a, uint16_t b)
{
uint16_t y;
/* too many digits just zero and return */
if (b >= a->used) {
pstm_zero(a);
return;
}
/* shift */
for (y = 0; y < a->used - b; y++) {
a->dp[y] = a->dp[y + b];
}
/* zero the rest */
for (; y < a->used; y++) {
a->dp[y] = 0;
}
/* decrement count */
a->used -= b;
pstm_clamp(a);
}
/******************************************************************************/
/**
Left shift 'a' by 'b' digits.
This will grow 'a', and possibly cause a reallocation of memory.
@note This is not a bit shift.
*/
int32_t pstm_lshd(pstm_int *a, uint16_t b)
{
uint16_t x;
int32_t res;
/* If its less than zero return. */
if (b <= 0) {
return PSTM_OKAY;
}
/* Grow to fit the new digits. */
if (a->alloc < a->used + b) {
if ((res = pstm_grow(a, a->used + b)) != PSTM_OKAY) {
return res;
}
}
{
register pstm_digit *top, *bottom;
/* Increment the used by the shift amount then copy upwards. */
a->used += b;
/* top */
top = a->dp + a->used - 1;
/* base */
bottom = a->dp + a->used - 1 - b;
/*
This is implemented using a sliding window except the window goes the
other way around. Copying from the bottom to the top.
*/
for (x = a->used - 1; x >= b; x--) {
*top-- = *bottom--;
}
/* zero the lower digits */
top = a->dp;
for (x = 0; x < b; x++) {
*top++ = 0;
}
}
return PSTM_OKAY;
}
/******************************************************************************/
/**
a = 2**b.
*/
int32_t pstm_2expt(pstm_int *a, int16_t b)
{
uint16_t z;
/* zero a as per default */
pstm_zero (a);
if (b < 0) {
return PSTM_OKAY;
}
z = b / DIGIT_BIT;
if (z >= PSTM_MAX_SIZE) {
return PS_LIMIT_FAIL;
}
/* set the used count of where the bit will go */
a->used = z + 1;
if (a->used > a->alloc) {
if (pstm_grow(a, a->used) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
}
/* put the single bit in its place */
a->dp[z] = ((pstm_digit)1) << (b % DIGIT_BIT);
return PSTM_OKAY;
}
/******************************************************************************/
/**
b = a * 2.
Implements multiplication as a left shift of all digits of 1 bit.
*/
int32_t pstm_mul_2(const pstm_int *a, pstm_int * b)
{
int32 res;
int16 x, oldused;
/* grow to accomodate result */
if (b->alloc < a->used + 1) {
if ((res = pstm_grow (b, a->used + 1)) != PSTM_OKAY) {
return res;
}
}
oldused = b->used;
b->used = a->used;
{
register pstm_digit r, rr, *tmpa, *tmpb;
/* alias for source */
tmpa = a->dp;
/* alias for dest */
tmpb = b->dp;
/* carry */
r = 0;
for (x = 0; x < a->used; x++) {
/*
get what will be the *next* carry bit from the
MSB of the current digit
*/
rr = *tmpa >> ((pstm_digit)(DIGIT_BIT - 1));
/* now shift up this digit, add in the carry [from the previous] */
*tmpb++ = ((*tmpa++ << ((pstm_digit)1)) | r);
/*
copy the carry that would be from the source
digit into the next iteration
*/
r = rr;
}
/* new leading digit? */
if (r != 0 && b->used != (PSTM_MAX_SIZE-1)) {
/* add a MSB which is always 1 at this point */
*tmpb = 1;
++(b->used);
}
/* now zero any excess digits on the destination that we didn't write to */
tmpb = b->dp + b->used;
for (x = b->used; x < oldused; x++) {
*tmpb++ = 0;
}
}
b->sign = a->sign;
return PSTM_OKAY;
}
/******************************************************************************/
/**
unsigned subtraction ||a|| must be >= ||b|| ALWAYS.
c = a - b.
*/
int32_t s_pstm_sub(const pstm_int *a, const pstm_int *b, pstm_int *c)
{
int16 oldbused, oldused;
int32 x;
pstm_word t;
if (b->used > a->used) {
return PS_LIMIT_FAIL;
}
if (c->alloc < a->used) {
if ((x = pstm_grow(c, a->used)) != PSTM_OKAY) {
return x;
}
}
oldused = c->used;
oldbused = b->used;
c->used = a->used;
t = 0;
for (x = 0; x < oldbused; x++) {
t = ((pstm_word)a->dp[x]) - (((pstm_word)b->dp[x]) + t);
c->dp[x] = (pstm_digit)t;
t = (t >> DIGIT_BIT) & 1;
}
for (; x < a->used; x++) {
t = ((pstm_word)a->dp[x]) - t;
c->dp[x] = (pstm_digit)t;
t = (t >> DIGIT_BIT);
}
for (; x < oldused; x++) {
c->dp[x] = 0;
}
pstm_clamp(c);
return PSTM_OKAY;
}
/******************************************************************************/
/**
Unsigned addition of two big integers.
c = a + b;
@param[in] pool Memory pool
@param[in] a Big integer operand
@param[in] b Big integer operand
@param[out] c Big integer result
@return < 0 on failure
*/
static int32_t s_pstm_add(const pstm_int *a, const pstm_int *b, pstm_int *c)
{
int16 x, y, oldused;
register pstm_word t, adp, bdp;
y = a->used;
if (b->used > y) {
y = b->used;
}
oldused = c->used;
c->used = y;
if (c->used > c->alloc) {
if (pstm_grow(c, c->used) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
}
t = 0;
for (x = 0; x < y; x++) {
if (a->used <= x) {
adp = 0;
} else {
adp = (pstm_word)a->dp[x];
}
if (b->used <= x) {
bdp = 0;
} else {
bdp = (pstm_word)b->dp[x];
}
t += (adp) + (bdp);
c->dp[x] = (pstm_digit)t;
t >>= DIGIT_BIT;
}
if (t != 0 && x < PSTM_MAX_SIZE) {
if (c->used == c->alloc) {
if (pstm_grow(c, c->alloc + 1) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
}
c->dp[c->used++] = (pstm_digit)t;
++x;
}
c->used = x;
for (; x < oldused; x++) {
c->dp[x] = 0;
}
pstm_clamp(c);
return PSTM_OKAY;
}
/******************************************************************************/
/**
Signed subtraction. a and b can be any value.
c = a - b.
*/
int32_t pstm_sub(const pstm_int *a, const pstm_int *b, pstm_int *c)
{
int32 res;
int16 sa, sb;
sa = a->sign;
sb = b->sign;
if (sa != sb) {
/*
subtract a negative from a positive, OR a positive from a negative.
