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a30942cc | 1 | /* -*-c-*- |
2 | * | |
a30942cc | 3 | * Generate `strong' prime numbers |
4 | * | |
5 | * (c) 1999 Straylight/Edgeware | |
6 | */ | |
7 | ||
45c0fd36 | 8 | /*----- Licensing notice --------------------------------------------------* |
a30942cc | 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. | |
45c0fd36 | 16 | * |
a30942cc | 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. | |
45c0fd36 | 21 | * |
a30942cc | 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 | ||
a30942cc | 28 | /*----- Header files ------------------------------------------------------*/ |
29 | ||
30 | #include <mLib/dstr.h> | |
31 | ||
32 | #include "grand.h" | |
a30942cc | 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 | ||
052b36d0 | 42 | /* --- @strongprime_setup@ --- * |
a30942cc | 43 | * |
44 | * Arguments: @const char *name@ = pointer to name root | |
052b36d0 | 45 | * @mp *d@ = destination for search start point |
46 | * @pfilt *f@ = where to store filter jump context | |
a30942cc | 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 | * | |
052b36d0 | 53 | * Returns: A starting point for a `strong' prime search, or zero. |
a30942cc | 54 | * |
052b36d0 | 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 | |
e62e86d3 MW |
58 | * congruent to 2 (mod 4); that the jump value is twice the |
59 | * product of two large primes; and that the starting point is | |
60 | * at least %$3 \cdot 2^{N-2}$%. (Hence, if you multiply two | |
61 | * such numbers, the product is at least | |
62 | * | |
63 | * %$9 \cdot 2^{2N-4} > 2^{2N-1}$% | |
64 | * | |
65 | * i.e., it will be (at least) a %$2 N$%-bit value. | |
a30942cc | 66 | */ |
67 | ||
052b36d0 | 68 | mp *strongprime_setup(const char *name, mp *d, pfilt *f, unsigned nbits, |
69 | grand *r, unsigned n, pgen_proc *event, void *ectx) | |
a30942cc | 70 | { |
052b36d0 | 71 | mp *s, *t, *q; |
a30942cc | 72 | dstr dn = DSTR_INIT; |
32bd36cf | 73 | unsigned slop, nb, u, i; |
a30942cc | 74 | |
052b36d0 | 75 | mp *rr = d; |
a30942cc | 76 | pgen_filterctx c; |
052b36d0 | 77 | pgen_jumpctx j; |
a30942cc | 78 | rabin rb; |
79 | ||
32bd36cf | 80 | /* --- Figure out how large the smaller primes should be --- * |
a30942cc | 81 | * |
32bd36cf MW |
82 | * We want them to be `as large as possible', subject to the constraint |
83 | * that we produce a number of the requested size at the end. This is | |
84 | * tricky, because the final prime search is going to involve quite large | |
85 | * jumps from its starting point; the size of the jumps are basically | |
86 | * determined by our choice here, and if they're too big then we won't find | |
87 | * a prime in time. | |
88 | * | |
89 | * Let's suppose we're trying to make an %$N$%-bit prime. The expected | |
90 | * number of steps tends to increase linearly with size, i.e., we need to | |
91 | * take about %2^k N$% steps for some %$k$%. If we're jumping by a | |
92 | * %$J$%-bit quantity each time, from an %$N$%-bit starting point, then we | |
93 | * will only be able to find a match if %$2^k N 2^{J-1} \le 2^{N-1}$%, | |
94 | * i.e., if %$J \le N - (k + \log_2 N)$%. | |
95 | * | |
96 | * Experimentation shows that taking %$k + \log_2 N = 12$% works well for | |
540ff246 | 97 | * %$N = 1024$%, so %$k = 2$%. Add a few extra bits for luck. |
a30942cc | 98 | */ |
99 | ||
32bd36cf | 100 | for (i = 1; i && nbits >> i; i <<= 1); assert(i); |
540ff246 | 101 | for (slop = 6, nb = nbits; nb > 1; i >>= 1) { |
32bd36cf MW |
102 | u = nb >> i; |
103 | if (u) { slop += i; nb = u; } | |
104 | } | |
105 | if (nbits/2 <= slop) return (0); | |
a30942cc | 106 | |
107 | /* --- Choose two primes %$s$% and %$t$% of half the required size --- */ | |
108 | ||
32bd36cf | 109 | nb = nbits/2 - slop; |
a30942cc | 110 | c.step = 1; |
111 | ||
0b09aab8 | 112 | rr = mprand(rr, nb, r, 1); |
a30942cc | 113 | DRESET(&dn); dstr_putf(&dn, "%s [s]", name); |
47566c4d | 114 | if ((s = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c, |
0b09aab8 | 115 | rabin_iters(nb), pgen_test, &rb)) == 0) |
a30942cc | 116 | goto fail_s; |
a30942cc | 117 | |
0b09aab8 | 118 | rr = mprand(rr, nb, r, 1); |
a30942cc | 119 | DRESET(&dn); dstr_putf(&dn, "%s [t]", name); |
