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