[457] | 1 | /* integer.c
|
---|
| 2 | *
|
---|
| 3 | * Copyright (C) 2006-2020 wolfSSL Inc.
|
---|
| 4 | *
|
---|
| 5 | * This file is part of wolfSSL.
|
---|
| 6 | *
|
---|
| 7 | * wolfSSL is free software; you can redistribute it and/or modify
|
---|
| 8 | * it under the terms of the GNU General Public License as published by
|
---|
| 9 | * the Free Software Foundation; either version 2 of the License, or
|
---|
| 10 | * (at your option) any later version.
|
---|
| 11 | *
|
---|
| 12 | * wolfSSL is distributed in the hope that it will be useful,
|
---|
| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
|
---|
| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
---|
| 15 | * GNU General Public License for more details.
|
---|
| 16 | *
|
---|
| 17 | * You should have received a copy of the GNU General Public License
|
---|
| 18 | * along with this program; if not, write to the Free Software
|
---|
| 19 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335, USA
|
---|
| 20 | */
|
---|
| 21 |
|
---|
| 22 |
|
---|
| 23 |
|
---|
| 24 | /*
|
---|
| 25 | * Based on public domain LibTomMath 0.38 by Tom St Denis, tomstdenis@iahu.ca,
|
---|
| 26 | * http://math.libtomcrypt.com
|
---|
| 27 | */
|
---|
| 28 |
|
---|
| 29 |
|
---|
| 30 | #ifdef HAVE_CONFIG_H
|
---|
| 31 | #include <config.h>
|
---|
| 32 | #endif
|
---|
| 33 |
|
---|
| 34 | /* in case user set USE_FAST_MATH there */
|
---|
| 35 | #include <wolfssl/wolfcrypt/settings.h>
|
---|
| 36 |
|
---|
| 37 | #ifdef NO_INLINE
|
---|
| 38 | #include <wolfssl/wolfcrypt/misc.h>
|
---|
| 39 | #else
|
---|
| 40 | #define WOLFSSL_MISC_INCLUDED
|
---|
| 41 | #include <wolfcrypt/src/misc.c>
|
---|
| 42 | #endif
|
---|
| 43 |
|
---|
| 44 | #ifndef NO_BIG_INT
|
---|
| 45 |
|
---|
| 46 | #ifndef USE_FAST_MATH
|
---|
| 47 |
|
---|
| 48 | #ifndef WOLFSSL_SP_MATH
|
---|
| 49 |
|
---|
| 50 | #include <wolfssl/wolfcrypt/integer.h>
|
---|
| 51 |
|
---|
| 52 | #if defined(FREESCALE_LTC_TFM)
|
---|
| 53 | #include <wolfssl/wolfcrypt/port/nxp/ksdk_port.h>
|
---|
| 54 | #endif
|
---|
| 55 | #ifdef WOLFSSL_DEBUG_MATH
|
---|
| 56 | #include <stdio.h>
|
---|
| 57 | #endif
|
---|
| 58 |
|
---|
| 59 | #ifdef SHOW_GEN
|
---|
| 60 | #ifndef NO_STDIO_FILESYSTEM
|
---|
| 61 | #include <stdio.h>
|
---|
| 62 | #endif
|
---|
| 63 | #endif
|
---|
| 64 |
|
---|
| 65 | #if defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH)
|
---|
| 66 | #ifdef __cplusplus
|
---|
| 67 | extern "C" {
|
---|
| 68 | #endif
|
---|
| 69 | WOLFSSL_LOCAL int sp_ModExp_1024(mp_int* base, mp_int* exp, mp_int* mod,
|
---|
| 70 | mp_int* res);
|
---|
| 71 | WOLFSSL_LOCAL int sp_ModExp_1536(mp_int* base, mp_int* exp, mp_int* mod,
|
---|
| 72 | mp_int* res);
|
---|
| 73 | WOLFSSL_LOCAL int sp_ModExp_2048(mp_int* base, mp_int* exp, mp_int* mod,
|
---|
| 74 | mp_int* res);
|
---|
| 75 | WOLFSSL_LOCAL int sp_ModExp_3072(mp_int* base, mp_int* exp, mp_int* mod,
|
---|
| 76 | mp_int* res);
|
---|
| 77 | WOLFSSL_LOCAL int sp_ModExp_4096(mp_int* base, mp_int* exp, mp_int* mod,
|
---|
| 78 | mp_int* res);
|
---|
| 79 | #ifdef __cplusplus
|
---|
| 80 | } /* extern "C" */
|
---|
| 81 | #endif
|
---|
| 82 | #endif
|
---|
| 83 |
|
---|
| 84 | /* reverse an array, used for radix code */
|
---|
| 85 | static void
|
---|
| 86 | bn_reverse (unsigned char *s, int len)
|
---|
| 87 | {
|
---|
| 88 | int ix, iy;
|
---|
| 89 | unsigned char t;
|
---|
| 90 |
|
---|
| 91 | ix = 0;
|
---|
| 92 | iy = len - 1;
|
---|
| 93 | while (ix < iy) {
|
---|
| 94 | t = s[ix];
|
---|
| 95 | s[ix] = s[iy];
|
---|
| 96 | s[iy] = t;
|
---|
| 97 | ++ix;
|
---|
| 98 | --iy;
|
---|
| 99 | }
|
---|
| 100 | }
|
---|
| 101 |
|
---|
| 102 | /* math settings check */
|
---|
| 103 | word32 CheckRunTimeSettings(void)
|
---|
| 104 | {
|
---|
| 105 | return CTC_SETTINGS;
|
---|
| 106 | }
|
---|
| 107 |
|
---|
| 108 |
|
---|
| 109 | /* handle up to 6 inits */
|
---|
| 110 | int mp_init_multi(mp_int* a, mp_int* b, mp_int* c, mp_int* d, mp_int* e,
|
---|
| 111 | mp_int* f)
|
---|
| 112 | {
|
---|
| 113 | int res = MP_OKAY;
|
---|
| 114 |
|
---|
| 115 | if (a) XMEMSET(a, 0, sizeof(mp_int));
|
---|
| 116 | if (b) XMEMSET(b, 0, sizeof(mp_int));
|
---|
| 117 | if (c) XMEMSET(c, 0, sizeof(mp_int));
|
---|
| 118 | if (d) XMEMSET(d, 0, sizeof(mp_int));
|
---|
| 119 | if (e) XMEMSET(e, 0, sizeof(mp_int));
|
---|
| 120 | if (f) XMEMSET(f, 0, sizeof(mp_int));
|
---|
| 121 |
|
---|
| 122 | if (a && ((res = mp_init(a)) != MP_OKAY))
|
---|
| 123 | return res;
|
---|
| 124 |
|
---|
| 125 | if (b && ((res = mp_init(b)) != MP_OKAY)) {
|
---|
| 126 | mp_clear(a);
|
---|
| 127 | return res;
|
---|
| 128 | }
|
---|
| 129 |
|
---|
| 130 | if (c && ((res = mp_init(c)) != MP_OKAY)) {
|
---|
| 131 | mp_clear(a); mp_clear(b);
|
---|
| 132 | return res;
|
---|
| 133 | }
|
---|
| 134 |
|
---|
| 135 | if (d && ((res = mp_init(d)) != MP_OKAY)) {
|
---|
| 136 | mp_clear(a); mp_clear(b); mp_clear(c);
|
---|
| 137 | return res;
|
---|
| 138 | }
|
---|
| 139 |
|
---|
| 140 | if (e && ((res = mp_init(e)) != MP_OKAY)) {
|
---|
| 141 | mp_clear(a); mp_clear(b); mp_clear(c); mp_clear(d);
|
---|
| 142 | return res;
|
---|
| 143 | }
|
---|
| 144 |
|
---|
| 145 | if (f && ((res = mp_init(f)) != MP_OKAY)) {
|
---|
| 146 | mp_clear(a); mp_clear(b); mp_clear(c); mp_clear(d); mp_clear(e);
|
---|
| 147 | return res;
|
---|
| 148 | }
|
---|
| 149 |
|
---|
| 150 | return res;
|
---|
| 151 | }
|
---|
| 152 |
|
---|
| 153 |
|
---|
| 154 | /* init a new mp_int */
|
---|
| 155 | int mp_init (mp_int * a)
|
---|
| 156 | {
|
---|
| 157 | /* Safeguard against passing in a null pointer */
|
---|
| 158 | if (a == NULL)
|
---|
| 159 | return MP_VAL;
|
---|
| 160 |
|
---|
| 161 | /* defer allocation until mp_grow */
|
---|
| 162 | a->dp = NULL;
|
---|
| 163 |
|
---|
| 164 | /* set the used to zero, allocated digits to the default precision
|
---|
| 165 | * and sign to positive */
|
---|
| 166 | a->used = 0;
|
---|
| 167 | a->alloc = 0;
|
---|
| 168 | a->sign = MP_ZPOS;
|
---|
| 169 | #ifdef HAVE_WOLF_BIGINT
|
---|
| 170 | wc_bigint_init(&a->raw);
|
---|
| 171 | #endif
|
---|
| 172 |
|
---|
| 173 | return MP_OKAY;
|
---|
| 174 | }
|
---|
| 175 |
|
---|
| 176 |
|
---|
| 177 | /* clear one (frees) */
|
---|
| 178 | void mp_clear (mp_int * a)
|
---|
| 179 | {
|
---|
| 180 | int i;
|
---|
| 181 |
|
---|
| 182 | if (a == NULL)
|
---|
| 183 | return;
|
---|
| 184 |
|
---|
| 185 | /* only do anything if a hasn't been freed previously */
|
---|
| 186 | if (a->dp != NULL) {
|
---|
| 187 | /* first zero the digits */
|
---|
| 188 | for (i = 0; i < a->used; i++) {
|
---|
| 189 | a->dp[i] = 0;
|
---|
| 190 | }
|
---|
| 191 |
|
---|
| 192 | /* free ram */
|
---|
| 193 | mp_free(a);
|
---|
| 194 |
|
---|
| 195 | /* reset members to make debugging easier */
|
---|
| 196 | a->alloc = a->used = 0;
|
---|
| 197 | a->sign = MP_ZPOS;
|
---|
| 198 | }
|
---|
| 199 | }
|
---|
| 200 |
|
---|
| 201 | void mp_free (mp_int * a)
|
---|
| 202 | {
|
---|
| 203 | /* only do anything if a hasn't been freed previously */
|
---|
| 204 | if (a->dp != NULL) {
|
---|
| 205 | /* free ram */
|
---|
| 206 | XFREE(a->dp, 0, DYNAMIC_TYPE_BIGINT);
|
---|
| 207 | a->dp = NULL;
|
---|
| 208 | }
|
---|
| 209 |
|
---|
| 210 | #ifdef HAVE_WOLF_BIGINT
|
---|
| 211 | wc_bigint_free(&a->raw);
|
---|
| 212 | #endif
|
---|
| 213 | }
|
---|
| 214 |
|
---|
| 215 | void mp_forcezero(mp_int * a)
|
---|
| 216 | {
|
---|
| 217 | if (a == NULL)
|
---|
| 218 | return;
|
---|
| 219 |
|
---|
| 220 | /* only do anything if a hasn't been freed previously */
|
---|
| 221 | if (a->dp != NULL) {
|
---|
| 222 | /* force zero the used digits */
|
---|
| 223 | ForceZero(a->dp, a->used * sizeof(mp_digit));
|
---|
| 224 | #ifdef HAVE_WOLF_BIGINT
|
---|
| 225 | wc_bigint_zero(&a->raw);
|
---|
| 226 | #endif
|
---|
| 227 | /* free ram */
|
---|
| 228 | mp_free(a);
|
---|
| 229 |
|
---|
| 230 | /* reset members to make debugging easier */
|
---|
| 231 | a->alloc = a->used = 0;
|
---|
| 232 | a->sign = MP_ZPOS;
|
---|
| 233 | }
|
---|
| 234 |
|
---|
| 235 | a->sign = MP_ZPOS;
|
---|
| 236 | a->used = 0;
|
---|
| 237 | }
|
---|
| 238 |
|
---|
| 239 |
|
---|
| 240 | /* get the size for an unsigned equivalent */
|
---|
| 241 | int mp_unsigned_bin_size (mp_int * a)
|
---|
| 242 | {
|
---|
| 243 | int size = mp_count_bits (a);
|
---|
| 244 | return (size / 8 + ((size & 7) != 0 ? 1 : 0));
|
---|
| 245 | }
|
---|
| 246 |
|
---|
| 247 |
|
---|
| 248 | /* returns the number of bits in an int */
|
---|
| 249 | int mp_count_bits (mp_int * a)
|
---|
| 250 | {
|
---|
| 251 | int r;
|
---|
| 252 | mp_digit q;
|
---|
| 253 |
|
---|
| 254 | /* shortcut */
|
---|
| 255 | if (a->used == 0) {
|
---|
| 256 | return 0;
|
---|
| 257 | }
|
---|
| 258 |
|
---|
| 259 | /* get number of digits and add that */
|
---|
| 260 | r = (a->used - 1) * DIGIT_BIT;
|
---|
| 261 |
|
---|
| 262 | /* take the last digit and count the bits in it */
|
---|
| 263 | q = a->dp[a->used - 1];
|
---|
| 264 | while (q > ((mp_digit) 0)) {
|
---|
| 265 | ++r;
|
---|
| 266 | q >>= ((mp_digit) 1);
|
---|
| 267 | }
|
---|
| 268 | return r;
|
---|
| 269 | }
|
---|
| 270 |
|
---|
| 271 |
|
---|
| 272 | int mp_leading_bit (mp_int * a)
|
---|
| 273 | {
|
---|
[464] | 274 | int c = mp_count_bits(a);
|
---|
[457] | 275 |
|
---|
[464] | 276 | if (c == 0) return 0;
|
---|
| 277 | return (c % 8) == 0;
|
---|
[457] | 278 | }
|
---|
| 279 |
|
---|
| 280 | int mp_to_unsigned_bin_at_pos(int x, mp_int *t, unsigned char *b)
|
---|
| 281 | {
|
---|
| 282 | int res = 0;
|
---|
| 283 | while (mp_iszero(t) == MP_NO) {
|
---|
| 284 | #ifndef MP_8BIT
|
---|
| 285 | b[x++] = (unsigned char) (t->dp[0] & 255);
|
---|
| 286 | #else
|
---|
| 287 | b[x++] = (unsigned char) (t->dp[0] | ((t->dp[1] & 0x01) << 7));
|
---|
| 288 | #endif
|
---|
| 289 | if ((res = mp_div_2d (t, 8, t, NULL)) != MP_OKAY) {
|
---|
| 290 | return res;
|
---|
| 291 | }
|
---|
| 292 | res = x;
|
---|
| 293 | }
|
---|
| 294 | return res;
|
---|
| 295 | }
|
---|
| 296 |
|
---|
| 297 | /* store in unsigned [big endian] format */
|
---|
| 298 | int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
|
---|
| 299 | {
|
---|
| 300 | int x, res;
|
---|
| 301 | mp_int t;
|
---|
| 302 |
|
---|
| 303 | if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
|
---|
| 304 | return res;
|
---|
| 305 | }
|
---|
| 306 |
|
---|
| 307 | x = mp_to_unsigned_bin_at_pos(0, &t, b);
|
---|
| 308 | if (x < 0) {
|
---|
| 309 | mp_clear(&t);
|
---|
| 310 | return x;
|
---|
| 311 | }
|
---|
| 312 |
|
---|
| 313 | bn_reverse (b, x);
|
---|
| 314 | mp_clear (&t);
|
---|
| 315 | return res;
|
---|
| 316 | }
|
---|
| 317 |
|
---|
| 318 | int mp_to_unsigned_bin_len(mp_int * a, unsigned char *b, int c)
|
---|
| 319 | {
|
---|
| 320 | int i, len;
|
---|
| 321 |
|
---|
| 322 | len = mp_unsigned_bin_size(a);
|
---|
| 323 |
|
---|
[464] | 324 | if (len > c) {
|
---|
| 325 | return MP_VAL;
|
---|
| 326 | }
|
---|
| 327 |
|
---|
[457] | 328 | /* pad front w/ zeros to match length */
|
---|
[464] | 329 | for (i = 0; i < c - len; i++) {
|
---|
| 330 | b[i] = 0x00;
|
---|
| 331 | }
|
---|
[457] | 332 | return mp_to_unsigned_bin(a, b + i);
|
---|
| 333 | }
|
---|
| 334 |
|
---|
| 335 | /* creates "a" then copies b into it */
|
---|
| 336 | int mp_init_copy (mp_int * a, mp_int * b)
|
---|
| 337 | {
|
---|
| 338 | int res;
|
---|
| 339 |
|
---|
| 340 | if ((res = mp_init_size (a, b->used)) != MP_OKAY) {
|
---|
| 341 | return res;
|
---|
| 342 | }
|
---|
| 343 |
|
---|
| 344 | if((res = mp_copy (b, a)) != MP_OKAY) {
|
---|
| 345 | mp_clear(a);
|
---|
| 346 | }
|
---|
| 347 |
|
---|
| 348 | return res;
|
---|
| 349 | }
|
---|
| 350 |
|
---|
| 351 |
|
---|
| 352 | /* copy, b = a */
|
---|
| 353 | int mp_copy (mp_int * a, mp_int * b)
|
---|
| 354 | {
|
---|
| 355 | int res, n;
|
---|
| 356 |
|
---|
| 357 | /* Safeguard against passing in a null pointer */
|
---|
| 358 | if (a == NULL || b == NULL)
|
---|
| 359 | return MP_VAL;
|
---|
| 360 |
|
---|
| 361 | /* if dst == src do nothing */
|
---|
| 362 | if (a == b) {
|
---|
| 363 | return MP_OKAY;
|
---|
| 364 | }
|
---|
| 365 |
|
---|
| 366 | /* grow dest */
|
---|
| 367 | if (b->alloc < a->used || b->alloc == 0) {
|
---|
| 368 | if ((res = mp_grow (b, a->used)) != MP_OKAY) {
|
---|
| 369 | return res;
|
---|
| 370 | }
|
---|
| 371 | }
|
---|
| 372 |
|
---|
| 373 | /* zero b and copy the parameters over */
|
---|
| 374 | {
|
---|
| 375 | mp_digit *tmpa, *tmpb;
|
---|
| 376 |
|
---|
| 377 | /* pointer aliases */
|
---|
| 378 |
|
---|
| 379 | /* source */
|
---|
| 380 | tmpa = a->dp;
|
---|
| 381 |
|
---|
| 382 | /* destination */
|
---|
| 383 | tmpb = b->dp;
|
---|
| 384 |
|
---|
| 385 | /* copy all the digits */
|
---|
| 386 | for (n = 0; n < a->used; n++) {
|
---|
| 387 | *tmpb++ = *tmpa++;
|
---|
| 388 | }
|
---|
| 389 |
|
---|
| 390 | /* clear high digits */
|
---|
| 391 | for (; n < b->used && b->dp; n++) {
|
---|
| 392 | *tmpb++ = 0;
|
---|
| 393 | }
|
---|
| 394 | }
|
---|
| 395 |
|
---|
| 396 | /* copy used count and sign */
|
---|
| 397 | b->used = a->used;
|
---|
| 398 | b->sign = a->sign;
|
---|
| 399 | return MP_OKAY;
|
---|
| 400 | }
|
---|
| 401 |
|
---|
| 402 |
|
---|
| 403 | /* grow as required */
|
---|
| 404 | int mp_grow (mp_int * a, int size)
|
---|
| 405 | {
|
---|
| 406 | int i;
|
---|
| 407 | mp_digit *tmp;
|
---|
| 408 |
|
---|
| 409 | /* if the alloc size is smaller alloc more ram */
|
---|
| 410 | if (a->alloc < size || size == 0) {
|
---|
| 411 | /* ensure there are always at least MP_PREC digits extra on top */
|
---|
| 412 | size += (MP_PREC * 2) - (size % MP_PREC);
|
---|
| 413 |
|
---|
| 414 | /* reallocate the array a->dp
|
---|
| 415 | *
|
---|
| 416 | * We store the return in a temporary variable
|
---|
| 417 | * in case the operation failed we don't want
|
---|
| 418 | * to overwrite the dp member of a.
|
---|
| 419 | */
|
---|
| 420 | tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size, NULL,
|
---|
| 421 | DYNAMIC_TYPE_BIGINT);
|
---|
| 422 | if (tmp == NULL) {
|
---|
| 423 | /* reallocation failed but "a" is still valid [can be freed] */
|
---|
| 424 | return MP_MEM;
|
---|
| 425 | }
|
---|
| 426 |
|
---|
| 427 | /* reallocation succeeded so set a->dp */
|
---|
| 428 | a->dp = tmp;
|
---|
| 429 |
|
---|
| 430 | /* zero excess digits */
|
---|
| 431 | i = a->alloc;
|
---|
| 432 | a->alloc = size;
|
---|
| 433 | for (; i < a->alloc; i++) {
|
---|
| 434 | a->dp[i] = 0;
|
---|
| 435 | }
|
---|
| 436 | }
|
---|
| 437 | return MP_OKAY;
|
---|
| 438 | }
|
---|
| 439 |
|
---|
| 440 |
|
---|
| 441 | /* shift right by a certain bit count (store quotient in c, optional
|
---|
| 442 | remainder in d) */
|
---|
| 443 | int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
|
---|
| 444 | {
|
---|
| 445 | int D, res;
|
---|
| 446 | mp_int t;
|
---|
| 447 |
|
---|
| 448 |
|
---|
| 449 | /* if the shift count is <= 0 then we do no work */
|
---|
| 450 | if (b <= 0) {
|
---|
| 451 | res = mp_copy (a, c);
|
---|
| 452 | if (d != NULL) {
|
---|
| 453 | mp_zero (d);
|
---|
| 454 | }
|
---|
| 455 | return res;
|
---|
| 456 | }
|
---|
| 457 |
|
---|
| 458 | if ((res = mp_init (&t)) != MP_OKAY) {
|
---|
| 459 | return res;
|
---|
| 460 | }
|
---|
| 461 |
|
---|
| 462 | /* get the remainder */
|
---|
| 463 | if (d != NULL) {
|
---|
| 464 | if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
|
---|
| 465 | mp_clear (&t);
|
---|
| 466 | return res;
|
---|
| 467 | }
|
---|
| 468 | }
|
---|
| 469 |
|
---|
| 470 | /* copy */
|
---|
| 471 | if ((res = mp_copy (a, c)) != MP_OKAY) {
|
---|
| 472 | mp_clear (&t);
|
---|
| 473 | return res;
|
---|
| 474 | }
|
---|
| 475 |
|
---|
| 476 | /* shift by as many digits in the bit count */
|
---|
| 477 | if (b >= (int)DIGIT_BIT) {
|
---|
| 478 | mp_rshd (c, b / DIGIT_BIT);
|
---|
| 479 | }
|
---|
| 480 |
|
---|
| 481 | /* shift any bit count < DIGIT_BIT */
|
---|
| 482 | D = (b % DIGIT_BIT);
|
---|
| 483 | if (D != 0) {
|
---|
| 484 | mp_rshb(c, D);
|
---|
| 485 | }
|
---|
| 486 | mp_clamp (c);
|
---|
| 487 | if (d != NULL) {
|
---|
| 488 | mp_exch (&t, d);
|
---|
| 489 | }
|
---|
| 490 | mp_clear (&t);
|
---|
| 491 | return MP_OKAY;
|
---|
| 492 | }
|
---|
| 493 |
|
---|
| 494 |
|
---|
| 495 | /* set to zero */
|
---|
| 496 | void mp_zero (mp_int * a)
|
---|
| 497 | {
|
---|
| 498 | int n;
|
---|
| 499 | mp_digit *tmp;
|
---|
| 500 |
|
---|
| 501 | if (a == NULL)
|
---|
| 502 | return;
|
---|
| 503 |
|
---|
| 504 | a->sign = MP_ZPOS;
|
---|
| 505 | a->used = 0;
|
---|
| 506 |
|
---|
| 507 | tmp = a->dp;
|
---|
| 508 | for (n = 0; n < a->alloc; n++) {
|
---|
| 509 | *tmp++ = 0;
|
---|
| 510 | }
|
---|
| 511 | }
|
---|
| 512 |
|
---|
| 513 |
|
---|
| 514 | /* trim unused digits
|
---|
| 515 | *
|
---|
| 516 | * This is used to ensure that leading zero digits are
|
---|
| 517 | * trimmed and the leading "used" digit will be non-zero
|
---|
| 518 | * Typically very fast. Also fixes the sign if there
|
---|
| 519 | * are no more leading digits
|
---|
| 520 | */
|
---|
| 521 | void mp_clamp (mp_int * a)
|
---|
| 522 | {
|
---|
| 523 | /* decrease used while the most significant digit is
|
---|
| 524 | * zero.
|
---|
| 525 | */
|
---|
| 526 | while (a->used > 0 && a->dp[a->used - 1] == 0) {
|
---|
| 527 | --(a->used);
|
---|
| 528 | }
|
---|
| 529 |
|
---|
| 530 | /* reset the sign flag if used == 0 */
|
---|
| 531 | if (a->used == 0) {
|
---|
| 532 | a->sign = MP_ZPOS;
|
---|
| 533 | }
|
---|
| 534 | }
|
---|
| 535 |
|
---|
| 536 |
|
---|
| 537 | /* swap the elements of two integers, for cases where you can't simply swap the
|
---|
| 538 | * mp_int pointers around
|
---|
| 539 | */
|
---|
| 540 | void mp_exch (mp_int * a, mp_int * b)
|
---|
| 541 | {
|
---|
| 542 | mp_int t;
|
---|
| 543 |
|
---|
| 544 | t = *a;
|
---|
| 545 | *a = *b;
|
---|
| 546 | *b = t;
|
---|
| 547 | }
|
---|
| 548 |
|
---|
[464] | 549 | int mp_cond_swap_ct (mp_int * a, mp_int * b, int c, int m)
|
---|
| 550 | {
|
---|
| 551 | (void)c;
|
---|
| 552 | if (m == 1)
|
---|
| 553 | mp_exch(a, b);
|
---|
| 554 | return MP_OKAY;
|
---|
| 555 | }
|
---|
[457] | 556 |
|
---|
[464] | 557 |
|
---|
[457] | 558 | /* shift right a certain number of bits */
|
---|
| 559 | void mp_rshb (mp_int *c, int x)
|
---|
| 560 | {
|
---|
| 561 | mp_digit *tmpc, mask, shift;
|
---|
| 562 | mp_digit r, rr;
|
---|
| 563 | mp_digit D = x;
|
---|
| 564 |
|
---|
[464] | 565 | /* shifting by a negative number not supported, and shifting by
|
---|
| 566 | * zero changes nothing.
|
---|
| 567 | */
|
---|
| 568 | if (x <= 0) return;
|
---|
| 569 |
|
---|
| 570 | /* shift digits first if needed */
|
---|
| 571 | if (x >= DIGIT_BIT) {
|
---|
| 572 | mp_rshd(c, x / DIGIT_BIT);
|
---|
| 573 | /* recalculate number of bits to shift */
|
---|
| 574 | D = x % DIGIT_BIT;
|
---|
| 575 | /* check if any more shifting needed */
|
---|
| 576 | if (D == 0) return;
|
---|
| 577 | }
|
---|
| 578 |
|
---|
| 579 | /* zero shifted is always zero */
|
---|
[457] | 580 | if (mp_iszero(c)) return;
|
---|
| 581 |
|
---|
| 582 | /* mask */
|
---|
| 583 | mask = (((mp_digit)1) << D) - 1;
|
---|
| 584 |
|
---|
| 585 | /* shift for lsb */
|
---|
| 586 | shift = DIGIT_BIT - D;
|
---|
| 587 |
|
---|
| 588 | /* alias */
|
---|
| 589 | tmpc = c->dp + (c->used - 1);
|
---|
| 590 |
|
---|
| 591 | /* carry */
|
---|
| 592 | r = 0;
|
---|
| 593 | for (x = c->used - 1; x >= 0; x--) {
|
---|
| 594 | /* get the lower bits of this word in a temp */
|
---|
| 595 | rr = *tmpc & mask;
|
---|
| 596 |
|
---|
| 597 | /* shift the current word and mix in the carry bits from previous word */
|
---|
| 598 | *tmpc = (*tmpc >> D) | (r << shift);
|
---|
| 599 | --tmpc;
|
---|
| 600 |
|
---|
| 601 | /* set the carry to the carry bits of the current word found above */
|
---|
| 602 | r = rr;
|
---|
| 603 | }
|
---|
| 604 | mp_clamp(c);
|
---|
| 605 | }
|
---|
| 606 |
|
---|
| 607 |
|
---|
| 608 | /* shift right a certain amount of digits */
|
---|
| 609 | void mp_rshd (mp_int * a, int b)
|
---|
| 610 | {
|
---|
| 611 | int x;
|
---|
| 612 |
|
---|
| 613 | /* if b <= 0 then ignore it */
|
---|
| 614 | if (b <= 0) {
|
---|
| 615 | return;
|
---|
| 616 | }
|
---|
| 617 |
|
---|
| 618 | /* if b > used then simply zero it and return */
|
---|
| 619 | if (a->used <= b) {
|
---|
| 620 | mp_zero (a);
|
---|
| 621 | return;
|
---|
| 622 | }
|
---|
| 623 |
|
---|
| 624 | {
|
---|
| 625 | mp_digit *bottom, *top;
|
---|
| 626 |
|
---|
| 627 | /* shift the digits down */
|
---|
| 628 |
|
---|
| 629 | /* bottom */
|
---|
| 630 | bottom = a->dp;
|
---|
| 631 |
|
---|
| 632 | /* top [offset into digits] */
|
---|
| 633 | top = a->dp + b;
|
---|
| 634 |
|
---|
| 635 | /* this is implemented as a sliding window where
|
---|
| 636 | * the window is b-digits long and digits from
|
---|
| 637 | * the top of the window are copied to the bottom
|
---|
| 638 | *
|
---|
| 639 | * e.g.
