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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: rabin.c,v 1.8 2004/04/02 01:03:49 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 1.8 2004/04/02 01:03:49 mdw |
34 | * Miscellaneous constification. |
35 | * |
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36 | * Revision 1.7 2002/01/13 13:42:53 mdw |
37 | * More efficient Rabin-Miller test: with random witnesses, skip redundant |
38 | * Montgomerization. (Being bijective, it can't affect the distribution.) |
39 | * |
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40 | * Revision 1.6 2001/06/16 12:56:38 mdw |
41 | * Fixes for interface change to @mpmont_expr@ and @mpmont_mexpr@. |
42 | * |
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43 | * Revision 1.5 2000/10/08 12:11:22 mdw |
44 | * Use @MP_EQ@ instead of @MP_CMP@. |
45 | * |
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46 | * Revision 1.4 2000/06/22 19:03:02 mdw |
47 | * Use the new @mp_odd@ function. |
48 | * |
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49 | * Revision 1.3 1999/12/22 15:50:29 mdw |
50 | * Reworking for new prime-search system. Add function for working out how |
51 | * many iterations to use for a particular number. |
52 | * |
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53 | * Revision 1.2 1999/12/10 23:29:48 mdw |
54 | * Change header file guard names. |
55 | * |
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56 | * Revision 1.1 1999/11/19 13:17:57 mdw |
57 | * Prime number generator and tester. |
58 | * |
59 | */ |
60 | |
61 | /*----- Header files ------------------------------------------------------*/ |
62 | |
63 | #include "mp.h" |
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64 | #include "mpbarrett.h" |
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65 | #include "mpmont.h" |
66 | #include "pgen.h" |
67 | #include "rabin.h" |
68 | |
69 | /*----- Main code ---------------------------------------------------------*/ |
70 | |
71 | /* --- @rabin_create@ --- * |
72 | * |
73 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
74 | * @mp *m@ = pointer to number to test |
75 | * |
76 | * Returns: --- |
77 | * |
78 | * Use: Precomputes some useful values for performing the |
79 | * Miller-Rabin probabilistic primality test. |
80 | */ |
81 | |
82 | void rabin_create(rabin *r, mp *m) |
83 | { |
84 | mp *m1 = mp_sub(MP_NEW, m, MP_ONE); |
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85 | mpmont_create(&r->mm, m); |
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86 | r->r = mp_odd(MP_NEW, m1, &r->s); |
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87 | r->m1 = mp_sub(MP_NEW, m, r->mm.r); |
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88 | mp_drop(m1); |
89 | } |
90 | |
91 | /* --- @rabin_destroy@ --- * |
92 | * |
93 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
94 | * |
95 | * Returns: --- |
96 | * |
97 | * Use: Disposes of a Rabin-Miller context when it's no longer |
98 | * needed. |
99 | */ |
100 | |
101 | void rabin_destroy(rabin *r) |
102 | { |
103 | mp_drop(r->r); |
104 | mp_drop(r->m1); |
105 | mpmont_destroy(&r->mm); |
106 | } |
107 | |
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108 | /* --- @rabin_test@, @rabin_rtest@ --- * |
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109 | * |
110 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
111 | * @mp *g@ = base to test the number against |
112 | * |
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113 | * Returns: Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@ |
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114 | * if it succeeded. |
115 | * |
116 | * Use: Performs a single iteration of the Rabin-Miller primality |
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117 | * test. The @rtest@ variant assumes that %$g$% is either |
118 | * already in Montgomery representation, or you don't care. |
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119 | */ |
120 | |
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121 | int rabin_rtest(rabin *r, mp *g) |
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122 | { |
123 | mp *y; |
124 | mp *dd, *spare = MP_NEW; |
125 | size_t j; |
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126 | int rc = PGEN_FAIL; |
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127 | |
128 | /* --- Calculate %$y R = g^r R \bmod m$% --- * |
129 | * |
130 | * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime. If course, note that |
131 | * @y@ here has an extra factor of %$R$%. |
132 | */ |
133 | |
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134 | y = mpmont_expr(&r->mm, MP_NEW, g, r->r); |
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135 | if (MP_EQ(y, r->mm.r) || MP_EQ(y, r->m1)) { |
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136 | rc = PGEN_PASS; |
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137 | goto done; |
138 | } |
139 | |
140 | /* --- Now for the main loop --- * |
141 | * |
142 | * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is |
143 | * composite. Of course, %$j = 0$% has already been tested. |
144 | */ |
145 | |
146 | for (j = 1; j < r->s; j++) { |
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147 | dd = mp_sqr(spare, y); |
148 | dd = mpmont_reduce(&r->mm, dd, dd); |
149 | spare = y; y = dd; |
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150 | if (MP_EQ(y, r->mm.r)) |
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151 | break; |
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152 | if (MP_EQ(y, r->m1)) { |
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153 | rc = PGEN_PASS; |
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154 | break; |
155 | } |
156 | } |
157 | |
158 | /* --- Done --- */ |
159 | |
160 | done: |
161 | if (spare != MP_NEW) |
162 | MP_DROP(spare); |
163 | MP_DROP(y); |
164 | return (rc); |
165 | } |
166 | |
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167 | int rabin_test(rabin *r, mp *g) |
168 | { |
169 | int rc; |
170 | g = mpmont_mul(&r->mm, MP_NEW, g, r->mm.r2); |
171 | rc = rabin_rtest(r, g); |
172 | mp_drop(g); |
173 | return (rc); |
174 | } |
175 | |
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176 | /* --- @rabin_iters@ --- * |
177 | * |
178 | * Arguments: @unsigned len@ = number of bits in value |
179 | * |
180 | * Returns: Number of iterations recommended. |
181 | * |
182 | * Use: Returns the recommended number of iterations to ensure that a |
183 | * number with @len@ bits is really prime. |
184 | */ |
185 | |
186 | int rabin_iters(unsigned len) |
187 | { |
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188 | static const struct { |
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189 | unsigned b; |
190 | int i; |
191 | } *p, *q, tab[] = { |
192 | { 100, 27 }, |
193 | { 150, 18 }, |
194 | { 200, 15 }, |
195 | { 250, 12 }, |
196 | { 300, 9 }, |
197 | { 350, 8 }, |
198 | { 400, 7 }, |
199 | { 450, 6 }, |
200 | { 550, 5 }, |
201 | { 650, 4 }, |
202 | { 850, 3 }, |
203 | { 1300, 2 } |
204 | }; |
205 | |
206 | unsigned i; |
207 | |
208 | /* --- Binary search through the table --- */ |
209 | |
210 | p = tab; |
211 | q = tab + (sizeof(tab)/sizeof(tab[0])); |
212 | for (;;) { |
213 | i = (q - p) / 2; |
214 | if (!i) |
215 | break; |
216 | if (len >= p[i].b && len < p[i + 1].b) |
217 | break; |
218 | if (len > p[i].b) |
219 | p = p + i; |
220 | else |
221 | q = p + i; |
222 | } |
223 | return (p[i].i); |
224 | } |
225 | |
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226 | /*----- That's all, folks -------------------------------------------------*/ |