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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: limlee.c,v 1.9 2004/04/08 01:36:15 mdw Exp $ |
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4 | * |
5 | * Generate Lim-Lee primes |
6 | * |
7 | * (c) 2000 Straylight/Edgeware |
8 | */ |
9 | |
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10 | /*----- Licensing notice --------------------------------------------------* |
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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. |
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18 | * |
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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. |
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23 | * |
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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 | |
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30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include <mLib/alloc.h> |
33 | #include <mLib/dstr.h> |
34 | |
35 | #include "limlee.h" |
36 | #include "mpmul.h" |
37 | #include "mprand.h" |
38 | #include "pgen.h" |
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39 | #include "rabin.h" |
40 | |
10217a5c |
41 | /*----- Stepping through combinations -------------------------------------*/ |
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42 | |
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43 | /* --- @comb_init@ --- * |
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44 | * |
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45 | * Arguments: @octet *c@ = pointer to byte-flag array |
46 | * @unsigned n@ = number of items in the array |
47 | * @unsigned r@ = number of desired items |
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48 | * |
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49 | * Returns: --- |
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50 | * |
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51 | * Use: Initializes a byte-flag array which, under the control of |
52 | * @comb_next@, will step through all combinations of @r@ chosen |
53 | * elements. |
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54 | */ |
55 | |
56 | static void comb_init(octet *c, unsigned n, unsigned r) |
57 | { |
58 | memset(c, 0, n - r); |
59 | memset(c + (n - r), 1, r); |
60 | } |
61 | |
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62 | /* --- @comb_next@ --- * |
63 | * |
64 | * Arguments: @octet *c@ = pointer to byte-flag array |
65 | * @unsigned n@ = number of items in the array |
66 | * @unsigned r@ = number of desired items |
67 | * |
68 | * Returns: Nonzero if another combination was returned, zero if we've |
69 | * reached the end. |
70 | * |
71 | * Use: Steps on to the next combination in sequence. |
72 | */ |
73 | |
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74 | static int comb_next(octet *c, unsigned n, unsigned r) |
75 | { |
76 | unsigned g = 0; |
77 | |
78 | /* --- How the algorithm works --- * |
79 | * |
80 | * Set bits start at the end and work their way towards the start. |
81 | * Excepting bits already at the start, we scan for the lowest set bit, and |
82 | * move it one place nearer the start. A group of bits at the start are |
83 | * counted and reset just below the `moved' bit. If there is no moved bit |
84 | * then we're done. |
85 | */ |
86 | |
87 | /* --- Count the group at the start --- */ |
88 | |
89 | for (; *c; c++) { |
90 | g++; |
91 | *c = 0; |
92 | } |
93 | if (g == r) |
94 | return (0); |
95 | |
96 | /* --- Move the next bit down one --- * |
97 | * |
98 | * There must be one, because otherwise we'd have counted %$r$% bits |
99 | * earlier. |
100 | */ |
101 | |
102 | for (; !*c; c++) |
103 | ; |
104 | *c = 0; |
105 | g++; |
106 | for (; g; g--) |
107 | *--c = 1; |
108 | return (1); |
109 | } |
110 | |
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111 | /*----- Default prime generator -------------------------------------------*/ |
112 | |
113 | static void llgen(limlee_factor *f, unsigned pl, limlee_stepctx *l) |
114 | { |
115 | pgen_filterctx pf; |
116 | rabin r; |
117 | mp *p; |
118 | |
119 | again: |
120 | p = mprand(l->newp, pl, l->r, 1); |
121 | pf.step = 2; |