|
---|
| 640 |
|
---|
| 641 | b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
|
---|
| 642 | /\ | ---->
|
---|
| 643 | \-------------------/ ---->
|
---|
| 644 | */
|
---|
| 645 | for (x = 0; x < (a->used - b); x++) {
|
---|
| 646 | *bottom++ = *top++;
|
---|
| 647 | }
|
---|
| 648 |
|
---|
| 649 | /* zero the top digits */
|
---|
| 650 | for (; x < a->used; x++) {
|
---|
| 651 | *bottom++ = 0;
|
---|
| 652 | }
|
---|
| 653 | }
|
---|
| 654 |
|
---|
| 655 | /* remove excess digits */
|
---|
| 656 | a->used -= b;
|
---|
| 657 | }
|
---|
| 658 |
|
---|
| 659 |
|
---|
| 660 | /* calc a value mod 2**b */
|
---|
| 661 | int mp_mod_2d (mp_int * a, int b, mp_int * c)
|
---|
| 662 | {
|
---|
| 663 | int x, res;
|
---|
| 664 |
|
---|
| 665 | /* if b is <= 0 then zero the int */
|
---|
| 666 | if (b <= 0) {
|
---|
| 667 | mp_zero (c);
|
---|
| 668 | return MP_OKAY;
|
---|
| 669 | }
|
---|
| 670 |
|
---|
| 671 | /* if the modulus is larger than the value than return */
|
---|
| 672 | if (b >= (int) (a->used * DIGIT_BIT)) {
|
---|
| 673 | res = mp_copy (a, c);
|
---|
| 674 | return res;
|
---|
| 675 | }
|
---|
| 676 |
|
---|
| 677 | /* copy */
|
---|
| 678 | if ((res = mp_copy (a, c)) != MP_OKAY) {
|
---|
| 679 | return res;
|
---|
| 680 | }
|
---|
| 681 |
|
---|
| 682 | /* zero digits above the last digit of the modulus */
|
---|
| 683 | for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
|
---|
| 684 | c->dp[x] = 0;
|
---|
| 685 | }
|
---|
| 686 | /* clear the digit that is not completely outside/inside the modulus */
|
---|
[464] | 687 | x = DIGIT_BIT - (b % DIGIT_BIT);
|
---|
| 688 | if (x != DIGIT_BIT) {
|
---|
| 689 | c->dp[b / DIGIT_BIT] &= ~((mp_digit)0) >> (x + ((sizeof(mp_digit)*8) - DIGIT_BIT));
|
---|
| 690 | }
|
---|
[457] | 691 | mp_clamp (c);
|
---|
| 692 | return MP_OKAY;
|
---|
| 693 | }
|
---|
| 694 |
|
---|
| 695 |
|
---|
| 696 | /* reads a unsigned char array, assumes the msb is stored first [big endian] */
|
---|
| 697 | int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
|
---|
| 698 | {
|
---|
| 699 | int res;
|
---|
[464] | 700 | int digits_needed;
|
---|
[457] | 701 |
|
---|
[464] | 702 | while (c > 0 && b[0] == 0) {
|
---|
| 703 | c--;
|
---|
| 704 | b++;
|
---|
| 705 | }
|
---|
| 706 |
|
---|
| 707 | digits_needed = ((c * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT;
|
---|
| 708 |
|
---|
| 709 | /* make sure there are enough digits available */
|
---|
| 710 | if (a->alloc < digits_needed) {
|
---|
| 711 | if ((res = mp_grow(a, digits_needed)) != MP_OKAY) {
|
---|
[457] | 712 | return res;
|
---|
| 713 | }
|
---|
| 714 | }
|
---|
| 715 |
|
---|
| 716 | /* zero the int */
|
---|
| 717 | mp_zero (a);
|
---|
| 718 |
|
---|
| 719 | /* read the bytes in */
|
---|
| 720 | while (c-- > 0) {
|
---|
| 721 | if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
|
---|
| 722 | return res;
|
---|
| 723 | }
|
---|
| 724 |
|
---|
| 725 | #ifndef MP_8BIT
|
---|
| 726 | a->dp[0] |= *b++;
|
---|
[464] | 727 | if (a->used == 0)
|
---|
| 728 | a->used = 1;
|
---|
[457] | 729 | #else
|
---|
| 730 | a->dp[0] = (*b & MP_MASK);
|
---|
| 731 | a->dp[1] |= ((*b++ >> 7U) & 1);
|
---|
[464] | 732 | if (a->used == 0)
|
---|
| 733 | a->used = 2;
|
---|
[457] | 734 | #endif
|
---|
| 735 | }
|
---|
| 736 | mp_clamp (a);
|
---|
| 737 | return MP_OKAY;
|
---|
| 738 | }
|
---|
| 739 |
|
---|
| 740 |
|
---|
| 741 | /* shift left by a certain bit count */
|
---|
| 742 | int mp_mul_2d (mp_int * a, int b, mp_int * c)
|
---|
| 743 | {
|
---|
| 744 | mp_digit d;
|
---|
| 745 | int res;
|
---|
| 746 |
|
---|
| 747 | /* copy */
|
---|
| 748 | if (a != c) {
|
---|
| 749 | if ((res = mp_copy (a, c)) != MP_OKAY) {
|
---|
| 750 | return res;
|
---|
| 751 | }
|
---|
| 752 | }
|
---|
| 753 |
|
---|
| 754 | if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
|
---|
| 755 | if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
|
---|
| 756 | return res;
|
---|
| 757 | }
|
---|
| 758 | }
|
---|
| 759 |
|
---|
| 760 | /* shift by as many digits in the bit count */
|
---|
| 761 | if (b >= (int)DIGIT_BIT) {
|
---|
| 762 | if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
|
---|
| 763 | return res;
|
---|
| 764 | }
|
---|
| 765 | }
|
---|
| 766 |
|
---|
| 767 | /* shift any bit count < DIGIT_BIT */
|
---|
| 768 | d = (mp_digit) (b % DIGIT_BIT);
|
---|
| 769 | if (d != 0) {
|
---|
| 770 | mp_digit *tmpc, shift, mask, r, rr;
|
---|
| 771 | int x;
|
---|
| 772 |
|
---|
| 773 | /* bitmask for carries */
|
---|
| 774 | mask = (((mp_digit)1) << d) - 1;
|
---|
| 775 |
|
---|
| 776 | /* shift for msbs */
|
---|
| 777 | shift = DIGIT_BIT - d;
|
---|
| 778 |
|
---|
| 779 | /* alias */
|
---|
| 780 | tmpc = c->dp;
|
---|
| 781 |
|
---|
| 782 | /* carry */
|
---|
| 783 | r = 0;
|
---|
| 784 | for (x = 0; x < c->used; x++) {
|
---|
| 785 | /* get the higher bits of the current word */
|
---|
| 786 | rr = (*tmpc >> shift) & mask;
|
---|
| 787 |
|
---|
| 788 | /* shift the current word and OR in the carry */
|
---|
| 789 | *tmpc = (mp_digit)(((*tmpc << d) | r) & MP_MASK);
|
---|
| 790 | ++tmpc;
|
---|
| 791 |
|
---|
| 792 | /* set the carry to the carry bits of the current word */
|
---|
| 793 | r = rr;
|
---|
| 794 | }
|
---|
| 795 |
|
---|
| 796 | /* set final carry */
|
---|
| 797 | if (r != 0) {
|
---|
| 798 | c->dp[(c->used)++] = r;
|
---|
| 799 | }
|
---|
| 800 | }
|
---|
| 801 | mp_clamp (c);
|
---|
| 802 | return MP_OKAY;
|
---|
| 803 | }
|
---|
| 804 |
|
---|
| 805 |
|
---|
| 806 | /* shift left a certain amount of digits */
|
---|
| 807 | int mp_lshd (mp_int * a, int b)
|
---|
| 808 | {
|
---|
| 809 | int x, res;
|
---|
| 810 |
|
---|
| 811 | /* if its less than zero return */
|
---|
| 812 | if (b <= 0) {
|
---|
| 813 | return MP_OKAY;
|
---|
| 814 | }
|
---|
| 815 |
|
---|
| 816 | /* grow to fit the new digits */
|
---|
| 817 | if (a->alloc < a->used + b) {
|
---|
| 818 | if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
|
---|
| 819 | return res;
|
---|
| 820 | }
|
---|
| 821 | }
|
---|
| 822 |
|
---|
| 823 | {
|
---|
| 824 | mp_digit *top, *bottom;
|
---|
| 825 |
|
---|
| 826 | /* increment the used by the shift amount then copy upwards */
|
---|
| 827 | a->used += b;
|
---|
| 828 |
|
---|
| 829 | /* top */
|
---|
| 830 | top = a->dp + a->used - 1;
|
---|
| 831 |
|
---|
| 832 | /* base */
|
---|
| 833 | bottom = a->dp + a->used - 1 - b;
|
---|
| 834 |
|
---|
| 835 | /* much like mp_rshd this is implemented using a sliding window
|
---|
| 836 | * except the window goes the other way around. Copying from
|
---|
| 837 | * the bottom to the top. see bn_mp_rshd.c for more info.
|
---|
| 838 | */
|
---|
| 839 | for (x = a->used - 1; x >= b; x--) {
|
---|
| 840 | *top-- = *bottom--;
|
---|
| 841 | }
|
---|
| 842 |
|
---|
| 843 | /* zero the lower digits */
|
---|
| 844 | top = a->dp;
|
---|
| 845 | for (x = 0; x < b; x++) {
|
---|
| 846 | *top++ = 0;
|
---|
| 847 | }
|
---|
| 848 | }
|
---|
| 849 | return MP_OKAY;
|
---|
| 850 | }
|
---|
| 851 |
|
---|
| 852 |
|
---|
| 853 | /* this is a shell function that calls either the normal or Montgomery
|
---|
| 854 | * exptmod functions. Originally the call to the montgomery code was
|
---|
| 855 | * embedded in the normal function but that wasted a lot of stack space
|
---|
| 856 | * for nothing (since 99% of the time the Montgomery code would be called)
|
---|
| 857 | */
|
---|
| 858 | #if defined(FREESCALE_LTC_TFM)
|
---|
| 859 | int wolfcrypt_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
|
---|
| 860 | #else
|
---|
| 861 | int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
|
---|
| 862 | #endif
|
---|
| 863 | {
|
---|
| 864 | int dr;
|
---|
| 865 |
|
---|
| 866 | /* modulus P must be positive */
|
---|
| 867 | if (mp_iszero(P) || P->sign == MP_NEG) {
|
---|
| 868 | return MP_VAL;
|
---|
| 869 | }
|
---|
| 870 | if (mp_isone(P)) {
|
---|
| 871 | mp_set(Y, 0);
|
---|
| 872 | return MP_OKAY;
|
---|
| 873 | }
|
---|
| 874 | if (mp_iszero(X)) {
|
---|
| 875 | mp_set(Y, 1);
|
---|
| 876 | return MP_OKAY;
|
---|
| 877 | }
|
---|
| 878 | if (mp_iszero(G)) {
|
---|
| 879 | mp_set(Y, 0);
|
---|
| 880 | return MP_OKAY;
|
---|
| 881 | }
|
---|
| 882 |
|
---|
| 883 | /* if exponent X is negative we have to recurse */
|
---|
| 884 | if (X->sign == MP_NEG) {
|
---|
| 885 | #ifdef BN_MP_INVMOD_C
|
---|
| 886 | mp_int tmpG, tmpX;
|
---|
| 887 | int err;
|
---|
| 888 |
|
---|
| 889 | /* first compute 1/G mod P */
|
---|
| 890 | if ((err = mp_init(&tmpG)) != MP_OKAY) {
|
---|
| 891 | return err;
|
---|
| 892 | }
|
---|
| 893 | if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
|
---|
| 894 | mp_clear(&tmpG);
|
---|
| 895 | return err;
|
---|
| 896 | }
|
---|
| 897 |
|
---|
| 898 | /* now get |X| */
|
---|
| 899 | if ((err = mp_init(&tmpX)) != MP_OKAY) {
|
---|
| 900 | mp_clear(&tmpG);
|
---|
| 901 | return err;
|
---|
| 902 | }
|
---|
| 903 | if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
|
---|
| 904 | mp_clear(&tmpG);
|
---|
| 905 | mp_clear(&tmpX);
|
---|
| 906 | return err;
|
---|
| 907 | }
|
---|
| 908 |
|
---|
| 909 | /* and now compute (1/G)**|X| instead of G**X [X < 0] */
|
---|
| 910 | err = mp_exptmod(&tmpG, &tmpX, P, Y);
|
---|
| 911 | mp_clear(&tmpG);
|
---|
| 912 | mp_clear(&tmpX);
|
---|
| 913 | return err;
|
---|
| 914 | #else
|
---|
| 915 | /* no invmod */
|
---|
| 916 | return MP_VAL;
|
---|
| 917 | #endif
|
---|
| 918 | }
|
---|
| 919 |
|
---|
| 920 | #ifdef BN_MP_EXPTMOD_BASE_2
|
---|
| 921 | if (G->used == 1 && G->dp[0] == 2) {
|
---|
| 922 | return mp_exptmod_base_2(X, P, Y);
|
---|
| 923 | }
|
---|
| 924 | #endif
|
---|
| 925 |
|
---|
| 926 | /* modified diminished radix reduction */
|
---|
| 927 | #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && \
|
---|
| 928 | defined(BN_S_MP_EXPTMOD_C)
|
---|
| 929 | if (mp_reduce_is_2k_l(P) == MP_YES) {
|
---|
| 930 | return s_mp_exptmod(G, X, P, Y, 1);
|
---|
| 931 | }
|
---|
| 932 | #endif
|
---|
| 933 |
|
---|
| 934 | #ifdef BN_MP_DR_IS_MODULUS_C
|
---|
| 935 | /* is it a DR modulus? */
|
---|
| 936 | dr = mp_dr_is_modulus(P);
|
---|
| 937 | #else
|
---|
| 938 | /* default to no */
|
---|
| 939 | dr = 0;
|
---|
| 940 | #endif
|
---|
| 941 |
|
---|
| 942 | (void)dr;
|
---|
| 943 |
|
---|
| 944 | #ifdef BN_MP_REDUCE_IS_2K_C
|
---|
| 945 | /* if not, is it a unrestricted DR modulus? */
|
---|
| 946 | if (dr == 0) {
|
---|
| 947 | dr = mp_reduce_is_2k(P) << 1;
|
---|
| 948 | }
|
---|
| 949 | #endif
|
---|
| 950 |
|
---|
| 951 | /* if the modulus is odd or dr != 0 use the montgomery method */
|
---|
| 952 | #ifdef BN_MP_EXPTMOD_FAST_C
|
---|
| 953 | if (mp_isodd (P) == MP_YES || dr != 0) {
|
---|
| 954 | return mp_exptmod_fast (G, X, P, Y, dr);
|
---|
| 955 | } else {
|
---|
| 956 | #endif
|
---|
| 957 | #ifdef BN_S_MP_EXPTMOD_C
|
---|
| 958 | /* otherwise use the generic Barrett reduction technique */
|
---|
| 959 | return s_mp_exptmod (G, X, P, Y, 0);
|
---|
| 960 | #else
|
---|
| 961 | /* no exptmod for evens */
|
---|
| 962 | return MP_VAL;
|
---|
| 963 | #endif
|
---|
| 964 | #ifdef BN_MP_EXPTMOD_FAST_C
|
---|
| 965 | }
|
---|
| 966 | #endif
|
---|
| 967 | }
|
---|
| 968 |
|
---|
| 969 | int mp_exptmod_ex (mp_int * G, mp_int * X, int digits, mp_int * P, mp_int * Y)
|
---|
| 970 | {
|
---|
| 971 | (void)digits;
|
---|
| 972 | return mp_exptmod(G, X, P, Y);
|
---|
| 973 | }
|
---|
| 974 |
|
---|
| 975 | /* b = |a|
|
---|
| 976 | *
|
---|
| 977 | * Simple function copies the input and fixes the sign to positive
|
---|
| 978 | */
|
---|
| 979 | int mp_abs (mp_int * a, mp_int * b)
|
---|
| 980 | {
|
---|
| 981 | int res;
|
---|
| 982 |
|
---|
| 983 | /* copy a to b */
|
---|
| 984 | if (a != b) {
|
---|
| 985 | if ((res = mp_copy (a, b)) != MP_OKAY) {
|
---|
| 986 | return res;
|
---|
| 987 | }
|
---|
| 988 | }
|
---|
| 989 |
|
---|
| 990 | /* force the sign of b to positive */
|
---|
| 991 | b->sign = MP_ZPOS;
|
---|
| 992 |
|
---|
| 993 | return MP_OKAY;
|
---|
| 994 | }
|
---|
| 995 |
|
---|
| 996 |
|
---|
| 997 | /* hac 14.61, pp608 */
|
---|
| 998 | #if defined(FREESCALE_LTC_TFM)
|
---|
| 999 | int wolfcrypt_mp_invmod(mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1000 | #else
|
---|
| 1001 | int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1002 | #endif
|
---|
| 1003 | {
|
---|
| 1004 | /* b cannot be negative or zero, and can not divide by 0 (1/a mod b) */
|
---|
| 1005 | if (b->sign == MP_NEG || mp_iszero(b) == MP_YES || mp_iszero(a) == MP_YES) {
|
---|
| 1006 | return MP_VAL;
|
---|
| 1007 | }
|
---|
| 1008 |
|
---|
| 1009 | #ifdef BN_FAST_MP_INVMOD_C
|
---|
| 1010 | /* if the modulus is odd we can use a faster routine instead */
|
---|
| 1011 | if ((mp_isodd(b) == MP_YES) && (mp_cmp_d(b, 1) != MP_EQ)) {
|
---|
| 1012 | return fast_mp_invmod (a, b, c);
|
---|
| 1013 | }
|
---|
| 1014 | #endif
|
---|
| 1015 |
|
---|
| 1016 | #ifdef BN_MP_INVMOD_SLOW_C
|
---|
| 1017 | return mp_invmod_slow(a, b, c);
|
---|
| 1018 | #else
|
---|
| 1019 | return MP_VAL;
|
---|
| 1020 | #endif
|
---|
| 1021 | }
|
---|
| 1022 |
|
---|
| 1023 |
|
---|
| 1024 | /* computes the modular inverse via binary extended euclidean algorithm,
|
---|
| 1025 | * that is c = 1/a mod b
|
---|
| 1026 | *
|
---|
| 1027 | * Based on slow invmod except this is optimized for the case where b is
|
---|
| 1028 | * odd as per HAC Note 14.64 on pp. 610
|
---|
| 1029 | */
|
---|
| 1030 | int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1031 | {
|
---|
| 1032 | mp_int x, y, u, v, B, D;
|
---|
| 1033 | int res, neg, loop_check = 0;
|
---|
| 1034 |
|
---|
| 1035 | /* 2. [modified] b must be odd */
|
---|
| 1036 | if (mp_iseven (b) == MP_YES) {
|
---|
| 1037 | return MP_VAL;
|
---|
| 1038 | }
|
---|
| 1039 |
|
---|
| 1040 | /* init all our temps */
|
---|
| 1041 | if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D)) != MP_OKAY) {
|
---|
| 1042 | return res;
|
---|
| 1043 | }
|
---|
| 1044 |
|
---|
| 1045 | /* x == modulus, y == value to invert */
|
---|
| 1046 | if ((res = mp_copy (b, &x)) != MP_OKAY) {
|
---|
| 1047 | goto LBL_ERR;
|
---|
| 1048 | }
|
---|
| 1049 |
|
---|
| 1050 | /* we need y = |a| */
|
---|
| 1051 | if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
|
---|
| 1052 | goto LBL_ERR;
|
---|
| 1053 | }
|
---|
| 1054 |
|
---|
| 1055 | /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
---|
| 1056 | if ((res = mp_copy (&x, &u)) != MP_OKAY) {
|
---|
| 1057 | goto LBL_ERR;
|
---|
| 1058 | }
|
---|
| 1059 | if ((res = mp_copy (&y, &v)) != MP_OKAY) {
|
---|
| 1060 | goto LBL_ERR;
|
---|
| 1061 | }
|
---|
| 1062 | if ((res = mp_set (&D, 1)) != MP_OKAY) {
|
---|
| 1063 | goto LBL_ERR;
|
---|
| 1064 | }
|
---|
| 1065 |
|
---|
| 1066 | top:
|
---|
| 1067 | /* 4. while u is even do */
|
---|
| 1068 | while (mp_iseven (&u) == MP_YES) {
|
---|
| 1069 | /* 4.1 u = u/2 */
|
---|
| 1070 | if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
|
---|
| 1071 | goto LBL_ERR;
|
---|
| 1072 | }
|
---|
| 1073 | /* 4.2 if B is odd then */
|
---|
| 1074 | if (mp_isodd (&B) == MP_YES) {
|
---|
| 1075 | if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
|
---|
| 1076 | goto LBL_ERR;
|
---|
| 1077 | }
|
---|
| 1078 | }
|
---|
| 1079 | /* B = B/2 */
|
---|
| 1080 | if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
|
---|
| 1081 | goto LBL_ERR;
|
---|
| 1082 | }
|
---|
| 1083 | }
|
---|
| 1084 |
|
---|
| 1085 | /* 5. while v is even do */
|
---|
| 1086 | while (mp_iseven (&v) == MP_YES) {
|
---|
| 1087 | /* 5.1 v = v/2 */
|
---|
| 1088 | if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
|
---|
| 1089 | goto LBL_ERR;
|
---|
| 1090 | }
|
---|
| 1091 | /* 5.2 if D is odd then */
|
---|
| 1092 | if (mp_isodd (&D) == MP_YES) {
|
---|
| 1093 | /* D = (D-x)/2 */
|
---|
| 1094 | if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
|
---|
| 1095 | goto LBL_ERR;
|
---|
| 1096 | }
|
---|
| 1097 | }
|
---|
| 1098 | /* D = D/2 */
|
---|
| 1099 | if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
|
---|
| 1100 | goto LBL_ERR;
|
---|
| 1101 | }
|
---|
| 1102 | }
|
---|
| 1103 |
|
---|
| 1104 | /* 6. if u >= v then */
|
---|
| 1105 | if (mp_cmp (&u, &v) != MP_LT) {
|
---|
| 1106 | /* u = u - v, B = B - D */
|
---|
| 1107 | if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
|
---|
| 1108 | goto LBL_ERR;
|
---|
| 1109 | }
|
---|
| 1110 |
|
---|
| 1111 | if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
|
---|
| 1112 | goto LBL_ERR;
|
---|
| 1113 | }
|
---|
| 1114 | } else {
|
---|
| 1115 | /* v - v - u, D = D - B */
|
---|
| 1116 | if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
|
---|
| 1117 | goto LBL_ERR;
|
---|
| 1118 | }
|
---|
| 1119 |
|
---|
| 1120 | if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
|
---|
| 1121 | goto LBL_ERR;
|
---|
| 1122 | }
|
---|
| 1123 | }
|
---|
| 1124 |
|
---|
| 1125 | /* if not zero goto step 4 */
|
---|
| 1126 | if (mp_iszero (&u) == MP_NO) {
|
---|
| 1127 | if (++loop_check > MAX_INVMOD_SZ) {
|
---|
| 1128 | res = MP_VAL;
|
---|
| 1129 | goto LBL_ERR;
|
---|
| 1130 | }
|
---|
| 1131 | goto top;
|
---|
| 1132 | }
|
---|
| 1133 |
|
---|
| 1134 | /* now a = C, b = D, gcd == g*v */
|
---|
| 1135 |
|
---|
| 1136 | /* if v != 1 then there is no inverse */
|
---|
| 1137 | if (mp_cmp_d (&v, 1) != MP_EQ) {
|
---|
| 1138 | res = MP_VAL;
|
---|
| 1139 | goto LBL_ERR;
|
---|
| 1140 | }
|
---|
| 1141 |
|
---|
| 1142 | /* b is now the inverse */
|
---|
| 1143 | neg = a->sign;
|
---|
| 1144 | while (D.sign == MP_NEG) {
|
---|
| 1145 | if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
|
---|
| 1146 | goto LBL_ERR;
|
---|
| 1147 | }
|
---|
| 1148 | }
|
---|
| 1149 | /* too big */
|
---|
| 1150 | while (mp_cmp_mag(&D, b) != MP_LT) {
|
---|
| 1151 | if ((res = mp_sub(&D, b, &D)) != MP_OKAY) {
|
---|
| 1152 | goto LBL_ERR;
|
---|
| 1153 | }
|
---|
| 1154 | }
|
---|
| 1155 | mp_exch (&D, c);
|
---|
| 1156 | c->sign = neg;
|
---|
| 1157 | res = MP_OKAY;
|
---|
| 1158 |
|
---|
| 1159 | LBL_ERR:mp_clear(&x);
|
---|
| 1160 | mp_clear(&y);
|
---|
| 1161 | mp_clear(&u);
|
---|
| 1162 | mp_clear(&v);
|
---|
| 1163 | mp_clear(&B);
|
---|
| 1164 | mp_clear(&D);
|
---|
| 1165 | return res;
|
---|
| 1166 | }
|
---|
| 1167 |
|
---|
| 1168 |
|
---|
| 1169 | /* hac 14.61, pp608 */
|
---|
| 1170 | int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1171 | {
|
---|
| 1172 | mp_int x, y, u, v, A, B, C, D;
|
---|
| 1173 | int res;
|
---|
| 1174 |
|
---|
| 1175 | /* b cannot be negative */
|
---|
| 1176 | if (b->sign == MP_NEG || mp_iszero(b) == MP_YES) {
|
---|
| 1177 | return MP_VAL;
|
---|
| 1178 | }
|
---|
| 1179 |
|
---|
| 1180 | /* init temps */
|
---|
| 1181 | if ((res = mp_init_multi(&x, &y, &u, &v,
|
---|
| 1182 | &A, &B)) != MP_OKAY) {
|
---|
| 1183 | return res;
|
---|
| 1184 | }
|
---|
| 1185 |
|
---|
| 1186 | /* init rest of tmps temps */
|
---|
| 1187 | if ((res = mp_init_multi(&C, &D, 0, 0, 0, 0)) != MP_OKAY) {
|
---|
| 1188 | mp_clear(&x);
|
---|
| 1189 | mp_clear(&y);
|
---|
| 1190 | mp_clear(&u);
|
---|
| 1191 | mp_clear(&v);
|
---|
| 1192 | mp_clear(&A);
|
---|
| 1193 | mp_clear(&B);
|
---|
| 1194 | return res;
|
---|
| 1195 | }
|
---|
| 1196 |
|
---|
| 1197 | /* x = a, y = b */
|
---|
| 1198 | if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
|
---|
| 1199 | goto LBL_ERR;
|
---|
| 1200 | }
|
---|
| 1201 | if (mp_isone(&x)) {
|
---|
| 1202 | mp_set(c, 1);
|
---|
| 1203 | res = MP_OKAY;
|
---|
| 1204 | goto LBL_ERR;
|
---|
| 1205 | }
|
---|
| 1206 | if ((res = mp_copy (b, &y)) != MP_OKAY) {
|
---|
| 1207 | goto LBL_ERR;
|
---|
| 1208 | }
|
---|
| 1209 |
|
---|
| 1210 | /* 2. [modified] if x,y are both even then return an error! */
|
---|
| 1211 | if (mp_iseven (&x) == MP_YES && mp_iseven (&y) == MP_YES) {
|
---|
| 1212 | res = MP_VAL;
|
---|
| 1213 | goto LBL_ERR;
|
---|
| 1214 | }
|
---|
| 1215 |
|
---|
| 1216 | /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
---|
| 1217 | if ((res = mp_copy (&x, &u)) != MP_OKAY) {
|
---|
| 1218 | goto LBL_ERR;
|
---|
| 1219 | }
|
---|
| 1220 | if ((res = mp_copy (&y, &v)) != MP_OKAY) {
|
---|
| 1221 | goto LBL_ERR;
|
---|
| 1222 | }
|
---|
| 1223 | if ((res = mp_set (&A, 1)) != MP_OKAY) {
|
---|
| 1224 | goto LBL_ERR;
|
---|
| 1225 | }
|
---|
| 1226 | if ((res = mp_set (&D, 1)) != MP_OKAY) {
|
---|
| 1227 | goto LBL_ERR;
|
---|
| 1228 | }
|
---|
| 1229 |
|
---|
| 1230 | top:
|
---|
| 1231 | /* 4. while u is even do */
|
---|
| 1232 | while (mp_iseven (&u) == MP_YES) {
|
---|
| 1233 | /* 4.1 u = u/2 */
|
---|
| 1234 | if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
|
---|
| 1235 | goto LBL_ERR;
|
---|
| 1236 | }
|
---|
| 1237 | /* 4.2 if A or B is odd then */
|
---|
| 1238 | if (mp_isodd (&A) == MP_YES || mp_isodd (&B) == MP_YES) {
|
---|
| 1239 | /* A = (A+y)/2, B = (B-x)/2 */
|
---|
| 1240 | if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
|
---|
| 1241 | goto LBL_ERR;
|
---|
| 1242 | }
|
---|
| 1243 | if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
|
---|
| 1244 | goto LBL_ERR;
|
---|
| 1245 | }
|
---|
| 1246 | }
|
---|
| 1247 | /* A = A/2, B = B/2 */
|
---|
| 1248 | if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
|
---|
| 1249 | goto LBL_ERR;
|
---|
| 1250 | }
|
---|
| 1251 | if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
|
---|
| 1252 | goto LBL_ERR;
|
---|
| 1253 | }
|
---|
| 1254 | }
|
---|
| 1255 |
|
---|
| 1256 | /* 5. while v is even do */
|
---|
| 1257 | while (mp_iseven (&v) == MP_YES) {
|
---|
| 1258 | /* 5.1 v = v/2 */
|
---|
| 1259 | if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
|
---|
| 1260 | goto LBL_ERR;
|
---|
| 1261 | }
|
---|
| 1262 | /* 5.2 if C or D is odd then */
|
---|
| 1263 | if (mp_isodd (&C) == MP_YES || mp_isodd (&D) == MP_YES) {
|
---|
| 1264 | /* C = (C+y)/2, D = (D-x)/2 */
|
---|
| 1265 | if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
|
---|
| 1266 | goto LBL_ERR;
|
---|
| 1267 | }
|
---|
| 1268 | if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
|
---|
| 1269 | goto LBL_ERR;
|
---|
| 1270 | }
|
---|
| 1271 | }
|
---|
| 1272 | /* C = C/2, D = D/2 */
|
---|
| 1273 | if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
|
---|
| 1274 | goto LBL_ERR;
|
---|
| 1275 | }
|
---|
| 1276 | if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
|
---|
| 1277 | goto LBL_ERR;
|
---|
| 1278 | }
|
---|
| 1279 | }
|
---|
| 1280 |
|
---|
| 1281 | /* 6. if u >= v then */
|
---|
| 1282 | if (mp_cmp (&u, &v) != MP_LT) {
|
---|
| 1283 | /* u = u - v, A = A - C, B = B - D */
|
---|
| 1284 | if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
|
---|
| 1285 | goto LBL_ERR;
|
---|
| 1286 | }
|
---|
| 1287 |
|
---|
| 1288 | if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
|
---|
| 1289 | goto LBL_ERR;
|
---|
| 1290 | }
|
---|
| 1291 |
|
---|
| 1292 | if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
|
---|
| 1293 | goto LBL_ERR;
|
---|
| 1294 | }
|
---|
