| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: limlee.c,v 1.4 2000/08/15 21:45:05 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 1.4 2000/08/15 21:45:05 mdw |
| 34 | * Use the new trial division equipment in pfilt. This gives a 10% |
| 35 | * performance improvement in dsa-gen.t. |
| 36 | * |
| 37 | * Revision 1.3 2000/07/29 09:58:32 mdw |
| 38 | * (limlee): Bug fix. Old versions didn't set the filter step if @ql@ was |
| 39 | * an exact divisor of @pl@. |
| 40 | * |
| 41 | * Revision 1.2 2000/07/26 18:00:00 mdw |
| 42 | * No footer line! |
| 43 | * |
| 44 | * Revision 1.1 2000/07/09 21:30:58 mdw |
| 45 | * Lim-Lee prime generation. |
| 46 | * |
| 47 | */ |
| 48 | |
| 49 | /*----- Header files ------------------------------------------------------*/ |
| 50 | |
| 51 | #include <mLib/alloc.h> |
| 52 | #include <mLib/dstr.h> |
| 53 | |
| 54 | #include "limlee.h" |
| 55 | #include "mpmul.h" |
| 56 | #include "mprand.h" |
| 57 | #include "pgen.h" |
| 58 | #include "primorial.h" |
| 59 | #include "rabin.h" |
| 60 | |
| 61 | /*----- Main code ---------------------------------------------------------*/ |
| 62 | |
| 63 | /* --- @limlee@ --- * |
| 64 | * |
| 65 | * Arguments: @const char *name@ = pointer to name root |
| 66 | * @mp *d@ = pointer to destination integer |
| 67 | * @mp *newp@ = how to generate factor primes |
| 68 | * @unsigned ql@ = size of individual factors |
| 69 | * @unsigned pl@ = size of large prime |
| 70 | * @grand *r@ = a random number source |
| 71 | * @unsigned on@ = number of outer attempts to make |
| 72 | * @pgen_proc *oev@ = outer event handler function |
| 73 | * @void *oec@ = argument for the outer event handler |
| 74 | * @pgen_proc *iev@ = inner event handler function |
| 75 | * @void *iec@ = argument for the inner event handler |
| 76 | * @size_t *nf@, @mp ***f@ = output array for factors |
| 77 | * |
| 78 | * Returns: A Lim-Lee prime, or null if generation failed. |
| 79 | * |
| 80 | * Use: Generates Lim-Lee primes. A Lim-Lee prime %$p$% is one which |
| 81 | * satisfies %$p = 2 \prod_i q_i + 1$%, where all of the %$q_i$% |
| 82 | * are large enough to resist square-root discrete log |
| 83 | * algorithms. |
| 84 | * |
| 85 | * If we succeed, and @f@ is non-null, we write the array of |
| 86 | * factors chosen to @f@ for the benefit of the caller. |
| 87 | */ |
| 88 | |
| 89 | static void comb_init(octet *c, unsigned n, unsigned r) |
| 90 | { |
| 91 | memset(c, 0, n - r); |
| 92 | memset(c + (n - r), 1, r); |
| 93 | } |
| 94 | |
| 95 | static int comb_next(octet *c, unsigned n, unsigned r) |
| 96 | { |
| 97 | unsigned g = 0; |
| 98 | |
| 99 | /* --- How the algorithm works --- * |
| 100 | * |
| 101 | * Set bits start at the end and work their way towards the start. |
| 102 | * Excepting bits already at the start, we scan for the lowest set bit, and |
| 103 | * move it one place nearer the start. A group of bits at the start are |
| 104 | * counted and reset just below the `moved' bit. If there is no moved bit |
