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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: pgen.c,v 1.3 1999/12/10 23:28:35 mdw Exp $ |
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4 | * |
5 | * Finding and testing prime numbers |
6 | * |
7 | * (c) 1999 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: pgen.c,v $ |
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33 | * Revision 1.3 1999/12/10 23:28:35 mdw |
34 | * Track suggested destination changes. |
35 | * |
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36 | * Revision 1.2 1999/11/20 22:23:05 mdw |
37 | * Add multiply-and-add function for Diffie-Hellman safe prime generation. |
38 | * |
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39 | * Revision 1.1 1999/11/19 13:17:57 mdw |
40 | * Prime number generator and tester. |
41 | * |
42 | */ |
43 | |
44 | /*----- Header files ------------------------------------------------------*/ |
45 | |
46 | #include "mp.h" |
47 | #include "mpmont.h" |
48 | #include "pgen.h" |
49 | #include "ptab.h" |
50 | #include "rabin.h" |
51 | |
52 | /*----- Main code ---------------------------------------------------------*/ |
53 | |
54 | /* --- @pgen_create@ --- * |
55 | * |
56 | * Arguments: @pgen *p@ = pointer to prime generation context |
57 | * @mp *m@ = pointer to initial number to test |
58 | * |
59 | * Returns: One of the @PGEN@ constants above. |
60 | * |
61 | * Use: Tests an initial number for primality by computing its |
62 | * residue modulo various small prime numbers. This is fairly |
63 | * quick, but not particularly certain. If a @PGEN_MAYBE@ |
64 | * result is returned, perform Rabin-Miller tests to confirm. |
65 | */ |
66 | |
67 | int pgen_create(pgen *p, mp *m) |
68 | { |
69 | int rc = PGEN_MAYBE; |
70 | int i; |
71 | mp *r = MP_NEW; |
72 | mpw qw; |
73 | mp q; |
74 | |
75 | /* --- Take a copy of the number --- */ |
76 | |
77 | mp_shrink(m); |
78 | p->m = MP_COPY(m); |
79 | |
80 | /* --- Fill in the residues --- */ |
81 | |
82 | mp_build(&q, &qw, &qw + 1); |
83 | for (i = 0; i < NPRIME; i++) { |
84 | qw = ptab[i]; |
85 | mp_div(0, &r, m, &q); |
86 | p->r[i] = r->v[0]; |
87 | if (!p->r[i] && rc == PGEN_MAYBE) { |
88 | if (MP_LEN(m) == 1 && m->v[0] == ptab[i]) |
89 | rc = PGEN_PRIME; |
90 | else |
91 | rc = PGEN_COMPOSITE; |
92 | } |
93 | } |
94 | |
95 | /* --- Done --- */ |
96 | |
97 | mp_drop(r); |
98 | return (rc); |
99 | } |
100 | |
101 | /* --- @pgen_destroy@ --- * |
102 | * |
103 | * Arguments: @pgen *p@ = pointer to prime generation context |
104 | * |
105 | * Returns: --- |
106 | * |
107 | * Use: Discards a context and all the resources it holds. |
108 | */ |
109 | |
110 | void pgen_destroy(pgen *p) |
111 | { |
112 | mp_drop(p->m); |
113 | } |
114 | |
115 | /* --- @pgen_step@ --- * |
116 | * |
117 | * Arguments: @pgen *p@ = pointer to prime generation context |
118 | * @mpw step@ = how much to step the number |
119 | * |
120 | * Returns: One of the @PGEN@ constants above. |
121 | * |
122 | * Use: Steps a number by a small amount. Stepping is much faster |
123 | * than initializing with a new number. The test performed is |
124 | * the same simple one used by @ptab_create@, so @PGEN_MAYBE@ |
125 | * results should be followed up by a Rabin-Miller test. |
126 | */ |
127 | |
128 | int pgen_step(pgen *p, mpw step) |
129 | { |
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130 | int rc = PGEN_MAYBE; |
