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/* 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@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* Miller-Rabin test of "a" to the base of "b" as described in
* HAC pp. 139 Algorithm 4.24
*
* Sets result to 0 if definitely composite or 1 if probably prime.
* Randomly the chance of error is no more than 1/4 and often
* very much lower.
*/
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 (mp_cmp_d(b, 1) != MP_GT) {
return MP_VAL;
}
/* get n1 = a - 1 */
if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
return err;
}
if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
goto __N1;
}
/* set 2**s * r = n1 */
if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
goto __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 = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
goto __R;
}
/* compute y = b**r mod a */
if ((err = mp_init (&y)) != MP_OKAY) {
goto __R;
}
if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
goto __Y;
}
/* if y != 1 and y != n1 do */
if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
j = 1;
/* while j <= s-1 and y != n1 */
while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
goto __Y;
}
/* if y == 1 then composite */
if (mp_cmp_d (&y, 1) == MP_EQ) {
goto __Y;
}
++j;
}
/* if y != n1 then composite */
if (mp_cmp (&y, &n1) != MP_EQ) {
goto __Y;
}
}
/* probably prime now */
*result = MP_YES;
__Y:mp_clear (&y);
__R:mp_clear (&r);
__N1:mp_clear (&n1);
return err;
}
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