| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: mpbarrett.c,v 1.7 2001/04/19 18:25:26 mdw Exp $ |
| 4 | * |
| 5 | * Barrett modular reduction |
| 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: mpbarrett.c,v $ |
| 33 | * Revision 1.7 2001/04/19 18:25:26 mdw |
| 34 | * Use sliding-window exponentiation. |
| 35 | * |
| 36 | * Revision 1.6 2000/10/08 12:03:44 mdw |
| 37 | * (mpbarrett_reduce): Cope with negative numbers. |
| 38 | * |
| 39 | * Revision 1.5 2000/07/29 17:04:33 mdw |
| 40 | * Change to use left-to-right bitwise exponentiation. This will improve |
| 41 | * performance when the base is small. |
| 42 | * |
| 43 | * Revision 1.4 2000/06/17 11:45:09 mdw |
| 44 | * Major memory management overhaul. Added arena support. Use the secure |
| 45 | * arena for secret integers. Replace and improve the MP management macros |
| 46 | * (e.g., replace MP_MODIFY by MP_DEST). |
| 47 | * |
| 48 | * Revision 1.3 1999/12/12 15:08:52 mdw |
| 49 | * Don't bother shifting %$q$% in @mpbarrett_reduce@, just skip the least |
| 50 | * significant digits. |
| 51 | * |
| 52 | * Revision 1.2 1999/12/11 01:50:56 mdw |
| 53 | * Improve initialization slightly. |
| 54 | * |
| 55 | * Revision 1.1 1999/12/10 23:21:59 mdw |
| 56 | * Barrett reduction support: works with even moduli. |
| 57 | * |
| 58 | */ |
| 59 | |
| 60 | /*----- Header files ------------------------------------------------------*/ |
| 61 | |
| 62 | #include "mp.h" |
| 63 | #include "mpbarrett.h" |
| 64 | |
| 65 | /*----- Main code ---------------------------------------------------------*/ |
| 66 | |
| 67 | /* --- @mpbarrett_create@ --- * |
| 68 | * |
| 69 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
| 70 | * @mp *m@ = modulus to work to |
| 71 | * |
| 72 | * |
| 73 | * Returns: --- |
| 74 | * |
| 75 | * Use: Initializes a Barrett reduction context ready for use. |
| 76 | */ |
| 77 | |
| 78 | void mpbarrett_create(mpbarrett *mb, mp *m) |
| 79 | { |
| 80 | mp *b; |
| 81 | |
| 82 | /* --- Validate the arguments --- */ |
| 83 | |
| 84 | assert(((void)"Barrett modulus must be positive", (m->f & MP_NEG) == 0)); |
| 85 | |
| 86 | /* --- Compute %$\mu$% --- */ |
| 87 | |
| 88 | mp_shrink(m); |
| 89 | mb->k = MP_LEN(m); |
| 90 | mb->m = MP_COPY(m); |
| 91 | b = mp_new(2 * mb->k + 1, 0); |
| 92 | MPX_ZERO(b->v, b->vl - 1); |
| 93 | b->vl[-1] = 1; |
| 94 | mp_div(&b, 0, b, m); |
| 95 | mb->mu = b; |
| 96 | } |
| 97 | |
| 98 | /* --- @mpbarrett_destroy@ --- * |
| 99 | * |
| 100 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
| 101 | * |
| 102 | * Returns: --- |
| 103 | * |
| 104 | * Use: Destroys a Barrett reduction context releasing any resources |
| 105 | * claimed. |
| 106 | */ |
| 107 | |
| 108 | void mpbarrett_destroy(mpbarrett *mb) |
| 109 | { |
| 110 | mp_drop(mb->m); |
| 111 | mp_drop(mb->mu); |
| 112 | } |
| 113 | |
| 114 | /* --- @mpbarrett_reduce@ --- * |
| 115 | * |
| 116 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
| 117 | * @mp *d@ = destination for result |
| 118 | * @mp *m@ = number to reduce |
| 119 | * |
| 120 | * Returns: The residue of @m@ modulo the number in the reduction |
| 121 | * context. |
| 122 | * |
| 123 | * Use: Performs an efficient modular reduction. |
| 124 | */ |
| 125 | |
