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04361334 | 1 | /* -*-c-*- |
04361334 | 2 | * |
3 | * Generate Lim-Lee primes | |
4 | * | |
5 | * (c) 2000 Straylight/Edgeware | |
6 | */ | |
7 | ||
45c0fd36 | 8 | /*----- Licensing notice --------------------------------------------------* |
04361334 | 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 | * |
04361334 | 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 | * |
04361334 | 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 | ||
04361334 | 28 | /*----- Header files ------------------------------------------------------*/ |
29 | ||
30 | #include <mLib/alloc.h> | |
31 | #include <mLib/dstr.h> | |
32 | ||
33 | #include "limlee.h" | |
34 | #include "mpmul.h" | |
35 | #include "mprand.h" | |
36 | #include "pgen.h" | |
04361334 | 37 | #include "rabin.h" |
38 | ||
10217a5c | 39 | /*----- Stepping through combinations -------------------------------------*/ |
04361334 | 40 | |
10217a5c | 41 | /* --- @comb_init@ --- * |
04361334 | 42 | * |
10217a5c | 43 | * Arguments: @octet *c@ = pointer to byte-flag array |
44 | * @unsigned n@ = number of items in the array | |
45 | * @unsigned r@ = number of desired items | |
04361334 | 46 | * |
10217a5c | 47 | * Returns: --- |
04361334 | 48 | * |
10217a5c | 49 | * Use: Initializes a byte-flag array which, under the control of |
50 | * @comb_next@, will step through all combinations of @r@ chosen | |
51 | * elements. | |
04361334 | 52 | */ |
53 | ||
54 | static void comb_init(octet *c, unsigned n, unsigned r) | |
55 | { | |
56 | memset(c, 0, n - r); | |
57 | memset(c + (n - r), 1, r); | |
58 | } | |
59 | ||
10217a5c | 60 | /* --- @comb_next@ --- * |
61 | * | |
62 | * Arguments: @octet *c@ = pointer to byte-flag array | |
63 | * @unsigned n@ = number of items in the array | |
64 | * @unsigned r@ = number of desired items | |
65 | * | |
66 | * Returns: Nonzero if another combination was returned, zero if we've | |
67 | * reached the end. | |
68 | * | |
69 | * Use: Steps on to the next combination in sequence. | |
70 | */ | |
71 | ||
04361334 | 72 | static int comb_next(octet *c, unsigned n, unsigned r) |
73 | { | |
74 | unsigned g = 0; | |
75 | ||
76 | /* --- How the algorithm works --- * | |
77 | * | |
78 | * Set bits start at the end and work their way towards the start. | |
79 | * Excepting bits already at the start, we scan for the lowest set bit, and | |
80 | * move it one place nearer the start. A group of bits at the start are | |
81 | * counted and reset just below the `moved' bit. If there is no moved bit | |
82 | * then we're done. | |
83 | */ | |
84 | ||
85 | /* --- Count the group at the start --- */ | |
86 | ||
87 | for (; *c; c++) { | |
88 | g++; | |
89 | *c = 0; | |
90 | } | |
91 | if (g == r) | |
92 | return (0); | |
93 | ||
94 | /* --- Move the next bit down one --- * | |
95 | * | |
96 | * There must be one, because otherwise we'd have counted %$r$% bits | |
97 | * earlier. | |
98 | */ | |
99 | ||
100 | for (; !*c; c++) | |
101 | ; | |
102 | *c = 0; | |
103 | g++; | |
104 | for (; g; g--) | |
105 | *--c = 1; | |
106 | return (1); | |
107 | } | |
108 | ||
10217a5c | 109 | /*----- Default prime generator -------------------------------------------*/ |
