/* 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 */
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 mp_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 ((digs < MP_WARRAY) &&
n->used <
(1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
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 * m' mod b */
mu = (x->dp[ix] * rho) & MP_MASK;
/* a = a + mu * m * b**i */
{
register int iy;
register mp_digit *tmpn, *tmpx, u;
register mp_word r;
/* aliases */
tmpn = n->dp;
tmpx = x->dp + ix;
/* set the carry to zero */
u = 0;
/* Multiply and add in place */
for (iy = 0; iy < n->used; iy++) {
r = ((mp_word) mu) * ((mp_word) * tmpn++) +
((mp_word) u) + ((mp_word) * tmpx);
u = (r >> ((mp_word) DIGIT_BIT));
*tmpx++ = (r & ((mp_word) MP_MASK));
}
/* propagate carries */
while (u) {
*tmpx += u;
u = *tmpx >> DIGIT_BIT;
*tmpx++ &= MP_MASK;
}
}
}
/* x = x/b**n.used */
mp_clamp(x);
mp_rshd (x, n->used);
/* if A >= m then A = A - m */
if (mp_cmp_mag (x, n) != MP_LT) {
return s_mp_sub (x, n, x);
}
return MP_OKAY;
}
