/* TomsFastMath, a fast ISO C bignum library.
 * 
 * This project is meant to fill in where LibTomMath
 * falls short.  That is speed ;-)
 *
 * This project is public domain and free for all purposes.
 * 
 * Tom St Denis, tomstdenis@gmail.com
 */
#include <tfm_private.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.
 */
void fp_prime_miller_rabin (fp_int * a, fp_int * b, int *result)
{
  fp_int  n1, y, r;
  int     s, j;

  /* default */
  *result = FP_NO;

  /* ensure b > 1 */
  if (fp_cmp_d(b, 1) != FP_GT) {
     return;
  }     

  /* get n1 = a - 1 */
  fp_init_copy(&n1, a);
  fp_sub_d(&n1, 1, &n1);

  /* set 2**s * r = n1 */
  fp_init_copy(&r, &n1);

  /* count the number of least significant bits
   * which are zero
   */
  s = fp_cnt_lsb(&r);

  /* now divide n - 1 by 2**s */
  fp_div_2d (&r, s, &r, NULL);

  /* compute y = b**r mod a */
  fp_init(&y);
  fp_exptmod(b, &r, a, &y);

  /* if y != 1 and y != n1 do */
  if (fp_cmp_d (&y, 1) != FP_EQ && fp_cmp (&y, &n1) != FP_EQ) {
    j = 1;
    /* while j <= s-1 and y != n1 */
    while ((j <= (s - 1)) && fp_cmp (&y, &n1) != FP_EQ) {
      fp_sqrmod (&y, a, &y);

      /* if y == 1 then composite */
      if (fp_cmp_d (&y, 1) == FP_EQ) {
         return;
      }
      ++j;
    }

    /* if y != n1 then composite */
    if (fp_cmp (&y, &n1) != FP_EQ) {
       return;
    }
  }

  /* probably prime now */
  *result = FP_YES;
}

/* $Source$ */
/* $Revision$ */
/* $Date$ */
