04361334 |
1 | /* -*-c-*- |
2 | * |
3 | * $Id: limlee.c,v 1.1 2000/07/09 21:30:58 mdw Exp $ |
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 $ |
33 | * Revision 1.1 2000/07/09 21:30:58 mdw |
34 | * Lim-Lee prime generation. |
35 | * |
36 | */ |
37 | |
38 | /*----- Header files ------------------------------------------------------*/ |
39 | |
40 | #include <mLib/alloc.h> |
41 | #include <mLib/dstr.h> |
42 | |
43 | #include "limlee.h" |
44 | #include "mpmul.h" |
45 | #include "mprand.h" |
46 | #include "pgen.h" |
47 | #include "primorial.h" |
48 | #include "rabin.h" |
49 | |
50 | /*----- Main code ---------------------------------------------------------*/ |
51 | |
52 | /* --- @limlee@ --- * |
53 | * |
54 | * Arguments: @const char *name@ = pointer to name root |
55 | * @mp *d@ = pointer to destination integer |
56 | * @mp *newp@ = how to generate factor primes |
57 | * @unsigned ql@ = size of individual factors |
58 | * @unsigned pl@ = size of large prime |
59 | * @grand *r@ = a random number source |
60 | * @unsigned on@ = number of outer attempts to make |
61 | * @pgen_proc *oev@ = outer event handler function |
62 | * @void *oec@ = argument for the outer event handler |
63 | * @pgen_proc *iev@ = inner event handler function |
64 | * @void *iec@ = argument for the inner event handler |
65 | * @size_t *nf@, @mp ***f@ = output array for factors |
66 | * |
67 | * Returns: A Lim-Lee prime, or null if generation failed. |
68 | * |
69 | * Use: Generates Lim-Lee primes. A Lim-Lee prime %$p$% is one which |
70 | * satisfies %$p = 2 \prod_i q_i + 1$%, where all of the %$q_i$% |
71 | * are large enough to resist square-root discrete log |
72 | * algorithms. |
73 | * |
74 | * If we succeed, and @f@ is non-null, we write the array of |
75 | * factors chosen to @f@ for the benefit of the caller. |
76 | */ |
77 | |
78 | static void comb_init(octet *c, unsigned n, unsigned r) |
79 | { |
80 | memset(c, 0, n - r); |
81 | memset(c + (n - r), 1, r); |
82 | } |
83 | |
84 | static int comb_next(octet *c, unsigned n, unsigned r) |
85 | { |
86 | unsigned g = 0; |
87 | |
88 | /* --- How the algorithm works --- * |
89 | * |
90 | * Set bits start at the end and work their way towards the start. |
91 | * Excepting bits already at the start, we scan for the lowest set bit, and |
92 | * move it one place nearer the start. A group of bits at the start are |
93 | * counted and reset just below the `moved' bit. If there is no moved bit |
94 | * then we're done. |
95 | */ |
96 | |
97 | /* --- Count the group at the start --- */ |
98 | |
99 | for (; *c; c++) { |
100 | g++; |
101 | *c = 0; |
102 | } |
103 | if (g == r) |
104 | return (0); |
105 | |
106 | /* --- Move the next bit down one --- * |
107 | * |
108 | * There must be one, because otherwise we'd have counted %$r$% bits |
109 | * earlier. |
110 | */ |
111 | |
112 | for (; !*c; c++) |
113 | ; |
114 | *c = 0; |
115 | g++; |
116 | for (; g; g--) |
117 | *--c = 1; |
118 | return (1); |
119 | } |
120 | |
121 | mp *limlee(const char *name, mp *d, mp *newp, |
122 | unsigned ql, unsigned pl, grand *r, |
123 | unsigned on, pgen_proc *oev, void *oec, |
124 | pgen_proc *iev, void *iec, |
125 | size_t *nf, mp ***f) |
126 | { |
127 | dstr dn = DSTR_INIT; |
128 | unsigned qql; |
129 | mp *qq = 0; |
130 | unsigned nn; |
131 | unsigned mm; |
132 | mp **v; |
133 | octet *c; |
134 | unsigned i; |
135 | unsigned long seq = 0; |
136 | pgen_event ev; |
137 | unsigned ntest; |
138 | rabin rb; |
139 | pgen_filterctx pf; |
140 | |
141 | /* --- First of all, decide on a number of factors to make --- */ |
142 | |
143 | nn = pl/ql; |
144 | qql = pl%ql; |
145 | if (!nn) |
146 | return (0); |
147 | else if (qql && nn > 1) { |
148 | nn--; |
149 | qql += ql; |
150 | } |
151 | |
152 | /* --- Now decide on how many primes I'll actually generate --- * |
153 | * |
154 | * The formula %$m = \max(3 n + 5, 25)$% comes from GPG's prime generation |
155 | * library. |
156 | */ |
157 | |