47566c4d | 120 | if ((t = pgen(dn.buf, MP_NEWSEC, rr, event, ectx, n, pgen_filter, &c, |
0b09aab8 | 121 | rabin_iters(nb), pgen_test, &rb)) == 0) |
a30942cc | 122 | goto fail_t; |
a30942cc | 123 | |
bd9fe975 MW |
124 | /* --- Choose a suitable value for %$r = 2it + 1$% for some %$i$% --- * |
125 | * | |
126 | * Then %$r \equiv 1 \pmod{t}$%, i.e., %$r - 1$% is a multiple of %$t$%. | |
127 | */ | |
a30942cc | 128 | |
129 | rr = mp_lsl(rr, t, 1); | |
130 | pfilt_create(&c.f, rr); | |
32bd36cf | 131 | rr = mp_lsl(rr, rr, slop - 1); |
a30942cc | 132 | rr = mp_add(rr, rr, MP_ONE); |
133 | DRESET(&dn); dstr_putf(&dn, "%s [r]", name); | |
052b36d0 | 134 | j.j = &c.f; |
052b36d0 | 135 | q = pgen(dn.buf, MP_NEW, rr, event, ectx, n, pgen_jump, &j, |
32bd36cf | 136 | rabin_iters(nb + slop), pgen_test, &rb); |
a30942cc | 137 | pfilt_destroy(&c.f); |
052b36d0 | 138 | if (!q) |
139 | goto fail_r; | |
a30942cc | 140 | |
e62e86d3 | 141 | /* --- Select a suitable congruence class for %$p$% --- * |
a30942cc | 142 | * |
bd9fe975 MW |
143 | * This computes %$p_0 = 2 s (s^{-1} \bmod r) - 1$%. Then %$p_0 + 1$% is |
144 | * clearly a multiple of %$s$%, and | |
145 | * | |
146 | * %$p_0 - 1 \equiv 2 s s^{-1} - 2 \equiv 0 \pmod{r}$% | |
147 | * | |
148 | * is a multiple of %$r$%. | |
a30942cc | 149 | */ |
150 | ||
bd490236 MW |
151 | rr = mp_modinv(rr, s, q); |
152 | rr = mp_mul(rr, rr, s); | |
153 | rr = mp_lsl(rr, rr, 1); | |
154 | rr = mp_sub(rr, rr, MP_ONE); | |
a30942cc | 155 | |
e62e86d3 MW |
156 | /* --- Pick a starting point for the search --- * |
157 | * | |
158 | * Select %$3 \cdot 2^{N-2} < p_1 < 2^N$% at random, only with | |
159 | * %$p_1 \equiv p_0 \pmod{2 r s}$. | |
160 | */ | |
a30942cc | 161 | |
162 | { | |
0b09aab8 | 163 | mp *x, *y; |
a30942cc | 164 | x = mp_mul(MP_NEW, q, s); |
165 | x = mp_lsl(x, x, 1); | |
e62e86d3 MW |
166 | pfilt_create(f, x); /* %$2 r s$% */ |
167 | y = mprand(MP_NEW, nbits, r, 0); | |
168 | y = mp_setbit(y, y, nbits - 2); | |
0b09aab8 MW |
169 | rr = mp_leastcongruent(rr, y, rr, x); |
170 | mp_drop(x); mp_drop(y); | |
a30942cc | 171 | } |
172 | ||
052b36d0 | 173 | /* --- Return the result --- */ |
a30942cc | 174 | |
a30942cc | 175 | mp_drop(q); |
052b36d0 | 176 | mp_drop(t); |
177 | mp_drop(s); | |
178 | dstr_destroy(&dn); | |
179 | return (rr); | |
180 | ||
181 | /* --- Tidy up if something failed --- */ | |
182 | ||
a30942cc | 183 | fail_r: |
a30942cc | 184 | mp_drop(t); |
185 | fail_t: | |
186 | mp_drop(s); | |
187 | fail_s: | |
188 | mp_drop(rr); | |
189 | dstr_destroy(&dn); | |
052b36d0 | 190 | return (0); |
a30942cc | 191 | } |
192 | ||
052b36d0 | 193 | /* --- @strongprime@ --- * |
194 | * | |
195 | * Arguments: @const char *name@ = pointer to name root | |
196 | * @mp *d@ = destination integer | |
197 | * @unsigned nbits@ = number of bits wanted | |
198 | * @grand *r@ = random number source | |
199 | * @unsigned n@ = number of attempts to make | |
200 | * @pgen_proc *event@ = event handler function | |
201 | * @void *ectx@ = argument for the event handler | |
202 | * | |
203 | * Returns: A `strong' prime, or zero. | |
204 | * | |
205 | * Use: Finds `strong' primes. A strong prime %$p$% is such that | |
206 | * | |
207 | * * %$p - 1$% has a large prime factor %$r$%, | |
208 | * * %$p + 1$% has a large prime factor %$s$%, and | |
209 | * * %$r - 1$% has a large prime factor %$t$%. | |
052b36d0 | 210 | */ |
211 | ||
212 | mp *strongprime(const char *name, mp *d, unsigned nbits, grand *r, | |
213 | unsigned n, pgen_proc *event, void *ectx) | |
214 | { | |
285bf989 | 215 | mp *p; |
052b36d0 | 216 | pfilt f; |
217 | pgen_jumpctx j; | |
218 | rabin rb; | |
45c0fd36 | 219 | |
285bf989 MW |
220 | if (d) mp_copy(d); |
221 | p = strongprime_setup(name, d, &f, nbits, r, n, event, ectx); | |
222 | if (!p) { mp_drop(d); return (0); } | |
052b36d0 | 223 | j.j = &f; |
285bf989 | 224 | p = pgen(name, p, p, event, ectx, n, pgen_jump, &j, |
052b36d0 | 225 | rabin_iters(nbits), pgen_test, &rb); |
32bd36cf | 226 | if (mp_bits(p) != nbits) { mp_drop(p); return (0); } |
052b36d0 | 227 | pfilt_destroy(&f); |
285bf989 MW |
228 | mp_drop(d); |
229 | return (p); | |
052b36d0 | 230 | } |
231 | ||
a30942cc | 232 | /*----- That's all, folks -------------------------------------------------*/ |