| 1295 | } else {
|
---|
| 1296 | /* v - v - u, C = C - A, D = D - B */
|
---|
| 1297 | if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
|
---|
| 1298 | goto LBL_ERR;
|
---|
| 1299 | }
|
---|
| 1300 |
|
---|
| 1301 | if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
|
---|
| 1302 | goto LBL_ERR;
|
---|
| 1303 | }
|
---|
| 1304 |
|
---|
| 1305 | if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
|
---|
| 1306 | goto LBL_ERR;
|
---|
| 1307 | }
|
---|
| 1308 | }
|
---|
| 1309 |
|
---|
| 1310 | /* if not zero goto step 4 */
|
---|
| 1311 | if (mp_iszero (&u) == MP_NO)
|
---|
| 1312 | goto top;
|
---|
| 1313 |
|
---|
| 1314 | /* now a = C, b = D, gcd == g*v */
|
---|
| 1315 |
|
---|
| 1316 | /* if v != 1 then there is no inverse */
|
---|
| 1317 | if (mp_cmp_d (&v, 1) != MP_EQ) {
|
---|
| 1318 | res = MP_VAL;
|
---|
| 1319 | goto LBL_ERR;
|
---|
| 1320 | }
|
---|
| 1321 |
|
---|
| 1322 | /* if its too low */
|
---|
| 1323 | while (mp_cmp_d(&C, 0) == MP_LT) {
|
---|
| 1324 | if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
|
---|
| 1325 | goto LBL_ERR;
|
---|
| 1326 | }
|
---|
| 1327 | }
|
---|
| 1328 |
|
---|
| 1329 | /* too big */
|
---|
| 1330 | while (mp_cmp_mag(&C, b) != MP_LT) {
|
---|
| 1331 | if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
|
---|
| 1332 | goto LBL_ERR;
|
---|
| 1333 | }
|
---|
| 1334 | }
|
---|
| 1335 |
|
---|
| 1336 | /* C is now the inverse */
|
---|
| 1337 | mp_exch (&C, c);
|
---|
| 1338 | res = MP_OKAY;
|
---|
| 1339 | LBL_ERR:mp_clear(&x);
|
---|
| 1340 | mp_clear(&y);
|
---|
| 1341 | mp_clear(&u);
|
---|
| 1342 | mp_clear(&v);
|
---|
| 1343 | mp_clear(&A);
|
---|
| 1344 | mp_clear(&B);
|
---|
| 1345 | mp_clear(&C);
|
---|
| 1346 | mp_clear(&D);
|
---|
| 1347 | return res;
|
---|
| 1348 | }
|
---|
| 1349 |
|
---|
| 1350 |
|
---|
| 1351 | /* compare magnitude of two ints (unsigned) */
|
---|
| 1352 | int mp_cmp_mag (mp_int * a, mp_int * b)
|
---|
| 1353 | {
|
---|
| 1354 | int n;
|
---|
| 1355 | mp_digit *tmpa, *tmpb;
|
---|
| 1356 |
|
---|
| 1357 | /* compare based on # of non-zero digits */
|
---|
| 1358 | if (a->used > b->used) {
|
---|
| 1359 | return MP_GT;
|
---|
| 1360 | }
|
---|
| 1361 |
|
---|
| 1362 | if (a->used < b->used) {
|
---|
| 1363 | return MP_LT;
|
---|
| 1364 | }
|
---|
| 1365 |
|
---|
| 1366 | /* alias for a */
|
---|
| 1367 | tmpa = a->dp + (a->used - 1);
|
---|
| 1368 |
|
---|
| 1369 | /* alias for b */
|
---|
| 1370 | tmpb = b->dp + (a->used - 1);
|
---|
| 1371 |
|
---|
| 1372 | /* compare based on digits */
|
---|
| 1373 | for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
|
---|
| 1374 | if (*tmpa > *tmpb) {
|
---|
| 1375 | return MP_GT;
|
---|
| 1376 | }
|
---|
| 1377 |
|
---|
| 1378 | if (*tmpa < *tmpb) {
|
---|
| 1379 | return MP_LT;
|
---|
| 1380 | }
|
---|
| 1381 | }
|
---|
| 1382 | return MP_EQ;
|
---|
| 1383 | }
|
---|
| 1384 |
|
---|
| 1385 |
|
---|
| 1386 | /* compare two ints (signed)*/
|
---|
| 1387 | int mp_cmp (mp_int * a, mp_int * b)
|
---|
| 1388 | {
|
---|
| 1389 | /* compare based on sign */
|
---|
| 1390 | if (a->sign != b->sign) {
|
---|
| 1391 | if (a->sign == MP_NEG) {
|
---|
| 1392 | return MP_LT;
|
---|
| 1393 | } else {
|
---|
| 1394 | return MP_GT;
|
---|
| 1395 | }
|
---|
| 1396 | }
|
---|
| 1397 |
|
---|
| 1398 | /* compare digits */
|
---|
| 1399 | if (a->sign == MP_NEG) {
|
---|
| 1400 | /* if negative compare opposite direction */
|
---|
| 1401 | return mp_cmp_mag(b, a);
|
---|
| 1402 | } else {
|
---|
| 1403 | return mp_cmp_mag(a, b);
|
---|
| 1404 | }
|
---|
| 1405 | }
|
---|
| 1406 |
|
---|
| 1407 |
|
---|
| 1408 | /* compare a digit */
|
---|
| 1409 | int mp_cmp_d(mp_int * a, mp_digit b)
|
---|
| 1410 | {
|
---|
| 1411 | /* special case for zero*/
|
---|
| 1412 | if (a->used == 0 && b == 0)
|
---|
| 1413 | return MP_EQ;
|
---|
| 1414 |
|
---|
| 1415 | /* compare based on sign */
|
---|
| 1416 | if ((b && a->used == 0) || a->sign == MP_NEG) {
|
---|
| 1417 | return MP_LT;
|
---|
| 1418 | }
|
---|
| 1419 |
|
---|
| 1420 | /* compare based on magnitude */
|
---|
| 1421 | if (a->used > 1) {
|
---|
| 1422 | return MP_GT;
|
---|
| 1423 | }
|
---|
| 1424 |
|
---|
| 1425 | /* compare the only digit of a to b */
|
---|
| 1426 | if (a->dp[0] > b) {
|
---|
| 1427 | return MP_GT;
|
---|
| 1428 | } else if (a->dp[0] < b) {
|
---|
| 1429 | return MP_LT;
|
---|
| 1430 | } else {
|
---|
| 1431 | return MP_EQ;
|
---|
| 1432 | }
|
---|
| 1433 | }
|
---|
| 1434 |
|
---|
| 1435 |
|
---|
| 1436 | /* set to a digit */
|
---|
| 1437 | int mp_set (mp_int * a, mp_digit b)
|
---|
| 1438 | {
|
---|
| 1439 | int res;
|
---|
| 1440 | mp_zero (a);
|
---|
| 1441 | res = mp_grow (a, 1);
|
---|
| 1442 | if (res == MP_OKAY) {
|
---|
| 1443 | a->dp[0] = (mp_digit)(b & MP_MASK);
|
---|
| 1444 | a->used = (a->dp[0] != 0) ? 1 : 0;
|
---|
| 1445 | }
|
---|
| 1446 | return res;
|
---|
| 1447 | }
|
---|
| 1448 |
|
---|
| 1449 | /* check if a bit is set */
|
---|
| 1450 | int mp_is_bit_set (mp_int *a, mp_digit b)
|
---|
| 1451 | {
|
---|
| 1452 | if ((mp_digit)a->used < b/DIGIT_BIT)
|
---|
| 1453 | return 0;
|
---|
| 1454 |
|
---|
| 1455 | return (int)((a->dp[b/DIGIT_BIT] >> b%DIGIT_BIT) & (mp_digit)1);
|
---|
| 1456 | }
|
---|
| 1457 |
|
---|
| 1458 | /* c = a mod b, 0 <= c < b */
|
---|
| 1459 | #if defined(FREESCALE_LTC_TFM)
|
---|
| 1460 | int wolfcrypt_mp_mod(mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1461 | #else
|
---|
| 1462 | int mp_mod (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1463 | #endif
|
---|
| 1464 | {
|
---|
| 1465 | mp_int t;
|
---|
| 1466 | int res;
|
---|
| 1467 |
|
---|
| 1468 | if ((res = mp_init_size (&t, b->used)) != MP_OKAY) {
|
---|
| 1469 | return res;
|
---|
| 1470 | }
|
---|
| 1471 |
|
---|
| 1472 | if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
|
---|
| 1473 | mp_clear (&t);
|
---|
| 1474 | return res;
|
---|
| 1475 | }
|
---|
| 1476 |
|
---|
| 1477 | if ((mp_iszero(&t) != MP_NO) || (t.sign == b->sign)) {
|
---|
| 1478 | res = MP_OKAY;
|
---|
| 1479 | mp_exch (&t, c);
|
---|
| 1480 | } else {
|
---|
| 1481 | res = mp_add (b, &t, c);
|
---|
| 1482 | }
|
---|
| 1483 |
|
---|
| 1484 | mp_clear (&t);
|
---|
| 1485 | return res;
|
---|
| 1486 | }
|
---|
| 1487 |
|
---|
| 1488 |
|
---|
| 1489 | /* slower bit-bang division... also smaller */
|
---|
| 1490 | int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
|
---|
| 1491 | {
|
---|
| 1492 | mp_int ta, tb, tq, q;
|
---|
| 1493 | int res, n, n2;
|
---|
| 1494 |
|
---|
| 1495 | /* is divisor zero ? */
|
---|
| 1496 | if (mp_iszero (b) == MP_YES) {
|
---|
| 1497 | return MP_VAL;
|
---|
| 1498 | }
|
---|
| 1499 |
|
---|
| 1500 | /* if a < b then q=0, r = a */
|
---|
| 1501 | if (mp_cmp_mag (a, b) == MP_LT) {
|
---|
| 1502 | if (d != NULL) {
|
---|
| 1503 | res = mp_copy (a, d);
|
---|
| 1504 | } else {
|
---|
| 1505 | res = MP_OKAY;
|
---|
| 1506 | }
|
---|
| 1507 | if (c != NULL) {
|
---|
| 1508 | mp_zero (c);
|
---|
| 1509 | }
|
---|
| 1510 | return res;
|
---|
| 1511 | }
|
---|
| 1512 |
|
---|
| 1513 | /* init our temps */
|
---|
| 1514 | if ((res = mp_init_multi(&ta, &tb, &tq, &q, 0, 0)) != MP_OKAY) {
|
---|
| 1515 | return res;
|
---|
| 1516 | }
|
---|
| 1517 |
|
---|
| 1518 | if ((res = mp_set(&tq, 1)) != MP_OKAY) {
|
---|
| 1519 | return res;
|
---|
| 1520 | }
|
---|
| 1521 | n = mp_count_bits(a) - mp_count_bits(b);
|
---|
| 1522 | if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
|
---|
| 1523 | ((res = mp_abs(b, &tb)) != MP_OKAY) ||
|
---|
| 1524 | ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
|
---|
| 1525 | ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
|
---|
| 1526 | goto LBL_ERR;
|
---|
| 1527 | }
|
---|
| 1528 |
|
---|
| 1529 | while (n-- >= 0) {
|
---|
| 1530 | if (mp_cmp(&tb, &ta) != MP_GT) {
|
---|
| 1531 | if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
|
---|
| 1532 | ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
|
---|
| 1533 | goto LBL_ERR;
|
---|
| 1534 | }
|
---|
| 1535 | }
|
---|
| 1536 | if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
|
---|
| 1537 | ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
|
---|
| 1538 | goto LBL_ERR;
|
---|
| 1539 | }
|
---|
| 1540 | }
|
---|
| 1541 |
|
---|
| 1542 | /* now q == quotient and ta == remainder */
|
---|
| 1543 | n = a->sign;
|
---|
| 1544 | n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
|
---|
| 1545 | if (c != NULL) {
|
---|
| 1546 | mp_exch(c, &q);
|
---|
| 1547 | c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
|
---|
| 1548 | }
|
---|
| 1549 | if (d != NULL) {
|
---|
| 1550 | mp_exch(d, &ta);
|
---|
| 1551 | d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
|
---|
| 1552 | }
|
---|
| 1553 | LBL_ERR:
|
---|
| 1554 | mp_clear(&ta);
|
---|
| 1555 | mp_clear(&tb);
|
---|
| 1556 | mp_clear(&tq);
|
---|
| 1557 | mp_clear(&q);
|
---|
| 1558 | return res;
|
---|
| 1559 | }
|
---|
| 1560 |
|
---|
| 1561 |
|
---|
| 1562 | /* b = a/2 */
|
---|
| 1563 | int mp_div_2(mp_int * a, mp_int * b)
|
---|
| 1564 | {
|
---|
| 1565 | int x, res, oldused;
|
---|
| 1566 |
|
---|
| 1567 | /* copy */
|
---|
| 1568 | if (b->alloc < a->used) {
|
---|
| 1569 | if ((res = mp_grow (b, a->used)) != MP_OKAY) {
|
---|
| 1570 | return res;
|
---|
| 1571 | }
|
---|
| 1572 | }
|
---|
| 1573 |
|
---|
| 1574 | oldused = b->used;
|
---|
| 1575 | b->used = a->used;
|
---|
| 1576 | {
|
---|
| 1577 | mp_digit r, rr, *tmpa, *tmpb;
|
---|
| 1578 |
|
---|
| 1579 | /* source alias */
|
---|
| 1580 | tmpa = a->dp + b->used - 1;
|
---|
| 1581 |
|
---|
| 1582 | /* dest alias */
|
---|
| 1583 | tmpb = b->dp + b->used - 1;
|
---|
| 1584 |
|
---|
| 1585 | /* carry */
|
---|
| 1586 | r = 0;
|
---|
| 1587 | for (x = b->used - 1; x >= 0; x--) {
|
---|
| 1588 | /* get the carry for the next iteration */
|
---|
| 1589 | rr = *tmpa & 1;
|
---|
| 1590 |
|
---|
| 1591 | /* shift the current digit, add in carry and store */
|
---|
| 1592 | *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
|
---|
| 1593 |
|
---|
| 1594 | /* forward carry to next iteration */
|
---|
| 1595 | r = rr;
|
---|
| 1596 | }
|
---|
| 1597 |
|
---|
| 1598 | /* zero excess digits */
|
---|
| 1599 | tmpb = b->dp + b->used;
|
---|
| 1600 | for (x = b->used; x < oldused; x++) {
|
---|
| 1601 | *tmpb++ = 0;
|
---|
| 1602 | }
|
---|
| 1603 | }
|
---|
| 1604 | b->sign = a->sign;
|
---|
| 1605 | mp_clamp (b);
|
---|
| 1606 | return MP_OKAY;
|
---|
| 1607 | }
|
---|
| 1608 |
|
---|
[464] | 1609 | /* c = a / 2 (mod b) - constant time (a < b and positive) */
|
---|
| 1610 | int mp_div_2_mod_ct(mp_int *a, mp_int *b, mp_int *c)
|
---|
| 1611 | {
|
---|
| 1612 | int res;
|
---|
[457] | 1613 |
|
---|
[464] | 1614 | if (mp_isodd(a)) {
|
---|
| 1615 | res = mp_add(a, b, c);
|
---|
| 1616 | if (res == MP_OKAY) {
|
---|
| 1617 | res = mp_div_2(c, c);
|
---|
| 1618 | }
|
---|
| 1619 | }
|
---|
| 1620 | else {
|
---|
| 1621 | res = mp_div_2(a, c);
|
---|
| 1622 | }
|
---|
| 1623 |
|
---|
| 1624 | return res;
|
---|
| 1625 | }
|
---|
| 1626 |
|
---|
| 1627 |
|
---|
[457] | 1628 | /* high level addition (handles signs) */
|
---|
| 1629 | int mp_add (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1630 | {
|
---|
| 1631 | int sa, sb, res;
|
---|
| 1632 |
|
---|
| 1633 | /* get sign of both inputs */
|
---|
| 1634 | sa = a->sign;
|
---|
| 1635 | sb = b->sign;
|
---|
| 1636 |
|
---|
| 1637 | /* handle two cases, not four */
|
---|
| 1638 | if (sa == sb) {
|
---|
| 1639 | /* both positive or both negative */
|
---|
| 1640 | /* add their magnitudes, copy the sign */
|
---|
| 1641 | c->sign = sa;
|
---|
| 1642 | res = s_mp_add (a, b, c);
|
---|
| 1643 | } else {
|
---|
| 1644 | /* one positive, the other negative */
|
---|
| 1645 | /* subtract the one with the greater magnitude from */
|
---|
| 1646 | /* the one of the lesser magnitude. The result gets */
|
---|
| 1647 | /* the sign of the one with the greater magnitude. */
|
---|
| 1648 | if (mp_cmp_mag (a, b) == MP_LT) {
|
---|
| 1649 | c->sign = sb;
|
---|
| 1650 | res = s_mp_sub (b, a, c);
|
---|
| 1651 | } else {
|
---|
| 1652 | c->sign = sa;
|
---|
| 1653 | res = s_mp_sub (a, b, c);
|
---|
| 1654 | }
|
---|
| 1655 | }
|
---|
| 1656 | return res;
|
---|
| 1657 | }
|
---|
| 1658 |
|
---|
| 1659 |
|
---|
| 1660 | /* low level addition, based on HAC pp.594, Algorithm 14.7 */
|
---|
| 1661 | int s_mp_add (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1662 | {
|
---|
| 1663 | mp_int *x;
|
---|
| 1664 | int olduse, res, min_ab, max_ab;
|
---|
| 1665 |
|
---|
| 1666 | /* find sizes, we let |a| <= |b| which means we have to sort
|
---|
| 1667 | * them. "x" will point to the input with the most digits
|
---|
| 1668 | */
|
---|
| 1669 | if (a->used > b->used) {
|
---|
| 1670 | min_ab = b->used;
|
---|
| 1671 | max_ab = a->used;
|
---|
| 1672 | x = a;
|
---|
| 1673 | } else {
|
---|
| 1674 | min_ab = a->used;
|
---|
| 1675 | max_ab = b->used;
|
---|
| 1676 | x = b;
|
---|
| 1677 | }
|
---|
| 1678 |
|
---|
| 1679 | /* init result */
|
---|
| 1680 | if (c->alloc < max_ab + 1) {
|
---|
| 1681 | if ((res = mp_grow (c, max_ab + 1)) != MP_OKAY) {
|
---|
| 1682 | return res;
|
---|
| 1683 | }
|
---|
| 1684 | }
|
---|
| 1685 |
|
---|
| 1686 | /* get old used digit count and set new one */
|
---|
| 1687 | olduse = c->used;
|
---|
| 1688 | c->used = max_ab + 1;
|
---|
| 1689 |
|
---|
| 1690 | {
|
---|
| 1691 | mp_digit u, *tmpa, *tmpb, *tmpc;
|
---|
| 1692 | int i;
|
---|
| 1693 |
|
---|
| 1694 | /* alias for digit pointers */
|
---|
| 1695 |
|
---|
| 1696 | /* first input */
|
---|
| 1697 | tmpa = a->dp;
|
---|
| 1698 |
|
---|
| 1699 | /* second input */
|
---|
| 1700 | tmpb = b->dp;
|
---|
| 1701 |
|
---|
| 1702 | /* destination */
|
---|
| 1703 | tmpc = c->dp;
|
---|
| 1704 |
|
---|
| 1705 | /* zero the carry */
|
---|
| 1706 | u = 0;
|
---|
| 1707 | for (i = 0; i < min_ab; i++) {
|
---|
| 1708 | /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
|
---|
| 1709 | *tmpc = *tmpa++ + *tmpb++ + u;
|
---|
| 1710 |
|
---|
| 1711 | /* U = carry bit of T[i] */
|
---|
| 1712 | u = *tmpc >> ((mp_digit)DIGIT_BIT);
|
---|
| 1713 |
|
---|
| 1714 | /* take away carry bit from T[i] */
|
---|
| 1715 | *tmpc++ &= MP_MASK;
|
---|
| 1716 | }
|
---|
| 1717 |
|
---|
| 1718 | /* now copy higher words if any, that is in A+B
|
---|
| 1719 | * if A or B has more digits add those in
|
---|
| 1720 | */
|
---|
| 1721 | if (min_ab != max_ab) {
|
---|
| 1722 | for (; i < max_ab; i++) {
|
---|
| 1723 | /* T[i] = X[i] + U */
|
---|
| 1724 | *tmpc = x->dp[i] + u;
|
---|
| 1725 |
|
---|
| 1726 | /* U = carry bit of T[i] */
|
---|
| 1727 | u = *tmpc >> ((mp_digit)DIGIT_BIT);
|
---|
| 1728 |
|
---|
| 1729 | /* take away carry bit from T[i] */
|
---|
| 1730 | *tmpc++ &= MP_MASK;
|
---|
| 1731 | }
|
---|
| 1732 | }
|
---|
| 1733 |
|
---|
| 1734 | /* add carry */
|
---|
| 1735 | *tmpc++ = u;
|
---|
| 1736 |
|
---|
| 1737 | /* clear digits above olduse */
|
---|
| 1738 | for (i = c->used; i < olduse; i++) {
|
---|
| 1739 | *tmpc++ = 0;
|
---|
| 1740 | }
|
---|
| 1741 | }
|
---|
| 1742 |
|
---|
| 1743 | mp_clamp (c);
|
---|
| 1744 | return MP_OKAY;
|
---|
| 1745 | }
|
---|
| 1746 |
|
---|
| 1747 |
|
---|
| 1748 | /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
|
---|
| 1749 | int s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1750 | {
|
---|
| 1751 | int olduse, res, min_b, max_a;
|
---|
| 1752 |
|
---|
| 1753 | /* find sizes */
|
---|
| 1754 | min_b = b->used;
|
---|
| 1755 | max_a = a->used;
|
---|
| 1756 |
|
---|
| 1757 | /* init result */
|
---|
| 1758 | if (c->alloc < max_a) {
|
---|
| 1759 | if ((res = mp_grow (c, max_a)) != MP_OKAY) {
|
---|
| 1760 | return res;
|
---|
| 1761 | }
|
---|
| 1762 | }
|
---|
| 1763 |
|
---|
| 1764 | /* sanity check on destination */
|
---|
| 1765 | if (c->dp == NULL)
|
---|
| 1766 | return MP_VAL;
|
---|
| 1767 |
|
---|
| 1768 | olduse = c->used;
|
---|
| 1769 | c->used = max_a;
|
---|
| 1770 |
|
---|
| 1771 | {
|
---|
| 1772 | mp_digit u, *tmpa, *tmpb, *tmpc;
|
---|
| 1773 | int i;
|
---|
| 1774 |
|
---|
| 1775 | /* alias for digit pointers */
|
---|
| 1776 | tmpa = a->dp;
|
---|
| 1777 | tmpb = b->dp;
|
---|
| 1778 | tmpc = c->dp;
|
---|
| 1779 |
|
---|
| 1780 | /* set carry to zero */
|
---|
| 1781 | u = 0;
|
---|
| 1782 | for (i = 0; i < min_b; i++) {
|
---|
| 1783 | /* T[i] = A[i] - B[i] - U */
|
---|
| 1784 | *tmpc = *tmpa++ - *tmpb++ - u;
|
---|
| 1785 |
|
---|
| 1786 | /* U = carry bit of T[i]
|
---|
| 1787 | * Note this saves performing an AND operation since
|
---|
| 1788 | * if a carry does occur it will propagate all the way to the
|
---|
| 1789 | * MSB. As a result a single shift is enough to get the carry
|
---|
| 1790 | */
|
---|
| 1791 | u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
|
---|
| 1792 |
|
---|
| 1793 | /* Clear carry from T[i] */
|
---|
| 1794 | *tmpc++ &= MP_MASK;
|
---|
| 1795 | }
|
---|
| 1796 |
|
---|
| 1797 | /* now copy higher words if any, e.g. if A has more digits than B */
|
---|
| 1798 | for (; i < max_a; i++) {
|
---|
| 1799 | /* T[i] = A[i] - U */
|
---|
| 1800 | *tmpc = *tmpa++ - u;
|
---|
| 1801 |
|
---|
| 1802 | /* U = carry bit of T[i] */
|
---|
| 1803 | u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
|
---|
| 1804 |
|
---|
| 1805 | /* Clear carry from T[i] */
|
---|
| 1806 | *tmpc++ &= MP_MASK;
|
---|
| 1807 | }
|
---|
| 1808 |
|
---|
| 1809 | /* clear digits above used (since we may not have grown result above) */
|
---|
| 1810 | for (i = c->used; i < olduse; i++) {
|
---|
| 1811 | *tmpc++ = 0;
|
---|
| 1812 | }
|
---|
| 1813 | }
|
---|
| 1814 |
|
---|
| 1815 | mp_clamp (c);
|
---|
| 1816 | return MP_OKAY;
|
---|
| 1817 | }
|
---|
| 1818 |
|
---|
| 1819 |
|
---|
| 1820 | /* high level subtraction (handles signs) */
|
---|
| 1821 | int mp_sub (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 1822 | {
|
---|
| 1823 | int sa, sb, res;
|
---|
| 1824 |
|
---|
| 1825 | sa = a->sign;
|
---|
| 1826 | sb = b->sign;
|
---|
| 1827 |
|
---|
| 1828 | if (sa != sb) {
|
---|
| 1829 | /* subtract a negative from a positive, OR */
|
---|
| 1830 | /* subtract a positive from a negative. */
|
---|
| 1831 | /* In either case, ADD their magnitudes, */
|
---|
| 1832 | /* and use the sign of the first number. */
|
---|
| 1833 | c->sign = sa;
|
---|
| 1834 | res = s_mp_add (a, b, c);
|
---|
| 1835 | } else {
|
---|
| 1836 | /* subtract a positive from a positive, OR */
|
---|
| 1837 | /* subtract a negative from a negative. */
|
---|
| 1838 | /* First, take the difference between their */
|
---|
| 1839 | /* magnitudes, then... */
|
---|
| 1840 | if (mp_cmp_mag (a, b) != MP_LT) {
|
---|
| 1841 | /* Copy the sign from the first */
|
---|
| 1842 | c->sign = sa;
|
---|
| 1843 | /* The first has a larger or equal magnitude */
|
---|
| 1844 | res = s_mp_sub (a, b, c);
|
---|
| 1845 | } else {
|
---|
| 1846 | /* The result has the *opposite* sign from */
|
---|
| 1847 | /* the first number. */
|
---|
| 1848 | c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
|
---|
| 1849 | /* The second has a larger magnitude */
|
---|
| 1850 | res = s_mp_sub (b, a, c);
|
---|
| 1851 | }
|
---|
| 1852 | }
|
---|
| 1853 | return res;
|
---|
| 1854 | }
|
---|
| 1855 |
|
---|
| 1856 |
|
---|
| 1857 | /* determines if reduce_2k_l can be used */
|
---|
| 1858 | int mp_reduce_is_2k_l(mp_int *a)
|
---|
| 1859 | {
|
---|
| 1860 | int ix, iy;
|
---|
| 1861 |
|
---|
| 1862 | if (a->used == 0) {
|
---|
| 1863 | return MP_NO;
|
---|
| 1864 | } else if (a->used == 1) {
|
---|
| 1865 | return MP_YES;
|
---|
| 1866 | } else if (a->used > 1) {
|
---|
| 1867 | /* if more than half of the digits are -1 we're sold */
|
---|
| 1868 | for (iy = ix = 0; ix < a->used; ix++) {
|
---|
| 1869 | if (a->dp[ix] == MP_MASK) {
|
---|
| 1870 | ++iy;
|
---|
| 1871 | }
|
---|
| 1872 | }
|
---|
| 1873 | return (iy >= (a->used/2)) ? MP_YES : MP_NO;
|
---|
| 1874 |
|
---|
| 1875 | }
|
---|
| 1876 | return MP_NO;
|
---|
| 1877 | }
|
---|
| 1878 |
|
---|
| 1879 |
|
---|
| 1880 | /* determines if mp_reduce_2k can be used */
|
---|
| 1881 | int mp_reduce_is_2k(mp_int *a)
|
---|
| 1882 | {
|
---|
| 1883 | int ix, iy, iw;
|
---|
| 1884 | mp_digit iz;
|
---|
| 1885 |
|
---|
| 1886 | if (a->used == 0) {
|
---|
| 1887 | return MP_NO;
|
---|
| 1888 | } else if (a->used == 1) {
|
---|
| 1889 | return MP_YES;
|
---|
| 1890 | } else if (a->used > 1) {
|
---|
| 1891 | iy = mp_count_bits(a);
|
---|
| 1892 | iz = 1;
|
---|
| 1893 | iw = 1;
|
---|
| 1894 |
|
---|
| 1895 | /* Test every bit from the second digit up, must be 1 */
|
---|
| 1896 | for (ix = DIGIT_BIT; ix < iy; ix++) {
|
---|
| 1897 | if ((a->dp[iw] & iz) == 0) {
|
---|
| 1898 | return MP_NO;
|
---|
| 1899 | }
|
---|
| 1900 | iz <<= 1;
|
---|
| 1901 | if (iz > (mp_digit)MP_MASK) {
|
---|
| 1902 | ++iw;
|
---|
| 1903 | iz = 1;
|
---|
| 1904 | }
|
---|
| 1905 | }
|
---|
| 1906 | }
|
---|
| 1907 | return MP_YES;
|
---|
| 1908 | }
|
---|
| 1909 |
|
---|
| 1910 |
|
---|
| 1911 | /* determines if a number is a valid DR modulus */
|
---|
| 1912 | int mp_dr_is_modulus(mp_int *a)
|
---|
| 1913 | {
|
---|
| 1914 | int ix;
|
---|
| 1915 |
|
---|
| 1916 | /* must be at least two digits */
|
---|
| 1917 | if (a->used < 2) {
|
---|
| 1918 | return 0;
|
---|
| 1919 | }
|
---|
| 1920 |
|
---|
| 1921 | /* must be of the form b**k - a [a <= b] so all
|
---|
| 1922 | * but the first digit must be equal to -1 (mod b).
|
---|
| 1923 | */
|
---|
| 1924 | for (ix = 1; ix < a->used; ix++) {
|
---|
| 1925 | if (a->dp[ix] != MP_MASK) {
|
---|
| 1926 | return 0;
|
---|
| 1927 | }
|
---|
| 1928 | }
|
---|
| 1929 | return 1;
|
---|
| 1930 | }
|
---|
| 1931 |
|
---|
| 1932 |
|
---|
| 1933 | /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
|
---|
| 1934 | *
|
---|
| 1935 | * Uses a left-to-right k-ary sliding window to compute the modular
|
---|
| 1936 | * exponentiation.
|
---|
| 1937 | * The value of k changes based on the size of the exponent.
|
---|
| 1938 | *
|
---|
| 1939 | * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
|
---|
| 1940 | */
|
---|
| 1941 |
|
---|
| 1942 | #ifdef MP_LOW_MEM
|
---|
| 1943 | #define TAB_SIZE 32
|
---|
| 1944 | #else
|
---|
| 1945 | #define TAB_SIZE 256
|
---|
| 1946 | #endif
|
---|
| 1947 |
|
---|
| 1948 | int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y,
|
---|
| 1949 | int redmode)
|
---|
| 1950 | {
|
---|
| 1951 | mp_int res;
|
---|
| 1952 | mp_digit buf, mp;
|
---|
| 1953 | int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
---|
| 1954 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 1955 | mp_int* M;
|
---|
| 1956 | #else
|
---|
| 1957 | mp_int M[TAB_SIZE];
|
---|
| 1958 | #endif
|
---|
| 1959 | /* use a pointer to the reduction algorithm. This allows us to use
|
---|
| 1960 | * one of many reduction algorithms without modding the guts of
|
---|
| 1961 | * the code with if statements everywhere.
