| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id$ |
| 4 | * |
| 5 | * Efficient reduction modulo nice primes |
| 6 | * |
| 7 | * (c) 2004 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 | /*----- Header files ------------------------------------------------------*/ |
| 31 | |
| 32 | #include <mLib/darray.h> |
| 33 | #include <mLib/macros.h> |
| 34 | |
| 35 | #include "mp.h" |
| 36 | #include "mpreduce.h" |
| 37 | #include "mpreduce-exp.h" |
| 38 | |
| 39 | /*----- Data structures ---------------------------------------------------*/ |
| 40 | |
| 41 | DA_DECL(instr_v, mpreduce_instr); |
| 42 | |
| 43 | /*----- Main code ---------------------------------------------------------*/ |
| 44 | |
| 45 | /* --- @mpreduce_create@ --- * |
| 46 | * |
| 47 | * Arguments: @gfreduce *r@ = structure to fill in |
| 48 | * @mp *x@ = an integer |
| 49 | * |
| 50 | * Returns: Zero if successful; nonzero on failure. |
| 51 | * |
| 52 | * Use: Initializes a context structure for reduction. |
| 53 | */ |
| 54 | |
| 55 | int mpreduce_create(mpreduce *r, mp *p) |
| 56 | { |
| 57 | mpscan sc; |
| 58 | enum { Z = 0, Z1 = 2, X = 4, X0 = 6 }; |
| 59 | unsigned st = Z; |
| 60 | instr_v iv = DA_INIT; |
| 61 | unsigned long d, i; |
| 62 | unsigned op; |
| 63 | size_t w, b; |
| 64 | |
| 65 | /* --- Fill in the easy stuff --- */ |
| 66 | |
| 67 | if (!MP_POSP(p)) |
| 68 | return (-1); |
| 69 | d = mp_bits(p); |
| 70 | r->lim = d/MPW_BITS; |
| 71 | r->s = d%MPW_BITS; |
| 72 | if (r->s) |
| 73 | r->lim++; |
| 74 | r->p = mp_copy(p); |
| 75 | |
| 76 | /* --- Stash a new instruction --- */ |
| 77 | |
| 78 | #define INSTR(op_, argx_, argy_) do { \ |
| 79 | DA_ENSURE(&iv, 1); \ |
| 80 | DA(&iv)[DA_LEN(&iv)].op = (op_); \ |
| 81 | DA(&iv)[DA_LEN(&iv)].argx = (argx_); \ |
| 82 | DA(&iv)[DA_LEN(&iv)].argy = (argy_); \ |
| 83 | DA_EXTEND(&iv, 1); \ |
| 84 | } while (0) |
| 85 | |
| 86 | /* --- Main loop --- * |
| 87 | * |
| 88 | * A simple state machine decomposes @p@ conveniently into positive and |
| 89 | * negative powers of 2. The pure form of the state machine is left below |
| 90 | * for reference (and in case I need inspiration for a NAF exponentiator). |
| 91 | */ |
| 92 | |
| 93 | #ifdef DEBUG |
| 94 | for (i = 0, mp_scan(&sc, p); mp_step(&sc); i++) { |
| 95 | switch (st | mp_bit(&sc)) { |
| 96 | case Z | 1: st = Z1; break; |
| 97 | case Z1 | 0: st = Z; printf("+ %lu\n", i - 1); break; |
| 98 | case Z1 | 1: st = X; printf("- %lu\n", i - 1); break; |
| 99 | case X | 0: st = X0; break; |
| 100 | case X0 | 1: st = X; printf("- %lu\n", i - 1); break; |
| 101 | case X0 | 0: st = Z; printf("+ %lu\n", i - 1); break; |
| 102 | } |
| 103 | } |
| 104 | if (st >= X) printf("+ %lu\n", i - 1); |
| 105 | st = Z; |
| 106 | #endif |
| 107 | |
| 108 | for (i = 0, mp_scan(&sc, p); i < d && mp_step(&sc); i++) { |
| 109 | switch (st | mp_bit(&sc)) { |
| 110 | case Z | 1: st = Z1; break; |
| 111 | case Z1 | 0: st = Z; op = MPRI_SUB; goto instr; |
| 112 | case Z1 | 1: st = X; op = MPRI_ADD; goto instr; |
| 113 | case X | 0: st = X0; break; |
| 114 | case X0 | 1: st = X; op = MPRI_ADD; goto instr; |
| 115 | case X0 | 0: st = Z; op = MPRI_SUB; goto instr; |
