1#include <tommath.h>
2#ifdef BN_MP_PRIME_MILLER_RABIN_C
3/* LibTomMath, multiple-precision integer library -- Tom St Denis
4 *
5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality.
7 *
8 * The library was designed directly after the MPI library by
9 * Michael Fromberger but has been written from scratch with
10 * additional optimizations in place.
11 *
12 * The library is free for all purposes without any express
13 * guarantee it works.
14 *
15 * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
16 */
17
18/* Miller-Rabin test of "a" to the base of "b" as described in
19 * HAC pp. 139 Algorithm 4.24
20 *
21 * Sets result to 0 if definitely composite or 1 if probably prime.
22 * Randomly the chance of error is no more than 1/4 and often
23 * very much lower.
24 */
25int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
26{
27  mp_int  n1, y, r;
28  int     s, j, err;
29
30  /* default */
31  *result = MP_NO;
32
33  /* ensure b > 1 */
34  if (mp_cmp_d(b, 1) != MP_GT) {
35     return MP_VAL;
36  }
37
38  /* get n1 = a - 1 */
39  if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
40    return err;
41  }
42  if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
43    goto LBL_N1;
44  }
45
46  /* set 2**s * r = n1 */
47  if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
48    goto LBL_N1;
49  }
50
51  /* count the number of least significant bits
52   * which are zero
53   */
54  s = mp_cnt_lsb(&r);
55
56  /* now divide n - 1 by 2**s */
57  if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
58    goto LBL_R;
59  }
60
61  /* compute y = b**r mod a */
62  if ((err = mp_init (&y)) != MP_OKAY) {
63    goto LBL_R;
64  }
65  if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
66    goto LBL_Y;
67  }
68
69  /* if y != 1 and y != n1 do */
70  if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
71    j = 1;
72    /* while j <= s-1 and y != n1 */
73    while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
74      if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
75         goto LBL_Y;
76      }
77
78      /* if y == 1 then composite */
79      if (mp_cmp_d (&y, 1) == MP_EQ) {
80         goto LBL_Y;
81      }
82
83      ++j;
84    }
85
86    /* if y != n1 then composite */
87    if (mp_cmp (&y, &n1) != MP_EQ) {
88      goto LBL_Y;
89    }
90  }
91
92  /* probably prime now */
93  *result = MP_YES;
94LBL_Y:mp_clear (&y);
95LBL_R:mp_clear (&r);
96LBL_N1:mp_clear (&n1);
97  return err;
98}
99#endif
100
101/* $Source$ */
102/* $Revision$ */
103/* $Date$ */
104