| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * Simple multiprecision arithmetic |
| 4 | * |
| 5 | * (c) 1999 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 | #ifndef CATACOMB_MP_H |
| 29 | #define CATACOMB_MP_H |
| 30 | |
| 31 | #ifdef __cplusplus |
| 32 | extern "C" { |
| 33 | #endif |
| 34 | |
| 35 | /*----- Header files ------------------------------------------------------*/ |
| 36 | |
| 37 | #include <assert.h> |
| 38 | #include <string.h> |
| 39 | |
| 40 | #include <mLib/sub.h> |
| 41 | |
| 42 | #ifndef CATACOMB_MPW_H |
| 43 | # include "mpw.h" |
| 44 | #endif |
| 45 | |
| 46 | #ifndef CATACOMB_ARENA_H |
| 47 | # include "arena.h" |
| 48 | #endif |
| 49 | |
| 50 | #ifndef CATACOMB_MPARENA_H |
| 51 | # include "mparena.h" |
| 52 | #endif |
| 53 | |
| 54 | #ifndef CATACOMB_MPX_H |
| 55 | # include "mpx.h" |
| 56 | #endif |
| 57 | |
| 58 | /*----- Data structures ---------------------------------------------------*/ |
| 59 | |
| 60 | /* --- A multiprecision integer --- */ |
| 61 | |
| 62 | typedef struct mp { |
| 63 | mpw *v, *vl; /* Vector of digits, current limit */ |
| 64 | size_t sz; /* Size of digit buffer in words */ |
| 65 | mparena *a; /* Arena for buffer allocation */ |
| 66 | unsigned f; /* Flags (see below) */ |
| 67 | unsigned ref; /* Reference counter */ |
| 68 | } mp; |
| 69 | |
| 70 | #define MP_NEG 1u /* Negative (signed magnitude) */ |
| 71 | #define MP_BURN 2u /* Secret (viral flag) */ |
| 72 | #define MP_CONST 4u /* Uses strange memory allocation */ |
| 73 | #define MP_UNDEF 8u /* Contains nothing interesting */ |
| 74 | #define MP_DESTROYED 16u /* Has been destroyed */ |
| 75 | |
| 76 | /* --- A factor for simultaneous exponentation --- * |
| 77 | * |
| 78 | * Used by the Montgomery and Barrett exponentiators. |
| 79 | */ |
| 80 | |
| 81 | typedef struct mp_expfactor { |
| 82 | mp *base; |
| 83 | mp *exp; |
| 84 | } mp_expfactor; |
| 85 | |
| 86 | /*----- Useful constants --------------------------------------------------*/ |
| 87 | |
| 88 | extern mp mp_const[]; |
| 89 | |
| 90 | #define MP_ZERO (&mp_const[0]) |
| 91 | #define MP_ONE (&mp_const[1]) |
| 92 | #define MP_TWO (&mp_const[2]) |
| 93 | #define MP_THREE (&mp_const[3]) |
| 94 | #define MP_FOUR (&mp_const[4]) |
| 95 | #define MP_FIVE (&mp_const[5]) |
| 96 | #define MP_TEN (&mp_const[6]) |
| 97 | #define MP_256 (&mp_const[7]) |
| 98 | #define MP_MONE (&mp_const[8]) |
| 99 | |
| 100 | #define MP_NEW ((mp *)0) |
| 101 | #define MP_NEWSEC (&mp_const[9]) |
| 102 | |
| 103 | /*----- Trivial macros ----------------------------------------------------*/ |
| 104 | |
| 105 | /* --- @MP_LEN@ --- * |
| 106 | * |
| 107 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 108 | * |
| 109 | * Returns: Length of the integer, in words. |
| 110 | */ |
| 111 | |
| 112 | #define MP_LEN(m) ((m)->vl - ((m)->v)) |
| 113 | |
| 114 | /*----- Memory management and reference counting --------------------------*/ |
| 115 | |
| 116 | /* --- @mp_new@ --- * |
| 117 | * |
| 118 | * Arguments: @size_t sz@ = size of vector required |
| 119 | * @unsigned f@ = flags to set |
| 120 | * |
| 121 | * Returns: Pointer to a new MP structure. |
| 122 | * |
| 123 | * Use: Allocates a new multiprecision integer. The data space is |
| 124 | * allocated from either the standard global or secret arena, |
| 125 | * depending on the initial flags requested. |
| 126 | */ |
| 127 | |
| 128 | extern mp *mp_new(size_t /*sz*/, unsigned /*f*/); |
| 129 | |
| 130 | /* --- @mp_create@ --- * |
| 131 | * |
| 132 | * Arguments: @size_t sz@ = size of vector required |
| 133 | * |
| 134 | * Returns: Pointer to pristine new MP structure with enough memory |
| 135 | * bolted onto it. |
| 136 | * |
| 137 | * Use: Creates a new multiprecision integer with indeterminate |
| 138 | * contents. The integer has a single reference. |
| 139 | */ |
| 140 | |
| 141 | extern mp *mp_create(size_t /*sz*/); |
| 142 | |
| 143 | /* --- @mp_createsecure@ --- * |
| 144 | * |
| 145 | * Arguments: @size_t sz@ = size of vector required |
| 146 | * |
| 147 | * Returns: Pointer to pristine new MP structure with enough memory |
| 148 | * bolted onto it. |
| 149 | * |
| 150 | * Use: Creates a new multiprecision integer with indeterminate |
| 151 | * contents. The integer has a single reference. The integer's |
| 152 | * data space is allocated from the secure arena. Its burn flag |
| 153 | * is set. |
| 154 | */ |
