5774 lines
120 KiB
C
5774 lines
120 KiB
C
/* $NetBSD: bignum.c,v 1.1 2017/02/13 11:16:46 nonaka Exp $ */
|
|
|
|
/*-
|
|
* Copyright (c) 2012 Alistair Crooks <agc@NetBSD.org>
|
|
* All rights reserved.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
* 1. Redistributions of source code must retain the above copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in the
|
|
* documentation and/or other materials provided with the distribution.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
|
|
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
|
|
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
|
|
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
|
|
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
|
|
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
|
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
|
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
|
|
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
*/
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis
|
|
*
|
|
* LibTomMath is a library that provides multiple-precision
|
|
* integer arithmetic as well as number theoretic functionality.
|
|
*
|
|
* The library was designed directly after the MPI library by
|
|
* Michael Fromberger but has been written from scratch with
|
|
* additional optimizations in place.
|
|
*
|
|
* The library is free for all purposes without any express
|
|
* guarantee it works.
|
|
*
|
|
* Tom St Denis, tomstdenis@gmail.com, http://libtom.org
|
|
*/
|
|
|
|
#include <sys/types.h>
|
|
#include <sys/param.h>
|
|
|
|
#include <limits.h>
|
|
#include <stdarg.h>
|
|
#include <stdio.h>
|
|
#include <stdlib.h>
|
|
#include <string.h>
|
|
#include <unistd.h>
|
|
|
|
#include "bn.h"
|
|
|
|
/**************************************************************************/
|
|
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis
|
|
*
|
|
* LibTomMath is a library that provides multiple-precision
|
|
* integer arithmetic as well as number theoretic functionality.
|
|
*
|
|
* The library was designed directly after the MPI library by
|
|
* Michael Fromberger but has been written from scratch with
|
|
* additional optimizations in place.
|
|
*
|
|
* The library is free for all purposes without any express
|
|
* guarantee it works.
|
|
*
|
|
* Tom St Denis, tomstdenis@gmail.com, http://libtom.org
|
|
*/
|
|
|
|
#define MP_PREC 32
|
|
#define DIGIT_BIT 28
|
|
#define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
|
|
|
|
#define MP_WARRAY /*LINTED*/(1U << (((sizeof(mp_word) * CHAR_BIT) - (2 * DIGIT_BIT) + 1)))
|
|
|
|
#define MP_NO 0
|
|
#define MP_YES 1
|
|
|
|
#ifndef USE_ARG
|
|
#define USE_ARG(x) /*LINTED*/(void)&(x)
|
|
#endif
|
|
|
|
#ifndef __arraycount
|
|
#define __arraycount(__x) (sizeof(__x) / sizeof(__x[0]))
|
|
#endif
|
|
|
|
#ifndef MIN
|
|
#define MIN(a,b) (((a)<(b))?(a):(b))
|
|
#endif
|
|
|
|
#define MP_ISZERO(a) (((a)->used == 0) ? MP_YES : MP_NO)
|
|
|
|
typedef int mp_err;
|
|
|
|
static int signed_multiply(mp_int * a, mp_int * b, mp_int * c);
|
|
static int square(mp_int * a, mp_int * b);
|
|
|
|
static int signed_subtract_word(mp_int *a, mp_digit b, mp_int *c);
|
|
|
|
static inline void *
|
|
allocate(size_t n, size_t m)
|
|
{
|
|
return calloc(n, m);
|
|
}
|
|
|
|
static inline void
|
|
deallocate(void *v, size_t sz)
|
|
{
|
|
USE_ARG(sz);
|
|
free(v);
|
|
}
|
|
|
|
/* set to zero */
|
|
static inline void
|
|
mp_zero(mp_int *a)
|
|
{
|
|
a->sign = MP_ZPOS;
|
|
a->used = 0;
|
|
memset(a->dp, 0x0, a->alloc * sizeof(*a->dp));
|
|
}
|
|
|
|
/* grow as required */
|
|
static int
|
|
mp_grow(mp_int *a, int size)
|
|
{
|
|
mp_digit *tmp;
|
|
|
|
/* if the alloc size is smaller alloc more ram */
|
|
if (a->alloc < size) {
|
|
/* ensure there are always at least MP_PREC digits extra on top */
|
|
size += (MP_PREC * 2) - (size % MP_PREC);
|
|
|
|
/* 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 = realloc(a->dp, sizeof(*tmp) * size);
|
|
if (tmp == NULL) {
|
|
/* reallocation failed but "a" is still valid [can be freed] */
|
|
return MP_MEM;
|
|
}
|
|
|
|
/* reallocation succeeded so set a->dp */
|
|
a->dp = tmp;
|
|
/* zero excess digits */
|
|
memset(&a->dp[a->alloc], 0x0, (size - a->alloc) * sizeof(*a->dp));
|
|
a->alloc = size;
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* shift left a certain amount of digits */
|
|
static int
|
|
lshift_digits(mp_int * a, int b)
|
|
{
|
|
mp_digit *top, *bottom;
|
|
int x, res;
|
|
|
|
/* if its less than zero return */
|
|
if (b <= 0) {
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* grow to fit the new digits */
|
|
if (a->alloc < a->used + b) {
|
|
if ((res = mp_grow(a, a->used + b)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* 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;
|
|
|
|
/* much like rshift_digits this is implemented using a sliding window
|
|
* except the window goes the otherway around. Copying from
|
|
* the bottom to the top.
|
|
*/
|
|
for (x = a->used - 1; x >= b; x--) {
|
|
*top-- = *bottom--;
|
|
}
|
|
|
|
/* zero the lower digits */
|
|
memset(a->dp, 0x0, b * sizeof(*a->dp));
|
|
return MP_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
|
|
*/
|
|
static void
|
|
trim_unused_digits(mp_int * a)
|
|
{
|
|
/* decrease used while the most significant digit is
|
|
* zero.
|
|
*/
|
|
while (a->used > 0 && a->dp[a->used - 1] == 0) {
|
|
a->used -= 1;
|
|
}
|
|
/* reset the sign flag if used == 0 */
|
|
if (a->used == 0) {
|
|
a->sign = MP_ZPOS;
|
|
}
|
|
}
|
|
|
|
/* copy, b = a */
|
|
static int
|
|
mp_copy(BIGNUM *a, BIGNUM *b)
|
|
{
|
|
int res;
|
|
|
|
/* if dst == src do nothing */
|
|
if (a == b) {
|
|
return MP_OKAY;
|
|
}
|
|
if (a == NULL || b == NULL) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* grow dest */
|
|
if (b->alloc < a->used) {
|
|
if ((res = mp_grow(b, a->used)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
memcpy(b->dp, a->dp, a->used * sizeof(*b->dp));
|
|
if (b->used > a->used) {
|
|
memset(&b->dp[a->used], 0x0, (b->used - a->used) * sizeof(*b->dp));
|
|
}
|
|
|
|
/* copy used count and sign */
|
|
b->used = a->used;
|
|
b->sign = a->sign;
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* shift left by a certain bit count */
|
|
static int
|
|
lshift_bits(mp_int *a, int b, mp_int *c)
|
|
{
|
|
mp_digit d;
|
|
int res;
|
|
|
|
/* copy */
|
|
if (a != c) {
|
|
if ((res = mp_copy(a, c)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
|
|
if ((res = mp_grow(c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* shift by as many digits in the bit count */
|
|
if (b >= (int)DIGIT_BIT) {
|
|
if ((res = lshift_digits(c, b / DIGIT_BIT)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* shift any bit count < DIGIT_BIT */
|
|
d = (mp_digit) (b % DIGIT_BIT);
|
|
if (d != 0) {
|
|
mp_digit *tmpc, shift, mask, carry, rr;
|
|
int x;
|
|
|
|
/* bitmask for carries */
|
|
mask = (((mp_digit)1) << d) - 1;
|
|
|
|
/* shift for msbs */
|
|
shift = DIGIT_BIT - d;
|
|
|
|
/* alias */
|
|
tmpc = c->dp;
|
|
|
|
/* carry */
|
|
carry = 0;
|
|
for (x = 0; x < c->used; x++) {
|
|
/* get the higher bits of the current word */
|
|
rr = (*tmpc >> shift) & mask;
|
|
|
|
/* shift the current word and OR in the carry */
|
|
*tmpc = ((*tmpc << d) | carry) & MP_MASK;
|
|
++tmpc;
|
|
|
|
/* set the carry to the carry bits of the current word */
|
|
carry = rr;
|
|
}
|
|
|
|
/* set final carry */
|
|
if (carry != 0) {
|
|
c->dp[c->used++] = carry;
|
|
}
|
|
}
|
|
trim_unused_digits(c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* reads a unsigned char array, assumes the msb is stored first [big endian] */
|
|
static int
|
|
mp_read_unsigned_bin(mp_int *a, const uint8_t *b, int c)
|
|
{
|
|
int res;
|
|
|
|
/* make sure there are at least two digits */
|
|
if (a->alloc < 2) {
|
|
if ((res = mp_grow(a, 2)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* zero the int */
|
|
mp_zero(a);
|
|
|
|
/* read the bytes in */
|
|
while (c-- > 0) {
|
|
if ((res = lshift_bits(a, 8, a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
a->dp[0] |= *b++;
|
|
a->used += 1;
|
|
}
|
|
trim_unused_digits(a);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* returns the number of bits in an mpi */
|
|
static int
|
|
mp_count_bits(const mp_int *a)
|
|
{
|
|
int r;
|
|
mp_digit q;
|
|
|
|
/* shortcut */
|
|
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 */
|
|
for (q = a->dp[a->used - 1]; q > ((mp_digit) 0) ; r++) {
|
|
q >>= ((mp_digit) 1);
|
|
}
|
|
return r;
|
|
}
|
|
|
|
/* compare maginitude of two ints (unsigned) */
|
|
static int
|
|
compare_magnitude(mp_int * a, mp_int * b)
|
|
{
|
|
int n;
|
|
mp_digit *tmpa, *tmpb;
|
|
|
|
/* compare based on # of non-zero digits */
|
|
if (a->used > b->used) {
|
|
return MP_GT;
|
|
}
|
|
|
|
if (a->used < b->used) {
|
|
return MP_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 MP_GT;
|
|
}
|
|
|
|
if (*tmpa < *tmpb) {
|
|
return MP_LT;
|
|
}
|
|
}
|
|
return MP_EQ;
|
|
}
|
|
|
|
/* compare two ints (signed)*/
|
|
static int
|
|
signed_compare(mp_int * a, mp_int * b)
|
|
{
|
|
/* compare based on sign */
|
|
if (a->sign != b->sign) {
|
|
return (a->sign == MP_NEG) ? MP_LT : MP_GT;
|
|
}
|
|
return (a->sign == MP_NEG) ? compare_magnitude(b, a) : compare_magnitude(a, b);
|
|
}
|
|
|
|
/* get the size for an unsigned equivalent */
|
|
static int
|
|
mp_unsigned_bin_size(mp_int * a)
|
|
{
|
|
int size = mp_count_bits(a);
|
|
|
|
return (size / 8 + ((size & 7) != 0 ? 1 : 0));
|
|
}
|
|
|
|
/* init a new mp_int */
|
|
static int
|
|
mp_init(mp_int * a)
|
|
{
|
|
/* allocate memory required and clear it */
|
|
a->dp = allocate(1, sizeof(*a->dp) * MP_PREC);
|
|
if (a->dp == NULL) {
|
|
return MP_MEM;
|
|
}
|
|
|
|
/* set the digits to zero */
|
|
memset(a->dp, 0x0, MP_PREC * sizeof(*a->dp));
|
|
|
|
/* set the used to zero, allocated digits to the default precision
|
|
* and sign to positive */
|
|
a->used = 0;
|
|
a->alloc = MP_PREC;
|
|
a->sign = MP_ZPOS;
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* clear one (frees) */
|
|
static void
|
|
mp_clear(mp_int * a)
|
|
{
|
|
/* only do anything if a hasn't been freed previously */
|
|
if (a->dp != NULL) {
|
|
memset(a->dp, 0x0, a->used * sizeof(*a->dp));
|
|
|
|
/* free ram */
|
|
deallocate(a->dp, (size_t)a->alloc);
|
|
|
|
/* reset members to make debugging easier */
|
|
a->dp = NULL;
|
|
a->alloc = a->used = 0;
|
|
a->sign = MP_ZPOS;
|
|
}
|
|
}
|
|
|
|
static int
|
|
mp_init_multi(mp_int *mp, ...)
|
|
{
|
|
mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
|
|
int n = 0; /* Number of ok inits */
|
|
mp_int* cur_arg = mp;
|
|
va_list args;
|
|
|
|
va_start(args, mp); /* init args to next argument from caller */
|
|
while (cur_arg != NULL) {
|
|
if (mp_init(cur_arg) != MP_OKAY) {
|
|
/* Oops - error! Back-track and mp_clear what we already
|
|
succeeded in init-ing, then return error.
|
|
*/
|
|
va_list clean_args;
|
|
|
|
/* end the current list */
|
|
va_end(args);
|
|
|
|
/* now start cleaning up */
|
|
cur_arg = mp;
|
|
va_start(clean_args, mp);
|
|
while (n--) {
|
|
mp_clear(cur_arg);
|
|
cur_arg = va_arg(clean_args, mp_int*);
|
|
}
|
|
va_end(clean_args);
|
|
res = MP_MEM;
|
|
break;
|
|
}
|
|
n++;
|
|
cur_arg = va_arg(args, mp_int*);
|
|
}
|
|
va_end(args);
|
|
return res; /* Assumed ok, if error flagged above. */
|
|
}
|
|
|
|
/* init an mp_init for a given size */
|
|
static int
|
|
mp_init_size(mp_int * a, int size)
|
|
{
|
|
/* pad size so there are always extra digits */
|
|
size += (MP_PREC * 2) - (size % MP_PREC);
|
|
|
|
/* alloc mem */
|
|
a->dp = allocate(1, sizeof(*a->dp) * size);
|
|
if (a->dp == NULL) {
|
|
return MP_MEM;
|
|
}
|
|
|
|
/* set the members */
|
|
a->used = 0;
|
|
a->alloc = size;
|
|
a->sign = MP_ZPOS;
|
|
|
|
/* zero the digits */
|
|
memset(a->dp, 0x0, size * sizeof(*a->dp));
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* creates "a" then copies b into it */
|
|
static int
|
|
mp_init_copy(mp_int * a, mp_int * b)
|
|
{
|
|
int res;
|
|
|
|
if ((res = mp_init(a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
return mp_copy(b, a);
|
|
}
|
|
|
|
/* low level addition, based on HAC pp.594, Algorithm 14.7 */
|
|
static int
|
|
basic_add(mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
mp_int *x;
|
|
int olduse, res, min, max;
|
|
|
|
/* find sizes, we let |a| <= |b| which means we have to sort
|
|
* them. "x" will point to the input with the most digits
|
|
*/
|
|
if (a->used > b->used) {
|
|
min = b->used;
|
|
max = a->used;
|
|
x = a;
|
|
} else {
|
|
min = a->used;
|
|
max = b->used;
|
|
x = b;
|
|
}
|
|
|
|
/* init result */
|
|
if (c->alloc < max + 1) {
|
|
if ((res = mp_grow(c, max + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* get old used digit count and set new one */
|
|
olduse = c->used;
|
|
c->used = max + 1;
|
|
|
|
{
|
|
mp_digit carry, *tmpa, *tmpb, *tmpc;
|
|
int i;
|
|
|
|
/* alias for digit pointers */
|
|
|
|
/* first input */
|
|
tmpa = a->dp;
|
|
|
|
/* second input */
|
|
tmpb = b->dp;
|
|
|
|
/* destination */
|
|
tmpc = c->dp;
|
|
|
|
/* zero the carry */
|
|
carry = 0;
|
|
for (i = 0; i < min; i++) {
|
|
/* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
|
|
*tmpc = *tmpa++ + *tmpb++ + carry;
|
|
|
|
/* U = carry bit of T[i] */
|
|
carry = *tmpc >> ((mp_digit)DIGIT_BIT);
|
|
|
|
/* take away carry bit from T[i] */
|
|
*tmpc++ &= MP_MASK;
|
|
}
|
|
|
|
/* now copy higher words if any, that is in A+B
|
|
* if A or B has more digits add those in
|
|
*/
|
|
if (min != max) {
|
|
for (; i < max; i++) {
|
|
/* T[i] = X[i] + U */
|
|
*tmpc = x->dp[i] + carry;
|
|
|
|
/* U = carry bit of T[i] */
|
|
carry = *tmpc >> ((mp_digit)DIGIT_BIT);
|
|
|
|
/* take away carry bit from T[i] */
|
|
*tmpc++ &= MP_MASK;
|
|
}
|
|
}
|
|
|
|
/* add carry */
|
|
*tmpc++ = carry;
|
|
|
|
/* clear digits above oldused */
|
|
if (olduse > c->used) {
|
|
memset(tmpc, 0x0, (olduse - c->used) * sizeof(*c->dp));
|
|
}
|
|
}
|
|
|
|
trim_unused_digits(c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
|
|
static int
|
|
basic_subtract(mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
int olduse, res, min, max;
|
|
|
|
/* find sizes */
|
|
min = b->used;
|
|
max = a->used;
|
|
|
|
/* init result */
|
|
if (c->alloc < max) {
|
|
if ((res = mp_grow(c, max)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
olduse = c->used;
|
|
c->used = max;
|
|
|
|
{
|
|
mp_digit carry, *tmpa, *tmpb, *tmpc;
|
|
int i;
|
|
|
|
/* alias for digit pointers */
|
|
tmpa = a->dp;
|
|
tmpb = b->dp;
|
|
tmpc = c->dp;
|
|
|
|
/* set carry to zero */
|
|
carry = 0;
|
|
for (i = 0; i < min; i++) {
|
|
/* T[i] = A[i] - B[i] - U */
|
|
*tmpc = *tmpa++ - *tmpb++ - carry;
|
|
|
|
/* U = carry bit of T[i]
|
|
* Note this saves performing an AND operation since
|
|
* if a carry does occur it will propagate all the way to the
|
|
* MSB. As a result a single shift is enough to get the carry
|
|
*/
|
|
carry = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof(mp_digit) - 1));
|
|
|
|
/* Clear carry from T[i] */
|
|
*tmpc++ &= MP_MASK;
|
|
}
|
|
|
|
/* now copy higher words if any, e.g. if A has more digits than B */
|
|
for (; i < max; i++) {
|
|
/* T[i] = A[i] - U */
|
|
*tmpc = *tmpa++ - carry;
|
|
|
|
/* U = carry bit of T[i] */
|
|
carry = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof(mp_digit) - 1));
|
|
|
|
/* Clear carry from T[i] */
|
|
*tmpc++ &= MP_MASK;
|
|
}
|
|
|
|
/* clear digits above used (since we may not have grown result above) */
|
|
if (olduse > c->used) {
|
|
memset(tmpc, 0x0, (olduse - c->used) * sizeof(*a->dp));
|
|
}
|
|
}
|
|
|
|
trim_unused_digits(c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* high level subtraction (handles signs) */
|
|
static int
|
|
signed_subtract(mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
int sa, sb, res;
|
|
|
|
sa = a->sign;
|
|
sb = b->sign;
|
|
|
|
if (sa != sb) {
|
|
/* subtract a negative from a positive, OR */
|
|
/* subtract a positive from a negative. */
|
|
/* In either case, ADD their magnitudes, */
|
|
/* and use the sign of the first number. */
|
|
c->sign = sa;
|
|
res = basic_add(a, b, c);
|
|
} else {
|
|
/* subtract a positive from a positive, OR */
|
|
/* subtract a negative from a negative. */
|
|
/* First, take the difference between their */
|
|
/* magnitudes, then... */
|
|
if (compare_magnitude(a, b) != MP_LT) {
|
|
/* Copy the sign from the first */
|
|
c->sign = sa;
|
|
/* The first has a larger or equal magnitude */
|
|
res = basic_subtract(a, b, c);
|
|
} else {
|
|
/* The result has the *opposite* sign from */
|
|
/* the first number. */
|
|
c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
|
|
/* The second has a larger magnitude */
|
|
res = basic_subtract(b, a, c);
|
|
}
|
|
}
|
|
return res;
|
|
}
|
|
|
|
/* shift right a certain amount of digits */
|
|
static int
|
|
rshift_digits(mp_int * a, int b)
|
|
{
|
|
/* if b <= 0 then ignore it */
|
|
if (b <= 0) {
|
|
return 0;
|
|
}
|
|
|
|
/* if b > used then simply zero it and return */
|
|
if (a->used <= b) {
|
|
mp_zero(a);
|
|
return 0;
|
|
}
|
|
|
|
/* this is implemented as a sliding window where
|
|
* the window is b-digits long and digits from
|
|
* the top of the window are copied to the bottom
|
|
*
|
|
* e.g.