| 126 | mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m) |
| 127 | { |
| 128 | mp *q; |
| 129 | size_t k = mb->k; |
| 130 | |
| 131 | /* --- Special case if @m@ is too small --- */ |
| 132 | |
| 133 | if (MP_LEN(m) < k) { |
| 134 | m = MP_COPY(m); |
| 135 | if (d) |
| 136 | MP_DROP(d); |
| 137 | return (m); |
| 138 | } |
| 139 | |
| 140 | /* --- First stage --- */ |
| 141 | |
| 142 | { |
| 143 | mp qq; |
| 144 | mp_build(&qq, m->v + (k - 1), m->vl); |
| 145 | q = mp_mul(MP_NEW, &qq, mb->mu); |
| 146 | if (MP_LEN(q) <= k) { |
| 147 | m = MP_COPY(m); |
| 148 | if (d) |
| 149 | MP_DROP(d); |
| 150 | return (m); |
| 151 | } |
| 152 | } |
| 153 | |
| 154 | /* --- Second stage --- */ |
| 155 | |
| 156 | { |
| 157 | mp *r; |
| 158 | mpw *mvl; |
| 159 | |
| 160 | MP_COPY(m); |
| 161 | if (MP_LEN(m) <= k + 1) |
| 162 | mvl = m->vl; |
| 163 | else |
| 164 | mvl = m->v + k + 1; |
| 165 | r = mp_new(k + 1, (q->f | mb->m->f) & MP_BURN); |
| 166 | mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl); |
| 167 | MP_DEST(d, k + 1, r->f); |
| 168 | mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl); |
| 169 | d->f = (m->f | r->f) & (MP_BURN | MP_NEG); |
| 170 | MP_DROP(r); |
| 171 | MP_DROP(q); |
| 172 | MP_DROP(m); |
| 173 | } |
| 174 | |
| 175 | /* --- Final stage --- */ |
| 176 | |
| 177 | MP_SHRINK(d); |
| 178 | while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl)) |
| 179 | mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl); |
| 180 | |
| 181 | /* --- Fix up the sign --- */ |
| 182 | |
| 183 | if (d->f & MP_NEG) { |
| 184 | mpx_usub(d->v, d->vl, mb->m->v, mb->m->vl, d->v, d->vl); |
| 185 | d->f &= ~MP_NEG; |
| 186 | } |
| 187 | |
| 188 | MP_SHRINK(d); |
| 189 | return (d); |
| 190 | } |
| 191 | |
| 192 | /* --- @mpbarrett_exp@ --- * |
| 193 | * |
| 194 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
| 195 | * @mp *d@ = fake destination |
| 196 | * @mp *a@ = base |
| 197 | * @mp *e@ = exponent |
| 198 | * |
| 199 | * Returns: Result, %$a^e \bmod m$%. |
| 200 | */ |
| 201 | |
| 202 | #define WINSZ 5 |
| 203 | #define TABSZ (1 << (WINSZ - 1)) |
| 204 | |
| 205 | #define THRESH (((MPW_BITS / WINSZ) << 2) + 1) |
| 206 | |
| 207 | static mp *exp_simple(mpbarrett *mb, mp *d, mp *a, mp *e) |
| 208 | { |
| 209 | mpscan sc; |
| 210 | mp *x = MP_ONE; |
| 211 | mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW; |
| 212 | unsigned sq = 0; |
| 213 | |
| 214 | a = MP_COPY(a); |
| 215 | mp_rscan(&sc, e); |
| 216 | if (!MP_RSTEP(&sc)) |
| 217 | goto exit; |
| 218 | while (!MP_RBIT(&sc)) |
| 219 | MP_RSTEP(&sc); |
| 220 | |
| 221 | /* --- Do the main body of the work --- */ |
| 222 | |
| 223 | for (;;) { |
| 224 | sq++; |
| 225 | while (sq) { |
| 226 | mp *y; |
| 227 | y = mp_sqr(spare, x); |
| 228 | y = mpbarrett_reduce(mb, y, y); |
| 229 | spare = x; x = y; |
| 230 | sq--; |
| 231 | } |
| 232 | { |
| 233 | mp *y = mp_mul(spare, x, a); |
| 234 | y = mpbarrett_reduce(mb, y, y); |
| 235 | spare = x; x = y; |
| 236 | } |
| 237 | for (;;) { |
| 238 | if (!MP_RSTEP(&sc)) |
| 239 | goto done; |
| 240 | if (MP_RBIT(&sc)) |
| 241 | break; |
| 242 | sq++; |
| 243 | } |
| 244 | } |
| 245 | |
| 246 | /* --- Do a final round of squaring --- */ |
| 247 | |
| 248 | done: |
| 249 | while (sq) { |
| 250 | mp *y; |