For both, ADD their magnitudes, and use the sign of the first number.
*/
c->sign = sa;
if ((res = s_pstm_add (a, b, c)) != PSTM_OKAY) {
return res;
}
} else {
/*
subtract a positive from a positive, OR a negative from a negative.
First, take the difference between their magnitudes, then...
*/
if (pstm_cmp_mag (a, b) != PSTM_LT) {
/* Copy the sign from the first */
c->sign = sa;
/* The first has a larger or equal magnitude */
if ((res = s_pstm_sub (a, b, c)) != PSTM_OKAY) {
return res;
}
} else {
/* The result has the _opposite_ sign from the first number. */
c->sign = (sa == PSTM_ZPOS) ? PSTM_NEG : PSTM_ZPOS;
/* The second has a larger magnitude */
if ((res = s_pstm_sub (b, a, c)) != PSTM_OKAY) {
return res;
}
}
}
return PS_SUCCESS;
}
/******************************************************************************/
/**
Signed subtraction of a digit.
c = a - b, where b is a digit
*/
int32_t pstm_sub_d(psPool_t *pool, const pstm_int *a, pstm_digit b, pstm_int *c)
{
pstm_int tmp;
int32_t res;
if (pstm_init_size(pool, &tmp, sizeof(pstm_digit)) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
pstm_set(&tmp, b);
res = pstm_sub(a, &tmp, c);
pstm_clear(&tmp);
return res;
}
/******************************************************************************/
/**
Sets up the montgomery reduction.
Fast inversion mod 2**k
Based on the fact that
XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
=> 2*X*A - X*X*A*A = 1
=> 2*(1) - (1) = 1
@param[in] a
@param[out] rho
*/
int32_t pstm_montgomery_setup(const pstm_int *a, pstm_digit *rho)
{
pstm_digit x, b;
b = a->dp[0];
if ((b & 1) == 0) {
psTraceCrypto("pstm_montogomery_setup failure\n");
return PS_ARG_FAIL;
}
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 */
#ifdef PSTM_64BIT
x *= 2 - b * x; /* here x*a==1 mod 2**64 */
#endif
/* rho = -1/m mod b */
*rho = (pstm_digit)(((pstm_word) 1 << ((pstm_word) DIGIT_BIT)) -
((pstm_word)x));
return PSTM_OKAY;
}
/******************************************************************************/
/**
a = B**n mod b, without division or multiplication.
Useful for normalizing numbers in a Montgomery system.
*/
int32_t pstm_montgomery_calc_normalization(pstm_int *a, const pstm_int *b)
{
uint16_t x, bits;
/* how many bits of last digit does b use */
bits = pstm_count_bits(b) % DIGIT_BIT;
if (!bits) bits = DIGIT_BIT;
/* compute A = B^(n-1) * 2^(bits-1) */
if (b->used > 1) {
if ((x = pstm_2expt(a, (b->used - 1) * DIGIT_BIT + bits - 1)) !=
PSTM_OKAY) {
return x;
}
} else {
pstm_set(a, 1);
bits = 1;
}
/* now compute C = A * B mod b */
for (x = bits - 1; x < (uint16_t)DIGIT_BIT; x++) {
if (pstm_mul_2 (a, a) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
if (pstm_cmp_mag (a, b) != PSTM_LT) {
if (s_pstm_sub (a, b, a) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
}
}
return PSTM_OKAY;
}
/******************************************************************************/
/*
c = a * 2**d
*/
static int32_t pstm_mul_2d(const pstm_int *a, int16_t b, pstm_int *c)
{
pstm_digit carry, carrytmp, shift;
uint16_t x;
/* copy it */
if (pstm_copy(a, c) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
/* handle whole digits */
if (b >= DIGIT_BIT) {
if (pstm_lshd(c, b/DIGIT_BIT) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
}
b %= DIGIT_BIT;
/* shift the digits */
if (b != 0) {
carry = 0;
shift = DIGIT_BIT - b;
for (x = 0; x < c->used; x++) {
carrytmp = c->dp[x] >> shift;
c->dp[x] = (c->dp[x] << b) + carry;
carry = carrytmp;
}
/* store last carry if room */
if (carry && x < PSTM_MAX_SIZE) {
if (c->used == c->alloc) {
if (pstm_grow(c, c->alloc + 1) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
}
c->dp[c->used++] = carry;
}
}
pstm_clamp(c);
return PSTM_OKAY;
}
/******************************************************************************/
/*
c = a mod 2**b
*/
static int32_t pstm_mod_2d(const pstm_int *a, int16_t b, pstm_int *c)
{
uint16_t x;
/* zero if count less than or equal to zero */
if (b <= 0) {
pstm_zero(c);
return PSTM_OKAY;
}
/* get copy of input */
if (pstm_copy(a, c) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
/* if 2**d is larger than we just return */
if (b >= (DIGIT_BIT * a->used)) {
return PSTM_OKAY;
}
/* zero digits above the last digit of the modulus */
for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++)
{
c->dp[x] = 0;
}
/* clear the digit that is not completely outside/inside the modulus */
c->dp[b / DIGIT_BIT] &= ~((pstm_digit)0) >> (DIGIT_BIT - b);
pstm_clamp (c);
return PSTM_OKAY;
}
/******************************************************************************/
/*
c = a * b
*/
int32_t pstm_mul_d(const pstm_int *a, const pstm_digit b, pstm_int *c)
{
pstm_word w;
int32 res;
int16 x, oldused;
if (c->alloc < a->used + 1) {
if ((res = pstm_grow (c, a->used + 1)) != PSTM_OKAY) {
return res;
}
}
oldused = c->used;
c->used = a->used;
c->sign = a->sign;
w = 0;
for (x = 0; x < a->used; x++) {
w = ((pstm_word)a->dp[x]) * ((pstm_word)b) + w;
c->dp[x] = (pstm_digit)w;
w = w >> DIGIT_BIT;
}
if (w != 0 && (a->used != PSTM_MAX_SIZE)) {
c->dp[c->used++] = (pstm_digit)w;
++x;
}
for (; x < oldused; x++) {
c->dp[x] = 0;
}
pstm_clamp(c);
return PSTM_OKAY;
}
/******************************************************************************/
/**
c = a / 2**b, d = remainder.