| 155 | |
| 156 | extern mp *mp_createsecure(size_t /*sz*/); |
| 157 | |
| 158 | /* --- @mp_build@ --- * |
| 159 | * |
| 160 | * Arguments: @mp *m@ = pointer to an MP block to fill in |
| 161 | * @mpw *v@ = pointer to a word array |
| 162 | * @mpw *vl@ = pointer just past end of array |
| 163 | * |
| 164 | * Returns: --- |
| 165 | * |
| 166 | * Use: Creates a multiprecision integer representing some smallish |
| 167 | * number. You must provide storage for the number and dispose |
| 168 | * of it when you've finished with it. The number is marked as |
| 169 | * constant while it exists. |
| 170 | */ |
| 171 | |
| 172 | extern void mp_build(mp */*m*/, mpw */*v*/, mpw */*vl*/); |
| 173 | |
| 174 | /* --- @mp_destroy@ --- * |
| 175 | * |
| 176 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 177 | * |
| 178 | * Returns: --- |
| 179 | * |
| 180 | * Use: Destroys a multiprecision integer. The reference count isn't |
| 181 | * checked. Don't use this function if you don't know what |
| 182 | * you're doing: use @mp_drop@ instead. |
| 183 | */ |
| 184 | |
| 185 | extern void mp_destroy(mp */*m*/); |
| 186 | |
| 187 | /* --- @mp_copy@ --- * |
| 188 | * |
| 189 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 190 | * |
| 191 | * Returns: A copy of the given multiprecision integer. |
| 192 | * |
| 193 | * Use: Copies the given integer. In fact you just get another |
| 194 | * reference to the same old one again. |
| 195 | */ |
| 196 | |
| 197 | extern mp *mp_copy(mp */*m*/); |
| 198 | |
| 199 | #define MP_COPY(m) ((m)->ref++, (m)) |
| 200 | |
| 201 | /* --- @mp_drop@ --- * |
| 202 | * |
| 203 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 204 | * |
| 205 | * Returns: --- |
| 206 | * |
| 207 | * Use: Drops a reference to an integer which isn't wanted any more. |
| 208 | * If there are no more references, the integer is destroyed. |
| 209 | */ |
| 210 | |
| 211 | extern void mp_drop(mp */*m*/); |
| 212 | |
| 213 | #define MP_DROP(m) do { \ |
| 214 | mp *_mm = (m); \ |
| 215 | _mm->ref--; \ |
| 216 | if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \ |
| 217 | mp_destroy(_mm); \ |
| 218 | } while (0) |
| 219 | |
| 220 | /* --- @mp_split@ --- * |
| 221 | * |
| 222 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 223 | * |
| 224 | * Returns: A reference to the same integer, possibly with a different |
| 225 | * address. |
| 226 | * |
| 227 | * Use: Splits off a modifiable version of the integer referred to. |
| 228 | */ |
| 229 | |
| 230 | extern mp *mp_split(mp */*m*/); |
| 231 | |
| 232 | #define MP_SPLIT(m) do { \ |
| 233 | mp *_m = (m); \ |
| 234 | if ((_m->f & MP_CONST) || _m->ref > 1) { \ |
| 235 | size_t _len = MP_LEN(_m); \ |
| 236 | mp *_mm = mp_new(_len, _m->f); \ |
| 237 | if (!(_m->f & MP_UNDEF)) \ |
| 238 | memcpy(_mm->v, _m->v, MPWS(_len)); \ |
| 239 | _m->ref--; \ |
| 240 | _m = _mm; \ |
| 241 | } \ |
| 242 | (m) = _m; \ |
| 243 | } while (0) |
| 244 | |
| 245 | /* --- @mp_resize@ --- * |
| 246 | * |
| 247 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 248 | * @size_t sz@ = new size |
| 249 | * |
| 250 | * Returns: --- |
| 251 | * |
| 252 | * Use: Resizes the vector containing the integer's digits. The new |
| 253 | * size must be at least as large as the current integer's |
| 254 | * length. This isn't really intended for client use. |
| 255 | */ |
| 256 | |
| 257 | extern void mp_resize(mp */*m*/, size_t /*sz*/); |
| 258 | |
| 259 | #define MP_RESIZE(m, ssz) do { \ |
| 260 | mp *_m = (m); \ |
| 261 | size_t _sz = (ssz); \ |
| 262 | mparena *_a = (_m->f & MP_BURN) ? MPARENA_SECURE : MPARENA_GLOBAL; \ |
| 263 | mpw *_v; \ |
| 264 | size_t _len = MP_LEN(_m); \ |
| 265 | assert(((void)"can't make size less than length", _sz >= _len)); \ |
| 266 | _v = mpalloc(_a, _sz); \ |
| 267 | if (!(_m->f & MP_UNDEF)) \ |
| 268 | memcpy(_v, _m->v, MPWS(_len)); \ |
| 269 | if (_m->f & MP_BURN) \ |
| 270 | memset(_m->v, 0, MPWS(_m->sz)); \ |
| 271 | mpfree(_m->a, _m->v); \ |
| 272 | _m->a = _a; \ |
| 273 | _m->v = _v; \ |
| 274 | _m->vl = _v + _len; \ |
| 275 | } while (0) |
| 276 | |
| 277 | /* --- @mp_ensure@ --- * |
| 278 | * |
| 279 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 280 | * @size_t sz@ = required size |
| 281 | * |
| 282 | * Returns: --- |
| 283 | * |
| 284 | * Use: Ensures that the integer has enough space for @sz@ digits. |
| 285 | * The value is not changed. |
| 286 | */ |