| 105 | * then we're done. |
| 106 | */ |
| 107 | |
| 108 | /* --- Count the group at the start --- */ |
| 109 | |
| 110 | for (; *c; c++) { |
| 111 | g++; |
| 112 | *c = 0; |
| 113 | } |
| 114 | if (g == r) |
| 115 | return (0); |
| 116 | |
| 117 | /* --- Move the next bit down one --- * |
| 118 | * |
| 119 | * There must be one, because otherwise we'd have counted %$r$% bits |
| 120 | * earlier. |
| 121 | */ |
| 122 | |
| 123 | for (; !*c; c++) |
| 124 | ; |
| 125 | *c = 0; |
| 126 | g++; |
| 127 | for (; g; g--) |
| 128 | *--c = 1; |
| 129 | return (1); |
| 130 | } |
| 131 | |
| 132 | mp *limlee(const char *name, mp *d, mp *newp, |
| 133 | unsigned ql, unsigned pl, grand *r, |
| 134 | unsigned on, pgen_proc *oev, void *oec, |
| 135 | pgen_proc *iev, void *iec, |
| 136 | size_t *nf, mp ***f) |
| 137 | { |
| 138 | dstr dn = DSTR_INIT; |
| 139 | unsigned qql; |
| 140 | mp *qq = 0; |
| 141 | unsigned nn; |
| 142 | unsigned mm; |
| 143 | mp **v; |
| 144 | octet *c; |
| 145 | unsigned i; |
| 146 | unsigned long seq = 0; |
| 147 | pgen_event ev; |
| 148 | unsigned ntest; |
| 149 | rabin rb; |
| 150 | pgen_filterctx pf; |
| 151 | |
| 152 | /* --- First of all, decide on a number of factors to make --- */ |
| 153 | |
| 154 | nn = pl/ql; |
| 155 | qql = pl%ql; |
| 156 | if (!nn) |
| 157 | return (0); |
| 158 | else if (qql && nn > 1) { |
| 159 | nn--; |
| 160 | qql += ql; |
| 161 | } |
| 162 | |
| 163 | /* --- Now decide on how many primes I'll actually generate --- * |
| 164 | * |
| 165 | * The formula %$m = \max(3 n + 5, 25)$% comes from GPG's prime generation |
| 166 | * library. |
| 167 | */ |
| 168 | |
| 169 | mm = nn * 3 + 5; |
| 170 | if (mm < 25) |
| 171 | mm = 25; |
| 172 | |
| 173 | /* --- Now allocate the working memory --- */ |
| 174 | |
| 175 | v = xmalloc(mm * sizeof(mp *)); |
| 176 | c = xmalloc(mm); |
| 177 | |
| 178 | /* --- Initialize everything and try to find a prime --- */ |
| 179 | |
| 180 | ev.name = name; |
| 181 | ev.m = 0; |
| 182 | ev.steps = on; |
| 183 | ev.tests = ntest = rabin_iters(pl); |
| 184 | ev.r = r; |
| 185 | |
| 186 | if (oev && oev(PGEN_BEGIN, &ev, oec) == PGEN_ABORT) |
| 187 | goto fail; |
| 188 | |
| 189 | pf.step = 2; |
| 190 | if (qql) { |
| 191 | dstr_putf(&dn, "%s [+]", name); |
| 192 | qq = mprand(d, qql, r, 1); |
| 193 | qq = pgen(dn.buf, qq, qq, iev, iec, |
| 194 | 0, pgen_filter, &pf, rabin_iters(qql), pgen_test, &rb); |
| 195 | } |
| 196 | |
| 197 | again: |
| 198 | comb_init(c, mm, nn); |
| 199 | for (i = 0; i < mm; i++) |
| 200 | v[i] = 0; |
| 201 | |
| 202 | /* --- The main combinations loop --- */ |
| 203 | |
| 204 | do { |
| 205 | mpmul mmul = MPMUL_INIT; |
| 206 | |
| 207 | /* --- Multiply a bunch of primes together --- */ |
| 208 | |
| 209 | if (qq) { |
| 210 | mpmul_add(&mmul, qq); |
| 211 | } |
| 212 | for (i = 0; i < mm; i++) { |
| 213 | if (!c[i]) |
| 214 | continue; |
| 215 | if (!v[i]) { |
| 216 | mp *z; |
| 217 | |
| 218 | DRESET(&dn); |
