| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * Generate Lim-Lee primes |
| 4 | * |
| 5 | * (c) 2000 Straylight/Edgeware |
| 6 | */ |
| 7 | |
| 8 | /*----- Licensing notice --------------------------------------------------* |
| 9 | * |
| 10 | * This file is part of Catacomb. |
| 11 | * |
| 12 | * Catacomb is free software; you can redistribute it and/or modify |
| 13 | * it under the terms of the GNU Library General Public License as |
| 14 | * published by the Free Software Foundation; either version 2 of the |
| 15 | * License, or (at your option) any later version. |
| 16 | * |
| 17 | * Catacomb is distributed in the hope that it will be useful, |
| 18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 20 | * GNU Library General Public License for more details. |
| 21 | * |
| 22 | * You should have received a copy of the GNU Library General Public |
| 23 | * License along with Catacomb; if not, write to the Free |
| 24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
| 25 | * MA 02111-1307, USA. |
| 26 | */ |
| 27 | |
| 28 | /*----- Header files ------------------------------------------------------*/ |
| 29 | |
| 30 | #include <mLib/alloc.h> |
| 31 | #include <mLib/dstr.h> |
| 32 | |
| 33 | #include "limlee.h" |
| 34 | #include "mpmul.h" |
| 35 | #include "mprand.h" |
| 36 | #include "pgen.h" |
| 37 | #include "rabin.h" |
| 38 | |
| 39 | /*----- Stepping through combinations -------------------------------------*/ |
| 40 | |
| 41 | /* --- @comb_init@ --- * |
| 42 | * |
| 43 | * Arguments: @octet *c@ = pointer to byte-flag array |
| 44 | * @unsigned n@ = number of items in the array |
| 45 | * @unsigned r@ = number of desired items |
| 46 | * |
| 47 | * Returns: --- |
| 48 | * |
| 49 | * Use: Initializes a byte-flag array which, under the control of |
| 50 | * @comb_next@, will step through all combinations of @r@ chosen |
| 51 | * elements. |
| 52 | */ |
| 53 | |
| 54 | static void comb_init(octet *c, unsigned n, unsigned r) |
| 55 | { |
| 56 | memset(c, 0, n - r); |
| 57 | memset(c + (n - r), 1, r); |
| 58 | } |
| 59 | |
| 60 | /* --- @comb_next@ --- * |
| 61 | * |
| 62 | * Arguments: @octet *c@ = pointer to byte-flag array |
| 63 | * @unsigned n@ = number of items in the array |
| 64 | * @unsigned r@ = number of desired items |
| 65 | * |
| 66 | * Returns: Nonzero if another combination was returned, zero if we've |
| 67 | * reached the end. |
| 68 | * |
| 69 | * Use: Steps on to the next combination in sequence. |
| 70 | */ |
| 71 | |
| 72 | static int comb_next(octet *c, unsigned n, unsigned r) |
| 73 | { |
| 74 | unsigned g = 0; |
| 75 | |
| 76 | /* --- How the algorithm works --- * |
| 77 | * |
| 78 | * Set bits start at the end and work their way towards the start. |
| 79 | * Excepting bits already at the start, we scan for the lowest set bit, and |
| 80 | * move it one place nearer the start. A group of bits at the start are |
| 81 | * counted and reset just below the `moved' bit. If there is no moved bit |
| 82 | * then we're done. |
| 83 | */ |
| 84 | |
| 85 | /* --- Count the group at the start --- */ |
| 86 | |
| 87 | for (; *c; c++) { |
| 88 | g++; |
| 89 | *c = 0; |
| 90 | } |
| 91 | if (g == r) |
| 92 | return (0); |
| 93 | |
| 94 | /* --- Move the next bit down one --- * |
| 95 | * |
