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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: rabin.c,v 1.2 1999/12/10 23:29:48 mdw Exp $ |
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4 | * |
5 | * Miller-Rabin primality test |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: rabin.c,v $ |
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33 | * Revision 1.2 1999/12/10 23:29:48 mdw |
34 | * Change header file guard names. |
35 | * |
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36 | * Revision 1.1 1999/11/19 13:17:57 mdw |
37 | * Prime number generator and tester. |
38 | * |
39 | */ |
40 | |
41 | /*----- Header files ------------------------------------------------------*/ |
42 | |
43 | #include "mp.h" |
44 | #include "mpmont.h" |
45 | #include "pgen.h" |
46 | #include "rabin.h" |
47 | |
48 | /*----- Main code ---------------------------------------------------------*/ |
49 | |
50 | /* --- @rabin_create@ --- * |
51 | * |
52 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
53 | * @mp *m@ = pointer to number to test |
54 | * |
55 | * Returns: --- |
56 | * |
57 | * Use: Precomputes some useful values for performing the |
58 | * Miller-Rabin probabilistic primality test. |
59 | */ |
60 | |
61 | void rabin_create(rabin *r, mp *m) |
62 | { |
63 | mp *m1 = mp_sub(MP_NEW, m, MP_ONE); |
64 | mpscan sc; |
65 | size_t s; |
66 | |
67 | /* --- Find @r@ and @s@ --- */ |
68 | |
69 | mpmont_create(&r->mm, m); |
70 | mp_scan(&sc, m1); |
71 | s = 0; |
72 | while (mp_step(&sc)) { |
73 | if (mp_bit(&sc)) |
74 | break; |
75 | s++; |
76 | } |
77 | r->s = s; |
78 | r->r = mp_lsr(MP_NEW, m1, s); |
79 | |
80 | /* --- Compute %$(m - 1)R \bmod m$% --- */ |
81 | |
82 | r->m1 = mpmont_mul(&r->mm, MP_NEW, m1, r->mm.r2); |
83 | mp_drop(m1); |
84 | } |
85 | |
86 | /* --- @rabin_destroy@ --- * |
87 | * |
88 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
89 | * |
90 | * Returns: --- |
91 | * |
92 | * Use: Disposes of a Rabin-Miller context when it's no longer |
93 | * needed. |
94 | */ |
95 | |
96 | void rabin_destroy(rabin *r) |
97 | { |
98 | mp_drop(r->r); |
99 | mp_drop(r->m1); |
100 | mpmont_destroy(&r->mm); |
101 | } |
102 | |
103 | /* --- @rabin_test@ --- * |
104 | * |
105 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
106 | * @mp *g@ = base to test the number against |
107 | * |
108 | * Returns: Either @PGEN_COMPOSITE@ if the test failed, or @PGEN_MAYBE@ |
109 | * if it succeeded. |
110 | * |
111 | * Use: Performs a single iteration of the Rabin-Miller primality |
112 | * test. |
113 | */ |
114 | |
115 | int rabin_test(rabin *r, mp *g) |
116 | { |
117 | mp *y; |
118 | mp *dd, *spare = MP_NEW; |
119 | size_t j; |
120 | int rc = PGEN_COMPOSITE; |
121 | |
122 | /* --- Calculate %$y R = g^r R \bmod m$% --- * |
123 | * |
124 | * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime. If course, note that |
125 | * @y@ here has an extra factor of %$R$%. |
126 | */ |
127 | |
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128 | y = mpmont_expr(&r->mm, MP_NEW, g, r->r); |
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129 | if (MP_CMP(y, ==, r->mm.r) || MP_CMP(y, ==, r->m1)) { |
130 | rc = PGEN_MAYBE; |
131 | goto done; |
132 | } |
133 | |
134 | /* --- Now for the main loop --- * |
135 | * |
136 | * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is |
137 | * composite. Of course, %$j = 0$% has already been tested. |
138 | */ |
139 | |
140 | for (j = 1; j < r->s; j++) { |
141 | dd = mpmont_mul(&r->mm, spare, y, y); spare = y; y = dd; |
142 | if (MP_CMP(y, ==, r->mm.r)) |
143 | break; |
144 | if (MP_CMP(y, ==, r->m1)) { |
145 | rc = PGEN_MAYBE; |
146 | break; |
147 | } |
148 | } |
149 | |
150 | /* --- Done --- */ |
151 | |
152 | done: |
153 | if (spare != MP_NEW) |
154 | MP_DROP(spare); |
155 | MP_DROP(y); |
156 | return (rc); |
157 | } |
158 | |
159 | /*----- That's all, folks -------------------------------------------------*/ |