@param[in] pool Memory pool
@param[in] a Numerator
@param[in] b Exponent of the denominator
@param[out] c The result
@param[out] d If non-NULL, the remainder of the division is stored here
@return < 0 on failure
*/
int32_t pstm_div_2d(psPool_t *pool, const pstm_int *a, int16_t b, pstm_int *c,
pstm_int *d)
{
pstm_digit D, r, rr;
int32 res;
int16 x;
/* if the shift count is <= 0 then we do no work */
if (b <= 0) {
if (pstm_copy (a, c) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
if (d != NULL) {
pstm_zero (d);
}
return PSTM_OKAY;
}
/* copy */
if (pstm_copy(a, c) != PSTM_OKAY) {
res = PS_MEM_FAIL;
goto LBL_DONE;
}
/* shift by as many digits in the bit count */
if (b >= (int16_t)DIGIT_BIT) {
pstm_rshd (c, b / DIGIT_BIT);
}
/* shift any bit count < DIGIT_BIT */
D = (pstm_digit) (b % DIGIT_BIT);
if (D != 0) {
register pstm_digit *tmpc, mask, shift;
/* mask */
mask = (((pstm_digit)1) << D) - 1;
/* shift for lsb */
shift = DIGIT_BIT - D;
/* alias */
tmpc = c->dp + (c->used - 1);
/* carry */
r = 0;
for (x = c->used - 1; x >= 0; x--) {
/* get the lower bits of this word in a temp */
rr = *tmpc & mask;
/* shift the current word and mix in the carry bits from previous */
*tmpc = (*tmpc >> D) | (r << shift);
--tmpc;
/* set the carry to the carry bits of the current word above */
r = rr;
}
}
pstm_clamp (c);
res = PSTM_OKAY;
LBL_DONE:
/* set the remainder */
if (d != NULL) {
if (pstm_mod_2d(a, b, d) != PSTM_OKAY) {
res = PS_MEM_FAIL;
}
}
return res;
}
/******************************************************************************/
/**
b = a / 2.
Implemented as a right shift of one bit.
*/
int32_t pstm_div_2(const pstm_int *a, pstm_int *b)
{
int16 x, oldused;
if (b->alloc < a->used) {
if (pstm_grow(b, a->used) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
}
oldused = b->used;
b->used = a->used;
{
register pstm_digit r, rr, *tmpa, *tmpb;
/* source alias */
tmpa = a->dp + b->used - 1;
/* dest alias */
tmpb = b->dp + b->used - 1;
/* carry */
r = 0;
for (x = b->used - 1; x >= 0; x--) {
/* get the carry for the next iteration */
rr = *tmpa & 1;
/* shift the current digit, add in carry and store */
*tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
/* forward carry to next iteration */
r = rr;
}
/* zero excess digits */
tmpb = b->dp + b->used;
for (x = b->used; x < oldused; x++) {
*tmpb++ = 0;
}
}
b->sign = a->sign;
pstm_clamp (b);
return PSTM_OKAY;
}
/******************************************************************************/
/*
Creates "a" then copies b into it
*/
int32_t pstm_init_copy(psPool_t *pool, pstm_int *a, const pstm_int *b,
uint8_t toSqr)
{
int32_t res;
uint16_t x;
if (a == b) {
return PSTM_OKAY;
}
x = b->alloc;
if (toSqr) {
/*
Smart-size: Increasing size of a if b->used is roughly half
of b->alloc because usage has shown that a lot of these copies
go on to be squared and need these extra digits
*/
if ((b->used * 2) + 2 >= x) {
x = (b->used * 2) + 3;
}
}
if ((res = pstm_init_size(pool, a, x)) != PSTM_OKAY) {
return res;
}
return pstm_copy(b, a);
}
/******************************************************************************/
/*
With some compilers, we have seen issues linking with the builtin
64 bit division routine. The issues with either manifest in a failure
to find 'udivdi3' at link time, or a runtime invalid instruction fault
during an RSA operation.
The routine below divides a 64 bit unsigned int by a 32 bit unsigned int
explicitly, rather than using the division operation
The 64 bit result is placed in the 'numerator' parameter
The 32 bit mod (remainder) of the division is the return parameter
Based on implementations by:
Copyright (C) 2003 Bernardo Innocenti <bernie@develer.com>
Copyright (C) 1999 Hewlett-Packard Co
Copyright (C) 1999 David Mosberger-Tang <davidm@hpl.hp.com>
*/
#if defined(USE_MATRIX_DIV64) && defined(PSTM_32BIT)
static uint32 psDiv64(uint64 *numerator, uint32 denominator)
{
uint64 rem = *numerator;
uint64 b = denominator;
uint64 res = 0;
uint64 d = 1;
uint32 high = rem >> 32;
if (high >= denominator) {
high /= denominator;
res = (uint64) high << 32;
rem -= (uint64) (high * denominator) << 32;
}
while ((int64)b > 0 && b < rem) {
b = b+b;
d = d+d;
}
do {
if (rem >= b) {
rem -= b;
res += d;
}
b >>= 1;
d >>= 1;
} while (d);
*numerator = res;
return rem;
}
#endif /* USE_MATRIX_DIV64 */
#if defined(USE_MATRIX_DIV128) && defined(PSTM_64BIT)
typedef unsigned long uint128 __attribute__ ((mode(TI)));
static uint64 psDiv128(uint128 *numerator, uint64 denominator)
{
uint128 rem = *numerator;
uint128 b = denominator;
uint128 res = 0;
uint128 d = 1;
uint64 high = rem >> 64;
if (high >= denominator) {
high /= denominator;
res = (uint128) high << 64;
rem -= (uint128) (high * denominator) << 64;
}
while ((uint128)b > 0 && b < rem) {
b = b+b;
d = d+d;
}
do {
if (rem >= b) {
rem -= b;
res += d;
}
b >>= 1;
d >>= 1;
} while (d);
*numerator = res;
return rem;
}
#endif /* USE_MATRIX_DIV128 */
#ifndef PSTM_LARGE_DIV
/* This version of division uses short & small function, but offers
bit worse performance than some others. */
