/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* computes xR^-1 == x (mod N) via Montgomery Reduction
*
* This is an optimized implementation of mp_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.
*/
int
fast_mp_montgomery_reduce (mp_int * a, mp_int * m, mp_digit mp)
{
int ix, res, olduse;
mp_word W[512];
/* get old used count */
olduse = a->used;
/* grow a as required */
if (a->alloc < m->used + 1) {
if ((res = mp_grow (a, m->used + 1)) != MP_OKAY) {
return res;
}
}
{
register mp_word *_W;
register mp_digit *tmpa;
_W = W;
tmpa = a->dp;
/* copy the digits of a into W[0..a->used-1] */
for (ix = 0; ix < a->used; ix++) {
*_W++ = *tmpa++;
}
/* zero the high words of W[a->used..m->used*2] */
for (; ix < m->used * 2 + 1; ix++) {
*_W++ = 0;
}
}
for (ix = 0; ix < m->used; ix++) {
/* ui = 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)
*/
register mp_digit ui;
ui = (((mp_digit) (W[ix] & MP_MASK)) * mp) & MP_MASK;
/* a = a + ui * 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
*/
{
register int iy;
register mp_digit *tmpx;
register mp_word *_W;
/* alias for the digits of the modulus */
tmpx = m->dp;
/* Alias for the columns set by an offset of ix */
_W = W + ix;
/* inner loop */
for (iy = 0; iy < m->used; iy++) {
*_W++ += ((mp_word) ui) * ((mp_word) * tmpx++);
}
}
/* now fix carry for next digit, W[ix+1] */
W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
}
{
register mp_digit *tmpa;
register mp_word *_W, *_W1;
/* nox fix rest of carries */
_W1 = W + ix;
_W = W + ++ix;
for (; ix <= m->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 mp_rshd we just copy them in the right
* order
*/
tmpa = a->dp;
_W = W + m->used;
for (ix = 0; ix < m->used + 1; ix++) {
*tmpa++ = *_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++) {
*tmpa++ = 0;
}
}
/* set the max used and clamp */
a->used = m->used + 1;
mp_clamp (a);
/* if A >= m then A = A - m */
if (mp_cmp_mag (a, m) != MP_LT) {
return s_mp_sub (a, m, a);
}
return MP_OKAY;
}