| 116 | instr: |
| 117 | w = (d - i)/MPW_BITS + 1; |
| 118 | b = (MPW_BITS + i - d - 1)%MPW_BITS; |
| 119 | INSTR(op | !!b, w, b); |
| 120 | } |
| 121 | } |
| 122 | if (DA_LEN(&iv) && (DA(&iv)[DA_LEN(&iv) - 1].op & ~1u) == MPRI_SUB) { |
| 123 | mp_drop(r->p); |
| 124 | DA_DESTROY(&iv); |
| 125 | return (-1); |
| 126 | } |
| 127 | |
| 128 | #undef INSTR |
| 129 | |
| 130 | /* --- Wrap up --- */ |
| 131 | |
| 132 | r->in = DA_LEN(&iv); |
| 133 | if (!r->in) |
| 134 | r->iv = 0; |
| 135 | else if (!r->s) { |
| 136 | r->iv = xmalloc(r->in * sizeof(mpreduce_instr)); |
| 137 | memcpy(r->iv, DA(&iv), r->in * sizeof(mpreduce_instr)); |
| 138 | } else { |
| 139 | r->iv = xmalloc(r->in * 2 * sizeof(mpreduce_instr)); |
| 140 | for (i = 0; i < r->in; i++) { |
| 141 | r->iv[i] = DA(&iv)[i]; |
| 142 | op = r->iv[i].op & ~1u; |
| 143 | w = r->iv[i].argx; |
| 144 | b = r->iv[i].argy; |
| 145 | b += r->s; |
| 146 | if (b >= MPW_BITS) { |
| 147 | b -= MPW_BITS; |
| 148 | w--; |
| 149 | } |
| 150 | if (b) op |= 1; |
| 151 | r->iv[i + r->in].op = op; |
| 152 | r->iv[i + r->in].argx = w; |
| 153 | r->iv[i + r->in].argy = b; |
| 154 | } |
| 155 | } |
| 156 | DA_DESTROY(&iv); |
| 157 | return (0); |
| 158 | } |
| 159 | |
| 160 | /* --- @mpreduce_destroy@ --- * |
| 161 | * |
| 162 | * Arguments: @mpreduce *r@ = structure to free |
| 163 | * |
| 164 | * Returns: --- |
| 165 | * |
| 166 | * Use: Reclaims the resources from a reduction context. |
| 167 | */ |
| 168 | |
| 169 | void mpreduce_destroy(mpreduce *r) |
| 170 | { |
| 171 | mp_drop(r->p); |
| 172 | if (r->iv) xfree(r->iv); |
| 173 | } |
| 174 | |
| 175 | /* --- @mpreduce_dump@ --- * |
| 176 | * |
| 177 | * Arguments: @mpreduce *r@ = structure to dump |
| 178 | * @FILE *fp@ = file to dump on |
| 179 | * |
| 180 | * Returns: --- |
| 181 | * |
| 182 | * Use: Dumps a reduction context. |
| 183 | */ |
| 184 | |
| 185 | void mpreduce_dump(mpreduce *r, FILE *fp) |
| 186 | { |
| 187 | size_t i; |
| 188 | static const char *opname[] = { "add", "addshift", "sub", "subshift" }; |
| 189 | |
| 190 | fprintf(fp, "mod = "); mp_writefile(r->p, fp, 16); |
| 191 | fprintf(fp, "\n lim = %lu; s = %d\n", (unsigned long)r->lim, r->s); |
| 192 | for (i = 0; i < r->in; i++) { |
| 193 | assert(r->iv[i].op < N(opname)); |
| 194 | fprintf(fp, " %s %lu %lu\n", |
| 195 | opname[r->iv[i].op], |
| 196 | (unsigned long)r->iv[i].argx, |
| 197 | (unsigned long)r->iv[i].argy); |
| 198 | } |
| 199 | if (r->s) { |
| 200 | fprintf(fp, "tail end charlie\n"); |
| 201 | for (i = r->in; i < 2 * r->in; i++) { |
| 202 | assert(r->iv[i].op < N(opname)); |
| 203 | fprintf(fp, " %s %lu %lu\n", |
| 204 | opname[r->iv[i].op], |
| 205 | (unsigned long)r->iv[i].argx, |
| 206 | (unsigned long)r->iv[i].argy); |
| 207 | } |
| 208 | } |
| 209 | } |
| 210 | |
| 211 | /* --- @mpreduce_do@ --- * |
| 212 | * |
| 213 | * Arguments: @mpreduce *r@ = reduction context |
| 214 | * @mp *d@ = destination |
| 215 | * @mp *x@ = source |
| 216 | * |
| 217 | * Returns: Destination, @x@ reduced modulo the reduction poly. |
| 218 | */ |
| 219 | |
| 220 | static void run(const mpreduce_instr *i, const mpreduce_instr *il, |
| 221 | mpw *v, mpw z) |
| 222 | { |