110 | ||
111 | static void llgen(limlee_factor *f, unsigned pl, limlee_stepctx *l) | |
112 | { | |
113 | pgen_filterctx pf; | |
114 | rabin r; | |
115 | mp *p; | |
116 | ||
117 | again: | |
118 | p = mprand(l->newp, pl, l->r, 1); | |
119 | pf.step = 2; | |
0b09aab8 | 120 | p = pgen(l->u.s.name, p, p, l->iev, l->iec, 0, pgen_filter, &pf, |
10217a5c | 121 | rabin_iters(pl), pgen_test, &r); |
122 | if (!p) | |
123 | goto again; | |
124 | f->p = p; | |
125 | } | |
126 | ||
127 | static void llfree(limlee_factor *f, limlee_stepctx *l) | |
128 | { | |
383e235b | 129 | mp_drop(f->p); |
10217a5c | 130 | } |
131 | ||
132 | static const limlee_primeops primeops_simple = { llgen, llfree }; | |
133 | ||
134 | /*----- Lim-Lee stepper ---------------------------------------------------*/ | |
135 | ||
136 | /* --- @init@ --- * | |
137 | * | |
138 | * Arguments: @pgen_event *ev@ = pointer to event block | |
139 | * @limlee_stepctx *l@ = pointer to Lim-Lee context | |
140 | * | |
141 | * Returns: A @PGEN@ result code. | |
142 | * | |
143 | * Use: Initializes the stepper. | |
144 | */ | |
145 | ||
146 | static int init(pgen_event *ev, limlee_stepctx *l) | |
147 | { | |
148 | size_t i; | |
10217a5c | 149 | |
150 | /* --- First of all, decide on a number of factors to make --- */ | |
151 | ||
152 | l->nf = l->pl / l->ql; | |
0b09aab8 MW |
153 | if (l->nf < 2) return (PGEN_ABORT); |
154 | l->nf--; | |
10217a5c | 155 | |
156 | /* --- Now decide on how many primes I'll actually generate --- * | |
157 | * | |
158 | * The formula %$m = \max(3 n + 5, 25)$% comes from GPG's prime generation | |
159 | * library. | |
160 | */ | |
161 | ||
162 | l->poolsz = l->nf * 3 + 5; | |
163 | if (l->poolsz < 25) | |
164 | l->poolsz = 25; | |
165 | ||
166 | /* --- Allocate and initialize the various tables --- */ | |
167 | ||
168 | l->c = xmalloc(l->poolsz); | |
169 | l->v = xmalloc(l->poolsz * sizeof(limlee_factor)); | |
170 | comb_init(l->c, l->poolsz, l->nf); | |
171 | for (i = 0; i < l->poolsz; i++) | |
172 | l->v[i].p = 0; | |
173 | ||
174 | /* --- Other bits of initialization --- */ | |
175 | ||
176 | l->seq = 0; | |
10217a5c | 177 | if (!l->pops) { |
178 | l->pops = &primeops_simple; | |
179 | l->pc = 0; | |
180 | } | |
181 | ||
0b09aab8 | 182 | /* --- Find a big prime later --- */ |
10217a5c | 183 | |
0b09aab8 | 184 | l->qq.p = 0; |
10217a5c | 185 | |
186 | return (PGEN_TRY); | |
187 | } | |
188 | ||
189 | /* --- @next@ --- * | |
190 | * | |
191 | * Arguments: @int rq@ = request which triggered this call | |
192 | * @pgen_event *ev@ = pointer to event block | |
193 | * @limlee_stepctx *l@ = pointer to Lim-Lee context | |
194 | * | |
195 | * Returns: A @PGEN@ result code. | |
196 | * | |
197 | * Use: Initializes the stepper. | |
198 | */ | |
199 | ||
200 | static int next(int rq, pgen_event *ev, limlee_stepctx *l) | |
201 | { | |
0b09aab8 | 202 | dstr d = DSTR_INIT; |
10217a5c | 203 | mp *p; |
204 | int rc; | |
0b09aab8 MW |
205 | int dist; |
206 | unsigned nb; | |
10217a5c | 207 | |
383e235b | 208 | mp_drop(ev->m); |
10217a5c | 209 | |
210 | for (;;) { | |
211 | size_t i; | |
212 | mpmul mm = MPMUL_INIT; | |
213 | ||
214 | /* --- Step on to next combination --- */ | |
