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1 | /* -*-c-*- |
2 | * |
8a1d1981 |
3 | * $Id: strongprime.c,v 1.4 2000/07/01 11:24:52 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 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: strongprime.c,v $ |
8a1d1981 |
33 | * Revision 1.4 2000/07/01 11:24:52 mdw |
34 | * Remove old debugging code. |
35 | * |
47566c4d |
36 | * Revision 1.3 2000/06/17 12:10:09 mdw |
37 | * Add some argument checking. Use MP secure memory interface. |
38 | * |
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39 | * Revision 1.2 2000/02/12 18:21:03 mdw |
40 | * Overhaul of key management (again). |
41 | * |
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42 | * Revision 1.1 1999/12/22 15:51:22 mdw |
43 | * Find `strong' RSA primes using Gordon's algorithm. |
44 | * |
45 | */ |
46 | |
47 | /*----- Header files ------------------------------------------------------*/ |
48 | |
49 | #include <mLib/dstr.h> |
50 | |
51 | #include "grand.h" |
52 | #include "rand.h" |
53 | #include "mp.h" |
54 | #include "mpmont.h" |
55 | #include "mprand.h" |
56 | #include "pgen.h" |
57 | #include "pfilt.h" |
58 | #include "rabin.h" |
59 | |
60 | /*----- Main code ---------------------------------------------------------*/ |
61 | |
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62 | /* --- @strongprime_setup@ --- * |
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63 | * |
64 | * Arguments: @const char *name@ = pointer to name root |
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65 | * @mp *d@ = destination for search start point |
66 | * @pfilt *f@ = where to store filter jump context |
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67 | * @unsigned nbits@ = number of bits wanted |
68 | * @grand *r@ = random number source |
69 | * @unsigned n@ = number of attempts to make |
70 | * @pgen_proc *event@ = event handler function |
71 | * @void *ectx@ = argument for the event handler |
72 | * |
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73 | * Returns: A starting point for a `strong' prime search, or zero. |
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74 | * |
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75 | * Use: Sets up for a strong prime search, so that primes with |
76 | * particular properties can be found. It's probably important |
77 | * to note that the number left in the filter context @f@ is |
78 | * congruent to 2 (mod 4). |
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79 | */ |
80 | |
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81 | mp *strongprime_setup(const char *name, mp *d, pfilt *f, unsigned nbits, |
82 | grand *r, unsigned n, pgen_proc *event, void *ectx) |
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83 | { |
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84 | mp *s, *t, *q; |
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85 | dstr dn = DSTR_INIT; |
86 | |
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87 | mp *rr = d; |
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88 | pgen_filterctx c; |
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89 | pgen_jumpctx j; |
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90 | rabin rb; |
91 | |
92 | /* --- The bitslop parameter --- * |
93 | * |
94 | * There's quite a lot of prime searching to be done. The constant |
95 | * @BITSLOP@ is a (low) approximation to the base-2 log of the expected |
96 | * number of steps to find a prime number. Experimentation shows that |
97 | * numbers around 10 seem to be good. |
98 | */ |
99 | |
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100 | #define BITSLOP 12 |
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101 | |
102 | /* --- Choose two primes %$s$% and %$t$% of half the required size --- */ |
103 | |
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104 | assert(((void)"nbits too small in strongprime_setup", nbits/2 > BITSLOP)); |
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105 | nbits = nbits/2 - BITSLOP; |
106 | c.step = 1; |
107 | |
108 | rr = mprand(rr, nbits, r, 1); |
109 | DRESET(&dn); dstr_putf(&dn, "%s [s]", name); |
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110 | if ((s = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c, |
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111 | rabin_iters(nbits), pgen_test, &rb)) == 0) |
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112 | goto fail_s; |