| 223 | for (; i < il; i++) { |
| 224 | #ifdef DEBUG |
| 225 | mp vv; |
| 226 | mp_build(&vv, v - i->argx, v + 1); |
| 227 | printf(" 0x"); mp_writefile(&vv, stdout, 16); |
| 228 | printf(" %c (0x%lx << %u) == 0x", |
| 229 | (i->op & ~1u) == MPRI_ADD ? '+' : '-', |
| 230 | (unsigned long)z, |
| 231 | i->argy); |
| 232 | #endif |
| 233 | switch (i->op) { |
| 234 | case MPRI_ADD: MPX_UADDN(v - i->argx, v + 1, z); break; |
| 235 | case MPRI_ADDLSL: mpx_uaddnlsl(v - i->argx, v + 1, z, i->argy); break; |
| 236 | case MPRI_SUB: MPX_USUBN(v - i->argx, v + 1, z); break; |
| 237 | case MPRI_SUBLSL: mpx_usubnlsl(v - i->argx, v + 1, z, i->argy); break; |
| 238 | default: |
| 239 | abort(); |
| 240 | } |
| 241 | #ifdef DEBUG |
| 242 | mp_build(&vv, v - i->argx, v + 1); |
| 243 | mp_writefile(&vv, stdout, 16); |
| 244 | printf("\n"); |
| 245 | #endif |
| 246 | } |
| 247 | } |
| 248 | |
| 249 | mp *mpreduce_do(mpreduce *r, mp *d, mp *x) |
| 250 | { |
| 251 | mpw *v, *vl; |
| 252 | const mpreduce_instr *il; |
| 253 | mpw z; |
| 254 | |
| 255 | #ifdef DEBUG |
| 256 | mp *_r = 0, *_rr = 0; |
| 257 | #endif |
| 258 | |
| 259 | /* --- If source is negative, divide --- */ |
| 260 | |
| 261 | if (MP_NEGP(x)) { |
| 262 | mp_div(0, &d, x, r->p); |
| 263 | return (d); |
| 264 | } |
| 265 | |
| 266 | /* --- Try to reuse the source's space --- */ |
| 267 | |
| 268 | MP_COPY(x); |
| 269 | if (d) MP_DROP(d); |
| 270 | MP_DEST(x, MP_LEN(x), x->f); |
| 271 | |
| 272 | /* --- Do the reduction --- */ |
| 273 | |
| 274 | #ifdef DEBUG |
| 275 | _r = MP_NEW; |
| 276 | mp_div(0, &_r, x, r->p); |
| 277 | MP_PRINTX("x", x); |
| 278 | _rr = 0; |
| 279 | #endif |
| 280 | |
| 281 | il = r->iv + r->in; |
| 282 | if (MP_LEN(x) >= r->lim) { |
| 283 | v = x->v + r->lim; |
| 284 | vl = x->vl; |
| 285 | while (vl-- > v) { |
| 286 | while (*vl) { |
| 287 | z = *vl; |
| 288 | *vl = 0; |
| 289 | run(r->iv, il, vl, z); |
| 290 | #ifdef DEBUG |
| 291 | MP_PRINTX("x", x); |
| 292 | mp_div(0, &_rr, x, r->p); |
| 293 | assert(MP_EQ(_r, _rr)); |
| 294 | #endif |
| 295 | } |
| 296 | } |
| 297 | if (r->s) { |
| 298 | while (*vl >> r->s) { |
| 299 | z = *vl >> r->s; |
| 300 | *vl &= ((1 << r->s) - 1); |
| 301 | run(r->iv + r->in, il + r->in, vl, z); |
| 302 | #ifdef DEBUG |
| 303 | MP_PRINTX("x", x); |
| 304 | mp_div(0, &_rr, x, r->p); |
| 305 | assert(MP_EQ(_r, _rr)); |
| 306 | #endif |
| 307 | } |
| 308 | } |
| 309 | } |
| 310 | |
| 311 | /* --- Finishing touches --- */ |
| 312 | |
| 313 | MP_SHRINK(x); |
| 314 | if (MP_CMP(x, >=, r->p)) |
| 315 | x = mp_sub(x, x, r->p); |
| 316 | |
| 317 | /* --- Done --- */ |
| 318 | |
| 319 | #ifdef DEBUG |
| 320 | assert(MP_EQ(_r, x)); |
| 321 | mp_drop(_r); |
| 322 | mp_drop(_rr); |
| 323 | #endif |
| 324 | return (x); |
| 325 | } |
| 326 | |
| 327 | /* --- @mpreduce_exp@ --- * |
| 328 | * |
| 329 | * Arguments: @mpreduce *mr@ = pointer to reduction context |
| 330 | * @mp *d@ = fake destination |
| 331 | * @mp *a@ = base |
| 332 | * @mp *e@ = exponent |
| 333 | * |
| 334 | * Returns: Result, %$a^e \bmod m$%. |
| 335 | */ |
| 336 | |
| 337 | mp *mpreduce_exp(mpreduce *mr, mp *d, mp *a, mp *e) |
| 338 | { |
| 339 | mp *x = MP_ONE; |
