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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: limlee.c,v 1.4 2000/08/15 21:45:05 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 1.4 2000/08/15 21:45:05 mdw |
34 | * Use the new trial division equipment in pfilt. This gives a 10% |
35 | * performance improvement in dsa-gen.t. |
36 | * |
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37 | * Revision 1.3 2000/07/29 09:58:32 mdw |
38 | * (limlee): Bug fix. Old versions didn't set the filter step if @ql@ was |
39 | * an exact divisor of @pl@. |
40 | * |
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41 | * Revision 1.2 2000/07/26 18:00:00 mdw |
42 | * No footer line! |
43 | * |
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44 | * Revision 1.1 2000/07/09 21:30:58 mdw |
45 | * Lim-Lee prime generation. |
46 | * |
47 | */ |
48 | |
49 | /*----- Header files ------------------------------------------------------*/ |
50 | |
51 | #include <mLib/alloc.h> |
52 | #include <mLib/dstr.h> |
53 | |
54 | #include "limlee.h" |
55 | #include "mpmul.h" |
56 | #include "mprand.h" |
57 | #include "pgen.h" |
58 | #include "primorial.h" |
59 | #include "rabin.h" |
60 | |
61 | /*----- Main code ---------------------------------------------------------*/ |
62 | |
63 | /* --- @limlee@ --- * |
64 | * |
65 | * Arguments: @const char *name@ = pointer to name root |
66 | * @mp *d@ = pointer to destination integer |
67 | * @mp *newp@ = how to generate factor primes |
68 | * @unsigned ql@ = size of individual factors |
69 | * @unsigned pl@ = size of large prime |
70 | * @grand *r@ = a random number source |
71 | * @unsigned on@ = number of outer attempts to make |
72 | * @pgen_proc *oev@ = outer event handler function |
73 | * @void *oec@ = argument for the outer event handler |
74 | * @pgen_proc *iev@ = inner event handler function |
75 | * @void *iec@ = argument for the inner event handler |
76 | * @size_t *nf@, @mp ***f@ = output array for factors |
77 | * |
78 | * Returns: A Lim-Lee prime, or null if generation failed. |
79 | * |
80 | * Use: Generates Lim-Lee primes. A Lim-Lee prime %$p$% is one which |
81 | * satisfies %$p = 2 \prod_i q_i + 1$%, where all of the %$q_i$% |
82 | * are large enough to resist square-root discrete log |
83 | * algorithms. |
84 | * |
85 | * If we succeed, and @f@ is non-null, we write the array of |
86 | * factors chosen to @f@ for the benefit of the caller. |
87 | */ |
88 | |
89 | static void comb_init(octet *c, unsigned n, unsigned r) |
90 | { |
91 | memset(c, 0, n - r); |
92 | memset(c + (n - r), 1, r); |
93 | } |
94 | |
95 | static int comb_next(octet *c, unsigned n, unsigned r) |
96 | { |
97 | unsigned g = 0; |
98 | |
99 | /* --- How the algorithm works --- * |
100 | * |
101 | * Set bits start at the end and work their way towards the start. |
102 | * Excepting bits already at the start, we scan for the lowest set bit, and |
103 | * move it one place nearer the start. A group of bits at the start are |
104 | * counted and reset just below the `moved' bit. If there is no moved bit |
105 | * then we're done. |
106 | */ |
107 | |
108 | /* --- Count the group at the start --- */ |
109 | |
110 | for (; *c; c++) { |
111 | g++; |
112 | *c = 0; |
113 | } |
114 | if (g == r) |
115 | return (0); |
116 | |
117 | /* --- Move the next bit down one --- * |
118 | * |
119 | * There must be one, because otherwise we'd have counted %$r$% bits |
120 | * earlier. |
121 | */ |
122 | |
123 | for (; !*c; c++) |
124 | ; |
125 | *c = 0; |
126 | g++; |
127 | for (; g; g--) |
128 | *--c = 1; |
129 | return (1); |
130 | } |
131 | |
132 | mp *limlee(const char *name, mp *d, mp *newp, |
133 | unsigned ql, unsigned pl, grand *r, |
134 | unsigned on, pgen_proc *oev, void *oec, |
135 | pgen_proc *iev, void *iec, |
136 | size_t *nf, mp ***f) |
137 | { |
138 | dstr dn = DSTR_INIT; |
139 | unsigned qql; |
140 | mp *qq = 0; |
141 | unsigned nn; |
142 | unsigned mm; |
143 | mp **v; |
144 | octet *c; |
145 | unsigned i; |
146 | unsigned long seq = 0; |
147 | pgen_event ev; |
148 | unsigned ntest; |
149 | rabin rb; |
150 | pgen_filterctx pf; |
151 | |
152 | /* --- First of all, decide on a number of factors to make --- */ |
153 | |
154 | nn = pl/ql; |
155 | qql = pl%ql; |
156 | if (!nn) |
157 | return (0); |
158 | else if (qql && nn > 1) { |
159 | nn--; |
160 | qql += ql; |
161 | } |
162 | |
163 | /* --- Now decide on how many primes I'll actually generate --- * |
164 | * |
165 | * The formula %$m = \max(3 n + 5, 25)$% comes from GPG's prime generation |
166 | * library. |
167 | */ |
168 | |
