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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: limlee.c,v 1.3 2000/07/29 09:58:32 mdw Exp $ |
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4 | * |
5 | * Generate Lim-Lee primes |
6 | * |
7 | * (c) 2000 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: limlee.c,v $ |
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33 | * Revision 1.3 2000/07/29 09:58:32 mdw |
34 | * (limlee): Bug fix. Old versions didn't set the filter step if @ql@ was |
35 | * an exact divisor of @pl@. |
36 | * |
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37 | * Revision 1.2 2000/07/26 18:00:00 mdw |
38 | * No footer line! |
39 | * |
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40 | * Revision 1.1 2000/07/09 21:30:58 mdw |
41 | * Lim-Lee prime generation. |
42 | * |
43 | */ |
44 | |
45 | /*----- Header files ------------------------------------------------------*/ |
46 | |
47 | #include <mLib/alloc.h> |
48 | #include <mLib/dstr.h> |
49 | |
50 | #include "limlee.h" |
51 | #include "mpmul.h" |
52 | #include "mprand.h" |
53 | #include "pgen.h" |
54 | #include "primorial.h" |
55 | #include "rabin.h" |
56 | |
57 | /*----- Main code ---------------------------------------------------------*/ |
58 | |
59 | /* --- @limlee@ --- * |
60 | * |
61 | * Arguments: @const char *name@ = pointer to name root |
62 | * @mp *d@ = pointer to destination integer |
63 | * @mp *newp@ = how to generate factor primes |
64 | * @unsigned ql@ = size of individual factors |
65 | * @unsigned pl@ = size of large prime |
66 | * @grand *r@ = a random number source |
67 | * @unsigned on@ = number of outer attempts to make |
68 | * @pgen_proc *oev@ = outer event handler function |
69 | * @void *oec@ = argument for the outer event handler |
70 | * @pgen_proc *iev@ = inner event handler function |
71 | * @void *iec@ = argument for the inner event handler |
72 | * @size_t *nf@, @mp ***f@ = output array for factors |
73 | * |
74 | * Returns: A Lim-Lee prime, or null if generation failed. |
75 | * |
76 | * Use: Generates Lim-Lee primes. A Lim-Lee prime %$p$% is one which |
77 | * satisfies %$p = 2 \prod_i q_i + 1$%, where all of the %$q_i$% |
78 | * are large enough to resist square-root discrete log |
79 | * algorithms. |
80 | * |
81 | * If we succeed, and @f@ is non-null, we write the array of |
82 | * factors chosen to @f@ for the benefit of the caller. |
83 | */ |
84 | |
85 | static void comb_init(octet *c, unsigned n, unsigned r) |
86 | { |
87 | memset(c, 0, n - r); |
88 | memset(c + (n - r), 1, r); |
89 | } |
90 | |
91 | static int comb_next(octet *c, unsigned n, unsigned r) |
92 | { |
93 | unsigned g = 0; |
94 | |
95 | /* --- How the algorithm works --- * |
96 | * |
97 | * Set bits start at the end and work their way towards the start. |
98 | * Excepting bits already at the start, we scan for the lowest set bit, and |
99 | * move it one place nearer the start. A group of bits at the start are |
100 | * counted and reset just below the `moved' bit. If there is no moved bit |
101 | * then we're done. |
102 | */ |
103 | |
104 | /* --- Count the group at the start --- */ |
105 | |
106 | for (; *c; c++) { |
107 | g++; |
108 | *c = 0; |
109 | } |
110 | if (g == r) |
111 | return (0); |
112 | |
113 | /* --- Move the next bit down one --- * |
114 | * |
115 | * There must be one, because otherwise we'd have counted %$r$% bits |
116 | * earlier. |
117 | */ |
118 | |
119 | for (; !*c; c++) |
120 | ; |
121 | *c = 0; |
122 | g++; |
123 | for (; g; g--) |
124 | *--c = 1; |
125 | return (1); |
126 | } |
127 | |
128 | mp *limlee(const char *name, mp *d, mp *newp, |
129 | unsigned ql, unsigned pl, grand *r, |
130 | unsigned on, pgen_proc *oev, void *oec, |
131 | pgen_proc *iev, void *iec, |
132 | size_t *nf, mp ***f) |
133 | { |
134 | dstr dn = DSTR_INIT; |
135 | unsigned qql; |
136 | mp *qq = 0; |
137 | unsigned nn; |
138 | unsigned mm; |
139 | mp **v; |
140 | octet *c; |
141 | unsigned i; |
142 | unsigned long seq = 0; |
143 | pgen_event ev; |
144 | unsigned ntest; |
145 | rabin rb; |
146 | pgen_filterctx pf; |
147 | |
148 | /* --- First of all, decide on a number of factors to make --- */ |
149 | |
150 | nn = pl/ql; |
151 | qql = pl%ql; |
152 | if (!nn) |
153 | return (0); |
154 | else if (qql && nn > 1) { |
155 | nn--; |
156 | qql += ql; |
157 | } |
158 | |
159 | /* --- Now decide on how many primes I'll actually generate --- * |
160 | * |