|
---|
| 1962 | */
|
---|
| 1963 | int (*redux)(mp_int*,mp_int*,mp_digit) = NULL;
|
---|
| 1964 |
|
---|
| 1965 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 1966 | M = (mp_int*) XMALLOC(sizeof(mp_int) * TAB_SIZE, NULL,
|
---|
| 1967 | DYNAMIC_TYPE_BIGINT);
|
---|
| 1968 | if (M == NULL)
|
---|
| 1969 | return MP_MEM;
|
---|
| 1970 | #endif
|
---|
| 1971 |
|
---|
| 1972 | /* find window size */
|
---|
| 1973 | x = mp_count_bits (X);
|
---|
| 1974 | if (x <= 7) {
|
---|
| 1975 | winsize = 2;
|
---|
| 1976 | } else if (x <= 36) {
|
---|
| 1977 | winsize = 3;
|
---|
| 1978 | } else if (x <= 140) {
|
---|
| 1979 | winsize = 4;
|
---|
| 1980 | } else if (x <= 450) {
|
---|
| 1981 | winsize = 5;
|
---|
| 1982 | } else if (x <= 1303) {
|
---|
| 1983 | winsize = 6;
|
---|
| 1984 | } else if (x <= 3529) {
|
---|
| 1985 | winsize = 7;
|
---|
| 1986 | } else {
|
---|
| 1987 | winsize = 8;
|
---|
| 1988 | }
|
---|
| 1989 |
|
---|
| 1990 | #ifdef MP_LOW_MEM
|
---|
| 1991 | if (winsize > 5) {
|
---|
| 1992 | winsize = 5;
|
---|
| 1993 | }
|
---|
| 1994 | #endif
|
---|
| 1995 |
|
---|
| 1996 | /* init M array */
|
---|
| 1997 | /* init first cell */
|
---|
| 1998 | if ((err = mp_init_size(&M[1], P->alloc)) != MP_OKAY) {
|
---|
| 1999 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2000 | XFREE(M, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 2001 | #endif
|
---|
| 2002 |
|
---|
| 2003 | return err;
|
---|
| 2004 | }
|
---|
| 2005 |
|
---|
| 2006 | /* now init the second half of the array */
|
---|
| 2007 | for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
---|
| 2008 | if ((err = mp_init_size(&M[x], P->alloc)) != MP_OKAY) {
|
---|
| 2009 | for (y = 1<<(winsize-1); y < x; y++) {
|
---|
| 2010 | mp_clear (&M[y]);
|
---|
| 2011 | }
|
---|
| 2012 | mp_clear(&M[1]);
|
---|
| 2013 |
|
---|
| 2014 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2015 | XFREE(M, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 2016 | #endif
|
---|
| 2017 |
|
---|
| 2018 | return err;
|
---|
| 2019 | }
|
---|
| 2020 | }
|
---|
| 2021 |
|
---|
| 2022 | /* determine and setup reduction code */
|
---|
| 2023 | if (redmode == 0) {
|
---|
| 2024 | #ifdef BN_MP_MONTGOMERY_SETUP_C
|
---|
| 2025 | /* now setup montgomery */
|
---|
| 2026 | if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
|
---|
| 2027 | goto LBL_M;
|
---|
| 2028 | }
|
---|
| 2029 | #else
|
---|
| 2030 | err = MP_VAL;
|
---|
| 2031 | goto LBL_M;
|
---|
| 2032 | #endif
|
---|
| 2033 |
|
---|
| 2034 | /* automatically pick the comba one if available (saves quite a few
|
---|
| 2035 | calls/ifs) */
|
---|
| 2036 | #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
|
---|
| 2037 | if (((P->used * 2 + 1) < (int)MP_WARRAY) &&
|
---|
[464] | 2038 | P->used < (1L << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
[457] | 2039 | redux = fast_mp_montgomery_reduce;
|
---|
| 2040 | } else
|
---|
| 2041 | #endif
|
---|
| 2042 | {
|
---|
| 2043 | #ifdef BN_MP_MONTGOMERY_REDUCE_C
|
---|
| 2044 | /* use slower baseline Montgomery method */
|
---|
| 2045 | redux = mp_montgomery_reduce;
|
---|
| 2046 | #endif
|
---|
| 2047 | }
|
---|
| 2048 | } else if (redmode == 1) {
|
---|
| 2049 | #if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
|
---|
| 2050 | /* setup DR reduction for moduli of the form B**k - b */
|
---|
| 2051 | mp_dr_setup(P, &mp);
|
---|
| 2052 | redux = mp_dr_reduce;
|
---|
| 2053 | #endif
|
---|
| 2054 | } else {
|
---|
| 2055 | #if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
|
---|
| 2056 | /* setup DR reduction for moduli of the form 2**k - b */
|
---|
| 2057 | if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
|
---|
| 2058 | goto LBL_M;
|
---|
| 2059 | }
|
---|
| 2060 | redux = mp_reduce_2k;
|
---|
| 2061 | #endif
|
---|
| 2062 | }
|
---|
| 2063 |
|
---|
| 2064 | if (redux == NULL) {
|
---|
| 2065 | err = MP_VAL;
|
---|
| 2066 | goto LBL_M;
|
---|
| 2067 | }
|
---|
| 2068 |
|
---|
| 2069 | /* setup result */
|
---|
| 2070 | if ((err = mp_init_size (&res, P->alloc)) != MP_OKAY) {
|
---|
| 2071 | goto LBL_M;
|
---|
| 2072 | }
|
---|
| 2073 |
|
---|
| 2074 | /* create M table
|
---|
| 2075 | *
|
---|
| 2076 |
|
---|
| 2077 | *
|
---|
| 2078 | * The first half of the table is not computed though accept for M[0] and M[1]
|
---|
| 2079 | */
|
---|
| 2080 |
|
---|
| 2081 | if (redmode == 0) {
|
---|
| 2082 | #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
|
---|
| 2083 | /* now we need R mod m */
|
---|
| 2084 | if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
|
---|
| 2085 | goto LBL_RES;
|
---|
| 2086 | }
|
---|
| 2087 |
|
---|
| 2088 | /* now set M[1] to G * R mod m */
|
---|
| 2089 | if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
|
---|
| 2090 | goto LBL_RES;
|
---|
| 2091 | }
|
---|
| 2092 | #else
|
---|
| 2093 | err = MP_VAL;
|
---|
| 2094 | goto LBL_RES;
|
---|
| 2095 | #endif
|
---|
| 2096 | } else {
|
---|
| 2097 | if ((err = mp_set(&res, 1)) != MP_OKAY) {
|
---|
| 2098 | goto LBL_RES;
|
---|
| 2099 | }
|
---|
| 2100 | if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
|
---|
| 2101 | goto LBL_RES;
|
---|
| 2102 | }
|
---|
| 2103 | }
|
---|
| 2104 |
|
---|
| 2105 | /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times*/
|
---|
| 2106 | if ((err = mp_copy (&M[1], &M[(mp_digit)(1 << (winsize - 1))])) != MP_OKAY) {
|
---|
| 2107 | goto LBL_RES;
|
---|
| 2108 | }
|
---|
| 2109 |
|
---|
| 2110 | for (x = 0; x < (winsize - 1); x++) {
|
---|
| 2111 | if ((err = mp_sqr (&M[(mp_digit)(1 << (winsize - 1))],
|
---|
| 2112 | &M[(mp_digit)(1 << (winsize - 1))])) != MP_OKAY) {
|
---|
| 2113 | goto LBL_RES;
|
---|
| 2114 | }
|
---|
| 2115 | if ((err = redux (&M[(mp_digit)(1 << (winsize - 1))], P, mp)) != MP_OKAY) {
|
---|
| 2116 | goto LBL_RES;
|
---|
| 2117 | }
|
---|
| 2118 | }
|
---|
| 2119 |
|
---|
| 2120 | /* create upper table */
|
---|
| 2121 | for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
---|
| 2122 | if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
|
---|
| 2123 | goto LBL_RES;
|
---|
| 2124 | }
|
---|
| 2125 | if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
|
---|
| 2126 | goto LBL_RES;
|
---|
| 2127 | }
|
---|
| 2128 | }
|
---|
| 2129 |
|
---|
| 2130 | /* set initial mode and bit cnt */
|
---|
| 2131 | mode = 0;
|
---|
| 2132 | bitcnt = 1;
|
---|
| 2133 | buf = 0;
|
---|
| 2134 | digidx = X->used - 1;
|
---|
| 2135 | bitcpy = 0;
|
---|
| 2136 | bitbuf = 0;
|
---|
| 2137 |
|
---|
| 2138 | for (;;) {
|
---|
| 2139 | /* grab next digit as required */
|
---|
| 2140 | if (--bitcnt == 0) {
|
---|
| 2141 | /* if digidx == -1 we are out of digits so break */
|
---|
| 2142 | if (digidx == -1) {
|
---|
| 2143 | break;
|
---|
| 2144 | }
|
---|
| 2145 | /* read next digit and reset bitcnt */
|
---|
| 2146 | buf = X->dp[digidx--];
|
---|
| 2147 | bitcnt = (int)DIGIT_BIT;
|
---|
| 2148 | }
|
---|
| 2149 |
|
---|
| 2150 | /* grab the next msb from the exponent */
|
---|
| 2151 | y = (int)(buf >> (DIGIT_BIT - 1)) & 1;
|
---|
| 2152 | buf <<= (mp_digit)1;
|
---|
| 2153 |
|
---|
| 2154 | /* if the bit is zero and mode == 0 then we ignore it
|
---|
| 2155 | * These represent the leading zero bits before the first 1 bit
|
---|
| 2156 | * in the exponent. Technically this opt is not required but it
|
---|
| 2157 | * does lower the # of trivial squaring/reductions used
|
---|
| 2158 | */
|
---|
| 2159 | if (mode == 0 && y == 0) {
|
---|
| 2160 | continue;
|
---|
| 2161 | }
|
---|
| 2162 |
|
---|
| 2163 | /* if the bit is zero and mode == 1 then we square */
|
---|
| 2164 | if (mode == 1 && y == 0) {
|
---|
| 2165 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 2166 | goto LBL_RES;
|
---|
| 2167 | }
|
---|
| 2168 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 2169 | goto LBL_RES;
|
---|
| 2170 | }
|
---|
| 2171 | continue;
|
---|
| 2172 | }
|
---|
| 2173 |
|
---|
| 2174 | /* else we add it to the window */
|
---|
| 2175 | bitbuf |= (y << (winsize - ++bitcpy));
|
---|
| 2176 | mode = 2;
|
---|
| 2177 |
|
---|
| 2178 | if (bitcpy == winsize) {
|
---|
| 2179 | /* ok window is filled so square as required and multiply */
|
---|
| 2180 | /* square first */
|
---|
| 2181 | for (x = 0; x < winsize; x++) {
|
---|
| 2182 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 2183 | goto LBL_RES;
|
---|
| 2184 | }
|
---|
| 2185 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 2186 | goto LBL_RES;
|
---|
| 2187 | }
|
---|
| 2188 | }
|
---|
| 2189 |
|
---|
| 2190 | /* then multiply */
|
---|
| 2191 | if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
|
---|
| 2192 | goto LBL_RES;
|
---|
| 2193 | }
|
---|
| 2194 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 2195 | goto LBL_RES;
|
---|
| 2196 | }
|
---|
| 2197 |
|
---|
| 2198 | /* empty window and reset */
|
---|
| 2199 | bitcpy = 0;
|
---|
| 2200 | bitbuf = 0;
|
---|
| 2201 | mode = 1;
|
---|
| 2202 | }
|
---|
| 2203 | }
|
---|
| 2204 |
|
---|
| 2205 | /* if bits remain then square/multiply */
|
---|
| 2206 | if (mode == 2 && bitcpy > 0) {
|
---|
| 2207 | /* square then multiply if the bit is set */
|
---|
| 2208 | for (x = 0; x < bitcpy; x++) {
|
---|
| 2209 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 2210 | goto LBL_RES;
|
---|
| 2211 | }
|
---|
| 2212 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 2213 | goto LBL_RES;
|
---|
| 2214 | }
|
---|
| 2215 |
|
---|
| 2216 | /* get next bit of the window */
|
---|
| 2217 | bitbuf <<= 1;
|
---|
| 2218 | if ((bitbuf & (1 << winsize)) != 0) {
|
---|
| 2219 | /* then multiply */
|
---|
| 2220 | if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
|
---|
| 2221 | goto LBL_RES;
|
---|
| 2222 | }
|
---|
| 2223 | if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
---|
| 2224 | goto LBL_RES;
|
---|
| 2225 | }
|
---|
| 2226 | }
|
---|
| 2227 | }
|
---|
| 2228 | }
|
---|
| 2229 |
|
---|
| 2230 | if (redmode == 0) {
|
---|
| 2231 | /* fixup result if Montgomery reduction is used
|
---|
| 2232 | * recall that any value in a Montgomery system is
|
---|
| 2233 | * actually multiplied by R mod n. So we have
|
---|
| 2234 | * to reduce one more time to cancel out the factor
|
---|
| 2235 | * of R.
|
---|
| 2236 | */
|
---|
| 2237 | if ((err = redux(&res, P, mp)) != MP_OKAY) {
|
---|
| 2238 | goto LBL_RES;
|
---|
| 2239 | }
|
---|
| 2240 | }
|
---|
| 2241 |
|
---|
| 2242 | /* swap res with Y */
|
---|
| 2243 | mp_exch (&res, Y);
|
---|
| 2244 | err = MP_OKAY;
|
---|
| 2245 | LBL_RES:mp_clear (&res);
|
---|
| 2246 | LBL_M:
|
---|
| 2247 | mp_clear(&M[1]);
|
---|
| 2248 | for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
---|
| 2249 | mp_clear (&M[x]);
|
---|
| 2250 | }
|
---|
| 2251 |
|
---|
| 2252 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2253 | XFREE(M, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 2254 | #endif
|
---|
| 2255 |
|
---|
| 2256 | return err;
|
---|
| 2257 | }
|
---|
| 2258 |
|
---|
| 2259 | #ifdef BN_MP_EXPTMOD_BASE_2
|
---|
| 2260 | #if DIGIT_BIT < 16
|
---|
| 2261 | #define WINSIZE 3
|
---|
| 2262 | #elif DIGIT_BIT < 32
|
---|
| 2263 | #define WINSIZE 4
|
---|
| 2264 | #elif DIGIT_BIT < 64
|
---|
| 2265 | #define WINSIZE 5
|
---|
| 2266 | #elif DIGIT_BIT < 128
|
---|
| 2267 | #define WINSIZE 6
|
---|
| 2268 | #endif
|
---|
| 2269 | int mp_exptmod_base_2(mp_int * X, mp_int * P, mp_int * Y)
|
---|
| 2270 | {
|
---|
| 2271 | mp_digit buf, mp;
|
---|
| 2272 | int err = MP_OKAY, bitbuf, bitcpy, bitcnt, digidx, x, y;
|
---|
| 2273 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2274 | mp_int *res = NULL;
|
---|
| 2275 | #else
|
---|
| 2276 | mp_int res[1];
|
---|
| 2277 | #endif
|
---|
| 2278 | int (*redux)(mp_int*,mp_int*,mp_digit) = NULL;
|
---|
| 2279 |
|
---|
| 2280 | /* automatically pick the comba one if available (saves quite a few
|
---|
| 2281 | calls/ifs) */
|
---|
| 2282 | #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
|
---|
| 2283 | if (((P->used * 2 + 1) < (int)MP_WARRAY) &&
|
---|
[464] | 2284 | P->used < (1L << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
[457] | 2285 | redux = fast_mp_montgomery_reduce;
|
---|
| 2286 | } else
|
---|
| 2287 | #endif
|
---|
[464] | 2288 | #ifdef BN_MP_MONTGOMERY_REDUCE_C
|
---|
[457] | 2289 | {
|
---|
| 2290 | /* use slower baseline Montgomery method */
|
---|
| 2291 | redux = mp_montgomery_reduce;
|
---|
[464] | 2292 | }
|
---|
[457] | 2293 | #endif
|
---|
[464] | 2294 |
|
---|
| 2295 | if (redux == NULL) {
|
---|
| 2296 | return MP_VAL;
|
---|
[457] | 2297 | }
|
---|
| 2298 |
|
---|
| 2299 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2300 | res = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 2301 | if (res == NULL) {
|
---|
| 2302 | return MP_MEM;
|
---|
| 2303 | }
|
---|
| 2304 | #endif
|
---|
| 2305 |
|
---|
| 2306 | /* now setup montgomery */
|
---|
| 2307 | if ((err = mp_montgomery_setup(P, &mp)) != MP_OKAY) {
|
---|
| 2308 | goto LBL_M;
|
---|
| 2309 | }
|
---|
| 2310 |
|
---|
| 2311 | /* setup result */
|
---|
| 2312 | if ((err = mp_init(res)) != MP_OKAY) {
|
---|
| 2313 | goto LBL_M;
|
---|
| 2314 | }
|
---|
| 2315 |
|
---|
| 2316 | /* now we need R mod m */
|
---|
| 2317 | if ((err = mp_montgomery_calc_normalization(res, P)) != MP_OKAY) {
|
---|
| 2318 | goto LBL_RES;
|
---|
| 2319 | }
|
---|
| 2320 |
|
---|
| 2321 | /* Get the top bits left over after taking WINSIZE bits starting at the
|
---|
| 2322 | * least-significant.
|
---|
| 2323 | */
|
---|
| 2324 | digidx = X->used - 1;
|
---|
| 2325 | bitcpy = (X->used * DIGIT_BIT) % WINSIZE;
|
---|
| 2326 | if (bitcpy > 0) {
|
---|
| 2327 | bitcnt = (int)DIGIT_BIT - bitcpy;
|
---|
| 2328 | buf = X->dp[digidx--];
|
---|
| 2329 | bitbuf = (int)(buf >> bitcnt);
|
---|
| 2330 | /* Multiply montgomery representation of 1 by 2 ^ top */
|
---|
| 2331 | err = mp_mul_2d(res, bitbuf, res);
|
---|
| 2332 | if (err != MP_OKAY) {
|
---|
| 2333 | goto LBL_RES;
|
---|
| 2334 | }
|
---|
| 2335 | err = mp_mod(res, P, res);
|
---|
| 2336 | if (err != MP_OKAY) {
|
---|
| 2337 | goto LBL_RES;
|
---|
| 2338 | }
|
---|
| 2339 | /* Move out bits used */
|
---|
| 2340 | buf <<= bitcpy;
|
---|
| 2341 | bitcnt++;
|
---|
| 2342 | }
|
---|
| 2343 | else {
|
---|
| 2344 | bitcnt = 1;
|
---|
| 2345 | buf = 0;
|
---|
| 2346 | }
|
---|
| 2347 |
|
---|
| 2348 | /* empty window and reset */
|
---|
| 2349 | bitbuf = 0;
|
---|
| 2350 | bitcpy = 0;
|
---|
| 2351 |
|
---|
| 2352 | for (;;) {
|
---|
| 2353 | /* grab next digit as required */
|
---|
| 2354 | if (--bitcnt == 0) {
|
---|
| 2355 | /* if digidx == -1 we are out of digits so break */
|
---|
| 2356 | if (digidx == -1) {
|
---|
| 2357 | break;
|
---|
| 2358 | }
|
---|
| 2359 | /* read next digit and reset bitcnt */
|
---|
| 2360 | buf = X->dp[digidx--];
|
---|
| 2361 | bitcnt = (int)DIGIT_BIT;
|
---|
| 2362 | }
|
---|
| 2363 |
|
---|
| 2364 | /* grab the next msb from the exponent */
|
---|
| 2365 | y = (int)(buf >> (DIGIT_BIT - 1)) & 1;
|
---|
| 2366 | buf <<= (mp_digit)1;
|
---|
| 2367 | /* add bit to the window */
|
---|
| 2368 | bitbuf |= (y << (WINSIZE - ++bitcpy));
|
---|
| 2369 |
|
---|
| 2370 | if (bitcpy == WINSIZE) {
|
---|
| 2371 | /* ok window is filled so square as required and multiply */
|
---|
| 2372 | /* square first */
|
---|
| 2373 | for (x = 0; x < WINSIZE; x++) {
|
---|
| 2374 | err = mp_sqr(res, res);
|
---|
| 2375 | if (err != MP_OKAY) {
|
---|
| 2376 | goto LBL_RES;
|
---|
| 2377 | }
|
---|
| 2378 | err = (*redux)(res, P, mp);
|
---|
| 2379 | if (err != MP_OKAY) {
|
---|
| 2380 | goto LBL_RES;
|
---|
| 2381 | }
|
---|
| 2382 | }
|
---|
| 2383 |
|
---|
| 2384 | /* then multiply by 2^bitbuf */
|
---|
| 2385 | err = mp_mul_2d(res, bitbuf, res);
|
---|
| 2386 | if (err != MP_OKAY) {
|
---|
| 2387 | goto LBL_RES;
|
---|
| 2388 | }
|
---|
| 2389 | err = mp_mod(res, P, res);
|
---|
| 2390 | if (err != MP_OKAY) {
|
---|
| 2391 | goto LBL_RES;
|
---|
| 2392 | }
|
---|
| 2393 |
|
---|
| 2394 | /* empty window and reset */
|
---|
| 2395 | bitcpy = 0;
|
---|
| 2396 | bitbuf = 0;
|
---|
| 2397 | }
|
---|
| 2398 | }
|
---|
| 2399 |
|
---|
| 2400 | /* fixup result if Montgomery reduction is used
|
---|
| 2401 | * recall that any value in a Montgomery system is
|
---|
| 2402 | * actually multiplied by R mod n. So we have
|
---|
| 2403 | * to reduce one more time to cancel out the factor
|
---|
| 2404 | * of R.
|
---|
| 2405 | */
|
---|
| 2406 | err = (*redux)(res, P, mp);
|
---|
| 2407 | if (err != MP_OKAY) {
|
---|
| 2408 | goto LBL_RES;
|
---|
| 2409 | }
|
---|
| 2410 |
|
---|
| 2411 | /* swap res with Y */
|
---|
| 2412 | mp_copy(res, Y);
|
---|
| 2413 |
|
---|
| 2414 | LBL_RES:mp_clear (res);
|
---|
| 2415 | LBL_M:
|
---|
| 2416 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2417 | XFREE(res, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 2418 | #endif
|
---|
| 2419 | return err;
|
---|
| 2420 | }
|
---|
| 2421 |
|
---|
| 2422 | #undef WINSIZE
|
---|
| 2423 | #endif /* BN_MP_EXPTMOD_BASE_2 */
|
---|
| 2424 |
|
---|
| 2425 |
|
---|
| 2426 | /* setups the montgomery reduction stuff */
|
---|
| 2427 | int mp_montgomery_setup (mp_int * n, mp_digit * rho)
|
---|
| 2428 | {
|
---|
| 2429 | mp_digit x, b;
|
---|
| 2430 |
|
---|
| 2431 | /* fast inversion mod 2**k
|
---|
| 2432 | *
|
---|
| 2433 | * Based on the fact that
|
---|
| 2434 | *
|
---|
| 2435 | * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
|
---|
| 2436 | * => 2*X*A - X*X*A*A = 1
|
---|
| 2437 | * => 2*(1) - (1) = 1
|
---|
| 2438 | */
|
---|
| 2439 | b = n->dp[0];
|
---|
| 2440 |
|
---|
| 2441 | if ((b & 1) == 0) {
|
---|
| 2442 | return MP_VAL;
|
---|
| 2443 | }
|
---|
| 2444 |
|
---|
| 2445 | x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
|
---|
| 2446 | x *= 2 - b * x; /* here x*a==1 mod 2**8 */
|
---|
| 2447 | #if !defined(MP_8BIT)
|
---|
| 2448 | x *= 2 - b * x; /* here x*a==1 mod 2**16 */
|
---|
| 2449 | #endif
|
---|
| 2450 | #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
|
---|
| 2451 | x *= 2 - b * x; /* here x*a==1 mod 2**32 */
|
---|
| 2452 | #endif
|
---|
| 2453 | #ifdef MP_64BIT
|
---|
| 2454 | x *= 2 - b * x; /* here x*a==1 mod 2**64 */
|
---|
| 2455 | #endif
|
---|
| 2456 |
|
---|
| 2457 | /* rho = -1/m mod b */
|
---|
| 2458 | /* TAO, switched mp_word casts to mp_digit to shut up compiler */
|
---|
| 2459 | *rho = (mp_digit)((((mp_digit)1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK);
|
---|
| 2460 |
|
---|
| 2461 | return MP_OKAY;
|
---|
| 2462 | }
|
---|
| 2463 |
|
---|
| 2464 |
|
---|
| 2465 | /* computes xR**-1 == x (mod N) via Montgomery Reduction
|
---|
| 2466 | *
|
---|
| 2467 | * This is an optimized implementation of montgomery_reduce
|
---|
| 2468 | * which uses the comba method to quickly calculate the columns of the
|
---|
| 2469 | * reduction.
|
---|
| 2470 | *
|
---|
| 2471 | * Based on Algorithm 14.32 on pp.601 of HAC.
|
---|
| 2472 | */
|
---|
| 2473 | int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
|
---|
| 2474 | {
|
---|
| 2475 | int ix, res, olduse;
|
---|
| 2476 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2477 | mp_word* W; /* uses dynamic memory and slower */
|
---|
| 2478 | #else
|
---|
| 2479 | mp_word W[MP_WARRAY];
|
---|
| 2480 | #endif
|
---|
| 2481 |
|
---|
| 2482 | /* get old used count */
|
---|
| 2483 | olduse = x->used;
|
---|
| 2484 |
|
---|
| 2485 | /* grow a as required */
|
---|
| 2486 | if (x->alloc < n->used + 1) {
|
---|
| 2487 | if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
|
---|
| 2488 | return res;
|
---|
| 2489 | }
|
---|
| 2490 | }
|
---|
| 2491 |
|
---|
| 2492 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2493 | W = (mp_word*)XMALLOC(sizeof(mp_word) * MP_WARRAY, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 2494 | if (W == NULL)
|
---|
| 2495 | return MP_MEM;
|
---|
| 2496 | #endif
|
---|
| 2497 |
|
---|
[464] | 2498 | XMEMSET(W, 0, (n->used * 2 + 1) * sizeof(mp_word));
|
---|
| 2499 |
|
---|
[457] | 2500 | /* first we have to get the digits of the input into
|
---|
| 2501 | * an array of double precision words W[...]
|
---|
| 2502 | */
|
---|
| 2503 | {
|
---|
| 2504 | mp_word *_W;
|
---|
| 2505 | mp_digit *tmpx;
|
---|
| 2506 |
|
---|
| 2507 | /* alias for the W[] array */
|
---|
| 2508 | _W = W;
|
---|
| 2509 |
|
---|
| 2510 | /* alias for the digits of x*/
|
---|
| 2511 | tmpx = x->dp;
|
---|
| 2512 |
|
---|
| 2513 | /* copy the digits of a into W[0..a->used-1] */
|
---|
| 2514 | for (ix = 0; ix < x->used; ix++) {
|
---|
| 2515 | *_W++ = *tmpx++;
|
---|
| 2516 | }
|
---|
| 2517 | }
|
---|
| 2518 |
|
---|
| 2519 | /* now we proceed to zero successive digits
|
---|
| 2520 | * from the least significant upwards
|
---|
| 2521 | */
|
---|
| 2522 | for (ix = 0; ix < n->used; ix++) {
|
---|
| 2523 | /* mu = ai * m' mod b
|
---|
| 2524 | *
|
---|
| 2525 | * We avoid a double precision multiplication (which isn't required)
|
---|
| 2526 | * by casting the value down to a mp_digit. Note this requires
|
---|
| 2527 | * that W[ix-1] have the carry cleared (see after the inner loop)
|
---|
| 2528 | */
|
---|
| 2529 | mp_digit mu;
|
---|
| 2530 | mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
|
---|
| 2531 |
|
---|
| 2532 | /* a = a + mu * m * b**i
|
---|
| 2533 | *
|
---|
| 2534 | * This is computed in place and on the fly. The multiplication
|
---|
| 2535 | * by b**i is handled by offsetting which columns the results
|
---|
| 2536 | * are added to.
|
---|
| 2537 | *
|
---|
| 2538 | * Note the comba method normally doesn't handle carries in the
|
---|
| 2539 | * inner loop In this case we fix the carry from the previous
|
---|
| 2540 | * column since the Montgomery reduction requires digits of the
|
---|
| 2541 | * result (so far) [see above] to work. This is
|
---|
| 2542 | * handled by fixing up one carry after the inner loop. The
|
---|
| 2543 | * carry fixups are done in order so after these loops the
|
---|
| 2544 | * first m->used words of W[] have the carries fixed
|
---|
| 2545 | */
|
---|
| 2546 | {
|
---|
| 2547 | int iy;
|
---|
| 2548 | mp_digit *tmpn;
|
---|
| 2549 | mp_word *_W;
|
---|
| 2550 |
|
---|
| 2551 | /* alias for the digits of the modulus */
|
---|
| 2552 | tmpn = n->dp;
|
---|
| 2553 |
|
---|
| 2554 | /* Alias for the columns set by an offset of ix */
|
---|
| 2555 | _W = W + ix;
|
---|
| 2556 |
|
---|
| 2557 | /* inner loop */
|
---|
| 2558 | for (iy = 0; iy < n->used; iy++) {
|
---|
| 2559 | *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
|
---|
| 2560 | }
|
---|
| 2561 | }
|
---|
| 2562 |
|
---|
| 2563 | /* now fix carry for next digit, W[ix+1] */
|
---|
| 2564 | W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
|
---|
| 2565 | }
|
---|
| 2566 |
|
---|
| 2567 | /* now we have to propagate the carries and
|
---|
| 2568 | * shift the words downward [all those least
|
---|
| 2569 | * significant digits we zeroed].
|
---|
| 2570 | */
|
---|
| 2571 | {
|
---|
| 2572 | mp_digit *tmpx;
|
---|
| 2573 | mp_word *_W, *_W1;
|
---|
| 2574 |
|
---|
| 2575 | /* nox fix rest of carries */
|
---|
| 2576 |
|
---|
| 2577 | /* alias for current word */
|
---|
| 2578 | _W1 = W + ix;
|
---|
| 2579 |
|
---|
| 2580 | /* alias for next word, where the carry goes */
|
---|
| 2581 | _W = W + ++ix;
|
---|
| 2582 |
|
---|
| 2583 | for (; ix <= n->used * 2 + 1; ix++) {
|
---|
| 2584 | *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
|
---|
| 2585 | }
|
---|
| 2586 |
|
---|
| 2587 | /* copy out, A = A/b**n
|
---|
| 2588 | *
|
---|
| 2589 | * The result is A/b**n but instead of converting from an
|
---|
| 2590 | * array of mp_word to mp_digit than calling mp_rshd
|
---|
| 2591 | * we just copy them in the right order
|
---|
| 2592 | */
|
---|
| 2593 |
|
---|
| 2594 | /* alias for destination word */
|
---|
| 2595 | tmpx = x->dp;
|
---|
| 2596 |
|
---|
| 2597 | /* alias for shifted double precision result */
|
---|
| 2598 | _W = W + n->used;
|
---|
| 2599 |
|
---|
| 2600 | for (ix = 0; ix < n->used + 1; ix++) {
|
---|
| 2601 | *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
|
---|
| 2602 | }
|
---|
| 2603 |
|
---|
| 2604 | /* zero olduse digits, if the input a was larger than
|
---|
| 2605 | * m->used+1 we'll have to clear the digits
|
---|
| 2606 | */
|
---|
| 2607 | for (; ix < olduse; ix++) {
|
---|
| 2608 | *tmpx++ = 0;
|
---|
| 2609 | }
|
---|
| 2610 | }
|
---|
| 2611 |
|
---|
| 2612 | /* set the max used and clamp */
|
---|
| 2613 | x->used = n->used + 1;
|
---|
| 2614 | mp_clamp (x);
|
---|
| 2615 |
|
---|
| 2616 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 2617 | XFREE(W, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 2618 | #endif
|
---|
| 2619 |
|
---|
| 2620 | /* if A >= m then A = A - m */
|
---|
| 2621 | if (mp_cmp_mag (x, n) != MP_LT) {
|
---|
| 2622 | return s_mp_sub (x, n, x);
|
---|
| 2623 | }
|
---|
| 2624 | return MP_OKAY;
|
---|
| 2625 | }
|
---|
| 2626 |
|
---|
| 2627 |
|
---|
| 2628 | /* computes xR**-1 == x (mod N) via Montgomery Reduction */
|
---|
| 2629 | int mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
|
---|
| 2630 | {
|
---|
| 2631 | int ix, res, digs;
|
---|
| 2632 | mp_digit mu;
|
---|
| 2633 |
|
---|
| 2634 | /* can the fast reduction [comba] method be used?
|
---|
| 2635 | *
|
---|
| 2636 | * Note that unlike in mul you're safely allowed *less*
|
---|
| 2637 | * than the available columns [255 per default] since carries
|
---|
| 2638 | * are fixed up in the inner loop.
|
---|
| 2639 | */
|
---|
| 2640 | digs = n->used * 2 + 1;
|
---|
| 2641 | if ((digs < (int)MP_WARRAY) &&
|
---|
| 2642 | n->used <
|
---|
[464] | 2643 | (1L << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
[457] | 2644 | return fast_mp_montgomery_reduce (x, n, rho);
|
---|
| 2645 | }
|
---|
| 2646 |
|
---|
| 2647 | /* grow the input as required */
|
---|
| 2648 | if (x->alloc < digs) {
|
---|
| 2649 | if ((res = mp_grow (x, digs)) != MP_OKAY) {
|
---|
| 2650 | return res;
|
---|
| 2651 | }
|
---|
| 2652 | }
|
---|
| 2653 | x->used = digs;
|
---|
| 2654 |
|
---|
| 2655 | for (ix = 0; ix < n->used; ix++) {
|
---|
| 2656 | /* mu = ai * rho mod b
|
---|
| 2657 | *
|
---|
| 2658 | * The value of rho must be precalculated via
|
---|
| 2659 | * montgomery_setup() such that
|
---|
| 2660 | * it equals -1/n0 mod b this allows the
|
---|
| 2661 | * following inner loop to reduce the
|
---|
| 2662 | * input one digit at a time
|
---|
| 2663 | */
|
---|
| 2664 | mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
|
---|
| 2665 |
|
---|
| 2666 | /* a = a + mu * m * b**i */
|
---|
| 2667 | {
|
---|
| 2668 | int iy;
|
---|
| 2669 | mp_digit *tmpn, *tmpx, u;
|
---|
| 2670 | mp_word r;
|
---|
| 2671 |
|
---|
| 2672 | /* alias for digits of the modulus */
|
---|
| 2673 | tmpn = n->dp;
|
---|
| 2674 |
|
---|
| 2675 | /* alias for the digits of x [the input] */
|
---|
| 2676 | tmpx = x->dp + ix;
|
---|
| 2677 |
|
---|
| 2678 | /* set the carry to zero */
|
---|
| 2679 | u = 0;
|
---|
| 2680 |
|
---|
| 2681 | /* Multiply and add in place */
|
---|
| 2682 | for (iy = 0; iy < n->used; iy++) {
|
---|
| 2683 | /* compute product and sum */
|
---|
| 2684 | r = ((mp_word)mu) * ((mp_word)*tmpn++) +
|
---|
| 2685 | ((mp_word) u) + ((mp_word) * tmpx);
|
---|
| 2686 |
|
---|
| 2687 | /* get carry */
|
---|
| 2688 | u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
---|
| 2689 |
|
---|
| 2690 | /* fix digit */
|
---|
| 2691 | *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
|
---|
| 2692 | }
|
---|
| 2693 | /* At this point the ix'th digit of x should be zero */
|
---|
| 2694 |
|
---|
| 2695 |
|
---|
| 2696 | /* propagate carries upwards as required*/
|
---|
| 2697 | while (u) {
|
---|
| 2698 | *tmpx += u;
|
---|
| 2699 | u = *tmpx >> DIGIT_BIT;
|
---|
| 2700 | *tmpx++ &= MP_MASK;
|
---|
| 2701 | }
|
---|
| 2702 | }
|
---|
| 2703 | }
|
---|
| 2704 |
|
---|
| 2705 | /* at this point the n.used'th least
|
---|
| 2706 | * significant digits of x are all zero
|
---|
| 2707 | * which means we can shift x to the
|
---|
| 2708 | * right by n.used digits and the
|
---|
| 2709 | * residue is unchanged.
