| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: limlee.c,v 1.1 2000/07/09 21:30:58 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 1.1 2000/07/09 21:30:58 mdw |
| 34 | * Lim-Lee prime generation. |
| 35 | * |
| 36 | */ |
| 37 | |
| 38 | /*----- Header files ------------------------------------------------------*/ |
| 39 | |
| 40 | #include <mLib/alloc.h> |
| 41 | #include <mLib/dstr.h> |
| 42 | |
| 43 | #include "limlee.h" |
| 44 | #include "mpmul.h" |
| 45 | #include "mprand.h" |
| 46 | #include "pgen.h" |
| 47 | #include "primorial.h" |
| 48 | #include "rabin.h" |
| 49 | |
| 50 | /*----- Main code ---------------------------------------------------------*/ |
| 51 | |
| 52 | /* --- @limlee@ --- * |
| 53 | * |
| 54 | * Arguments: @const char *name@ = pointer to name root |
| 55 | * @mp *d@ = pointer to destination integer |
| 56 | * @mp *newp@ = how to generate factor primes |
| 57 | * @unsigned ql@ = size of individual factors |
| 58 | * @unsigned pl@ = size of large prime |
| 59 | * @grand *r@ = a random number source |
| 60 | * @unsigned on@ = number of outer attempts to make |
| 61 | * @pgen_proc *oev@ = outer event handler function |
| 62 | * @void *oec@ = argument for the outer event handler |
| 63 | * @pgen_proc *iev@ = inner event handler function |
| 64 | * @void *iec@ = argument for the inner event handler |
| 65 | * @size_t *nf@, @mp ***f@ = output array for factors |
| 66 | * |
| 67 | * Returns: A Lim-Lee prime, or null if generation failed. |
| 68 | * |
| 69 | * Use: Generates Lim-Lee primes. A Lim-Lee prime %$p$% is one which |
| 70 | * satisfies %$p = 2 \prod_i q_i + 1$%, where all of the %$q_i$% |
| 71 | * are large enough to resist square-root discrete log |
| 72 | * algorithms. |
| 73 | * |
| 74 | * If we succeed, and @f@ is non-null, we write the array of |
| 75 | * factors chosen to @f@ for the benefit of the caller. |
| 76 | */ |
| 77 | |
| 78 | static void comb_init(octet *c, unsigned n, unsigned r) |
| 79 | { |
| 80 | memset(c, 0, n - r); |
| 81 | memset(c + (n - r), 1, r); |
| 82 | } |
| 83 | |
| 84 | static int comb_next(octet *c, unsigned n, unsigned r) |
| 85 | { |
| 86 | unsigned g = 0; |
| 87 | |
| 88 | /* --- How the algorithm works --- * |
| 89 | * |
| 90 | * Set bits start at the end and work their way towards the start. |
| 91 | * Excepting bits already at the start, we scan for the lowest set bit, and |
| 92 | * move it one place nearer the start. A group of bits at the start are |
| 93 | * counted and reset just below the `moved' bit. If there is no moved bit |
| 94 | * then we're done. |
| 95 | */ |
| 96 | |
| 97 | /* --- Count the group at the start --- */ |
| 98 | |
| 99 | for (; *c; c++) { |
| 100 | g++; |
| 101 | *c = 0; |
| 102 | } |
| 103 | if (g == r) |
| 104 | return (0); |
| 105 | |
| 106 | /* --- Move the next bit down one --- * |