| 251 | y = mp_sqr(spare, x); |
| 252 | y = mpbarrett_reduce(mb, y, y); |
| 253 | spare = x; x = y; |
| 254 | sq--; |
| 255 | } |
| 256 | |
| 257 | exit: |
| 258 | MP_DROP(a); |
| 259 | if (spare != MP_NEW) |
| 260 | MP_DROP(spare); |
| 261 | if (d != MP_NEW) |
| 262 | MP_DROP(d); |
| 263 | return (x); |
| 264 | } |
| 265 | |
| 266 | mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e) |
| 267 | { |
| 268 | mp **tab; |
| 269 | mp *a2; |
| 270 | mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW; |
| 271 | mp *x = MP_ONE; |
| 272 | unsigned i, sq = 0; |
| 273 | mpscan sc; |
| 274 | |
| 275 | /* --- Do we bother? --- */ |
| 276 | |
| 277 | MP_SHRINK(e); |
| 278 | if (MP_LEN(e) == 0) |
| 279 | goto exit; |
| 280 | if (MP_LEN(e) < THRESH) { |
| 281 | x->ref--; |
| 282 | return (exp_simple(mb, d, a, e)); |
| 283 | } |
| 284 | |
| 285 | /* --- Do the precomputation --- */ |
| 286 | |
| 287 | a2 = mp_sqr(MP_NEW, a); |
| 288 | a2 = mpbarrett_reduce(mb, a2, a2); |
| 289 | tab = xmalloc(TABSZ * sizeof(mp *)); |
| 290 | tab[0] = MP_COPY(a); |
| 291 | for (i = 1; i < TABSZ; i++) { |
| 292 | mp *x = mp_mul(MP_NEW, tab[i - 1], a2); |
| 293 | tab[i] = mpbarrett_reduce(mb, x, x); |
| 294 | } |
| 295 | mp_drop(a2); |
| 296 | mp_rscan(&sc, e); |
| 297 | |
| 298 | /* --- Skip top-end zero bits --- * |
| 299 | * |
| 300 | * If the initial step worked, there must be a set bit somewhere, so keep |
| 301 | * stepping until I find it. |
| 302 | */ |
| 303 | |
| 304 | MP_RSTEP(&sc); |
| 305 | while (!MP_RBIT(&sc)) |
| 306 | MP_RSTEP(&sc); |
| 307 | |
| 308 | /* --- Now for the main work --- */ |
| 309 | |
| 310 | for (;;) { |
| 311 | unsigned l = 0; |
| 312 | unsigned z = 0; |
| 313 | |
| 314 | /* --- The next bit is set, so read a window index --- * |
| 315 | * |
| 316 | * Reset @i@ to zero and increment @sq@. Then, until either I read |
| 317 | * @WINSZ@ bits or I run out of bits, scan in a bit: if it's clear, bump |
| 318 | * the @z@ counter; if it's set, push a set bit into @i@, shift it over |
| 319 | * by @z@ bits, bump @sq@ by @z + 1@ and clear @z@. By the end of this |
| 320 | * palaver, @i@ is an index to the precomputed value in @tab@. |
| 321 | */ |
| 322 | |
| 323 | i = 0; |
| 324 | sq++; |
| 325 | for (;;) { |
| 326 | l++; |
| 327 | if (l >= WINSZ || !MP_RSTEP(&sc)) |
| 328 | break; |
| 329 | if (!MP_RBIT(&sc)) |
| 330 | z++; |
| 331 | else { |
| 332 | i = ((i << 1) | 1) << z; |
| 333 | sq += z + 1; |
| 334 | z = 0; |
| 335 | } |
| 336 | } |
| 337 | |
| 338 | /* --- Do the squaring --- * |
| 339 | * |
| 340 | * Remember that @sq@ carries over from the zero-skipping stuff below. |
| 341 | */ |
| 342 | |
| 343 | while (sq) { |
| 344 | mp *y; |
| 345 | y = mp_sqr(spare, x); |
| 346 | y = mpbarrett_reduce(mb, y, y); |
| 347 | spare = x; x = y; |
| 348 | sq--; |
| 349 | } |
| 350 | |
| 351 | /* --- Do the multiply --- */ |
| 352 | |
| 353 | { mp *y = mp_mul(spare, x, tab[i]); spare = x; |
| 354 | x = mpbarrett_reduce(mb, y, y); } |
| 355 | |
| 356 | /* --- Now grind along through the rest of the bits --- */ |
| 357 | |
| 358 | sq = z; |
| 359 | for (;;) { |
| 360 | if (!MP_RSTEP(&sc)) |
| 361 | goto done; |
| 362 | if (MP_RBIT(&sc)) |
| 363 | break; |
| 364 | sq++; |
| 365 | } |
| 366 | } |