|
|
|
|
b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
|
|
/\ | ---->
|
|
\-------------------/ ---->
|
|
*/
|
|
memmove(a->dp, &a->dp[b], (a->used - b) * sizeof(*a->dp));
|
|
memset(&a->dp[a->used - b], 0x0, b * sizeof(*a->dp));
|
|
|
|
/* remove excess digits */
|
|
a->used -= b;
|
|
return 1;
|
|
}
|
|
|
|
/* multiply by a digit */
|
|
static int
|
|
multiply_digit(mp_int * a, mp_digit b, mp_int * c)
|
|
{
|
|
mp_digit carry, *tmpa, *tmpc;
|
|
mp_word r;
|
|
int ix, res, olduse;
|
|
|
|
/* make sure c is big enough to hold a*b */
|
|
if (c->alloc < a->used + 1) {
|
|
if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* get the original destinations used count */
|
|
olduse = c->used;
|
|
|
|
/* set the sign */
|
|
c->sign = a->sign;
|
|
|
|
/* alias for a->dp [source] */
|
|
tmpa = a->dp;
|
|
|
|
/* alias for c->dp [dest] */
|
|
tmpc = c->dp;
|
|
|
|
/* zero carry */
|
|
carry = 0;
|
|
|
|
/* compute columns */
|
|
for (ix = 0; ix < a->used; ix++) {
|
|
/* compute product and carry sum for this term */
|
|
r = ((mp_word) carry) + ((mp_word)*tmpa++) * ((mp_word)b);
|
|
|
|
/* mask off higher bits to get a single digit */
|
|
*tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
|
|
|
/* send carry into next iteration */
|
|
carry = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
|
}
|
|
|
|
/* store final carry [if any] and increment ix offset */
|
|
*tmpc++ = carry;
|
|
++ix;
|
|
if (olduse > ix) {
|
|
memset(tmpc, 0x0, (olduse - ix) * sizeof(*tmpc));
|
|
}
|
|
|
|
/* set used count */
|
|
c->used = a->used + 1;
|
|
trim_unused_digits(c);
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* high level addition (handles signs) */
|
|
static int
|
|
signed_add(mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
int asign, bsign, res;
|
|
|
|
/* get sign of both inputs */
|
|
asign = a->sign;
|
|
bsign = b->sign;
|
|
|
|
/* handle two cases, not four */
|
|
if (asign == bsign) {
|
|
/* both positive or both negative */
|
|
/* add their magnitudes, copy the sign */
|
|
c->sign = asign;
|
|
res = basic_add(a, b, c);
|
|
} 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 magnitude. */
|
|
if (compare_magnitude(a, b) == MP_LT) {
|
|
c->sign = bsign;
|
|
res = basic_subtract(b, a, c);
|
|
} else {
|
|
c->sign = asign;
|
|
res = basic_subtract(a, b, c);
|
|
}
|
|
}
|
|
return res;
|
|
}
|
|
|
|
/* swap the elements of two integers, for cases where you can't simply swap the
|
|
* mp_int pointers around
|
|
*/
|
|
static void
|
|
mp_exch(mp_int *a, mp_int *b)
|
|
{
|
|
mp_int t;
|
|
|
|
t = *a;
|
|
*a = *b;
|
|
*b = t;
|
|
}
|
|
|
|
/* calc a value mod 2**b */
|
|
static int
|
|
modulo_2_to_power(mp_int * a, int b, mp_int * c)
|
|
{
|
|
int x, res;
|
|
|
|
/* if b is <= 0 then zero the int */
|
|
if (b <= 0) {
|
|
mp_zero(c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* if the modulus is larger than the value than return */
|
|
if (b >= (int) (a->used * DIGIT_BIT)) {
|
|
res = mp_copy(a, c);
|
|
return res;
|
|
}
|
|
|
|
/* copy */
|
|
if ((res = mp_copy(a, c)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* 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] &=
|
|
(mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
|
|
trim_unused_digits(c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
|
|
static int
|
|
rshift_bits(mp_int * a, int b, mp_int * c, mp_int * d)
|
|
{
|
|
mp_digit D, r, rr;
|
|
int x, res;
|
|
mp_int t;
|
|
|
|
|
|
/* if the shift count is <= 0 then we do no work */
|
|
if (b <= 0) {
|
|
res = mp_copy(a, c);
|
|
if (d != NULL) {
|
|
mp_zero(d);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
if ((res = mp_init(&t)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* get the remainder */
|
|
if (d != NULL) {
|
|
if ((res = modulo_2_to_power(a, b, &t)) != MP_OKAY) {
|
|
mp_clear(&t);
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* copy */
|
|
if ((res = mp_copy(a, c)) != MP_OKAY) {
|
|
mp_clear(&t);
|
|
return res;
|
|
}
|
|
|
|
/* shift by as many digits in the bit count */
|
|
if (b >= (int)DIGIT_BIT) {
|
|
rshift_digits(c, b / DIGIT_BIT);
|
|
}
|
|
|
|
/* shift any bit count < DIGIT_BIT */
|
|
D = (mp_digit) (b % DIGIT_BIT);
|
|
if (D != 0) {
|
|
mp_digit *tmpc, mask, shift;
|
|
|
|
/* mask */
|
|
mask = (((mp_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 the previous word */
|
|
*tmpc = (*tmpc >> D) | (r << shift);
|
|
--tmpc;
|
|
|
|
/* set the carry to the carry bits of the current word found above */
|
|
r = rr;
|
|
}
|
|
}
|
|
trim_unused_digits(c);
|
|
if (d != NULL) {
|
|
mp_exch(&t, d);
|
|
}
|
|
mp_clear(&t);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* integer signed division.
|
|
* c*b + d == a [e.g. a/b, c=quotient, d=remainder]
|
|
* HAC pp.598 Algorithm 14.20
|
|
*
|
|
* Note that the description in HAC is horribly
|
|
* incomplete. For example, it doesn't consider
|
|
* the case where digits are removed from 'x' in
|
|
* the inner loop. It also doesn't consider the
|
|
* case that y has fewer than three digits, etc..
|
|
*
|
|
* The overall algorithm is as described as
|
|
* 14.20 from HAC but fixed to treat these cases.
|
|
*/
|
|
static int
|
|
signed_divide(mp_int *c, mp_int *d, mp_int *a, mp_int *b)
|
|
{
|
|
mp_int q, x, y, t1, t2;
|
|
int res, n, t, i, norm, neg;
|
|
|
|
/* is divisor zero ? */
|
|
if (MP_ISZERO(b) == MP_YES) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* if a < b then q=0, r = a */
|
|
if (compare_magnitude(a, b) == MP_LT) {
|
|
if (d != NULL) {
|
|
res = mp_copy(a, d);
|
|
} else {
|
|
res = MP_OKAY;
|
|
}
|
|
if (c != NULL) {
|
|
mp_zero(c);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
if ((res = mp_init_size(&q, a->used + 2)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
q.used = a->used + 2;
|
|
|
|
if ((res = mp_init(&t1)) != MP_OKAY) {
|
|
goto LBL_Q;
|
|
}
|
|
|
|
if ((res = mp_init(&t2)) != MP_OKAY) {
|
|
goto LBL_T1;
|
|
}
|
|
|
|
if ((res = mp_init_copy(&x, a)) != MP_OKAY) {
|
|
goto LBL_T2;
|
|
}
|
|
|
|
if ((res = mp_init_copy(&y, b)) != MP_OKAY) {
|
|
goto LBL_X;
|
|
}
|
|
|
|
/* fix the sign */
|
|
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
|
|
x.sign = y.sign = MP_ZPOS;
|
|
|
|
/* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
|
|
norm = mp_count_bits(&y) % DIGIT_BIT;
|
|
if (norm < (int)(DIGIT_BIT-1)) {
|
|
norm = (DIGIT_BIT-1) - norm;
|
|
if ((res = lshift_bits(&x, norm, &x)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
if ((res = lshift_bits(&y, norm, &y)) != MP_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;
|
|
|
|
/* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
|
|
if ((res = lshift_digits(&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
|
|
goto LBL_Y;
|
|
}
|
|
|
|
while (signed_compare(&x, &y) != MP_LT) {
|
|
++(q.dp[n - t]);
|
|
if ((res = signed_subtract(&x, &y, &x)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
}
|
|
|
|
/* reset y by shifting it back down */
|
|
rshift_digits(&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] = ((((mp_digit)1) << DIGIT_BIT) - 1);
|
|
} else {
|
|
mp_word tmp;
|
|
tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
|
|
tmp |= ((mp_word) x.dp[i - 1]);
|
|
tmp /= ((mp_word) y.dp[t]);
|
|
if (tmp > (mp_word) MP_MASK) {
|
|
tmp = MP_MASK;
|
|
}
|
|
q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
|
|
}
|
|
|
|
/* 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) & MP_MASK;
|
|
do {
|
|
q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
|
|
|
|
/* find left hand */
|
|
mp_zero(&t1);
|
|
t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
|
|
t1.dp[1] = y.dp[t];
|
|
t1.used = 2;
|
|
if ((res = multiply_digit(&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
|
|
/* 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 (compare_magnitude(&t1, &t2) == MP_GT);
|
|
|
|
/* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
|
|
if ((res = multiply_digit(&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
|
|
if ((res = lshift_digits(&t1, i - t - 1)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
|
|
if ((res = signed_subtract(&x, &t1, &x)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
|
|
/* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
|
|
if (x.sign == MP_NEG) {
|
|
if ((res = mp_copy(&y, &t1)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
if ((res = lshift_digits(&t1, i - t - 1)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
if ((res = signed_add(&x, &t1, &x)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
|
|
q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
|
|
}
|
|
}
|
|
|
|
/* 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 ? MP_ZPOS : a->sign;
|
|
|
|
if (c != NULL) {
|
|
trim_unused_digits(&q);
|
|
mp_exch(&q, c);
|
|
c->sign = neg;
|
|
}
|
|
|
|
if (d != NULL) {
|
|
rshift_bits(&x, norm, &x, NULL);
|
|
mp_exch(&x, d);
|
|
}
|
|
|
|
res = MP_OKAY;
|
|
|
|
LBL_Y:
|
|
mp_clear(&y);
|
|
LBL_X:
|
|
mp_clear(&x);
|
|
LBL_T2:
|
|
mp_clear(&t2);
|
|
LBL_T1:
|
|
mp_clear(&t1);
|
|
LBL_Q:
|
|
mp_clear(&q);
|
|
return res;
|
|
}
|
|
|
|
/* c = a mod b, 0 <= c < b */
|
|
static int
|
|
modulo(mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
mp_int t;
|
|
int res;
|
|
|
|
if ((res = mp_init(&t)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
if ((res = signed_divide(NULL, &t, a, b)) != MP_OKAY) {
|
|
mp_clear(&t);
|
|
return res;
|
|
}
|
|
|
|
if (t.sign != b->sign) {
|
|
res = signed_add(b, &t, c);
|
|
} else {
|
|
res = MP_OKAY;
|
|
mp_exch(&t, c);
|
|
}
|
|
|
|
mp_clear(&t);
|
|
return res;
|
|
}
|
|
|
|
/* set to a digit */
|
|
static void
|
|
set_word(mp_int * a, mp_digit b)
|
|
{
|
|
mp_zero(a);
|
|
a->dp[0] = b & MP_MASK;
|
|
a->used = (a->dp[0] != 0) ? 1 : 0;
|
|
}
|
|
|
|
/* b = a/2 */
|
|
static int
|
|
half(mp_int * a, mp_int * b)
|
|
{
|
|
int x, res, oldused;
|
|
|
|
/* copy */
|
|
if (b->alloc < a->used) {
|
|
if ((res = mp_grow(b, a->used)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
oldused = b->used;
|
|
b->used = a->used;
|
|
{
|
|
mp_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;
|
|
trim_unused_digits(b);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* compare a digit */
|
|
static int
|
|
compare_digit(mp_int * a, mp_digit b)
|
|
{
|
|
/* compare based on sign */
|
|
if (a->sign == MP_NEG) {
|
|
return MP_LT;
|
|
}
|
|
|
|
/* compare based on magnitude */
|
|
if (a->used > 1) {
|
|
return MP_GT;
|
|
}
|
|
|
|
/* compare the only digit of a to b */
|
|
if (a->dp[0] > b) {
|
|
return MP_GT;
|
|
} else if (a->dp[0] < b) {
|
|
return MP_LT;
|
|
} else {
|
|
return MP_EQ;
|
|
}
|
|
}
|
|
|
|
static void
|
|
mp_clear_multi(mp_int *mp, ...)
|
|
{
|
|
mp_int* next_mp = mp;
|
|
va_list args;
|
|
|
|
va_start(args, mp);
|
|
while (next_mp != NULL) {
|
|
mp_clear(next_mp);
|
|
next_mp = va_arg(args, mp_int*);
|
|
}
|
|
va_end(args);
|
|
}
|
|
|
|
/* computes the modular inverse via binary extended euclidean algorithm,
|
|
* that is c = 1/a mod b
|
|
*
|
|
* Based on slow invmod except this is optimized for the case where b is
|
|
* odd as per HAC Note 14.64 on pp. 610
|
|
*/
|
|
static int
|
|
fast_modular_inverse(mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
mp_int x, y, u, v, B, D;
|
|
int res, neg;
|
|
|
|
/* 2. [modified] b must be odd */
|
|
if (MP_ISZERO(b) == MP_YES) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* init all our temps */
|
|
if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* x == modulus, y == value to invert */
|
|
if ((res = mp_copy(b, &x)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* we need y = |a| */
|
|
if ((res = modulo(a, b, &y)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
|
if ((res = mp_copy(&x, &u)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((res = mp_copy(&y, &v)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
set_word(&D, 1);
|
|
|
|
top:
|
|
/* 4. while u is even do */
|
|
while (BN_is_even(&u) == 1) {
|
|
/* 4.1 u = u/2 */
|
|
if ((res = half(&u, &u)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
/* 4.2 if B is odd then */
|
|
if (BN_is_odd(&B) == 1) {
|
|
if ((res = signed_subtract(&B, &x, &B)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
/* B = B/2 */
|
|
if ((res = half(&B, &B)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* 5. while v is even do */
|
|
while (BN_is_even(&v) == 1) {
|
|
/* 5.1 v = v/2 */
|
|
if ((res = half(&v, &v)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
/* 5.2 if D is odd then */
|
|
if (BN_is_odd(&D) == 1) {
|
|
/* D = (D-x)/2 */
|
|
if ((res = signed_subtract(&D, &x, &D)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
/* D = D/2 */
|
|
if ((res = half(&D, &D)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* 6. if u >= v then */
|
|
if (signed_compare(&u, &v) != MP_LT) {
|
|
/* u = u - v, B = B - D */
|
|
if ((res = signed_subtract(&u, &v, &u)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if ((res = signed_subtract(&B, &D, &B)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
} else {
|
|
/* v - v - u, D = D - B */
|
|
if ((res = signed_subtract(&v, &u, &v)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if ((res = signed_subtract(&D, &B, &D)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* if not zero goto step 4 */
|
|
if (MP_ISZERO(&u) == MP_NO) {
|
|
goto top;
|
|
}
|
|
|
|
/* now a = C, b = D, gcd == g*v */
|
|
|
|
/* if v != 1 then there is no inverse */
|
|
if (compare_digit(&v, 1) != MP_EQ) {
|
|
res = MP_VAL;
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* b is now the inverse */
|
|
neg = a->sign;
|
|
while (D.sign == MP_NEG) {
|
|
if ((res = signed_add(&D, b, &D)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
mp_exch(&D, c);
|
|
c->sign = neg;
|
|
res = MP_OKAY;
|
|
|
|
LBL_ERR:
|
|
mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
|
|
return res;
|
|
}
|
|
|
|
/* hac 14.61, pp608 */
|
|
static int
|
|
slow_modular_inverse(mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
mp_int x, y, u, v, A, B, C, D;
|
|
int res;
|
|
|
|
/* b cannot be negative */
|
|
if (b->sign == MP_NEG || MP_ISZERO(b) == MP_YES) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* init temps */
|
|
if ((res = mp_init_multi(&x, &y, &u, &v,
|
|
&A, &B, &C, &D, NULL)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* x = a, y = b */
|
|
if ((res = modulo(a, b, &x)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((res = mp_copy(b, &y)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* 2. [modified] if x,y are both even then return an error! */
|
|
if (BN_is_even(&x) == 1 && BN_is_even(&y) == 1) {
|
|
res = MP_VAL;
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
|
if ((res = mp_copy(&x, &u)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((res = mp_copy(&y, &v)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
set_word(&A, 1);
|
|
set_word(&D, 1);
|
|
|
|
top:
|
|
/* 4. while u is even do */
|
|
while (BN_is_even(&u) == 1) {
|
|
/* 4.1 u = u/2 */
|
|
if ((res = half(&u, &u)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
/* 4.2 if A or B is odd then */
|
|
if (BN_is_odd(&A) == 1 || BN_is_odd(&B) == 1) {
|
|
/* A = (A+y)/2, B = (B-x)/2 */
|
|
if ((res = signed_add(&A, &y, &A)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((res = signed_subtract(&B, &x, &B)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
/* A = A/2, B = B/2 */
|
|
if ((res = half(&A, &A)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((res = half(&B, &B)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* 5. while v is even do */
|
|
while (BN_is_even(&v) == 1) {
|
|
/* 5.1 v = v/2 */
|
|
if ((res = half(&v, &v)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
/* 5.2 if C or D is odd then */
|
|
if (BN_is_odd(&C) == 1 || BN_is_odd(&D) == 1) {
|
|
/* C = (C+y)/2, D = (D-x)/2 */
|
|
if ((res = signed_add(&C, &y, &C)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((res = signed_subtract(&D, &x, &D)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
/* C = C/2, D = D/2 */
|
|
if ((res = half(&C, &C)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((res = half(&D, &D)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* 6. if u >= v then */
|
|
if (signed_compare(&u, &v) != MP_LT) {
|
|
/* u = u - v, A = A - C, B = B - D */
|
|
if ((res = signed_subtract(&u, &v, &u)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if ((res = signed_subtract(&A, &C, &A)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if ((res = signed_subtract(&B, &D, &B)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
} else {
|
|
/* v - v - u, C = C - A, D = D - B */
|
|
if ((res = signed_subtract(&v, &u, &v)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if ((res = signed_subtract(&C, &A, &C)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if ((res = signed_subtract(&D, &B, &D)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* if not zero goto step 4 */
|
|
if (BN_is_zero(&u) == 0) {
|
|
goto top;
|
|
}
|
|
/* now a = C, b = D, gcd == g*v */
|
|
|
|
/* if v != 1 then there is no inverse */
|
|
if (compare_digit(&v, 1) != MP_EQ) {
|
|
res = MP_VAL;
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* if its too low */
|
|
while (compare_digit(&C, 0) == MP_LT) {
|
|
if ((res = signed_add(&C, b, &C)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* too big */
|
|
while (compare_magnitude(&C, b) != MP_LT) {
|
|
if ((res = signed_subtract(&C, b, &C)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* C is now the inverse */
|
|
mp_exch(&C, c);
|
|
res = MP_OKAY;
|
|
LBL_ERR:
|
|
mp_clear_multi(&x, &y, &u, &v, &A, &B, &C, &D, NULL);
|
|
return res;
|
|
}
|
|
|
|
static int
|
|
modular_inverse(mp_int *c, mp_int *a, mp_int *b)
|
|
{
|
|
/* b cannot be negative */
|
|
if (b->sign == MP_NEG || MP_ISZERO(b) == MP_YES) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* if the modulus is odd we can use a faster routine instead */
|
|
if (BN_is_odd(b) == 1) {
|
|
return fast_modular_inverse(a, b, c);
|
|
}
|
|
return slow_modular_inverse(a, b, c);
|
|
}
|
|
|
|
/* b = |a|
|
|
*
|
|
* Simple function copies the input and fixes the sign to positive
|
|
*/
|
|
static int
|
|
absolute(mp_int * a, mp_int * b)
|
|
{
|
|
int res;
|
|
|
|
/* copy a to b */
|
|
if (a != b) {
|
|
if ((res = mp_copy(a, b)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* force the sign of b to positive */
|
|
b->sign = MP_ZPOS;
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* determines if reduce_2k_l can be used */
|
|
static int
|
|
mp_reduce_is_2k_l(mp_int *a)
|
|
{
|
|
int ix, iy;
|
|
|
|
if (a->used == 0) {
|
|
return MP_NO;
|
|
} else if (a->used == 1) {
|
|
return MP_YES;
|
|
} else if (a->used > 1) {
|
|
/* if more than half of the digits are -1 we're sold */
|
|
for (iy = ix = 0; ix < a->used; ix++) {
|
|
if (a->dp[ix] == MP_MASK) {
|
|
++iy;
|
|
}
|
|
}
|
|
return (iy >= (a->used/2)) ? MP_YES : MP_NO;
|
|
|
|
}
|
|
return MP_NO;
|
|
}
|
|
|
|
/* computes a = 2**b
|
|
*
|
|
* Simple algorithm which zeroes the int, grows it then just sets one bit
|
|
* as required.