| 340 | mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW; |
| 341 | |
| 342 | MP_SHRINK(e); |
| 343 | MP_COPY(a); |
| 344 | if (MP_ZEROP(e)) |
| 345 | ; |
| 346 | else { |
| 347 | if (MP_NEGP(e)) |
| 348 | a = mp_modinv(a, a, mr->p); |
| 349 | if (MP_LEN(e) < EXP_THRESH) |
| 350 | EXP_SIMPLE(x, a, e); |
| 351 | else |
| 352 | EXP_WINDOW(x, a, e); |
| 353 | } |
| 354 | mp_drop(a); |
| 355 | mp_drop(d); |
| 356 | mp_drop(spare); |
| 357 | return (x); |
| 358 | } |
| 359 | |
| 360 | /*----- Test rig ----------------------------------------------------------*/ |
| 361 | |
| 362 | |
| 363 | #ifdef TEST_RIG |
| 364 | |
| 365 | #define MP(x) mp_readstring(MP_NEW, #x, 0, 0) |
| 366 | |
| 367 | static int vreduce(dstr *v) |
| 368 | { |
| 369 | mp *d = *(mp **)v[0].buf; |
| 370 | mp *n = *(mp **)v[1].buf; |
| 371 | mp *r = *(mp **)v[2].buf; |
| 372 | mp *c; |
| 373 | int ok = 1; |
| 374 | mpreduce rr; |
| 375 | |
| 376 | mpreduce_create(&rr, d); |
| 377 | c = mpreduce_do(&rr, MP_NEW, n); |
| 378 | if (!MP_EQ(c, r)) { |
| 379 | fprintf(stderr, "\n*** reduction failed\n*** "); |
| 380 | mpreduce_dump(&rr, stderr); |
| 381 | fprintf(stderr, "\n*** n = "); mp_writefile(n, stderr, 10); |
| 382 | fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 10); |
| 383 | fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 10); |
| 384 | fprintf(stderr, "\n"); |
| 385 | ok = 0; |
| 386 | } |
| 387 | mpreduce_destroy(&rr); |
| 388 | mp_drop(n); mp_drop(d); mp_drop(r); mp_drop(c); |
| 389 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
| 390 | return (ok); |
| 391 | } |
| 392 | |
| 393 | static int vmodexp(dstr *v) |
| 394 | { |
| 395 | mp *p = *(mp **)v[0].buf; |
| 396 | mp *g = *(mp **)v[1].buf; |
| 397 | mp *x = *(mp **)v[2].buf; |
| 398 | mp *r = *(mp **)v[3].buf; |
| 399 | mp *c; |
| 400 | int ok = 1; |
| 401 | mpreduce rr; |
| 402 | |
| 403 | mpreduce_create(&rr, p); |
| 404 | c = mpreduce_exp(&rr, MP_NEW, g, x); |
| 405 | if (!MP_EQ(c, r)) { |
| 406 | fprintf(stderr, "\n*** modexp failed\n*** "); |
| 407 | fprintf(stderr, "\n*** p = "); mp_writefile(p, stderr, 10); |
| 408 | fprintf(stderr, "\n*** g = "); mp_writefile(g, stderr, 10); |
| 409 | fprintf(stderr, "\n*** x = "); mp_writefile(x, stderr, 10); |
| 410 | fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 10); |
| 411 | fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 10); |
| 412 | fprintf(stderr, "\n"); |
| 413 | ok = 0; |
| 414 | } |
| 415 | mpreduce_destroy(&rr); |
| 416 | mp_drop(p); mp_drop(g); mp_drop(r); mp_drop(x); mp_drop(c); |
| 417 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
| 418 | return (ok); |
| 419 | } |
| 420 | |
| 421 | static test_chunk defs[] = { |
| 422 | { "reduce", vreduce, { &type_mp, &type_mp, &type_mp, 0 } }, |
| 423 | { "modexp", vmodexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
| 424 | { 0, 0, { 0 } } |
| 425 | }; |
| 426 | |
| 427 | int main(int argc, char *argv[]) |
| 428 | { |
| 429 | test_run(argc, argv, defs, SRCDIR"/tests/mpreduce"); |
| 430 | return (0); |
| 431 | } |
| 432 | |
| 433 | #endif |
| 434 | |
| 435 | /*----- That's all, folks -------------------------------------------------*/ |