| 96 | * There must be one, because otherwise we'd have counted %$r$% bits |
| 97 | * earlier. |
| 98 | */ |
| 99 | |
| 100 | for (; !*c; c++) |
| 101 | ; |
| 102 | *c = 0; |
| 103 | g++; |
| 104 | for (; g; g--) |
| 105 | *--c = 1; |
| 106 | return (1); |
| 107 | } |
| 108 | |
| 109 | /*----- Default prime generator -------------------------------------------*/ |
| 110 | |
| 111 | static void llgen(limlee_factor *f, unsigned pl, limlee_stepctx *l) |
| 112 | { |
| 113 | pgen_filterctx pf; |
| 114 | rabin r; |
| 115 | mp *p; |
| 116 | |
| 117 | p = mprand(l->newp, pl, l->r, 1); |
| 118 | pf.step = 2; |
| 119 | p = pgen(l->u.s.name, p, p, l->iev, l->iec, 0, pgen_filter, &pf, |
| 120 | rabin_iters(pl), pgen_test, &r); |
| 121 | f->p = p; |
| 122 | } |
| 123 | |
| 124 | static void llfree(limlee_factor *f, limlee_stepctx *l) |
| 125 | { |
| 126 | mp_drop(f->p); |
| 127 | } |
| 128 | |
| 129 | static const limlee_primeops primeops_simple = { llgen, llfree }; |
| 130 | |
| 131 | /*----- Lim-Lee stepper ---------------------------------------------------*/ |
| 132 | |
| 133 | /* --- @init@ --- * |
| 134 | * |
| 135 | * Arguments: @pgen_event *ev@ = pointer to event block |
| 136 | * @limlee_stepctx *l@ = pointer to Lim-Lee context |
| 137 | * |
| 138 | * Returns: A @PGEN@ result code. |
| 139 | * |
| 140 | * Use: Initializes the stepper. |
| 141 | */ |
| 142 | |
| 143 | static int init(pgen_event *ev, limlee_stepctx *l) |
| 144 | { |
| 145 | size_t i; |
| 146 | |
| 147 | /* --- First of all, decide on a number of factors to make --- */ |
| 148 | |
| 149 | l->nf = l->pl / l->ql; |
| 150 | if (l->nf < 2) return (PGEN_ABORT); |
| 151 | l->nf--; |
| 152 | |
| 153 | /* --- Now decide on how many primes I'll actually generate --- * |
| 154 | * |
| 155 | * The formula %$m = \max(3 n + 5, 25)$% comes from GPG's prime generation |
| 156 | * library. |
| 157 | */ |
| 158 | |
| 159 | l->poolsz = l->nf * 3 + 5; |
| 160 | if (l->poolsz < 25) |
| 161 | l->poolsz = 25; |
| 162 | |
| 163 | /* --- Allocate and initialize the various tables --- */ |
| 164 | |
| 165 | l->c = xmalloc(l->poolsz); |
| 166 | l->v = xmalloc(l->poolsz * sizeof(limlee_factor)); |
| 167 | comb_init(l->c, l->poolsz, l->nf); |
| 168 | for (i = 0; i < l->poolsz; i++) |
| 169 | l->v[i].p = 0; |
| 170 | |
| 171 | /* --- Other bits of initialization --- */ |
| 172 | |
| 173 | l->seq = 0; |
| 174 | if (!l->pops) { |
| 175 | l->pops = &primeops_simple; |
| 176 | l->pc = 0; |
| 177 | } |
| 178 | |
| 179 | /* --- Find a big prime later --- */ |
| 180 | |
| 181 | l->qq.p = 0; |
| 182 | |
| 183 | return (PGEN_TRY); |
| 184 | } |
| 185 | |
| 186 | /* --- @next@ --- * |
| 187 | * |
| 188 | * Arguments: @int rq@ = request which triggered this call |
| 189 | * @pgen_event *ev@ = pointer to event block |
| 190 | * @limlee_stepctx *l@ = pointer to Lim-Lee context |
| 191 | * |
| 192 | * Returns: A @PGEN@ result code. |
| 193 | * |
| 194 | * Use: Initializes the stepper. |
| 195 | */ |
| 196 | |
| 197 | static int next(int rq, pgen_event *ev, limlee_stepctx *l) |
| 198 | { |
| 199 | dstr d = DSTR_INIT; |
| 200 | mp *p = 0; |
| 201 | int rc; |
| 202 | int dist; |
| 203 | unsigned nb; |
| 204 | |
| 205 | mp_drop(ev->m); |
| 206 | |
| 207 | for (;;) { |
| 208 | size_t i; |
| 209 | mpmul mm = MPMUL_INIT; |