|
|
*/
|
|
static int
|
|
mp_2expt(mp_int * a, int b)
|
|
{
|
|
int res;
|
|
|
|
/* zero a as per default */
|
|
mp_zero(a);
|
|
|
|
/* grow a to accomodate the single bit */
|
|
if ((res = mp_grow(a, b / DIGIT_BIT + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* set the used count of where the bit will go */
|
|
a->used = b / DIGIT_BIT + 1;
|
|
|
|
/* put the single bit in its place */
|
|
a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* pre-calculate the value required for Barrett reduction
|
|
* For a given modulus "b" it calulates the value required in "a"
|
|
*/
|
|
static int
|
|
mp_reduce_setup(mp_int * a, mp_int * b)
|
|
{
|
|
int res;
|
|
|
|
if ((res = mp_2expt(a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
return signed_divide(a, NULL, a, b);
|
|
}
|
|
|
|
/* b = a*2 */
|
|
static int
|
|
doubled(mp_int * a, mp_int * b)
|
|
{
|
|
int x, res, oldused;
|
|
|
|
/* grow to accomodate result */
|
|
if (b->alloc < a->used + 1) {
|
|
if ((res = mp_grow(b, a->used + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
oldused = b->used;
|
|
b->used = a->used;
|
|
|
|
{
|
|
mp_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 >> ((mp_digit)(DIGIT_BIT - 1));
|
|
|
|
/* now shift up this digit, add in the carry [from the previous] */
|
|
*tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
|
|
|
|
/* copy the carry that would be from the source
|
|
* digit into the next iteration
|
|
*/
|
|
r = rr;
|
|
}
|
|
|
|
/* new leading digit? */
|
|
if (r != 0) {
|
|
/* 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 MP_OKAY;
|
|
}
|
|
|
|
/* divide by three (based on routine from MPI and the GMP manual) */
|
|
static int
|
|
third(mp_int * a, mp_int *c, mp_digit * d)
|
|
{
|
|
mp_int q;
|
|
mp_word w, t;
|
|
mp_digit b;
|
|
int res, ix;
|
|
|
|
/* b = 2**DIGIT_BIT / 3 */
|
|
b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3);
|
|
|
|
if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
q.used = a->used;
|
|
q.sign = a->sign;
|
|
w = 0;
|
|
for (ix = a->used - 1; ix >= 0; ix--) {
|
|
w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
|
|
|
|
if (w >= 3) {
|
|
/* multiply w by [1/3] */
|
|
t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);
|
|
|
|
/* now subtract 3 * [w/3] from w, to get the remainder */
|
|
w -= t+t+t;
|
|
|
|
/* fixup the remainder as required since
|
|
* the optimization is not exact.
|
|
*/
|
|
while (w >= 3) {
|
|
t += 1;
|
|
w -= 3;
|
|
}
|
|
} else {
|
|
t = 0;
|
|
}
|
|
q.dp[ix] = (mp_digit)t;
|
|
}
|
|
|
|
/* [optional] store the remainder */
|
|
if (d != NULL) {
|
|
*d = (mp_digit)w;
|
|
}
|
|
|
|
/* [optional] store the quotient */
|
|
if (c != NULL) {
|
|
trim_unused_digits(&q);
|
|
mp_exch(&q, c);
|
|
}
|
|
mp_clear(&q);
|
|
|
|
return res;
|
|
}
|
|
|
|
/* multiplication using the Toom-Cook 3-way algorithm
|
|
*
|
|
* Much more complicated than Karatsuba but has a lower
|
|
* asymptotic running time of O(N**1.464). This algorithm is
|
|
* only particularly useful on VERY large inputs
|
|
* (we're talking 1000s of digits here...).
|
|
*/
|
|
static int
|
|
toom_cook_multiply(mp_int *a, mp_int *b, mp_int *c)
|
|
{
|
|
mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
|
|
int res, B;
|
|
|
|
/* init temps */
|
|
if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
|
|
&a0, &a1, &a2, &b0, &b1,
|
|
&b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* B */
|
|
B = MIN(a->used, b->used) / 3;
|
|
|
|
/* a = a2 * B**2 + a1 * B + a0 */
|
|
if ((res = modulo_2_to_power(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if ((res = mp_copy(a, &a1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
rshift_digits(&a1, B);
|
|
modulo_2_to_power(&a1, DIGIT_BIT * B, &a1);
|
|
|
|
if ((res = mp_copy(a, &a2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
rshift_digits(&a2, B*2);
|
|
|
|
/* b = b2 * B**2 + b1 * B + b0 */
|
|
if ((res = modulo_2_to_power(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if ((res = mp_copy(b, &b1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
rshift_digits(&b1, B);
|
|
modulo_2_to_power(&b1, DIGIT_BIT * B, &b1);
|
|
|
|
if ((res = mp_copy(b, &b2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
rshift_digits(&b2, B*2);
|
|
|
|
/* w0 = a0*b0 */
|
|
if ((res = signed_multiply(&a0, &b0, &w0)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
/* w4 = a2 * b2 */
|
|
if ((res = signed_multiply(&a2, &b2, &w4)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
/* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
|
|
if ((res = doubled(&a0, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = doubled(&tmp1, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if ((res = doubled(&b0, &tmp2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = doubled(&tmp2, &tmp2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if ((res = signed_multiply(&tmp1, &tmp2, &w1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
/* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
|
|
if ((res = doubled(&a2, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = doubled(&tmp1, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if ((res = doubled(&b2, &tmp2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = doubled(&tmp2, &tmp2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if ((res = signed_multiply(&tmp1, &tmp2, &w3)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
|
|
/* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
|
|
if ((res = signed_add(&a2, &a1, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&b2, &b1, &tmp2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_multiply(&tmp1, &tmp2, &w2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
/* now solve the matrix
|
|
|
|
0 0 0 0 1
|
|
1 2 4 8 16
|
|
1 1 1 1 1
|
|
16 8 4 2 1
|
|
1 0 0 0 0
|
|
|
|
using 12 subtractions, 4 shifts,
|
|
2 small divisions and 1 small multiplication
|
|
*/
|
|
|
|
/* r1 - r4 */
|
|
if ((res = signed_subtract(&w1, &w4, &w1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r3 - r0 */
|
|
if ((res = signed_subtract(&w3, &w0, &w3)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r1/2 */
|
|
if ((res = half(&w1, &w1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r3/2 */
|
|
if ((res = half(&w3, &w3)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r2 - r0 - r4 */
|
|
if ((res = signed_subtract(&w2, &w0, &w2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_subtract(&w2, &w4, &w2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r1 - r2 */
|
|
if ((res = signed_subtract(&w1, &w2, &w1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r3 - r2 */
|
|
if ((res = signed_subtract(&w3, &w2, &w3)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r1 - 8r0 */
|
|
if ((res = lshift_bits(&w0, 3, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_subtract(&w1, &tmp1, &w1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r3 - 8r4 */
|
|
if ((res = lshift_bits(&w4, 3, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_subtract(&w3, &tmp1, &w3)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* 3r2 - r1 - r3 */
|
|
if ((res = multiply_digit(&w2, 3, &w2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_subtract(&w2, &w1, &w2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_subtract(&w2, &w3, &w2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r1 - r2 */
|
|
if ((res = signed_subtract(&w1, &w2, &w1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r3 - r2 */
|
|
if ((res = signed_subtract(&w3, &w2, &w3)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r1/3 */
|
|
if ((res = third(&w1, &w1, NULL)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r3/3 */
|
|
if ((res = third(&w3, &w3, NULL)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
/* at this point shift W[n] by B*n */
|
|
if ((res = lshift_digits(&w1, 1*B)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = lshift_digits(&w2, 2*B)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = lshift_digits(&w3, 3*B)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = lshift_digits(&w4, 4*B)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if ((res = signed_add(&w0, &w1, c)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&w2, &w3, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp1, c, c)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
ERR:
|
|
mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
|
|
&a0, &a1, &a2, &b0, &b1,
|
|
&b2, &tmp1, &tmp2, NULL);
|
|
return res;
|
|
}
|
|
|
|
#define TOOM_MUL_CUTOFF 350
|
|
#define KARATSUBA_MUL_CUTOFF 80
|
|
|
|
/* c = |a| * |b| using Karatsuba Multiplication using
|
|
* three half size multiplications
|
|
*
|
|
* Let B represent the radix [e.g. 2**DIGIT_BIT] and
|
|
* let n represent half of the number of digits in
|
|
* the min(a,b)
|
|
*
|
|
* a = a1 * B**n + a0
|
|
* b = b1 * B**n + b0
|
|
*
|
|
* Then, a * b =>
|
|
a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
|
|
*
|
|
* Note that a1b1 and a0b0 are used twice and only need to be
|
|
* computed once. So in total three half size (half # of
|
|
* digit) multiplications are performed, a0b0, a1b1 and
|
|
* (a1+b1)(a0+b0)
|
|
*
|
|
* Note that a multiplication of half the digits requires
|
|
* 1/4th the number of single precision multiplications so in
|
|
* total after one call 25% of the single precision multiplications
|
|
* are saved. Note also that the call to signed_multiply can end up back
|
|
* in this function if the a0, a1, b0, or b1 are above the threshold.
|
|
* This is known as divide-and-conquer and leads to the famous
|
|
* O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
|
|
* the standard O(N**2) that the baseline/comba methods use.
|
|
* Generally though the overhead of this method doesn't pay off
|
|
* until a certain size (N ~ 80) is reached.
|
|
*/
|
|
static int
|
|
karatsuba_multiply(mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
|
|
int B;
|
|
int err;
|
|
|
|
/* default the return code to an error */
|
|
err = MP_MEM;
|
|
|
|
/* min # of digits */
|
|
B = MIN(a->used, b->used);
|
|
|
|
/* now divide in two */
|
|
B = (int)((unsigned)B >> 1);
|
|
|
|
/* init copy all the temps */
|
|
if (mp_init_size(&x0, B) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if (mp_init_size(&x1, a->used - B) != MP_OKAY) {
|
|
goto X0;
|
|
}
|
|
if (mp_init_size(&y0, B) != MP_OKAY) {
|
|
goto X1;
|
|
}
|
|
if (mp_init_size(&y1, b->used - B) != MP_OKAY) {
|
|
goto Y0;
|
|
}
|
|
/* init temps */
|
|
if (mp_init_size(&t1, B * 2) != MP_OKAY) {
|
|
goto Y1;
|
|
}
|
|
if (mp_init_size(&x0y0, B * 2) != MP_OKAY) {
|
|
goto T1;
|
|
}
|
|
if (mp_init_size(&x1y1, B * 2) != MP_OKAY) {
|
|
goto X0Y0;
|
|
}
|
|
/* now shift the digits */
|
|
x0.used = y0.used = B;
|
|
x1.used = a->used - B;
|
|
y1.used = b->used - B;
|
|
|
|
{
|
|
int x;
|
|
mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
|
|
|
|
/* we copy the digits directly instead of using higher level functions
|
|
* since we also need to shift the digits
|
|
*/
|
|
tmpa = a->dp;
|
|
tmpb = b->dp;
|
|
|
|
tmpx = x0.dp;
|
|
tmpy = y0.dp;
|
|
for (x = 0; x < B; x++) {
|
|
*tmpx++ = *tmpa++;
|
|
*tmpy++ = *tmpb++;
|
|
}
|
|
|
|
tmpx = x1.dp;
|
|
for (x = B; x < a->used; x++) {
|
|
*tmpx++ = *tmpa++;
|
|
}
|
|
|
|
tmpy = y1.dp;
|
|
for (x = B; x < b->used; x++) {
|
|
*tmpy++ = *tmpb++;
|
|
}
|
|
}
|
|
|
|
/* only need to clamp the lower words since by definition the
|
|
* upper words x1/y1 must have a known number of digits
|
|
*/
|
|
trim_unused_digits(&x0);
|
|
trim_unused_digits(&y0);
|
|
|
|
/* now calc the products x0y0 and x1y1 */
|
|
/* after this x0 is no longer required, free temp [x0==t2]! */
|
|
if (signed_multiply(&x0, &y0, &x0y0) != MP_OKAY) {
|
|
goto X1Y1; /* x0y0 = x0*y0 */
|
|
}
|
|
if (signed_multiply(&x1, &y1, &x1y1) != MP_OKAY) {
|
|
goto X1Y1; /* x1y1 = x1*y1 */
|
|
}
|
|
/* now calc x1+x0 and y1+y0 */
|
|
if (basic_add(&x1, &x0, &t1) != MP_OKAY) {
|
|
goto X1Y1; /* t1 = x1 - x0 */
|
|
}
|
|
if (basic_add(&y1, &y0, &x0) != MP_OKAY) {
|
|
goto X1Y1; /* t2 = y1 - y0 */
|
|
}
|
|
if (signed_multiply(&t1, &x0, &t1) != MP_OKAY) {
|
|
goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */
|
|
}
|
|
/* add x0y0 */
|
|
if (signed_add(&x0y0, &x1y1, &x0) != MP_OKAY) {
|
|
goto X1Y1; /* t2 = x0y0 + x1y1 */
|
|
}
|
|
if (basic_subtract(&t1, &x0, &t1) != MP_OKAY) {
|
|
goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
|
|
}
|
|
/* shift by B */
|
|
if (lshift_digits(&t1, B) != MP_OKAY) {
|
|
goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
|
|
}
|
|
if (lshift_digits(&x1y1, B * 2) != MP_OKAY) {
|
|
goto X1Y1; /* x1y1 = x1y1 << 2*B */
|
|
}
|
|
if (signed_add(&x0y0, &t1, &t1) != MP_OKAY) {
|
|
goto X1Y1; /* t1 = x0y0 + t1 */
|
|
}
|
|
if (signed_add(&t1, &x1y1, c) != MP_OKAY) {
|
|
goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
|
|
}
|
|
/* Algorithm succeeded set the return code to MP_OKAY */
|
|
err = MP_OKAY;
|
|
|
|
X1Y1:
|
|
mp_clear(&x1y1);
|
|
X0Y0:
|
|
mp_clear(&x0y0);
|
|
T1:
|
|
mp_clear(&t1);
|
|
Y1:
|
|
mp_clear(&y1);
|
|
Y0:
|
|
mp_clear(&y0);
|
|
X1:
|
|
mp_clear(&x1);
|
|
X0:
|
|
mp_clear(&x0);
|
|
ERR:
|
|
return err;
|
|
}
|
|
|
|
/* Fast (comba) multiplier
|
|
*
|
|
* This is the fast column-array [comba] multiplier. It is
|
|
* designed to compute the columns of the product first
|
|
* then handle the carries afterwards. This has the effect
|
|
* of making the nested loops that compute the columns very
|
|
* simple and schedulable on super-scalar processors.
|
|
*
|
|
* This has been modified to produce a variable number of
|
|
* digits of output so if say only a half-product is required
|
|
* you don't have to compute the upper half (a feature
|
|
* required for fast Barrett reduction).
|
|
*
|
|
* Based on Algorithm 14.12 on pp.595 of HAC.