| 107 | * |
| 108 | * There must be one, because otherwise we'd have counted %$r$% bits |
| 109 | * earlier. |
| 110 | */ |
| 111 | |
| 112 | for (; !*c; c++) |
| 113 | ; |
| 114 | *c = 0; |
| 115 | g++; |
| 116 | for (; g; g--) |
| 117 | *--c = 1; |
| 118 | return (1); |
| 119 | } |
| 120 | |
| 121 | mp *limlee(const char *name, mp *d, mp *newp, |
| 122 | unsigned ql, unsigned pl, grand *r, |
| 123 | unsigned on, pgen_proc *oev, void *oec, |
| 124 | pgen_proc *iev, void *iec, |
| 125 | size_t *nf, mp ***f) |
| 126 | { |
| 127 | dstr dn = DSTR_INIT; |
| 128 | unsigned qql; |
| 129 | mp *qq = 0; |
| 130 | unsigned nn; |
| 131 | unsigned mm; |
| 132 | mp **v; |
| 133 | octet *c; |
| 134 | unsigned i; |
| 135 | unsigned long seq = 0; |
| 136 | pgen_event ev; |
| 137 | unsigned ntest; |
| 138 | rabin rb; |
| 139 | pgen_filterctx pf; |
| 140 | |
| 141 | /* --- First of all, decide on a number of factors to make --- */ |
| 142 | |
| 143 | nn = pl/ql; |
| 144 | qql = pl%ql; |
| 145 | if (!nn) |
| 146 | return (0); |
| 147 | else if (qql && nn > 1) { |
| 148 | nn--; |
| 149 | qql += ql; |
| 150 | } |
| 151 | |
| 152 | /* --- Now decide on how many primes I'll actually generate --- * |
| 153 | * |
| 154 | * The formula %$m = \max(3 n + 5, 25)$% comes from GPG's prime generation |
| 155 | * library. |
| 156 | */ |
| 157 | |
| 158 | mm = nn * 3 + 5; |
| 159 | if (mm < 25) |
| 160 | mm = 25; |
| 161 | |
| 162 | /* --- Now allocate the working memory --- */ |
| 163 | |
| 164 | primorial_setup(); |
| 165 | v = xmalloc(mm * sizeof(mp *)); |
| 166 | c = xmalloc(mm); |
| 167 | |
| 168 | /* --- Initialize everything and try to find a prime --- */ |
| 169 | |
| 170 | ev.name = name; |
| 171 | ev.m = 0; |
| 172 | ev.steps = on; |
| 173 | ev.tests = ntest = rabin_iters(pl); |
| 174 | ev.r = r; |
| 175 | |
| 176 | if (oev && oev(PGEN_BEGIN, &ev, oec) == PGEN_ABORT) |
| 177 | goto fail; |
| 178 | |
| 179 | if (qql) { |
| 180 | dstr_putf(&dn, "%s [+]", name); |
| 181 | qq = mprand(d, qql, r, 1); |
| 182 | pf.step = 2; |
| 183 | qq = pgen(dn.buf, qq, qq, iev, iec, |
| 184 | 0, pgen_filter, &pf, rabin_iters(qql), pgen_test, &rb); |
| 185 | } |
| 186 | |
| 187 | again: |
| 188 | comb_init(c, mm, nn); |
| 189 | for (i = 0; i < mm; i++) |
| 190 | v[i] = 0; |
| 191 | |
| 192 | /* --- The main combinations loop --- */ |
| 193 | |
| 194 | do { |
| 195 | mpmul mmul = MPMUL_INIT; |
| 196 | |
| 197 | /* --- Multiply a bunch of primes together --- */ |
| 198 | |
| 199 | if (qq) { |
| 200 | mpmul_add(&mmul, qq); |
| 201 | } |
| 202 | for (i = 0; i < mm; i++) { |
| 203 | if (!c[i]) |
| 204 | continue; |
| 205 | if (!v[i]) { |
| 206 | mp *z; |
| 207 | |
| 208 | DRESET(&dn); |
| 209 | dstr_putf(&dn, "%s [%lu] = ", name, seq++); |
| 210 | z = mprand(newp, ql, ev.r, 1); |
| 211 | z = pgen(dn.buf, z, z, iev, iec, |