int pstm_div(psPool_t *pool, const pstm_int *a, const pstm_int *b,
pstm_int *c, pstm_int *d)
{
pstm_int ta, tb, tq, q;
int res, n, n2;
/* is divisor zero ? */
if (pstm_iszero(b) == PSTM_YES) {
return PS_LIMIT_FAIL;
}
/* if a < b then q=0, r = a */
if (pstm_cmp_mag(a, b) == PSTM_LT) {
if (d != NULL) {
res = pstm_copy(a, d);
} else {
res = PSTM_OKAY;
}
if (c != NULL) {
pstm_zero(c);
}
return res;
}
/* init our temps */
res = pstm_init(pool, &ta);
if (res != PSTM_OKAY) {
return res;
}
res = pstm_init(pool, &tb);
if (res != PSTM_OKAY) {
pstm_clear(&ta);
return res;
}
res = pstm_init(pool, &tq);
if (res != PSTM_OKAY) {
pstm_clear(&ta);
pstm_clear(&tb);
return res;
}
res = pstm_init(pool, &q);
if (res != PSTM_OKAY) {
pstm_clear(&ta);
pstm_clear(&tb);
pstm_clear(&tq);
return res;
}
pstm_set(&tq, 1);
n = pstm_count_bits(a) - pstm_count_bits(b);
if (((res = pstm_abs(a, &ta)) != PSTM_OKAY) ||
((res = pstm_abs(b, &tb)) != PSTM_OKAY) ||
((res = pstm_mul_2d(&tb, n, &tb)) != PSTM_OKAY) ||
((res = pstm_mul_2d(&tq, n, &tq)) != PSTM_OKAY)) {
goto LBL_ERR;
}
while (n-- >= 0) {
if (pstm_cmp(&tb, &ta) != PSTM_GT) {
if (((res = pstm_sub(&ta, &tb, &ta)) != PSTM_OKAY) ||
((res = pstm_add(&q, &tq, &q)) != PSTM_OKAY)) {
goto LBL_ERR;
}
}
if (((res = pstm_div_2d(pool, &tb, 1, &tb, NULL)) !=
PSTM_OKAY) ||
((res = pstm_div_2d(pool, &tq, 1, &tq, NULL)) !=
PSTM_OKAY)) {
goto LBL_ERR;
}
}
/* now q == quotient and ta == remainder */
n = a->sign;
n2 = (a->sign == b->sign) ? PSTM_ZPOS : PSTM_NEG;
if (c != NULL) {
pstm_exch(c, &q);
c->sign = (pstm_iszero(c) == PSTM_YES) ? PSTM_ZPOS : n2;
}
if (d != NULL) {
pstm_exch(d, &ta);
d->sign = (pstm_iszero(d) == PSTM_YES) ? PSTM_ZPOS : n;
}
LBL_ERR:
pstm_clear (&ta);
pstm_clear (&tb);
pstm_clear (&tq);
pstm_clear (&q);
return res;
}
#else /* defined PSTM_LARGE_DIV */
/* This noticed is accompanied with this function to discourage its use. */
#warning "This function has been noticed to give wrong results for some inputs."
/******************************************************************************/
/**
c = a / b, d = remainder.
@param[in] pool Memory pool
@param[in] a Numerator
@param[in] b Denominator
@param[out] c The result
@param[out] d If non-NULL, the remainder of the division is stored here
@return < 0 on failure
a/b => cb + d == a
*/
int32_t pstm_div(psPool_t *pool, const pstm_int *a, const pstm_int *b,
pstm_int *c, pstm_int *d)
{
pstm_int q, x, y, t1, t2;
int32_t res;
int16 n, t, i, norm, neg;
/* is divisor zero ? */
if (pstm_iszero (b) == 1) {
return PS_LIMIT_FAIL;
}
/* if a < b then q=0, r = a */
if (pstm_cmp_mag (a, b) == PSTM_LT) {
if (d != NULL) {
if (pstm_copy(a, d) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
}
if (c != NULL) {
pstm_zero (c);
}
return PSTM_OKAY;
}
/* Smart-size inits */
if ((res = pstm_init_size(pool, &t1, a->alloc)) != PSTM_OKAY) {
return res;
}
if ((res = pstm_init_size(pool, &t2, 3)) != PSTM_OKAY) {
goto LBL_T1;
}
if ((res = pstm_init_copy(pool, &x, a, 0)) != PSTM_OKAY) {
goto LBL_T2;
}
/* Used to be an init_copy on b but pstm_grow was always hit with triple
size */
if ((res = pstm_init_size(pool, &y, b->used * 3)) != PSTM_OKAY) {
goto LBL_X;
}
if ((res = pstm_copy(b, &y)) != PSTM_OKAY) {
goto LBL_Y;
}
/* fix the sign */
neg = (a->sign == b->sign) ? PSTM_ZPOS : PSTM_NEG;
x.sign = y.sign = PSTM_ZPOS;
/* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
norm = pstm_count_bits(&y) % DIGIT_BIT;
if (norm < (int16_t)(DIGIT_BIT-1)) {
norm = (DIGIT_BIT-1) - norm;
if ((res = pstm_mul_2d(&x, norm, &x)) != PSTM_OKAY) {
goto LBL_Y;
}
if ((res = pstm_mul_2d(&y, norm, &y)) != PSTM_OKAY) {
goto LBL_Y;
}
} else {
norm = 0;
}
/* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
n = x.used - 1;
t = y.used - 1;
if ((res = pstm_init_size(pool, &q, (n - t) + 1)) != PSTM_OKAY) {
goto LBL_Y;
}
q.used = (n - t) + 1;
/* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
if ((res = pstm_lshd(&y, n - t)) != PSTM_OKAY) { /* y = y*b**{n-t} */
goto LBL_Q;
}
while (pstm_cmp(&x, &y) != PSTM_LT) {
++(q.dp[n - t]);
if ((res = pstm_sub(&x, &y, &x)) != PSTM_OKAY) {
goto LBL_Q;
}
}
/* reset y by shifting it back down */
pstm_rshd (&y, n - t);
/* step 3. for i from n down to (t + 1) */
for (i = n; i >= (t + 1); i--) {
if (i > x.used) {
continue;
}
/* step 3.1 if xi == yt then set q{i-t-1} to b-1,
* otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
if (x.dp[i] == y.dp[t]) {
q.dp[i - t - 1] = (pstm_digit)((((pstm_word)1) << DIGIT_BIT) - 1);
} else {
pstm_word tmp;
tmp = ((pstm_word) x.dp[i]) << ((pstm_word) DIGIT_BIT);
tmp |= ((pstm_word) x.dp[i - 1]);
#if defined(USE_MATRIX_DIV64) && defined(PSTM_32BIT)
psDiv64(&tmp, y.dp[t]);
#elif defined(USE_MATRIX_DIV128) && defined(PSTM_64BIT)
psDiv128(&tmp, y.dp[t]);
#else
tmp /= ((pstm_word) y.dp[t]);
#endif /* USE_MATRIX_DIV64 */
q.dp[i - t - 1] = (pstm_digit) (tmp);
}
/* while (q{i-t-1} * (yt * b + y{t-1})) >
xi * b**2 + xi-1 * b + xi-2
do q{i-t-1} -= 1;
*/
q.dp[i - t - 1] = (q.dp[i - t - 1] + 1);
do {
q.dp[i - t - 1] = (q.dp[i - t - 1] - 1);