|
|
*
|
|
*/
|
|
static int
|
|
fast_col_array_multiply(mp_int * a, mp_int * b, mp_int * c, int digs)
|
|
{
|
|
int olduse, res, pa, ix, iz;
|
|
/*LINTED*/
|
|
mp_digit W[MP_WARRAY];
|
|
mp_word _W;
|
|
|
|
/* grow the destination as required */
|
|
if (c->alloc < digs) {
|
|
if ((res = mp_grow(c, digs)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* number of output digits to produce */
|
|
pa = MIN(digs, a->used + b->used);
|
|
|
|
/* clear the carry */
|
|
_W = 0;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
int tx, ty;
|
|
int iy;
|
|
mp_digit *tmpx, *tmpy;
|
|
|
|
/* get offsets into the two bignums */
|
|
ty = MIN(b->used-1, ix);
|
|
tx = ix - ty;
|
|
|
|
/* setup temp aliases */
|
|
tmpx = a->dp + tx;
|
|
tmpy = b->dp + ty;
|
|
|
|
/* this is the number of times the loop will iterrate, essentially
|
|
while (tx++ < a->used && ty-- >= 0) { ... }
|
|
*/
|
|
iy = MIN(a->used-tx, ty+1);
|
|
|
|
/* execute loop */
|
|
for (iz = 0; iz < iy; ++iz) {
|
|
_W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
|
|
|
|
}
|
|
|
|
/* store term */
|
|
W[ix] = ((mp_digit)_W) & MP_MASK;
|
|
|
|
/* make next carry */
|
|
_W = _W >> ((mp_word)DIGIT_BIT);
|
|
}
|
|
|
|
/* setup dest */
|
|
olduse = c->used;
|
|
c->used = pa;
|
|
|
|
{
|
|
mp_digit *tmpc;
|
|
tmpc = c->dp;
|
|
for (ix = 0; ix < pa+1; ix++) {
|
|
/* now extract the previous digit [below the carry] */
|
|
*tmpc++ = W[ix];
|
|
}
|
|
|
|
/* clear unused digits [that existed in the old copy of c] */
|
|
for (; ix < olduse; ix++) {
|
|
*tmpc++ = 0;
|
|
}
|
|
}
|
|
trim_unused_digits(c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* return 1 if we can use fast column array multiply */
|
|
/*
|
|
* The fast multiplier can be used if the output will
|
|
* have less than MP_WARRAY digits and the number of
|
|
* digits won't affect carry propagation
|
|
*/
|
|
static inline int
|
|
can_use_fast_column_array(int ndigits, int used)
|
|
{
|
|
return (((unsigned)ndigits < MP_WARRAY) &&
|
|
used < (1 << (unsigned)((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))));
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_s_mp_mul_digs.c,v $ */
|
|
/* Revision: 1.2 $ */
|
|
/* Date: 2011/03/18 16:22:09 $ */
|
|
|
|
|
|
/* multiplies |a| * |b| and only computes upto digs digits of result
|
|
* HAC pp. 595, Algorithm 14.12 Modified so you can control how
|
|
* many digits of output are created.
|
|
*/
|
|
static int
|
|
basic_multiply_partial_lower(mp_int * a, mp_int * b, mp_int * c, int digs)
|
|
{
|
|
mp_int t;
|
|
int res, pa, pb, ix, iy;
|
|
mp_digit u;
|
|
mp_word r;
|
|
mp_digit tmpx, *tmpt, *tmpy;
|
|
|
|
/* can we use the fast multiplier? */
|
|
if (can_use_fast_column_array(digs, MIN(a->used, b->used))) {
|
|
return fast_col_array_multiply(a, b, c, digs);
|
|
}
|
|
|
|
if ((res = mp_init_size(&t, digs)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
t.used = digs;
|
|
|
|
/* compute the digits of the product directly */
|
|
pa = a->used;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
/* set the carry to zero */
|
|
u = 0;
|
|
|
|
/* limit ourselves to making digs digits of output */
|
|
pb = MIN(b->used, digs - ix);
|
|
|
|
/* setup some aliases */
|
|
/* copy of the digit from a used within the nested loop */
|
|
tmpx = a->dp[ix];
|
|
|
|
/* an alias for the destination shifted ix places */
|
|
tmpt = t.dp + ix;
|
|
|
|
/* an alias for the digits of b */
|
|
tmpy = b->dp;
|
|
|
|
/* compute the columns of the output and propagate the carry */
|
|
for (iy = 0; iy < pb; iy++) {
|
|
/* compute the column as a mp_word */
|
|
r = ((mp_word)*tmpt) +
|
|
((mp_word)tmpx) * ((mp_word)*tmpy++) +
|
|
((mp_word) u);
|
|
|
|
/* the new column is the lower part of the result */
|
|
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
|
|
|
/* get the carry word from the result */
|
|
u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
|
}
|
|
/* set carry if it is placed below digs */
|
|
if (ix + iy < digs) {
|
|
*tmpt = u;
|
|
}
|
|
}
|
|
|
|
trim_unused_digits(&t);
|
|
mp_exch(&t, c);
|
|
|
|
mp_clear(&t);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_s_mp_mul_digs.c,v $ */
|
|
/* Revision: 1.3 $ */
|
|
/* Date: 2011/03/18 16:43:04 $ */
|
|
|
|
/* high level multiplication (handles sign) */
|
|
static int
|
|
signed_multiply(mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
int res, neg;
|
|
|
|
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
|
|
/* use Toom-Cook? */
|
|
if (MIN(a->used, b->used) >= TOOM_MUL_CUTOFF) {
|
|
res = toom_cook_multiply(a, b, c);
|
|
} else if (MIN(a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
|
|
/* use Karatsuba? */
|
|
res = karatsuba_multiply(a, b, c);
|
|
} else {
|
|
/* can we use the fast multiplier? */
|
|
int digs = a->used + b->used + 1;
|
|
|
|
if (can_use_fast_column_array(digs, MIN(a->used, b->used))) {
|
|
res = fast_col_array_multiply(a, b, c, digs);
|
|
} else {
|
|
res = basic_multiply_partial_lower(a, b, c, (a)->used + (b)->used + 1);
|
|
}
|
|
}
|
|
c->sign = (c->used > 0) ? neg : MP_ZPOS;
|
|
return res;
|
|
}
|
|
|
|
/* this is a modified version of fast_s_mul_digs that only produces
|
|
* output digits *above* digs. See the comments for fast_s_mul_digs
|
|
* to see how it works.
|
|
*
|
|
* This is used in the Barrett reduction since for one of the multiplications
|
|
* only the higher digits were needed. This essentially halves the work.
|
|
*
|
|
* Based on Algorithm 14.12 on pp.595 of HAC.
|
|
*/
|
|
static int
|
|
fast_basic_multiply_partial_upper(mp_int * a, mp_int * b, mp_int * c, int digs)
|
|
{
|
|
int olduse, res, pa, ix, iz;
|
|
mp_digit W[MP_WARRAY];
|
|
mp_word _W;
|
|
|
|
/* grow the destination as required */
|
|
pa = a->used + b->used;
|
|
if (c->alloc < pa) {
|
|
if ((res = mp_grow(c, pa)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* number of output digits to produce */
|
|
pa = a->used + b->used;
|
|
_W = 0;
|
|
for (ix = digs; ix < pa; ix++) {
|
|
int tx, ty, iy;
|
|
mp_digit *tmpx, *tmpy;
|
|
|
|
/* get offsets into the two bignums */
|
|
ty = MIN(b->used-1, ix);
|
|
tx = ix - ty;
|
|
|
|
/* setup temp aliases */
|
|
tmpx = a->dp + tx;
|
|
tmpy = b->dp + ty;
|
|
|
|
/* this is the number of times the loop will iterrate, essentially its
|
|
while (tx++ < a->used && ty-- >= 0) { ... }
|
|
*/
|
|
iy = MIN(a->used-tx, ty+1);
|
|
|
|
/* execute loop */
|
|
for (iz = 0; iz < iy; iz++) {
|
|
_W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
|
|
}
|
|
|
|
/* store term */
|
|
W[ix] = ((mp_digit)_W) & MP_MASK;
|
|
|
|
/* make next carry */
|
|
_W = _W >> ((mp_word)DIGIT_BIT);
|
|
}
|
|
|
|
/* setup dest */
|
|
olduse = c->used;
|
|
c->used = pa;
|
|
|
|
{
|
|
mp_digit *tmpc;
|
|
|
|
tmpc = c->dp + digs;
|
|
for (ix = digs; ix < pa; ix++) {
|
|
/* now extract the previous digit [below the carry] */
|
|
*tmpc++ = W[ix];
|
|
}
|
|
|
|
/* clear unused digits [that existed in the old copy of c] */
|
|
for (; ix < olduse; ix++) {
|
|
*tmpc++ = 0;
|
|
}
|
|
}
|
|
trim_unused_digits(c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_s_mp_mul_high_digs.c,v $ */
|
|
/* Revision: 1.1.1.1 $ */
|
|
/* Date: 2011/03/12 22:58:18 $ */
|
|
|
|
/* multiplies |a| * |b| and does not compute the lower digs digits
|
|
* [meant to get the higher part of the product]
|
|
*/
|
|
static int
|
|
basic_multiply_partial_upper(mp_int * a, mp_int * b, mp_int * c, int digs)
|
|
{
|
|
mp_int t;
|
|
int res, pa, pb, ix, iy;
|
|
mp_digit carry;
|
|
mp_word r;
|
|
mp_digit tmpx, *tmpt, *tmpy;
|
|
|
|
/* can we use the fast multiplier? */
|
|
if (can_use_fast_column_array(a->used + b->used + 1, MIN(a->used, b->used))) {
|
|
return fast_basic_multiply_partial_upper(a, b, c, digs);
|
|
}
|
|
|
|
if ((res = mp_init_size(&t, a->used + b->used + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
t.used = a->used + b->used + 1;
|
|
|
|
pa = a->used;
|
|
pb = b->used;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
/* clear the carry */
|
|
carry = 0;
|
|
|
|
/* left hand side of A[ix] * B[iy] */
|
|
tmpx = a->dp[ix];
|
|
|
|
/* alias to the address of where the digits will be stored */
|
|
tmpt = &(t.dp[digs]);
|
|
|
|
/* alias for where to read the right hand side from */
|
|
tmpy = b->dp + (digs - ix);
|
|
|
|
for (iy = digs - ix; iy < pb; iy++) {
|
|
/* calculate the double precision result */
|
|
r = ((mp_word)*tmpt) +
|
|
((mp_word)tmpx) * ((mp_word)*tmpy++) +
|
|
((mp_word) carry);
|
|
|
|
/* get the lower part */
|
|
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
|
|
|
/* carry the carry */
|
|
carry = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
|
}
|
|
*tmpt = carry;
|
|
}
|
|
trim_unused_digits(&t);
|
|
mp_exch(&t, c);
|
|
mp_clear(&t);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_s_mp_mul_high_digs.c,v $ */
|
|
/* Revision: 1.3 $ */
|
|
/* Date: 2011/03/18 16:43:04 $ */
|
|
|
|
/* reduces x mod m, assumes 0 < x < m**2, mu is
|
|
* precomputed via mp_reduce_setup.
|
|
* From HAC pp.604 Algorithm 14.42
|
|
*/
|
|
static int
|
|
mp_reduce(mp_int * x, mp_int * m, mp_int * mu)
|
|
{
|
|
mp_int q;
|
|
int res, um = m->used;
|
|
|
|
/* q = x */
|
|
if ((res = mp_init_copy(&q, x)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* q1 = x / b**(k-1) */
|
|
rshift_digits(&q, um - 1);
|
|
|
|
/* according to HAC this optimization is ok */
|
|
if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
|
|
if ((res = signed_multiply(&q, mu, &q)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
} else {
|
|
if ((res = basic_multiply_partial_upper(&q, mu, &q, um)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
}
|
|
|
|
/* q3 = q2 / b**(k+1) */
|
|
rshift_digits(&q, um + 1);
|
|
|
|
/* x = x mod b**(k+1), quick (no division) */
|
|
if ((res = modulo_2_to_power(x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* q = q * m mod b**(k+1), quick (no division) */
|
|
if ((res = basic_multiply_partial_lower(&q, m, &q, um + 1)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* x = x - q */
|
|
if ((res = signed_subtract(x, &q, x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* If x < 0, add b**(k+1) to it */
|
|
if (compare_digit(x, 0) == MP_LT) {
|
|
set_word(&q, 1);
|
|
if ((res = lshift_digits(&q, um + 1)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
if ((res = signed_add(x, &q, x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
}
|
|
|
|
/* Back off if it's too big */
|
|
while (signed_compare(x, m) != MP_LT) {
|
|
if ((res = basic_subtract(x, m, x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
}
|
|
|
|
CLEANUP:
|
|
mp_clear(&q);
|
|
|
|
return res;
|
|
}
|
|
|
|
/* determines the setup value */
|
|
static int
|
|
mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
|
|
{
|
|
int res;
|
|
mp_int tmp;
|
|
|
|
if ((res = mp_init(&tmp)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if ((res = basic_subtract(&tmp, a, d)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
ERR:
|
|
mp_clear(&tmp);
|
|
return res;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_2k_setup_l.c,v $ */
|
|
/* Revision: 1.1.1.1 $ */
|
|
/* Date: 2011/03/12 22:58:18 $ */
|
|
|
|
/* reduces a modulo n where n is of the form 2**p - d
|
|
This differs from reduce_2k since "d" can be larger
|
|
than a single digit.
|
|
*/
|
|
static int
|
|
mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
|
|
{
|
|
mp_int q;
|
|
int p, res;
|
|
|
|
if ((res = mp_init(&q)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
p = mp_count_bits(n);
|
|
top:
|
|
/* q = a/2**p, a = a mod 2**p */
|
|
if ((res = rshift_bits(a, p, &q, a)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
/* q = q * d */
|
|
if ((res = signed_multiply(&q, d, &q)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
/* a = a + q */
|
|
if ((res = basic_add(a, &q, a)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if (compare_magnitude(a, n) != MP_LT) {
|
|
basic_subtract(a, n, a);
|
|
goto top;
|
|
}
|
|
|
|
ERR:
|
|
mp_clear(&q);
|
|
return res;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_2k_l.c,v $ */
|
|
/* Revision: 1.1.1.1 $ */
|
|
/* Date: 2011/03/12 22:58:18 $ */
|
|
|
|
/* squaring using Toom-Cook 3-way algorithm */
|
|
static int
|
|
toom_cook_square(mp_int *a, mp_int *b)
|
|
{
|
|
mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
|
|
int res, B;
|
|
|
|
/* init temps */
|
|
if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* B */
|
|
B = a->used / 3;
|
|
|
|
/* a = a2 * B**2 + a1 * B + a0 */
|
|
if ((res = modulo_2_to_power(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if ((res = mp_copy(a, &a1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
rshift_digits(&a1, B);
|
|
modulo_2_to_power(&a1, DIGIT_BIT * B, &a1);
|
|
|
|
if ((res = mp_copy(a, &a2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
rshift_digits(&a2, B*2);
|
|
|
|
/* w0 = a0*a0 */
|
|
if ((res = square(&a0, &w0)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
/* w4 = a2 * a2 */
|
|
if ((res = square(&a2, &w4)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
/* w1 = (a2 + 2(a1 + 2a0))**2 */
|
|
if ((res = doubled(&a0, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = doubled(&tmp1, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if ((res = square(&tmp1, &w1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
/* w3 = (a0 + 2(a1 + 2a2))**2 */
|
|
if ((res = doubled(&a2, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = doubled(&tmp1, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if ((res = square(&tmp1, &w3)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
|
|
/* w2 = (a2 + a1 + a0)**2 */
|
|
if ((res = signed_add(&a2, &a1, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = square(&tmp1, &w2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
/* now solve the matrix
|
|
|
|
0 0 0 0 1
|
|
1 2 4 8 16
|
|
1 1 1 1 1
|
|
16 8 4 2 1
|
|
1 0 0 0 0
|
|
|
|
using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication.
|
|
*/
|
|
|
|
/* r1 - r4 */
|
|
if ((res = signed_subtract(&w1, &w4, &w1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r3 - r0 */
|
|
if ((res = signed_subtract(&w3, &w0, &w3)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r1/2 */
|
|
if ((res = half(&w1, &w1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r3/2 */
|
|
if ((res = half(&w3, &w3)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r2 - r0 - r4 */
|
|
if ((res = signed_subtract(&w2, &w0, &w2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_subtract(&w2, &w4, &w2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r1 - r2 */
|
|
if ((res = signed_subtract(&w1, &w2, &w1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r3 - r2 */
|
|
if ((res = signed_subtract(&w3, &w2, &w3)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r1 - 8r0 */
|
|
if ((res = lshift_bits(&w0, 3, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_subtract(&w1, &tmp1, &w1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r3 - 8r4 */
|
|
if ((res = lshift_bits(&w4, 3, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_subtract(&w3, &tmp1, &w3)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* 3r2 - r1 - r3 */
|
|
if ((res = multiply_digit(&w2, 3, &w2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_subtract(&w2, &w1, &w2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_subtract(&w2, &w3, &w2)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r1 - r2 */
|
|
if ((res = signed_subtract(&w1, &w2, &w1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r3 - r2 */
|
|
if ((res = signed_subtract(&w3, &w2, &w3)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r1/3 */
|
|
if ((res = third(&w1, &w1, NULL)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
/* r3/3 */
|
|
if ((res = third(&w3, &w3, NULL)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
/* at this point shift W[n] by B*n */
|
|
if ((res = lshift_digits(&w1, 1*B)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = lshift_digits(&w2, 2*B)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = lshift_digits(&w3, 3*B)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = lshift_digits(&w4, 4*B)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if ((res = signed_add(&w0, &w1, b)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&w2, &w3, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if ((res = signed_add(&tmp1, b, b)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
ERR:
|
|
mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
|
|
return res;
|
|
}
|
|
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_toom_sqr.c,v $ */
|
|
/* Revision: 1.1.1.1 $ */
|
|
/* Date: 2011/03/12 22:58:18 $ */
|
|
|
|
/* Karatsuba squaring, computes b = a*a using three
|
|
* half size squarings
|
|
*
|
|
* See comments of karatsuba_mul for details. It
|
|
* is essentially the same algorithm but merely
|
|
* tuned to perform recursive squarings.
|
|
*/
|
|
static int
|
|
karatsuba_square(mp_int * a, mp_int * b)
|
|
{
|
|
mp_int x0, x1, t1, t2, x0x0, x1x1;
|
|
int B, err;
|
|
|
|
err = MP_MEM;
|
|
|
|
/* min # of digits */
|
|
B = a->used;
|
|
|
|
/* now divide in two */
|
|
B = (unsigned)B >> 1;
|
|
|
|
/* init copy all the temps */
|
|
if (mp_init_size(&x0, B) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
if (mp_init_size(&x1, a->used - B) != MP_OKAY) {
|
|
goto X0;
|
|
}
|
|
/* init temps */
|
|
if (mp_init_size(&t1, a->used * 2) != MP_OKAY) {
|
|
goto X1;
|
|
}
|
|
if (mp_init_size(&t2, a->used * 2) != MP_OKAY) {
|
|
goto T1;
|
|
}
|
|
if (mp_init_size(&x0x0, B * 2) != MP_OKAY) {
|
|
goto T2;
|
|
}
|
|
if (mp_init_size(&x1x1, (a->used - B) * 2) != MP_OKAY) {
|
|
goto X0X0;
|
|
}
|
|
|
|
memcpy(x0.dp, a->dp, B * sizeof(*x0.dp));
|
|
memcpy(x1.dp, &a->dp[B], (a->used - B) * sizeof(*x1.dp));
|
|
|
|
x0.used = B;
|
|
x1.used = a->used - B;
|
|
|
|
trim_unused_digits(&x0);
|
|
|
|
/* now calc the products x0*x0 and x1*x1 */
|
|
if (square(&x0, &x0x0) != MP_OKAY) {
|
|
goto X1X1; /* x0x0 = x0*x0 */
|
|
}
|
|
if (square(&x1, &x1x1) != MP_OKAY) {
|
|
goto X1X1; /* x1x1 = x1*x1 */
|
|
}
|
|
/* now calc (x1+x0)**2 */
|
|
if (basic_add(&x1, &x0, &t1) != MP_OKAY) {
|
|
goto X1X1; /* t1 = x1 - x0 */
|
|
}
|
|
if (square(&t1, &t1) != MP_OKAY) {
|
|
goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */
|
|
}
|
|
/* add x0y0 */
|
|
if (basic_add(&x0x0, &x1x1, &t2) != MP_OKAY) {
|
|
goto X1X1; /* t2 = x0x0 + x1x1 */
|
|
}
|
|
if (basic_subtract(&t1, &t2, &t1) != MP_OKAY) {
|
|
goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */
|
|
}
|
|
/* shift by B */
|
|
if (lshift_digits(&t1, B) != MP_OKAY) {
|
|
goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
|
|
}
|
|
if (lshift_digits(&x1x1, B * 2) != MP_OKAY) {
|
|
goto X1X1; /* x1x1 = x1x1 << 2*B */
|
|
}
|
|
if (signed_add(&x0x0, &t1, &t1) != MP_OKAY) {
|
|
goto X1X1; /* t1 = x0x0 + t1 */
|
|
}
|
|
if (signed_add(&t1, &x1x1, b) != MP_OKAY) {
|
|
goto X1X1; /* t1 = x0x0 + t1 + x1x1 */
|
|
}
|
|
err = MP_OKAY;
|
|
|
|
X1X1:
|
|
mp_clear(&x1x1);
|
|
X0X0:
|
|
mp_clear(&x0x0);
|
|
T2:
|
|
mp_clear(&t2);
|
|
T1:
|
|
mp_clear(&t1);
|
|
X1:
|
|
mp_clear(&x1);
|
|
X0:
|
|
mp_clear(&x0);
|
|
ERR:
|
|
return err;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_karatsuba_sqr.c,v $ */
|
|
/* Revision: 1.2 $ */
|
|
/* Date: 2011/03/12 23:43:54 $ */
|
|
|
|
/* the jist of squaring...