169 | mm = nn * 3 + 5; |
170 | if (mm < 25) |
171 | mm = 25; |
172 | |
173 | /* --- Now allocate the working memory --- */ |
174 | |
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175 | v = xmalloc(mm * sizeof(mp *)); |
176 | c = xmalloc(mm); |
177 | |
178 | /* --- Initialize everything and try to find a prime --- */ |
179 | |
180 | ev.name = name; |
181 | ev.m = 0; |
182 | ev.steps = on; |
183 | ev.tests = ntest = rabin_iters(pl); |
184 | ev.r = r; |
185 | |
186 | if (oev && oev(PGEN_BEGIN, &ev, oec) == PGEN_ABORT) |
187 | goto fail; |
188 | |
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189 | pf.step = 2; |
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190 | if (qql) { |
191 | dstr_putf(&dn, "%s [+]", name); |
192 | qq = mprand(d, qql, r, 1); |
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193 | qq = pgen(dn.buf, qq, qq, iev, iec, |
194 | 0, pgen_filter, &pf, rabin_iters(qql), pgen_test, &rb); |
195 | } |
196 | |
197 | again: |
198 | comb_init(c, mm, nn); |
199 | for (i = 0; i < mm; i++) |
200 | v[i] = 0; |
201 | |
202 | /* --- The main combinations loop --- */ |
203 | |
204 | do { |
205 | mpmul mmul = MPMUL_INIT; |
206 | |
207 | /* --- Multiply a bunch of primes together --- */ |
208 | |
209 | if (qq) { |
210 | mpmul_add(&mmul, qq); |
211 | } |
212 | for (i = 0; i < mm; i++) { |
213 | if (!c[i]) |
214 | continue; |
215 | if (!v[i]) { |
216 | mp *z; |
217 | |
218 | DRESET(&dn); |
219 | dstr_putf(&dn, "%s [%lu] = ", name, seq++); |
220 | z = mprand(newp, ql, ev.r, 1); |
221 | z = pgen(dn.buf, z, z, iev, iec, |
222 | 0, pgen_filter, &pf, rabin_iters(ql), pgen_test, &rb); |
223 | v[i] = z; |
224 | } |
225 | mpmul_add(&mmul, v[i]); |
226 | } |
227 | |
228 | /* --- Now do some testing --- */ |
229 | |
230 | { |
231 | mp *p = mpmul_done(&mmul); |
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232 | mp *g; |
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233 | int rc; |
234 | |
235 | /* --- Check for small factors --- */ |
236 | |
237 | p = mp_lsl(p, p, 1); |
238 | p = mp_add(p, p, MP_ONE); |
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239 | rc = pfilt_smallfactor(p); |
240 | if (rc == PGEN_FAIL) { |
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241 | mp_drop(p); |
242 | continue; |
243 | } |
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244 | |
245 | /* --- Send an event out --- */ |
246 | |
247 | ev.m = p; |
248 | if (oev && oev(PGEN_TRY, &ev, oec) == PGEN_ABORT) { |
249 | mp_drop(p); |
250 | goto fail; |
251 | } |
252 | |
253 | /* --- Do the Rabin testing --- */ |
254 | |
255 | rabin_create(&rb, p); |
256 | g = MP_NEW; |
257 | do { |
258 | g = mprand_range(g, p, ev.r, 1); |
259 | rc = rabin_test(&rb, g); |
260 | if (rc == PGEN_PASS) { |
261 | ev.tests--; |
262 | if (!ev.tests) |
263 | rc = PGEN_DONE; |
264 | } |
265 | if (oev &&oev(rc, &ev, oec) == PGEN_ABORT) |
266 | rc = PGEN_ABORT; |
267 | } while (rc == PGEN_PASS); |
268 | |
269 | rabin_destroy(&rb); |
270 | mp_drop(g); |
271 | if (rc == PGEN_DONE) |
272 | d = p; |
273 | else |
274 | mp_drop(p); |
275 | if (rc == PGEN_ABORT) |
276 | goto fail; |
277 | if (rc == PGEN_DONE) |
278 | goto done; |
279 | ev.tests = ntest; |
280 | ev.m = 0; |
281 | } |
282 | } while (comb_next(c, mm, nn)); |
283 | |
284 | /* --- That failed --- */ |
285 | |
286 | if (ev.steps) { |
287 | ev.steps--; |
288 | if (!ev.steps) { |
289 | if (oev) |
290 | oev(PGEN_ABORT, &ev, &oec); |
291 | goto fail; |
292 | } |
293 | } |
294 | |
295 | for (i = 0; i < mm; i++) |
296 | mp_drop(v[i]); |
297 | goto again; |
298 | |
299 | /* --- We did it! --- */ |
300 | |
301 | done: { |
302 | mp **vv = 0; |
303 | if (f) { |
304 | if (qq) |
305 | nn++; |
306 | *nf = nn; |
307 | *f = vv = xmalloc(nn * sizeof(mp *)); |
308 | } |
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309 | |
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310 | for (i = 0; i < mm; i++) { |
311 | if (c[i] && vv) |
312 | *vv++ = v[i]; |
313 | else if (v[i]) |
314 | mp_drop(v[i]); |
315 | } |
316 | if (qq) { |
317 | if (vv) |
318 | *vv++ = qq; |
319 | else |
320 | mp_drop(qq); |
321 | } |
322 | xfree(v); |
323 | xfree(c); |
324 | dstr_destroy(&dn); |
325 | return (d); |
326 | } |
327 | |
328 | /* --- We blew it --- */ |
329 | |
330 | fail: |
331 | for (i = 0; i < mm; i++) |
332 | mp_drop(v[i]); |
333 | if (qq) |
334 | mp_drop(qq); |
335 | xfree(v); |
336 | xfree(c); |
337 | dstr_destroy(&dn); |
338 | return (0); |
339 | } |
340 | |
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341 | /*----- That's all, folks -------------------------------------------------*/ |