122 | p = pgen(l->d.buf, p, p, l->iev, l->iec, 0, pgen_filter, &pf, |
123 | rabin_iters(pl), pgen_test, &r); |
124 | if (!p) |
125 | goto again; |
126 | f->p = p; |
127 | } |
128 | |
129 | static void llfree(limlee_factor *f, limlee_stepctx *l) |
130 | { |
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131 | mp_drop(f->p); |
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132 | } |
133 | |
134 | static const limlee_primeops primeops_simple = { llgen, llfree }; |
135 | |
136 | /*----- Lim-Lee stepper ---------------------------------------------------*/ |
137 | |
138 | /* --- @init@ --- * |
139 | * |
140 | * Arguments: @pgen_event *ev@ = pointer to event block |
141 | * @limlee_stepctx *l@ = pointer to Lim-Lee context |
142 | * |
143 | * Returns: A @PGEN@ result code. |
144 | * |
145 | * Use: Initializes the stepper. |
146 | */ |
147 | |
148 | static int init(pgen_event *ev, limlee_stepctx *l) |
149 | { |
150 | size_t i; |
151 | unsigned qql; |
152 | |
153 | /* --- First of all, decide on a number of factors to make --- */ |
154 | |
155 | l->nf = l->pl / l->ql; |
156 | qql = l->pl % l->ql; |
157 | if (!l->nf) |
158 | return (PGEN_ABORT); |
159 | else if (qql && l->nf > 1) { |
160 | l->nf--; |
161 | qql += l->ql; |
162 | } |
163 | |
164 | /* --- Now decide on how many primes I'll actually generate --- * |
165 | * |
166 | * The formula %$m = \max(3 n + 5, 25)$% comes from GPG's prime generation |
167 | * library. |
168 | */ |
169 | |
170 | l->poolsz = l->nf * 3 + 5; |
171 | if (l->poolsz < 25) |
172 | l->poolsz = 25; |
173 | |
174 | /* --- Allocate and initialize the various tables --- */ |
175 | |
176 | l->c = xmalloc(l->poolsz); |
177 | l->v = xmalloc(l->poolsz * sizeof(limlee_factor)); |
178 | comb_init(l->c, l->poolsz, l->nf); |
179 | for (i = 0; i < l->poolsz; i++) |
180 | l->v[i].p = 0; |
181 | |
182 | /* --- Other bits of initialization --- */ |
183 | |
184 | l->seq = 0; |
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185 | dstr_create(&l->d); |
186 | if (!l->pops) { |
187 | l->pops = &primeops_simple; |
188 | l->pc = 0; |
189 | } |
190 | |
191 | /* --- Find a big prime --- */ |
192 | |
193 | if (!qql) |
194 | l->qq.p = 0; |
195 | else { |
196 | dstr_putf(&l->d, "%s*", ev->name); |
197 | l->pops->pgen(&l->qq, qql, l); |
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198 | } |
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199 | |
200 | return (PGEN_TRY); |
201 | } |
202 | |
203 | /* --- @next@ --- * |
204 | * |
205 | * Arguments: @int rq@ = request which triggered this call |
206 | * @pgen_event *ev@ = pointer to event block |
207 | * @limlee_stepctx *l@ = pointer to Lim-Lee context |
208 | * |
209 | * Returns: A @PGEN@ result code. |
210 | * |
211 | * Use: Initializes the stepper. |
212 | */ |
213 | |
214 | static int next(int rq, pgen_event *ev, limlee_stepctx *l) |
215 | { |
216 | mp *p; |
217 | int rc; |
218 | |
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219 | mp_drop(ev->m); |
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220 | |
221 | for (;;) { |
222 | size_t i; |
223 | mpmul mm = MPMUL_INIT; |
224 | |
225 | /* --- Step on to next combination --- */ |
226 | |
227 | if (rq == PGEN_TRY && !comb_next(l->c, l->poolsz, l->nf)) { |
228 | for (i = 0; i < l->poolsz; i++) { |
229 | l->pops->pfree(&l->v[i], l); |
230 | l->v[i].p = 0; |
231 | } |
232 | } |
233 | rq = PGEN_TRY; /* For next time through */ |
234 | |
235 | /* --- Gather up some factors --- */ |
236 | |
237 | if (l->qq.p) |
238 | mpmul_add(&mm, l->qq.p); |
239 | for (i = 0; i < l->poolsz; i++) { |
240 | if (!l->c[i]) |
241 | continue; |
242 | if (!l->v[i].p) { |
243 | DRESET(&l->d); |
244 | dstr_putf(&l->d, "%s_%lu", ev->name, l->seq++); |
245 | l->pops->pgen(&l->v[i], l->ql, l); |
246 | } |
247 | mpmul_add(&mm, l->v[i].p); |
248 | } |
249 | |
250 | /* --- Check it for small factors --- */ |
251 | |
252 | p = mpmul_done(&mm); |
253 | p = mp_lsl(p, p, 1); |
254 | p->v[0] |= 1; |
255 | if ((rc = pfilt_smallfactor(p)) != PGEN_FAIL) |
256 | break; |
257 | mp_drop(p); |
258 | } |
259 | |
260 | ev->m = p; |
261 | return (rc); |
262 | } |
263 | |
264 | /* --- @done@ --- * |
265 | * |
266 | * Arguments: @pgen_event *ev@ = pointer to event block |
267 | * @limlee_stepctx *l@ = pointer to Lim-Lee context |
268 | * |
269 | * Returns: A @PGEN@ result code. |