|
|
* you do like mult except the offset of the tmpx [one that
|
|
* starts closer to zero] can't equal the offset of tmpy.
|
|
* So basically you set up iy like before then you min it with
|
|
* (ty-tx) so that it never happens. You double all those
|
|
* you add in the inner loop
|
|
|
|
After that loop you do the squares and add them in.
|
|
*/
|
|
|
|
static int
|
|
fast_basic_square(mp_int * a, mp_int * b)
|
|
{
|
|
int olduse, res, pa, ix, iz;
|
|
mp_digit W[MP_WARRAY], *tmpx;
|
|
mp_word W1;
|
|
|
|
/* grow the destination as required */
|
|
pa = a->used + a->used;
|
|
if (b->alloc < pa) {
|
|
if ((res = mp_grow(b, pa)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* number of output digits to produce */
|
|
W1 = 0;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
int tx, ty, iy;
|
|
mp_word _W;
|
|
mp_digit *tmpy;
|
|
|
|
/* clear counter */
|
|
_W = 0;
|
|
|
|
/* get offsets into the two bignums */
|
|
ty = MIN(a->used-1, ix);
|
|
tx = ix - ty;
|
|
|
|
/* setup temp aliases */
|
|
tmpx = a->dp + tx;
|
|
tmpy = a->dp + ty;
|
|
|
|
/* this is the number of times the loop will iterrate, essentially
|
|
while (tx++ < a->used && ty-- >= 0) { ... }
|
|
*/
|
|
iy = MIN(a->used-tx, ty+1);
|
|
|
|
/* now for squaring tx can never equal ty
|
|
* we halve the distance since they approach at a rate of 2x
|
|
* and we have to round because odd cases need to be executed
|
|
*/
|
|
iy = MIN(iy, (int)((unsigned)(ty-tx+1)>>1));
|
|
|
|
/* execute loop */
|
|
for (iz = 0; iz < iy; iz++) {
|
|
_W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
|
|
}
|
|
|
|
/* double the inner product and add carry */
|
|
_W = _W + _W + W1;
|
|
|
|
/* even columns have the square term in them */
|
|
if ((ix&1) == 0) {
|
|
_W += ((mp_word)a->dp[(unsigned)ix>>1])*((mp_word)a->dp[(unsigned)ix>>1]);
|
|
}
|
|
|
|
/* store it */
|
|
W[ix] = (mp_digit)(_W & MP_MASK);
|
|
|
|
/* make next carry */
|
|
W1 = _W >> ((mp_word)DIGIT_BIT);
|
|
}
|
|
|
|
/* setup dest */
|
|
olduse = b->used;
|
|
b->used = a->used+a->used;
|
|
|
|
{
|
|
mp_digit *tmpb;
|
|
tmpb = b->dp;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
*tmpb++ = W[ix] & MP_MASK;
|
|
}
|
|
|
|
/* clear unused digits [that existed in the old copy of c] */
|
|
for (; ix < olduse; ix++) {
|
|
*tmpb++ = 0;
|
|
}
|
|
}
|
|
trim_unused_digits(b);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_s_mp_sqr.c,v $ */
|
|
/* Revision: 1.3 $ */
|
|
/* Date: 2011/03/18 16:43:04 $ */
|
|
|
|
/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
|
|
static int
|
|
basic_square(mp_int * a, mp_int * b)
|
|
{
|
|
mp_int t;
|
|
int res, ix, iy, pa;
|
|
mp_word r;
|
|
mp_digit carry, tmpx, *tmpt;
|
|
|
|
pa = a->used;
|
|
if ((res = mp_init_size(&t, 2*pa + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* default used is maximum possible size */
|
|
t.used = 2*pa + 1;
|
|
|
|
for (ix = 0; ix < pa; ix++) {
|
|
/* first calculate the digit at 2*ix */
|
|
/* calculate double precision result */
|
|
r = ((mp_word) t.dp[2*ix]) +
|
|
((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
|
|
|
|
/* store lower part in result */
|
|
t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
|
|
|
|
/* get the carry */
|
|
carry = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
|
|
|
/* left hand side of A[ix] * A[iy] */
|
|
tmpx = a->dp[ix];
|
|
|
|
/* alias for where to store the results */
|
|
tmpt = t.dp + (2*ix + 1);
|
|
|
|
for (iy = ix + 1; iy < pa; iy++) {
|
|
/* first calculate the product */
|
|
r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
|
|
|
|
/* now calculate the double precision result, note we use
|
|
* addition instead of *2 since it's easier to optimize
|
|
*/
|
|
r = ((mp_word) *tmpt) + r + r + ((mp_word) carry);
|
|
|
|
/* store lower part */
|
|
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
|
|
|
/* get carry */
|
|
carry = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
|
}
|
|
/* propagate upwards */
|
|
while (carry != ((mp_digit) 0)) {
|
|
r = ((mp_word) *tmpt) + ((mp_word) carry);
|
|
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
|
carry = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
|
}
|
|
}
|
|
|
|
trim_unused_digits(&t);
|
|
mp_exch(&t, b);
|
|
mp_clear(&t);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_s_mp_sqr.c,v $ */
|
|
/* Revision: 1.1.1.1 $ */
|
|
/* Date: 2011/03/12 22:58:18 $ */
|
|
|
|
#define TOOM_SQR_CUTOFF 400
|
|
#define KARATSUBA_SQR_CUTOFF 120
|
|
|
|
/* computes b = a*a */
|
|
static int
|
|
square(mp_int * a, mp_int * b)
|
|
{
|
|
int res;
|
|
|
|
/* use Toom-Cook? */
|
|
if (a->used >= TOOM_SQR_CUTOFF) {
|
|
res = toom_cook_square(a, b);
|
|
/* Karatsuba? */
|
|
} else if (a->used >= KARATSUBA_SQR_CUTOFF) {
|
|
res = karatsuba_square(a, b);
|
|
} else {
|
|
/* can we use the fast comba multiplier? */
|
|
if (can_use_fast_column_array(a->used + a->used + 1, a->used)) {
|
|
res = fast_basic_square(a, b);
|
|
} else {
|
|
res = basic_square(a, b);
|
|
}
|
|
}
|
|
b->sign = MP_ZPOS;
|
|
return res;
|
|
}
|
|
|
|
/* find window size */
|
|
static inline int
|
|
find_window_size(mp_int *X)
|
|
{
|
|
int x;
|
|
|
|
x = mp_count_bits(X);
|
|
return (x <= 7) ? 2 : (x <= 36) ? 3 : (x <= 140) ? 4 : (x <= 450) ? 5 : (x <= 1303) ? 6 : (x <= 3529) ? 7 : 8;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_sqr.c,v $ */
|
|
/* Revision: 1.3 $ */
|
|
/* Date: 2011/03/18 16:43:04 $ */
|
|
|
|
#define TAB_SIZE 256
|
|
|
|
static int
|
|
basic_exponent_mod(mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
|
|
{
|
|
mp_digit buf;
|
|
mp_int M[TAB_SIZE], res, mu;
|
|
int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
|
int (*redux)(mp_int*,mp_int*,mp_int*);
|
|
|
|
winsize = find_window_size(X);
|
|
|
|
/* init M array */
|
|
/* init first cell */
|
|
if ((err = mp_init(&M[1])) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* now init the second half of the array */
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
if ((err = mp_init(&M[x])) != MP_OKAY) {
|
|
for (y = 1<<(winsize-1); y < x; y++) {
|
|
mp_clear(&M[y]);
|
|
}
|
|
mp_clear(&M[1]);
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* create mu, used for Barrett reduction */
|
|
if ((err = mp_init(&mu)) != MP_OKAY) {
|
|
goto LBL_M;
|
|
}
|
|
|
|
if (redmode == 0) {
|
|
if ((err = mp_reduce_setup(&mu, P)) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
redux = mp_reduce;
|
|
} else {
|
|
if ((err = mp_reduce_2k_setup_l(P, &mu)) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
redux = mp_reduce_2k_l;
|
|
}
|
|
|
|
/* create M table
|
|
*
|
|
* The M table contains powers of the base,
|
|
* e.g. M[x] = G**x mod P
|
|
*
|
|
* The first half of the table is not
|
|
* computed though accept for M[0] and M[1]
|
|
*/
|
|
if ((err = modulo(G, P, &M[1])) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
|
|
/* compute the value at M[1<<(winsize-1)] by squaring
|
|
* M[1] (winsize-1) times
|
|
*/
|
|
if ((err = mp_copy( &M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
|
|
for (x = 0; x < (winsize - 1); x++) {
|
|
/* square it */
|
|
if ((err = square(&M[1 << (winsize - 1)],
|
|
&M[1 << (winsize - 1)])) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
|
|
/* reduce modulo P */
|
|
if ((err = redux(&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
}
|
|
|
|
/* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
|
|
* for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
|
|
*/
|
|
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
|
if ((err = signed_multiply(&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
if ((err = redux(&M[x], P, &mu)) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
}
|
|
|
|
/* setup result */
|
|
if ((err = mp_init(&res)) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
set_word(&res, 1);
|
|
|
|
/* 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 */
|
|
if (digidx == -1) {
|
|
break;
|
|
}
|
|
/* read next digit and reset the bitcnt */
|
|
buf = X->dp[digidx--];
|
|
bitcnt = (int) DIGIT_BIT;
|
|
}
|
|
|
|
/* grab the next msb from the exponent */
|
|
y = (unsigned)(buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
|
|
buf <<= (mp_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 = square(&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux(&res, P, &mu)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
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 multiply */
|
|
/* square first */
|
|
for (x = 0; x < winsize; x++) {
|
|
if ((err = square(&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux(&res, P, &mu)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* then multiply */
|
|
if ((err = signed_multiply(&res, &M[bitbuf], &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux(&res, P, &mu)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
/* 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 = square(&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux(&res, P, &mu)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
bitbuf <<= 1;
|
|
if ((bitbuf & (1 << winsize)) != 0) {
|
|
/* then multiply */
|
|
if ((err = signed_multiply(&res, &M[1], &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux(&res, P, &mu)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
mp_exch(&res, Y);
|
|
err = MP_OKAY;
|
|
LBL_RES:
|
|
mp_clear(&res);
|
|
LBL_MU:
|
|
mp_clear(&mu);
|
|
LBL_M:
|
|
mp_clear(&M[1]);
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
mp_clear(&M[x]);
|
|
}
|
|
return err;
|
|
}
|
|
|
|
/* determines if a number is a valid DR modulus */
|
|
static int
|
|
is_diminished_radix_modulus(mp_int *a)
|
|
{
|
|
int ix;
|
|
|
|
/* must be at least two digits */
|
|
if (a->used < 2) {
|
|
return 0;
|
|
}
|
|
|
|
/* must be of the form b**k - a [a <= b] so all
|
|
* but the first digit must be equal to -1 (mod b).
|
|
*/
|
|
for (ix = 1; ix < a->used; ix++) {
|
|
if (a->dp[ix] != MP_MASK) {
|
|
return 0;
|
|
}
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_dr_is_modulus.c,v $ */
|
|
/* Revision: 1.1.1.1 $ */
|
|
/* Date: 2011/03/12 22:58:18 $ */
|
|
|
|
/* determines if mp_reduce_2k can be used */
|
|
static int
|
|
mp_reduce_is_2k(mp_int *a)
|
|
{
|
|
int ix, iy, iw;
|
|
mp_digit iz;
|
|
|
|
if (a->used == 0) {
|
|
return MP_NO;
|
|
}
|
|
if (a->used == 1) {
|
|
return MP_YES;
|
|
}
|
|
if (a->used > 1) {
|
|
iy = mp_count_bits(a);
|
|
iz = 1;
|
|
iw = 1;
|
|
|
|
/* Test every bit from the second digit up, must be 1 */
|
|
for (ix = DIGIT_BIT; ix < iy; ix++) {
|
|
if ((a->dp[iw] & iz) == 0) {
|
|
return MP_NO;
|
|
}
|
|
iz <<= 1;
|
|
if (iz > (mp_digit)MP_MASK) {
|
|
++iw;
|
|
iz = 1;
|
|
}
|
|
}
|
|
}
|
|
return MP_YES;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_is_2k.c,v $ */
|
|
/* Revision: 1.1.1.1 $ */
|
|
/* Date: 2011/03/12 22:58:18 $ */
|
|
|
|
|
|
/* d = a * b (mod c) */
|
|
static int
|
|
multiply_modulo(mp_int *d, mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
mp_int t;
|
|
int res;
|
|
|
|
if ((res = mp_init(&t)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
if ((res = signed_multiply(a, b, &t)) != MP_OKAY) {
|
|
mp_clear(&t);
|
|
return res;
|
|
}
|
|
res = modulo(&t, c, d);
|
|
mp_clear(&t);
|
|
return res;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_mulmod.c,v $ */
|
|
/* Revision: 1.1.1.1 $ */
|
|
/* Date: 2011/03/12 22:58:18 $ */
|
|
|
|
/* setups the montgomery reduction stuff */
|
|
static int
|
|
mp_montgomery_setup(mp_int * n, mp_digit * rho)
|
|
{
|
|
mp_digit x, b;
|
|
|
|
/* 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
|
|
*/
|
|
b = n->dp[0];
|
|
|
|
if ((b & 1) == 0) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
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 */
|
|
if (/*CONSTCOND*/sizeof(mp_digit) == 8) {
|
|
x *= 2 - b * x; /* here x*a==1 mod 2**64 */
|
|
}
|
|
|
|
/* rho = -1/m mod b */
|
|
*rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_montgomery_setup.c,v $ */
|
|
/* Revision: 1.1.1.1 $ */
|
|
/* Date: 2011/03/12 22:58:18 $ */
|
|
|
|
/* computes xR**-1 == x (mod N) via Montgomery Reduction
|
|
*
|
|
* This is an optimized implementation of montgomery_reduce
|
|
* which uses the comba method to quickly calculate the columns of the
|
|
* reduction.
|
|
*
|
|
* Based on Algorithm 14.32 on pp.601 of HAC.
|
|
*/
|
|
static int
|
|
fast_mp_montgomery_reduce(mp_int * x, mp_int * n, mp_digit rho)
|
|
{
|
|
int ix, res, olduse;
|
|
/*LINTED*/
|
|
mp_word W[MP_WARRAY];
|
|
|
|
/* get old used count */
|
|
olduse = x->used;
|
|
|
|
/* grow a as required */
|
|
if (x->alloc < n->used + 1) {
|
|
if ((res = mp_grow(x, n->used + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* first we have to get the digits of the input into
|
|
* an array of double precision words W[...]
|
|
*/
|
|
{
|
|
mp_word *_W;
|
|
mp_digit *tmpx;
|
|
|
|
/* alias for the W[] array */
|
|
_W = W;
|
|
|
|
/* alias for the digits of x*/
|
|
tmpx = x->dp;
|
|
|
|
/* copy the digits of a into W[0..a->used-1] */
|
|
for (ix = 0; ix < x->used; ix++) {
|
|
*_W++ = *tmpx++;
|
|
}
|
|
|
|
/* zero the high words of W[a->used..m->used*2] */
|
|
for (; ix < n->used * 2 + 1; ix++) {
|
|
*_W++ = 0;
|
|
}
|
|
}
|
|
|
|
/* now we proceed to zero successive digits
|
|
* from the least significant upwards
|
|
*/
|
|
for (ix = 0; ix < n->used; ix++) {
|
|
/* mu = ai * m' mod b
|
|
*
|
|
* We avoid a double precision multiplication (which isn't required)
|
|
* by casting the value down to a mp_digit. Note this requires
|
|
* that W[ix-1] have the carry cleared (see after the inner loop)
|
|
*/
|
|
mp_digit mu;
|
|
mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
|
|
|
|
/* a = a + mu * m * b**i
|
|
*
|
|
* This is computed in place and on the fly. The multiplication
|
|
* by b**i is handled by offseting which columns the results
|
|
* are added to.
|
|
*
|
|
* Note the comba method normally doesn't handle carries in the
|
|
* inner loop In this case we fix the carry from the previous
|
|
* column since the Montgomery reduction requires digits of the
|
|
* result (so far) [see above] to work. This is
|
|
* handled by fixing up one carry after the inner loop. The
|
|
* carry fixups are done in order so after these loops the
|
|
* first m->used words of W[] have the carries fixed
|
|
*/
|
|
{
|
|
int iy;
|
|
mp_digit *tmpn;
|
|
mp_word *_W;
|
|
|
|
/* alias for the digits of the modulus */
|
|
tmpn = n->dp;
|
|
|
|
/* Alias for the columns set by an offset of ix */
|
|
_W = W + ix;
|
|
|
|
/* inner loop */
|
|
for (iy = 0; iy < n->used; iy++) {
|
|
*_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
|
|
}
|
|
}
|
|
|
|
/* now fix carry for next digit, W[ix+1] */
|
|
W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
|
|
}
|
|
|
|
/* now we have to propagate the carries and
|
|
* shift the words downward [all those least
|
|
* significant digits we zeroed].