/* find left hand */
pstm_zero (&t1);
t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
t1.dp[1] = y.dp[t];
t1.used = 2;
if ((res = pstm_mul_d (&t1, q.dp[i - t - 1], &t1)) != PSTM_OKAY) {
goto LBL_Q;
}
/* find right hand */
t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
t2.dp[2] = x.dp[i];
t2.used = 3;
} while (pstm_cmp_mag(&t1, &t2) == PSTM_GT);
/* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
if ((res = pstm_mul_d(&y, q.dp[i - t - 1], &t1)) != PSTM_OKAY) {
goto LBL_Q;
}
if ((res = pstm_lshd(&t1, i - t - 1)) != PSTM_OKAY) {
goto LBL_Q;
}
if ((res = pstm_sub(&x, &t1, &x)) != PSTM_OKAY) {
goto LBL_Q;
}
/* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
if (x.sign == PSTM_NEG) {
if ((res = pstm_copy(&y, &t1)) != PSTM_OKAY) {
goto LBL_Q;
}
if ((res = pstm_lshd (&t1, i - t - 1)) != PSTM_OKAY) {
goto LBL_Q;
}
if ((res = pstm_add (&x, &t1, &x)) != PSTM_OKAY) {
goto LBL_Q;
}
q.dp[i - t - 1] = q.dp[i - t - 1] - 1;
}
}
/*
now q is the quotient and x is the remainder (which we have to normalize)
*/
/* get sign before writing to c */
x.sign = x.used == 0 ? PSTM_ZPOS : a->sign;
if (c != NULL) {
pstm_clamp (&q);
if (pstm_copy (&q, c) != PSTM_OKAY) {
res = PS_MEM_FAIL;
goto LBL_Q;
}
c->sign = neg;
}
if (d != NULL) {
if ((res = pstm_div_2d (pool, &x, norm, &x, NULL)) != PSTM_OKAY) {
goto LBL_Q;
}
/*
the following is a kludge, essentially we were seeing the right
remainder but with excess digits that should have been zero
*/
for (i = b->used; i < x.used; i++) {
x.dp[i] = 0;
}
pstm_clamp(&x);
if (pstm_copy (&x, d) != PSTM_OKAY) {
res = PS_MEM_FAIL;
goto LBL_Q;
}
}
res = PSTM_OKAY;
LBL_Q:pstm_clear (&q);
LBL_Y:pstm_clear (&y);
LBL_X:pstm_clear (&x);
LBL_T2:pstm_clear (&t2);
LBL_T1:pstm_clear (&t1);
return res;
}
#endif /* PSTM_LARGE_DIV */
/******************************************************************************/
/*
Swap the elements of two integers, for cases where you can't simply swap
the pstm_int pointers around
*/
void pstm_exch(pstm_int * a, pstm_int * b)
{
pstm_int t;
t = *a;
*a = *b;
*b = t;
}
/******************************************************************************/
/*
c = a mod b, 0 <= c < b
*/
int32_t pstm_mod(psPool_t *pool, const pstm_int *a, const pstm_int *b, pstm_int *c)
{
pstm_int t;
int32_t err;
/* Smart-size */
if ((err = pstm_init_size(pool, &t, b->alloc)) != PSTM_OKAY) {
return err;
}
if ((err = pstm_div(pool, a, b, NULL, &t)) != PSTM_OKAY) {
pstm_clear(&t);
return err;
}
if (t.sign != b->sign) {
err = pstm_add(&t, b, c);
} else {
pstm_exch(&t, c);
}
pstm_clear(&t);
return err;
}
#if defined USE_MATRIX_RSA || defined USE_MATRIX_ECC || defined USE_MATRIX_DH
/******************************************************************************/
/*
d = a * b (mod c)
*/
int32_t pstm_mulmod(psPool_t *pool, const pstm_int *a, const pstm_int *b,
const pstm_int *c, pstm_int *d)
{
int32_t res;
uint16_t size;
pstm_int tmp;
/*
Smart-size pstm_inits. d is an output that is influenced by this local 't'
so don't shrink 'd' if it wants to becuase this will lead to an pstm_grow
in RSA operations
*/
size = a->used + b->used + 1;
if ((a == d) && (size < a->alloc)) {
size = a->alloc;
}
if ((res = pstm_init_size(pool, &tmp, size)) != PSTM_OKAY) {
return res;
}
if ((res = pstm_mul_comba(pool, a, b, &tmp, NULL, 0)) != PSTM_OKAY) {
pstm_clear(&tmp);
return res;
}
res = pstm_mod(pool, &tmp, c, d);
pstm_clear(&tmp);
return res;
}
/******************************************************************************/
/*
* y = g**x (mod p)
* Some restrictions...
* x must be positive and < p
* p must be positive, odd, and [512,1024,1536,2048,3072,4096] bits
*/
int32_t pstm_exptmod(psPool_t *pool, const pstm_int *G, const pstm_int *X,
const pstm_int *P, pstm_int *Y)
{
pstm_int M[32], res; /* Keep this winsize based: (1 << max_winsize) */
pstm_digit buf, mp;
pstm_digit *paD;
int32 err, bitbuf;
int16 bitcpy, bitcnt, mode, digidx, x, y, winsize;
uint32 paDlen;
x = pstm_count_bits(P);
switch(x) {
case 512:
case 1024:
case 1536:
case 2048:
case 3072:
case 4096:
break;
default:
psTraceIntCrypto("pstm_exptmod prime size failed: %hu\n", x);
return -1;
}
/* set window size from what user set as optimization */
x = pstm_count_bits(X);
if (x < 50) {
winsize = 2;
} else {
winsize = PS_EXPTMOD_WINSIZE;
}
/* now setup montgomery */
if ((err = pstm_montgomery_setup (P, &mp)) != PSTM_OKAY) {
return err;
}
/* setup result */
if ((err = pstm_init_size(pool, &res, (P->used * 2) + 1)) != PSTM_OKAY) {
return err;
}
/*
create M table
The M table contains powers of the input base, e.g. M[x] = G^x mod P
The first half of the table is not computed though except for M[0] and M[1]
*/
/* now we need R mod m */
if ((err = pstm_montgomery_calc_normalization (&res, P)) != PSTM_OKAY) {
goto LBL_RES;
}
/*
init M array
init first cell
*/
if ((err = pstm_init_size(pool, &M[1], res.used)) != PSTM_OKAY) {
goto LBL_RES;
}
/* now set M[1] to G * R mod m */
if (pstm_cmp_mag(P, G) != PSTM_GT) {
/* G > P so we reduce it first */
if ((err = pstm_mod(pool, G, P, &M[1])) != PSTM_OKAY) {