| 210 | |
| 211 | /* --- Step on to next combination --- */ |
| 212 | |
| 213 | if (rq == PGEN_TRY && !comb_next(l->c, l->poolsz, l->nf)) { |
| 214 | for (i = 0; i < l->poolsz; i++) { |
| 215 | l->pops->pfree(&l->v[i], l); |
| 216 | l->v[i].p = 0; |
| 217 | } |
| 218 | } |
| 219 | rq = PGEN_TRY; /* For next time through */ |
| 220 | |
| 221 | /* --- If the large factor is performing badly, make a new one --- */ |
| 222 | |
| 223 | if (l->qq.p) { |
| 224 | dist = l->u.s.disp < 0 ? -l->u.s.disp : l->u.s.disp; |
| 225 | if (dist && dist > l->u.s.steps/3) { |
| 226 | l->pops->pfree(&l->qq, l); |
| 227 | l->qq.p = 0; |
| 228 | } |
| 229 | } |
| 230 | |
| 231 | /* --- Gather up some factors --- */ |
| 232 | |
| 233 | if (l->qq.p) mpmul_add(&mm, l->qq.p); |
| 234 | for (i = 0; i < l->poolsz; i++) { |
| 235 | if (!l->c[i]) |
| 236 | continue; |
| 237 | if (!l->v[i].p) { |
| 238 | DRESET(&d); |
| 239 | dstr_putf(&d, "%s_%lu", ev->name, l->seq++); |
| 240 | l->u.s.name = d.buf; |
| 241 | l->pops->pgen(&l->v[i], l->ql, l); |
| 242 | if (!l->v[i].p) |
| 243 | { mp_drop(mpmul_done(&mm)); rc = PGEN_ABORT; goto end; } |
| 244 | } |
| 245 | mpmul_add(&mm, l->v[i].p); |
| 246 | } |
| 247 | |
| 248 | /* --- Check on the large factor --- */ |
| 249 | |
| 250 | p = mpmul_done(&mm); |
| 251 | if (!l->qq.p) { |
| 252 | DRESET(&d); |
| 253 | dstr_putf(&d, "%s*_%lu", ev->name, l->seq++); |
| 254 | l->u.s.name = d.buf; |
| 255 | l->pops->pgen(&l->qq, l->pl - mp_bits(p), l); |
| 256 | if (!l->qq.p) { MP_DROP(p); p = 0; rc = PGEN_ABORT; break; } |
| 257 | l->u.s.steps = l->u.s.disp = 0; |
| 258 | p = mp_mul(p, p, l->qq.p); |
| 259 | } |
| 260 | p = mp_lsl(p, p, 1); |
| 261 | p->v[0] |= 1; |
| 262 | |
| 263 | nb = mp_bits(p); |
| 264 | l->u.s.steps++; |
| 265 | if (nb < l->pl) { |
| 266 | l->u.s.disp--; |
| 267 | continue; |
| 268 | } else if (nb > l->pl) { |
| 269 | l->u.s.disp++; |
| 270 | continue; |
| 271 | } |
| 272 | |
| 273 | /* --- Check it for small factors --- */ |
| 274 | |
| 275 | if ((rc = pfilt_smallfactor(p)) != PGEN_FAIL) |
| 276 | break; |
| 277 | MP_DROP(p); p = 0; |
| 278 | } |
| 279 | |
| 280 | end: |
| 281 | ev->m = p; |
| 282 | DDESTROY(&d); |
| 283 | return (rc); |
| 284 | } |
| 285 | |
| 286 | /* --- @done@ --- * |
| 287 | * |
| 288 | * Arguments: @pgen_event *ev@ = pointer to event block |
| 289 | * @limlee_stepctx *l@ = pointer to Lim-Lee context |
| 290 | * |
| 291 | * Returns: A @PGEN@ result code. |
| 292 | * |
| 293 | * Use: Finalizes the stepper. The output values in the context |
| 294 | * take on their final results; other resources are discarded. |
| 295 | */ |
| 296 | |
| 297 | static int done(pgen_event *ev, limlee_stepctx *l) |
| 298 | { |
| 299 | size_t i, j; |
| 300 | limlee_factor *v; |
| 301 | |
| 302 | /* --- If an output vector of factors is wanted, produce one --- */ |
| 303 | |
| 304 | if (!(l->f & LIMLEE_KEEPFACTORS)) |
| 305 | v = 0; |
| 306 | else { |
| 307 | if (l->qq.p) |
| 308 | l->nf++; |
| 309 | v = xmalloc(l->nf * sizeof(limlee_factor)); |
| 310 | } |
| 311 | |
| 312 | for (i = 0, j = 0; i < l->poolsz; i++) { |
| 313 | if (v && l->c[i]) |
| 314 | v[j++] = l->v[i]; |
| 315 | else if (l->v[i].p) |
| 316 | l->pops->pfree(&l->v[i], l); |
| 317 | } |
| 318 | |
| 319 | if (l->qq.p) { |
| 320 | if (v) |