215 | ||
216 | if (rq == PGEN_TRY && !comb_next(l->c, l->poolsz, l->nf)) { | |
217 | for (i = 0; i < l->poolsz; i++) { | |
218 | l->pops->pfree(&l->v[i], l); | |
219 | l->v[i].p = 0; | |
220 | } | |
221 | } | |
222 | rq = PGEN_TRY; /* For next time through */ | |
223 | ||
0b09aab8 MW |
224 | /* --- If the large factor is performing badly, make a new one --- */ |
225 | ||
226 | if (l->qq.p) { | |
227 | dist = l->u.s.disp < 0 ? -l->u.s.disp : l->u.s.disp; | |
2427b43e | 228 | if (dist && dist > l->u.s.steps/3) { |
0b09aab8 MW |
229 | l->pops->pfree(&l->qq, l); |
230 | l->qq.p = 0; | |
231 | } | |
232 | } | |
233 | ||
10217a5c | 234 | /* --- Gather up some factors --- */ |
235 | ||
0b09aab8 | 236 | if (l->qq.p) mpmul_add(&mm, l->qq.p); |
10217a5c | 237 | for (i = 0; i < l->poolsz; i++) { |
238 | if (!l->c[i]) | |
239 | continue; | |
240 | if (!l->v[i].p) { | |
0b09aab8 MW |
241 | DRESET(&d); |
242 | dstr_putf(&d, "%s_%lu", ev->name, l->seq++); | |
243 | l->u.s.name = d.buf; | |
10217a5c | 244 | l->pops->pgen(&l->v[i], l->ql, l); |
245 | } | |
246 | mpmul_add(&mm, l->v[i].p); | |
247 | } | |
248 | ||
0b09aab8 | 249 | /* --- Check on the large factor --- */ |
10217a5c | 250 | |
251 | p = mpmul_done(&mm); | |
0b09aab8 MW |
252 | if (!l->qq.p) { |
253 | DRESET(&d); | |
254 | dstr_putf(&d, "%s*_%lu", ev->name, l->seq++); | |
255 | l->u.s.name = d.buf; | |
256 | l->pops->pgen(&l->qq, l->pl - mp_bits(p), l); | |
257 | l->u.s.steps = l->u.s.disp = 0; | |
258 | p = mp_mul(p, p, l->qq.p); | |
259 | } | |
10217a5c | 260 | p = mp_lsl(p, p, 1); |
261 | p->v[0] |= 1; | |
0b09aab8 MW |
262 | |
263 | nb = mp_bits(p); | |
264 | l->u.s.steps++; | |
265 | if (nb < l->pl) { | |
266 | l->u.s.disp--; | |
267 | continue; | |
268 | } else if (nb > l->pl) { | |
269 | l->u.s.disp++; | |
270 | continue; | |
271 | } | |
272 | ||
273 | /* --- Check it for small factors --- */ | |
274 | ||
10217a5c | 275 | if ((rc = pfilt_smallfactor(p)) != PGEN_FAIL) |
276 | break; | |
277 | mp_drop(p); | |
278 | } | |
279 | ||
280 | ev->m = p; | |
0b09aab8 | 281 | DDESTROY(&d); |
10217a5c | 282 | return (rc); |
283 | } | |
284 | ||
285 | /* --- @done@ --- * | |
286 | * | |
287 | * Arguments: @pgen_event *ev@ = pointer to event block | |
288 | * @limlee_stepctx *l@ = pointer to Lim-Lee context | |
289 | * | |
290 | * Returns: A @PGEN@ result code. | |
291 | * | |
292 | * Use: Finalizes the stepper. The output values in the context | |
293 | * take on their final results; other resources are discarded. | |
294 | */ | |
295 | ||
296 | static int done(pgen_event *ev, limlee_stepctx *l) | |
297 | { | |
298 | size_t i, j; | |
299 | limlee_factor *v; | |
300 | ||
301 | /* --- If an output vector of factors is wanted, produce one --- */ | |
302 | ||
303 | if (!(l->f & LIMLEE_KEEPFACTORS)) | |
304 | v = 0; | |
305 | else { | |
306 | if (l->qq.p) | |
307 | l->nf++; | |
308 | v = xmalloc(l->nf * sizeof(limlee_factor)); | |
309 | } | |
310 | ||
311 | for (i = 0, j = 0; i < l->poolsz; i++) { | |
312 | if (v && l->c[i]) | |
313 | v[j++] = l->v[i]; | |
314 | else if (l->v[i].p) | |
315 | l->pops->pfree(&l->v[i], l); | |
316 | } | |
317 | ||
318 | if (l->qq.p) { | |
319 | if (v) | |
320 | v[j++] = l->qq; | |