| 212 | 0, pgen_filter, &pf, rabin_iters(ql), pgen_test, &rb); |
| 213 | v[i] = z; |
| 214 | } |
| 215 | mpmul_add(&mmul, v[i]); |
| 216 | } |
| 217 | |
| 218 | /* --- Now do some testing --- */ |
| 219 | |
| 220 | { |
| 221 | mp *p = mpmul_done(&mmul); |
| 222 | mp *g = newp; |
| 223 | int rc; |
| 224 | |
| 225 | /* --- Check for small factors --- */ |
| 226 | |
| 227 | p = mp_lsl(p, p, 1); |
| 228 | p = mp_add(p, p, MP_ONE); |
| 229 | mp_gcd(&g, 0, 0, p, primorial); |
| 230 | if (MP_CMP(g, !=, MP_ONE)) { |
| 231 | mp_drop(g); |
| 232 | mp_drop(p); |
| 233 | continue; |
| 234 | } |
| 235 | mp_drop(g); |
| 236 | |
| 237 | /* --- Send an event out --- */ |
| 238 | |
| 239 | ev.m = p; |
| 240 | if (oev && oev(PGEN_TRY, &ev, oec) == PGEN_ABORT) { |
| 241 | mp_drop(p); |
| 242 | goto fail; |
| 243 | } |
| 244 | |
| 245 | /* --- Do the Rabin testing --- */ |
| 246 | |
| 247 | rabin_create(&rb, p); |
| 248 | g = MP_NEW; |
| 249 | do { |
| 250 | g = mprand_range(g, p, ev.r, 1); |
| 251 | rc = rabin_test(&rb, g); |
| 252 | if (rc == PGEN_PASS) { |
| 253 | ev.tests--; |
| 254 | if (!ev.tests) |
| 255 | rc = PGEN_DONE; |
| 256 | } |
| 257 | if (oev &&oev(rc, &ev, oec) == PGEN_ABORT) |
| 258 | rc = PGEN_ABORT; |
| 259 | } while (rc == PGEN_PASS); |
| 260 | |
| 261 | rabin_destroy(&rb); |
| 262 | mp_drop(g); |
| 263 | if (rc == PGEN_DONE) |
| 264 | d = p; |
| 265 | else |
| 266 | mp_drop(p); |
| 267 | if (rc == PGEN_ABORT) |
| 268 | goto fail; |
| 269 | if (rc == PGEN_DONE) |
| 270 | goto done; |
| 271 | ev.tests = ntest; |
| 272 | ev.m = 0; |
| 273 | } |
| 274 | } while (comb_next(c, mm, nn)); |
| 275 | |
| 276 | /* --- That failed --- */ |
| 277 | |
| 278 | if (ev.steps) { |
| 279 | ev.steps--; |
| 280 | if (!ev.steps) { |
| 281 | if (oev) |
| 282 | oev(PGEN_ABORT, &ev, &oec); |
| 283 | goto fail; |
| 284 | } |
| 285 | } |
| 286 | |
| 287 | for (i = 0; i < mm; i++) |
| 288 | mp_drop(v[i]); |
| 289 | goto again; |
| 290 | |
| 291 | /* --- We did it! --- */ |
| 292 | |
| 293 | done: { |
| 294 | mp **vv = 0; |
| 295 | if (f) { |
| 296 | if (qq) |
| 297 | nn++; |
| 298 | *nf = nn; |
| 299 | *f = vv = xmalloc(nn * sizeof(mp *)); |
| 300 | } |
| 301 | |
| 302 | for (i = 0; i < mm; i++) { |
| 303 | if (c[i] && vv) |
| 304 | *vv++ = v[i]; |
| 305 | else if (v[i]) |
| 306 | mp_drop(v[i]); |
| 307 | } |
| 308 | if (qq) { |
| 309 | if (vv) |
| 310 | *vv++ = qq; |
| 311 | else |
| 312 | mp_drop(qq); |
| 313 | } |
| 314 | xfree(v); |
| 315 | xfree(c); |
| 316 | dstr_destroy(&dn); |
| 317 | return (d); |
| 318 | } |
| 319 | |
| 320 | /* --- We blew it --- */ |
| 321 | |
| 322 | fail: |
| 323 | for (i = 0; i < mm; i++) |
| 324 | mp_drop(v[i]); |
| 325 | if (qq) |
| 326 | mp_drop(qq); |
| 327 | xfree(v); |
| 328 | xfree(c); |
| 329 | dstr_destroy(&dn); |
| 330 | return (0); |
| 331 | } |
| 332 | |