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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 | /* mpihelp-mul.c - MPI helper functions * Copyright (C) 1994, 1996, 1998, 1999, * 2000 Free Software Foundation, Inc. * * This file is part of GnuPG. * * GnuPG is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * GnuPG is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA * * Note: This code is heavily based on the GNU MP Library. * Actually it's the same code with only minor changes in the * way the data is stored; this is to support the abstraction * of an optional secure memory allocation which may be used * to avoid revealing of sensitive data due to paging etc. * The GNU MP Library itself is published under the LGPL; * however I decided to publish this code under the plain GPL. */ #include <linux/string.h> #include "mpi-internal.h" #include "longlong.h" #define MPN_MUL_N_RECURSE(prodp, up, vp, size, tspace) \ do { \ if ((size) < KARATSUBA_THRESHOLD) \ mul_n_basecase(prodp, up, vp, size); \ else \ mul_n(prodp, up, vp, size, tspace); \ } while (0); #define MPN_SQR_N_RECURSE(prodp, up, size, tspace) \ do { \ if ((size) < KARATSUBA_THRESHOLD) \ mpih_sqr_n_basecase(prodp, up, size); \ else \ mpih_sqr_n(prodp, up, size, tspace); \ } while (0); /* Multiply the natural numbers u (pointed to by UP) and v (pointed to by VP), * both with SIZE limbs, and store the result at PRODP. 2 * SIZE limbs are * always stored. Return the most significant limb. * * Argument constraints: * 1. PRODP != UP and PRODP != VP, i.e. the destination * must be distinct from the multiplier and the multiplicand. * * * Handle simple cases with traditional multiplication. * * This is the most critical code of multiplication. All multiplies rely * on this, both small and huge. Small ones arrive here immediately. Huge * ones arrive here as this is the base case for Karatsuba's recursive * algorithm below. */ static mpi_limb_t mul_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size) { mpi_size_t i; mpi_limb_t cy; mpi_limb_t v_limb; /* Multiply by the first limb in V separately, as the result can be * stored (not added) to PROD. We also avoid a loop for zeroing. */ v_limb = vp[0]; if (v_limb <= 1) { if (v_limb == 1) MPN_COPY(prodp, up, size); else MPN_ZERO(prodp, size); cy = 0; } else cy = mpihelp_mul_1(prodp, up, size, v_limb); prodp[size] = cy; prodp++; /* For each iteration in the outer loop, multiply one limb from * U with one limb from V, and add it to PROD. */ for (i = 1; i < size; i++) { v_limb = vp[i]; if (v_limb <= 1) { cy = 0; if (v_limb == 1) cy = mpihelp_add_n(prodp, prodp, up, size); } else cy = mpihelp_addmul_1(prodp, up, size, v_limb); prodp[size] = cy; prodp++; } return cy; } static void mul_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size, mpi_ptr_t tspace) { if (size & 1) { /* The size is odd, and the code below doesn't handle that. * Multiply the least significant (size - 1) limbs with a recursive * call, and handle the most significant limb of S1 and S2 * separately. * A slightly faster way to do this would be to make the Karatsuba * code below behave as if the size were even, and let it check for * odd size in the end. I.e., in essence move this code to the end. * Doing so would save us a recursive call, and potentially make the * stack grow a lot less. */ mpi_size_t esize = size - 1; /* even size */ mpi_limb_t cy_limb; MPN_MUL_N_RECURSE(prodp, up, vp, esize, tspace); cy_limb = mpihelp_addmul_1(prodp + esize, up, esize, vp[esize]); prodp[esize + esize] = cy_limb; cy_limb = mpihelp_addmul_1(prodp + esize, vp, size, up[esize]); prodp[esize + size] = cy_limb; } else { /* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm. * * Split U in two pieces, U1 and U0, such that * U = U0 + U1*(B**n), * and V in V1 and V0, such that * V = V0 + V1*(B**n). * * UV is then computed recursively using the identity * * 2n n n n * UV = (B + B )U V + B (U -U )(V -V ) + (B + 1)U V * 1 1 1 0 0 1 0 0 * * Where B = 2**BITS_PER_MP_LIMB. */ mpi_size_t hsize = size >> 1; mpi_limb_t cy; int negflg; /* Product H. ________________ ________________ * |_____U1 x V1____||____U0 x V0_____| * Put result in upper part of PROD and pass low part of TSPACE * as new TSPACE. */ MPN_MUL_N_RECURSE(prodp + size, up + hsize, vp + hsize, hsize, tspace); /* Product M. ________________ * |_(U1-U0)(V0-V1)_| */ if (mpihelp_cmp(up + hsize, up, hsize) >= 0) { mpihelp_sub_n(prodp, up + hsize, up, hsize); negflg = 0; } else { mpihelp_sub_n(prodp, up, up + hsize, hsize); negflg = 1; } if (mpihelp_cmp(vp + hsize, vp, hsize) >= 0) { mpihelp_sub_n(prodp + hsize, vp + hsize, vp, hsize); negflg ^= 1; } else { mpihelp_sub_n(prodp + hsize, vp, vp + hsize, hsize); /* No change of NEGFLG. */ } /* Read temporary operands from low part of PROD. * Put result in low part of TSPACE using upper part of TSPACE * as new TSPACE. */ MPN_MUL_N_RECURSE(tspace, prodp, prodp + hsize, hsize, tspace + size); /* Add/copy product H. */ MPN_COPY(prodp + hsize, prodp + size, hsize); cy = mpihelp_add_n(prodp + size, prodp + size, prodp + size + hsize, hsize); /* Add product M (if NEGFLG M is a negative number) */ if (negflg) cy -= mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace, size); else cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size); /* Product L. ________________ ________________ * |________________||____U0 x V0_____| * Read temporary operands from low part of PROD. * Put result in low part of TSPACE using upper part of TSPACE * as new TSPACE. */ MPN_MUL_N_RECURSE(tspace, up, vp, hsize, tspace + size); /* Add/copy Product L (twice) */ cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size); if (cy) mpihelp_add_1(prodp + hsize + size, prodp + hsize + size, hsize, cy); MPN_COPY(prodp, tspace, hsize); cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize, hsize); if (cy) mpihelp_add_1(prodp + size, prodp + size, size, 1); } } void mpih_sqr_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size) { mpi_size_t i; mpi_limb_t cy_limb; mpi_limb_t v_limb; /* Multiply by the first limb in V separately, as the result can be * stored (not added) to PROD. We also avoid a loop for zeroing. */ v_limb = up[0]; if (v_limb <= 1) { if (v_limb == 1) MPN_COPY(prodp, up, size); else MPN_ZERO(prodp, size); cy_limb = 0; } else cy_limb = mpihelp_mul_1(prodp, up, size, v_limb); prodp[size] = cy_limb; prodp++; /* For each iteration in the outer loop, multiply one limb from * U with one limb from V, and add it to PROD. */ for (i = 1; i < size; i++) { v_limb = up[i]; if (v_limb <= 1) { cy_limb = 0; if (v_limb == 1) cy_limb = mpihelp_add_n(prodp, prodp, up, size); } else cy_limb = mpihelp_addmul_1(prodp, up, size, v_limb); prodp[size] = cy_limb; prodp++; } } void mpih_sqr_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size, mpi_ptr_t tspace) { if (size & 1) { /* The size is odd, and the code below doesn't handle that. * Multiply the least significant (size - 1) limbs with a recursive * call, and handle the most significant limb of S1 and S2 * separately. * A slightly faster way to do this would be to make the Karatsuba * code below behave as if the size were even, and let it check for * odd size in the end. I.e., in essence move this code to the end. * Doing so would save us a recursive call, and potentially make the * stack grow a lot less. */ mpi_size_t esize = size - 1; /* even size */ mpi_limb_t cy_limb; MPN_SQR_N_RECURSE(prodp, up, esize, tspace); cy_limb = mpihelp_addmul_1(prodp + esize, up, esize, up[esize]); prodp[esize + esize] = cy_limb; cy_limb = mpihelp_addmul_1(prodp + esize, up, size, up[esize]); prodp[esize + size] = cy_limb; } else { mpi_size_t hsize = size >> 1; mpi_limb_t cy; /* Product H. ________________ ________________ * |_____U1 x U1____||____U0 x U0_____| * Put result in upper part of PROD and pass low part of TSPACE * as new TSPACE. */ MPN_SQR_N_RECURSE(prodp + size, up + hsize, hsize, tspace); /* Product M. ________________ * |_(U1-U0)(U0-U1)_| */ if (mpihelp_cmp(up + hsize, up, hsize) >= 0) mpihelp_sub_n(prodp, up + hsize, up, hsize); else mpihelp_sub_n(prodp, up, up + hsize, hsize); /* Read temporary operands from low part of PROD. * Put result in low part of TSPACE using upper part of TSPACE * as new TSPACE. */ MPN_SQR_N_RECURSE(tspace, prodp, hsize, tspace + size); /* Add/copy product H */ MPN_COPY(prodp + hsize, prodp + size, hsize); cy = mpihelp_add_n(prodp + size, prodp + size, prodp + size + hsize, hsize); /* Add product M (if NEGFLG M is a negative number). */ cy -= mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace, size); /* Product L. ________________ ________________ * |________________||____U0 x U0_____| * Read temporary operands from low part of PROD. * Put result in low part of TSPACE using upper part of TSPACE * as new TSPACE. */ MPN_SQR_N_RECURSE(tspace, up, hsize, tspace + size); /* Add/copy Product L (twice). */ cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size); if (cy) mpihelp_add_1(prodp + hsize + size, prodp + hsize + size, hsize, cy); MPN_COPY(prodp, tspace, hsize); cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize, hsize); if (cy) mpihelp_add_1(prodp + size, prodp + size, size, 1); } } int mpihelp_mul_karatsuba_case(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize, mpi_ptr_t vp, mpi_size_t vsize, struct karatsuba_ctx *ctx) { mpi_limb_t cy; if (!ctx->tspace || ctx->tspace_size < vsize) { if (ctx->tspace) mpi_free_limb_space(ctx->tspace); ctx->tspace = mpi_alloc_limb_space(2 * vsize); if (!ctx->tspace) return -ENOMEM; ctx->tspace_size = vsize; } MPN_MUL_N_RECURSE(prodp, up, vp, vsize, ctx->tspace); prodp += vsize; up += vsize; usize -= vsize; if (usize >= vsize) { if (!ctx->tp || ctx->tp_size < vsize) { if (ctx->tp) mpi_free_limb_space(ctx->tp); ctx->tp = mpi_alloc_limb_space(2 * vsize); if (!ctx->tp) { if (ctx->tspace) mpi_free_limb_space(ctx->tspace); ctx->tspace = NULL; return -ENOMEM; } ctx->tp_size = vsize; } do { MPN_MUL_N_RECURSE(ctx->tp, up, vp, vsize, ctx->tspace); cy = mpihelp_add_n(prodp, prodp, ctx->tp, vsize); mpihelp_add_1(prodp + vsize, ctx->tp + vsize, vsize, cy); prodp += vsize; up += vsize; usize -= vsize; } while (usize >= vsize); } if (usize) { if (usize < KARATSUBA_THRESHOLD) { mpi_limb_t tmp; if (mpihelp_mul(ctx->tspace, vp, vsize, up, usize, &tmp) < 0) return -ENOMEM; } else { if (!ctx->next) { ctx->next = kzalloc(sizeof *ctx, GFP_KERNEL); if (!ctx->next) return -ENOMEM; } if (mpihelp_mul_karatsuba_case(ctx->tspace, vp, vsize, up, usize, ctx->next) < 0) return -ENOMEM; } cy = mpihelp_add_n(prodp, prodp, ctx->tspace, vsize); mpihelp_add_1(prodp + vsize, ctx->tspace + vsize, usize, cy); } return 0; } void mpihelp_release_karatsuba_ctx(struct karatsuba_ctx *ctx) { struct karatsuba_ctx *ctx2; if (ctx->tp) mpi_free_limb_space(ctx->tp); if (ctx->tspace) mpi_free_limb_space(ctx->tspace); for (ctx = ctx->next; ctx; ctx = ctx2) { ctx2 = ctx->next; if (ctx->tp) mpi_free_limb_space(ctx->tp); if (ctx->tspace) mpi_free_limb_space(ctx->tspace); kfree(ctx); } } /* Multiply the natural numbers u (pointed to by UP, with USIZE limbs) * and v (pointed to by VP, with VSIZE limbs), and store the result at * PRODP. USIZE + VSIZE limbs are always stored, but if the input * operands are normalized. Return the most significant limb of the * result. * * NOTE: The space pointed to by PRODP is overwritten before finished * with U and V, so overlap is an error. * * Argument constraints: * 1. USIZE >= VSIZE. * 2. PRODP != UP and PRODP != VP, i.e. the destination * must be distinct from the multiplier and the multiplicand. */ int mpihelp_mul(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize, mpi_ptr_t vp, mpi_size_t vsize, mpi_limb_t *_result) { mpi_ptr_t prod_endp = prodp + usize + vsize - 1; mpi_limb_t cy; struct karatsuba_ctx ctx; if (vsize < KARATSUBA_THRESHOLD) { mpi_size_t i; mpi_limb_t v_limb; if (!vsize) { *_result = 0; return 0; } /* Multiply by the first limb in V separately, as the result can be * stored (not added) to PROD. We also avoid a loop for zeroing. */ v_limb = vp[0]; if (v_limb <= 1) { if (v_limb == 1) MPN_COPY(prodp, up, usize); else MPN_ZERO(prodp, usize); cy = 0; } else cy = mpihelp_mul_1(prodp, up, usize, v_limb); prodp[usize] = cy; prodp++; /* For each iteration in the outer loop, multiply one limb from * U with one limb from V, and add it to PROD. */ for (i = 1; i < vsize; i++) { v_limb = vp[i]; if (v_limb <= 1) { cy = 0; if (v_limb == 1) cy = mpihelp_add_n(prodp, prodp, up, usize); } else cy = mpihelp_addmul_1(prodp, up, usize, v_limb); prodp[usize] = cy; prodp++; } *_result = cy; return 0; } memset(&ctx, 0, sizeof ctx); if (mpihelp_mul_karatsuba_case(prodp, up, usize, vp, vsize, &ctx) < 0) return -ENOMEM; mpihelp_release_karatsuba_ctx(&ctx); *_result = *prod_endp; return 0; } |