| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: pgen.c,v 1.2 1999/11/20 22:23:05 mdw Exp $ |
| 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 $ |
| 33 | * Revision 1.2 1999/11/20 22:23:05 mdw |
| 34 | * Add multiply-and-add function for Diffie-Hellman safe prime generation. |
| 35 | * |
| 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 | { |
| 127 | int rc = PGEN_MAYBE; |
| 128 | int i; |
| 129 | |
| 130 | /* --- Add the step on to the number --- */ |
| 131 | |
| 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); |
| 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 | |
| 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 | |
| 154 | /* --- Done --- */ |
| 155 | |
| 156 | return (rc); |
| 157 | } |
| 158 | |
| 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 | |
| 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 | |
| 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 | |
| 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 -------------------------------------------------*/ |