| 287 | |
| 288 | extern void mp_ensure(mp */*m*/, size_t /*sz*/); |
| 289 | |
| 290 | #define MP_ENSURE(m, ssz) do { \ |
| 291 | mp *_m = (m); \ |
| 292 | size_t _ssz = (ssz); \ |
| 293 | size_t _len = MP_LEN(_m); \ |
| 294 | if (_ssz >= _len) { \ |
| 295 | if (_ssz > _m->sz) \ |
| 296 | mp_resize(_m, _ssz); \ |
| 297 | if (!(_m->f & MP_UNDEF) && _ssz > _len) \ |
| 298 | memset(_m->vl, 0, MPWS(_ssz - _len)); \ |
| 299 | _m->vl = _m->v + _ssz; \ |
| 300 | } \ |
| 301 | } while (0) |
| 302 | |
| 303 | /* --- @mp_dest@ --- * |
| 304 | * |
| 305 | * Arguments: @mp *m@ = a suggested destination integer |
| 306 | * @size_t sz@ = size required for result, in digits |
| 307 | * @unsigned f@ = various flags |
| 308 | * |
| 309 | * Returns: A pointer to an appropriate destination. |
| 310 | * |
| 311 | * Use: Converts a suggested destination into a real destination with |
| 312 | * the required properties. If the real destination is @d@, |
| 313 | * then the following properties will hold: |
| 314 | * |
| 315 | * * @d@ will have exactly one reference. |
| 316 | * |
| 317 | * * If @m@ is not @MP_NEW@, then the contents of @m@ will not |
| 318 | * change, unless @f@ has the @MP_UNDEF@ flag set. |
| 319 | * |
| 320 | * * If @m@ is not @MP_NEW@, then he reference count of @m@ on |
| 321 | * entry is equal to the sum of the counts of @d@ and @m@ on |
| 322 | * exit. |
| 323 | * |
| 324 | * * The size of @d@ will be at least @sz@. |
| 325 | * |
| 326 | * * If @f@ has the @MP_BURN@ flag set, then @d@ will be |
| 327 | * allocated from @MPARENA_SECURE@. |
| 328 | * |
| 329 | * Understanding this function is crucial to using Catacomb's |
| 330 | * multiprecision integer library effectively. |
| 331 | */ |
| 332 | |
| 333 | extern mp *mp_dest(mp */*m*/, size_t /*sz*/, unsigned /*f*/); |
| 334 | |
| 335 | #define MP_DEST(m, ssz, f) do { \ |
| 336 | mp *_m = (m); \ |
| 337 | size_t _ssz = (ssz); \ |
| 338 | unsigned _f = (f); \ |
| 339 | _m = mp_dest(_m, _ssz, _f); \ |
| 340 | (m) = _m; \ |
| 341 | } while (0) |
| 342 | |
| 343 | /*----- Size manipulation -------------------------------------------------*/ |
| 344 | |
| 345 | /* --- @mp_shrink@ --- * |
| 346 | * |
| 347 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 348 | * |
| 349 | * Returns: --- |
| 350 | * |
| 351 | * Use: Reduces the recorded length of an integer. This doesn't |
| 352 | * reduce the amount of memory used, although it can improve |
| 353 | * performance a bit. To reduce memory, use @mp_minimize@ |
| 354 | * instead. This can't change the value of an integer, and is |
| 355 | * therefore safe to use even when there are multiple |
| 356 | * references. |
| 357 | */ |
| 358 | |
| 359 | extern void mp_shrink(mp */*m*/); |
| 360 | |
| 361 | #define MP_SHRINK(m) do { \ |
| 362 | mp *_mm = (m); \ |
| 363 | MPX_SHRINK(_mm->v, _mm->vl); \ |
| 364 | if (MP_ZEROP(_mm)) \ |
| 365 | _mm->f &= ~MP_NEG; \ |
| 366 | } while (0) |
| 367 | |
| 368 | /* --- @mp_minimize@ --- * |
| 369 | * |
| 370 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 371 | * |
| 372 | * Returns: --- |
| 373 | * |
| 374 | * Use: Reduces the amount of memory an integer uses. It's best to |
| 375 | * do this to numbers which aren't going to change in the |
| 376 | * future. |
| 377 | */ |
| 378 | |
| 379 | extern void mp_minimize(mp */*m*/); |
| 380 | |
| 381 | /*----- Bit scanning ------------------------------------------------------*/ |
| 382 | |
| 383 | #ifndef CATACOMB_MPSCAN_H |
| 384 | # include "mpscan.h" |
| 385 | #endif |
| 386 | |
| 387 | /* --- @mp_scan@ --- * |
| 388 | * |
| 389 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
| 390 | * @const mp *m@ = pointer to a multiprecision integer |
| 391 | * |
| 392 | * Returns: --- |
| 393 | * |
| 394 | * Use: Initializes a bitscanner on a multiprecision integer. |
| 395 | */ |
| 396 | |
| 397 | extern void mp_scan(mpscan */*sc*/, const mp */*m*/); |
| 398 | |
| 399 | #define MP_SCAN(sc, m) do { \ |
| 400 | const mp *_mm = (m); \ |
| 401 | mpscan *_sc = (sc); \ |
| 402 | MPSCAN_INITX(_sc, _mm->v, _mm->vl); \ |
| 403 | } while (0) |
| 404 | |
| 405 | /* --- @mp_rscan@ --- * |
| 406 | * |
| 407 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
| 408 | * @const mp *m@ = pointer to a multiprecision integer |
| 409 | * |
| 410 | * Returns: --- |
| 411 | * |
| 412 | * Use: Initializes a reverse bitscanner on a multiprecision |
| 413 | * integer. |