|
---|
| 2710 | */
|
---|
| 2711 |
|
---|
| 2712 | /* x = x/b**n.used */
|
---|
| 2713 | mp_clamp(x);
|
---|
| 2714 | mp_rshd (x, n->used);
|
---|
| 2715 |
|
---|
| 2716 | /* if x >= n then x = x - n */
|
---|
| 2717 | if (mp_cmp_mag (x, n) != MP_LT) {
|
---|
| 2718 | return s_mp_sub (x, n, x);
|
---|
| 2719 | }
|
---|
| 2720 |
|
---|
| 2721 | return MP_OKAY;
|
---|
| 2722 | }
|
---|
| 2723 |
|
---|
| 2724 |
|
---|
| 2725 | /* determines the setup value */
|
---|
| 2726 | void mp_dr_setup(mp_int *a, mp_digit *d)
|
---|
| 2727 | {
|
---|
| 2728 | /* the casts are required if DIGIT_BIT is one less than
|
---|
| 2729 | * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
|
---|
| 2730 | */
|
---|
| 2731 | *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
|
---|
| 2732 | ((mp_word)a->dp[0]));
|
---|
| 2733 | }
|
---|
| 2734 |
|
---|
| 2735 |
|
---|
| 2736 | /* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
|
---|
| 2737 | *
|
---|
| 2738 | * Based on algorithm from the paper
|
---|
| 2739 | *
|
---|
| 2740 | * "Generating Efficient Primes for Discrete Log Cryptosystems"
|
---|
| 2741 | * Chae Hoon Lim, Pil Joong Lee,
|
---|
| 2742 | * POSTECH Information Research Laboratories
|
---|
| 2743 | *
|
---|
| 2744 | * The modulus must be of a special format [see manual]
|
---|
| 2745 | *
|
---|
| 2746 | * Has been modified to use algorithm 7.10 from the LTM book instead
|
---|
| 2747 | *
|
---|
| 2748 | * Input x must be in the range 0 <= x <= (n-1)**2
|
---|
| 2749 | */
|
---|
| 2750 | int mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
|
---|
| 2751 | {
|
---|
| 2752 | int err, i, m;
|
---|
| 2753 | mp_word r;
|
---|
| 2754 | mp_digit mu, *tmpx1, *tmpx2;
|
---|
| 2755 |
|
---|
| 2756 | /* m = digits in modulus */
|
---|
| 2757 | m = n->used;
|
---|
| 2758 |
|
---|
| 2759 | /* ensure that "x" has at least 2m digits */
|
---|
| 2760 | if (x->alloc < m + m) {
|
---|
| 2761 | if ((err = mp_grow (x, m + m)) != MP_OKAY) {
|
---|
| 2762 | return err;
|
---|
| 2763 | }
|
---|
| 2764 | }
|
---|
| 2765 |
|
---|
| 2766 | /* top of loop, this is where the code resumes if
|
---|
| 2767 | * another reduction pass is required.
|
---|
| 2768 | */
|
---|
| 2769 | top:
|
---|
| 2770 | /* aliases for digits */
|
---|
| 2771 | /* alias for lower half of x */
|
---|
| 2772 | tmpx1 = x->dp;
|
---|
| 2773 |
|
---|
| 2774 | /* alias for upper half of x, or x/B**m */
|
---|
| 2775 | tmpx2 = x->dp + m;
|
---|
| 2776 |
|
---|
| 2777 | /* set carry to zero */
|
---|
| 2778 | mu = 0;
|
---|
| 2779 |
|
---|
| 2780 | /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
|
---|
| 2781 | for (i = 0; i < m; i++) {
|
---|
| 2782 | r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
|
---|
| 2783 | *tmpx1++ = (mp_digit)(r & MP_MASK);
|
---|
| 2784 | mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
|
---|
| 2785 | }
|
---|
| 2786 |
|
---|
| 2787 | /* set final carry */
|
---|
| 2788 | *tmpx1++ = mu;
|
---|
| 2789 |
|
---|
| 2790 | /* zero words above m */
|
---|
| 2791 | for (i = m + 1; i < x->used; i++) {
|
---|
| 2792 | *tmpx1++ = 0;
|
---|
| 2793 | }
|
---|
| 2794 |
|
---|
| 2795 | /* clamp, sub and return */
|
---|
| 2796 | mp_clamp (x);
|
---|
| 2797 |
|
---|
| 2798 | /* if x >= n then subtract and reduce again
|
---|
| 2799 | * Each successive "recursion" makes the input smaller and smaller.
|
---|
| 2800 | */
|
---|
| 2801 | if (mp_cmp_mag (x, n) != MP_LT) {
|
---|
| 2802 | if ((err = s_mp_sub(x, n, x)) != MP_OKAY) {
|
---|
| 2803 | return err;
|
---|
| 2804 | }
|
---|
| 2805 | goto top;
|
---|
| 2806 | }
|
---|
| 2807 | return MP_OKAY;
|
---|
| 2808 | }
|
---|
| 2809 |
|
---|
| 2810 |
|
---|
| 2811 | /* reduces a modulo n where n is of the form 2**p - d */
|
---|
| 2812 | int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
|
---|
| 2813 | {
|
---|
| 2814 | mp_int q;
|
---|
| 2815 | int p, res;
|
---|
| 2816 |
|
---|
| 2817 | if ((res = mp_init(&q)) != MP_OKAY) {
|
---|
| 2818 | return res;
|
---|
| 2819 | }
|
---|
| 2820 |
|
---|
| 2821 | p = mp_count_bits(n);
|
---|
| 2822 | top:
|
---|
| 2823 | /* q = a/2**p, a = a mod 2**p */
|
---|
| 2824 | if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
|
---|
| 2825 | goto ERR;
|
---|
| 2826 | }
|
---|
| 2827 |
|
---|
| 2828 | if (d != 1) {
|
---|
| 2829 | /* q = q * d */
|
---|
| 2830 | if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
|
---|
| 2831 | goto ERR;
|
---|
| 2832 | }
|
---|
| 2833 | }
|
---|
| 2834 |
|
---|
| 2835 | /* a = a + q */
|
---|
| 2836 | if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
|
---|
| 2837 | goto ERR;
|
---|
| 2838 | }
|
---|
| 2839 |
|
---|
| 2840 | if (mp_cmp_mag(a, n) != MP_LT) {
|
---|
| 2841 | if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
|
---|
| 2842 | goto ERR;
|
---|
| 2843 | }
|
---|
| 2844 | goto top;
|
---|
| 2845 | }
|
---|
| 2846 |
|
---|
| 2847 | ERR:
|
---|
| 2848 | mp_clear(&q);
|
---|
| 2849 | return res;
|
---|
| 2850 | }
|
---|
| 2851 |
|
---|
| 2852 |
|
---|
| 2853 | /* determines the setup value */
|
---|
| 2854 | int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
|
---|
| 2855 | {
|
---|
| 2856 | int res, p;
|
---|
| 2857 | mp_int tmp;
|
---|
| 2858 |
|
---|
| 2859 | if ((res = mp_init(&tmp)) != MP_OKAY) {
|
---|
| 2860 | return res;
|
---|
| 2861 | }
|
---|
| 2862 |
|
---|
| 2863 | p = mp_count_bits(a);
|
---|
| 2864 | if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
|
---|
| 2865 | mp_clear(&tmp);
|
---|
| 2866 | return res;
|
---|
| 2867 | }
|
---|
| 2868 |
|
---|
| 2869 | if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
|
---|
| 2870 | mp_clear(&tmp);
|
---|
| 2871 | return res;
|
---|
| 2872 | }
|
---|
| 2873 |
|
---|
| 2874 | *d = tmp.dp[0];
|
---|
| 2875 | mp_clear(&tmp);
|
---|
| 2876 | return MP_OKAY;
|
---|
| 2877 | }
|
---|
| 2878 |
|
---|
| 2879 |
|
---|
| 2880 | /* set the b bit of a */
|
---|
| 2881 | int mp_set_bit (mp_int * a, int b)
|
---|
| 2882 | {
|
---|
| 2883 | int i = b / DIGIT_BIT, res;
|
---|
| 2884 |
|
---|
| 2885 | /*
|
---|
| 2886 | * Require:
|
---|
| 2887 | * bit index b >= 0
|
---|
| 2888 | * a->alloc == a->used == 0 if a->dp == NULL
|
---|
| 2889 | */
|
---|
| 2890 | if (b < 0 || (a->dp == NULL && (a->alloc != 0 || a->used != 0)))
|
---|
| 2891 | return MP_VAL;
|
---|
| 2892 |
|
---|
| 2893 | if (a->dp == NULL || a->used < (int)(i + 1)) {
|
---|
| 2894 | /* grow a to accommodate the single bit */
|
---|
| 2895 | if ((res = mp_grow (a, i + 1)) != MP_OKAY) {
|
---|
| 2896 | return res;
|
---|
| 2897 | }
|
---|
| 2898 |
|
---|
| 2899 | /* set the used count of where the bit will go */
|
---|
| 2900 | a->used = (int)(i + 1);
|
---|
| 2901 | }
|
---|
| 2902 |
|
---|
| 2903 | /* put the single bit in its place */
|
---|
| 2904 | a->dp[i] |= ((mp_digit)1) << (b % DIGIT_BIT);
|
---|
| 2905 |
|
---|
| 2906 | return MP_OKAY;
|
---|
| 2907 | }
|
---|
| 2908 |
|
---|
| 2909 | /* computes a = 2**b
|
---|
| 2910 | *
|
---|
| 2911 | * Simple algorithm which zeros the int, set the required bit
|
---|
| 2912 | */
|
---|
| 2913 | int mp_2expt (mp_int * a, int b)
|
---|
| 2914 | {
|
---|
| 2915 | /* zero a as per default */
|
---|
| 2916 | mp_zero (a);
|
---|
| 2917 |
|
---|
| 2918 | return mp_set_bit(a, b);
|
---|
| 2919 | }
|
---|
| 2920 |
|
---|
| 2921 | /* multiply by a digit */
|
---|
| 2922 | int mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
|
---|
| 2923 | {
|
---|
| 2924 | mp_digit u, *tmpa, *tmpc;
|
---|
| 2925 | mp_word r;
|
---|
| 2926 | int ix, res, olduse;
|
---|
| 2927 |
|
---|
| 2928 | /* make sure c is big enough to hold a*b */
|
---|
| 2929 | if (c->alloc < a->used + 1) {
|
---|
| 2930 | if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
|
---|
| 2931 | return res;
|
---|
| 2932 | }
|
---|
| 2933 | }
|
---|
| 2934 |
|
---|
| 2935 | /* get the original destinations used count */
|
---|
| 2936 | olduse = c->used;
|
---|
| 2937 |
|
---|
| 2938 | /* set the sign */
|
---|
| 2939 | c->sign = a->sign;
|
---|
| 2940 |
|
---|
| 2941 | /* alias for a->dp [source] */
|
---|
| 2942 | tmpa = a->dp;
|
---|
| 2943 |
|
---|
| 2944 | /* alias for c->dp [dest] */
|
---|
| 2945 | tmpc = c->dp;
|
---|
| 2946 |
|
---|
| 2947 | /* zero carry */
|
---|
| 2948 | u = 0;
|
---|
| 2949 |
|
---|
| 2950 | /* compute columns */
|
---|
| 2951 | for (ix = 0; ix < a->used; ix++) {
|
---|
| 2952 | /* compute product and carry sum for this term */
|
---|
| 2953 | r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
|
---|
| 2954 |
|
---|
| 2955 | /* mask off higher bits to get a single digit */
|
---|
| 2956 | *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 2957 |
|
---|
| 2958 | /* send carry into next iteration */
|
---|
| 2959 | u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
---|
| 2960 | }
|
---|
| 2961 |
|
---|
| 2962 | /* store final carry [if any] and increment ix offset */
|
---|
| 2963 | *tmpc++ = u;
|
---|
| 2964 | ++ix;
|
---|
| 2965 |
|
---|
| 2966 | /* now zero digits above the top */
|
---|
| 2967 | while (ix++ < olduse) {
|
---|
| 2968 | *tmpc++ = 0;
|
---|
| 2969 | }
|
---|
| 2970 |
|
---|
| 2971 | /* set used count */
|
---|
| 2972 | c->used = a->used + 1;
|
---|
| 2973 | mp_clamp(c);
|
---|
| 2974 |
|
---|
| 2975 | return MP_OKAY;
|
---|
| 2976 | }
|
---|
| 2977 |
|
---|
| 2978 |
|
---|
| 2979 | /* d = a * b (mod c) */
|
---|
| 2980 | #if defined(FREESCALE_LTC_TFM)
|
---|
| 2981 | int wolfcrypt_mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d)
|
---|
| 2982 | #else
|
---|
| 2983 | int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
|
---|
| 2984 | #endif
|
---|
| 2985 | {
|
---|
| 2986 | int res;
|
---|
| 2987 | mp_int t;
|
---|
| 2988 |
|
---|
| 2989 | if ((res = mp_init_size (&t, c->used)) != MP_OKAY) {
|
---|
| 2990 | return res;
|
---|
| 2991 | }
|
---|
| 2992 |
|
---|
| 2993 | res = mp_mul (a, b, &t);
|
---|
| 2994 | if (res == MP_OKAY) {
|
---|
| 2995 | res = mp_mod (&t, c, d);
|
---|
| 2996 | }
|
---|
| 2997 |
|
---|
| 2998 | mp_clear (&t);
|
---|
| 2999 | return res;
|
---|
| 3000 | }
|
---|
| 3001 |
|
---|
| 3002 |
|
---|
| 3003 | /* d = a - b (mod c) */
|
---|
| 3004 | int mp_submod(mp_int* a, mp_int* b, mp_int* c, mp_int* d)
|
---|
| 3005 | {
|
---|
| 3006 | int res;
|
---|
| 3007 | mp_int t;
|
---|
| 3008 |
|
---|
| 3009 | if ((res = mp_init (&t)) != MP_OKAY) {
|
---|
| 3010 | return res;
|
---|
| 3011 | }
|
---|
| 3012 |
|
---|
| 3013 | res = mp_sub (a, b, &t);
|
---|
| 3014 | if (res == MP_OKAY) {
|
---|
| 3015 | res = mp_mod (&t, c, d);
|
---|
| 3016 | }
|
---|
| 3017 |
|
---|
| 3018 | mp_clear (&t);
|
---|
| 3019 |
|
---|
| 3020 | return res;
|
---|
| 3021 | }
|
---|
| 3022 |
|
---|
| 3023 | /* d = a + b (mod c) */
|
---|
| 3024 | int mp_addmod(mp_int* a, mp_int* b, mp_int* c, mp_int* d)
|
---|
| 3025 | {
|
---|
| 3026 | int res;
|
---|
| 3027 | mp_int t;
|
---|
| 3028 |
|
---|
| 3029 | if ((res = mp_init (&t)) != MP_OKAY) {
|
---|
| 3030 | return res;
|
---|
| 3031 | }
|
---|
| 3032 |
|
---|
| 3033 | res = mp_add (a, b, &t);
|
---|
| 3034 | if (res == MP_OKAY) {
|
---|
| 3035 | res = mp_mod (&t, c, d);
|
---|
| 3036 | }
|
---|
| 3037 |
|
---|
| 3038 | mp_clear (&t);
|
---|
| 3039 |
|
---|
| 3040 | return res;
|
---|
| 3041 | }
|
---|
| 3042 |
|
---|
[464] | 3043 | /* d = a - b (mod c) - a < c and b < c and positive */
|
---|
| 3044 | int mp_submod_ct(mp_int* a, mp_int* b, mp_int* c, mp_int* d)
|
---|
| 3045 | {
|
---|
| 3046 | int res;
|
---|
| 3047 |
|
---|
| 3048 | res = mp_sub(a, b, d);
|
---|
| 3049 | if (res == MP_OKAY && mp_isneg(d)) {
|
---|
| 3050 | res = mp_add(d, c, d);
|
---|
| 3051 | }
|
---|
| 3052 |
|
---|
| 3053 | return res;
|
---|
| 3054 | }
|
---|
| 3055 |
|
---|
| 3056 | /* d = a + b (mod c) - a < c and b < c and positive */
|
---|
| 3057 | int mp_addmod_ct(mp_int* a, mp_int* b, mp_int* c, mp_int* d)
|
---|
| 3058 | {
|
---|
| 3059 | int res;
|
---|
| 3060 |
|
---|
| 3061 | res = mp_add(a, b, d);
|
---|
| 3062 | if (res == MP_OKAY && mp_cmp(d, c) != MP_LT) {
|
---|
| 3063 | res = mp_sub(d, c, d);
|
---|
| 3064 | }
|
---|
| 3065 |
|
---|
| 3066 | return res;
|
---|
| 3067 | }
|
---|
| 3068 |
|
---|
[457] | 3069 | /* computes b = a*a */
|
---|
| 3070 | int mp_sqr (mp_int * a, mp_int * b)
|
---|
| 3071 | {
|
---|
| 3072 | int res;
|
---|
| 3073 |
|
---|
| 3074 | {
|
---|
| 3075 | #ifdef BN_FAST_S_MP_SQR_C
|
---|
| 3076 | /* can we use the fast comba multiplier? */
|
---|
| 3077 | if ((a->used * 2 + 1) < (int)MP_WARRAY &&
|
---|
| 3078 | a->used <
|
---|
| 3079 | (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
|
---|
| 3080 | res = fast_s_mp_sqr (a, b);
|
---|
| 3081 | } else
|
---|
| 3082 | #endif
|
---|
| 3083 | #ifdef BN_S_MP_SQR_C
|
---|
| 3084 | res = s_mp_sqr (a, b);
|
---|
| 3085 | #else
|
---|
| 3086 | res = MP_VAL;
|
---|
| 3087 | #endif
|
---|
| 3088 | }
|
---|
| 3089 | b->sign = MP_ZPOS;
|
---|
| 3090 | return res;
|
---|
| 3091 | }
|
---|
| 3092 |
|
---|
| 3093 |
|
---|
| 3094 | /* high level multiplication (handles sign) */
|
---|
| 3095 | #if defined(FREESCALE_LTC_TFM)
|
---|
| 3096 | int wolfcrypt_mp_mul(mp_int *a, mp_int *b, mp_int *c)
|
---|
| 3097 | #else
|
---|
| 3098 | int mp_mul (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 3099 | #endif
|
---|
| 3100 | {
|
---|
| 3101 | int res, neg;
|
---|
| 3102 | neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
|
---|
| 3103 |
|
---|
| 3104 | {
|
---|
| 3105 | #ifdef BN_FAST_S_MP_MUL_DIGS_C
|
---|
| 3106 | /* can we use the fast multiplier?
|
---|
| 3107 | *
|
---|
| 3108 | * The fast multiplier can be used if the output will
|
---|
| 3109 | * have less than MP_WARRAY digits and the number of
|
---|
| 3110 | * digits won't affect carry propagation
|
---|
| 3111 | */
|
---|
| 3112 | int digs = a->used + b->used + 1;
|
---|
| 3113 |
|
---|
| 3114 | if ((digs < (int)MP_WARRAY) &&
|
---|
| 3115 | MIN(a->used, b->used) <=
|
---|
[464] | 3116 | (1L << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
[457] | 3117 | res = fast_s_mp_mul_digs (a, b, c, digs);
|
---|
| 3118 | } else
|
---|
| 3119 | #endif
|
---|
| 3120 | #ifdef BN_S_MP_MUL_DIGS_C
|
---|
| 3121 | res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
|
---|
| 3122 | #else
|
---|
| 3123 | res = MP_VAL;
|
---|
| 3124 | #endif
|
---|
| 3125 |
|
---|
| 3126 | }
|
---|
| 3127 | c->sign = (c->used > 0) ? neg : MP_ZPOS;
|
---|
| 3128 | return res;
|
---|
| 3129 | }
|
---|
| 3130 |
|
---|
| 3131 |
|
---|
| 3132 | /* b = a*2 */
|
---|
| 3133 | int mp_mul_2(mp_int * a, mp_int * b)
|
---|
| 3134 | {
|
---|
| 3135 | int x, res, oldused;
|
---|
| 3136 |
|
---|
| 3137 | /* grow to accommodate result */
|
---|
| 3138 | if (b->alloc < a->used + 1) {
|
---|
| 3139 | if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
|
---|
| 3140 | return res;
|
---|
| 3141 | }
|
---|
| 3142 | }
|
---|
| 3143 |
|
---|
| 3144 | oldused = b->used;
|
---|
| 3145 | b->used = a->used;
|
---|
| 3146 |
|
---|
| 3147 | {
|
---|
| 3148 | mp_digit r, rr, *tmpa, *tmpb;
|
---|
| 3149 |
|
---|
| 3150 | /* alias for source */
|
---|
| 3151 | tmpa = a->dp;
|
---|
| 3152 |
|
---|
| 3153 | /* alias for dest */
|
---|
| 3154 | tmpb = b->dp;
|
---|
| 3155 |
|
---|
| 3156 | /* carry */
|
---|
| 3157 | r = 0;
|
---|
| 3158 | for (x = 0; x < a->used; x++) {
|
---|
| 3159 |
|
---|
| 3160 | /* get what will be the *next* carry bit from the
|
---|
| 3161 | * MSB of the current digit
|
---|
| 3162 | */
|
---|
| 3163 | rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
|
---|
| 3164 |
|
---|
| 3165 | /* now shift up this digit, add in the carry [from the previous] */
|
---|
| 3166 | *tmpb++ = (mp_digit)(((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK);
|
---|
| 3167 |
|
---|
| 3168 | /* copy the carry that would be from the source
|
---|
| 3169 | * digit into the next iteration
|
---|
| 3170 | */
|
---|
| 3171 | r = rr;
|
---|
| 3172 | }
|
---|
| 3173 |
|
---|
| 3174 | /* new leading digit? */
|
---|
| 3175 | if (r != 0) {
|
---|
| 3176 | /* add a MSB which is always 1 at this point */
|
---|
| 3177 | *tmpb = 1;
|
---|
| 3178 | ++(b->used);
|
---|
| 3179 | }
|
---|
| 3180 |
|
---|
| 3181 | /* now zero any excess digits on the destination
|
---|
| 3182 | * that we didn't write to
|
---|
| 3183 | */
|
---|
| 3184 | tmpb = b->dp + b->used;
|
---|
| 3185 | for (x = b->used; x < oldused; x++) {
|
---|
| 3186 | *tmpb++ = 0;
|
---|
| 3187 | }
|
---|
| 3188 | }
|
---|
| 3189 | b->sign = a->sign;
|
---|
| 3190 | return MP_OKAY;
|
---|
| 3191 | }
|
---|
| 3192 |
|
---|
| 3193 |
|
---|
| 3194 | /* divide by three (based on routine from MPI and the GMP manual) */
|
---|
| 3195 | int mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
|
---|
| 3196 | {
|
---|
| 3197 | mp_int q;
|
---|
| 3198 | mp_word w, t;
|
---|
| 3199 | mp_digit b;
|
---|
| 3200 | int res, ix;
|
---|
| 3201 |
|
---|
| 3202 | /* b = 2**DIGIT_BIT / 3 */
|
---|
| 3203 | b = (mp_digit) ( (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3) );
|
---|
| 3204 |
|
---|
| 3205 | if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
|
---|
| 3206 | return res;
|
---|
| 3207 | }
|
---|
| 3208 |
|
---|
| 3209 | q.used = a->used;
|
---|
| 3210 | q.sign = a->sign;
|
---|
| 3211 | w = 0;
|
---|
| 3212 | for (ix = a->used - 1; ix >= 0; ix--) {
|
---|
| 3213 | w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
|
---|
| 3214 |
|
---|
| 3215 | if (w >= 3) {
|
---|
| 3216 | /* multiply w by [1/3] */
|
---|
| 3217 | t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);
|
---|
| 3218 |
|
---|
| 3219 | /* now subtract 3 * [w/3] from w, to get the remainder */
|
---|
| 3220 | w -= t+t+t;
|
---|
| 3221 |
|
---|
| 3222 | /* fixup the remainder as required since
|
---|
| 3223 | * the optimization is not exact.
|
---|
| 3224 | */
|
---|
| 3225 | while (w >= 3) {
|
---|
| 3226 | t += 1;
|
---|
| 3227 | w -= 3;
|
---|
| 3228 | }
|
---|
| 3229 | } else {
|
---|
| 3230 | t = 0;
|
---|
| 3231 | }
|
---|
| 3232 | q.dp[ix] = (mp_digit)t;
|
---|
| 3233 | }
|
---|
| 3234 |
|
---|
| 3235 | /* [optional] store the remainder */
|
---|
| 3236 | if (d != NULL) {
|
---|
| 3237 | *d = (mp_digit)w;
|
---|
| 3238 | }
|
---|
| 3239 |
|
---|
| 3240 | /* [optional] store the quotient */
|
---|
| 3241 | if (c != NULL) {
|
---|
| 3242 | mp_clamp(&q);
|
---|
| 3243 | mp_exch(&q, c);
|
---|
| 3244 | }
|
---|
| 3245 | mp_clear(&q);
|
---|
| 3246 |
|
---|
| 3247 | return res;
|
---|
| 3248 | }
|
---|
| 3249 |
|
---|
| 3250 |
|
---|
| 3251 | /* init an mp_init for a given size */
|
---|
| 3252 | int mp_init_size (mp_int * a, int size)
|
---|
| 3253 | {
|
---|
| 3254 | int x;
|
---|
| 3255 |
|
---|
| 3256 | /* pad size so there are always extra digits */
|
---|
| 3257 | size += (MP_PREC * 2) - (size % MP_PREC);
|
---|
| 3258 |
|
---|
| 3259 | /* alloc mem */
|
---|
| 3260 | a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size, NULL,
|
---|
| 3261 | DYNAMIC_TYPE_BIGINT);
|
---|
| 3262 | if (a->dp == NULL) {
|
---|
| 3263 | return MP_MEM;
|
---|
| 3264 | }
|
---|
| 3265 |
|
---|
| 3266 | /* set the members */
|
---|
| 3267 | a->used = 0;
|
---|
| 3268 | a->alloc = size;
|
---|
| 3269 | a->sign = MP_ZPOS;
|
---|
| 3270 | #ifdef HAVE_WOLF_BIGINT
|
---|
| 3271 | wc_bigint_init(&a->raw);
|
---|
| 3272 | #endif
|
---|
| 3273 |
|
---|
| 3274 | /* zero the digits */
|
---|
| 3275 | for (x = 0; x < size; x++) {
|
---|
| 3276 | a->dp[x] = 0;
|
---|
| 3277 | }
|
---|
| 3278 |
|
---|
| 3279 | return MP_OKAY;
|
---|
| 3280 | }
|
---|
| 3281 |
|
---|
| 3282 |
|
---|
| 3283 | /* the jist of squaring...
|
---|
| 3284 | * you do like mult except the offset of the tmpx [one that
|
---|
| 3285 | * starts closer to zero] can't equal the offset of tmpy.
|
---|
| 3286 | * So basically you set up iy like before then you min it with
|
---|
| 3287 | * (ty-tx) so that it never happens. You double all those
|
---|
| 3288 | * you add in the inner loop
|
---|
| 3289 |
|
---|
| 3290 | After that loop you do the squares and add them in.
|
---|
| 3291 | */
|
---|
| 3292 |
|
---|
| 3293 | int fast_s_mp_sqr (mp_int * a, mp_int * b)
|
---|
| 3294 | {
|
---|
| 3295 | int olduse, res, pa, ix, iz;
|
---|
| 3296 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3297 | mp_digit* W; /* uses dynamic memory and slower */
|
---|
| 3298 | #else
|
---|
| 3299 | mp_digit W[MP_WARRAY];
|
---|
| 3300 | #endif
|
---|
| 3301 | mp_digit *tmpx;
|
---|
| 3302 | mp_word W1;
|
---|
| 3303 |
|
---|
| 3304 | /* grow the destination as required */
|
---|
| 3305 | pa = a->used + a->used;
|
---|
| 3306 | if (b->alloc < pa) {
|
---|
| 3307 | if ((res = mp_grow (b, pa)) != MP_OKAY) {
|
---|
| 3308 | return res;
|
---|
| 3309 | }
|
---|
| 3310 | }
|
---|
| 3311 |
|
---|
| 3312 | if (pa > (int)MP_WARRAY)
|
---|
| 3313 | return MP_RANGE; /* TAO range check */
|
---|
| 3314 |
|
---|
| 3315 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3316 | W = (mp_digit*)XMALLOC(sizeof(mp_digit) * MP_WARRAY, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 3317 | if (W == NULL)
|
---|
| 3318 | return MP_MEM;
|
---|
| 3319 | #endif
|
---|
| 3320 |
|
---|
| 3321 | /* number of output digits to produce */
|
---|
| 3322 | W1 = 0;
|
---|
| 3323 | for (ix = 0; ix < pa; ix++) {
|
---|
| 3324 | int tx, ty, iy;
|
---|
| 3325 | mp_word _W;
|
---|
| 3326 | mp_digit *tmpy;
|
---|
| 3327 |
|
---|
| 3328 | /* clear counter */
|
---|
| 3329 | _W = 0;
|
---|
| 3330 |
|
---|
| 3331 | /* get offsets into the two bignums */
|
---|
| 3332 | ty = MIN(a->used-1, ix);
|
---|
| 3333 | tx = ix - ty;
|
---|
| 3334 |
|
---|
| 3335 | /* setup temp aliases */
|
---|
| 3336 | tmpx = a->dp + tx;
|
---|
| 3337 | tmpy = a->dp + ty;
|
---|
| 3338 |
|
---|
| 3339 | /* this is the number of times the loop will iterate, essentially
|
---|
| 3340 | while (tx++ < a->used && ty-- >= 0) { ... }
|
---|
| 3341 | */
|
---|
| 3342 | iy = MIN(a->used-tx, ty+1);
|
---|
| 3343 |
|
---|
| 3344 | /* now for squaring tx can never equal ty
|
---|
| 3345 | * we halve the distance since they approach at a rate of 2x
|
---|
| 3346 | * and we have to round because odd cases need to be executed
|
---|
| 3347 | */
|
---|
| 3348 | iy = MIN(iy, (ty-tx+1)>>1);
|
---|
| 3349 |
|
---|
| 3350 | /* execute loop */
|
---|
| 3351 | for (iz = 0; iz < iy; iz++) {
|
---|
| 3352 | _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
|
---|
| 3353 | }
|
---|
| 3354 |
|
---|
| 3355 | /* double the inner product and add carry */
|
---|
| 3356 | _W = _W + _W + W1;
|
---|
| 3357 |
|
---|
| 3358 | /* even columns have the square term in them */
|
---|
| 3359 | if ((ix&1) == 0) {
|
---|
| 3360 | _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
|
---|
| 3361 | }
|
---|
| 3362 |
|
---|
| 3363 | /* store it */
|
---|
| 3364 | W[ix] = (mp_digit)(_W & MP_MASK);
|
---|
| 3365 |
|
---|
| 3366 | /* make next carry */
|
---|
| 3367 | W1 = _W >> ((mp_word)DIGIT_BIT);
|
---|
| 3368 | }
|
---|
| 3369 |
|
---|
| 3370 | /* setup dest */
|
---|
| 3371 | olduse = b->used;
|
---|
| 3372 | b->used = a->used+a->used;
|
---|
| 3373 |
|
---|
| 3374 | {
|
---|
| 3375 | mp_digit *tmpb;
|
---|
| 3376 | tmpb = b->dp;
|
---|
| 3377 | for (ix = 0; ix < pa; ix++) {
|
---|
| 3378 | *tmpb++ = (mp_digit)(W[ix] & MP_MASK);
|
---|
| 3379 | }
|
---|
| 3380 |
|
---|
| 3381 | /* clear unused digits [that existed in the old copy of c] */
|
---|
| 3382 | for (; ix < olduse; ix++) {
|
---|
| 3383 | *tmpb++ = 0;
|
---|
| 3384 | }
|
---|
| 3385 | }
|
---|
| 3386 | mp_clamp (b);
|
---|
| 3387 |
|
---|
| 3388 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3389 | XFREE(W, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 3390 | #endif
|
---|
| 3391 |
|
---|
| 3392 | return MP_OKAY;
|
---|
| 3393 | }
|
---|
| 3394 |
|
---|
| 3395 |
|
---|
| 3396 | /* Fast (comba) multiplier
|
---|
| 3397 | *
|
---|
| 3398 | * This is the fast column-array [comba] multiplier. It is
|
---|
| 3399 | * designed to compute the columns of the product first
|
---|
| 3400 | * then handle the carries afterwards. This has the effect
|
---|
| 3401 | * of making the nested loops that compute the columns very
|
---|
| 3402 | * simple and schedulable on super-scalar processors.