| 321 | v[j++] = l->qq; |
| 322 | else |
| 323 | l->pops->pfree(&l->qq, l); |
| 324 | } |
| 325 | |
| 326 | xfree(l->v); |
| 327 | l->v = v; |
| 328 | |
| 329 | /* --- Free other resources --- */ |
| 330 | |
| 331 | xfree(l->c); |
| 332 | |
| 333 | /* --- Done --- */ |
| 334 | |
| 335 | return (PGEN_DONE); |
| 336 | } |
| 337 | |
| 338 | /* --- @limlee_step@ --- */ |
| 339 | |
| 340 | int limlee_step(int rq, pgen_event *ev, void *p) |
| 341 | { |
| 342 | limlee_stepctx *l = p; |
| 343 | int rc; |
| 344 | |
| 345 | switch (rq) { |
| 346 | case PGEN_BEGIN: |
| 347 | if ((rc = init(ev, l)) != PGEN_TRY) |
| 348 | return (rc); |
| 349 | case PGEN_TRY: |
| 350 | return (next(rq, ev, l)); |
| 351 | case PGEN_DONE: |
| 352 | return (done(ev, l)); |
| 353 | } |
| 354 | return (PGEN_ABORT); |
| 355 | } |
| 356 | |
| 357 | /*----- Main code ---------------------------------------------------------*/ |
| 358 | |
| 359 | /* --- @limlee@ --- * |
| 360 | * |
| 361 | * Arguments: @const char *name@ = pointer to name root |
| 362 | * @mp *d@ = pointer to destination integer |
| 363 | * @mp *newp@ = how to generate factor primes |
| 364 | * @unsigned ql@ = size of individual factors |
| 365 | * @unsigned pl@ = size of large prime |
| 366 | * @grand *r@ = a random number source |
| 367 | * @unsigned on@ = number of outer attempts to make |
| 368 | * @pgen_proc *oev@ = outer event handler function |
| 369 | * @void *oec@ = argument for the outer event handler |
| 370 | * @pgen_proc *iev@ = inner event handler function |
| 371 | * @void *iec@ = argument for the inner event handler |
| 372 | * @size_t *nf@, @mp ***f@ = output array for factors |
| 373 | * |
| 374 | * Returns: A Lim-Lee prime, or null if generation failed. |
| 375 | * |
| 376 | * Use: Generates Lim-Lee primes. A Lim-Lee prime %$p$% is one which |
| 377 | * satisfies %$p = 2 \prod_i q_i + 1$%, where all of the %$q_i$% |
| 378 | * are large enough to resist square-root discrete log |
| 379 | * algorithms. |
| 380 | * |
| 381 | * If we succeed, and @f@ is non-null, we write the array of |
| 382 | * factors chosen to @f@ for the benefit of the caller. |
| 383 | */ |
| 384 | |
| 385 | mp *limlee(const char *name, mp *d, mp *newp, |
| 386 | unsigned ql, unsigned pl, grand *r, |
| 387 | unsigned on, pgen_proc *oev, void *oec, |
| 388 | pgen_proc *iev, void *iec, |
| 389 | size_t *nf, mp ***f) |
| 390 | { |
| 391 | limlee_stepctx l; |
| 392 | rabin rr; |
| 393 | mp **v; |
| 394 | size_t i; |
| 395 | |
| 396 | l.f = 0; if (f) l.f |= LIMLEE_KEEPFACTORS; |
| 397 | l.newp = newp; |
| 398 | l.pl = pl; l.ql = ql; |
| 399 | l.pops = 0; |
| 400 | l.iev = iev; |
| 401 | l.iec = iec; |
| 402 | l.r = r; |
| 403 | |
| 404 | d = pgen(name, d, 0, oev, oec, on, limlee_step, &l, |
| 405 | rabin_iters(pl), pgen_test, &rr); |
| 406 | |
| 407 | if (f) { |
| 408 | if (!d) { |
| 409 | for (i = 0; i < l.nf; i++) |
| 410 | if (l.v[i].p) llfree(&l.v[i], &l); |
| 411 | } else { |
| 412 | v = xmalloc(l.nf * sizeof(mp *)); |
| 413 | for (i = 0; i < l.nf; i++) |
| 414 | v[i] = l.v[i].p; |
| 415 | xfree(l.v); |
| 416 | *f = v; |
| 417 | *nf = l.nf; |
| 418 | } |
| 419 | } |
| 420 | |
| 421 | return (d); |
| 422 | } |
| 423 | |
| 424 | /*----- That's all, folks -------------------------------------------------*/ |