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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: rabin.c,v 1.4 2000/06/22 19:03:02 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 1.4 2000/06/22 19:03:02 mdw |
34 | * Use the new @mp_odd@ function. |
35 | * |
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36 | * Revision 1.3 1999/12/22 15:50:29 mdw |
37 | * Reworking for new prime-search system. Add function for working out how |
38 | * many iterations to use for a particular number. |
39 | * |
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40 | * Revision 1.2 1999/12/10 23:29:48 mdw |
41 | * Change header file guard names. |
42 | * |
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43 | * Revision 1.1 1999/11/19 13:17:57 mdw |
44 | * Prime number generator and tester. |
45 | * |
46 | */ |
47 | |
48 | /*----- Header files ------------------------------------------------------*/ |
49 | |
50 | #include "mp.h" |
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51 | #include "mpbarrett.h" |
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52 | #include "mpmont.h" |
53 | #include "pgen.h" |
54 | #include "rabin.h" |
55 | |
56 | /*----- Main code ---------------------------------------------------------*/ |
57 | |
58 | /* --- @rabin_create@ --- * |
59 | * |
60 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
61 | * @mp *m@ = pointer to number to test |
62 | * |
63 | * Returns: --- |
64 | * |
65 | * Use: Precomputes some useful values for performing the |
66 | * Miller-Rabin probabilistic primality test. |
67 | */ |
68 | |
69 | void rabin_create(rabin *r, mp *m) |
70 | { |
71 | mp *m1 = mp_sub(MP_NEW, m, MP_ONE); |
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72 | mpmont_create(&r->mm, m); |
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73 | r->r = mp_odd(MP_NEW, m1, &r->s); |
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74 | r->m1 = mp_sub(MP_NEW, m, r->mm.r); |
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75 | mp_drop(m1); |
76 | } |
77 | |
78 | /* --- @rabin_destroy@ --- * |
79 | * |
80 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
81 | * |
82 | * Returns: --- |
83 | * |
84 | * Use: Disposes of a Rabin-Miller context when it's no longer |
85 | * needed. |
86 | */ |
87 | |
88 | void rabin_destroy(rabin *r) |
89 | { |
90 | mp_drop(r->r); |
91 | mp_drop(r->m1); |
92 | mpmont_destroy(&r->mm); |
93 | } |
94 | |
95 | /* --- @rabin_test@ --- * |
96 | * |
97 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
98 | * @mp *g@ = base to test the number against |
99 | * |
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100 | * Returns: Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@ |
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101 | * if it succeeded. |
102 | * |
103 | * Use: Performs a single iteration of the Rabin-Miller primality |
104 | * test. |
105 | */ |
106 | |
107 | int rabin_test(rabin *r, mp *g) |
108 | { |
109 | mp *y; |
110 | mp *dd, *spare = MP_NEW; |
111 | size_t j; |
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112 | int rc = PGEN_FAIL; |
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113 | |
114 | /* --- Calculate %$y R = g^r R \bmod m$% --- * |
115 | * |
116 | * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime. If course, note that |
117 | * @y@ here has an extra factor of %$R$%. |
118 | */ |
119 | |
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120 | y = mpmont_expr(&r->mm, MP_NEW, g, r->r); |
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121 | if (MP_CMP(y, ==, r->mm.r) || MP_CMP(y, ==, r->m1)) { |
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122 | rc = PGEN_PASS; |
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123 | goto done; |
124 | } |
125 | |
126 | /* --- Now for the main loop --- * |
127 | * |
128 | * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is |
129 | * composite. Of course, %$j = 0$% has already been tested. |
130 | */ |
131 | |
132 | for (j = 1; j < r->s; j++) { |
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133 | dd = mp_sqr(spare, y); |
134 | dd = mpmont_reduce(&r->mm, dd, dd); |
135 | spare = y; y = dd; |
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136 | if (MP_CMP(y, ==, r->mm.r)) |
137 | break; |
138 | if (MP_CMP(y, ==, r->m1)) { |
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139 | rc = PGEN_PASS; |
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140 | break; |
141 | } |
142 | } |
143 | |
144 | /* --- Done --- */ |
145 | |
146 | done: |
147 | if (spare != MP_NEW) |
148 | MP_DROP(spare); |
149 | MP_DROP(y); |
150 | return (rc); |
151 | } |
152 | |
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153 | /* --- @rabin_iters@ --- * |
154 | * |
155 | * Arguments: @unsigned len@ = number of bits in value |
156 | * |
157 | * Returns: Number of iterations recommended. |
158 | * |
159 | * Use: Returns the recommended number of iterations to ensure that a |
160 | * number with @len@ bits is really prime. |
161 | */ |
162 | |
163 | int rabin_iters(unsigned len) |
164 | { |
165 | static struct { |
166 | unsigned b; |
167 | int i; |
168 | } *p, *q, tab[] = { |
169 | { 100, 27 }, |
170 | { 150, 18 }, |
171 | { 200, 15 }, |
172 | { 250, 12 }, |
173 | { 300, 9 }, |
174 | { 350, 8 }, |
175 | { 400, 7 }, |
176 | { 450, 6 }, |
177 | { 550, 5 }, |
178 | { 650, 4 }, |
179 | { 850, 3 }, |
180 | { 1300, 2 } |
181 | }; |
182 | |
183 | unsigned i; |
184 | |
185 | /* --- Binary search through the table --- */ |
186 | |
187 | p = tab; |
188 | q = tab + (sizeof(tab)/sizeof(tab[0])); |
189 | for (;;) { |
190 | i = (q - p) / 2; |
191 | if (!i) |
192 | break; |
193 | if (len >= p[i].b && len < p[i + 1].b) |
194 | break; |
195 | if (len > p[i].b) |
196 | p = p + i; |
197 | else |
198 | q = p + i; |
199 | } |
200 | return (p[i].i); |
201 | } |
202 | |
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203 | /*----- That's all, folks -------------------------------------------------*/ |