goto LBL_M;
}
} else {
if ((err = pstm_copy(G, &M[1])) != PSTM_OKAY) {
goto LBL_M;
}
}
if ((err = pstm_mulmod (pool, &M[1], &res, P, &M[1])) != PSTM_OKAY) {
goto LBL_M;
}
/* Pre-allocated digit. Used for mul, sqr, AND reduce */
paDlen = ((M[1].used + 3) * 2) * sizeof(pstm_digit);
if ((paD = psMalloc(pool, paDlen)) == NULL) {
err = PS_MEM_FAIL;
goto LBL_M;
}
/* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
if (pstm_init_copy(pool, &M[1 << (winsize - 1)], &M[1], 1) != PSTM_OKAY) {
err = PS_MEM_FAIL;
goto LBL_PAD;
}
for (x = 0; x < (winsize - 1); x++) {
if ((err = pstm_sqr_comba (pool, &M[1 << (winsize - 1)],
&M[1 << (winsize - 1)], paD, paDlen)) != PSTM_OKAY) {
goto LBL_PAD;
}
if ((err = pstm_montgomery_reduce(pool, &M[1 << (winsize - 1)], P, mp,
paD, paDlen)) != PSTM_OKAY) {
goto LBL_PAD;
}
}
/* now init the second half of the array */
for (x = (1<<(winsize-1)) + 1; x < (1 << winsize); x++) {
if ((err = pstm_init_size(pool, &M[x], M[1<<(winsize-1)].alloc + 1))
!= PSTM_OKAY) {
for (y = 1<<(winsize-1); y < x; y++) {
pstm_clear(&M[y]);
}
goto LBL_PAD;
}
}
/* create upper table */
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
if ((err = pstm_mul_comba(pool, &M[x - 1], &M[1], &M[x], paD, paDlen))
!= PSTM_OKAY) {
goto LBL_MARRAY;
}
if ((err = pstm_montgomery_reduce(pool, &M[x], P, mp, paD, paDlen)) !=
PSTM_OKAY) {
goto LBL_MARRAY;
}
}
/* set initial mode and bit cnt */
mode = 0;
bitcnt = 1;
buf = 0;
digidx = X->used - 1;
bitcpy = 0;
bitbuf = 0;
for (;;) {
/* grab next digit as required */
if (--bitcnt == 0) {
/* if digidx == -1 we are out of digits so break */
if (digidx == -1) {
break;
}
/* read next digit and reset bitcnt */
buf = X->dp[digidx--];
bitcnt = (int32)DIGIT_BIT;
}
/* grab the next msb from the exponent */
y = (pstm_digit)(buf >> (DIGIT_BIT - 1)) & 1;
buf <<= (pstm_digit)1;
/*
If the bit is zero and mode == 0 then we ignore it.
These represent the leading zero bits before the first 1 bit
in the exponent. Technically this opt is not required but it
does lower the # of trivial squaring/reductions used
*/
if (mode == 0 && y == 0) {
continue;
}
/* if the bit is zero and mode == 1 then we square */
if (mode == 1 && y == 0) {
if ((err = pstm_sqr_comba(pool, &res, &res, paD, paDlen)) !=
PSTM_OKAY) {
goto LBL_MARRAY;
}
if ((err = pstm_montgomery_reduce(pool, &res, P, mp, paD, paDlen))
!= PSTM_OKAY) {
goto LBL_MARRAY;
}
continue;
}
/* else we add it to the window */
bitbuf |= (y << (winsize - ++bitcpy));
mode = 2;
if (bitcpy == winsize) {
/* ok window is filled so square as required and mul square first */
for (x = 0; x < winsize; x++) {
if ((err = pstm_sqr_comba(pool, &res, &res, paD, paDlen)) !=
PSTM_OKAY) {
goto LBL_MARRAY;
}
if ((err = pstm_montgomery_reduce(pool, &res, P, mp, paD,
paDlen)) != PSTM_OKAY) {
goto LBL_MARRAY;
}
}
/* then multiply */
if ((err = pstm_mul_comba(pool, &res, &M[bitbuf], &res, paD,
paDlen)) != PSTM_OKAY) {
goto LBL_MARRAY;
}
if ((err = pstm_montgomery_reduce(pool, &res, P, mp, paD, paDlen))
!= PSTM_OKAY) {
goto LBL_MARRAY;
}
/* empty window and reset */
bitcpy = 0;
bitbuf = 0;
mode = 1;
}
}
/* if bits remain then square/multiply */
if (mode == 2 && bitcpy > 0) {
/* square then multiply if the bit is set */
for (x = 0; x < bitcpy; x++) {
if ((err = pstm_sqr_comba(pool, &res, &res, paD, paDlen)) !=
PSTM_OKAY) {
goto LBL_MARRAY;
}
if ((err = pstm_montgomery_reduce(pool, &res, P, mp, paD, paDlen))
!= PSTM_OKAY) {
goto LBL_MARRAY;
}
/* get next bit of the window */
bitbuf <<= 1;
if ((bitbuf & (1 << winsize)) != 0) {
/* then multiply */
if ((err = pstm_mul_comba(pool, &res, &M[1], &res, paD, paDlen))
!= PSTM_OKAY) {
goto LBL_MARRAY;
}
if ((err = pstm_montgomery_reduce(pool, &res, P, mp, paD,
paDlen)) != PSTM_OKAY) {
goto LBL_MARRAY;
}
}
}
}
/*
Fix up result if Montgomery reduction is used recall that any value in a
Montgomery system is actually multiplied by R mod n. So we have to reduce
one more time to cancel out the factor of R.
*/
if ((err = pstm_montgomery_reduce(pool, &res, P, mp, paD, paDlen)) !=
PSTM_OKAY) {
goto LBL_MARRAY;
}
/* swap res with Y */
if ((err = pstm_copy (&res, Y)) != PSTM_OKAY) {
goto LBL_MARRAY;
}
err = PSTM_OKAY;
LBL_MARRAY:
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
pstm_clear(&M[x]);
}
LBL_PAD:psFree(paD, pool);
LBL_M: pstm_clear(&M[1]);
LBL_RES:pstm_clear(&res);
return err;
}
#endif /* USE_MATRIX_RSA || USE_MATRIX_ECC || USE_MATRIX_DH */
/******************************************************************************/
/**
c = a + b.
*/
int32_t pstm_add(const pstm_int *a, const pstm_int *b, pstm_int *c)
{
int32_t res;
uint8_t sa, sb;
/* get sign of both inputs */
sa = a->sign;
sb = b->sign;
/* handle two cases, not four */
if (sa == sb) {
/* both positive or both negative, add their mags, copy the sign */
c->sign = sa;
if ((res = s_pstm_add (a, b, c)) != PSTM_OKAY) {
return res;
}
} else {
/*
one positive, the other negative
subtract the one with the greater magnitude from the one of the lesser
magnitude. The result gets the sign of the one with the greater mag.
