| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: exp.h,v 1.1 2001/06/16 13:00:59 mdw Exp $ |
| 4 | * |
| 5 | * Generalized exponentiation |
| 6 | * |
| 7 | * (c) 2001 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: exp.h,v $ |
| 33 | * Revision 1.1 2001/06/16 13:00:59 mdw |
| 34 | * New generic exponentation code. Includes sliding-window simultaneous |
| 35 | * exponentiation. |
| 36 | * |
| 37 | */ |
| 38 | |
| 39 | #ifdef CATACOMB_EXP_H |
| 40 | # error "Multiple inclusion of <catacomb/exp.h>" |
| 41 | #endif |
| 42 | |
| 43 | #define CATACOMB_EXP_H |
| 44 | |
| 45 | #ifdef __cplusplus |
| 46 | extern "C" { |
| 47 | #endif |
| 48 | |
| 49 | /*----- Header files ------------------------------------------------------*/ |
| 50 | |
| 51 | #include <stddef.h> |
| 52 | |
| 53 | #include <mLib/alloc.h> |
| 54 | |
| 55 | #ifndef CATACOMB_MP_H |
| 56 | # include "mp.h" |
| 57 | #endif |
| 58 | |
| 59 | /*----- Data structures ---------------------------------------------------*/ |
| 60 | |
| 61 | typedef struct exp_simulscan { |
| 62 | mpw w; |
| 63 | size_t len; |
| 64 | const mpw *v; |
| 65 | } exp_simulscan; |
| 66 | |
| 67 | typedef struct exp_simul { |
| 68 | unsigned b; |
| 69 | size_t o, n; |
| 70 | exp_simulscan *s; |
| 71 | } exp_simul; |
| 72 | |
| 73 | /*----- Macros provided ---------------------------------------------------*/ |
| 74 | |
| 75 | /* --- Parameters --- */ |
| 76 | |
| 77 | #ifndef EXP_WINSZ /* Sliding window size */ |
| 78 | # define EXP_WINSZ 4 /* Predefine if you need to */ |
| 79 | #endif |
| 80 | |
| 81 | /* --- These are determined from the window size --- */ |
| 82 | |
| 83 | #define EXP_TABSZ (1 << EXP_WINSZ) |
| 84 | #define EXP_THRESH (((MPW_BITS / EXP_WINSZ) << 2) + 1) |
| 85 | |
| 86 | /* --- Required operations --- * |
| 87 | * |
| 88 | * The macros here are independent of the underlying group elements. You |
| 89 | * must provide the necessary group operations and other definitions. The |
| 90 | * group operation is assumed to be written multiplicatively. |
| 91 | * |
| 92 | * @EXP_TYPE@ The type of a group element, e.g., @mp *@. |
| 93 | * |
| 94 | * @EXP_COPY(d, x)@ Makes @d@ be a copy of @x@. |
| 95 | * |
| 96 | * @EXP_DROP(x)@ Discards the element @x@, reclaiming any |
| 97 | * memory it used. |
| 98 | * |
| 99 | * @EXP_MUL(a, x)@ Multiplies @a@ by @x@ (writing the result |
| 100 | * back to @a@). |
| 101 | * |
| 102 | * @EXP_SQR(a)@ Multiplies @a@ by itself. |
| 103 | * |
| 104 | * @EXP_SETMUL(d, x, y)@ Sets @d@ to be the product of @x@ and @y@. |
| 105 | * The value @d@ has not been initialized. |
| 106 | * |
| 107 | * @EXP_SETSQR(d, x)@ Sets @d@ to be the square of @x@. |
| 108 | * |
| 109 | * Only @EXP_TYPE@, @EXP_MUL@ and @EXP_SQR@ are required for simple |
| 110 | * exponentation. Sliding window and simultaneous exponentation require all |
| 111 | * of the operations. |
| 112 | */ |
| 113 | |
| 114 | #ifndef EXP_TYPE |
| 115 | # error "EXP_TYPE not defined for <catacomb/exp.h>" |
| 116 | #endif |
| 117 | |
| 118 | /* --- @EXP_SIMPLE@ --- * |