| 367 | |
| 368 | /* --- Do a final round of squaring --- */ |
| 369 | |
| 370 | done: |
| 371 | while (sq) { |
| 372 | mp *y; |
| 373 | y = mp_sqr(spare, x); |
| 374 | y = mpbarrett_reduce(mb, y, y); |
| 375 | spare = x; x = y; |
| 376 | sq--; |
| 377 | } |
| 378 | |
| 379 | /* --- Done --- */ |
| 380 | |
| 381 | for (i = 0; i < TABSZ; i++) |
| 382 | mp_drop(tab[i]); |
| 383 | xfree(tab); |
| 384 | exit: |
| 385 | mp_drop(d); |
| 386 | mp_drop(spare); |
| 387 | return (x); |
| 388 | } |
| 389 | |
| 390 | /*----- Test rig ----------------------------------------------------------*/ |
| 391 | |
| 392 | #ifdef TEST_RIG |
| 393 | |
| 394 | static int vmod(dstr *v) |
| 395 | { |
| 396 | mp *x = *(mp **)v[0].buf; |
| 397 | mp *n = *(mp **)v[1].buf; |
| 398 | mp *r = *(mp **)v[2].buf; |
| 399 | mp *s; |
| 400 | mpbarrett mb; |
| 401 | int ok = 1; |
| 402 | |
| 403 | mpbarrett_create(&mb, n); |
| 404 | s = mpbarrett_reduce(&mb, MP_NEW, x); |
| 405 | |
| 406 | if (!MP_EQ(s, r)) { |
| 407 | fputs("\n*** barrett reduction failure\n", stderr); |
| 408 | fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr); |
| 409 | fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr); |
| 410 | fputs("r = ", stderr); mp_writefile(r, stderr, 10); fputc('\n', stderr); |
| 411 | fputs("s = ", stderr); mp_writefile(s, stderr, 10); fputc('\n', stderr); |
| 412 | ok = 0; |
| 413 | } |
| 414 | |
| 415 | mpbarrett_destroy(&mb); |
| 416 | mp_drop(x); |
| 417 | mp_drop(n); |
| 418 | mp_drop(r); |
| 419 | mp_drop(s); |
| 420 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
| 421 | return (ok); |
| 422 | } |
| 423 | |
| 424 | static int vexp(dstr *v) |
| 425 | { |
| 426 | mp *m = *(mp **)v[0].buf; |
| 427 | mp *a = *(mp **)v[1].buf; |
| 428 | mp *b = *(mp **)v[2].buf; |
| 429 | mp *r = *(mp **)v[3].buf; |
| 430 | mp *mr; |
| 431 | int ok = 1; |
| 432 | |
| 433 | mpbarrett mb; |
| 434 | mpbarrett_create(&mb, m); |
| 435 | |
| 436 | mr = mpbarrett_exp(&mb, MP_NEW, a, b); |
| 437 | |
| 438 | if (!MP_EQ(mr, r)) { |
| 439 | fputs("\n*** barrett modexp failed", stderr); |
| 440 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
| 441 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
| 442 | fputs("\n e = ", stderr); mp_writefile(b, stderr, 10); |
| 443 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
| 444 | fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10); |
| 445 | fputc('\n', stderr); |
| 446 | ok = 0; |
| 447 | } |
| 448 | |
| 449 | mp_drop(m); |
| 450 | mp_drop(a); |
| 451 | mp_drop(b); |
| 452 | mp_drop(r); |
| 453 | mp_drop(mr); |
| 454 | mpbarrett_destroy(&mb); |
| 455 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
| 456 | return ok; |
| 457 | } |
| 458 | |
| 459 | static test_chunk tests[] = { |
| 460 | { "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } }, |
| 461 | { "mpbarrett-exp", vexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
| 462 | { 0, 0, { 0 } } |
| 463 | }; |
| 464 | |
| 465 | int main(int argc, char *argv[]) |
| 466 | { |
| 467 | sub_init(); |
| 468 | test_run(argc, argv, tests, SRCDIR "/tests/mpbarrett"); |
| 469 | return (0); |
| 470 | } |
| 471 | |
| 472 | #endif |
| 473 | |
| 474 | /*----- That's all, folks -------------------------------------------------*/ |