| 414 | */ |
| 415 | |
| 416 | extern void mp_rscan(mpscan */*sc*/, const mp */*m*/); |
| 417 | |
| 418 | #define MP_RSCAN(sc, m) do { \ |
| 419 | const mp *_mm = (m); \ |
| 420 | mpscan *_sc = (sc); \ |
| 421 | MPSCAN_RINITX(_sc, _mm->v, _mm->vl); \ |
| 422 | } while (0) |
| 423 | |
| 424 | /* --- Other bitscanning aliases --- */ |
| 425 | |
| 426 | #define mp_step mpscan_step |
| 427 | #define mp_bit mpscan_bit |
| 428 | #define mp_rstep mpscan_rstep |
| 429 | #define mp_rbit mpscan_rbit |
| 430 | |
| 431 | #define MP_STEP MPSCAN_STEP |
| 432 | #define MP_BIT MPSCAN_BIT |
| 433 | #define MP_RSTEP MPSCAN_RSTEP |
| 434 | #define MP_RBIT MPSCAN_RBIT |
| 435 | |
| 436 | /*----- Loading and storing -----------------------------------------------*/ |
| 437 | |
| 438 | /* --- @mp_octets@ --- * |
| 439 | * |
| 440 | * Arguments: @const mp *m@ = a multiprecision integer |
| 441 | * |
| 442 | * Returns: The number of octets required to represent @m@. |
| 443 | * |
| 444 | * Use: Calculates the external storage required for a multiprecision |
| 445 | * integer. |
| 446 | */ |
| 447 | |
| 448 | extern size_t mp_octets(const mp */*m*/); |
| 449 | |
| 450 | /* --- @mp_octets2c@ --- * |
| 451 | * |
| 452 | * Arguments: @const mp *m@ = a multiprecision integer |
| 453 | * |
| 454 | * Returns: The number of octets required to represent @m@. |
| 455 | * |
| 456 | * Use: Calculates the external storage required for a multiprecision |
| 457 | * integer represented as two's complement. |
| 458 | */ |
| 459 | |
| 460 | extern size_t mp_octets2c(const mp */*m*/); |
| 461 | |
| 462 | /* --- @mp_bits@ --- * |
| 463 | * |
| 464 | * Arguments: @const mp *m@ = a multiprecision integer |
| 465 | * |
| 466 | * Returns: The number of bits required to represent @m@. |
| 467 | * |
| 468 | * Use: Calculates the external storage required for a multiprecision |
| 469 | * integer. |
| 470 | */ |
| 471 | |
| 472 | extern unsigned long mp_bits(const mp */*m*/); |
| 473 | |
| 474 | /* --- @mp_loadl@ --- * |
| 475 | * |
| 476 | * Arguments: @mp *d@ = destination |
| 477 | * @const void *pv@ = pointer to source data |
| 478 | * @size_t sz@ = size of the source data |
| 479 | * |
| 480 | * Returns: Resulting multiprecision number. |
| 481 | * |
| 482 | * Use: Loads a multiprecision number from an array of octets. The |
| 483 | * first byte in the array is the least significant. More |
| 484 | * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$% |
| 485 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
| 486 | */ |
| 487 | |
| 488 | extern mp *mp_loadl(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
| 489 | |
| 490 | /* --- @mp_storel@ --- * |
| 491 | * |
| 492 | * Arguments: @const mp *m@ = source |
| 493 | * @void *pv@ = pointer to output array |
| 494 | * @size_t sz@ = size of the output array |
| 495 | * |
| 496 | * Returns: --- |
| 497 | * |
| 498 | * Use: Stores a multiprecision number in an array of octets. The |
| 499 | * first byte in the array is the least significant. If the |
| 500 | * array is too small to represent the number, high-order bits |
| 501 | * are truncated; if the array is too large, high order bytes |
| 502 | * are filled with zeros. More formally, if the number is |
| 503 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
| 504 | * then the array is %$b_0, b_1, \ldots, b_{n-1}$%. |
| 505 | */ |
| 506 | |
| 507 | extern void mp_storel(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
| 508 | |
| 509 | /* --- @mp_loadb@ --- * |
| 510 | * |
| 511 | * Arguments: @mp *d@ = destination |
| 512 | * @const void *pv@ = pointer to source data |
| 513 | * @size_t sz@ = size of the source data |
| 514 | * |
| 515 | * Returns: Resulting multiprecision number. |
| 516 | * |
| 517 | * Use: Loads a multiprecision number from an array of octets. The |
| 518 | * last byte in the array is the least significant. More |
| 519 | * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$% |
| 520 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
| 521 | */ |
| 522 | |
| 523 | extern mp *mp_loadb(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
| 524 | |
| 525 | /* --- @mp_storeb@ --- * |
| 526 | * |
| 527 | * Arguments: @const mp *m@ = source |
| 528 | * @void *pv@ = pointer to output array |
| 529 | * @size_t sz@ = size of the output array |
| 530 | * |
| 531 | * Returns: --- |
| 532 | * |
| 533 | * Use: Stores a multiprecision number in an array of octets. The |