| 119 | * |
| 120 | * Arguments: @a@ = the result object, initially a multiplicative identity |
| 121 | * @g@ = the object to exponentiate |
| 122 | * @x@ = the exponent, as a multiprecision integer |
| 123 | * |
| 124 | * Use: Performs a simple left-to-right exponentiation. At the end |
| 125 | * of the code, the answer is left in @a@; @g@ and @x@ are |
| 126 | * unchanged. |
| 127 | */ |
| 128 | |
| 129 | #define EXP_SIMPLE(a, g, x) do { \ |
| 130 | mpscan sc; \ |
| 131 | unsigned sq = 0; \ |
| 132 | \ |
| 133 | /* --- Begin scanning --- */ \ |
| 134 | \ |
| 135 | mp_rscan(&sc, x); \ |
| 136 | if (!MP_RSTEP(&sc)) \ |
| 137 | goto exp_simple_exit; \ |
| 138 | while (!MP_RBIT(&sc)) \ |
| 139 | MP_RSTEP(&sc); \ |
| 140 | \ |
| 141 | /* --- Do the main body of the work --- */ \ |
| 142 | \ |
| 143 | for (;;) { \ |
| 144 | EXP_MUL(a, g); \ |
| 145 | sq = 0; \ |
| 146 | for (;;) { \ |
| 147 | if (!MP_RSTEP(&sc)) \ |
| 148 | goto exp_simple_done; \ |
| 149 | sq++; \ |
| 150 | if (MP_RBIT(&sc)) \ |
| 151 | break; \ |
| 152 | } \ |
| 153 | while (sq--) EXP_SQR(a); \ |
| 154 | } \ |
| 155 | \ |
| 156 | /* --- Do a final round of squaring --- */ \ |
| 157 | \ |
| 158 | exp_simple_done: \ |
| 159 | while (sq--) EXP_SQR(a); \ |
| 160 | exp_simple_exit:; \ |
| 161 | } while (0) |
| 162 | |
| 163 | /* --- @EXP_WINDOW@ --- * |
| 164 | * |
| 165 | * Arguments: @a@ = the result object, initially a multiplicative identity |
| 166 | * @g@ = the object to exponentiate |
| 167 | * @x@ = the exponent, as a multiprecision integer |
| 168 | * |
| 169 | * Use: Performs a sliding-window exponentiation. At the end of the |
| 170 | * code, the answer is left in @a@; @g@ and @x@ are unchanged. |
| 171 | */ |
| 172 | |
| 173 | #define EXP_WINDOW(a, g, x) do { \ |
| 174 | EXP_TYPE *v; \ |
| 175 | EXP_TYPE g2; \ |
| 176 | unsigned i, sq = 0; \ |
| 177 | mpscan sc; \ |
| 178 | \ |
| 179 | /* --- Get going --- */ \ |
| 180 | \ |
| 181 | mp_rscan(&sc, x); \ |
| 182 | if (!MP_RSTEP(&sc)) \ |
| 183 | goto exp_window_exit; \ |
| 184 | \ |
| 185 | /* --- Do the precomputation --- */ \ |
| 186 | \ |
| 187 | EXP_SETSQR(g2, g); \ |
| 188 | v = xmalloc(EXP_TABSZ * sizeof(EXP_TYPE)); \ |
| 189 | EXP_COPY(v[0], g); \ |
| 190 | for (i = 1; i < EXP_TABSZ; i++) \ |
| 191 | EXP_SETMUL(v[i], v[i - 1], g2); \ |
| 192 | EXP_DROP(g2); \ |
| 193 | \ |
| 194 | /* --- Skip top-end zero bits --- * \ |
| 195 | * \ |
| 196 | * If the initial step worked, there must be a set bit somewhere, so \ |
| 197 | * keep stepping until I find it. \ |
| 198 | */ \ |
| 199 | \ |
| 200 | while (!MP_RBIT(&sc)) \ |
| 201 | MP_RSTEP(&sc); \ |
| 202 | \ |
| 203 | /* --- Now for the main work --- */ \ |
| 204 | \ |
| 205 | for (;;) { \ |
| 206 | unsigned l = 1; \ |
| 207 | unsigned z = 0; \ |
| 208 | \ |
| 209 | /* --- The next bit is set, so read a window index --- * \ |
| 210 | * \ |
| 211 | * Reset @i@ to zero and increment @sq@. Then, until either I read \ |
| 212 | * @WINSZ@ bits or I run out of bits, scan in a bit: if it's clear, \ |
