|
142
|
1 #include <tommath.h> |
|
|
2 #ifdef BN_MP_PRIME_MILLER_RABIN_C |
|
2
|
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, [email protected], http://math.libtomcrypt.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 */ |
|
|
25 int 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 __N1; |
|
|
44 } |
|
|
45 |
|
|
46 /* set 2**s * r = n1 */ |
|
|
47 if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) { |
|
|
48 goto __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 __R; |
|
|
59 } |
|
|
60 |
|
|
61 /* compute y = b**r mod a */ |
|
|
62 if ((err = mp_init (&y)) != MP_OKAY) { |
|
|
63 goto __R; |
|
|
64 } |
|
|
65 if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) { |
|
|
66 goto __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 __Y; |
|
|
76 } |
|
|
77 |
|
|
78 /* if y == 1 then composite */ |
|
|
79 if (mp_cmp_d (&y, 1) == MP_EQ) { |
|
|
80 goto __Y; |
|
|
81 } |
|
|
82 |
|
|
83 ++j; |
|
|
84 } |
|
|
85 |
|
|
86 /* if y != n1 then composite */ |
|
|
87 if (mp_cmp (&y, &n1) != MP_EQ) { |
|
|
88 goto __Y; |
|
|
89 } |
|
|
90 } |
|
|
91 |
|
|
92 /* probably prime now */ |
|
|
93 *result = MP_YES; |
|
|
94 __Y:mp_clear (&y); |
|
|
95 __R:mp_clear (&r); |
|
|
96 __N1:mp_clear (&n1); |
|
|
97 return err; |
|
|
98 } |
|
142
|
99 #endif |
