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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: strongprime.c,v 1.5 2004/04/08 01:36:15 mdw Exp $ |
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4 | * |
5 | * Generate `strong' prime numbers |
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 <mLib/dstr.h> |
33 | |
34 | #include "grand.h" |
35 | #include "rand.h" |
36 | #include "mp.h" |
37 | #include "mpmont.h" |
38 | #include "mprand.h" |
39 | #include "pgen.h" |
40 | #include "pfilt.h" |
41 | #include "rabin.h" |
42 | |
43 | /*----- Main code ---------------------------------------------------------*/ |
44 | |
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45 | /* --- @strongprime_setup@ --- * |
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46 | * |
47 | * Arguments: @const char *name@ = pointer to name root |
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48 | * @mp *d@ = destination for search start point |
49 | * @pfilt *f@ = where to store filter jump context |
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50 | * @unsigned nbits@ = number of bits wanted |
51 | * @grand *r@ = random number source |
52 | * @unsigned n@ = number of attempts to make |
53 | * @pgen_proc *event@ = event handler function |
54 | * @void *ectx@ = argument for the event handler |
55 | * |
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56 | * Returns: A starting point for a `strong' prime search, or zero. |
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57 | * |
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58 | * Use: Sets up for a strong prime search, so that primes with |
59 | * particular properties can be found. It's probably important |
60 | * to note that the number left in the filter context @f@ is |
61 | * congruent to 2 (mod 4). |
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62 | */ |
63 | |
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64 | mp *strongprime_setup(const char *name, mp *d, pfilt *f, unsigned nbits, |
65 | grand *r, unsigned n, pgen_proc *event, void *ectx) |
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66 | { |
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67 | mp *s, *t, *q; |
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68 | dstr dn = DSTR_INIT; |
69 | |
052b36d0 |
70 | mp *rr = d; |
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71 | pgen_filterctx c; |
052b36d0 |
72 | pgen_jumpctx j; |
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73 | rabin rb; |
74 | |
75 | /* --- The bitslop parameter --- * |
76 | * |
77 | * There's quite a lot of prime searching to be done. The constant |
78 | * @BITSLOP@ is a (low) approximation to the base-2 log of the expected |
79 | * number of steps to find a prime number. Experimentation shows that |
80 | * numbers around 10 seem to be good. |
81 | */ |
82 | |
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83 | #define BITSLOP 12 |
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84 | |
85 | /* --- Choose two primes %$s$% and %$t$% of half the required size --- */ |
86 | |
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87 | assert(((void)"nbits too small in strongprime_setup", nbits/2 > BITSLOP)); |
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88 | nbits = nbits/2 - BITSLOP; |
89 | c.step = 1; |
90 | |
91 | rr = mprand(rr, nbits, r, 1); |
92 | DRESET(&dn); dstr_putf(&dn, "%s [s]", name); |
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93 | if ((s = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c, |
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94 | rabin_iters(nbits), pgen_test, &rb)) == 0) |
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95 | goto fail_s; |
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96 | |
97 | rr = mprand(rr, nbits, r, 1); |
98 | DRESET(&dn); dstr_putf(&dn, "%s [t]", name); |
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99 | if ((t = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c, |