| 534 | * last byte in the array is the least significant. If the |
| 535 | * array is too small to represent the number, high-order bits |
| 536 | * are truncated; if the array is too large, high order bytes |
| 537 | * are filled with zeros. More formally, if the number is |
| 538 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
| 539 | * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%. |
| 540 | */ |
| 541 | |
| 542 | extern void mp_storeb(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
| 543 | |
| 544 | /* --- @mp_loadl2c@ --- * |
| 545 | * |
| 546 | * Arguments: @mp *d@ = destination |
| 547 | * @const void *pv@ = pointer to source data |
| 548 | * @size_t sz@ = size of the source data |
| 549 | * |
| 550 | * Returns: Resulting multiprecision number. |
| 551 | * |
| 552 | * Use: Loads a multiprecision number from an array of octets as |
| 553 | * two's complement. The first byte in the array is the least |
| 554 | * significant. |
| 555 | */ |
| 556 | |
| 557 | extern mp *mp_loadl2c(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
| 558 | |
| 559 | /* --- @mp_storel2c@ --- * |
| 560 | * |
| 561 | * Arguments: @const mp *m@ = source |
| 562 | * @void *pv@ = pointer to output array |
| 563 | * @size_t sz@ = size of the output array |
| 564 | * |
| 565 | * Returns: --- |
| 566 | * |
| 567 | * Use: Stores a multiprecision number in an array of octets as two's |
| 568 | * complement. The first byte in the array is the least |
| 569 | * significant. If the array is too small to represent the |
| 570 | * number, high-order bits are truncated; if the array is too |
| 571 | * large, high order bytes are sign-extended. |
| 572 | */ |
| 573 | |
| 574 | extern void mp_storel2c(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
| 575 | |
| 576 | /* --- @mp_loadb2c@ --- * |
| 577 | * |
| 578 | * Arguments: @mp *d@ = destination |
| 579 | * @const void *pv@ = pointer to source data |
| 580 | * @size_t sz@ = size of the source data |
| 581 | * |
| 582 | * Returns: Resulting multiprecision number. |
| 583 | * |
| 584 | * Use: Loads a multiprecision number from an array of octets as |
| 585 | * two's complement. The last byte in the array is the least |
| 586 | * significant. |
| 587 | */ |
| 588 | |
| 589 | extern mp *mp_loadb2c(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
| 590 | |
| 591 | /* --- @mp_storeb2c@ --- * |
| 592 | * |
| 593 | * Arguments: @const mp *m@ = source |
| 594 | * @void *pv@ = pointer to output array |
| 595 | * @size_t sz@ = size of the output array |
| 596 | * |
| 597 | * Returns: --- |
| 598 | * |
| 599 | * Use: Stores a multiprecision number in an array of octets, as |
| 600 | * two's complement. The last byte in the array is the least |
| 601 | * significant. If the array is too small to represent the |
| 602 | * number, high-order bits are truncated; if the array is too |
| 603 | * large, high order bytes are sign-extended. |
| 604 | */ |
| 605 | |
| 606 | extern void mp_storeb2c(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
| 607 | |
| 608 | /*----- Bit operations ----------------------------------------------------*/ |
| 609 | |
| 610 | /* --- @mp_not@ --- * |
| 611 | * |
| 612 | * Arguments: @mp *d@ = destination |
| 613 | * @mp *a@ = source |
| 614 | * |
| 615 | * Returns: The bitwise complement of the source. |
| 616 | */ |
| 617 | |
| 618 | extern mp *mp_not(mp */*d*/, mp */*a*/); |
| 619 | |
| 620 | /* --- @mp_bitop@ --- * |
| 621 | * |
| 622 | * Arguments: @mp *d@ = destination |
| 623 | * @mp *a, *b@ = sources |
| 624 | * |
| 625 | * Returns: The result of the given bitwise operation. These functions |
| 626 | * don't handle negative numbers at all sensibly. For that, use |
| 627 | * the @...2c@ variants. The functions are named after the |
| 628 | * truth tables they generate: |
| 629 | * |
| 630 | * a: 0011 |
| 631 | * b: 0101 |
| 632 | * @mpx_bitXXXX@ |
| 633 | */ |
| 634 | |
| 635 | #define MP_BITDECL(string) \ |
| 636 | extern mp *mp_bit##string(mp */*d*/, mp */*a*/, mp */*b*/); |
| 637 | MPX_DOBIN(MP_BITDECL) |
| 638 | |
| 639 | /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- * |
| 640 | * |
| 641 | * Synonyms for the commonly-used functions. |
| 642 | */ |
| 643 | |
| 644 | #define mp_and mp_bit0001 |
| 645 | #define mp_or mp_bit0111 |
| 646 | #define mp_nand mp_bit1110 |
| 647 | #define mp_nor mp_bit1000 |