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113 | |
114 | rr = mprand(rr, nbits, r, 1); |
115 | DRESET(&dn); dstr_putf(&dn, "%s [t]", name); |
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116 | if ((t = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c, |
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117 | rabin_iters(nbits), pgen_test, &rb)) == 0) |
118 | goto fail_t; |
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119 | |
120 | /* --- Choose a suitable value for %$r = 2it + 1$% for some %$i$% --- */ |
121 | |
122 | rr = mp_lsl(rr, t, 1); |
123 | pfilt_create(&c.f, rr); |
124 | rr = mp_lsl(rr, rr, BITSLOP - 1); |
125 | rr = mp_add(rr, rr, MP_ONE); |
126 | DRESET(&dn); dstr_putf(&dn, "%s [r]", name); |
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127 | j.j = &c.f; |
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128 | nbits += BITSLOP; |
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129 | q = pgen(dn.buf, MP_NEW, rr, event, ectx, n, pgen_jump, &j, |
130 | rabin_iters(nbits), pgen_test, &rb); |
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131 | pfilt_destroy(&c.f); |
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132 | if (!q) |
133 | goto fail_r; |
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134 | |
135 | /* --- Select a suitable starting-point for finding %$p$% --- * |
136 | * |
137 | * This computes %$p_0 = 2(s^{r - 2} \bmod r)s - 1$%. |
138 | */ |
139 | |
140 | { |
141 | mpmont mm; |
142 | |
143 | mpmont_create(&mm, q); |
144 | rr = mp_sub(rr, q, MP_TWO); |
145 | rr = mpmont_exp(&mm, rr, s, rr); |
146 | mpmont_destroy(&mm); |
147 | rr = mp_mul(rr, rr, s); |
148 | rr = mp_lsl(rr, rr, 1); |
149 | rr = mp_sub(rr, rr, MP_ONE); |
150 | } |
151 | |
152 | /* --- Now find %$p = p_0 + 2jrs$% for some %$j$% --- */ |
153 | |
154 | { |
155 | mp *x; |
156 | x = mp_mul(MP_NEW, q, s); |
157 | x = mp_lsl(x, x, 1); |
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158 | pfilt_create(f, x); |
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159 | x = mp_lsl(x, x, BITSLOP - 1); |
160 | rr = mp_add(rr, rr, x); |
161 | mp_drop(x); |
162 | } |
163 | |
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164 | /* --- Return the result --- */ |
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165 | |
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166 | mp_drop(q); |
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167 | mp_drop(t); |
168 | mp_drop(s); |
169 | dstr_destroy(&dn); |
170 | return (rr); |
171 | |
172 | /* --- Tidy up if something failed --- */ |
173 | |
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174 | fail_r: |
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175 | mp_drop(t); |
176 | fail_t: |
177 | mp_drop(s); |
178 | fail_s: |
179 | mp_drop(rr); |
180 | dstr_destroy(&dn); |
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181 | return (0); |
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182 | |
183 | #undef BITSLOP |
184 | } |
185 | |
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186 | /* --- @strongprime@ --- * |
187 | * |
188 | * Arguments: @const char *name@ = pointer to name root |
189 | * @mp *d@ = destination integer |
190 | * @unsigned nbits@ = number of bits wanted |
191 | * @grand *r@ = random number source |
192 | * @unsigned n@ = number of attempts to make |
193 | * @pgen_proc *event@ = event handler function |
194 | * @void *ectx@ = argument for the event handler |
195 | * |
196 | * Returns: A `strong' prime, or zero. |
197 | * |
198 | * Use: Finds `strong' primes. A strong prime %$p$% is such that |
199 | * |
200 | * * %$p - 1$% has a large prime factor %$r$%, |
201 | * * %$p + 1$% has a large prime factor %$s$%, and |
202 | * * %$r - 1$% has a large prime factor %$t$%. |
203 | * |
204 | * The numbers produced may be slightly larger than requested, |
205 | * by a few bits. |
206 | */ |
207 | |
208 | mp *strongprime(const char *name, mp *d, unsigned nbits, grand *r, |
209 | unsigned n, pgen_proc *event, void *ectx) |
210 | { |
211 | pfilt f; |
212 | pgen_jumpctx j; |
213 | rabin rb; |
214 | |
215 | d = strongprime_setup(name, d, &f, nbits, r, n, event, ectx); |
216 | j.j = &f; |
217 | d = pgen(name, d, d, event, ectx, n, pgen_jump, &j, |
218 | rabin_iters(nbits), pgen_test, &rb); |
219 | pfilt_destroy(&f); |
220 | return (d); |
221 | } |
222 | |
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223 | /*----- That's all, folks -------------------------------------------------*/ |