|
---|
| 3403 | *
|
---|
| 3404 | * This has been modified to produce a variable number of
|
---|
| 3405 | * digits of output so if say only a half-product is required
|
---|
| 3406 | * you don't have to compute the upper half (a feature
|
---|
| 3407 | * required for fast Barrett reduction).
|
---|
| 3408 | *
|
---|
| 3409 | * Based on Algorithm 14.12 on pp.595 of HAC.
|
---|
| 3410 | *
|
---|
| 3411 | */
|
---|
| 3412 | int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
---|
| 3413 | {
|
---|
| 3414 | int olduse, res, pa, ix, iz;
|
---|
| 3415 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3416 | mp_digit* W; /* uses dynamic memory and slower */
|
---|
| 3417 | #else
|
---|
| 3418 | mp_digit W[MP_WARRAY];
|
---|
| 3419 | #endif
|
---|
| 3420 | mp_word _W;
|
---|
| 3421 |
|
---|
| 3422 | /* grow the destination as required */
|
---|
| 3423 | if (c->alloc < digs) {
|
---|
| 3424 | if ((res = mp_grow (c, digs)) != MP_OKAY) {
|
---|
| 3425 | return res;
|
---|
| 3426 | }
|
---|
| 3427 | }
|
---|
| 3428 |
|
---|
| 3429 | /* number of output digits to produce */
|
---|
| 3430 | pa = MIN(digs, a->used + b->used);
|
---|
| 3431 | if (pa > (int)MP_WARRAY)
|
---|
| 3432 | return MP_RANGE; /* TAO range check */
|
---|
| 3433 |
|
---|
| 3434 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3435 | W = (mp_digit*)XMALLOC(sizeof(mp_digit) * MP_WARRAY, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 3436 | if (W == NULL)
|
---|
| 3437 | return MP_MEM;
|
---|
| 3438 | #endif
|
---|
| 3439 |
|
---|
| 3440 | /* clear the carry */
|
---|
| 3441 | _W = 0;
|
---|
| 3442 | for (ix = 0; ix < pa; ix++) {
|
---|
| 3443 | int tx, ty;
|
---|
| 3444 | int iy;
|
---|
| 3445 | mp_digit *tmpx, *tmpy;
|
---|
| 3446 |
|
---|
| 3447 | /* get offsets into the two bignums */
|
---|
| 3448 | ty = MIN(b->used-1, ix);
|
---|
| 3449 | tx = ix - ty;
|
---|
| 3450 |
|
---|
| 3451 | /* setup temp aliases */
|
---|
| 3452 | tmpx = a->dp + tx;
|
---|
| 3453 | tmpy = b->dp + ty;
|
---|
| 3454 |
|
---|
| 3455 | /* this is the number of times the loop will iterate, essentially
|
---|
| 3456 | while (tx++ < a->used && ty-- >= 0) { ... }
|
---|
| 3457 | */
|
---|
| 3458 | iy = MIN(a->used-tx, ty+1);
|
---|
| 3459 |
|
---|
| 3460 | /* execute loop */
|
---|
| 3461 | for (iz = 0; iz < iy; ++iz) {
|
---|
| 3462 | _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
|
---|
| 3463 |
|
---|
| 3464 | }
|
---|
| 3465 |
|
---|
| 3466 | /* store term */
|
---|
| 3467 | W[ix] = (mp_digit)(((mp_digit)_W) & MP_MASK);
|
---|
| 3468 |
|
---|
| 3469 | /* make next carry */
|
---|
| 3470 | _W = _W >> ((mp_word)DIGIT_BIT);
|
---|
| 3471 | }
|
---|
| 3472 |
|
---|
| 3473 | /* setup dest */
|
---|
| 3474 | olduse = c->used;
|
---|
| 3475 | c->used = pa;
|
---|
| 3476 |
|
---|
| 3477 | {
|
---|
| 3478 | mp_digit *tmpc;
|
---|
| 3479 | tmpc = c->dp;
|
---|
| 3480 | for (ix = 0; ix < pa; ix++) { /* JRB, +1 could read uninitialized data */
|
---|
| 3481 | /* now extract the previous digit [below the carry] */
|
---|
| 3482 | *tmpc++ = W[ix];
|
---|
| 3483 | }
|
---|
| 3484 |
|
---|
| 3485 | /* clear unused digits [that existed in the old copy of c] */
|
---|
| 3486 | for (; ix < olduse; ix++) {
|
---|
| 3487 | *tmpc++ = 0;
|
---|
| 3488 | }
|
---|
| 3489 | }
|
---|
| 3490 | mp_clamp (c);
|
---|
| 3491 |
|
---|
| 3492 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 3493 | XFREE(W, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 3494 | #endif
|
---|
| 3495 |
|
---|
| 3496 | return MP_OKAY;
|
---|
| 3497 | }
|
---|
| 3498 |
|
---|
| 3499 |
|
---|
| 3500 | /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
|
---|
| 3501 | int s_mp_sqr (mp_int * a, mp_int * b)
|
---|
| 3502 | {
|
---|
| 3503 | mp_int t;
|
---|
| 3504 | int res, ix, iy, pa;
|
---|
| 3505 | mp_word r;
|
---|
| 3506 | mp_digit u, tmpx, *tmpt;
|
---|
| 3507 |
|
---|
| 3508 | pa = a->used;
|
---|
| 3509 | if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
|
---|
| 3510 | return res;
|
---|
| 3511 | }
|
---|
| 3512 |
|
---|
| 3513 | /* default used is maximum possible size */
|
---|
| 3514 | t.used = 2*pa + 1;
|
---|
| 3515 |
|
---|
| 3516 | for (ix = 0; ix < pa; ix++) {
|
---|
| 3517 | /* first calculate the digit at 2*ix */
|
---|
| 3518 | /* calculate double precision result */
|
---|
| 3519 | r = ((mp_word) t.dp[2*ix]) +
|
---|
| 3520 | ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
|
---|
| 3521 |
|
---|
| 3522 | /* store lower part in result */
|
---|
| 3523 | t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 3524 |
|
---|
| 3525 | /* get the carry */
|
---|
| 3526 | u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
---|
| 3527 |
|
---|
| 3528 | /* left hand side of A[ix] * A[iy] */
|
---|
| 3529 | tmpx = a->dp[ix];
|
---|
| 3530 |
|
---|
| 3531 | /* alias for where to store the results */
|
---|
| 3532 | tmpt = t.dp + (2*ix + 1);
|
---|
| 3533 |
|
---|
| 3534 | for (iy = ix + 1; iy < pa; iy++) {
|
---|
| 3535 | /* first calculate the product */
|
---|
| 3536 | r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
|
---|
| 3537 |
|
---|
| 3538 | /* now calculate the double precision result, note we use
|
---|
| 3539 | * addition instead of *2 since it's easier to optimize
|
---|
| 3540 | */
|
---|
| 3541 | r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
|
---|
| 3542 |
|
---|
| 3543 | /* store lower part */
|
---|
| 3544 | *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 3545 |
|
---|
| 3546 | /* get carry */
|
---|
| 3547 | u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
---|
| 3548 | }
|
---|
| 3549 | /* propagate upwards */
|
---|
| 3550 | while (u != ((mp_digit) 0)) {
|
---|
| 3551 | r = ((mp_word) *tmpt) + ((mp_word) u);
|
---|
| 3552 | *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 3553 | u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
---|
| 3554 | }
|
---|
| 3555 | }
|
---|
| 3556 |
|
---|
| 3557 | mp_clamp (&t);
|
---|
| 3558 | mp_exch (&t, b);
|
---|
| 3559 | mp_clear (&t);
|
---|
| 3560 | return MP_OKAY;
|
---|
| 3561 | }
|
---|
| 3562 |
|
---|
| 3563 |
|
---|
| 3564 | /* multiplies |a| * |b| and only computes up to digs digits of result
|
---|
| 3565 | * HAC pp. 595, Algorithm 14.12 Modified so you can control how
|
---|
| 3566 | * many digits of output are created.
|
---|
| 3567 | */
|
---|
| 3568 | int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
---|
| 3569 | {
|
---|
| 3570 | mp_int t;
|
---|
| 3571 | int res, pa, pb, ix, iy;
|
---|
| 3572 | mp_digit u;
|
---|
| 3573 | mp_word r;
|
---|
| 3574 | mp_digit tmpx, *tmpt, *tmpy;
|
---|
| 3575 |
|
---|
| 3576 | /* can we use the fast multiplier? */
|
---|
| 3577 | if ((digs < (int)MP_WARRAY) &&
|
---|
| 3578 | MIN (a->used, b->used) <
|
---|
[464] | 3579 | (1L << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
[457] | 3580 | return fast_s_mp_mul_digs (a, b, c, digs);
|
---|
| 3581 | }
|
---|
| 3582 |
|
---|
| 3583 | if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
|
---|
| 3584 | return res;
|
---|
| 3585 | }
|
---|
| 3586 | t.used = digs;
|
---|
| 3587 |
|
---|
| 3588 | /* compute the digits of the product directly */
|
---|
| 3589 | pa = a->used;
|
---|
| 3590 | for (ix = 0; ix < pa; ix++) {
|
---|
| 3591 | /* set the carry to zero */
|
---|
| 3592 | u = 0;
|
---|
| 3593 |
|
---|
| 3594 | /* limit ourselves to making digs digits of output */
|
---|
| 3595 | pb = MIN (b->used, digs - ix);
|
---|
| 3596 |
|
---|
| 3597 | /* setup some aliases */
|
---|
| 3598 | /* copy of the digit from a used within the nested loop */
|
---|
| 3599 | tmpx = a->dp[ix];
|
---|
| 3600 |
|
---|
| 3601 | /* an alias for the destination shifted ix places */
|
---|
| 3602 | tmpt = t.dp + ix;
|
---|
| 3603 |
|
---|
| 3604 | /* an alias for the digits of b */
|
---|
| 3605 | tmpy = b->dp;
|
---|
| 3606 |
|
---|
| 3607 | /* compute the columns of the output and propagate the carry */
|
---|
| 3608 | for (iy = 0; iy < pb; iy++) {
|
---|
| 3609 | /* compute the column as a mp_word */
|
---|
| 3610 | r = ((mp_word)*tmpt) +
|
---|
| 3611 | ((mp_word)tmpx) * ((mp_word)*tmpy++) +
|
---|
| 3612 | ((mp_word) u);
|
---|
| 3613 |
|
---|
| 3614 | /* the new column is the lower part of the result */
|
---|
| 3615 | *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 3616 |
|
---|
| 3617 | /* get the carry word from the result */
|
---|
| 3618 | u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
---|
| 3619 | }
|
---|
| 3620 | /* set carry if it is placed below digs */
|
---|
| 3621 | if (ix + iy < digs) {
|
---|
| 3622 | *tmpt = u;
|
---|
| 3623 | }
|
---|
| 3624 | }
|
---|
| 3625 |
|
---|
| 3626 | mp_clamp (&t);
|
---|
| 3627 | mp_exch (&t, c);
|
---|
| 3628 |
|
---|
| 3629 | mp_clear (&t);
|
---|
| 3630 | return MP_OKAY;
|
---|
| 3631 | }
|
---|
| 3632 |
|
---|
| 3633 |
|
---|
| 3634 | /*
|
---|
| 3635 | * shifts with subtractions when the result is greater than b.
|
---|
| 3636 | *
|
---|
| 3637 | * The method is slightly modified to shift B unconditionally up to just under
|
---|
| 3638 | * the leading bit of b. This saves a lot of multiple precision shifting.
|
---|
| 3639 | */
|
---|
| 3640 | int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
|
---|
| 3641 | {
|
---|
| 3642 | int x, bits, res;
|
---|
| 3643 |
|
---|
| 3644 | /* how many bits of last digit does b use */
|
---|
| 3645 | bits = mp_count_bits (b) % DIGIT_BIT;
|
---|
| 3646 |
|
---|
| 3647 | if (b->used > 1) {
|
---|
| 3648 | if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1))
|
---|
| 3649 | != MP_OKAY) {
|
---|
| 3650 | return res;
|
---|
| 3651 | }
|
---|
| 3652 | } else {
|
---|
| 3653 | if ((res = mp_set(a, 1)) != MP_OKAY) {
|
---|
| 3654 | return res;
|
---|
| 3655 | }
|
---|
| 3656 | bits = 1;
|
---|
| 3657 | }
|
---|
| 3658 |
|
---|
| 3659 | /* now compute C = A * B mod b */
|
---|
| 3660 | for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
|
---|
| 3661 | if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
|
---|
| 3662 | return res;
|
---|
| 3663 | }
|
---|
| 3664 | if (mp_cmp_mag (a, b) != MP_LT) {
|
---|
| 3665 | if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
|
---|
| 3666 | return res;
|
---|
| 3667 | }
|
---|
| 3668 | }
|
---|
| 3669 | }
|
---|
| 3670 |
|
---|
| 3671 | return MP_OKAY;
|
---|
| 3672 | }
|
---|
| 3673 |
|
---|
| 3674 |
|
---|
| 3675 | #ifdef MP_LOW_MEM
|
---|
| 3676 | #define TAB_SIZE 32
|
---|
| 3677 | #else
|
---|
| 3678 | #define TAB_SIZE 256
|
---|
| 3679 | #endif
|
---|
| 3680 |
|
---|
| 3681 | int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
|
---|
| 3682 | {
|
---|
| 3683 | mp_int M[TAB_SIZE], res, mu;
|
---|
| 3684 | mp_digit buf;
|
---|
| 3685 | int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
---|
| 3686 | int (*redux)(mp_int*,mp_int*,mp_int*);
|
---|
| 3687 |
|
---|
| 3688 | /* find window size */
|
---|
| 3689 | x = mp_count_bits (X);
|
---|
| 3690 | if (x <= 7) {
|
---|
| 3691 | winsize = 2;
|
---|
| 3692 | } else if (x <= 36) {
|
---|
| 3693 | winsize = 3;
|
---|
| 3694 | } else if (x <= 140) {
|
---|
| 3695 | winsize = 4;
|
---|
| 3696 | } else if (x <= 450) {
|
---|
| 3697 | winsize = 5;
|
---|
| 3698 | } else if (x <= 1303) {
|
---|
| 3699 | winsize = 6;
|
---|
| 3700 | } else if (x <= 3529) {
|
---|
| 3701 | winsize = 7;
|
---|
| 3702 | } else {
|
---|
| 3703 | winsize = 8;
|
---|
| 3704 | }
|
---|
| 3705 |
|
---|
| 3706 | #ifdef MP_LOW_MEM
|
---|
| 3707 | if (winsize > 5) {
|
---|
| 3708 | winsize = 5;
|
---|
| 3709 | }
|
---|
| 3710 | #endif
|
---|
| 3711 |
|
---|
| 3712 | /* init M array */
|
---|
| 3713 | /* init first cell */
|
---|
| 3714 | if ((err = mp_init(&M[1])) != MP_OKAY) {
|
---|
| 3715 | return err;
|
---|
| 3716 | }
|
---|
| 3717 |
|
---|
| 3718 | /* now init the second half of the array */
|
---|
| 3719 | for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
---|
| 3720 | if ((err = mp_init(&M[x])) != MP_OKAY) {
|
---|
| 3721 | for (y = 1<<(winsize-1); y < x; y++) {
|
---|
| 3722 | mp_clear (&M[y]);
|
---|
| 3723 | }
|
---|
| 3724 | mp_clear(&M[1]);
|
---|
| 3725 | return err;
|
---|
| 3726 | }
|
---|
| 3727 | }
|
---|
| 3728 |
|
---|
| 3729 | /* create mu, used for Barrett reduction */
|
---|
| 3730 | if ((err = mp_init (&mu)) != MP_OKAY) {
|
---|
| 3731 | goto LBL_M;
|
---|
| 3732 | }
|
---|
| 3733 |
|
---|
| 3734 | if (redmode == 0) {
|
---|
| 3735 | if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
|
---|
| 3736 | goto LBL_MU;
|
---|
| 3737 | }
|
---|
| 3738 | redux = mp_reduce;
|
---|
| 3739 | } else {
|
---|
| 3740 | if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
|
---|
| 3741 | goto LBL_MU;
|
---|
| 3742 | }
|
---|
| 3743 | redux = mp_reduce_2k_l;
|
---|
| 3744 | }
|
---|
| 3745 |
|
---|
| 3746 | /* create M table
|
---|
| 3747 | *
|
---|
| 3748 | * The M table contains powers of the base,
|
---|
| 3749 | * e.g. M[x] = G**x mod P
|
---|
| 3750 | *
|
---|
| 3751 | * The first half of the table is not
|
---|
| 3752 | * computed though accept for M[0] and M[1]
|
---|
| 3753 | */
|
---|
| 3754 | if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
|
---|
| 3755 | goto LBL_MU;
|
---|
| 3756 | }
|
---|
| 3757 |
|
---|
| 3758 | /* compute the value at M[1<<(winsize-1)] by squaring
|
---|
| 3759 | * M[1] (winsize-1) times
|
---|
| 3760 | */
|
---|
| 3761 | if ((err = mp_copy (&M[1], &M[(mp_digit)(1 << (winsize - 1))])) != MP_OKAY) {
|
---|
| 3762 | goto LBL_MU;
|
---|
| 3763 | }
|
---|
| 3764 |
|
---|
| 3765 | for (x = 0; x < (winsize - 1); x++) {
|
---|
| 3766 | /* square it */
|
---|
| 3767 | if ((err = mp_sqr (&M[(mp_digit)(1 << (winsize - 1))],
|
---|
| 3768 | &M[(mp_digit)(1 << (winsize - 1))])) != MP_OKAY) {
|
---|
| 3769 | goto LBL_MU;
|
---|
| 3770 | }
|
---|
| 3771 |
|
---|
| 3772 | /* reduce modulo P */
|
---|
| 3773 | if ((err = redux (&M[(mp_digit)(1 << (winsize - 1))], P, &mu)) != MP_OKAY) {
|
---|
| 3774 | goto LBL_MU;
|
---|
| 3775 | }
|
---|
| 3776 | }
|
---|
| 3777 |
|
---|
| 3778 | /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
|
---|
| 3779 | * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
|
---|
| 3780 | */
|
---|
| 3781 | for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
---|
| 3782 | if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
|
---|
| 3783 | goto LBL_MU;
|
---|
| 3784 | }
|
---|
| 3785 | if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
|
---|
| 3786 | goto LBL_MU;
|
---|
| 3787 | }
|
---|
| 3788 | }
|
---|
| 3789 |
|
---|
| 3790 | /* setup result */
|
---|
| 3791 | if ((err = mp_init (&res)) != MP_OKAY) {
|
---|
| 3792 | goto LBL_MU;
|
---|
| 3793 | }
|
---|
| 3794 | if ((err = mp_set (&res, 1)) != MP_OKAY) {
|
---|
| 3795 | goto LBL_MU;
|
---|
| 3796 | }
|
---|
| 3797 |
|
---|
| 3798 | /* set initial mode and bit cnt */
|
---|
| 3799 | mode = 0;
|
---|
| 3800 | bitcnt = 1;
|
---|
| 3801 | buf = 0;
|
---|
| 3802 | digidx = X->used - 1;
|
---|
| 3803 | bitcpy = 0;
|
---|
| 3804 | bitbuf = 0;
|
---|
| 3805 |
|
---|
| 3806 | for (;;) {
|
---|
| 3807 | /* grab next digit as required */
|
---|
| 3808 | if (--bitcnt == 0) {
|
---|
| 3809 | /* if digidx == -1 we are out of digits */
|
---|
| 3810 | if (digidx == -1) {
|
---|
| 3811 | break;
|
---|
| 3812 | }
|
---|
| 3813 | /* read next digit and reset the bitcnt */
|
---|
| 3814 | buf = X->dp[digidx--];
|
---|
| 3815 | bitcnt = (int) DIGIT_BIT;
|
---|
| 3816 | }
|
---|
| 3817 |
|
---|
| 3818 | /* grab the next msb from the exponent */
|
---|
| 3819 | y = (int)(buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
|
---|
| 3820 | buf <<= (mp_digit)1;
|
---|
| 3821 |
|
---|
| 3822 | /* if the bit is zero and mode == 0 then we ignore it
|
---|
| 3823 | * These represent the leading zero bits before the first 1 bit
|
---|
| 3824 | * in the exponent. Technically this opt is not required but it
|
---|
| 3825 | * does lower the # of trivial squaring/reductions used
|
---|
| 3826 | */
|
---|
| 3827 | if (mode == 0 && y == 0) {
|
---|
| 3828 | continue;
|
---|
| 3829 | }
|
---|
| 3830 |
|
---|
| 3831 | /* if the bit is zero and mode == 1 then we square */
|
---|
| 3832 | if (mode == 1 && y == 0) {
|
---|
| 3833 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 3834 | goto LBL_RES;
|
---|
| 3835 | }
|
---|
| 3836 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3837 | goto LBL_RES;
|
---|
| 3838 | }
|
---|
| 3839 | continue;
|
---|
| 3840 | }
|
---|
| 3841 |
|
---|
| 3842 | /* else we add it to the window */
|
---|
| 3843 | bitbuf |= (y << (winsize - ++bitcpy));
|
---|
| 3844 | mode = 2;
|
---|
| 3845 |
|
---|
| 3846 | if (bitcpy == winsize) {
|
---|
| 3847 | /* ok window is filled so square as required and multiply */
|
---|
| 3848 | /* square first */
|
---|
| 3849 | for (x = 0; x < winsize; x++) {
|
---|
| 3850 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 3851 | goto LBL_RES;
|
---|
| 3852 | }
|
---|
| 3853 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3854 | goto LBL_RES;
|
---|
| 3855 | }
|
---|
| 3856 | }
|
---|
| 3857 |
|
---|
| 3858 | /* then multiply */
|
---|
| 3859 | if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
|
---|
| 3860 | goto LBL_RES;
|
---|
| 3861 | }
|
---|
| 3862 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3863 | goto LBL_RES;
|
---|
| 3864 | }
|
---|
| 3865 |
|
---|
| 3866 | /* empty window and reset */
|
---|
| 3867 | bitcpy = 0;
|
---|
| 3868 | bitbuf = 0;
|
---|
| 3869 | mode = 1;
|
---|
| 3870 | }
|
---|
| 3871 | }
|
---|
| 3872 |
|
---|
| 3873 | /* if bits remain then square/multiply */
|
---|
| 3874 | if (mode == 2 && bitcpy > 0) {
|
---|
| 3875 | /* square then multiply if the bit is set */
|
---|
| 3876 | for (x = 0; x < bitcpy; x++) {
|
---|
| 3877 | if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
---|
| 3878 | goto LBL_RES;
|
---|
| 3879 | }
|
---|
| 3880 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3881 | goto LBL_RES;
|
---|
| 3882 | }
|
---|
| 3883 |
|
---|
| 3884 | bitbuf <<= 1;
|
---|
| 3885 | if ((bitbuf & (1 << winsize)) != 0) {
|
---|
| 3886 | /* then multiply */
|
---|
| 3887 | if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
|
---|
| 3888 | goto LBL_RES;
|
---|
| 3889 | }
|
---|
| 3890 | if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
---|
| 3891 | goto LBL_RES;
|
---|
| 3892 | }
|
---|
| 3893 | }
|
---|
| 3894 | }
|
---|
| 3895 | }
|
---|
| 3896 |
|
---|
| 3897 | mp_exch (&res, Y);
|
---|
| 3898 | err = MP_OKAY;
|
---|
| 3899 | LBL_RES:mp_clear (&res);
|
---|
| 3900 | LBL_MU:mp_clear (&mu);
|
---|
| 3901 | LBL_M:
|
---|
| 3902 | mp_clear(&M[1]);
|
---|
| 3903 | for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
---|
| 3904 | mp_clear (&M[x]);
|
---|
| 3905 | }
|
---|
| 3906 | return err;
|
---|
| 3907 | }
|
---|
| 3908 |
|
---|
| 3909 |
|
---|
| 3910 | /* pre-calculate the value required for Barrett reduction
|
---|
| 3911 | * For a given modulus "b" it calculates the value required in "a"
|
---|
| 3912 | */
|
---|
| 3913 | int mp_reduce_setup (mp_int * a, mp_int * b)
|
---|
| 3914 | {
|
---|
| 3915 | int res;
|
---|
| 3916 |
|
---|
| 3917 | if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
|
---|
| 3918 | return res;
|
---|
| 3919 | }
|
---|
| 3920 | return mp_div (a, b, a, NULL);
|
---|
| 3921 | }
|
---|
| 3922 |
|
---|
| 3923 |
|
---|
| 3924 | /* reduces x mod m, assumes 0 < x < m**2, mu is
|
---|
| 3925 | * precomputed via mp_reduce_setup.
|
---|
| 3926 | * From HAC pp.604 Algorithm 14.42
|
---|
| 3927 | */
|
---|
| 3928 | int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
|
---|
| 3929 | {
|
---|
| 3930 | mp_int q;
|
---|
| 3931 | int res, um = m->used;
|
---|
| 3932 |
|
---|
| 3933 | /* q = x */
|
---|
| 3934 | if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
|
---|
| 3935 | return res;
|
---|
| 3936 | }
|
---|
| 3937 |
|
---|
| 3938 | /* q1 = x / b**(k-1) */
|
---|
| 3939 | mp_rshd (&q, um - 1);
|
---|
| 3940 |
|
---|
| 3941 | /* according to HAC this optimization is ok */
|
---|
| 3942 | if (((mp_word) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
|
---|
| 3943 | if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
|
---|
| 3944 | goto CLEANUP;
|
---|
| 3945 | }
|
---|
| 3946 | } else {
|
---|
| 3947 | #ifdef BN_S_MP_MUL_HIGH_DIGS_C
|
---|
| 3948 | if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
|
---|
| 3949 | goto CLEANUP;
|
---|
| 3950 | }
|
---|
| 3951 | #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
|
---|
| 3952 | if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
|
---|
| 3953 | goto CLEANUP;
|
---|
| 3954 | }
|
---|
| 3955 | #else
|
---|
| 3956 | {
|
---|
| 3957 | res = MP_VAL;
|
---|
| 3958 | goto CLEANUP;
|
---|
| 3959 | }
|
---|
| 3960 | #endif
|
---|
| 3961 | }
|
---|
| 3962 |
|
---|
| 3963 | /* q3 = q2 / b**(k+1) */
|
---|
| 3964 | mp_rshd (&q, um + 1);
|
---|
| 3965 |
|
---|
| 3966 | /* x = x mod b**(k+1), quick (no division) */
|
---|
| 3967 | if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
|
---|
| 3968 | goto CLEANUP;
|
---|
| 3969 | }
|
---|
| 3970 |
|
---|
| 3971 | /* q = q * m mod b**(k+1), quick (no division) */
|
---|
| 3972 | if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
|
---|
| 3973 | goto CLEANUP;
|
---|
| 3974 | }
|
---|
| 3975 |
|
---|
| 3976 | /* x = x - q */
|
---|
| 3977 | if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
|
---|
| 3978 | goto CLEANUP;
|
---|
| 3979 | }
|
---|
| 3980 |
|
---|
| 3981 | /* If x < 0, add b**(k+1) to it */
|
---|
| 3982 | if (mp_cmp_d (x, 0) == MP_LT) {
|
---|
| 3983 | if ((res = mp_set (&q, 1)) != MP_OKAY)
|
---|
| 3984 | goto CLEANUP;
|
---|
| 3985 | if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
|
---|
| 3986 | goto CLEANUP;
|
---|
| 3987 | if ((res = mp_add (x, &q, x)) != MP_OKAY)
|
---|
| 3988 | goto CLEANUP;
|
---|
| 3989 | }
|
---|
| 3990 |
|
---|
| 3991 | /* Back off if it's too big */
|
---|
| 3992 | while (mp_cmp (x, m) != MP_LT) {
|
---|
| 3993 | if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
|
---|
| 3994 | goto CLEANUP;
|
---|
| 3995 | }
|
---|
| 3996 | }
|
---|
| 3997 |
|
---|
| 3998 | CLEANUP:
|
---|
| 3999 | mp_clear (&q);
|
---|
| 4000 |
|
---|
| 4001 | return res;
|
---|
| 4002 | }
|
---|
| 4003 |
|
---|
| 4004 |
|
---|
| 4005 | /* reduces a modulo n where n is of the form 2**p - d
|
---|
| 4006 | This differs from reduce_2k since "d" can be larger
|
---|
| 4007 | than a single digit.
|
---|
| 4008 | */
|
---|
| 4009 | int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
|
---|
| 4010 | {
|
---|
| 4011 | mp_int q;
|
---|
| 4012 | int p, res;
|
---|
| 4013 |
|
---|
| 4014 | if ((res = mp_init(&q)) != MP_OKAY) {
|
---|
| 4015 | return res;
|
---|
| 4016 | }
|
---|
| 4017 |
|
---|
| 4018 | p = mp_count_bits(n);
|
---|
| 4019 | top:
|
---|
| 4020 | /* q = a/2**p, a = a mod 2**p */
|
---|
| 4021 | if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
|
---|
| 4022 | goto ERR;
|
---|
| 4023 | }
|
---|
| 4024 |
|
---|
| 4025 | /* q = q * d */
|
---|
| 4026 | if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
|
---|
| 4027 | goto ERR;
|
---|
| 4028 | }
|
---|
| 4029 |
|
---|
| 4030 | /* a = a + q */
|
---|
| 4031 | if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
|
---|
| 4032 | goto ERR;
|
---|
| 4033 | }
|
---|
| 4034 |
|
---|
| 4035 | if (mp_cmp_mag(a, n) != MP_LT) {
|
---|
| 4036 | if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
|
---|
| 4037 | goto ERR;
|
---|
| 4038 | }
|
---|
| 4039 | goto top;
|
---|
| 4040 | }
|
---|
| 4041 |
|
---|
| 4042 | ERR:
|
---|
| 4043 | mp_clear(&q);
|
---|
| 4044 | return res;
|
---|
| 4045 | }
|
---|
| 4046 |
|
---|
| 4047 |
|
---|
| 4048 | /* determines the setup value */
|
---|
| 4049 | int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
|
---|
| 4050 | {
|
---|
| 4051 | int res;
|
---|
| 4052 | mp_int tmp;
|
---|
| 4053 |
|
---|
| 4054 | if ((res = mp_init(&tmp)) != MP_OKAY) {
|
---|
| 4055 | return res;
|
---|
| 4056 | }
|
---|
| 4057 |
|
---|
| 4058 | if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
|
---|
| 4059 | goto ERR;
|
---|
| 4060 | }
|
---|
| 4061 |
|
---|
| 4062 | if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
|
---|
| 4063 | goto ERR;
|
---|
| 4064 | }
|
---|
| 4065 |
|
---|
| 4066 | ERR:
|
---|
| 4067 | mp_clear(&tmp);
|
---|
| 4068 | return res;
|
---|
| 4069 | }
|
---|
| 4070 |
|
---|
| 4071 |
|
---|
| 4072 | /* multiplies |a| * |b| and does not compute the lower digs digits
|
---|
| 4073 | * [meant to get the higher part of the product]
|
---|
| 4074 | */
|
---|
| 4075 | int s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
---|
| 4076 | {
|
---|
| 4077 | mp_int t;
|
---|
| 4078 | int res, pa, pb, ix, iy;
|
---|
| 4079 | mp_digit u;
|
---|
| 4080 | mp_word r;
|
---|
| 4081 | mp_digit tmpx, *tmpt, *tmpy;
|
---|
| 4082 |
|
---|
| 4083 | /* can we use the fast multiplier? */
|
---|
| 4084 | #ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
|
---|
| 4085 | if (((a->used + b->used + 1) < (int)MP_WARRAY)
|
---|
| 4086 | && MIN (a->used, b->used) <
|
---|
[464] | 4087 | (1L << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
---|
[457] | 4088 | return fast_s_mp_mul_high_digs (a, b, c, digs);
|
---|
| 4089 | }
|
---|
| 4090 | #endif
|
---|
| 4091 |
|
---|
| 4092 | if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
|
---|
| 4093 | return res;
|
---|
| 4094 | }
|
---|
| 4095 | t.used = a->used + b->used + 1;
|
---|
| 4096 |
|
---|
| 4097 | pa = a->used;
|
---|
| 4098 | pb = b->used;
|
---|
| 4099 | for (ix = 0; ix < pa && a->dp; ix++) {
|
---|
| 4100 | /* clear the carry */
|
---|
| 4101 | u = 0;
|
---|
| 4102 |
|
---|
| 4103 | /* left hand side of A[ix] * B[iy] */
|
---|
| 4104 | tmpx = a->dp[ix];
|
---|
| 4105 |
|
---|
| 4106 | /* alias to the address of where the digits will be stored */
|
---|
| 4107 | tmpt = &(t.dp[digs]);
|
---|
| 4108 |
|
---|
| 4109 | /* alias for where to read the right hand side from */
|
---|
| 4110 | tmpy = b->dp + (digs - ix);
|
---|
| 4111 |
|
---|
| 4112 | for (iy = digs - ix; iy < pb; iy++) {
|
---|
| 4113 | /* calculate the double precision result */
|
---|
| 4114 | r = ((mp_word)*tmpt) +
|
---|
| 4115 | ((mp_word)tmpx) * ((mp_word)*tmpy++) +
|
---|
| 4116 | ((mp_word) u);
|
---|
| 4117 |
|
---|
| 4118 | /* get the lower part */
|
---|
| 4119 | *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
---|
| 4120 |
|
---|
| 4121 | /* carry the carry */
|
---|
| 4122 | u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
---|
| 4123 | }
|
---|
| 4124 | *tmpt = u;
|
---|
| 4125 | }
|
---|
| 4126 | mp_clamp (&t);
|
---|
| 4127 | mp_exch (&t, c);
|
---|
| 4128 | mp_clear (&t);
|
---|
| 4129 | return MP_OKAY;
|
---|
| 4130 | }
|
---|
| 4131 |
|
---|
| 4132 |
|
---|
| 4133 | /* this is a modified version of fast_s_mul_digs that only produces
|
---|
| 4134 | * output digits *above* digs. See the comments for fast_s_mul_digs
|
---|
| 4135 | * to see how it works.
