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1 | /* -*-c-*- |
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2 | * |
3 | * Miller-Rabin primality test |
4 | * |
5 | * (c) 1999 Straylight/Edgeware |
6 | */ |
7 | |
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8 | /*----- Licensing notice --------------------------------------------------* |
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9 | * |
10 | * This file is part of Catacomb. |
11 | * |
12 | * Catacomb is free software; you can redistribute it and/or modify |
13 | * it under the terms of the GNU Library General Public License as |
14 | * published by the Free Software Foundation; either version 2 of the |
15 | * License, or (at your option) any later version. |
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16 | * |
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17 | * Catacomb is distributed in the hope that it will be useful, |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
20 | * GNU Library General Public License for more details. |
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21 | * |
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22 | * You should have received a copy of the GNU Library General Public |
23 | * License along with Catacomb; if not, write to the Free |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
25 | * MA 02111-1307, USA. |
26 | */ |
27 | |
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28 | /*----- Header files ------------------------------------------------------*/ |
29 | |
30 | #include "mp.h" |
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31 | #include "mpbarrett.h" |
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32 | #include "mpmont.h" |
33 | #include "pgen.h" |
34 | #include "rabin.h" |
35 | |
36 | /*----- Main code ---------------------------------------------------------*/ |
37 | |
38 | /* --- @rabin_create@ --- * |
39 | * |
40 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
41 | * @mp *m@ = pointer to number to test |
42 | * |
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43 | * Returns: Zero on success, nonzero on failure. |
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44 | * |
45 | * Use: Precomputes some useful values for performing the |
46 | * Miller-Rabin probabilistic primality test. |
47 | */ |
48 | |
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49 | int rabin_create(rabin *r, mp *m) |
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50 | { |
51 | mp *m1 = mp_sub(MP_NEW, m, MP_ONE); |
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52 | if (mpmont_create(&r->mm, m)) { |
53 | MP_DROP(m1); |
54 | return (-1); |
55 | } |
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56 | r->r = mp_odd(MP_NEW, m1, &r->s); |
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57 | r->m1 = mp_sub(MP_NEW, m, r->mm.r); |
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58 | mp_drop(m1); |
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59 | return (0); |
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60 | } |
61 | |
62 | /* --- @rabin_destroy@ --- * |
63 | * |
64 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
65 | * |
66 | * Returns: --- |
67 | * |
68 | * Use: Disposes of a Rabin-Miller context when it's no longer |
69 | * needed. |
70 | */ |
71 | |
72 | void rabin_destroy(rabin *r) |
73 | { |
74 | mp_drop(r->r); |
75 | mp_drop(r->m1); |
76 | mpmont_destroy(&r->mm); |
77 | } |
78 | |
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79 | /* --- @rabin_test@, @rabin_rtest@ --- * |
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80 | * |
81 | * Arguments: @rabin *r@ = pointer to Rabin-Miller context |
82 | * @mp *g@ = base to test the number against |
83 | * |
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84 | * Returns: Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@ |
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85 | * if it succeeded. |
86 | * |
87 | * Use: Performs a single iteration of the Rabin-Miller primality |
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88 | * test. The @rtest@ variant assumes that %$g$% is either |
89 | * already in Montgomery representation, or you don't care. |
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90 | */ |
91 | |
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92 | int rabin_rtest(rabin *r, mp *g) |
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93 | { |
94 | mp *y; |
95 | mp *dd, *spare = MP_NEW; |
96 | size_t j; |
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97 | int rc = PGEN_FAIL; |
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98 | |
99 | /* --- Calculate %$y R = g^r R \bmod m$% --- * |
100 | * |
101 | * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime. If course, note that |
102 | * @y@ here has an extra factor of %$R$%. |
103 | */ |
104 | |
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105 | y = mpmont_expr(&r->mm, MP_NEW, g, r->r); |
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106 | if (MP_EQ(y, r->mm.r) || MP_EQ(y, r->m1)) { |
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107 | rc = PGEN_PASS; |
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108 | goto done; |
109 | } |
110 | |
111 | /* --- Now for the main loop --- * |
112 | * |
113 | * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is |
114 | * composite. Of course, %$j = 0$% has already been tested. |
115 | */ |
116 | |
117 | for (j = 1; j < r->s; j++) { |
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118 | dd = mp_sqr(spare, y); |
119 | dd = mpmont_reduce(&r->mm, dd, dd); |
120 | spare = y; y = dd; |
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121 | if (MP_EQ(y, r->mm.r)) |
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122 | break; |
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123 | if (MP_EQ(y, r->m1)) { |
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124 | rc = PGEN_PASS; |
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125 | break; |
126 | } |
127 | } |
128 | |
129 | /* --- Done --- */ |
130 | |
131 | done: |
132 | if (spare != MP_NEW) |
133 | MP_DROP(spare); |
134 | MP_DROP(y); |
135 | return (rc); |
136 | } |
137 | |
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138 | int rabin_test(rabin *r, mp *g) |
139 | { |
140 | int rc; |
141 | g = mpmont_mul(&r->mm, MP_NEW, g, r->mm.r2); |
142 | rc = rabin_rtest(r, g); |
143 | mp_drop(g); |
144 | return (rc); |
145 | } |
146 | |
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147 | /* --- @rabin_iters@ --- * |
148 | * |
149 | * Arguments: @unsigned len@ = number of bits in value |
150 | * |
151 | * Returns: Number of iterations recommended. |
152 | * |
153 | * Use: Returns the recommended number of iterations to ensure that a |
154 | * number with @len@ bits is really prime. |
155 | */ |
156 | |
157 | int rabin_iters(unsigned len) |
158 | { |
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159 | static const struct { |
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160 | unsigned b; |
161 | int i; |
162 | } *p, *q, tab[] = { |
163 | { 100, 27 }, |
164 | { 150, 18 }, |
165 | { 200, 15 }, |
166 | { 250, 12 }, |
167 | { 300, 9 }, |
168 | { 350, 8 }, |
169 | { 400, 7 }, |
170 | { 450, 6 }, |
171 | { 550, 5 }, |
172 | { 650, 4 }, |
173 | { 850, 3 }, |
174 | { 1300, 2 } |
175 | }; |
176 | |
177 | unsigned i; |
178 | |
179 | /* --- Binary search through the table --- */ |
180 | |
181 | p = tab; |
182 | q = tab + (sizeof(tab)/sizeof(tab[0])); |
183 | for (;;) { |
184 | i = (q - p) / 2; |
185 | if (!i) |
186 | break; |
187 | if (len >= p[i].b && len < p[i + 1].b) |
188 | break; |
189 | if (len > p[i].b) |
190 | p = p + i; |
191 | else |
192 | q = p + i; |
193 | } |
194 | return (p[i].i); |
195 | } |
196 | |
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197 | /*----- That's all, folks -------------------------------------------------*/ |