321 | else | |
322 | l->pops->pfree(&l->qq, l); | |
323 | } | |
324 | ||
325 | xfree(l->v); | |
326 | l->v = v; | |
327 | ||
328 | /* --- Free other resources --- */ | |
329 | ||
330 | xfree(l->c); | |
10217a5c | 331 | |
332 | /* --- Done --- */ | |
333 | ||
334 | return (PGEN_DONE); | |
335 | } | |
336 | ||
337 | /* --- @limlee_step@ --- */ | |
338 | ||
339 | int limlee_step(int rq, pgen_event *ev, void *p) | |
340 | { | |
341 | limlee_stepctx *l = p; | |
342 | int rc; | |
343 | ||
344 | switch (rq) { | |
345 | case PGEN_BEGIN: | |
346 | if ((rc = init(ev, l)) != PGEN_TRY) | |
347 | return (rc); | |
348 | case PGEN_TRY: | |
349 | return (next(rq, ev, l)); | |
350 | case PGEN_DONE: | |
351 | return (done(ev, l)); | |
352 | } | |
353 | return (PGEN_ABORT); | |
45c0fd36 | 354 | } |
10217a5c | 355 | |
356 | /*----- Main code ---------------------------------------------------------*/ | |
357 | ||
358 | /* --- @limlee@ --- * | |
359 | * | |
360 | * Arguments: @const char *name@ = pointer to name root | |
361 | * @mp *d@ = pointer to destination integer | |
362 | * @mp *newp@ = how to generate factor primes | |
363 | * @unsigned ql@ = size of individual factors | |
364 | * @unsigned pl@ = size of large prime | |
365 | * @grand *r@ = a random number source | |
366 | * @unsigned on@ = number of outer attempts to make | |
367 | * @pgen_proc *oev@ = outer event handler function | |
368 | * @void *oec@ = argument for the outer event handler | |
369 | * @pgen_proc *iev@ = inner event handler function | |
370 | * @void *iec@ = argument for the inner event handler | |
371 | * @size_t *nf@, @mp ***f@ = output array for factors | |
372 | * | |
373 | * Returns: A Lim-Lee prime, or null if generation failed. | |
374 | * | |
375 | * Use: Generates Lim-Lee primes. A Lim-Lee prime %$p$% is one which | |
376 | * satisfies %$p = 2 \prod_i q_i + 1$%, where all of the %$q_i$% | |
377 | * are large enough to resist square-root discrete log | |
378 | * algorithms. | |
379 | * | |
380 | * If we succeed, and @f@ is non-null, we write the array of | |
381 | * factors chosen to @f@ for the benefit of the caller. | |
382 | */ | |
383 | ||
04361334 | 384 | mp *limlee(const char *name, mp *d, mp *newp, |
385 | unsigned ql, unsigned pl, grand *r, | |
386 | unsigned on, pgen_proc *oev, void *oec, | |
387 | pgen_proc *iev, void *iec, | |
388 | size_t *nf, mp ***f) | |
389 | { | |
10217a5c | 390 | limlee_stepctx l; |
391 | rabin rr; | |
392 | ||
393 | l.f = 0; if (f) l.f |= LIMLEE_KEEPFACTORS; | |
394 | l.newp = newp; | |
395 | l.pl = pl; l.ql = ql; | |
396 | l.pops = 0; | |
397 | l.iev = iev; | |
398 | l.iec = iec; | |
383e235b | 399 | l.r = r; |
10217a5c | 400 | |
401 | d = pgen(name, d, 0, oev, oec, on, limlee_step, &l, | |
402 | rabin_iters(pl), pgen_test, &rr); | |
403 | ||
b817bfc6 | 404 | if (d && f) { |
10217a5c | 405 | mp **v; |
406 | size_t i; | |
407 | v = xmalloc(l.nf * sizeof(mp *)); | |
408 | for (i = 0; i < l.nf; i++) | |
409 | v[i] = l.v[i].p; | |
410 | xfree(l.v); | |
411 | *f = v; | |
412 | *nf = l.nf; | |
413 | } | |
414 | ||
415 | return (d); | |
04361334 | 416 | } |
417 | ||
d28d625a | 418 | /*----- That's all, folks -------------------------------------------------*/ |