| 648 | #define mp_xor mp_bit0110 |
| 649 | |
| 650 | /* --- @mp_testbit@ --- * |
| 651 | * |
| 652 | * Arguments: @mp *x@ = a large integer |
| 653 | * @unsigned long n@ = which bit to test |
| 654 | * |
| 655 | * Returns: Nonzero if the bit is set, zero if not. |
| 656 | */ |
| 657 | |
| 658 | extern int mp_testbit(mp */*x*/, unsigned long /*n*/); |
| 659 | |
| 660 | /* --- @mp_setbit@, @mp_clearbit@ --- * |
| 661 | * |
| 662 | * Arguments: @mp *d@ = a destination |
| 663 | * @mp *x@ = a large integer |
| 664 | * @unsigned long n@ = which bit to modify |
| 665 | * |
| 666 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
| 667 | */ |
| 668 | |
| 669 | extern mp *mp_setbit(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
| 670 | extern mp *mp_clearbit(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
| 671 | |
| 672 | /* --- @mp_lsl@, @mp_lslc@, @mp_lsr@ --- * |
| 673 | * |
| 674 | * Arguments: @mp *d@ = destination |
| 675 | * @mp *a@ = source |
| 676 | * @size_t n@ = number of bits to move |
| 677 | * |
| 678 | * Returns: Result, @a@ shifted left or right by @n@. |
| 679 | * |
| 680 | * Use: Bitwise shift operators. @mp_lslc@ fills the bits introduced |
| 681 | * on the right with ones instead of zeroes: it's used |
| 682 | * internally by @mp_lsl2c@, though it may be useful on its |
| 683 | * own. |
| 684 | */ |
| 685 | |
| 686 | extern mp *mp_lsl(mp */*d*/, mp */*a*/, size_t /*n*/); |
| 687 | extern mp *mp_lslc(mp */*d*/, mp */*a*/, size_t /*n*/); |
| 688 | extern mp *mp_lsr(mp */*d*/, mp */*a*/, size_t /*n*/); |
| 689 | |
| 690 | /* --- @mp_not2c@ --- * |
| 691 | * |
| 692 | * Arguments: @mp *d@ = destination |
| 693 | * @mp *a@ = source |
| 694 | * |
| 695 | * Returns: The sign-extended complement of the argument. |
| 696 | */ |
| 697 | |
| 698 | extern mp *mp_not2c(mp */*d*/, mp */*a*/); |
| 699 | |
| 700 | /* --- @mp_bitop2c@ --- * |
| 701 | * |
| 702 | * Arguments: @mp *d@ = destination |
| 703 | * @mp *a, *b@ = sources |
| 704 | * |
| 705 | * Returns: The result of the given bitwise operation. Negative numbers |
| 706 | * are treated as two's complement, sign-extended infinitely to |
| 707 | * the left. The functions are named after the truth tables |
| 708 | * they generate: |
| 709 | * |
| 710 | * a: 0011 |
| 711 | * b: 0101 |
| 712 | * @mpx_bitXXXX@ |
| 713 | */ |
| 714 | |
| 715 | #define MP_BIT2CDECL(string) \ |
| 716 | extern mp *mp_bit##string##2c(mp */*d*/, mp */*a*/, mp */*b*/); |
| 717 | MPX_DOBIN(MP_BIT2CDECL) |
| 718 | |
| 719 | /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- * |
| 720 | * |
| 721 | * Synonyms for the commonly-used functions. |
| 722 | */ |
| 723 | |
| 724 | #define mp_and2c mp_bit00012c |
| 725 | #define mp_or2c mp_bit01112c |
| 726 | #define mp_nand2c mp_bit11102c |
| 727 | #define mp_nor2c mp_bit10002c |
| 728 | #define mp_xor2c mp_bit01102c |
| 729 | |
| 730 | /* --- @mp_lsl2c@, @mp_lsr2c@ --- * |
| 731 | * |
| 732 | * Arguments: @mp *d@ = destination |
| 733 | * @mp *a@ = source |
| 734 | * @size_t n@ = number of bits to move |
| 735 | * |
| 736 | * Returns: Result, @a@ shifted left or right by @n@. Handles the |
| 737 | * pretence of sign-extension for negative numbers. |
| 738 | */ |
| 739 | |
| 740 | extern mp *mp_lsl2c(mp */*d*/, mp */*a*/, size_t /*n*/); |
| 741 | extern mp *mp_lsr2c(mp */*d*/, mp */*a*/, size_t /*n*/); |
| 742 | |
| 743 | /* --- @mp_testbit2c@ --- * |
| 744 | * |
| 745 | * Arguments: @mp *x@ = a large integer |
| 746 | * @unsigned long n@ = which bit to test |
| 747 | * |
| 748 | * Returns: Nonzero if the bit is set, zero if not. Fakes up two's |
| 749 | * complement representation. |
| 750 | */ |
| 751 | |
| 752 | extern int mp_testbit2c(mp */*x*/, unsigned long /*n*/); |
| 753 | |
| 754 | /* --- @mp_setbit2c@, @mp_clearbit2c@ --- * |
| 755 | * |
| 756 | * Arguments: @mp *d@ = a destination |
| 757 | * @mp *x@ = a large integer |
| 758 | * @unsigned long n@ = which bit to modify |
| 759 | * |
| 760 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
| 761 | * Fakes up two's complement representation. |
| 762 | */ |
| 763 | |
| 764 | extern mp *mp_setbit2c(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
| 765 | extern mp *mp_clearbit2c(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
| 766 | |
| 767 | /*----- Comparisons -------------------------------------------------------*/ |
| 768 | |
| 769 | /* --- @mp_eq@ --- * |
| 770 | * |