270 | * |
271 | * Use: Finalizes the stepper. The output values in the context |
272 | * take on their final results; other resources are discarded. |
273 | */ |
274 | |
275 | static int done(pgen_event *ev, limlee_stepctx *l) |
276 | { |
277 | size_t i, j; |
278 | limlee_factor *v; |
279 | |
280 | /* --- If an output vector of factors is wanted, produce one --- */ |
281 | |
282 | if (!(l->f & LIMLEE_KEEPFACTORS)) |
283 | v = 0; |
284 | else { |
285 | if (l->qq.p) |
286 | l->nf++; |
287 | v = xmalloc(l->nf * sizeof(limlee_factor)); |
288 | } |
289 | |
290 | for (i = 0, j = 0; i < l->poolsz; i++) { |
291 | if (v && l->c[i]) |
292 | v[j++] = l->v[i]; |
293 | else if (l->v[i].p) |
294 | l->pops->pfree(&l->v[i], l); |
295 | } |
296 | |
297 | if (l->qq.p) { |
298 | if (v) |
299 | v[j++] = l->qq; |
300 | else |
301 | l->pops->pfree(&l->qq, l); |
302 | } |
303 | |
304 | xfree(l->v); |
305 | l->v = v; |
306 | |
307 | /* --- Free other resources --- */ |
308 | |
309 | xfree(l->c); |
310 | dstr_destroy(&l->d); |
311 | |
312 | /* --- Done --- */ |
313 | |
314 | return (PGEN_DONE); |
315 | } |
316 | |
317 | /* --- @limlee_step@ --- */ |
318 | |
319 | int limlee_step(int rq, pgen_event *ev, void *p) |
320 | { |
321 | limlee_stepctx *l = p; |
322 | int rc; |
323 | |
324 | switch (rq) { |
325 | case PGEN_BEGIN: |
326 | if ((rc = init(ev, l)) != PGEN_TRY) |
327 | return (rc); |
328 | case PGEN_TRY: |
329 | return (next(rq, ev, l)); |
330 | case PGEN_DONE: |
331 | return (done(ev, l)); |
332 | } |
333 | return (PGEN_ABORT); |
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334 | } |
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335 | |
336 | /*----- Main code ---------------------------------------------------------*/ |
337 | |
338 | /* --- @limlee@ --- * |
339 | * |
340 | * Arguments: @const char *name@ = pointer to name root |
341 | * @mp *d@ = pointer to destination integer |
342 | * @mp *newp@ = how to generate factor primes |
343 | * @unsigned ql@ = size of individual factors |
344 | * @unsigned pl@ = size of large prime |
345 | * @grand *r@ = a random number source |
346 | * @unsigned on@ = number of outer attempts to make |
347 | * @pgen_proc *oev@ = outer event handler function |
348 | * @void *oec@ = argument for the outer event handler |
349 | * @pgen_proc *iev@ = inner event handler function |
350 | * @void *iec@ = argument for the inner event handler |
351 | * @size_t *nf@, @mp ***f@ = output array for factors |
352 | * |
353 | * Returns: A Lim-Lee prime, or null if generation failed. |
354 | * |
355 | * Use: Generates Lim-Lee primes. A Lim-Lee prime %$p$% is one which |
356 | * satisfies %$p = 2 \prod_i q_i + 1$%, where all of the %$q_i$% |
357 | * are large enough to resist square-root discrete log |
358 | * algorithms. |
359 | * |
360 | * If we succeed, and @f@ is non-null, we write the array of |
361 | * factors chosen to @f@ for the benefit of the caller. |
362 | */ |
363 | |
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364 | mp *limlee(const char *name, mp *d, mp *newp, |
365 | unsigned ql, unsigned pl, grand *r, |
366 | unsigned on, pgen_proc *oev, void *oec, |
367 | pgen_proc *iev, void *iec, |
368 | size_t *nf, mp ***f) |
369 | { |
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370 | limlee_stepctx l; |
371 | rabin rr; |
372 | |
373 | l.f = 0; if (f) l.f |= LIMLEE_KEEPFACTORS; |
374 | l.newp = newp; |
375 | l.pl = pl; l.ql = ql; |
376 | l.pops = 0; |
377 | l.iev = iev; |
378 | l.iec = iec; |
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379 | l.r = r; |
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380 | |
381 | d = pgen(name, d, 0, oev, oec, on, limlee_step, &l, |
382 | rabin_iters(pl), pgen_test, &rr); |
383 | |
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384 | if (d && f) { |
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385 | mp **v; |
386 | size_t i; |
387 | v = xmalloc(l.nf * sizeof(mp *)); |
388 | for (i = 0; i < l.nf; i++) |
389 | v[i] = l.v[i].p; |
390 | xfree(l.v); |
391 | *f = v; |
392 | *nf = l.nf; |
393 | } |
394 | |
395 | return (d); |
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396 | } |
397 | |
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398 | /*----- That's all, folks -------------------------------------------------*/ |