131 | int i; |
132 | |
133 | /* --- Add the step on to the number --- */ |
134 | |
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135 | p->m = mp_split(p->m); |
136 | mp_ensure(p->m, MP_LEN(p->m) + 1); |
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137 | mpx_uaddn(p->m->v, p->m->vl, step); |
138 | mp_shrink(p->m); |
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139 | |
140 | /* --- Update the residue table --- */ |
141 | |
142 | for (i = 0; i < NPRIME; i++) { |
143 | p->r[i] = (p->r[i] + step) % ptab[i]; |
144 | if (!p->r[i] && rc == PGEN_MAYBE) { |
145 | if (MP_LEN(p->m) == 1 && p->m->v[0] == ptab[i]) |
146 | rc = PGEN_PRIME; |
147 | else |
148 | rc = PGEN_COMPOSITE; |
149 | } |
150 | } |
151 | |
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152 | /* --- Small numbers must be prime --- */ |
153 | |
154 | if (rc == PGEN_MAYBE && MP_LEN(p->m) == 1 && |
155 | p->m->v[0] < MAXPRIME * MAXPRIME) |
156 | rc = PGEN_PRIME; |
157 | |
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158 | /* --- Done --- */ |
159 | |
160 | return (rc); |
161 | } |
162 | |
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163 | /* --- @pgen_muladd@ --- * |
164 | * |
165 | * Arguments: @pgen *p@ = destination prime generation context |
166 | * @const pgen *q@ = source prime generation context |
167 | * @mpw m@ = number to multiply by |
168 | * @mpw a@ = number to add |
169 | * |
170 | * Returns: One of the @PGEN@ constants above. |
171 | * |
172 | * Use: Multiplies the number in a prime generation context by a |
173 | * small value and then adds a small value. The destination |
174 | * should either be uninitialized or the same as the source. |
175 | * |
176 | * Common things to do include multiplying by 2 and adding 0 to |
177 | * turn a prime into a jump for finding other primes with @q@ as |
178 | * a factor of @p - 1@, or multiplying by 2 and adding 1. |
179 | */ |
180 | |
181 | int pgen_muladd(pgen *p, const pgen *q, mpw m, mpw a) |
182 | { |
183 | int rc = PGEN_MAYBE; |
184 | int i; |
185 | |
186 | /* --- Multiply the big number --- */ |
187 | |
188 | { |
189 | mp *d = mp_create(MP_LEN(q->m) + 2); |
190 | mpx_umuln(d->v, d->vl, q->m->v, q->m->vl, m); |
191 | mpx_uaddn(d->v, d->vl, a); |
192 | d->f = q->m->f; |
193 | if (p == q) |
194 | mp_drop(p->m); |
195 | mp_shrink(d); |
196 | p->m = d; |
197 | } |
198 | |
199 | /* --- Gallivant through the residue table --- */ |
200 | |
201 | for (i = 0; i < NPRIME; i++) { |
202 | p->r[i] = (q->r[i] * m + a) % ptab[i]; |
203 | if (!p->r[i] && rc == PGEN_MAYBE) { |
204 | if (MP_LEN(p->m) == 1 && p->m->v[0] == ptab[i]) |
205 | rc = PGEN_PRIME; |
206 | else |
207 | rc = PGEN_COMPOSITE; |
208 | } |
209 | } |
210 | |
211 | /* --- Small numbers must be prime --- */ |
212 | |
213 | if (rc == PGEN_MAYBE && MP_LEN(p->m) == 1 && |
214 | p->m->v[0] < MAXPRIME * MAXPRIME) |
215 | rc = PGEN_PRIME; |
216 | |
217 | /* --- Finished --- */ |
218 | |
219 | return (rc); |
220 | } |
221 | |
222 | |
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223 | /* --- @pgen_jump@ --- * |
224 | * |
225 | * Arguments: @pgen *p@ = pointer to prime generation context |
226 | * @pgen *j@ = pointer to another generation context |
227 | * |
228 | * Returns: One of the @PGEN@ constants above. |
229 | * |
230 | * Use: Steps a number by a large amount. Even so, jumping is much |