| 771 | * Arguments: @const mp *a, *b@ = two numbers |
| 772 | * |
| 773 | * Returns: Nonzero if the numbers are equal. |
| 774 | */ |
| 775 | |
| 776 | extern int mp_eq(const mp */*a*/, const mp */*b*/); |
| 777 | |
| 778 | #define MP_EQ(a, b) \ |
| 779 | ((((a)->f ^ (b)->f) & MP_NEG) == 0 && \ |
| 780 | mpx_ueq((a)->v, (a)->vl, (b)->v, (b)->vl)) |
| 781 | |
| 782 | /* --- @mp_cmp@ --- * |
| 783 | * |
| 784 | * Arguments: @const mp *a, *b@ = two numbers |
| 785 | * |
| 786 | * Returns: Less than, equal to or greater than zero, according to |
| 787 | * whether @a@ is less than, equal to or greater than @b@. |
| 788 | */ |
| 789 | |
| 790 | extern int mp_cmp(const mp */*a*/, const mp */*b*/); |
| 791 | |
| 792 | #define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0) |
| 793 | |
| 794 | /* --- Other handy macros --- */ |
| 795 | |
| 796 | #define MP_NEGP(x) ((x)->f & MP_NEG) |
| 797 | #define MP_ZEROP(x) (!MP_LEN(x)) |
| 798 | #define MP_POSP(x) (!MP_NEGP(x) && !MP_ZEROP(x)) |
| 799 | #define MP_ODDP(x) (!MP_ZEROP(x) && ((x)->v[0] & 1u)) |
| 800 | #define MP_EVENP(x) (!MP_ODDP(x)) |
| 801 | |
| 802 | /*----- Arithmetic operations ---------------------------------------------*/ |
| 803 | |
| 804 | /* --- @mp_neg@ --- * |
| 805 | * |
| 806 | * Arguments: @mp *d@ = destination |
| 807 | * @mp *a@ = argument |
| 808 | * |
| 809 | * Returns: The negation of the argument. |
| 810 | * |
| 811 | * Use: Negates its argument. |
| 812 | */ |
| 813 | |
| 814 | extern mp *mp_neg(mp */*d*/, mp */*a*/); |
| 815 | |
| 816 | /* --- @mp_add@ --- * |
| 817 | * |
| 818 | * Arguments: @mp *d@ = destination |
| 819 | * @mp *a, *b@ = sources |
| 820 | * |
| 821 | * Returns: Result, @a@ added to @b@. |
| 822 | */ |
| 823 | |
| 824 | extern mp *mp_add(mp */*d*/, mp */*a*/, mp */*b*/); |
| 825 | |
| 826 | /* --- @mp_sub@ --- * |
| 827 | * |
| 828 | * Arguments: @mp *d@ = destination |
| 829 | * @mp *a, *b@ = sources |
| 830 | * |
| 831 | * Returns: Result, @b@ subtracted from @a@. |
| 832 | */ |
| 833 | |
| 834 | extern mp *mp_sub(mp */*d*/, mp */*a*/, mp */*b*/); |
| 835 | |
| 836 | /* --- @mp_mul@ --- * |
| 837 | * |
| 838 | * Arguments: @mp *d@ = destination |
| 839 | * @mp *a, *b@ = sources |
| 840 | * |
| 841 | * Returns: Result, @a@ multiplied by @b@. |
| 842 | */ |
| 843 | |
| 844 | extern mp *mp_mul(mp */*d*/, mp */*a*/, mp */*b*/); |
| 845 | |
| 846 | /* --- @mp_sqr@ --- * |
| 847 | * |
| 848 | * Arguments: @mp *d@ = destination |
| 849 | * @mp *a@ = source |
| 850 | * |
| 851 | * Returns: Result, @a@ squared. |
| 852 | */ |
| 853 | |
| 854 | extern mp *mp_sqr(mp */*d*/, mp */*a*/); |
| 855 | |
| 856 | /* --- @mp_div@ --- * |
| 857 | * |
| 858 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
| 859 | * @mp *a, *b@ = sources |
| 860 | * |
| 861 | * Use: Calculates the quotient and remainder when @a@ is divided by |
| 862 | * @b@. |
| 863 | */ |
| 864 | |
| 865 | extern void mp_div(mp **/*qq*/, mp **/*rr*/, mp */*a*/, mp */*b*/); |
| 866 | |
| 867 | /* --- @mp_exp@ --- * |
| 868 | * |
| 869 | * Arguments: @mp *d@ = fake destination |
| 870 | * @mp *a@ = base |
| 871 | * @mp *e@ = exponent |
| 872 | * |
| 873 | * Returns: Result, %$a^e$%. |
| 874 | */ |
| 875 | |
| 876 | extern mp *mp_exp(mp */*d*/, mp */*a*/, mp */*e*/); |
| 877 | |
| 878 | /* --- @mp_odd@ --- * |
| 879 | * |
| 880 | * Arguments: @mp *d@ = pointer to destination integer |
| 881 | * @mp *m@ = pointer to source integer |
| 882 | * @size_t *s@ = where to store the power of 2 |
| 883 | * |
| 884 | * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%. |
| 885 | * |
| 886 | * Use: Computes a power of two and an odd integer which, when |
| 887 | * multiplied, give a specified result. This sort of thing is |
| 888 | * useful in number theory quite often. |
| 889 | */ |
| 890 | |
| 891 | extern mp *mp_odd(mp */*d*/, mp */*m*/, size_t */*s*/); |
| 892 | |
| 893 | /*----- More advanced algorithms ------------------------------------------*/ |
| 894 | |
| 895 | /* --- @mp_sqrt@ --- * |
| 896 | * |
| 897 | * Arguments: @mp *d@ = pointer to destination integer |
| 898 | * @mp *a@ = (nonnegative) integer to take square root of |
| 899 | * |
| 900 | * Returns: The largest integer %$x$% such that %$x^2 \le a$%. |
| 901 | * |
| 902 | * Use: Computes integer square roots. |
| 903 | * |
| 904 | * The current implementation isn't very good: it uses the |