*/
if (pstm_cmp_mag(a, b) == PSTM_LT) {
c->sign = sb;
if ((res = s_pstm_sub (b, a, c)) != PSTM_OKAY) {
return res;
}
} else {
c->sign = sa;
if ((res = s_pstm_sub (a, b, c)) != PSTM_OKAY) {
return res;
}
}
}
return PS_SUCCESS;
}
/******************************************************************************/
/*
No reverse. Useful in some of the EIP-154 PKA stuff where special byte
order seems to come into play more often
*/
int32_t pstm_to_unsigned_bin_nr(psPool_t *pool, const pstm_int *a, unsigned char *b)
{
int32_t res;
uint16_t x;
pstm_int t = { 0 };
if ((res = pstm_init_copy(pool, &t, a, 0)) != PSTM_OKAY) {
return res;
}
x = 0;
while (pstm_iszero (&t) == 0) {
b[x++] = (unsigned char) (t.dp[0] & 255);
if ((res = pstm_div_2d (pool, &t, 8, &t, NULL)) != PSTM_OKAY) {
pstm_clear(&t);
return res;
}
}
pstm_clear(&t);
return PS_SUCCESS;
}
/******************************************************************************/
/*
reverse an array, used for unsigned bin code
*/
static void pstm_reverse(unsigned char *s, uint16_t len)
{
uint16_t ix, iy;
unsigned char t;
if (len == 0) {
return;
}
ix = 0;
iy = len - 1;
while (ix < iy) {
t = s[ix];
s[ix] = s[iy];
s[iy] = t;
++ix;
--iy;
}
}
/******************************************************************************/
/**
Write a pstm format integer to a raw binary format.
@return < 0 on failure. PS_SUCCESS on success.
*/
int32_t pstm_to_unsigned_bin(psPool_t *pool, const pstm_int *a, unsigned char *b)
{
int32_t res;
uint16_t x;
pstm_int t = { 0 };
if ((res = pstm_init_copy(pool, &t, a, 0)) != PSTM_OKAY) {
return res;
}
x = 0;
while (pstm_iszero (&t) == 0) {
b[x++] = (unsigned char) (t.dp[0] & 255);
if ((res = pstm_div_2d (pool, &t, 8, &t, NULL)) != PSTM_OKAY) {
pstm_clear(&t);
return res;
}
}
pstm_reverse (b, x);
pstm_clear(&t);
return PS_SUCCESS;
}
/******************************************************************************/
/**
c = 1/a (mod b).
@note Slow version supporting an even 'b'. Should call pstm_invmod() and let it
decide which to use.
Need invmod for ECC and also private key loading for hardware crypto
in cases where dQ > dP. The values must be switched and a new qP must be
calculated using this function
*/
static int32_t pstm_invmod_slow(psPool_t *pool, const pstm_int *a,
const pstm_int *b, pstm_int * c)
{
pstm_int x, y, u, v, A, B, C, D;
int32 res;
/* b cannot be negative */
if (b->sign == PSTM_NEG || pstm_iszero(b) == 1) {
return PS_LIMIT_FAIL;
}
/* init temps */
if (pstm_init_size(pool, &x, b->used) != PSTM_OKAY) {
return PS_MEM_FAIL;
}
/* x = a, y = b */
if ((res = pstm_mod(pool, a, b, &x)) != PSTM_OKAY) {
goto LBL_X;
}
if (pstm_init_copy(pool, &y, b, 0) != PSTM_OKAY) {
goto LBL_X;
}
/* 2. [modified] if x,y are both even then return an error! */
if (pstm_iseven (&x) == 1 && pstm_iseven (&y) == 1) {
res = PS_FAILURE;
goto LBL_Y;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = pstm_init_copy(pool, &u, &x, 0)) != PSTM_OKAY) {
goto LBL_Y;
}
if ((res = pstm_init_copy(pool, &v, &y, 0)) != PSTM_OKAY) {
goto LBL_U;
}
if ((res = pstm_init_size(pool, &A, sizeof(pstm_digit))) != PSTM_OKAY) {
goto LBL_V;
}
if ((res = pstm_init_size(pool, &D, sizeof(pstm_digit))) != PSTM_OKAY) {
goto LBL_A;
}
pstm_set (&A, 1);
pstm_set (&D, 1);
if ((res = pstm_init(pool, &B)) != PSTM_OKAY) {
goto LBL_D;
}
if ((res = pstm_init(pool, &C)) != PSTM_OKAY) {
goto LBL_B;
}
top:
/* 4. while u is even do */
while (pstm_iseven (&u) == 1) {
/* 4.1 u = u/2 */
if ((res = pstm_div_2(&u, &u)) != PSTM_OKAY) {
goto LBL_C;
}
/* 4.2 if A or B is odd then */
if (pstm_isodd(&A) == 1 || pstm_isodd (&B) == 1) {
/* A = (A+y)/2, B = (B-x)/2 */
if ((res = pstm_add(&A, &y, &A)) != PSTM_OKAY) {
goto LBL_C;
}
if ((res = pstm_sub(&B, &x, &B)) != PSTM_OKAY) {
goto LBL_C;
}
}
/* A = A/2, B = B/2 */
if ((res = pstm_div_2(&A, &A)) != PSTM_OKAY) {
goto LBL_C;
}
if ((res = pstm_div_2(&B, &B)) != PSTM_OKAY) {
goto LBL_C;
}
}
/* 5. while v is even do */
while (pstm_iseven(&v) == 1) {
/* 5.1 v = v/2 */
if ((res = pstm_div_2(&v, &v)) != PSTM_OKAY) {
goto LBL_C;
}
/* 5.2 if C or D is odd then */
if (pstm_isodd(&C) == 1 || pstm_isodd(&D) == 1) {
/* C = (C+y)/2, D = (D-x)/2 */
if ((res = pstm_add(&C, &y, &C)) != PSTM_OKAY) {
goto LBL_C;
}
if ((res = pstm_sub(&D, &x, &D)) != PSTM_OKAY) {
goto LBL_C;
}
}
/* C = C/2, D = D/2 */
if ((res = pstm_div_2(&C, &C)) != PSTM_OKAY) {
goto LBL_C;
}