| 213 | * bump the @z@ counter; if it's set, push a set bit into @i@, \ |
| 214 | * shift it over by @z@ bits, bump @sq@ by @z + 1@ and clear @z@. \ |
| 215 | * By the end of this palaver, @i@ is an index to the precomputed \ |
| 216 | * value in @v@. \ |
| 217 | */ \ |
| 218 | \ |
| 219 | i = 0; \ |
| 220 | sq++; \ |
| 221 | while (l < EXP_WINSZ && MP_RSTEP(&sc)) { \ |
| 222 | l++; \ |
| 223 | if (!MP_RBIT(&sc)) \ |
| 224 | z++; \ |
| 225 | else { \ |
| 226 | i = ((i << 1) | 1) << z; \ |
| 227 | sq += z + 1; \ |
| 228 | z = 0; \ |
| 229 | } \ |
| 230 | } \ |
| 231 | \ |
| 232 | /* --- Do the squaring --- * \ |
| 233 | * \ |
| 234 | * Remember that @sq@ carries over from the zero-skipping stuff \ |
| 235 | * below. \ |
| 236 | */ \ |
| 237 | \ |
| 238 | while (sq--) EXP_SQR(a); \ |
| 239 | \ |
| 240 | /* --- Do the multiply --- */ \ |
| 241 | \ |
| 242 | EXP_MUL(a, v[i]); \ |
| 243 | \ |
| 244 | /* --- Now grind along through the rest of the bits --- */ \ |
| 245 | \ |
| 246 | sq = z; \ |
| 247 | for (;;) { \ |
| 248 | if (!MP_RSTEP(&sc)) \ |
| 249 | goto exp_window_done; \ |
| 250 | if (MP_RBIT(&sc)) \ |
| 251 | break; \ |
| 252 | sq++; \ |
| 253 | } \ |
| 254 | } \ |
| 255 | \ |
| 256 | /* --- Do a final round of squaring --- */ \ |
| 257 | \ |
| 258 | exp_window_done: \ |
| 259 | while (sq--) EXP_SQR(a); \ |
| 260 | for (i = 0; i < EXP_TABSZ; i++) \ |
| 261 | EXP_DROP(v[i]); \ |
| 262 | xfree(v); \ |
| 263 | exp_window_exit:; \ |
| 264 | } while (0) |
| 265 | |
| 266 | /* --- @EXP_SIMUL@ --- * |
| 267 | * |
| 268 | * Arguments: @a@ = the result object, initially a multiplicative identity |
| 269 | * @f@ = pointer to a vector of base/exp pairs |
| 270 | * @n@ = the number of base/exp pairs |
| 271 | * |
| 272 | * Use: Performs a simultaneous sliding-window exponentiation. The |
| 273 | * @f@ table is an array of structures containing members @base@ |
| 274 | * of type @EXP_TYPE@, and @exp@ of type @mp *@. |
| 275 | */ |
| 276 | |
| 277 | #define EXP_SIMUL(a, f, n) do { \ |
| 278 | size_t i, j, jj, k; \ |
| 279 | size_t vn = 1 << (EXP_WINSZ * n), m = (1 << n) - 1; \ |
| 280 | EXP_TYPE *v = xmalloc(vn * sizeof(EXP_TYPE)); \ |
| 281 | exp_simul e; \ |
| 282 | unsigned sq = 0; \ |
| 283 | \ |
| 284 | /* --- Fill in the precomputed table --- */ \ |
| 285 | \ |
| 286 | j = 1; \ |
| 287 | for (i = 0; i < n; i++) { \ |
| 288 | EXP_COPY(v[j], f[n - 1 - i].base); \ |
| 289 | j <<= 1; \ |
| 290 | } \ |
| 291 | k = n * EXP_WINSZ; \ |
| 292 | jj = 1; \ |
| 293 | for (; i < k; i++) { \ |
| 294 | EXP_SETSQR(v[j], v[jj]); \ |
| 295 | j <<= 1; jj <<= 1; \ |
| 296 | } \ |
| 297 | for (i = 1; i < vn; i <<= 1) { \ |
| 298 | for (j = 1; j < i; j++) \ |
| 299 | EXP_SETMUL(v[j + i], v[j], v[i]); \ |
| 300 | } \ |
| 301 | \ |
| 302 | /* --- Set up the bitscanners --- * \ |
| 303 | * \ |
| 304 | * Got to use custom scanners, to keep them all in sync. \ |
| 305 | */ \ |
| 306 | \ |
| 307 | e.n = n; \ |
| 308 | e.b = 0; \ |
| 309 | e.s = xmalloc(n * sizeof(*e.s)); \ |
| 310 | e.o = 0; \ |