158 | mm = nn * 3 + 5; |
159 | if (mm < 25) |
160 | mm = 25; |
161 | |
162 | /* --- Now allocate the working memory --- */ |
163 | |
164 | primorial_setup(); |
165 | v = xmalloc(mm * sizeof(mp *)); |
166 | c = xmalloc(mm); |
167 | |
168 | /* --- Initialize everything and try to find a prime --- */ |
169 | |
170 | ev.name = name; |
171 | ev.m = 0; |
172 | ev.steps = on; |
173 | ev.tests = ntest = rabin_iters(pl); |
174 | ev.r = r; |
175 | |
176 | if (oev && oev(PGEN_BEGIN, &ev, oec) == PGEN_ABORT) |
177 | goto fail; |
178 | |
179 | if (qql) { |
180 | dstr_putf(&dn, "%s [+]", name); |
181 | qq = mprand(d, qql, r, 1); |
182 | pf.step = 2; |
183 | qq = pgen(dn.buf, qq, qq, iev, iec, |
184 | 0, pgen_filter, &pf, rabin_iters(qql), pgen_test, &rb); |
185 | } |
186 | |
187 | again: |
188 | comb_init(c, mm, nn); |
189 | for (i = 0; i < mm; i++) |
190 | v[i] = 0; |
191 | |
192 | /* --- The main combinations loop --- */ |
193 | |
194 | do { |
195 | mpmul mmul = MPMUL_INIT; |
196 | |
197 | /* --- Multiply a bunch of primes together --- */ |
198 | |
199 | if (qq) { |
200 | mpmul_add(&mmul, qq); |
201 | } |
202 | for (i = 0; i < mm; i++) { |
203 | if (!c[i]) |
204 | continue; |
205 | if (!v[i]) { |
206 | mp *z; |
207 | |
208 | DRESET(&dn); |
209 | dstr_putf(&dn, "%s [%lu] = ", name, seq++); |
210 | z = mprand(newp, ql, ev.r, 1); |
211 | z = pgen(dn.buf, z, z, iev, iec, |
212 | 0, pgen_filter, &pf, rabin_iters(ql), pgen_test, &rb); |
213 | v[i] = z; |
214 | } |
215 | mpmul_add(&mmul, v[i]); |
216 | } |
217 | |
218 | /* --- Now do some testing --- */ |
219 | |
220 | { |
221 | mp *p = mpmul_done(&mmul); |
222 | mp *g = newp; |
223 | int rc; |
224 | |
225 | /* --- Check for small factors --- */ |
226 | |
227 | p = mp_lsl(p, p, 1); |
228 | p = mp_add(p, p, MP_ONE); |
229 | mp_gcd(&g, 0, 0, p, primorial); |
230 | if (MP_CMP(g, !=, MP_ONE)) { |
231 | mp_drop(g); |
232 | mp_drop(p); |
233 | continue; |
234 | } |
235 | mp_drop(g); |
236 | |
237 | /* --- Send an event out --- */ |
238 | |
239 | ev.m = p; |
240 | if (oev && oev(PGEN_TRY, &ev, oec) == PGEN_ABORT) { |
241 | mp_drop(p); |
242 | goto fail; |
243 | } |
244 | |
245 | /* --- Do the Rabin testing --- */ |
246 | |
247 | rabin_create(&rb, p); |
248 | g = MP_NEW; |
249 | do { |
250 | g = mprand_range(g, p, ev.r, 1); |
251 | rc = rabin_test(&rb, g); |
252 | if (rc == PGEN_PASS) { |
253 | ev.tests--; |
254 | if (!ev.tests) |
255 | rc = PGEN_DONE; |
256 | } |
257 | if (oev &&oev(rc, &ev, oec) == PGEN_ABORT) |
258 | rc = PGEN_ABORT; |
259 | } while (rc == PGEN_PASS); |
260 | |
261 | rabin_destroy(&rb); |
262 | mp_drop(g); |
263 | if (rc == PGEN_DONE) |
264 | d = p; |
265 | else |
266 | mp_drop(p); |
267 | if (rc == PGEN_ABORT) |
268 | goto fail; |
269 | if (rc == PGEN_DONE) |
270 | goto done; |
271 | ev.tests = ntest; |
272 | ev.m = 0; |
273 | } |
274 | } while (comb_next(c, mm, nn)); |
275 | |
276 | /* --- That failed --- */ |
277 | |
278 | if (ev.steps) { |
279 | ev.steps--; |
280 | if (!ev.steps) { |
281 | if (oev) |
282 | oev(PGEN_ABORT, &ev, &oec); |
283 | goto fail; |
284 | } |
285 | } |
286 | |
287 | for (i = 0; i < mm; i++) |
288 | mp_drop(v[i]); |
289 | goto again; |
290 | |
291 | /* --- We did it! --- */ |
292 | |
293 | done: { |
294 | mp **vv = 0; |
295 | if (f) { |
296 | if (qq) |
297 | nn++; |
298 | *nf = nn; |
299 | *f = vv = xmalloc(nn * sizeof(mp *)); |
300 | } |
301 | |
302 | for (i = 0; i < mm; i++) { |
303 | if (c[i] && vv) |
304 | *vv++ = v[i]; |
305 | else if (v[i]) |
306 | mp_drop(v[i]); |
307 | } |
308 | if (qq) { |
309 | if (vv) |
310 | *vv++ = qq; |
311 | else |
312 | mp_drop(qq); |
313 | } |
314 | xfree(v); |
315 | xfree(c); |
316 | dstr_destroy(&dn); |
317 | return (d); |
318 | } |
319 | |
320 | /* --- We blew it --- */ |
321 | |
322 | fail: |
323 | for (i = 0; i < mm; i++) |
324 | mp_drop(v[i]); |
325 | if (qq) |
326 | mp_drop(qq); |
327 | xfree(v); |
328 | xfree(c); |
329 | dstr_destroy(&dn); |
330 | return (0); |
331 | } |
332 | |