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