/* 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* pre-calculate the value required for Barrett reduction
* For a given modulus "b" it calulates the value required in "a"
*/
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;
}
res = mp_div (a, b, a, NULL);
return res;
}
/* reduces x mod m, assumes 0 < x < m^2, mu is precomputed via mp_reduce_setup
* From HAC pp.604 Algorithm 14.42
*/
int
mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
{
mp_int q;
int res, um = m->used;
if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
return res;
}
mp_rshd (&q, um - 1); /* q1 = x / b^(k-1) */
/* according to HAC this is optimization is ok */
if (((unsigned long) m->used) > (1UL << (unsigned long) (DIGIT_BIT - 1UL))) {
if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
goto CLEANUP;
}
} else {
if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
goto CLEANUP;
}
}
mp_rshd (&q, um + 1); /* q3 = q2 / b^(k+1) */
/* x = x mod b^(k+1), quick (no division) */
if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
goto CLEANUP;
}
/* q = q * m mod b^(k+1), quick (no division) */
if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
goto CLEANUP;
}
/* x = x - q */
if ((res = mp_sub (x, &q, x)) != MP_OKAY)
goto CLEANUP;
/* If x < 0, add b^(k+1) to it */
if (mp_cmp_d (x, 0) == MP_LT) {
mp_set (&q, 1);
if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
goto CLEANUP;
if ((res = mp_add (x, &q, x)) != MP_OKAY)
goto CLEANUP;
}
/* Back off if it's too big */
while (mp_cmp (x, m) != MP_LT) {
if ((res = s_mp_sub (x, m, x)) != MP_OKAY)
break;
}
CLEANUP:
mp_clear (&q);
return res;
}