|
---|
| 4136 | *
|
---|
| 4137 | * This is used in the Barrett reduction since for one of the multiplications
|
---|
| 4138 | * only the higher digits were needed. This essentially halves the work.
|
---|
| 4139 | *
|
---|
| 4140 | * Based on Algorithm 14.12 on pp.595 of HAC.
|
---|
| 4141 | */
|
---|
| 4142 | int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
---|
| 4143 | {
|
---|
| 4144 | int olduse, res, pa, ix, iz;
|
---|
| 4145 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 4146 | mp_digit* W; /* uses dynamic memory and slower */
|
---|
| 4147 | #else
|
---|
| 4148 | mp_digit W[MP_WARRAY];
|
---|
| 4149 | #endif
|
---|
| 4150 | mp_word _W;
|
---|
| 4151 |
|
---|
| 4152 | if (a->dp == NULL) { /* JRB, avoid reading uninitialized values */
|
---|
| 4153 | return MP_VAL;
|
---|
| 4154 | }
|
---|
| 4155 |
|
---|
| 4156 | /* grow the destination as required */
|
---|
| 4157 | pa = a->used + b->used;
|
---|
| 4158 | if (c->alloc < pa) {
|
---|
| 4159 | if ((res = mp_grow (c, pa)) != MP_OKAY) {
|
---|
| 4160 | return res;
|
---|
| 4161 | }
|
---|
| 4162 | }
|
---|
| 4163 |
|
---|
| 4164 | if (pa > (int)MP_WARRAY)
|
---|
| 4165 | return MP_RANGE; /* TAO range check */
|
---|
| 4166 |
|
---|
| 4167 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 4168 | W = (mp_digit*)XMALLOC(sizeof(mp_digit) * MP_WARRAY, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 4169 | if (W == NULL)
|
---|
| 4170 | return MP_MEM;
|
---|
| 4171 | #endif
|
---|
| 4172 |
|
---|
| 4173 | /* number of output digits to produce */
|
---|
| 4174 | pa = a->used + b->used;
|
---|
| 4175 | _W = 0;
|
---|
| 4176 | for (ix = digs; ix < pa; ix++) { /* JRB, have a->dp check at top of function*/
|
---|
| 4177 | int tx, ty, iy;
|
---|
| 4178 | mp_digit *tmpx, *tmpy;
|
---|
| 4179 |
|
---|
| 4180 | /* get offsets into the two bignums */
|
---|
| 4181 | ty = MIN(b->used-1, ix);
|
---|
| 4182 | tx = ix - ty;
|
---|
| 4183 |
|
---|
| 4184 | /* setup temp aliases */
|
---|
| 4185 | tmpx = a->dp + tx;
|
---|
| 4186 | tmpy = b->dp + ty;
|
---|
| 4187 |
|
---|
| 4188 | /* this is the number of times the loop will iterate, essentially its
|
---|
| 4189 | while (tx++ < a->used && ty-- >= 0) { ... }
|
---|
| 4190 | */
|
---|
| 4191 | iy = MIN(a->used-tx, ty+1);
|
---|
| 4192 |
|
---|
| 4193 | /* execute loop */
|
---|
| 4194 | for (iz = 0; iz < iy; iz++) {
|
---|
| 4195 | _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
|
---|
| 4196 | }
|
---|
| 4197 |
|
---|
| 4198 | /* store term */
|
---|
| 4199 | W[ix] = (mp_digit)(((mp_digit)_W) & MP_MASK);
|
---|
| 4200 |
|
---|
| 4201 | /* make next carry */
|
---|
| 4202 | _W = _W >> ((mp_word)DIGIT_BIT);
|
---|
| 4203 | }
|
---|
| 4204 |
|
---|
| 4205 | /* setup dest */
|
---|
| 4206 | olduse = c->used;
|
---|
| 4207 | c->used = pa;
|
---|
| 4208 |
|
---|
| 4209 | {
|
---|
| 4210 | mp_digit *tmpc;
|
---|
| 4211 |
|
---|
| 4212 | tmpc = c->dp + digs;
|
---|
| 4213 | for (ix = digs; ix < pa; ix++) { /* TAO, <= could potentially overwrite */
|
---|
| 4214 | /* now extract the previous digit [below the carry] */
|
---|
| 4215 | *tmpc++ = W[ix];
|
---|
| 4216 | }
|
---|
| 4217 |
|
---|
| 4218 | /* clear unused digits [that existed in the old copy of c] */
|
---|
| 4219 | for (; ix < olduse; ix++) {
|
---|
| 4220 | *tmpc++ = 0;
|
---|
| 4221 | }
|
---|
| 4222 | }
|
---|
| 4223 | mp_clamp (c);
|
---|
| 4224 |
|
---|
| 4225 | #ifdef WOLFSSL_SMALL_STACK
|
---|
| 4226 | XFREE(W, NULL, DYNAMIC_TYPE_BIGINT);
|
---|
| 4227 | #endif
|
---|
| 4228 |
|
---|
| 4229 | return MP_OKAY;
|
---|
| 4230 | }
|
---|
| 4231 |
|
---|
| 4232 |
|
---|
| 4233 | #ifndef MP_SET_CHUNK_BITS
|
---|
| 4234 | #define MP_SET_CHUNK_BITS 4
|
---|
| 4235 | #endif
|
---|
| 4236 | int mp_set_int (mp_int * a, unsigned long b)
|
---|
| 4237 | {
|
---|
| 4238 | int x, res;
|
---|
| 4239 |
|
---|
| 4240 | /* use direct mp_set if b is less than mp_digit max */
|
---|
| 4241 | if (b < MP_DIGIT_MAX) {
|
---|
| 4242 | return mp_set (a, (mp_digit)b);
|
---|
| 4243 | }
|
---|
| 4244 |
|
---|
| 4245 | mp_zero (a);
|
---|
| 4246 |
|
---|
| 4247 | /* set chunk bits at a time */
|
---|
| 4248 | for (x = 0; x < (int)(sizeof(b) * 8) / MP_SET_CHUNK_BITS; x++) {
|
---|
| 4249 | /* shift the number up chunk bits */
|
---|
| 4250 | if ((res = mp_mul_2d (a, MP_SET_CHUNK_BITS, a)) != MP_OKAY) {
|
---|
| 4251 | return res;
|
---|
| 4252 | }
|
---|
| 4253 |
|
---|
| 4254 | /* OR in the top bits of the source */
|
---|
| 4255 | a->dp[0] |= (b >> ((sizeof(b) * 8) - MP_SET_CHUNK_BITS)) &
|
---|
| 4256 | ((1 << MP_SET_CHUNK_BITS) - 1);
|
---|
| 4257 |
|
---|
| 4258 | /* shift the source up to the next chunk bits */
|
---|
| 4259 | b <<= MP_SET_CHUNK_BITS;
|
---|
| 4260 |
|
---|
| 4261 | /* ensure that digits are not clamped off */
|
---|
| 4262 | a->used += 1;
|
---|
| 4263 | }
|
---|
| 4264 | mp_clamp (a);
|
---|
| 4265 | return MP_OKAY;
|
---|
| 4266 | }
|
---|
| 4267 |
|
---|
| 4268 |
|
---|
| 4269 | #if defined(WOLFSSL_KEY_GEN) || defined(HAVE_ECC) || !defined(NO_RSA) || \
|
---|
| 4270 | !defined(NO_DSA) | !defined(NO_DH)
|
---|
| 4271 |
|
---|
| 4272 | /* c = a * a (mod b) */
|
---|
| 4273 | int mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 4274 | {
|
---|
| 4275 | int res;
|
---|
| 4276 | mp_int t;
|
---|
| 4277 |
|
---|
| 4278 | if ((res = mp_init (&t)) != MP_OKAY) {
|
---|
| 4279 | return res;
|
---|
| 4280 | }
|
---|
| 4281 |
|
---|
| 4282 | if ((res = mp_sqr (a, &t)) != MP_OKAY) {
|
---|
| 4283 | mp_clear (&t);
|
---|
| 4284 | return res;
|
---|
| 4285 | }
|
---|
| 4286 | res = mp_mod (&t, b, c);
|
---|
| 4287 | mp_clear (&t);
|
---|
| 4288 | return res;
|
---|
| 4289 | }
|
---|
| 4290 |
|
---|
| 4291 | #endif
|
---|
| 4292 |
|
---|
| 4293 |
|
---|
| 4294 | #if defined(HAVE_ECC) || !defined(NO_PWDBASED) || defined(WOLFSSL_SNIFFER) || \
|
---|
| 4295 | defined(WOLFSSL_HAVE_WOLFSCEP) || defined(WOLFSSL_KEY_GEN) || \
|
---|
| 4296 | defined(OPENSSL_EXTRA) || defined(WC_RSA_BLINDING) || \
|
---|
| 4297 | (!defined(NO_RSA) && !defined(NO_RSA_BOUNDS_CHECK))
|
---|
| 4298 |
|
---|
| 4299 | /* single digit addition */
|
---|
| 4300 | int mp_add_d (mp_int* a, mp_digit b, mp_int* c)
|
---|
| 4301 | {
|
---|
| 4302 | int res, ix, oldused;
|
---|
| 4303 | mp_digit *tmpa, *tmpc, mu;
|
---|
| 4304 |
|
---|
| 4305 | /* grow c as required */
|
---|
| 4306 | if (c->alloc < a->used + 1) {
|
---|
| 4307 | if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
|
---|
| 4308 | return res;
|
---|
| 4309 | }
|
---|
| 4310 | }
|
---|
| 4311 |
|
---|
| 4312 | /* if a is negative and |a| >= b, call c = |a| - b */
|
---|
| 4313 | if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
|
---|
| 4314 | /* temporarily fix sign of a */
|
---|
| 4315 | a->sign = MP_ZPOS;
|
---|
| 4316 |
|
---|
| 4317 | /* c = |a| - b */
|
---|
| 4318 | res = mp_sub_d(a, b, c);
|
---|
| 4319 |
|
---|
| 4320 | /* fix sign */
|
---|
| 4321 | a->sign = c->sign = MP_NEG;
|
---|
| 4322 |
|
---|
| 4323 | /* clamp */
|
---|
| 4324 | mp_clamp(c);
|
---|
| 4325 |
|
---|
| 4326 | return res;
|
---|
| 4327 | }
|
---|
| 4328 |
|
---|
| 4329 | /* old number of used digits in c */
|
---|
| 4330 | oldused = c->used;
|
---|
| 4331 |
|
---|
| 4332 | /* sign always positive */
|
---|
| 4333 | c->sign = MP_ZPOS;
|
---|
| 4334 |
|
---|
| 4335 | /* source alias */
|
---|
| 4336 | tmpa = a->dp;
|
---|
| 4337 |
|
---|
| 4338 | /* destination alias */
|
---|
| 4339 | tmpc = c->dp;
|
---|
| 4340 |
|
---|
| 4341 | /* if a is positive */
|
---|
| 4342 | if (a->sign == MP_ZPOS) {
|
---|
| 4343 | /* add digit, after this we're propagating
|
---|
| 4344 | * the carry.
|
---|
| 4345 | */
|
---|
| 4346 | *tmpc = *tmpa++ + b;
|
---|
| 4347 | mu = *tmpc >> DIGIT_BIT;
|
---|
| 4348 | *tmpc++ &= MP_MASK;
|
---|
| 4349 |
|
---|
| 4350 | /* now handle rest of the digits */
|
---|
| 4351 | for (ix = 1; ix < a->used; ix++) {
|
---|
| 4352 | *tmpc = *tmpa++ + mu;
|
---|
| 4353 | mu = *tmpc >> DIGIT_BIT;
|
---|
| 4354 | *tmpc++ &= MP_MASK;
|
---|
| 4355 | }
|
---|
| 4356 | /* set final carry */
|
---|
| 4357 | if (ix < c->alloc) {
|
---|
| 4358 | ix++;
|
---|
| 4359 | *tmpc++ = mu;
|
---|
| 4360 | }
|
---|
| 4361 |
|
---|
| 4362 | /* setup size */
|
---|
| 4363 | c->used = a->used + 1;
|
---|
| 4364 | } else {
|
---|
| 4365 | /* a was negative and |a| < b */
|
---|
| 4366 | c->used = 1;
|
---|
| 4367 |
|
---|
| 4368 | /* the result is a single digit */
|
---|
| 4369 | if (a->used == 1) {
|
---|
| 4370 | *tmpc++ = b - a->dp[0];
|
---|
| 4371 | } else {
|
---|
| 4372 | *tmpc++ = b;
|
---|
| 4373 | }
|
---|
| 4374 |
|
---|
| 4375 | /* setup count so the clearing of oldused
|
---|
| 4376 | * can fall through correctly
|
---|
| 4377 | */
|
---|
| 4378 | ix = 1;
|
---|
| 4379 | }
|
---|
| 4380 |
|
---|
| 4381 | /* now zero to oldused */
|
---|
| 4382 | while (ix++ < oldused) {
|
---|
| 4383 | *tmpc++ = 0;
|
---|
| 4384 | }
|
---|
| 4385 | mp_clamp(c);
|
---|
| 4386 |
|
---|
| 4387 | return MP_OKAY;
|
---|
| 4388 | }
|
---|
| 4389 |
|
---|
| 4390 |
|
---|
| 4391 | /* single digit subtraction */
|
---|
| 4392 | int mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
|
---|
| 4393 | {
|
---|
| 4394 | mp_digit *tmpa, *tmpc, mu;
|
---|
| 4395 | int res, ix, oldused;
|
---|
| 4396 |
|
---|
[464] | 4397 | if (b > MP_MASK) return MP_VAL;
|
---|
| 4398 |
|
---|
[457] | 4399 | /* grow c as required */
|
---|
| 4400 | if (c->alloc < a->used + 1) {
|
---|
| 4401 | if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
|
---|
| 4402 | return res;
|
---|
| 4403 | }
|
---|
| 4404 | }
|
---|
| 4405 |
|
---|
| 4406 | /* if a is negative just do an unsigned
|
---|
| 4407 | * addition [with fudged signs]
|
---|
| 4408 | */
|
---|
| 4409 | if (a->sign == MP_NEG) {
|
---|
| 4410 | a->sign = MP_ZPOS;
|
---|
| 4411 | res = mp_add_d(a, b, c);
|
---|
| 4412 | a->sign = c->sign = MP_NEG;
|
---|
| 4413 |
|
---|
| 4414 | /* clamp */
|
---|
| 4415 | mp_clamp(c);
|
---|
| 4416 |
|
---|
| 4417 | return res;
|
---|
| 4418 | }
|
---|
| 4419 |
|
---|
| 4420 | /* setup regs */
|
---|
| 4421 | oldused = c->used;
|
---|
| 4422 | tmpa = a->dp;
|
---|
| 4423 | tmpc = c->dp;
|
---|
| 4424 |
|
---|
| 4425 | /* if a <= b simply fix the single digit */
|
---|
| 4426 | if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) {
|
---|
| 4427 | if (a->used == 1) {
|
---|
| 4428 | *tmpc++ = b - *tmpa;
|
---|
| 4429 | } else {
|
---|
| 4430 | *tmpc++ = b;
|
---|
| 4431 | }
|
---|
| 4432 | ix = 1;
|
---|
| 4433 |
|
---|
| 4434 | /* negative/1digit */
|
---|
| 4435 | c->sign = MP_NEG;
|
---|
| 4436 | c->used = 1;
|
---|
| 4437 | } else {
|
---|
| 4438 | /* positive/size */
|
---|
| 4439 | c->sign = MP_ZPOS;
|
---|
| 4440 | c->used = a->used;
|
---|
| 4441 |
|
---|
| 4442 | /* subtract first digit */
|
---|
| 4443 | *tmpc = *tmpa++ - b;
|
---|
| 4444 | mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
|
---|
| 4445 | *tmpc++ &= MP_MASK;
|
---|
| 4446 |
|
---|
| 4447 | /* handle rest of the digits */
|
---|
| 4448 | for (ix = 1; ix < a->used; ix++) {
|
---|
| 4449 | *tmpc = *tmpa++ - mu;
|
---|
| 4450 | mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
|
---|
| 4451 | *tmpc++ &= MP_MASK;
|
---|
| 4452 | }
|
---|
| 4453 | }
|
---|
| 4454 |
|
---|
| 4455 | /* zero excess digits */
|
---|
| 4456 | while (ix++ < oldused) {
|
---|
| 4457 | *tmpc++ = 0;
|
---|
| 4458 | }
|
---|
| 4459 | mp_clamp(c);
|
---|
| 4460 | return MP_OKAY;
|
---|
| 4461 | }
|
---|
| 4462 |
|
---|
| 4463 | #endif /* defined(HAVE_ECC) || !defined(NO_PWDBASED) */
|
---|
| 4464 |
|
---|
| 4465 |
|
---|
| 4466 | #if defined(WOLFSSL_KEY_GEN) || defined(HAVE_COMP_KEY) || defined(HAVE_ECC) || \
|
---|
| 4467 | defined(DEBUG_WOLFSSL) || !defined(NO_RSA) || !defined(NO_DSA) || \
|
---|
| 4468 | !defined(NO_DH)
|
---|
| 4469 |
|
---|
| 4470 | static const int lnz[16] = {
|
---|
| 4471 | 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
|
---|
| 4472 | };
|
---|
| 4473 |
|
---|
| 4474 | /* Counts the number of lsbs which are zero before the first zero bit */
|
---|
| 4475 | int mp_cnt_lsb(mp_int *a)
|
---|
| 4476 | {
|
---|
| 4477 | int x;
|
---|
| 4478 | mp_digit q = 0, qq;
|
---|
| 4479 |
|
---|
| 4480 | /* easy out */
|
---|
| 4481 | if (mp_iszero(a) == MP_YES) {
|
---|
| 4482 | return 0;
|
---|
| 4483 | }
|
---|
| 4484 |
|
---|
| 4485 | /* scan lower digits until non-zero */
|
---|
| 4486 | for (x = 0; x < a->used && a->dp[x] == 0; x++) {}
|
---|
| 4487 | if (a->dp)
|
---|
| 4488 | q = a->dp[x];
|
---|
| 4489 | x *= DIGIT_BIT;
|
---|
| 4490 |
|
---|
| 4491 | /* now scan this digit until a 1 is found */
|
---|
| 4492 | if ((q & 1) == 0) {
|
---|
| 4493 | do {
|
---|
| 4494 | qq = q & 15;
|
---|
| 4495 | x += lnz[qq];
|
---|
| 4496 | q >>= 4;
|
---|
| 4497 | } while (qq == 0);
|
---|
| 4498 | }
|
---|
| 4499 | return x;
|
---|
| 4500 | }
|
---|
| 4501 |
|
---|
| 4502 |
|
---|
| 4503 |
|
---|
| 4504 |
|
---|
| 4505 | static int s_is_power_of_two(mp_digit b, int *p)
|
---|
| 4506 | {
|
---|
| 4507 | int x;
|
---|
| 4508 |
|
---|
| 4509 | /* fast return if no power of two */
|
---|
| 4510 | if ((b==0) || (b & (b-1))) {
|
---|
| 4511 | return 0;
|
---|
| 4512 | }
|
---|
| 4513 |
|
---|
| 4514 | for (x = 0; x < DIGIT_BIT; x++) {
|
---|
| 4515 | if (b == (((mp_digit)1)<<x)) {
|
---|
| 4516 | *p = x;
|
---|
| 4517 | return 1;
|
---|
| 4518 | }
|
---|
| 4519 | }
|
---|
| 4520 | return 0;
|
---|
| 4521 | }
|
---|
| 4522 |
|
---|
| 4523 | /* single digit division (based on routine from MPI) */
|
---|
| 4524 | static int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
|
---|
| 4525 | {
|
---|
| 4526 | mp_int q;
|
---|
| 4527 | mp_word w;
|
---|
| 4528 | mp_digit t;
|
---|
| 4529 | int res = MP_OKAY, ix;
|
---|
| 4530 |
|
---|
| 4531 | /* cannot divide by zero */
|
---|
| 4532 | if (b == 0) {
|
---|
| 4533 | return MP_VAL;
|
---|
| 4534 | }
|
---|
| 4535 |
|
---|
| 4536 | /* quick outs */
|
---|
| 4537 | if (b == 1 || mp_iszero(a) == MP_YES) {
|
---|
| 4538 | if (d != NULL) {
|
---|
| 4539 | *d = 0;
|
---|
| 4540 | }
|
---|
| 4541 | if (c != NULL) {
|
---|
| 4542 | return mp_copy(a, c);
|
---|
| 4543 | }
|
---|
| 4544 | return MP_OKAY;
|
---|
| 4545 | }
|
---|
| 4546 |
|
---|
| 4547 | /* power of two ? */
|
---|
| 4548 | if (s_is_power_of_two(b, &ix) == 1) {
|
---|
| 4549 | if (d != NULL) {
|
---|
| 4550 | *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
|
---|
| 4551 | }
|
---|
| 4552 | if (c != NULL) {
|
---|
| 4553 | return mp_div_2d(a, ix, c, NULL);
|
---|
| 4554 | }
|
---|
| 4555 | return MP_OKAY;
|
---|
| 4556 | }
|
---|
| 4557 |
|
---|
| 4558 | #ifdef BN_MP_DIV_3_C
|
---|
| 4559 | /* three? */
|
---|
| 4560 | if (b == 3) {
|
---|
| 4561 | return mp_div_3(a, c, d);
|
---|
| 4562 | }
|
---|
| 4563 | #endif
|
---|
| 4564 |
|
---|
| 4565 | /* no easy answer [c'est la vie]. Just division */
|
---|
| 4566 | if (c != NULL) {
|
---|
| 4567 | if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
|
---|
| 4568 | return res;
|
---|
| 4569 | }
|
---|
| 4570 |
|
---|
| 4571 | q.used = a->used;
|
---|
| 4572 | q.sign = a->sign;
|
---|
| 4573 | }
|
---|
| 4574 | else {
|
---|
| 4575 | if ((res = mp_init(&q)) != MP_OKAY) {
|
---|
| 4576 | return res;
|
---|
| 4577 | }
|
---|
| 4578 | }
|
---|
| 4579 |
|
---|
| 4580 |
|
---|
| 4581 | w = 0;
|
---|
| 4582 | for (ix = a->used - 1; ix >= 0; ix--) {
|
---|
| 4583 | w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
|
---|
| 4584 |
|
---|
| 4585 | if (w >= b) {
|
---|
[464] | 4586 | #ifdef WOLFSSL_LINUXKM
|
---|
| 4587 | t = (mp_digit)w;
|
---|
| 4588 | /* Linux kernel macro for in-place 64 bit integer division. */
|
---|
| 4589 | do_div(t, b);
|
---|
| 4590 | #else
|
---|
[457] | 4591 | t = (mp_digit)(w / b);
|
---|
[464] | 4592 | #endif
|
---|
[457] | 4593 | w -= ((mp_word)t) * ((mp_word)b);
|
---|
| 4594 | } else {
|
---|
| 4595 | t = 0;
|
---|
| 4596 | }
|
---|
| 4597 | if (c != NULL)
|
---|
| 4598 | q.dp[ix] = (mp_digit)t;
|
---|
| 4599 | }
|
---|
| 4600 |
|
---|
| 4601 | if (d != NULL) {
|
---|
| 4602 | *d = (mp_digit)w;
|
---|
| 4603 | }
|
---|
| 4604 |
|
---|
| 4605 | if (c != NULL) {
|
---|
| 4606 | mp_clamp(&q);
|
---|
| 4607 | mp_exch(&q, c);
|
---|
| 4608 | }
|
---|
| 4609 | mp_clear(&q);
|
---|
| 4610 |
|
---|
| 4611 | return res;
|
---|
| 4612 | }
|
---|
| 4613 |
|
---|
| 4614 |
|
---|
| 4615 | int mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
|
---|
| 4616 | {
|
---|
| 4617 | return mp_div_d(a, b, NULL, c);
|
---|
| 4618 | }
|
---|
| 4619 |
|
---|
| 4620 | #endif /* WOLFSSL_KEY_GEN || HAVE_COMP_KEY || HAVE_ECC || DEBUG_WOLFSSL */
|
---|
| 4621 |
|
---|
| 4622 | #if defined(WOLFSSL_KEY_GEN) || !defined(NO_DH) || !defined(NO_DSA) || !defined(NO_RSA)
|
---|
| 4623 |
|
---|
[464] | 4624 | const FLASH_QUALIFIER mp_digit ltm_prime_tab[PRIME_SIZE] = {
|
---|
[457] | 4625 | 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
|
---|
| 4626 | 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
|
---|
| 4627 | 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
|
---|
| 4628 | 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
|
---|
| 4629 | #ifndef MP_8BIT
|
---|
| 4630 | 0x0083,
|
---|
| 4631 | 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
|
---|
| 4632 | 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
|
---|
| 4633 | 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
|
---|
| 4634 | 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
|
---|
| 4635 |
|
---|
| 4636 | 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
|
---|
| 4637 | 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
|
---|
| 4638 | 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
|
---|
| 4639 | 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
|
---|
| 4640 | 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
|
---|
| 4641 | 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
|
---|
| 4642 | 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
|
---|
| 4643 | 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
|
---|
| 4644 |
|
---|
| 4645 | 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
|
---|
| 4646 | 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
|
---|
| 4647 | 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
|
---|
| 4648 | 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
|
---|
| 4649 | 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
|
---|
| 4650 | 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
|
---|
| 4651 | 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
|
---|
| 4652 | 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
|
---|
| 4653 |
|
---|
| 4654 | 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
|
---|
| 4655 | 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
|
---|
| 4656 | 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
|
---|
| 4657 | 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
|
---|
| 4658 | 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
|
---|
| 4659 | 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
|
---|
| 4660 | 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
|
---|
| 4661 | 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
|
---|
| 4662 | #endif
|
---|
| 4663 | };
|
---|
| 4664 |
|
---|
| 4665 |
|
---|
| 4666 | /* Miller-Rabin test of "a" to the base of "b" as described in
|
---|
| 4667 | * HAC pp. 139 Algorithm 4.24
|
---|
| 4668 | *
|
---|
| 4669 | * Sets result to 0 if definitely composite or 1 if probably prime.
|
---|
| 4670 | * Randomly the chance of error is no more than 1/4 and often
|
---|
| 4671 | * very much lower.