| 219 | dstr_putf(&dn, "%s [%lu] = ", name, seq++); |
| 220 | z = mprand(newp, ql, ev.r, 1); |
| 221 | z = pgen(dn.buf, z, z, iev, iec, |
| 222 | 0, pgen_filter, &pf, rabin_iters(ql), pgen_test, &rb); |
| 223 | v[i] = z; |
| 224 | } |
| 225 | mpmul_add(&mmul, v[i]); |
| 226 | } |
| 227 | |
| 228 | /* --- Now do some testing --- */ |
| 229 | |
| 230 | { |
| 231 | mp *p = mpmul_done(&mmul); |
| 232 | mp *g; |
| 233 | int rc; |
| 234 | |
| 235 | /* --- Check for small factors --- */ |
| 236 | |
| 237 | p = mp_lsl(p, p, 1); |
| 238 | p = mp_add(p, p, MP_ONE); |
| 239 | rc = pfilt_smallfactor(p); |
| 240 | if (rc == PGEN_FAIL) { |
| 241 | mp_drop(p); |
| 242 | continue; |
| 243 | } |
| 244 | |
| 245 | /* --- Send an event out --- */ |
| 246 | |
| 247 | ev.m = p; |
| 248 | if (oev && oev(PGEN_TRY, &ev, oec) == PGEN_ABORT) { |
| 249 | mp_drop(p); |
| 250 | goto fail; |
| 251 | } |
| 252 | |
| 253 | /* --- Do the Rabin testing --- */ |
| 254 | |
| 255 | rabin_create(&rb, p); |
| 256 | g = MP_NEW; |
| 257 | do { |
| 258 | g = mprand_range(g, p, ev.r, 1); |
| 259 | rc = rabin_test(&rb, g); |
| 260 | if (rc == PGEN_PASS) { |
| 261 | ev.tests--; |
| 262 | if (!ev.tests) |
| 263 | rc = PGEN_DONE; |
| 264 | } |
| 265 | if (oev &&oev(rc, &ev, oec) == PGEN_ABORT) |
| 266 | rc = PGEN_ABORT; |
| 267 | } while (rc == PGEN_PASS); |
| 268 | |
| 269 | rabin_destroy(&rb); |
| 270 | mp_drop(g); |
| 271 | if (rc == PGEN_DONE) |
| 272 | d = p; |
| 273 | else |
| 274 | mp_drop(p); |
| 275 | if (rc == PGEN_ABORT) |
| 276 | goto fail; |
| 277 | if (rc == PGEN_DONE) |
| 278 | goto done; |
| 279 | ev.tests = ntest; |
| 280 | ev.m = 0; |
| 281 | } |
| 282 | } while (comb_next(c, mm, nn)); |
| 283 | |
| 284 | /* --- That failed --- */ |
| 285 | |
| 286 | if (ev.steps) { |
| 287 | ev.steps--; |
| 288 | if (!ev.steps) { |
| 289 | if (oev) |
| 290 | oev(PGEN_ABORT, &ev, &oec); |
| 291 | goto fail; |
| 292 | } |
| 293 | } |
| 294 | |
| 295 | for (i = 0; i < mm; i++) |
| 296 | mp_drop(v[i]); |
| 297 | goto again; |
| 298 | |
| 299 | /* --- We did it! --- */ |
| 300 | |
| 301 | done: { |
| 302 | mp **vv = 0; |
| 303 | if (f) { |
| 304 | if (qq) |
| 305 | nn++; |
| 306 | *nf = nn; |
| 307 | *f = vv = xmalloc(nn * sizeof(mp *)); |
| 308 | } |
| 309 | |
| 310 | for (i = 0; i < mm; i++) { |
| 311 | if (c[i] && vv) |
| 312 | *vv++ = v[i]; |
| 313 | else if (v[i]) |
| 314 | mp_drop(v[i]); |
| 315 | } |
| 316 | if (qq) { |
| 317 | if (vv) |
| 318 | *vv++ = qq; |
| 319 | else |
| 320 | mp_drop(qq); |
| 321 | } |
| 322 | xfree(v); |
| 323 | xfree(c); |
| 324 | dstr_destroy(&dn); |
| 325 | return (d); |
| 326 | } |
| 327 | |
| 328 | /* --- We blew it --- */ |
| 329 | |
| 330 | fail: |
| 331 | for (i = 0; i < mm; i++) |
| 332 | mp_drop(v[i]); |
| 333 | if (qq) |
| 334 | mp_drop(qq); |
| 335 | xfree(v); |
| 336 | xfree(c); |
| 337 | dstr_destroy(&dn); |
| 338 | return (0); |
| 339 | } |
| 340 | |
| 341 | /*----- That's all, folks -------------------------------------------------*/ |