if ((res = pstm_div_2(&D, &D)) != PSTM_OKAY) {
goto LBL_C;
}
}
/* 6. if u >= v then */
if (pstm_cmp(&u, &v) != PSTM_LT) {
/* u = u - v, A = A - C, B = B - D */
if ((res = pstm_sub(&u, &v, &u)) != PSTM_OKAY) {
goto LBL_C;
}
if ((res = pstm_sub(&A, &C, &A)) != PSTM_OKAY) {
goto LBL_C;
}
if ((res = pstm_sub(&B, &D, &B)) != PSTM_OKAY) {
goto LBL_C;
}
} else {
/* v - v - u, C = C - A, D = D - B */
if ((res = pstm_sub(&v, &u, &v)) != PSTM_OKAY) {
goto LBL_C;
}
if ((res = pstm_sub(&C, &A, &C)) != PSTM_OKAY) {
goto LBL_C;
}
if ((res = pstm_sub(&D, &B, &D)) != PSTM_OKAY) {
goto LBL_C;
}
}
/* if not zero goto step 4 */
if (pstm_iszero(&u) == 0)
goto top;
/* now a = C, b = D, gcd == g*v */
/* if v != 1 then there is no inverse */
if (pstm_cmp_d(&v, 1) != PSTM_EQ) {
res = PS_FAILURE;
goto LBL_C;
}
/* if its too low */
while (pstm_cmp_d(&C, 0) == PSTM_LT) {
if ((res = pstm_add(&C, b, &C)) != PSTM_OKAY) {
goto LBL_C;
}
}
/* too big */
while (pstm_cmp_mag(&C, b) != PSTM_LT) {
if ((res = pstm_sub(&C, b, &C)) != PSTM_OKAY) {
goto LBL_C;
}
}
/* C is now the inverse */
if ((res = pstm_copy(&C, c)) != PSTM_OKAY) {
goto LBL_C;
}
res = PSTM_OKAY;
LBL_C: pstm_clear(&C);
LBL_D: pstm_clear(&D);
LBL_B: pstm_clear(&B);
LBL_A: pstm_clear(&A);
LBL_V: pstm_clear(&v);
LBL_U: pstm_clear(&u);
LBL_Y: pstm_clear(&y);
LBL_X: pstm_clear(&x);
return res;
}
/**
c = 1/a (mod b).
This code is for for odd 'b'. pstm_invmod_slow() will be called if 'b'
is even.
*/
int32_t pstm_invmod(psPool_t *pool, const pstm_int *a, const pstm_int *b, pstm_int *c)
{
pstm_int x, y, u, v, B, D;
int32 res;
uint16 neg, sanity;
/* 2. [modified] b must be odd */
if (pstm_iseven (b) == 1) {
return pstm_invmod_slow(pool, a,b,c);
}
/* x == modulus, y == value to invert */
if ((res = pstm_init_copy(pool, &x, b, 0)) != PSTM_OKAY) {
return res;
}
if ((res = pstm_init_size(pool, &y, a->alloc)) != PSTM_OKAY) {
goto LBL_X;
}
/* we need y = |a| */
if ((res = pstm_abs(a, &y)) != PSTM_OKAY) {
goto LBL_X;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = pstm_init_copy(pool, &u, &x, 0)) != PSTM_OKAY) {
goto LBL_Y;
}
if ((res = pstm_init_copy(pool, &v, &y, 0)) != PSTM_OKAY) {
goto LBL_U;
}
if ((res = pstm_init(pool, &B)) != PSTM_OKAY) {
goto LBL_V;
}
if ((res = pstm_init(pool, &D)) != PSTM_OKAY) {
goto LBL_B;
}
pstm_set (&D, 1);
sanity = 0;
top:
/* 4. while u is even do */
while (pstm_iseven (&u) == 1) {
/* 4.1 u = u/2 */
if ((res = pstm_div_2 (&u, &u)) != PSTM_OKAY) {
goto LBL_D;
}
/* 4.2 if B is odd then */
if (pstm_isodd (&B) == 1) {
if ((res = pstm_sub (&B, &x, &B)) != PSTM_OKAY) {
goto LBL_D;
}
}
/* B = B/2 */
if ((res = pstm_div_2 (&B, &B)) != PSTM_OKAY) {
goto LBL_D;
}
}
/* 5. while v is even do */
while (pstm_iseven (&v) == 1) {
/* 5.1 v = v/2 */
if ((res = pstm_div_2 (&v, &v)) != PSTM_OKAY) {
goto LBL_D;
}
/* 5.2 if D is odd then */
if (pstm_isodd (&D) == 1) {
/* D = (D-x)/2 */
if ((res = pstm_sub (&D, &x, &D)) != PSTM_OKAY) {
goto LBL_D;
}
}
/* D = D/2 */
if ((res = pstm_div_2 (&D, &D)) != PSTM_OKAY) {
goto LBL_D;
}
}
/* 6. if u >= v then */
if (pstm_cmp(&u, &v) != PSTM_LT) {
/* u = u - v, B = B - D */
if ((res = pstm_sub (&u, &v, &u)) != PSTM_OKAY) {
goto LBL_D;
}
if ((res = pstm_sub (&B, &D, &B)) != PSTM_OKAY) {
goto LBL_D;
}
} else {
/* v - v - u, D = D - B */
if ((res = pstm_sub (&v, &u, &v)) != PSTM_OKAY) {
goto LBL_D;
}
if ((res = pstm_sub (&D, &B, &D)) != PSTM_OKAY) {
goto LBL_D;
}
}
/* if not zero goto step 4 */
if (sanity++ > 4096) {
res = PS_LIMIT_FAIL;
goto LBL_D;
}
if (pstm_iszero (&u) == 0) {
goto top;
}
/* now a = C, b = D, gcd == g*v */
/* if v != 1 then there is no inverse */
if (pstm_cmp_d(&v, 1) != PSTM_EQ) {
res = PS_FAILURE;
goto LBL_D;
}
/* b is now the inverse */
neg = a->sign;
while (D.sign == PSTM_NEG) {
if ((res = pstm_add (&D, b, &D)) != PSTM_OKAY) {
goto LBL_D;
}
}
if ((res = pstm_copy (&D, c)) != PSTM_OKAY) {
goto LBL_D;
}
c->sign = neg;
res = PSTM_OKAY;
LBL_D: pstm_clear(&D);
LBL_B: pstm_clear(&B);
LBL_V: pstm_clear(&v);
LBL_U: pstm_clear(&u);
LBL_Y: pstm_clear(&y);
LBL_X: pstm_clear(&x);
return res;
}
/******************************************************************************/
#endif /* USE_MATRIX_RSA || USE_MATRIX_ECC || USE_MATRIX_DH || USE_CL_RSA || USE_CL_DH || USE_QUICK_ASSIST_RSA || USE_QUICK_ASSIST_ECC */
/******************************************************************************/
Reference in New Issue View Git Blame Copy Permalink