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