|
|
*/
|
|
{
|
|
mp_digit *tmpx;
|
|
mp_word *_W, *_W1;
|
|
|
|
/* nox fix rest of carries */
|
|
|
|
/* alias for current word */
|
|
_W1 = W + ix;
|
|
|
|
/* alias for next word, where the carry goes */
|
|
_W = W + ++ix;
|
|
|
|
for (; ix <= n->used * 2 + 1; ix++) {
|
|
*_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
|
|
}
|
|
|
|
/* copy out, A = A/b**n
|
|
*
|
|
* The result is A/b**n but instead of converting from an
|
|
* array of mp_word to mp_digit than calling rshift_digits
|
|
* we just copy them in the right order
|
|
*/
|
|
|
|
/* alias for destination word */
|
|
tmpx = x->dp;
|
|
|
|
/* alias for shifted double precision result */
|
|
_W = W + n->used;
|
|
|
|
for (ix = 0; ix < n->used + 1; ix++) {
|
|
*tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
|
|
}
|
|
|
|
/* zero oldused digits, if the input a was larger than
|
|
* m->used+1 we'll have to clear the digits
|
|
*/
|
|
for (; ix < olduse; ix++) {
|
|
*tmpx++ = 0;
|
|
}
|
|
}
|
|
|
|
/* set the max used and clamp */
|
|
x->used = n->used + 1;
|
|
trim_unused_digits(x);
|
|
|
|
/* if A >= m then A = A - m */
|
|
if (compare_magnitude(x, n) != MP_LT) {
|
|
return basic_subtract(x, n, x);
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_mp_montgomery_reduce.c,v $ */
|
|
/* Revision: 1.2 $ */
|
|
/* Date: 2011/03/18 16:22:09 $ */
|
|
|
|
/* computes xR**-1 == x (mod N) via Montgomery Reduction */
|
|
static int
|
|
mp_montgomery_reduce(mp_int * x, mp_int * n, mp_digit rho)
|
|
{
|
|
int ix, res, digs;
|
|
mp_digit mu;
|
|
|
|
/* can the fast reduction [comba] method be used?
|
|
*
|
|
* Note that unlike in mul you're safely allowed *less*
|
|
* than the available columns [255 per default] since carries
|
|
* are fixed up in the inner loop.
|
|
*/
|
|
digs = n->used * 2 + 1;
|
|
if (can_use_fast_column_array(digs, n->used)) {
|
|
return fast_mp_montgomery_reduce(x, n, rho);
|
|
}
|
|
|
|
/* grow the input as required */
|
|
if (x->alloc < digs) {
|
|
if ((res = mp_grow(x, digs)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
x->used = digs;
|
|
|
|
for (ix = 0; ix < n->used; ix++) {
|
|
/* mu = ai * rho mod b
|
|
*
|
|
* The value of rho must be precalculated via
|
|
* montgomery_setup() such that
|
|
* it equals -1/n0 mod b this allows the
|
|
* following inner loop to reduce the
|
|
* input one digit at a time
|
|
*/
|
|
mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
|
|
|
|
/* a = a + mu * m * b**i */
|
|
{
|
|
int iy;
|
|
mp_digit *tmpn, *tmpx, carry;
|
|
mp_word r;
|
|
|
|
/* alias for digits of the modulus */
|
|
tmpn = n->dp;
|
|
|
|
/* alias for the digits of x [the input] */
|
|
tmpx = x->dp + ix;
|
|
|
|
/* set the carry to zero */
|
|
carry = 0;
|
|
|
|
/* Multiply and add in place */
|
|
for (iy = 0; iy < n->used; iy++) {
|
|
/* compute product and sum */
|
|
r = ((mp_word)mu) * ((mp_word)*tmpn++) +
|
|
((mp_word) carry) + ((mp_word) * tmpx);
|
|
|
|
/* get carry */
|
|
carry = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
|
|
|
/* fix digit */
|
|
*tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
|
|
}
|
|
/* At this point the ix'th digit of x should be zero */
|
|
|
|
|
|
/* propagate carries upwards as required*/
|
|
while (carry) {
|
|
*tmpx += carry;
|
|
carry = *tmpx >> DIGIT_BIT;
|
|
*tmpx++ &= MP_MASK;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* at this point the n.used'th least
|
|
* significant digits of x are all zero
|
|
* which means we can shift x to the
|
|
* right by n.used digits and the
|
|
* residue is unchanged.
|
|
*/
|
|
|
|
/* x = x/b**n.used */
|
|
trim_unused_digits(x);
|
|
rshift_digits(x, n->used);
|
|
|
|
/* if x >= n then x = x - n */
|
|
if (compare_magnitude(x, n) != MP_LT) {
|
|
return basic_subtract(x, n, x);
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_montgomery_reduce.c,v $ */
|
|
/* Revision: 1.3 $ */
|
|
/* Date: 2011/03/18 16:43:04 $ */
|
|
|
|
/* determines the setup value */
|
|
static void
|
|
diminished_radix_setup(mp_int *a, mp_digit *d)
|
|
{
|
|
/* the casts are required if DIGIT_BIT is one less than
|
|
* the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
|
|
*/
|
|
*d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
|
|
((mp_word)a->dp[0]));
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_dr_setup.c,v $ */
|
|
/* Revision: 1.1.1.1 $ */
|
|
/* Date: 2011/03/12 22:58:18 $ */
|
|
|
|
/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
|
|
*
|
|
* Based on algorithm from the paper
|
|
*
|
|
* "Generating Efficient Primes for Discrete Log Cryptosystems"
|
|
* Chae Hoon Lim, Pil Joong Lee,
|
|
* POSTECH Information Research Laboratories
|
|
*
|
|
* The modulus must be of a special format [see manual]
|
|
*
|
|
* Has been modified to use algorithm 7.10 from the LTM book instead
|
|
*
|
|
* Input x must be in the range 0 <= x <= (n-1)**2
|
|
*/
|
|
static int
|
|
diminished_radix_reduce(mp_int * x, mp_int * n, mp_digit k)
|
|
{
|
|
int err, i, m;
|
|
mp_word r;
|
|
mp_digit mu, *tmpx1, *tmpx2;
|
|
|
|
/* m = digits in modulus */
|
|
m = n->used;
|
|
|
|
/* ensure that "x" has at least 2m digits */
|
|
if (x->alloc < m + m) {
|
|
if ((err = mp_grow(x, m + m)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* top of loop, this is where the code resumes if
|
|
* another reduction pass is required.
|
|
*/
|
|
top:
|
|
/* aliases for digits */
|
|
/* alias for lower half of x */
|
|
tmpx1 = x->dp;
|
|
|
|
/* alias for upper half of x, or x/B**m */
|
|
tmpx2 = x->dp + m;
|
|
|
|
/* set carry to zero */
|
|
mu = 0;
|
|
|
|
/* compute (x mod B**m) + k * [x/B**m] inline and inplace */
|
|
for (i = 0; i < m; i++) {
|
|
r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
|
|
*tmpx1++ = (mp_digit)(r & MP_MASK);
|
|
mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
|
|
}
|
|
|
|
/* set final carry */
|
|
*tmpx1++ = mu;
|
|
|
|
/* zero words above m */
|
|
for (i = m + 1; i < x->used; i++) {
|
|
*tmpx1++ = 0;
|
|
}
|
|
|
|
/* clamp, sub and return */
|
|
trim_unused_digits(x);
|
|
|
|
/* if x >= n then subtract and reduce again
|
|
* Each successive "recursion" makes the input smaller and smaller.
|
|
*/
|
|
if (compare_magnitude(x, n) != MP_LT) {
|
|
basic_subtract(x, n, x);
|
|
goto top;
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_dr_reduce.c,v $ */
|
|
/* Revision: 1.1.1.1 $ */
|
|
/* Date: 2011/03/12 22:58:18 $ */
|
|
|
|
/* determines the setup value */
|
|
static int
|
|
mp_reduce_2k_setup(mp_int *a, mp_digit *d)
|
|
{
|
|
int res, p;
|
|
mp_int tmp;
|
|
|
|
if ((res = mp_init(&tmp)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
p = mp_count_bits(a);
|
|
if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
|
|
mp_clear(&tmp);
|
|
return res;
|
|
}
|
|
|
|
if ((res = basic_subtract(&tmp, a, &tmp)) != MP_OKAY) {
|
|
mp_clear(&tmp);
|
|
return res;
|
|
}
|
|
|
|
*d = tmp.dp[0];
|
|
mp_clear(&tmp);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_2k_setup.c,v $ */
|
|
/* Revision: 1.1.1.1 $ */
|
|
/* Date: 2011/03/12 22:58:18 $ */
|
|
|
|
/* reduces a modulo n where n is of the form 2**p - d */
|
|
static int
|
|
mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
|
|
{
|
|
mp_int q;
|
|
int p, res;
|
|
|
|
if ((res = mp_init(&q)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
p = mp_count_bits(n);
|
|
top:
|
|
/* q = a/2**p, a = a mod 2**p */
|
|
if ((res = rshift_bits(a, p, &q, a)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if (d != 1) {
|
|
/* q = q * d */
|
|
if ((res = multiply_digit(&q, d, &q)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
}
|
|
|
|
/* a = a + q */
|
|
if ((res = basic_add(a, &q, a)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if (compare_magnitude(a, n) != MP_LT) {
|
|
basic_subtract(a, n, a);
|
|
goto top;
|
|
}
|
|
|
|
ERR:
|
|
mp_clear(&q);
|
|
return res;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_2k.c,v $ */
|
|
/* Revision: 1.1.1.1 $ */
|
|
/* Date: 2011/03/12 22:58:18 $ */
|
|
|
|
/*
|
|
* shifts with subtractions when the result is greater than b.
|
|
*
|
|
* The method is slightly modified to shift B unconditionally upto just under
|
|
* the leading bit of b. This saves alot of multiple precision shifting.
|
|
*/
|
|
static int
|
|
mp_montgomery_calc_normalization(mp_int * a, mp_int * b)
|
|
{
|
|
int x, bits, res;
|
|
|
|
/* how many bits of last digit does b use */
|
|
bits = mp_count_bits(b) % DIGIT_BIT;
|
|
|
|
if (b->used > 1) {
|
|
if ((res = mp_2expt(a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
} else {
|
|
set_word(a, 1);
|
|
bits = 1;
|
|
}
|
|
|
|
|
|
/* now compute C = A * B mod b */
|
|
for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
|
|
if ((res = doubled(a, a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
if (compare_magnitude(a, b) != MP_LT) {
|
|
if ((res = basic_subtract(a, b, a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_montgomery_calc_normalization.c,v $ */
|
|
/* Revision: 1.1.1.1 $ */
|
|
/* Date: 2011/03/12 22:58:18 $ */
|
|
|
|
/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
|
|
*
|
|
* Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
|
|
* The value of k changes based on the size of the exponent.
|
|
*
|
|
* Uses Montgomery or Diminished Radix reduction [whichever appropriate]
|
|
*/
|
|
|
|
#define TAB_SIZE 256
|
|
|
|
static int
|
|
fast_exponent_modulo(mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
|
|
{
|
|
mp_int M[TAB_SIZE], res;
|
|
mp_digit buf, mp;
|
|
int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
|
|
|
/* use a pointer to the reduction algorithm. This allows us to use
|
|
* one of many reduction algorithms without modding the guts of
|
|
* the code with if statements everywhere.
|
|
*/
|
|
int (*redux)(mp_int*,mp_int*,mp_digit);
|
|
|
|
winsize = find_window_size(X);
|
|
|
|
/* init M array */
|
|
/* init first cell */
|
|
if ((err = mp_init(&M[1])) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* now init the second half of the array */
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
if ((err = mp_init(&M[x])) != MP_OKAY) {
|
|
for (y = 1<<(winsize-1); y < x; y++) {
|
|
mp_clear(&M[y]);
|
|
}
|
|
mp_clear(&M[1]);
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* determine and setup reduction code */
|
|
if (redmode == 0) {
|
|
/* now setup montgomery */
|
|
if ((err = mp_montgomery_setup(P, &mp)) != MP_OKAY) {
|
|
goto LBL_M;
|
|
}
|
|
|
|
/* automatically pick the comba one if available (saves quite a few calls/ifs) */
|
|
if (can_use_fast_column_array(P->used + P->used + 1, P->used)) {
|
|
redux = fast_mp_montgomery_reduce;
|
|
} else {
|
|
/* use slower baseline Montgomery method */
|
|
redux = mp_montgomery_reduce;
|
|
}
|
|
} else if (redmode == 1) {
|
|
/* setup DR reduction for moduli of the form B**k - b */
|
|
diminished_radix_setup(P, &mp);
|
|
redux = diminished_radix_reduce;
|
|
} else {
|
|
/* setup DR reduction for moduli of the form 2**k - b */
|
|
if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
|
|
goto LBL_M;
|
|
}
|
|
redux = mp_reduce_2k;
|
|
}
|
|
|
|
/* setup result */
|
|
if ((err = mp_init(&res)) != MP_OKAY) {
|
|
goto LBL_M;
|
|
}
|
|
|
|
/* create M table
|
|
*
|
|
|
|
*
|
|
* The first half of the table is not computed though accept for M[0] and M[1]
|
|
*/
|
|
|
|
if (redmode == 0) {
|
|
/* now we need R mod m */
|
|
if ((err = mp_montgomery_calc_normalization(&res, P)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
/* now set M[1] to G * R mod m */
|
|
if ((err = multiply_modulo(&M[1], G, &res, P)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
} else {
|
|
set_word(&res, 1);
|
|
if ((err = modulo(G, P, &M[1])) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
|
|
if ((err = mp_copy( &M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
for (x = 0; x < (winsize - 1); x++) {
|
|
if ((err = square(&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = (*redux)(&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* create upper table */
|
|
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
|
if ((err = signed_multiply(&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = (*redux)(&M[x], P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* 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 = (int)DIGIT_BIT;
|
|
}
|
|
|
|
/* grab the next msb from the exponent */
|
|
y = (int)(mp_digit)((mp_digit)buf >> (unsigned)(DIGIT_BIT - 1)) & 1;
|
|
buf <<= (mp_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 = square(&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = (*redux)(&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
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 multiply */
|
|
/* square first */
|
|
for (x = 0; x < winsize; x++) {
|
|
if ((err = square(&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = (*redux)(&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* then multiply */
|
|
if ((err = signed_multiply(&res, &M[bitbuf], &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = (*redux)(&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
/* 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 = square(&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = (*redux)(&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
/* get next bit of the window */
|
|
bitbuf <<= 1;
|
|
if ((bitbuf & (1 << winsize)) != 0) {
|
|
/* then multiply */
|
|
if ((err = signed_multiply(&res, &M[1], &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = (*redux)(&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
if (redmode == 0) {
|
|
/* fixup 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 = (*redux)(&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* swap res with Y */
|
|
mp_exch(&res, Y);
|
|
err = MP_OKAY;
|
|
LBL_RES:
|
|
mp_clear(&res);
|
|
LBL_M:
|
|
mp_clear(&M[1]);
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
mp_clear(&M[x]);
|
|
}
|
|
return err;
|
|
}
|
|
|
|
/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_exponent_modulo.c,v $ */
|
|
/* Revision: 1.4 $ */
|
|
/* Date: 2011/03/18 16:43:04 $ */
|
|
|
|
/* this is a shell function that calls either the normal or Montgomery
|
|
* exptmod functions. Originally the call to the montgomery code was
|
|
* embedded in the normal function but that wasted alot of stack space
|
|
* for nothing (since 99% of the time the Montgomery code would be called)
|
|
*/
|
|
static int
|
|
exponent_modulo(mp_int * G, mp_int * X, mp_int * P, mp_int *Y)
|
|
{
|
|
int diminished_radix;
|
|
|
|
/* modulus P must be positive */
|
|
if (P->sign == MP_NEG) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* if exponent X is negative we have to recurse */
|
|
if (X->sign == MP_NEG) {
|
|
mp_int tmpG, tmpX;
|
|
int err;
|
|
|
|
/* first compute 1/G mod P */
|
|
if ((err = mp_init(&tmpG)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if ((err = modular_inverse(&tmpG, G, P)) != MP_OKAY) {
|
|
mp_clear(&tmpG);
|
|
return err;
|
|
}
|
|
|
|
/* now get |X| */
|
|
if ((err = mp_init(&tmpX)) != MP_OKAY) {
|
|
mp_clear(&tmpG);
|
|
return err;
|
|
}
|
|
if ((err = absolute(X, &tmpX)) != MP_OKAY) {
|
|
mp_clear_multi(&tmpG, &tmpX, NULL);
|
|
return err;
|
|
}
|
|
|
|
/* and now compute (1/G)**|X| instead of G**X [X < 0] */
|
|
err = exponent_modulo(&tmpG, &tmpX, P, Y);
|
|
mp_clear_multi(&tmpG, &tmpX, NULL);
|
|
return err;
|
|
}
|
|
|
|
/* modified diminished radix reduction */
|
|
if (mp_reduce_is_2k_l(P) == MP_YES) {
|
|
return basic_exponent_mod(G, X, P, Y, 1);
|
|
}
|
|
|
|
/* is it a DR modulus? */
|
|
diminished_radix = is_diminished_radix_modulus(P);
|
|
|
|
/* if not, is it a unrestricted DR modulus? */
|
|
if (!diminished_radix) {
|
|
diminished_radix = mp_reduce_is_2k(P) << 1;
|
|
}
|
|
|
|
/* if the modulus is odd or diminished_radix, use the montgomery method */
|
|
if (BN_is_odd(P) == 1 || diminished_radix) {
|
|
return fast_exponent_modulo(G, X, P, Y, diminished_radix);
|
|
}
|
|
/* otherwise use the generic Barrett reduction technique */
|
|
return basic_exponent_mod(G, X, P, Y, 0);
|
|
}
|
|
|
|
/* reverse an array, used for radix code */
|
|
static void
|
|
bn_reverse(unsigned char *s, int len)
|
|
{
|
|
int ix, iy;
|
|
uint8_t t;
|
|
|
|
for (ix = 0, iy = len - 1; ix < iy ; ix++, --iy) {
|
|
t = s[ix];
|
|
s[ix] = s[iy];
|
|
s[iy] = t;
|
|
}
|
|
}
|
|
|
|
static inline int
|
|
is_power_of_two(mp_digit b, int *p)
|
|
{
|
|
int x;
|
|
|
|
/* fast return if no power of two */
|
|
if ((b==0) || (b & (b-1))) {
|
|
return 0;
|
|
}
|
|
|
|
for (x = 0; x < DIGIT_BIT; x++) {
|
|
if (b == (((mp_digit)1)<<x)) {
|
|
*p = x;
|
|
return 1;
|
|
}
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
/* single digit division (based on routine from MPI) */
|
|
static int
|
|
signed_divide_word(mp_int *a, mp_digit b, mp_int *c, mp_digit *d)
|
|
{
|
|
mp_int q;
|
|
mp_word w;
|
|
mp_digit t;
|
|
int res, ix;
|
|
|
|
/* cannot divide by zero */
|
|
if (b == 0) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* quick outs */
|
|
if (b == 1 || MP_ISZERO(a) == 1) {
|
|
if (d != NULL) {
|
|
*d = 0;
|
|
}
|
|
if (c != NULL) {
|
|
return mp_copy(a, c);
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* power of two ? */
|
|
if (is_power_of_two(b, &ix) == 1) {
|
|
if (d != NULL) {
|
|
*d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
|
|
}
|
|
if (c != NULL) {
|
|
return rshift_bits(a, ix, c, NULL);
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* three? */
|
|
if (b == 3) {
|
|
return third(a, c, d);
|
|
}
|
|
|
|
/* no easy answer [c'est la vie]. Just division */
|
|
if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
q.used = a->used;
|
|
q.sign = a->sign;
|
|
w = 0;
|
|
for (ix = a->used - 1; ix >= 0; ix--) {
|
|
w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
|
|
|
|
if (w >= b) {
|
|
t = (mp_digit)(w / b);
|
|
w -= ((mp_word)t) * ((mp_word)b);
|
|
} else {
|
|
t = 0;
|
|
}
|
|
q.dp[ix] = (mp_digit)t;
|
|
}
|
|
|
|
if (d != NULL) {
|
|
*d = (mp_digit)w;
|
|
}
|
|
|
|
if (c != NULL) {
|
|
trim_unused_digits(&q);
|
|
mp_exch(&q, c);
|
|
}
|
|
mp_clear(&q);
|
|
|
|
return res;
|
|
}
|
|
|
|
static const mp_digit ltm_prime_tab[] = {
|
|
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,
|
|
#ifndef MP_8BIT
|
|
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
|
|
#endif
|
|
};
|
|
|
|
#define PRIME_SIZE __arraycount(ltm_prime_tab)
|
|
|
|
static inline int
|
|
mp_prime_is_divisible(mp_int *a, int *result)
|
|
{
|
|
int err, ix;
|
|
mp_digit res;
|
|
|
|
/* default to not */
|
|
*result = MP_NO;
|
|
|
|
for (ix = 0; ix < (int)PRIME_SIZE; ix++) {
|
|
/* what is a mod LBL_prime_tab[ix] */
|
|
if ((err = signed_divide_word(a, ltm_prime_tab[ix], NULL, &res)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* is the residue zero? */
|
|
if (res == 0) {
|
|
*result = MP_YES;
|
|
return MP_OKAY;
|
|
}
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* single digit addition */
|
|
static int
|
|
add_single_digit(mp_int *a, mp_digit b, mp_int *c)
|
|
{
|
|
int res, ix, oldused;
|
|
mp_digit *tmpa, *tmpc, mu;
|
|
|
|
/* grow c as required */
|
|
if (c->alloc < a->used + 1) {
|
|
if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* if a is negative and |a| >= b, call c = |a| - b */
|
|
if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
|
|
/* temporarily fix sign of a */
|
|
a->sign = MP_ZPOS;
|
|
|
|
/* c = |a| - b */
|
|
res = signed_subtract_word(a, b, c);
|
|
|
|
/* fix sign */
|
|
a->sign = c->sign = MP_NEG;
|
|
|
|
/* clamp */
|
|
trim_unused_digits(c);
|
|
|
|
return res;
|
|
}
|
|
|
|
/* old number of used digits in c */
|
|
oldused = c->used;
|
|
|
|
/* sign always positive */
|
|
c->sign = MP_ZPOS;
|
|
|
|
/* source alias */
|
|
tmpa = a->dp;
|
|
|
|
/* destination alias */
|
|
tmpc = c->dp;
|
|
|
|
/* if a is positive */
|
|
if (a->sign == MP_ZPOS) {
|
|
/* add digit, after this we're propagating
|
|
* the carry.
