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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: rabin.c,v 1.9 2004/04/08 01:36:15 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 | |
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30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include "mp.h" |
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33 | #include "mpbarrett.h" |
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34 | #include "mpmont.h" |
35 | #include "pgen.h" |
36 | #include "rabin.h" |
37 | |
38 | /*----- Main code ---------------------------------------------------------*/ |
39 | |
40 | /* --- @rabin_create@ --- * |
41 | * |
42 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
43 | * @mp *m@ = pointer to number to test |
44 | * |
45 | * Returns: --- |
46 | * |
47 | * Use: Precomputes some useful values for performing the |
48 | * Miller-Rabin probabilistic primality test. |
49 | */ |
50 | |
51 | void rabin_create(rabin *r, mp *m) |
52 | { |
53 | mp *m1 = mp_sub(MP_NEW, m, MP_ONE); |
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54 | mpmont_create(&r->mm, m); |
31cb4e2e |
55 | r->r = mp_odd(MP_NEW, m1, &r->s); |
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56 | r->m1 = mp_sub(MP_NEW, m, r->mm.r); |
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57 | mp_drop(m1); |
58 | } |
59 | |
60 | /* --- @rabin_destroy@ --- * |
61 | * |
62 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
63 | * |
64 | * Returns: --- |
65 | * |
66 | * Use: Disposes of a Rabin-Miller context when it's no longer |
67 | * needed. |
68 | */ |
69 | |
70 | void rabin_destroy(rabin *r) |
71 | { |
72 | mp_drop(r->r); |
73 | mp_drop(r->m1); |
74 | mpmont_destroy(&r->mm); |
75 | } |
76 | |
283b9af0 |
77 | /* --- @rabin_test@, @rabin_rtest@ --- * |
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78 | * |
79 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
80 | * @mp *g@ = base to test the number against |
81 | * |
dfdacfdc |
82 | * Returns: Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@ |
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83 | * if it succeeded. |
84 | * |
85 | * Use: Performs a single iteration of the Rabin-Miller primality |
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86 | * test. The @rtest@ variant assumes that %$g$% is either |
87 | * already in Montgomery representation, or you don't care. |
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88 | */ |
89 | |
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90 | int rabin_rtest(rabin *r, mp *g) |
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91 | { |
92 | mp *y; |
93 | mp *dd, *spare = MP_NEW; |
94 | size_t j; |
dfdacfdc |
95 | int rc = PGEN_FAIL; |
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96 | |
97 | /* --- Calculate %$y R = g^r R \bmod m$% --- * |
98 | * |
99 | * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime. If course, note that |
100 | * @y@ here has an extra factor of %$R$%. |
101 | */ |
102 | |
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103 | y = mpmont_expr(&r->mm, MP_NEW, g, r->r); |
22bab86c |
104 | if (MP_EQ(y, r->mm.r) || MP_EQ(y, r->m1)) { |
dfdacfdc |
105 | rc = PGEN_PASS; |
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106 | goto done; |
107 | } |
108 | |
109 | /* --- Now for the main loop --- * |
110 | * |
111 | * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is |
112 | * composite. Of course, %$j = 0$% has already been tested. |
113 | */ |
114 | |
115 | for (j = 1; j < r->s; j++) { |
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116 | dd = mp_sqr(spare, y); |
117 | dd = mpmont_reduce(&r->mm, dd, dd); |
118 | spare = y; y = dd; |
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119 | if (MP_EQ(y, r->mm.r)) |
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120 | break; |
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121 | if (MP_EQ(y, r->m1)) { |
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122 | rc = PGEN_PASS; |
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123 | break; |
124 | } |
125 | } |
126 | |
127 | /* --- Done --- */ |
128 | |
129 | done: |
130 | if (spare != MP_NEW) |
131 | MP_DROP(spare); |
132 | MP_DROP(y); |
133 | return (rc); |
134 | } |
135 | |
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136 | int rabin_test(rabin *r, mp *g) |
137 | { |
138 | int rc; |
139 | g = mpmont_mul(&r->mm, MP_NEW, g, r->mm.r2); |
140 | rc = rabin_rtest(r, g); |
141 | mp_drop(g); |
142 | return (rc); |
143 | } |
144 | |
dfdacfdc |
145 | /* --- @rabin_iters@ --- * |
146 | * |
147 | * Arguments: @unsigned len@ = number of bits in value |
148 | * |
149 | * Returns: Number of iterations recommended. |
150 | * |
151 | * Use: Returns the recommended number of iterations to ensure that a |
152 | * number with @len@ bits is really prime. |
153 | */ |
154 | |
155 | int rabin_iters(unsigned len) |
156 | { |
4e66da02 |
157 | static const struct { |
dfdacfdc |
158 | unsigned b; |
159 | int i; |
160 | } *p, *q, tab[] = { |
161 | { 100, 27 }, |
162 | { 150, 18 }, |
163 | { 200, 15 }, |
164 | { 250, 12 }, |
165 | { 300, 9 }, |
166 | { 350, 8 }, |
167 | { 400, 7 }, |
168 | { 450, 6 }, |
169 | { 550, 5 }, |
170 | { 650, 4 }, |
171 | { 850, 3 }, |
172 | { 1300, 2 } |
173 | }; |
174 | |
175 | unsigned i; |
176 | |
177 | /* --- Binary search through the table --- */ |
178 | |
179 | p = tab; |
180 | q = tab + (sizeof(tab)/sizeof(tab[0])); |
181 | for (;;) { |
182 | i = (q - p) / 2; |
183 | if (!i) |
184 | break; |
185 | if (len >= p[i].b && len < p[i + 1].b) |
186 | break; |
187 | if (len > p[i].b) |
188 | p = p + i; |
189 | else |
190 | q = p + i; |
191 | } |
192 | return (p[i].i); |
193 | } |
194 | |
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195 | /*----- That's all, folks -------------------------------------------------*/ |