|
---|
| 4672 | */
|
---|
| 4673 | static int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
|
---|
| 4674 | {
|
---|
| 4675 | mp_int n1, y, r;
|
---|
| 4676 | int s, j, err;
|
---|
| 4677 |
|
---|
| 4678 | /* default */
|
---|
| 4679 | *result = MP_NO;
|
---|
| 4680 |
|
---|
| 4681 | /* ensure b > 1 */
|
---|
| 4682 | if (mp_cmp_d(b, 1) != MP_GT) {
|
---|
| 4683 | return MP_VAL;
|
---|
| 4684 | }
|
---|
| 4685 |
|
---|
| 4686 | /* get n1 = a - 1 */
|
---|
| 4687 | if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
|
---|
| 4688 | return err;
|
---|
| 4689 | }
|
---|
| 4690 | if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
|
---|
| 4691 | goto LBL_N1;
|
---|
| 4692 | }
|
---|
| 4693 |
|
---|
| 4694 | /* set 2**s * r = n1 */
|
---|
| 4695 | if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
|
---|
| 4696 | goto LBL_N1;
|
---|
| 4697 | }
|
---|
| 4698 |
|
---|
| 4699 | /* count the number of least significant bits
|
---|
| 4700 | * which are zero
|
---|
| 4701 | */
|
---|
| 4702 | s = mp_cnt_lsb(&r);
|
---|
| 4703 |
|
---|
| 4704 | /* now divide n - 1 by 2**s */
|
---|
| 4705 | if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
|
---|
| 4706 | goto LBL_R;
|
---|
| 4707 | }
|
---|
| 4708 |
|
---|
| 4709 | /* compute y = b**r mod a */
|
---|
| 4710 | if ((err = mp_init (&y)) != MP_OKAY) {
|
---|
| 4711 | goto LBL_R;
|
---|
| 4712 | }
|
---|
| 4713 | #if defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH)
|
---|
| 4714 | #ifndef WOLFSSL_SP_NO_2048
|
---|
[464] | 4715 | if (mp_count_bits(a) == 1024 && mp_isodd(a))
|
---|
[457] | 4716 | err = sp_ModExp_1024(b, &r, a, &y);
|
---|
[464] | 4717 | else if (mp_count_bits(a) == 2048 && mp_isodd(a))
|
---|
[457] | 4718 | err = sp_ModExp_2048(b, &r, a, &y);
|
---|
| 4719 | else
|
---|
| 4720 | #endif
|
---|
| 4721 | #ifndef WOLFSSL_SP_NO_3072
|
---|
[464] | 4722 | if (mp_count_bits(a) == 1536 && mp_isodd(a))
|
---|
[457] | 4723 | err = sp_ModExp_1536(b, &r, a, &y);
|
---|
[464] | 4724 | else if (mp_count_bits(a) == 3072 && mp_isodd(a))
|
---|
[457] | 4725 | err = sp_ModExp_3072(b, &r, a, &y);
|
---|
| 4726 | else
|
---|
| 4727 | #endif
|
---|
| 4728 | #ifdef WOLFSSL_SP_4096
|
---|
[464] | 4729 | if (mp_count_bits(a) == 4096 && mp_isodd(a))
|
---|
[457] | 4730 | err = sp_ModExp_4096(b, &r, a, &y);
|
---|
| 4731 | else
|
---|
| 4732 | #endif
|
---|
| 4733 | #endif
|
---|
| 4734 | err = mp_exptmod (b, &r, a, &y);
|
---|
| 4735 | if (err != MP_OKAY)
|
---|
| 4736 | goto LBL_Y;
|
---|
| 4737 |
|
---|
| 4738 | /* if y != 1 and y != n1 do */
|
---|
| 4739 | if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
|
---|
| 4740 | j = 1;
|
---|
| 4741 | /* while j <= s-1 and y != n1 */
|
---|
| 4742 | while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
|
---|
| 4743 | if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
|
---|
| 4744 | goto LBL_Y;
|
---|
| 4745 | }
|
---|
| 4746 |
|
---|
| 4747 | /* if y == 1 then composite */
|
---|
| 4748 | if (mp_cmp_d (&y, 1) == MP_EQ) {
|
---|
| 4749 | goto LBL_Y;
|
---|
| 4750 | }
|
---|
| 4751 |
|
---|
| 4752 | ++j;
|
---|
| 4753 | }
|
---|
| 4754 |
|
---|
| 4755 | /* if y != n1 then composite */
|
---|
| 4756 | if (mp_cmp (&y, &n1) != MP_EQ) {
|
---|
| 4757 | goto LBL_Y;
|
---|
| 4758 | }
|
---|
| 4759 | }
|
---|
| 4760 |
|
---|
| 4761 | /* probably prime now */
|
---|
| 4762 | *result = MP_YES;
|
---|
| 4763 | LBL_Y:mp_clear (&y);
|
---|
| 4764 | LBL_R:mp_clear (&r);
|
---|
| 4765 | LBL_N1:mp_clear (&n1);
|
---|
| 4766 | return err;
|
---|
| 4767 | }
|
---|
| 4768 |
|
---|
| 4769 |
|
---|
| 4770 | /* determines if an integers is divisible by one
|
---|
| 4771 | * of the first PRIME_SIZE primes or not
|
---|
| 4772 | *
|
---|
| 4773 | * sets result to 0 if not, 1 if yes
|
---|
| 4774 | */
|
---|
| 4775 | static int mp_prime_is_divisible (mp_int * a, int *result)
|
---|
| 4776 | {
|
---|
| 4777 | int err, ix;
|
---|
| 4778 | mp_digit res;
|
---|
| 4779 |
|
---|
| 4780 | /* default to not */
|
---|
| 4781 | *result = MP_NO;
|
---|
| 4782 |
|
---|
| 4783 | for (ix = 0; ix < PRIME_SIZE; ix++) {
|
---|
| 4784 | /* what is a mod LBL_prime_tab[ix] */
|
---|
| 4785 | if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) {
|
---|
| 4786 | return err;
|
---|
| 4787 | }
|
---|
| 4788 |
|
---|
| 4789 | /* is the residue zero? */
|
---|
| 4790 | if (res == 0) {
|
---|
| 4791 | *result = MP_YES;
|
---|
| 4792 | return MP_OKAY;
|
---|
| 4793 | }
|
---|
| 4794 | }
|
---|
| 4795 |
|
---|
| 4796 | return MP_OKAY;
|
---|
| 4797 | }
|
---|
| 4798 |
|
---|
| 4799 | /*
|
---|
| 4800 | * Sets result to 1 if probably prime, 0 otherwise
|
---|
| 4801 | */
|
---|
| 4802 | int mp_prime_is_prime (mp_int * a, int t, int *result)
|
---|
| 4803 | {
|
---|
| 4804 | mp_int b;
|
---|
| 4805 | int ix, err, res;
|
---|
| 4806 |
|
---|
| 4807 | /* default to no */
|
---|
| 4808 | *result = MP_NO;
|
---|
| 4809 |
|
---|
| 4810 | /* valid value of t? */
|
---|
| 4811 | if (t <= 0 || t > PRIME_SIZE) {
|
---|
| 4812 | return MP_VAL;
|
---|
| 4813 | }
|
---|
| 4814 |
|
---|
| 4815 | if (mp_isone(a)) {
|
---|
| 4816 | *result = MP_NO;
|
---|
| 4817 | return MP_OKAY;
|
---|
| 4818 | }
|
---|
| 4819 |
|
---|
| 4820 | /* is the input equal to one of the primes in the table? */
|
---|
| 4821 | for (ix = 0; ix < PRIME_SIZE; ix++) {
|
---|
| 4822 | if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
|
---|
| 4823 | *result = MP_YES;
|
---|
| 4824 | return MP_OKAY;
|
---|
| 4825 | }
|
---|
| 4826 | }
|
---|
| 4827 |
|
---|
| 4828 | /* first perform trial division */
|
---|
| 4829 | if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
|
---|
| 4830 | return err;
|
---|
| 4831 | }
|
---|
| 4832 |
|
---|
| 4833 | /* return if it was trivially divisible */
|
---|
| 4834 | if (res == MP_YES) {
|
---|
| 4835 | return MP_OKAY;
|
---|
| 4836 | }
|
---|
| 4837 |
|
---|
| 4838 | /* now perform the miller-rabin rounds */
|
---|
| 4839 | if ((err = mp_init (&b)) != MP_OKAY) {
|
---|
| 4840 | return err;
|
---|
| 4841 | }
|
---|
| 4842 |
|
---|
| 4843 | for (ix = 0; ix < t; ix++) {
|
---|
| 4844 | /* set the prime */
|
---|
| 4845 | if ((err = mp_set (&b, ltm_prime_tab[ix])) != MP_OKAY) {
|
---|
| 4846 | goto LBL_B;
|
---|
| 4847 | }
|
---|
| 4848 |
|
---|
| 4849 | if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
|
---|
| 4850 | goto LBL_B;
|
---|
| 4851 | }
|
---|
| 4852 |
|
---|
| 4853 | if (res == MP_NO) {
|
---|
| 4854 | goto LBL_B;
|
---|
| 4855 | }
|
---|
| 4856 | }
|
---|
| 4857 |
|
---|
| 4858 | /* passed the test */
|
---|
| 4859 | *result = MP_YES;
|
---|
| 4860 | LBL_B:mp_clear (&b);
|
---|
| 4861 | return err;
|
---|
| 4862 | }
|
---|
| 4863 |
|
---|
| 4864 |
|
---|
| 4865 | /*
|
---|
| 4866 | * Sets result to 1 if probably prime, 0 otherwise
|
---|
| 4867 | */
|
---|
| 4868 | int mp_prime_is_prime_ex (mp_int * a, int t, int *result, WC_RNG *rng)
|
---|
| 4869 | {
|
---|
| 4870 | mp_int b, c;
|
---|
| 4871 | int ix, err, res;
|
---|
| 4872 | byte* base = NULL;
|
---|
| 4873 | word32 baseSz = 0;
|
---|
| 4874 |
|
---|
| 4875 | /* default to no */
|
---|
| 4876 | *result = MP_NO;
|
---|
| 4877 |
|
---|
| 4878 | /* valid value of t? */
|
---|
| 4879 | if (t <= 0 || t > PRIME_SIZE) {
|
---|
| 4880 | return MP_VAL;
|
---|
| 4881 | }
|
---|
| 4882 |
|
---|
| 4883 | if (mp_isone(a)) {
|
---|
| 4884 | *result = MP_NO;
|
---|
| 4885 | return MP_OKAY;
|
---|
| 4886 | }
|
---|
| 4887 |
|
---|
| 4888 | /* is the input equal to one of the primes in the table? */
|
---|
| 4889 | for (ix = 0; ix < PRIME_SIZE; ix++) {
|
---|
| 4890 | if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
|
---|
| 4891 | *result = MP_YES;
|
---|
| 4892 | return MP_OKAY;
|
---|
| 4893 | }
|
---|
| 4894 | }
|
---|
| 4895 |
|
---|
| 4896 | /* first perform trial division */
|
---|
| 4897 | if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
|
---|
| 4898 | return err;
|
---|
| 4899 | }
|
---|
| 4900 |
|
---|
| 4901 | /* return if it was trivially divisible */
|
---|
| 4902 | if (res == MP_YES) {
|
---|
| 4903 | return MP_OKAY;
|
---|
| 4904 | }
|
---|
| 4905 |
|
---|
| 4906 | /* now perform the miller-rabin rounds */
|
---|
| 4907 | if ((err = mp_init (&b)) != MP_OKAY) {
|
---|
| 4908 | return err;
|
---|
| 4909 | }
|
---|
| 4910 | if ((err = mp_init (&c)) != MP_OKAY) {
|
---|
| 4911 | mp_clear(&b);
|
---|
| 4912 | return err;
|
---|
| 4913 | }
|
---|
| 4914 |
|
---|
| 4915 | baseSz = mp_count_bits(a);
|
---|
| 4916 | baseSz = (baseSz / 8) + ((baseSz % 8) ? 1 : 0);
|
---|
| 4917 |
|
---|
| 4918 | base = (byte*)XMALLOC(baseSz, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 4919 | if (base == NULL) {
|
---|
| 4920 | err = MP_MEM;
|
---|
| 4921 | goto LBL_B;
|
---|
| 4922 | }
|
---|
| 4923 |
|
---|
| 4924 | if ((err = mp_sub_d(a, 2, &c)) != MP_OKAY) {
|
---|
| 4925 | goto LBL_B;
|
---|
| 4926 | }
|
---|
| 4927 |
|
---|
| 4928 | /* now do a miller rabin with up to t random numbers, this should
|
---|
| 4929 | * give a (1/4)^t chance of a false prime. */
|
---|
| 4930 | for (ix = 0; ix < t; ix++) {
|
---|
| 4931 | /* Set a test candidate. */
|
---|
| 4932 | if ((err = wc_RNG_GenerateBlock(rng, base, baseSz)) != 0) {
|
---|
| 4933 | goto LBL_B;
|
---|
| 4934 | }
|
---|
| 4935 |
|
---|
| 4936 | if ((err = mp_read_unsigned_bin(&b, base, baseSz)) != MP_OKAY) {
|
---|
| 4937 | goto LBL_B;
|
---|
| 4938 | }
|
---|
| 4939 |
|
---|
| 4940 | if (mp_cmp_d(&b, 2) != MP_GT || mp_cmp(&b, &c) != MP_LT) {
|
---|
| 4941 | ix--;
|
---|
| 4942 | continue;
|
---|
| 4943 | }
|
---|
| 4944 |
|
---|
| 4945 | if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
|
---|
| 4946 | goto LBL_B;
|
---|
| 4947 | }
|
---|
| 4948 |
|
---|
| 4949 | if (res == MP_NO) {
|
---|
| 4950 | goto LBL_B;
|
---|
| 4951 | }
|
---|
| 4952 | }
|
---|
| 4953 |
|
---|
| 4954 | /* passed the test */
|
---|
| 4955 | *result = MP_YES;
|
---|
| 4956 | LBL_B:mp_clear (&b);
|
---|
| 4957 | mp_clear (&c);
|
---|
| 4958 | XFREE(base, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 4959 | return err;
|
---|
| 4960 | }
|
---|
| 4961 |
|
---|
| 4962 | #endif /* WOLFSSL_KEY_GEN NO_DH NO_DSA NO_RSA */
|
---|
| 4963 |
|
---|
| 4964 | #ifdef WOLFSSL_KEY_GEN
|
---|
| 4965 |
|
---|
| 4966 | static const int USE_BBS = 1;
|
---|
| 4967 |
|
---|
| 4968 | int mp_rand_prime(mp_int* N, int len, WC_RNG* rng, void* heap)
|
---|
| 4969 | {
|
---|
| 4970 | int err, res, type;
|
---|
| 4971 | byte* buf;
|
---|
| 4972 |
|
---|
| 4973 | if (N == NULL || rng == NULL)
|
---|
| 4974 | return MP_VAL;
|
---|
| 4975 |
|
---|
| 4976 | /* get type */
|
---|
| 4977 | if (len < 0) {
|
---|
| 4978 | type = USE_BBS;
|
---|
| 4979 | len = -len;
|
---|
| 4980 | } else {
|
---|
| 4981 | type = 0;
|
---|
| 4982 | }
|
---|
| 4983 |
|
---|
| 4984 | /* allow sizes between 2 and 512 bytes for a prime size */
|
---|
| 4985 | if (len < 2 || len > 512) {
|
---|
| 4986 | return MP_VAL;
|
---|
| 4987 | }
|
---|
| 4988 |
|
---|
| 4989 | /* allocate buffer to work with */
|
---|
| 4990 | buf = (byte*)XMALLOC(len, heap, DYNAMIC_TYPE_RSA);
|
---|
| 4991 | if (buf == NULL) {
|
---|
| 4992 | return MP_MEM;
|
---|
| 4993 | }
|
---|
| 4994 | XMEMSET(buf, 0, len);
|
---|
| 4995 |
|
---|
| 4996 | do {
|
---|
| 4997 | #ifdef SHOW_GEN
|
---|
| 4998 | printf(".");
|
---|
| 4999 | fflush(stdout);
|
---|
| 5000 | #endif
|
---|
| 5001 | /* generate value */
|
---|
| 5002 | err = wc_RNG_GenerateBlock(rng, buf, len);
|
---|
| 5003 | if (err != 0) {
|
---|
| 5004 | XFREE(buf, heap, DYNAMIC_TYPE_RSA);
|
---|
| 5005 | return err;
|
---|
| 5006 | }
|
---|
| 5007 |
|
---|
| 5008 | /* munge bits */
|
---|
| 5009 | buf[0] |= 0x80 | 0x40;
|
---|
| 5010 | buf[len-1] |= 0x01 | ((type & USE_BBS) ? 0x02 : 0x00);
|
---|
| 5011 |
|
---|
| 5012 | /* load value */
|
---|
| 5013 | if ((err = mp_read_unsigned_bin(N, buf, len)) != MP_OKAY) {
|
---|
| 5014 | XFREE(buf, heap, DYNAMIC_TYPE_RSA);
|
---|
| 5015 | return err;
|
---|
| 5016 | }
|
---|
| 5017 |
|
---|
| 5018 | /* test */
|
---|
| 5019 | /* Running Miller-Rabin up to 3 times gives us a 2^{-80} chance
|
---|
| 5020 | * of a 1024-bit candidate being a false positive, when it is our
|
---|
| 5021 | * prime candidate. (Note 4.49 of Handbook of Applied Cryptography.)
|
---|
| 5022 | * Using 8 because we've always used 8. */
|
---|
| 5023 | if ((err = mp_prime_is_prime_ex(N, 8, &res, rng)) != MP_OKAY) {
|
---|
| 5024 | XFREE(buf, heap, DYNAMIC_TYPE_RSA);
|
---|
| 5025 | return err;
|
---|
| 5026 | }
|
---|
| 5027 | } while (res == MP_NO);
|
---|
| 5028 |
|
---|
| 5029 | XMEMSET(buf, 0, len);
|
---|
| 5030 | XFREE(buf, heap, DYNAMIC_TYPE_RSA);
|
---|
| 5031 |
|
---|
| 5032 | return MP_OKAY;
|
---|
| 5033 | }
|
---|
| 5034 |
|
---|
| 5035 |
|
---|
| 5036 | /* computes least common multiple as |a*b|/(a, b) */
|
---|
| 5037 | int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 5038 | {
|
---|
| 5039 | int res;
|
---|
| 5040 | mp_int t1, t2;
|
---|
| 5041 |
|
---|
| 5042 |
|
---|
| 5043 | if ((res = mp_init_multi (&t1, &t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
|
---|
| 5044 | return res;
|
---|
| 5045 | }
|
---|
| 5046 |
|
---|
| 5047 | /* t1 = get the GCD of the two inputs */
|
---|
| 5048 | if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
|
---|
| 5049 | goto LBL_T;
|
---|
| 5050 | }
|
---|
| 5051 |
|
---|
| 5052 | /* divide the smallest by the GCD */
|
---|
| 5053 | if (mp_cmp_mag(a, b) == MP_LT) {
|
---|
| 5054 | /* store quotient in t2 such that t2 * b is the LCM */
|
---|
| 5055 | if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
|
---|
| 5056 | goto LBL_T;
|
---|
| 5057 | }
|
---|
| 5058 | res = mp_mul(b, &t2, c);
|
---|
| 5059 | } else {
|
---|
| 5060 | /* store quotient in t2 such that t2 * a is the LCM */
|
---|
| 5061 | if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
|
---|
| 5062 | goto LBL_T;
|
---|
| 5063 | }
|
---|
| 5064 | res = mp_mul(a, &t2, c);
|
---|
| 5065 | }
|
---|
| 5066 |
|
---|
| 5067 | /* fix the sign to positive */
|
---|
| 5068 | c->sign = MP_ZPOS;
|
---|
| 5069 |
|
---|
| 5070 | LBL_T:
|
---|
| 5071 | mp_clear(&t1);
|
---|
| 5072 | mp_clear(&t2);
|
---|
| 5073 | return res;
|
---|
| 5074 | }
|
---|
| 5075 |
|
---|
| 5076 |
|
---|
| 5077 |
|
---|
| 5078 | /* Greatest Common Divisor using the binary method */
|
---|
| 5079 | int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
|
---|
| 5080 | {
|
---|
| 5081 | mp_int u, v;
|
---|
| 5082 | int k, u_lsb, v_lsb, res;
|
---|
| 5083 |
|
---|
| 5084 | /* either zero than gcd is the largest */
|
---|
| 5085 | if (mp_iszero (a) == MP_YES) {
|
---|
| 5086 | return mp_abs (b, c);
|
---|
| 5087 | }
|
---|
| 5088 | if (mp_iszero (b) == MP_YES) {
|
---|
| 5089 | return mp_abs (a, c);
|
---|
| 5090 | }
|
---|
| 5091 |
|
---|
| 5092 | /* get copies of a and b we can modify */
|
---|
| 5093 | if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
|
---|
| 5094 | return res;
|
---|
| 5095 | }
|
---|
| 5096 |
|
---|
| 5097 | if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
|
---|
| 5098 | goto LBL_U;
|
---|
| 5099 | }
|
---|
| 5100 |
|
---|
| 5101 | /* must be positive for the remainder of the algorithm */
|
---|
| 5102 | u.sign = v.sign = MP_ZPOS;
|
---|
| 5103 |
|
---|
| 5104 | /* B1. Find the common power of two for u and v */
|
---|
| 5105 | u_lsb = mp_cnt_lsb(&u);
|
---|
| 5106 | v_lsb = mp_cnt_lsb(&v);
|
---|
| 5107 | k = MIN(u_lsb, v_lsb);
|
---|
| 5108 |
|
---|
| 5109 | if (k > 0) {
|
---|
| 5110 | /* divide the power of two out */
|
---|
| 5111 | if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
|
---|
| 5112 | goto LBL_V;
|
---|
| 5113 | }
|
---|
| 5114 |
|
---|
| 5115 | if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
|
---|
| 5116 | goto LBL_V;
|
---|
| 5117 | }
|
---|
| 5118 | }
|
---|
| 5119 |
|
---|
| 5120 | /* divide any remaining factors of two out */
|
---|
| 5121 | if (u_lsb != k) {
|
---|
| 5122 | if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
|
---|
| 5123 | goto LBL_V;
|
---|
| 5124 | }
|
---|
| 5125 | }
|
---|
| 5126 |
|
---|
| 5127 | if (v_lsb != k) {
|
---|
| 5128 | if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
|
---|
| 5129 | goto LBL_V;
|
---|
| 5130 | }
|
---|
| 5131 | }
|
---|
| 5132 |
|
---|
| 5133 | while (mp_iszero(&v) == MP_NO) {
|
---|
| 5134 | /* make sure v is the largest */
|
---|
| 5135 | if (mp_cmp_mag(&u, &v) == MP_GT) {
|
---|
| 5136 | /* swap u and v to make sure v is >= u */
|
---|
| 5137 | mp_exch(&u, &v);
|
---|
| 5138 | }
|
---|
| 5139 |
|
---|
| 5140 | /* subtract smallest from largest */
|
---|
| 5141 | if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
|
---|
| 5142 | goto LBL_V;
|
---|
| 5143 | }
|
---|
| 5144 |
|
---|
| 5145 | /* Divide out all factors of two */
|
---|
| 5146 | if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
|
---|
| 5147 | goto LBL_V;
|
---|
| 5148 | }
|
---|
| 5149 | }
|
---|
| 5150 |
|
---|
| 5151 | /* multiply by 2**k which we divided out at the beginning */
|
---|
| 5152 | if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
|
---|
| 5153 | goto LBL_V;
|
---|
| 5154 | }
|
---|
| 5155 | c->sign = MP_ZPOS;
|
---|
| 5156 | res = MP_OKAY;
|
---|
| 5157 | LBL_V:mp_clear (&v);
|
---|
| 5158 | LBL_U:mp_clear (&u);
|
---|
| 5159 | return res;
|
---|
| 5160 | }
|
---|
| 5161 |
|
---|
| 5162 | #endif /* WOLFSSL_KEY_GEN */
|
---|
| 5163 |
|
---|
| 5164 |
|
---|
| 5165 | #if !defined(NO_DSA) || defined(HAVE_ECC) || defined(WOLFSSL_KEY_GEN) || \
|
---|
| 5166 | defined(HAVE_COMP_KEY) || defined(WOLFSSL_DEBUG_MATH) || \
|
---|
| 5167 | defined(DEBUG_WOLFSSL) || defined(OPENSSL_EXTRA)
|
---|
| 5168 |
|
---|
| 5169 | /* chars used in radix conversions */
|
---|
[464] | 5170 | const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
|
---|
| 5171 | "abcdefghijklmnopqrstuvwxyz+/";
|
---|
[457] | 5172 | #endif
|
---|
| 5173 |
|
---|
| 5174 | #if !defined(NO_DSA) || defined(HAVE_ECC)
|
---|
| 5175 | /* read a string [ASCII] in a given radix */
|
---|
| 5176 | int mp_read_radix (mp_int * a, const char *str, int radix)
|
---|
| 5177 | {
|
---|
| 5178 | int y, res, neg;
|
---|
| 5179 | char ch;
|
---|
| 5180 |
|
---|
| 5181 | /* zero the digit bignum */
|
---|
| 5182 | mp_zero(a);
|
---|
| 5183 |
|
---|
| 5184 | /* make sure the radix is ok */
|
---|
| 5185 | if (radix < MP_RADIX_BIN || radix > MP_RADIX_MAX) {
|
---|
| 5186 | return MP_VAL;
|
---|
| 5187 | }
|
---|
| 5188 |
|
---|
| 5189 | /* if the leading digit is a
|
---|
| 5190 | * minus set the sign to negative.
|
---|
| 5191 | */
|
---|
| 5192 | if (*str == '-') {
|
---|
| 5193 | ++str;
|
---|
| 5194 | neg = MP_NEG;
|
---|
| 5195 | } else {
|
---|
| 5196 | neg = MP_ZPOS;
|
---|
| 5197 | }
|
---|
| 5198 |
|
---|
| 5199 | /* set the integer to the default of zero */
|
---|
| 5200 | mp_zero (a);
|
---|
| 5201 |
|
---|
| 5202 | /* process each digit of the string */
|
---|
| 5203 | while (*str != '\0') {
|
---|
| 5204 | /* if the radix <= 36 the conversion is case insensitive
|
---|
| 5205 | * this allows numbers like 1AB and 1ab to represent the same value
|
---|
| 5206 | * [e.g. in hex]
|
---|
| 5207 | */
|
---|
| 5208 | ch = (radix <= 36) ? (char)XTOUPPER((unsigned char)*str) : *str;
|
---|
| 5209 | for (y = 0; y < 64; y++) {
|
---|
| 5210 | if (ch == mp_s_rmap[y]) {
|
---|
| 5211 | break;
|
---|
| 5212 | }
|
---|
| 5213 | }
|
---|
| 5214 |
|
---|
| 5215 | /* if the char was found in the map
|
---|
| 5216 | * and is less than the given radix add it
|
---|
| 5217 | * to the number, otherwise exit the loop.
|
---|
| 5218 | */
|
---|
| 5219 | if (y < radix) {
|
---|
| 5220 | if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) {
|
---|
| 5221 | return res;
|
---|
| 5222 | }
|
---|
| 5223 | if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) {
|
---|
| 5224 | return res;
|
---|
| 5225 | }
|
---|
| 5226 | } else {
|
---|
| 5227 | break;
|
---|
| 5228 | }
|
---|
| 5229 | ++str;
|
---|
| 5230 | }
|
---|
| 5231 |
|
---|
| 5232 | /* if digit in isn't null term, then invalid character was found */
|
---|
| 5233 | if (*str != '\0') {
|
---|
| 5234 | mp_zero (a);
|
---|
| 5235 | return MP_VAL;
|
---|
| 5236 | }
|
---|
| 5237 |
|
---|
| 5238 | /* set the sign only if a != 0 */
|
---|
| 5239 | if (mp_iszero(a) != MP_YES) {
|
---|
| 5240 | a->sign = neg;
|
---|
| 5241 | }
|
---|
| 5242 | return MP_OKAY;
|
---|
| 5243 | }
|
---|
| 5244 | #endif /* !defined(NO_DSA) || defined(HAVE_ECC) */
|
---|
| 5245 |
|
---|
| 5246 | #ifdef WC_MP_TO_RADIX
|
---|
| 5247 |
|
---|
| 5248 | /* returns size of ASCII representation */
|
---|
| 5249 | int mp_radix_size (mp_int *a, int radix, int *size)
|
---|
| 5250 | {
|
---|
| 5251 | int res, digs;
|
---|
| 5252 | mp_int t;
|
---|
| 5253 | mp_digit d;
|
---|
| 5254 |
|
---|
| 5255 | *size = 0;
|
---|
| 5256 |
|
---|
| 5257 | /* special case for binary */
|
---|
| 5258 | if (radix == MP_RADIX_BIN) {
|
---|
[464] | 5259 | *size = mp_count_bits(a);
|
---|
| 5260 | if (*size == 0)
|
---|
| 5261 | *size = 1;
|
---|
| 5262 | *size += (a->sign == MP_NEG ? 1 : 0) + 1; /* "-" sign + null term */
|
---|
[457] | 5263 | return MP_OKAY;
|
---|
| 5264 | }
|
---|
| 5265 |
|
---|
| 5266 | /* make sure the radix is in range */
|
---|
| 5267 | if (radix < MP_RADIX_BIN || radix > MP_RADIX_MAX) {
|
---|
| 5268 | return MP_VAL;
|
---|
| 5269 | }
|
---|
| 5270 |
|
---|
| 5271 | if (mp_iszero(a) == MP_YES) {
|
---|
[464] | 5272 | #ifndef WC_DISABLE_RADIX_ZERO_PAD
|
---|
| 5273 | if (radix == 16)
|
---|
| 5274 | *size = 3;
|
---|
| 5275 | else
|
---|
| 5276 | #endif
|
---|
| 5277 | *size = 2;
|
---|
[457] | 5278 | return MP_OKAY;
|
---|
| 5279 | }
|
---|
| 5280 |
|
---|
| 5281 | /* digs is the digit count */
|
---|
| 5282 | digs = 0;
|
---|
| 5283 |
|
---|
| 5284 | /* init a copy of the input */
|
---|
| 5285 | if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
|
---|
| 5286 | return res;
|
---|
| 5287 | }
|
---|
| 5288 |
|
---|
| 5289 | /* force temp to positive */
|
---|
| 5290 | t.sign = MP_ZPOS;
|
---|
| 5291 |
|
---|
| 5292 | /* fetch out all of the digits */
|
---|
| 5293 | while (mp_iszero (&t) == MP_NO) {
|
---|
| 5294 | if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
|
---|
| 5295 | mp_clear (&t);
|
---|
| 5296 | return res;
|
---|
| 5297 | }
|
---|
| 5298 | ++digs;
|
---|
| 5299 | }
|
---|
| 5300 | mp_clear (&t);
|
---|
| 5301 |
|
---|
[464] | 5302 | #ifndef WC_DISABLE_RADIX_ZERO_PAD
|
---|
| 5303 | /* For hexadecimal output, add zero padding when number of digits is odd */
|
---|
| 5304 | if ((digs & 1) && (radix == 16)) {
|
---|
| 5305 | ++digs;
|
---|
| 5306 | }
|
---|
| 5307 | #endif
|
---|
| 5308 |
|
---|
| 5309 | /* if it's negative add one for the sign */
|
---|
| 5310 | if (a->sign == MP_NEG) {
|
---|
| 5311 | ++digs;
|
---|
| 5312 | }
|
---|
| 5313 |
|
---|
[457] | 5314 | /* return digs + 1, the 1 is for the NULL byte that would be required. */
|
---|
| 5315 | *size = digs + 1;
|
---|
| 5316 | return MP_OKAY;
|
---|
| 5317 | }
|
---|
| 5318 |
|
---|
| 5319 | /* stores a bignum as a ASCII string in a given radix (2..64) */
|
---|
| 5320 | int mp_toradix (mp_int *a, char *str, int radix)
|
---|
| 5321 | {
|
---|
| 5322 | int res, digs;
|
---|
| 5323 | mp_int t;
|
---|
| 5324 | mp_digit d;
|
---|
| 5325 | char *_s = str;
|
---|
| 5326 |
|
---|
| 5327 | /* check range of the radix */
|
---|
| 5328 | if (radix < MP_RADIX_BIN || radix > MP_RADIX_MAX) {
|
---|
| 5329 | return MP_VAL;
|
---|
| 5330 | }
|
---|
| 5331 |
|
---|
| 5332 | /* quick out if its zero */
|
---|
| 5333 | if (mp_iszero(a) == MP_YES) {
|
---|
[464] | 5334 | #ifndef WC_DISABLE_RADIX_ZERO_PAD
|
---|
| 5335 | if (radix == 16) {
|
---|
| 5336 | *str++ = '0';
|
---|
| 5337 | }
|
---|
| 5338 | #endif
|
---|
[457] | 5339 | *str++ = '0';
|
---|
| 5340 | *str = '\0';
|
---|
| 5341 | return MP_OKAY;
|
---|
| 5342 | }
|
---|
| 5343 |
|
---|
| 5344 | if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
|
---|
| 5345 | return res;
|
---|
| 5346 | }
|
---|
| 5347 |
|
---|
| 5348 | /* if it is negative output a - */
|
---|
| 5349 | if (t.sign == MP_NEG) {
|
---|
| 5350 | ++_s;
|
---|
| 5351 | *str++ = '-';
|
---|
| 5352 | t.sign = MP_ZPOS;
|
---|
| 5353 | }
|
---|
| 5354 |
|
---|
| 5355 | digs = 0;
|
---|
| 5356 | while (mp_iszero (&t) == MP_NO) {
|
---|
| 5357 | if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
|
---|
| 5358 | mp_clear (&t);
|
---|
| 5359 | return res;
|
---|
| 5360 | }
|
---|
| 5361 | *str++ = mp_s_rmap[d];
|
---|
| 5362 | ++digs;
|
---|
| 5363 | }
|
---|
| 5364 | #ifndef WC_DISABLE_RADIX_ZERO_PAD
|
---|
| 5365 | /* For hexadecimal output, add zero padding when number of digits is odd */
|
---|
| 5366 | if ((digs & 1) && (radix == 16)) {
|
---|
| 5367 | *str++ = mp_s_rmap[0];
|
---|
| 5368 | ++digs;
|
---|
| 5369 | }
|
---|
| 5370 | #endif
|
---|
| 5371 | /* reverse the digits of the string. In this case _s points
|
---|
| 5372 | * to the first digit [excluding the sign] of the number]
|
---|
| 5373 | */
|
---|
| 5374 | bn_reverse ((unsigned char *)_s, digs);
|
---|
| 5375 |
|
---|
| 5376 | /* append a NULL so the string is properly terminated */
|
---|
| 5377 | *str = '\0';
|
---|
| 5378 |
|
---|
| 5379 | mp_clear (&t);
|
---|
| 5380 | return MP_OKAY;
|
---|
| 5381 | }
|
---|
| 5382 |
|
---|
| 5383 | #ifdef WOLFSSL_DEBUG_MATH
|
---|
| 5384 | void mp_dump(const char* desc, mp_int* a, byte verbose)
|
---|
| 5385 | {
|
---|
| 5386 | char *buffer;
|
---|
| 5387 | int size = a->alloc;
|
---|
| 5388 |
|
---|
| 5389 | buffer = (char*)XMALLOC(size * sizeof(mp_digit) * 2, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 5390 | if (buffer == NULL) {
|
---|
| 5391 | return;
|
---|
| 5392 | }
|
---|
| 5393 |
|
---|
| 5394 | printf("%s: ptr=%p, used=%d, sign=%d, size=%d, mpd=%d\n",
|
---|
| 5395 | desc, a, a->used, a->sign, size, (int)sizeof(mp_digit));
|
---|
| 5396 |
|
---|
| 5397 | mp_tohex(a, buffer);
|
---|
| 5398 | printf(" %s\n ", buffer);
|
---|
| 5399 |
|
---|
| 5400 | if (verbose) {
|
---|
| 5401 | int i;
|
---|
| 5402 | for(i=0; i<a->alloc * (int)sizeof(mp_digit); i++) {
|
---|
| 5403 | printf("%02x ", *(((byte*)a->dp) + i));
|
---|
| 5404 | }
|
---|
| 5405 | printf("\n");
|
---|
| 5406 | }
|
---|
| 5407 |
|
---|
| 5408 | XFREE(buffer, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
| 5409 | }
|
---|
| 5410 | #endif /* WOLFSSL_DEBUG_MATH */
|
---|
| 5411 |
|
---|
| 5412 | #endif /* WC_MP_TO_RADIX */
|
---|
| 5413 |
|
---|
| 5414 | #endif /* WOLFSSL_SP_MATH */
|
---|
| 5415 |
|
---|
| 5416 | #endif /* USE_FAST_MATH */
|
---|
| 5417 |
|
---|
| 5418 | #endif /* NO_BIG_INT */
|
---|