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100 | rabin_iters(nbits), pgen_test, &rb)) == 0) |
101 | goto fail_t; |
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102 | |
103 | /* --- Choose a suitable value for %$r = 2it + 1$% for some %$i$% --- */ |
104 | |
105 | rr = mp_lsl(rr, t, 1); |
106 | pfilt_create(&c.f, rr); |
107 | rr = mp_lsl(rr, rr, BITSLOP - 1); |
108 | rr = mp_add(rr, rr, MP_ONE); |
109 | DRESET(&dn); dstr_putf(&dn, "%s [r]", name); |
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110 | j.j = &c.f; |
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111 | nbits += BITSLOP; |
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112 | q = pgen(dn.buf, MP_NEW, rr, event, ectx, n, pgen_jump, &j, |
113 | rabin_iters(nbits), pgen_test, &rb); |
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114 | pfilt_destroy(&c.f); |
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115 | if (!q) |
116 | goto fail_r; |
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117 | |
118 | /* --- Select a suitable starting-point for finding %$p$% --- * |
119 | * |
120 | * This computes %$p_0 = 2(s^{r - 2} \bmod r)s - 1$%. |
121 | */ |
122 | |
123 | { |
124 | mpmont mm; |
125 | |
126 | mpmont_create(&mm, q); |
127 | rr = mp_sub(rr, q, MP_TWO); |
128 | rr = mpmont_exp(&mm, rr, s, rr); |
129 | mpmont_destroy(&mm); |
130 | rr = mp_mul(rr, rr, s); |
131 | rr = mp_lsl(rr, rr, 1); |
132 | rr = mp_sub(rr, rr, MP_ONE); |
133 | } |
134 | |
135 | /* --- Now find %$p = p_0 + 2jrs$% for some %$j$% --- */ |
136 | |
137 | { |
138 | mp *x; |
139 | x = mp_mul(MP_NEW, q, s); |
140 | x = mp_lsl(x, x, 1); |
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141 | pfilt_create(f, x); |
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142 | x = mp_lsl(x, x, BITSLOP - 1); |
143 | rr = mp_add(rr, rr, x); |
144 | mp_drop(x); |
145 | } |
146 | |
052b36d0 |
147 | /* --- Return the result --- */ |
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148 | |
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149 | mp_drop(q); |
052b36d0 |
150 | mp_drop(t); |
151 | mp_drop(s); |
152 | dstr_destroy(&dn); |
153 | return (rr); |
154 | |
155 | /* --- Tidy up if something failed --- */ |
156 | |
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157 | fail_r: |
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158 | mp_drop(t); |
159 | fail_t: |
160 | mp_drop(s); |
161 | fail_s: |
162 | mp_drop(rr); |
163 | dstr_destroy(&dn); |
052b36d0 |
164 | return (0); |
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165 | |
166 | #undef BITSLOP |
167 | } |
168 | |
052b36d0 |
169 | /* --- @strongprime@ --- * |
170 | * |
171 | * Arguments: @const char *name@ = pointer to name root |
172 | * @mp *d@ = destination integer |
173 | * @unsigned nbits@ = number of bits wanted |
174 | * @grand *r@ = random number source |
175 | * @unsigned n@ = number of attempts to make |
176 | * @pgen_proc *event@ = event handler function |
177 | * @void *ectx@ = argument for the event handler |
178 | * |
179 | * Returns: A `strong' prime, or zero. |
180 | * |
181 | * Use: Finds `strong' primes. A strong prime %$p$% is such that |
182 | * |
183 | * * %$p - 1$% has a large prime factor %$r$%, |
184 | * * %$p + 1$% has a large prime factor %$s$%, and |
185 | * * %$r - 1$% has a large prime factor %$t$%. |
186 | * |
187 | * The numbers produced may be slightly larger than requested, |
188 | * by a few bits. |
189 | */ |
190 | |
191 | mp *strongprime(const char *name, mp *d, unsigned nbits, grand *r, |
192 | unsigned n, pgen_proc *event, void *ectx) |
193 | { |
194 | pfilt f; |
195 | pgen_jumpctx j; |
196 | rabin rb; |
197 | |
198 | d = strongprime_setup(name, d, &f, nbits, r, n, event, ectx); |
199 | j.j = &f; |
200 | d = pgen(name, d, d, event, ectx, n, pgen_jump, &j, |
201 | rabin_iters(nbits), pgen_test, &rb); |
202 | pfilt_destroy(&f); |
203 | return (d); |
204 | } |
205 | |
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206 | /*----- That's all, folks -------------------------------------------------*/ |