| 311 | for (i = 0; i < n; i++) { \ |
| 312 | MP_SHRINK(f[i].exp); \ |
| 313 | e.s[i].len = MP_LEN(f[i].exp); \ |
| 314 | e.s[i].v = f[i].exp->v; \ |
| 315 | if (e.s[i].len > e.o) \ |
| 316 | e.o = e.s[i].len; \ |
| 317 | } \ |
| 318 | \ |
| 319 | /* --- Skip as far as a nonzero column in the exponent matrix --- */ \ |
| 320 | \ |
| 321 | do { \ |
| 322 | if (!e.o && !e.b) \ |
| 323 | goto exp_simul_done; \ |
| 324 | i = exp_simulnext(&e, 0); \ |
| 325 | } while (!(i & m)); \ |
| 326 | \ |
| 327 | /* --- Now for the main work --- */ \ |
| 328 | \ |
| 329 | for (;;) { \ |
| 330 | unsigned l = 1; \ |
| 331 | unsigned z = 0; \ |
| 332 | \ |
| 333 | /* --- Just read a nonzero column, so read a window index --- * \ |
| 334 | * \ |
| 335 | * Clear high bits of @i@ and increment @sq@. Then, until either I \ |
| 336 | * read @WINSZ@ columns or I run out, scan in a column and append \ |
| 337 | * it to @i@. If it's zero, bump the @z@ counter; if it's nonzero, \ |
| 338 | * bump @sq@ by @z + 1@ and clear @z@. By the end of this palaver, \ |
| 339 | * @i@ is an index to the precomputed value in @v@, followed by \ |
| 340 | * @n * z@ zero bits. \ |
| 341 | */ \ |
| 342 | \ |
| 343 | sq++; \ |
| 344 | while (l < EXP_WINSZ && (e.o || e.b)) { \ |
| 345 | l++; \ |
| 346 | i = exp_simulnext(&e, i); \ |
| 347 | if (!(i & m)) \ |
| 348 | z++; \ |
| 349 | else { \ |
| 350 | sq += z + 1; \ |
| 351 | z = 0; \ |
| 352 | } \ |
| 353 | } \ |
| 354 | \ |
| 355 | /* --- Do the squaring --- * \ |
| 356 | * \ |
| 357 | * Remember that @sq@ carries over from the zero-skipping stuff \ |
| 358 | * below. \ |
| 359 | */ \ |
| 360 | \ |
| 361 | while (sq--) EXP_SQR(a); \ |
| 362 | \ |
| 363 | /* --- Do the multiply --- */ \ |
| 364 | \ |
| 365 | i >>= (z * n); \ |
| 366 | EXP_MUL(a, v[i]); \ |
| 367 | \ |
| 368 | /* --- Now grind along through the rest of the bits --- */ \ |
| 369 | \ |
| 370 | sq = z; \ |
| 371 | for (;;) { \ |
| 372 | if (!e.o && !e.b) \ |
| 373 | goto exp_simul_done; \ |
| 374 | if ((i = exp_simulnext(&e, 0)) != 0) \ |
| 375 | break; \ |
| 376 | sq++; \ |
| 377 | } \ |
| 378 | } \ |
| 379 | \ |
| 380 | /* --- Do a final round of squaring --- */ \ |
| 381 | \ |
| 382 | exp_simul_done: \ |
| 383 | while (sq--) EXP_SQR(a); \ |
| 384 | for (i = 1; i < vn; i++) \ |
| 385 | EXP_DROP(v[i]); \ |
| 386 | xfree(v); \ |
| 387 | } while (0) |
| 388 | |
| 389 | /*----- Functions provided ------------------------------------------------*/ |
| 390 | |
| 391 | /* --- @exp_simulnext@ --- * |
| 392 | * |
| 393 | * Arguments: @exp_simul *e@ = pointer to state structure |
| 394 | * @size_t x@ = a current accumulator |
| 395 | * |
| 396 | * Returns: The next column of bits. |
| 397 | * |
| 398 | * Use: Scans the next column of bits for a simultaneous |
| 399 | * exponentiation. |
| 400 | */ |
| 401 | |
| 402 | extern size_t exp_simulnext(exp_simul */*e*/, size_t /*x*/); |
| 403 | |
| 404 | /*----- That's all, folks -------------------------------------------------*/ |
| 405 | |
| 406 | #ifdef __cplusplus |
| 407 | } |
| 408 | #endif |