| 905 | * Newton-Raphson method to find an approximation to %$a$%. If |
| 906 | * there's any demand for a better version, I'll write one. |
| 907 | */ |
| 908 | |
| 909 | extern mp *mp_sqrt(mp */*d*/, mp */*a*/); |
| 910 | |
| 911 | /* --- @mp_gcd@ --- * |
| 912 | * |
| 913 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
| 914 | * @mp *a, *b@ = sources (must be nonzero) |
| 915 | * |
| 916 | * Returns: --- |
| 917 | * |
| 918 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
| 919 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
| 920 | * inverses. Neither @a@ nor @b@ may be zero. |
| 921 | */ |
| 922 | |
| 923 | extern void mp_gcd(mp **/*gcd*/, mp **/*xx*/, mp **/*yy*/, |
| 924 | mp */*a*/, mp */*b*/); |
| 925 | |
| 926 | /* -- @mp_modinv@ --- * |
| 927 | * |
| 928 | * Arguments: @mp *d@ = destination |
| 929 | * @mp *x@ = argument |
| 930 | * @mp *p@ = modulus |
| 931 | * |
| 932 | * Returns: The inverse %$x^{-1} \bmod p$%. |
| 933 | * |
| 934 | * Use: Computes a modular inverse. An assertion fails if %$p$% |
| 935 | * has no inverse. |
| 936 | */ |
| 937 | |
| 938 | extern mp *mp_modinv(mp */*d*/, mp */*x*/, mp */*p*/); |
| 939 | |
| 940 | /* --- @mp_jacobi@ --- * |
| 941 | * |
| 942 | * Arguments: @mp *a@ = an integer |
| 943 | * @mp *n@ = another integer |
| 944 | * |
| 945 | * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%. |
| 946 | * |
| 947 | * Use: Computes the Kronecker symbol %$\jacobi{a}{n}$%. If @n@ is |
| 948 | * prime, this is the Legendre symbol and is equal to 1 if and |
| 949 | * only if @a@ is a quadratic residue mod @n@. The result is |
| 950 | * zero if and only if @a@ and @n@ have a common factor greater |
| 951 | * than one. |
| 952 | * |
| 953 | * If @n@ is composite, then this computes the Kronecker symbol |
| 954 | * |
| 955 | * %$\jacobi{a}{n}=\jacobi{a}{u}\prod_i\jacobi{a}{p_i}^{e_i}$% |
| 956 | * |
| 957 | * where %$n = u p_0^{e_0} \ldots p_{n-1}^{e_{n-1}}$% is the |
| 958 | * prime factorization of %$n$%. The missing bits are: |
| 959 | * |
| 960 | * * %$\jacobi{a}{1} = 1$%; |
| 961 | * * %$\jacobi{a}{-1} = 1$% if @a@ is negative, or 1 if |
| 962 | * positive; |
| 963 | * * %$\jacobi{a}{0} = 0$%; |
| 964 | * * %$\jacobi{a}{2}$ is 0 if @a@ is even, 1 if @a@ is |
| 965 | * congruent to 1 or 7 (mod 8), or %$-1$% otherwise. |
| 966 | * |
| 967 | * If %$n$% is positive and odd, then this is the Jacobi |
| 968 | * symbol. (The Kronecker symbol is a consistant domain |
| 969 | * extension; the Jacobi symbol was implemented first, and the |
| 970 | * name stuck.) |
| 971 | */ |
| 972 | |
| 973 | extern int mp_jacobi(mp */*a*/, mp */*n*/); |
| 974 | |
| 975 | /* --- @mp_modsqrt@ --- * |
| 976 | * |
| 977 | * Arguments: @mp *d@ = destination integer |
| 978 | * @mp *a@ = source integer |
| 979 | * @mp *p@ = modulus (must be prime) |
| 980 | * |
| 981 | * Returns: If %$a$% is a quadratic residue, a square root of %$a$%; else |
| 982 | * a null pointer. |
| 983 | * |
| 984 | * Use: Returns an integer %$x$% such that %$x^2 \equiv a \pmod{p}$%, |
| 985 | * if one exists; else a null pointer. This function will not |
| 986 | * work if %$p$% is composite: you must factor the modulus, take |
| 987 | * a square root mod each factor, and recombine the results |
| 988 | * using the Chinese Remainder Theorem. |
| 989 | * |
| 990 | * We guarantee that the square root returned is the smallest |
| 991 | * one (i.e., the `positive' square root). |
| 992 | */ |
| 993 | |
| 994 | extern mp *mp_modsqrt(mp */*d*/, mp */*a*/, mp */*p*/); |
| 995 | |
| 996 | /* --- @mp_modexp@ --- * |
| 997 | * |
| 998 | * Arguments: @mp *d@ = fake destination |
| 999 | * @mp *x@ = base of exponentiation |
| 1000 | * @mp *e@ = exponent |
| 1001 | * @mp *n@ = modulus (must be positive) |
| 1002 | * |
| 1003 | * Returns: The value %$x^e \bmod n$%. |
| 1004 | */ |
| 1005 | |
| 1006 | extern mp *mp_modexp(mp */*d*/, mp */*x*/, mp */*e*/, mp */*n*/); |
| 1007 | |
| 1008 | /*----- Test harness support ----------------------------------------------*/ |
| 1009 | |
| 1010 | #include <mLib/testrig.h> |
| 1011 | |
| 1012 | #ifndef CATACOMB_MPTEXT_H |
| 1013 | # include "mptext.h" |
| 1014 | #endif |
| 1015 | |
| 1016 | extern const test_type type_mp; |
| 1017 | |
| 1018 | /*----- That's all, folks -------------------------------------------------*/ |
| 1019 | |
| 1020 | #ifdef __cplusplus |
| 1021 | } |
| 1022 | #endif |
| 1023 | |
| 1024 | #endif |