libtommath/bn_mp_prime_miller_rabin.c

/* 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;
}