|
|
*/
|
|
*tmpc = *tmpa++ + b;
|
|
mu = *tmpc >> DIGIT_BIT;
|
|
*tmpc++ &= MP_MASK;
|
|
|
|
/* now handle rest of the digits */
|
|
for (ix = 1; ix < a->used; ix++) {
|
|
*tmpc = *tmpa++ + mu;
|
|
mu = *tmpc >> DIGIT_BIT;
|
|
*tmpc++ &= MP_MASK;
|
|
}
|
|
/* set final carry */
|
|
ix++;
|
|
*tmpc++ = mu;
|
|
|
|
/* setup size */
|
|
c->used = a->used + 1;
|
|
} else {
|
|
/* a was negative and |a| < b */
|
|
c->used = 1;
|
|
|
|
/* the result is a single digit */
|
|
if (a->used == 1) {
|
|
*tmpc++ = b - a->dp[0];
|
|
} else {
|
|
*tmpc++ = b;
|
|
}
|
|
|
|
/* setup count so the clearing of oldused
|
|
* can fall through correctly
|
|
*/
|
|
ix = 1;
|
|
}
|
|
|
|
/* now zero to oldused */
|
|
while (ix++ < oldused) {
|
|
*tmpc++ = 0;
|
|
}
|
|
trim_unused_digits(c);
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* single digit subtraction */
|
|
static int
|
|
signed_subtract_word(mp_int *a, mp_digit b, mp_int *c)
|
|
{
|
|
mp_digit *tmpa, *tmpc, mu;
|
|
int res, ix, oldused;
|
|
|
|
/* grow c as required */
|
|
if (c->alloc < a->used + 1) {
|
|
if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* if a is negative just do an unsigned
|
|
* addition [with fudged signs]
|
|
*/
|
|
if (a->sign == MP_NEG) {
|
|
a->sign = MP_ZPOS;
|
|
res = add_single_digit(a, b, c);
|
|
a->sign = c->sign = MP_NEG;
|
|
|
|
/* clamp */
|
|
trim_unused_digits(c);
|
|
|
|
return res;
|
|
}
|
|
|
|
/* setup regs */
|
|
oldused = c->used;
|
|
tmpa = a->dp;
|
|
tmpc = c->dp;
|
|
|
|
/* if a <= b simply fix the single digit */
|
|
if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) {
|
|
if (a->used == 1) {
|
|
*tmpc++ = b - *tmpa;
|
|
} else {
|
|
*tmpc++ = b;
|
|
}
|
|
ix = 1;
|
|
|
|
/* negative/1digit */
|
|
c->sign = MP_NEG;
|
|
c->used = 1;
|
|
} else {
|
|
/* positive/size */
|
|
c->sign = MP_ZPOS;
|
|
c->used = a->used;
|
|
|
|
/* subtract first digit */
|
|
*tmpc = *tmpa++ - b;
|
|
mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
|
|
*tmpc++ &= MP_MASK;
|
|
|
|
/* handle rest of the digits */
|
|
for (ix = 1; ix < a->used; ix++) {
|
|
*tmpc = *tmpa++ - mu;
|
|
mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
|
|
*tmpc++ &= MP_MASK;
|
|
}
|
|
}
|
|
|
|
/* zero excess digits */
|
|
while (ix++ < oldused) {
|
|
*tmpc++ = 0;
|
|
}
|
|
trim_unused_digits(c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
static const int lnz[16] = {
|
|
4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
|
|
};
|
|
|
|
/* Counts the number of lsbs which are zero before the first zero bit */
|
|
static int
|
|
mp_cnt_lsb(mp_int *a)
|
|
{
|
|
int x;
|
|
mp_digit q, qq;
|
|
|
|
/* easy out */
|
|
if (MP_ISZERO(a) == 1) {
|
|
return 0;
|
|
}
|
|
|
|
/* scan lower digits until non-zero */
|
|
for (x = 0; x < a->used && a->dp[x] == 0; x++) {
|
|
}
|
|
q = a->dp[x];
|
|
x *= DIGIT_BIT;
|
|
|
|
/* now scan this digit until a 1 is found */
|
|
if ((q & 1) == 0) {
|
|
do {
|
|
qq = q & 15;
|
|
/* LINTED previous op ensures range of qq */
|
|
x += lnz[qq];
|
|
q >>= 4;
|
|
} while (qq == 0);
|
|
}
|
|
return x;
|
|
}
|
|
|
|
/* c = a * a (mod b) */
|
|
static int
|
|
square_modulo(mp_int *a, mp_int *b, mp_int *c)
|
|
{
|
|
int res;
|
|
mp_int t;
|
|
|
|
if ((res = mp_init(&t)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
if ((res = square(a, &t)) != MP_OKAY) {
|
|
mp_clear(&t);
|
|
return res;
|
|
}
|
|
res = modulo(&t, b, c);
|
|
mp_clear(&t);
|
|
return res;
|
|
}
|
|
|
|
static int
|
|
mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result)
|
|
{
|
|
mp_int n1, y, r;
|
|
int s, j, err;
|
|
|
|
/* default */
|
|
*result = MP_NO;
|
|
|
|
/* ensure b > 1 */
|
|
if (compare_digit(b, 1) != MP_GT) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* get n1 = a - 1 */
|
|
if ((err = mp_init_copy(&n1, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if ((err = signed_subtract_word(&n1, 1, &n1)) != MP_OKAY) {
|
|
goto LBL_N1;
|
|
}
|
|
|
|
/* set 2**s * r = n1 */
|
|
if ((err = mp_init_copy(&r, &n1)) != MP_OKAY) {
|
|
goto LBL_N1;
|
|
}
|
|
|
|
/* count the number of least significant bits
|
|
* which are zero
|
|
*/
|
|
s = mp_cnt_lsb(&r);
|
|
|
|
/* now divide n - 1 by 2**s */
|
|
if ((err = rshift_bits(&r, s, &r, NULL)) != MP_OKAY) {
|
|
goto LBL_R;
|
|
}
|
|
|
|
/* compute y = b**r mod a */
|
|
if ((err = mp_init(&y)) != MP_OKAY) {
|
|
goto LBL_R;
|
|
}
|
|
if ((err = exponent_modulo(b, &r, a, &y)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
|
|
/* if y != 1 and y != n1 do */
|
|
if (compare_digit(&y, 1) != MP_EQ && signed_compare(&y, &n1) != MP_EQ) {
|
|
j = 1;
|
|
/* while j <= s-1 and y != n1 */
|
|
while ((j <= (s - 1)) && signed_compare(&y, &n1) != MP_EQ) {
|
|
if ((err = square_modulo(&y, a, &y)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
|
|
/* if y == 1 then composite */
|
|
if (compare_digit(&y, 1) == MP_EQ) {
|
|
goto LBL_Y;
|
|
}
|
|
|
|
++j;
|
|
}
|
|
|
|
/* if y != n1 then composite */
|
|
if (signed_compare(&y, &n1) != MP_EQ) {
|
|
goto LBL_Y;
|
|
}
|
|
}
|
|
|
|
/* probably prime now */
|
|
*result = MP_YES;
|
|
LBL_Y:
|
|
mp_clear(&y);
|
|
LBL_R:
|
|
mp_clear(&r);
|
|
LBL_N1:
|
|
mp_clear(&n1);
|
|
return err;
|
|
}
|
|
|
|
/* performs a variable number of rounds of Miller-Rabin
|
|
*
|
|
* Probability of error after t rounds is no more than
|
|
|
|
*
|
|
* Sets result to 1 if probably prime, 0 otherwise
|
|
*/
|
|
static int
|
|
mp_prime_is_prime(mp_int *a, int t, int *result)
|
|
{
|
|
mp_int b;
|
|
int ix, err, res;
|
|
|
|
/* default to no */
|
|
*result = MP_NO;
|
|
|
|
/* valid value of t? */
|
|
if (t <= 0 || t > (int)PRIME_SIZE) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* is the input equal to one of the primes in the table? */
|
|
for (ix = 0; ix < (int)PRIME_SIZE; ix++) {
|
|
if (compare_digit(a, ltm_prime_tab[ix]) == MP_EQ) {
|
|
*result = 1;
|
|
return MP_OKAY;
|
|
}
|
|
}
|
|
|
|
/* first perform trial division */
|
|
if ((err = mp_prime_is_divisible(a, &res)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* return if it was trivially divisible */
|
|
if (res == MP_YES) {
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* now perform the miller-rabin rounds */
|
|
if ((err = mp_init(&b)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
for (ix = 0; ix < t; ix++) {
|
|
/* set the prime */
|
|
set_word(&b, ltm_prime_tab[ix]);
|
|
|
|
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
|
|
goto LBL_B;
|
|
}
|
|
|
|
if (res == MP_NO) {
|
|
goto LBL_B;
|
|
}
|
|
}
|
|
|
|
/* passed the test */
|
|
*result = MP_YES;
|
|
LBL_B:
|
|
mp_clear(&b);
|
|
return err;
|
|
}
|
|
|
|
/* returns size of ASCII reprensentation */
|
|
static int
|
|
mp_radix_size(mp_int *a, int radix, int *size)
|
|
{
|
|
int res, digs;
|
|
mp_int t;
|
|
mp_digit d;
|
|
|
|
*size = 0;
|
|
|
|
/* special case for binary */
|
|
if (radix == 2) {
|
|
*size = mp_count_bits(a) + (a->sign == MP_NEG ? 1 : 0) + 1;
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* make sure the radix is in range */
|
|
if (radix < 2 || radix > 64) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
if (MP_ISZERO(a) == MP_YES) {
|
|
*size = 2;
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* digs is the digit count */
|
|
digs = 0;
|
|
|
|
/* if it's negative add one for the sign */
|
|
if (a->sign == MP_NEG) {
|
|
++digs;
|
|
}
|
|
|
|
/* init a copy of the input */
|
|
if ((res = mp_init_copy(&t, a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* force temp to positive */
|
|
t.sign = MP_ZPOS;
|
|
|
|
/* fetch out all of the digits */
|
|
while (MP_ISZERO(&t) == MP_NO) {
|
|
if ((res = signed_divide_word(&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
|
|
mp_clear(&t);
|
|
return res;
|
|
}
|
|
++digs;
|
|
}
|
|
mp_clear(&t);
|
|
|
|
/* return digs + 1, the 1 is for the NULL byte that would be required. */
|
|
*size = digs + 1;
|
|
return MP_OKAY;
|
|
}
|
|
|
|
static const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
|
|
|
|
/* stores a bignum as a ASCII string in a given radix (2..64)
|
|
*
|
|
* Stores upto maxlen-1 chars and always a NULL byte
|
|
*/
|
|
static int
|
|
mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
|
|
{
|
|
int res, digs;
|
|
mp_int t;
|
|
mp_digit d;
|
|
char *_s = str;
|
|
|
|
/* check range of the maxlen, radix */
|
|
if (maxlen < 2 || radix < 2 || radix > 64) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* quick out if its zero */
|
|
if (MP_ISZERO(a) == MP_YES) {
|
|
*str++ = '0';
|
|
*str = '\0';
|
|
return MP_OKAY;
|
|
}
|
|
|
|
if ((res = mp_init_copy(&t, a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* if it is negative output a - */
|
|
if (t.sign == MP_NEG) {
|
|
/* we have to reverse our digits later... but not the - sign!! */
|
|
++_s;
|
|
|
|
/* store the flag and mark the number as positive */
|
|
*str++ = '-';
|
|
t.sign = MP_ZPOS;
|
|
|
|
/* subtract a char */
|
|
--maxlen;
|
|
}
|
|
|
|
digs = 0;
|
|
while (MP_ISZERO(&t) == 0) {
|
|
if (--maxlen < 1) {
|
|
/* no more room */
|
|
break;
|
|
}
|
|
if ((res = signed_divide_word(&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
|
|
mp_clear(&t);
|
|
return res;
|
|
}
|
|
/* LINTED -- radix' range is checked above, limits d's range */
|
|
*str++ = mp_s_rmap[d];
|
|
++digs;
|
|
}
|
|
|
|
/* reverse the digits of the string. In this case _s points
|
|
* to the first digit [exluding the sign] of the number
|
|
*/
|
|
bn_reverse((unsigned char *)_s, digs);
|
|
|
|
/* append a NULL so the string is properly terminated */
|
|
*str = '\0';
|
|
|
|
mp_clear(&t);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
static char *
|
|
formatbn(const BIGNUM *a, const int radix)
|
|
{
|
|
char *s;
|
|
int len;
|
|
|
|
if (mp_radix_size(__UNCONST(a), radix, &len) != MP_OKAY) {
|
|
return NULL;
|
|
}
|
|
if ((s = allocate(1, (size_t)len)) != NULL) {
|
|
if (mp_toradix_n(__UNCONST(a), s, radix, len) != MP_OKAY) {
|
|
deallocate(s, (size_t)len);
|
|
return NULL;
|
|
}
|
|
}
|
|
return s;
|
|
}
|
|
|
|
static int
|
|
mp_getradix_num(mp_int *a, int radix, char *s)
|
|
{
|
|
int err, ch, neg, y;
|
|
|
|
/* clear a */
|
|
mp_zero(a);
|
|
|
|
/* if first digit is - then set negative */
|
|
if ((ch = *s++) == '-') {
|
|
neg = MP_NEG;
|
|
ch = *s++;
|
|
} else {
|
|
neg = MP_ZPOS;
|
|
}
|
|
|
|
for (;;) {
|
|
/* find y in the radix map */
|
|
for (y = 0; y < radix; y++) {
|
|
if (mp_s_rmap[y] == ch) {
|
|
break;
|
|
}
|
|
}
|
|
if (y == radix) {
|
|
break;
|
|
}
|
|
|
|
/* shift up and add */
|
|
if ((err = multiply_digit(a, radix, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if ((err = add_single_digit(a, y, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
ch = *s++;
|
|
}
|
|
if (compare_digit(a, 0) != MP_EQ) {
|
|
a->sign = neg;
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
static int
|
|
getbn(BIGNUM **a, const char *str, int radix)
|
|
{
|
|
int len;
|
|
|
|
if (a == NULL || str == NULL || (*a = BN_new()) == NULL) {
|
|
return 0;
|
|
}
|
|
if (mp_getradix_num(*a, radix, __UNCONST(str)) != MP_OKAY) {
|
|
return 0;
|
|
}
|
|
mp_radix_size(__UNCONST(*a), radix, &len);
|
|
return len - 1;
|
|
}
|
|
|
|
/* d = a - b (mod c) */
|
|
static int
|
|
subtract_modulo(mp_int *a, mp_int *b, mp_int *c, mp_int *d)
|
|
{
|
|
int res;
|
|
mp_int t;
|
|
|
|
|
|
if ((res = mp_init(&t)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
if ((res = signed_subtract(a, b, &t)) != MP_OKAY) {
|
|
mp_clear(&t);
|
|
return res;
|
|
}
|
|
res = modulo(&t, c, d);
|
|
mp_clear(&t);
|
|
return res;
|
|
}
|
|
|
|
/* bn_mp_gcd.c */
|
|
/* Greatest Common Divisor using the binary method */
|
|
static int
|
|
mp_gcd(mp_int *a, mp_int *b, mp_int *c)
|
|
{
|
|
mp_int u, v;
|
|
int k, u_lsb, v_lsb, res;
|
|
|
|
/* either zero than gcd is the largest */
|
|
if (BN_is_zero(a) == MP_YES) {
|
|
return absolute(b, c);
|
|
}
|
|
if (BN_is_zero(b) == MP_YES) {
|
|
return absolute(a, c);
|
|
}
|
|
|
|
/* get copies of a and b we can modify */
|
|
if ((res = mp_init_copy(&u, a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
if ((res = mp_init_copy(&v, b)) != MP_OKAY) {
|
|
goto LBL_U;
|
|
}
|
|
|
|
/* must be positive for the remainder of the algorithm */
|
|
u.sign = v.sign = MP_ZPOS;
|
|
|
|
/* B1. Find the common power of two for u and v */
|
|
u_lsb = mp_cnt_lsb(&u);
|
|
v_lsb = mp_cnt_lsb(&v);
|
|
k = MIN(u_lsb, v_lsb);
|
|
|
|
if (k > 0) {
|
|
/* divide the power of two out */
|
|
if ((res = rshift_bits(&u, k, &u, NULL)) != MP_OKAY) {
|
|
goto LBL_V;
|
|
}
|
|
|
|
