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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: rabin.c,v 1.3 1999/12/22 15:50:29 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 1.3 1999/12/22 15:50:29 mdw |
34 | * Reworking for new prime-search system. Add function for working out how |
35 | * many iterations to use for a particular number. |
36 | * |
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37 | * Revision 1.2 1999/12/10 23:29:48 mdw |
38 | * Change header file guard names. |
39 | * |
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40 | * Revision 1.1 1999/11/19 13:17:57 mdw |
41 | * Prime number generator and tester. |
42 | * |
43 | */ |
44 | |
45 | /*----- Header files ------------------------------------------------------*/ |
46 | |
47 | #include "mp.h" |
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48 | #include "mpbarrett.h" |
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49 | #include "mpmont.h" |
50 | #include "pgen.h" |
51 | #include "rabin.h" |
52 | |
53 | /*----- Main code ---------------------------------------------------------*/ |
54 | |
55 | /* --- @rabin_create@ --- * |
56 | * |
57 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
58 | * @mp *m@ = pointer to number to test |
59 | * |
60 | * Returns: --- |
61 | * |
62 | * Use: Precomputes some useful values for performing the |
63 | * Miller-Rabin probabilistic primality test. |
64 | */ |
65 | |
66 | void rabin_create(rabin *r, mp *m) |
67 | { |
68 | mp *m1 = mp_sub(MP_NEW, m, MP_ONE); |
69 | mpscan sc; |
70 | size_t s; |
71 | |
72 | /* --- Find @r@ and @s@ --- */ |
73 | |
74 | mpmont_create(&r->mm, m); |
75 | mp_scan(&sc, m1); |
76 | s = 0; |
77 | while (mp_step(&sc)) { |
78 | if (mp_bit(&sc)) |
79 | break; |
80 | s++; |
81 | } |
82 | r->s = s; |
83 | r->r = mp_lsr(MP_NEW, m1, s); |
84 | |
85 | /* --- Compute %$(m - 1)R \bmod m$% --- */ |
86 | |
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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 | |
108 | /* --- @rabin_test@ --- * |
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 |
117 | * test. |
118 | */ |
119 | |
120 | int rabin_test(rabin *r, mp *g) |
121 | { |
122 | mp *y; |
123 | mp *dd, *spare = MP_NEW; |
124 | size_t j; |
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125 | int rc = PGEN_FAIL; |
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126 | |
127 | /* --- Calculate %$y R = g^r R \bmod m$% --- * |
128 | * |
129 | * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime. If course, note that |
130 | * @y@ here has an extra factor of %$R$%. |
131 | */ |
132 | |
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133 | y = mpmont_expr(&r->mm, MP_NEW, g, r->r); |
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134 | if (MP_CMP(y, ==, r->mm.r) || MP_CMP(y, ==, r->m1)) { |
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135 | rc = PGEN_PASS; |
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136 | goto done; |
137 | } |
138 | |
139 | /* --- Now for the main loop --- * |
140 | * |
141 | * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is |
142 | * composite. Of course, %$j = 0$% has already been tested. |
143 | */ |
144 | |
145 | for (j = 1; j < r->s; j++) { |
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146 | dd = mp_sqr(spare, y); |
147 | dd = mpmont_reduce(&r->mm, dd, dd); |
148 | spare = y; y = dd; |
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149 | if (MP_CMP(y, ==, r->mm.r)) |
150 | break; |
151 | if (MP_CMP(y, ==, r->m1)) { |
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152 | rc = PGEN_PASS; |
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153 | break; |
154 | } |
155 | } |
156 | |
157 | /* --- Done --- */ |
158 | |
159 | done: |
160 | if (spare != MP_NEW) |
161 | MP_DROP(spare); |
162 | MP_DROP(y); |
163 | return (rc); |
164 | } |
165 | |
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166 | /* --- @rabin_iters@ --- * |
167 | * |
168 | * Arguments: @unsigned len@ = number of bits in value |
169 | * |
170 | * Returns: Number of iterations recommended. |
171 | * |
172 | * Use: Returns the recommended number of iterations to ensure that a |
173 | * number with @len@ bits is really prime. |
174 | */ |
175 | |
176 | int rabin_iters(unsigned len) |
177 | { |
178 | static struct { |
179 | unsigned b; |
180 | int i; |
181 | } *p, *q, tab[] = { |
182 | { 100, 27 }, |
183 | { 150, 18 }, |
184 | { 200, 15 }, |
185 | { 250, 12 }, |
186 | { 300, 9 }, |
187 | { 350, 8 }, |
188 | { 400, 7 }, |
189 | { 450, 6 }, |
190 | { 550, 5 }, |
191 | { 650, 4 }, |
192 | { 850, 3 }, |
193 | { 1300, 2 } |
194 | }; |
195 | |
196 | unsigned i; |
197 | |
198 | /* --- Binary search through the table --- */ |
199 | |
200 | p = tab; |
201 | q = tab + (sizeof(tab)/sizeof(tab[0])); |
202 | for (;;) { |
203 | i = (q - p) / 2; |
204 | if (!i) |
205 | break; |
206 | if (len >= p[i].b && len < p[i + 1].b) |
207 | break; |
208 | if (len > p[i].b) |
209 | p = p + i; |
210 | else |
211 | q = p + i; |
212 | } |
213 | return (p[i].i); |
214 | } |
215 | |
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216 | /*----- That's all, folks -------------------------------------------------*/ |