161 | * The formula %$m = \max(3 n + 5, 25)$% comes from GPG's prime generation |
162 | * library. |
163 | */ |
164 | |
165 | mm = nn * 3 + 5; |
166 | if (mm < 25) |
167 | mm = 25; |
168 | |
169 | /* --- Now allocate the working memory --- */ |
170 | |
171 | primorial_setup(); |
172 | v = xmalloc(mm * sizeof(mp *)); |
173 | c = xmalloc(mm); |
174 | |
175 | /* --- Initialize everything and try to find a prime --- */ |
176 | |
177 | ev.name = name; |
178 | ev.m = 0; |
179 | ev.steps = on; |
180 | ev.tests = ntest = rabin_iters(pl); |
181 | ev.r = r; |
182 | |
183 | if (oev && oev(PGEN_BEGIN, &ev, oec) == PGEN_ABORT) |
184 | goto fail; |
185 | |
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186 | pf.step = 2; |
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187 | if (qql) { |
188 | dstr_putf(&dn, "%s [+]", name); |
189 | qq = mprand(d, qql, r, 1); |
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190 | qq = pgen(dn.buf, qq, qq, iev, iec, |
191 | 0, pgen_filter, &pf, rabin_iters(qql), pgen_test, &rb); |
192 | } |
193 | |
194 | again: |
195 | comb_init(c, mm, nn); |
196 | for (i = 0; i < mm; i++) |
197 | v[i] = 0; |
198 | |
199 | /* --- The main combinations loop --- */ |
200 | |
201 | do { |
202 | mpmul mmul = MPMUL_INIT; |
203 | |
204 | /* --- Multiply a bunch of primes together --- */ |
205 | |
206 | if (qq) { |
207 | mpmul_add(&mmul, qq); |
208 | } |
209 | for (i = 0; i < mm; i++) { |
210 | if (!c[i]) |
211 | continue; |
212 | if (!v[i]) { |
213 | mp *z; |
214 | |
215 | DRESET(&dn); |
216 | dstr_putf(&dn, "%s [%lu] = ", name, seq++); |
217 | z = mprand(newp, ql, ev.r, 1); |
218 | z = pgen(dn.buf, z, z, iev, iec, |
219 | 0, pgen_filter, &pf, rabin_iters(ql), pgen_test, &rb); |
220 | v[i] = z; |
221 | } |
222 | mpmul_add(&mmul, v[i]); |
223 | } |
224 | |
225 | /* --- Now do some testing --- */ |
226 | |
227 | { |
228 | mp *p = mpmul_done(&mmul); |
229 | mp *g = newp; |
230 | int rc; |
231 | |
232 | /* --- Check for small factors --- */ |
233 | |
234 | p = mp_lsl(p, p, 1); |
235 | p = mp_add(p, p, MP_ONE); |
236 | mp_gcd(&g, 0, 0, p, primorial); |
237 | if (MP_CMP(g, !=, MP_ONE)) { |
238 | mp_drop(g); |
239 | mp_drop(p); |
240 | continue; |
241 | } |
242 | mp_drop(g); |
243 | |
244 | /* --- Send an event out --- */ |
245 | |
246 | ev.m = p; |
247 | if (oev && oev(PGEN_TRY, &ev, oec) == PGEN_ABORT) { |
248 | mp_drop(p); |
249 | goto fail; |
250 | } |
251 | |
252 | /* --- Do the Rabin testing --- */ |
253 | |
254 | rabin_create(&rb, p); |
255 | g = MP_NEW; |
256 | do { |
257 | g = mprand_range(g, p, ev.r, 1); |
258 | rc = rabin_test(&rb, g); |
259 | if (rc == PGEN_PASS) { |
260 | ev.tests--; |
261 | if (!ev.tests) |
262 | rc = PGEN_DONE; |
263 | } |
264 | if (oev &&oev(rc, &ev, oec) == PGEN_ABORT) |
265 | rc = PGEN_ABORT; |
266 | } while (rc == PGEN_PASS); |
267 | |
268 | rabin_destroy(&rb); |
269 | mp_drop(g); |
270 | if (rc == PGEN_DONE) |
271 | d = p; |
272 | else |
273 | mp_drop(p); |
274 | if (rc == PGEN_ABORT) |
275 | goto fail; |
276 | if (rc == PGEN_DONE) |
277 | goto done; |
278 | ev.tests = ntest; |
279 | ev.m = 0; |
280 | } |
281 | } while (comb_next(c, mm, nn)); |
282 | |
283 | /* --- That failed --- */ |
284 | |
285 | if (ev.steps) { |
286 | ev.steps--; |
287 | if (!ev.steps) { |
288 | if (oev) |
289 | oev(PGEN_ABORT, &ev, &oec); |
290 | goto fail; |
291 | } |
292 | } |
293 | |
294 | for (i = 0; i < mm; i++) |
295 | mp_drop(v[i]); |
296 | goto again; |
297 | |
298 | /* --- We did it! --- */ |
299 | |
300 | done: { |
301 | mp **vv = 0; |
302 | if (f) { |
303 | if (qq) |
304 | nn++; |
305 | *nf = nn; |
306 | *f = vv = xmalloc(nn * sizeof(mp *)); |
307 | } |
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308 | |
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309 | for (i = 0; i < mm; i++) { |
310 | if (c[i] && vv) |
311 | *vv++ = v[i]; |
312 | else if (v[i]) |
313 | mp_drop(v[i]); |
314 | } |
315 | if (qq) { |
316 | if (vv) |
317 | *vv++ = qq; |
318 | else |
319 | mp_drop(qq); |
320 | } |
321 | xfree(v); |
322 | xfree(c); |
323 | dstr_destroy(&dn); |
324 | return (d); |
325 | } |
326 | |
327 | /* --- We blew it --- */ |
328 | |
329 | fail: |
330 | for (i = 0; i < mm; i++) |
331 | mp_drop(v[i]); |
332 | if (qq) |
333 | mp_drop(qq); |
334 | xfree(v); |
335 | xfree(c); |
336 | dstr_destroy(&dn); |
337 | return (0); |
338 | } |
339 | |
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340 | /*----- That's all, folks -------------------------------------------------*/ |