libtommath/bn_fast_mp_montgomery_reduce.c

147 lines
3.8 KiB
C
Raw Normal View History

2003-02-28 16:08:34 +00:00
/* 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.
*
2003-03-13 02:11:11 +00:00
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
2003-02-28 16:08:34 +00:00
*/
#include <tommath.h>
2003-05-29 13:35:26 +00:00
/* computes xR**-1 == x (mod N) via Montgomery Reduction
2003-02-28 16:09:08 +00:00
*
* 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.
*/
2003-02-28 16:08:34 +00:00
int
2003-05-29 13:35:26 +00:00
fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
2003-02-28 16:08:34 +00:00
{
2003-02-28 16:09:08 +00:00
int ix, res, olduse;
2003-05-17 12:33:54 +00:00
mp_word W[MP_WARRAY];
2003-02-28 16:08:34 +00:00
/* get old used count */
2003-05-29 13:35:26 +00:00
olduse = x->used;
2003-02-28 16:08:34 +00:00
/* grow a as required */
2003-05-29 13:35:26 +00:00
if (x->alloc < n->used + 1) {
if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
2003-02-28 16:08:34 +00:00
return res;
}
}
2003-02-28 16:09:08 +00:00
{
register mp_word *_W;
2003-05-29 13:35:26 +00:00
register mp_digit *tmpx;
2003-02-28 16:09:08 +00:00
_W = W;
2003-05-29 13:35:26 +00:00
tmpx = x->dp;
2003-02-28 16:09:08 +00:00
2003-03-29 18:16:01 +00:00
/* copy the digits of a into W[0..a->used-1] */
2003-05-29 13:35:26 +00:00
for (ix = 0; ix < x->used; ix++) {
*_W++ = *tmpx++;
2003-02-28 16:09:08 +00:00
}
2003-02-28 16:08:34 +00:00
2003-03-29 18:16:01 +00:00
/* zero the high words of W[a->used..m->used*2] */
2003-05-29 13:35:26 +00:00
for (; ix < n->used * 2 + 1; ix++) {
2003-02-28 16:09:08 +00:00
*_W++ = 0;
}
2003-02-28 16:08:34 +00:00
}
2003-05-29 13:35:26 +00:00
for (ix = 0; ix < n->used; ix++) {
/* mu = ai * m' mod b
2003-02-28 16:08:34 +00:00
*
* We avoid a double precision multiplication (which isn't required)
2003-05-29 13:35:26 +00:00
* 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)
2003-02-28 16:08:34 +00:00
*/
2003-05-29 13:35:26 +00:00
register mp_digit mu;
mu = (((mp_digit) (W[ix] & MP_MASK)) * rho) & MP_MASK;
2003-02-28 16:08:34 +00:00
2003-05-29 13:35:26 +00:00
/* a = a + mu * m * b**i
2003-02-28 16:08:34 +00:00
*
* This is computed in place and on the fly. The multiplication
2003-05-29 13:35:26 +00:00
* by b**i is handled by offseting which columns the results
2003-02-28 16:08:34 +00:00
* are added to.
*
2003-05-29 13:35:26 +00:00
* 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
2003-02-28 16:08:34 +00:00
*/
{
register int iy;
2003-05-29 13:35:26 +00:00
register mp_digit *tmpn;
2003-02-28 16:08:34 +00:00
register mp_word *_W;
2003-02-28 16:09:08 +00:00
/* alias for the digits of the modulus */
2003-05-29 13:35:26 +00:00
tmpn = n->dp;
2003-02-28 16:09:08 +00:00
/* Alias for the columns set by an offset of ix */
2003-02-28 16:08:34 +00:00
_W = W + ix;
/* inner loop */
2003-05-29 13:35:26 +00:00
for (iy = 0; iy < n->used; iy++) {
*_W++ += ((mp_word) mu) * ((mp_word) * tmpn++);
2003-02-28 16:08:34 +00:00
}
}
/* now fix carry for next digit, W[ix+1] */
W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
}
2003-02-28 16:09:08 +00:00
{
2003-05-29 13:35:26 +00:00
register mp_digit *tmpx;
2003-03-13 02:11:11 +00:00
register mp_word *_W, *_W1;
/* nox fix rest of carries */
_W1 = W + ix;
_W = W + ++ix;
2003-05-29 13:35:26 +00:00
for (; ix <= n->used * 2 + 1; ix++) {
2003-03-13 02:11:11 +00:00
*_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
}
2003-02-28 16:08:34 +00:00
2003-05-29 13:35:26 +00:00
/* copy out, A = A/b**n
2003-02-28 16:09:08 +00:00
*
2003-05-29 13:35:26 +00:00
* 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
2003-02-28 16:09:08 +00:00
*/
2003-05-29 13:35:26 +00:00
tmpx = x->dp;
_W = W + n->used;
2003-02-28 16:09:08 +00:00
2003-05-29 13:35:26 +00:00
for (ix = 0; ix < n->used + 1; ix++) {
*tmpx++ = *_W++ & ((mp_word) MP_MASK);
2003-02-28 16:09:08 +00:00
}
2003-02-28 16:08:34 +00:00
2003-02-28 16:09:08 +00:00
/* zero oldused digits, if the input a was larger than
* m->used+1 we'll have to clear the digits */
for (; ix < olduse; ix++) {
2003-05-29 13:35:26 +00:00
*tmpx++ = 0;
2003-02-28 16:09:08 +00:00
}
2003-02-28 16:08:34 +00:00
}
2003-02-28 16:09:08 +00:00
/* set the max used and clamp */
2003-05-29 13:35:26 +00:00
x->used = n->used + 1;
mp_clamp (x);
2003-02-28 16:08:34 +00:00
/* if A >= m then A = A - m */
2003-05-29 13:35:26 +00:00
if (mp_cmp_mag (x, n) != MP_LT) {
return s_mp_sub (x, n, x);
2003-02-28 16:08:34 +00:00
}
return MP_OKAY;
}