231 | * faster than initializing a new number. The test peformed is |
232 | * the same simple one used by @ptab_create@, so @PGEN_MAYBE@ |
233 | * results should be followed up by a Rabin-Miller test. |
234 | * |
235 | * Note that the number stored in the @j@ context is probably |
236 | * better off being even than prime. The important thing is |
237 | * that all of the residues for the number have already been |
238 | * computed. |
239 | */ |
240 | |
241 | int pgen_jump(pgen *p, pgen *j) |
242 | { |
243 | int rc = PGEN_MAYBE; |
244 | int i; |
245 | |
246 | /* --- Add the step on --- */ |
247 | |
248 | p->m = mp_add(p->m, p->m, j->m); |
249 | |
250 | /* --- Update the residue table --- */ |
251 | |
252 | for (i = 0; i < NPRIME; i++) { |
253 | p->r[i] = p->r[i] + j->r[i]; |
254 | if (p->r[i] > ptab[i]) |
255 | p->r[i] -= ptab[i]; |
256 | if (!p->r[i] && rc == PGEN_MAYBE) { |
257 | if (MP_LEN(p->m) == 1 && p->m->v[0] == ptab[i]) |
258 | rc = PGEN_PRIME; |
259 | else |
260 | rc = PGEN_COMPOSITE; |
261 | } |
262 | } |
263 | |
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264 | /* --- Small numbers must be prime --- */ |
265 | |
266 | if (rc == PGEN_MAYBE && MP_LEN(p->m) == 1 && |
267 | p->m->v[0] < MAXPRIME * MAXPRIME) |
268 | rc = PGEN_PRIME; |
269 | |
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270 | /* --- Done --- */ |
271 | |
272 | return (rc); |
273 | } |
274 | |
275 | /*----- Test code ---------------------------------------------------------*/ |
276 | |
277 | #ifdef TEST_RIG |
278 | |
279 | #include <mLib/testrig.h> |
280 | |
281 | static int verify(dstr *v) |
282 | { |
283 | mp *m = *(mp **)v[0].buf; |
284 | mp *r = *(mp **)v[1].buf; |
285 | pgen p; |
286 | mpw gw; |
287 | mp g; |
288 | int rc; |
289 | static char baton[] = "/-\\|"; |
290 | char *b = baton; |
291 | int ok = 1; |
292 | |
293 | mp_build(&g, &gw, &gw + 1); |
294 | rc = pgen_create(&p, m); |
295 | for (;;) { |
296 | if (rc == PGEN_PRIME) |
297 | break; |
298 | if (rc == PGEN_MAYBE) { |
299 | int i; |
300 | rabin r; |
301 | rabin_create(&r, p.m); |
302 | for (i = 0; i < 5; i++) { |
303 | gw = rand(); |
304 | if (rabin_test(&r, &g) == PGEN_COMPOSITE) |
305 | break; |
306 | } |
307 | rabin_destroy(&r); |
308 | if (i == 5) |
309 | break; |
310 | putc(*b++, stderr); |
311 | putc('\b', stderr); |
312 | if (!*b) |
313 | b = baton; |
314 | } |
315 | rc = pgen_step(&p, 2); |
316 | } |
317 | |
318 | if (MP_CMP(p.m, !=, r)) { |
319 | fputs("\n*** failed.", stderr); |
320 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
321 | fputs("\np = ", stderr); mp_writefile(p.m, stderr, 10); |
322 | fputs("\nr = ", stderr); mp_writefile(r, stderr, 10); |
323 | fputc('\n', stderr); |
324 | ok = 0; |
325 | } |
326 | |
327 | mp_drop(m); |
328 | mp_drop(r); |
329 | pgen_destroy(&p); |
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330 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
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331 | return (ok); |
332 | } |
333 | |
334 | static test_chunk tests[] = { |
335 | { "pgen", verify, { &type_mp, &type_mp, 0 } }, |
336 | { 0, 0, { 0 } } |
337 | }; |
338 | |
339 | int main(int argc, char *argv[]) |
340 | { |
341 | sub_init(); |
342 | test_run(argc, argv, tests, SRCDIR "/tests/pgen"); |
343 | return (0); |
344 | } |
345 | |
346 | #endif |
347 | |
348 | /*----- That's all, folks -------------------------------------------------*/ |