if ((res = rshift_bits(&v, k, &v, NULL)) != MP_OKAY) {
|
|
goto LBL_V;
|
|
}
|
|
}
|
|
|
|
/* divide any remaining factors of two out */
|
|
if (u_lsb != k) {
|
|
if ((res = rshift_bits(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
|
|
goto LBL_V;
|
|
}
|
|
}
|
|
|
|
if (v_lsb != k) {
|
|
if ((res = rshift_bits(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
|
|
goto LBL_V;
|
|
}
|
|
}
|
|
|
|
while (BN_is_zero(&v) == 0) {
|
|
/* make sure v is the largest */
|
|
if (compare_magnitude(&u, &v) == MP_GT) {
|
|
/* swap u and v to make sure v is >= u */
|
|
mp_exch(&u, &v);
|
|
}
|
|
|
|
/* subtract smallest from largest */
|
|
if ((res = signed_subtract(&v, &u, &v)) != MP_OKAY) {
|
|
goto LBL_V;
|
|
}
|
|
|
|
/* Divide out all factors of two */
|
|
if ((res = rshift_bits(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
|
|
goto LBL_V;
|
|
}
|
|
}
|
|
|
|
/* multiply by 2**k which we divided out at the beginning */
|
|
if ((res = lshift_bits(&u, k, c)) != MP_OKAY) {
|
|
goto LBL_V;
|
|
}
|
|
c->sign = MP_ZPOS;
|
|
res = MP_OKAY;
|
|
LBL_V:
|
|
mp_clear (&u);
|
|
LBL_U:
|
|
mp_clear (&v);
|
|
return res;
|
|
}
|
|
|
|
/**************************************************************************/
|
|
|
|
/* BIGNUM emulation layer */
|
|
|
|
/* essentiually, these are just wrappers around the libtommath functions */
|
|
/* usually the order of args changes */
|
|
/* the BIGNUM API tends to have more const poisoning */
|
|
/* these wrappers also check the arguments passed for sanity */
|
|
|
|
BIGNUM *
|
|
BN_bin2bn(const uint8_t *data, int len, BIGNUM *ret)
|
|
{
|
|
if (data == NULL) {
|
|
return BN_new();
|
|
}
|
|
if (ret == NULL) {
|
|
ret = BN_new();
|
|
}
|
|
return (mp_read_unsigned_bin(ret, data, len) == MP_OKAY) ? ret : NULL;
|
|
}
|
|
|
|
/* store in unsigned [big endian] format */
|
|
int
|
|
BN_bn2bin(const BIGNUM *a, unsigned char *b)
|
|
{
|
|
BIGNUM t;
|
|
int x;
|
|
|
|
if (a == NULL || b == NULL) {
|
|
return -1;
|
|
}
|
|
if (mp_init_copy (&t, __UNCONST(a)) != MP_OKAY) {
|
|
return -1;
|
|
}
|
|
for (x = 0; !BN_is_zero(&t) ; ) {
|
|
b[x++] = (unsigned char) (t.dp[0] & 0xff);
|
|
if (rshift_bits(&t, 8, &t, NULL) != MP_OKAY) {
|
|
mp_clear(&t);
|
|
return -1;
|
|
}
|
|
}
|
|
bn_reverse(b, x);
|
|
mp_clear(&t);
|
|
return x;
|
|
}
|
|
|
|
void
|
|
BN_init(BIGNUM *a)
|
|
{
|
|
if (a != NULL) {
|
|
mp_init(a);
|
|
}
|
|
}
|
|
|
|
BIGNUM *
|
|
BN_new(void)
|
|
{
|
|
BIGNUM *a;
|
|
|
|
if ((a = allocate(1, sizeof(*a))) != NULL) {
|
|
mp_init(a);
|
|
}
|
|
return a;
|
|
}
|
|
|
|
/* copy, b = a */
|
|
int
|
|
BN_copy(BIGNUM *b, const BIGNUM *a)
|
|
{
|
|
if (a == NULL || b == NULL) {
|
|
return MP_VAL;
|
|
}
|
|
return mp_copy(__UNCONST(a), b);
|
|
}
|
|
|
|
BIGNUM *
|
|
BN_dup(const BIGNUM *a)
|
|
{
|
|
BIGNUM *ret;
|
|
|
|
if (a == NULL) {
|
|
return NULL;
|
|
}
|
|
if ((ret = BN_new()) != NULL) {
|
|
BN_copy(ret, a);
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
void
|
|
BN_swap(BIGNUM *a, BIGNUM *b)
|
|
{
|
|
if (a && b) {
|
|
mp_exch(a, b);
|
|
}
|
|
}
|
|
|
|
int
|
|
BN_lshift(BIGNUM *r, const BIGNUM *a, int n)
|
|
{
|
|
if (r == NULL || a == NULL || n < 0) {
|
|
return 0;
|
|
}
|
|
BN_copy(r, a);
|
|
return lshift_digits(r, n) == MP_OKAY;
|
|
}
|
|
|
|
int
|
|
BN_lshift1(BIGNUM *r, BIGNUM *a)
|
|
{
|
|
if (r == NULL || a == NULL) {
|
|
return 0;
|
|
}
|
|
BN_copy(r, a);
|
|
return lshift_digits(r, 1) == MP_OKAY;
|
|
}
|
|
|
|
int
|
|
BN_rshift(BIGNUM *r, const BIGNUM *a, int n)
|
|
{
|
|
if (r == NULL || a == NULL || n < 0) {
|
|
return MP_VAL;
|
|
}
|
|
BN_copy(r, a);
|
|
return rshift_digits(r, n) == MP_OKAY;
|
|
}
|
|
|
|
int
|
|
BN_rshift1(BIGNUM *r, BIGNUM *a)
|
|
{
|
|
if (r == NULL || a == NULL) {
|
|
return 0;
|
|
}
|
|
BN_copy(r, a);
|
|
return rshift_digits(r, 1) == MP_OKAY;
|
|
}
|
|
|
|
int
|
|
BN_set_word(BIGNUM *a, BN_ULONG w)
|
|
{
|
|
if (a == NULL) {
|
|
return 0;
|
|
}
|
|
set_word(a, w);
|
|
return 1;
|
|
}
|
|
|
|
int
|
|
BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)
|
|
{
|
|
if (a == NULL || b == NULL || r == NULL) {
|
|
return 0;
|
|
}
|
|
return signed_add(__UNCONST(a), __UNCONST(b), r) == MP_OKAY;
|
|
}
|
|
|
|
int
|
|
BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)
|
|
{
|
|
if (a == NULL || b == NULL || r == NULL) {
|
|
return 0;
|
|
}
|
|
return signed_subtract(__UNCONST(a), __UNCONST(b), r) == MP_OKAY;
|
|
}
|
|
|
|
int
|
|
BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
|
|
{
|
|
if (a == NULL || b == NULL || r == NULL) {
|
|
return 0;
|
|
}
|
|
USE_ARG(ctx);
|
|
return signed_multiply(__UNCONST(a), __UNCONST(b), r) == MP_OKAY;
|
|
}
|
|
|
|
int
|
|
BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d, BN_CTX *ctx)
|
|
{
|
|
if ((dv == NULL && rem == NULL) || a == NULL || d == NULL) {
|
|
return 0;
|
|
}
|
|
USE_ARG(ctx);
|
|
return signed_divide(dv, rem, __UNCONST(a), __UNCONST(d)) == MP_OKAY;
|
|
}
|
|
|
|
/* perform a bit operation on the 2 bignums */
|
|
int
|
|
BN_bitop(BIGNUM *r, const BIGNUM *a, char op, const BIGNUM *b)
|
|
{
|
|
unsigned ndigits;
|
|
mp_digit ad;
|
|
mp_digit bd;
|
|
int i;
|
|
|
|
if (a == NULL || b == NULL || r == NULL) {
|
|
return 0;
|
|
}
|
|
if (BN_cmp(__UNCONST(a), __UNCONST(b)) >= 0) {
|
|
BN_copy(r, a);
|
|
ndigits = a->used;
|
|
} else {
|
|
BN_copy(r, b);
|
|
ndigits = b->used;
|
|
}
|
|
for (i = 0 ; i < (int)ndigits ; i++) {
|
|
ad = (i > a->used) ? 0 : a->dp[i];
|
|
bd = (i > b->used) ? 0 : b->dp[i];
|
|
switch(op) {
|
|
case '&':
|
|
r->dp[i] = (ad & bd);
|
|
break;
|
|
case '|':
|
|
r->dp[i] = (ad | bd);
|
|
break;
|
|
case '^':
|
|
r->dp[i] = (ad ^ bd);
|
|
break;
|
|
default:
|
|
break;
|
|
}
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
void
|
|
BN_free(BIGNUM *a)
|
|
{
|
|
if (a) {
|
|
mp_clear(a);
|
|
free(a);
|
|
}
|
|
}
|
|
|
|
void
|
|
BN_clear(BIGNUM *a)
|
|
{
|
|
if (a) {
|
|
mp_clear(a);
|
|
}
|
|
}
|
|
|
|
void
|
|
BN_clear_free(BIGNUM *a)
|
|
{
|
|
BN_clear(a);
|
|
free(a);
|
|
}
|
|
|
|
int
|
|
BN_num_bytes(const BIGNUM *a)
|
|
{
|
|
if (a == NULL) {
|
|
return MP_VAL;
|
|
}
|
|
return mp_unsigned_bin_size(__UNCONST(a));
|
|
}
|
|
|
|
int
|
|
BN_num_bits(const BIGNUM *a)
|
|
{
|
|
if (a == NULL) {
|
|
return 0;
|
|
}
|
|
return mp_count_bits(a);
|
|
}
|
|
|
|
void
|
|
BN_set_negative(BIGNUM *a, int n)
|
|
{
|
|
if (a) {
|
|
a->sign = (n) ? MP_NEG : 0;
|
|
}
|
|
}
|
|
|
|
int
|
|
BN_cmp(BIGNUM *a, BIGNUM *b)
|
|
{
|
|
if (a == NULL || b == NULL) {
|
|
return MP_VAL;
|
|
}
|
|
switch(signed_compare(a, b)) {
|
|
case MP_LT:
|
|
return -1;
|
|
case MP_GT:
|
|
return 1;
|
|
case MP_EQ:
|
|
default:
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
int
|
|
BN_mod_exp(BIGNUM *Y, BIGNUM *G, BIGNUM *X, BIGNUM *P, BN_CTX *ctx)
|
|
{
|
|
if (Y == NULL || G == NULL || X == NULL || P == NULL) {
|
|
return MP_VAL;
|
|
}
|
|
USE_ARG(ctx);
|
|
return exponent_modulo(G, X, P, Y) == MP_OKAY;
|
|
}
|
|
|
|
BIGNUM *
|
|
BN_mod_inverse(BIGNUM *r, BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
|
|
{
|
|
USE_ARG(ctx);
|
|
if (r == NULL || a == NULL || n == NULL) {
|
|
return NULL;
|
|
}
|
|
return (modular_inverse(r, a, __UNCONST(n)) == MP_OKAY) ? r : NULL;
|
|
}
|
|
|
|
int
|
|
BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx)
|
|
{
|
|
USE_ARG(ctx);
|
|
if (ret == NULL || a == NULL || b == NULL || m == NULL) {
|
|
return 0;
|
|
}
|
|
return multiply_modulo(ret, a, b, __UNCONST(m)) == MP_OKAY;
|
|
}
|
|
|
|
BN_CTX *
|
|
BN_CTX_new(void)
|
|
{
|
|
return allocate(1, sizeof(BN_CTX));
|
|
}
|
|
|
|
void
|
|
BN_CTX_init(BN_CTX *c)
|
|
{
|
|
if (c != NULL) {
|
|
c->arraysize = 15;
|
|
if ((c->v = allocate(sizeof(*c->v), c->arraysize)) == NULL) {
|
|
c->arraysize = 0;
|
|
}
|
|
}
|
|
}
|
|
|
|
BIGNUM *
|
|
BN_CTX_get(BN_CTX *ctx)
|
|
{
|
|
if (ctx == NULL || ctx->v == NULL || ctx->arraysize == 0 || ctx->count == ctx->arraysize - 1) {
|
|
return NULL;
|
|
}
|
|
return ctx->v[ctx->count++] = BN_new();
|
|
}
|
|
|
|
void
|
|
BN_CTX_start(BN_CTX *ctx)
|
|
{
|
|
BN_CTX_init(ctx);
|
|
}
|
|
|
|
void
|
|
BN_CTX_free(BN_CTX *c)
|
|
{
|
|
unsigned i;
|
|
|
|
if (c != NULL && c->v != NULL) {
|
|
for (i = 0 ; i < c->count ; i++) {
|
|
BN_clear_free(c->v[i]);
|
|
}
|
|
deallocate(c->v, sizeof(*c->v) * c->arraysize);
|
|
}
|
|
}
|
|
|
|
void
|
|
BN_CTX_end(BN_CTX *ctx)
|
|
{
|
|
BN_CTX_free(ctx);
|
|
}
|
|
|
|
char *
|
|
BN_bn2hex(const BIGNUM *a)
|
|
{
|
|
return (a == NULL) ? NULL : formatbn(a, 16);
|
|
}
|
|
|
|
char *
|
|
BN_bn2dec(const BIGNUM *a)
|
|
{
|
|
return (a == NULL) ? NULL : formatbn(a, 10);
|
|
}
|
|
|
|
char *
|
|
BN_bn2radix(const BIGNUM *a, unsigned radix)
|
|
{
|
|
return (a == NULL) ? NULL : formatbn(a, (int)radix);
|
|
}
|
|
|
|
int
|
|
BN_print_fp(FILE *fp, const BIGNUM *a)
|
|
{
|
|
char *s;
|
|
int ret;
|
|
|
|
if (fp == NULL || a == NULL) {
|
|
return 0;
|
|
}
|
|
s = BN_bn2hex(a);
|
|
ret = fprintf(fp, "%s", s);
|
|
deallocate(s, strlen(s) + 1);
|
|
return ret;
|
|
}
|
|
|
|
#ifdef BN_RAND_NEEDED
|
|
int
|
|
BN_rand(BIGNUM *rnd, int bits, int top, int bottom)
|
|
{
|
|
uint64_t r;
|
|
int digits;
|
|
int i;
|
|
|
|
if (rnd == NULL) {
|
|
return 0;
|
|
}
|
|
mp_init_size(rnd, digits = howmany(bits, DIGIT_BIT));
|
|
for (i = 0 ; i < digits ; i++) {
|
|
r = (uint64_t)arc4random();
|
|
r <<= 32;
|
|
r |= arc4random();
|
|
rnd->dp[i] = (r & MP_MASK);
|
|
rnd->used += 1;
|
|
}
|
|
if (top == 0) {
|
|
rnd->dp[rnd->used - 1] |= (((mp_digit)1)<<((mp_digit)DIGIT_BIT));
|
|
}
|
|
if (top == 1) {
|
|
rnd->dp[rnd->used - 1] |= (((mp_digit)1)<<((mp_digit)DIGIT_BIT));
|
|
rnd->dp[rnd->used - 1] |= (((mp_digit)1)<<((mp_digit)(DIGIT_BIT - 1)));
|
|
}
|
|
if (bottom) {
|
|
rnd->dp[0] |= 0x1;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
int
|
|
BN_rand_range(BIGNUM *rnd, BIGNUM *range)
|
|
{
|
|
if (rnd == NULL || range == NULL || BN_is_zero(range)) {
|
|
return 0;
|
|
}
|
|
BN_rand(rnd, BN_num_bits(range), 1, 0);
|
|
return modulo(rnd, range, rnd) == MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
int
|
|
BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg)
|
|
{
|
|
int primality;
|
|
|
|
if (a == NULL) {
|
|
return 0;
|
|
}
|
|
USE_ARG(ctx);
|
|
USE_ARG(cb_arg);
|
|
USE_ARG(callback);
|
|
return (mp_prime_is_prime(__UNCONST(a), checks, &primality) == MP_OKAY) ? primality : 0;
|
|
}
|
|
|
|
const BIGNUM *
|
|
BN_value_one(void)
|
|
{
|
|
static mp_digit digit = 1UL;
|
|
static const BIGNUM one = { &digit, 1, 1, 0 };
|
|
|
|
return &one;
|
|
}
|
|
|
|
int
|
|
BN_hex2bn(BIGNUM **a, const char *str)
|
|
{
|
|
return getbn(a, str, 16);
|
|
}
|
|
|
|
int
|
|
BN_dec2bn(BIGNUM **a, const char *str)
|
|
{
|
|
return getbn(a, str, 10);
|
|
}
|
|
|
|
int
|
|
BN_radix2bn(BIGNUM **a, const char *str, unsigned radix)
|
|
{
|
|
return getbn(a, str, (int)radix);
|
|
}
|
|
|
|
int
|
|
BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx)
|
|
{
|
|
USE_ARG(ctx);
|
|
if (r == NULL || a == NULL || b == NULL || m == NULL) {
|
|
return 0;
|
|
}
|
|
return subtract_modulo(a, b, __UNCONST(m), r) == MP_OKAY;
|
|
}
|
|
|
|
int
|
|
BN_is_bit_set(const BIGNUM *a, int n)
|
|
{
|
|
if (a == NULL || n < 0 || n >= a->used * DIGIT_BIT) {
|
|
return 0;
|
|
}
|
|
return (a->dp[n / DIGIT_BIT] & (1 << (n % DIGIT_BIT))) ? 1 : 0;
|
|
}
|
|
|
|
/* raise 'a' to power of 'b' */
|
|
int
|
|
BN_raise(BIGNUM *res, BIGNUM *a, BIGNUM *b)
|
|
{
|
|
uint64_t exponent;
|
|
BIGNUM *power;
|
|
BIGNUM *temp;
|
|
char *t;
|
|
|
|
t = BN_bn2dec(b);
|
|
exponent = (uint64_t)strtoull(t, NULL, 10);
|
|
free(t);
|
|
if (exponent == 0) {
|
|
BN_copy(res, BN_value_one());
|
|
} else {
|
|
power = BN_dup(a);
|
|
for ( ; (exponent & 1) == 0 ; exponent >>= 1) {
|
|
BN_mul(power, power, power, NULL);
|
|
}
|
|
temp = BN_dup(power);
|
|
for (exponent >>= 1 ; exponent > 0 ; exponent >>= 1) {
|
|
BN_mul(power, power, power, NULL);
|
|
if (exponent & 1) {
|
|
BN_mul(temp, power, temp, NULL);
|
|
}
|
|
}
|
|
BN_copy(res, temp);
|
|
BN_free(power);
|
|
BN_free(temp);
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
/* compute the factorial */
|
|
int
|
|
BN_factorial(BIGNUM *res, BIGNUM *f)
|
|
{
|
|
BIGNUM *one;
|
|
BIGNUM *i;
|
|
|
|
i = BN_dup(f);
|
|
one = __UNCONST(BN_value_one());
|
|
BN_sub(i, i, one);
|
|
BN_copy(res, f);
|
|
while (BN_cmp(i, one) > 0) {
|
|
BN_mul(res, res, i, NULL);
|
|
BN_sub(i, i, one);
|
|
}
|
|
BN_free(i);
|
|
return 1;
|
|
}
|
|
|
|
/* get greatest common divisor */
|
|
int
|
|
BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
|
|
{
|
|
return mp_gcd(a, b, r);
|
|
}
|