| 1 | /* |
| 2 | * Multi-precision integer library |
| 3 | * |
| 4 | * Copyright (C) 2006-2010, Brainspark B.V. |
| 5 | * |
| 6 | * This file is part of PolarSSL (http://www.polarssl.org) |
| 7 | * Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org> |
| 8 | * |
| 9 | * All rights reserved. |
| 10 | * |
| 11 | * This program is free software; you can redistribute it and/or modify |
| 12 | * it under the terms of the GNU General Public License as published by |
| 13 | * the Free Software Foundation; either version 2 of the License, or |
| 14 | * (at your option) any later version. |
| 15 | * |
| 16 | * This program is distributed in the hope that it will be useful, |
| 17 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 18 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 19 | * GNU General Public License for more details. |
| 20 | * |
| 21 | * You should have received a copy of the GNU General Public License along |
| 22 | * with this program; if not, write to the Free Software Foundation, Inc., |
| 23 | * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. |
| 24 | */ |
| 25 | /* |
| 26 | * This MPI implementation is based on: |
| 27 | * |
| 28 | * http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf |
| 29 | * http://www.stillhq.com/extracted/gnupg-api/mpi/ |
| 30 | * http://math.libtomcrypt.com/files/tommath.pdf |
| 31 | */ |
| 32 | |
| 33 | #include "bignum.h" |
| 34 | #include "bn_mul.h" |
| 35 | |
| 36 | #include <string.h> |
| 37 | #include <stdlib.h> |
| 38 | #include <stdarg.h> |
| 39 | |
| 40 | #define ciL ((int) sizeof(t_int)) /* chars in limb */ |
| 41 | #define biL (ciL << 3) /* bits in limb */ |
| 42 | #define biH (ciL << 2) /* half limb size */ |
| 43 | |
| 44 | /* |
| 45 | * Convert between bits/chars and number of limbs |
| 46 | */ |
| 47 | #define BITS_TO_LIMBS(i) (((i) + biL - 1) / biL) |
| 48 | #define CHARS_TO_LIMBS(i) (((i) + ciL - 1) / ciL) |
| 49 | |
| 50 | /* |
| 51 | * Initialize one or more mpi |
| 52 | */ |
| 53 | void mpi_init( mpi *X, ... ) |
| 54 | { |
| 55 | va_list args; |
| 56 | |
| 57 | va_start( args, X ); |
| 58 | |
| 59 | while( X != NULL ) |
| 60 | { |
| 61 | X->s = 1; |
| 62 | X->n = 0; |
| 63 | X->p = NULL; |
| 64 | |
| 65 | X = va_arg( args, mpi* ); |
| 66 | } |
| 67 | |
| 68 | va_end( args ); |
| 69 | } |
| 70 | |
| 71 | /* |
| 72 | * Unallocate one or more mpi |
| 73 | */ |
| 74 | void mpi_free( mpi *X, ... ) |
| 75 | { |
| 76 | va_list args; |
| 77 | |
| 78 | va_start( args, X ); |
| 79 | |
| 80 | while( X != NULL ) |
| 81 | { |
| 82 | if( X->p != NULL ) |
| 83 | { |
| 84 | memset( X->p, 0, X->n * ciL ); |
| 85 | free( X->p ); |
| 86 | } |
| 87 | |
| 88 | X->s = 1; |
| 89 | X->n = 0; |
| 90 | X->p = NULL; |
| 91 | |
| 92 | X = va_arg( args, mpi* ); |
| 93 | } |
| 94 | |
| 95 | va_end( args ); |
| 96 | } |
| 97 | |
| 98 | /* |
| 99 | * Enlarge to the specified number of limbs |
| 100 | */ |
| 101 | int mpi_grow( mpi *X, int nblimbs ) |
| 102 | { |
| 103 | t_int *p; |
| 104 | |
| 105 | if( X->n < nblimbs ) |
| 106 | { |
| 107 | if( ( p = (t_int *) malloc( nblimbs * ciL ) ) == NULL ) |
| 108 | return( 1 ); |
| 109 | |
| 110 | memset( p, 0, nblimbs * ciL ); |
| 111 | |
| 112 | if( X->p != NULL ) |
| 113 | { |
| 114 | memcpy( p, X->p, X->n * ciL ); |
| 115 | memset( X->p, 0, X->n * ciL ); |
| 116 | free( X->p ); |
| 117 | } |
| 118 | |
| 119 | X->n = nblimbs; |
| 120 | X->p = p; |
| 121 | } |
| 122 | |
| 123 | return( 0 ); |
| 124 | } |
| 125 | |
| 126 | /* |
| 127 | * Copy the contents of Y into X |
| 128 | */ |
| 129 | int mpi_copy( mpi *X, const mpi *Y ) |
| 130 | { |
| 131 | int ret, i; |
| 132 | |
| 133 | if( X == Y ) |
| 134 | return( 0 ); |
| 135 | |
| 136 | for( i = Y->n - 1; i > 0; i-- ) |
| 137 | if( Y->p[i] != 0 ) |
| 138 | break; |
| 139 | i++; |
| 140 | |
| 141 | X->s = Y->s; |
| 142 | |
| 143 | MPI_CHK( mpi_grow( X, i ) ); |
| 144 | |
| 145 | memset( X->p, 0, X->n * ciL ); |
| 146 | memcpy( X->p, Y->p, i * ciL ); |
| 147 | |
| 148 | cleanup: |
| 149 | |
| 150 | return( ret ); |
| 151 | } |
| 152 | |
| 153 | /* |
| 154 | * Swap the contents of X and Y |
| 155 | */ |
| 156 | void mpi_swap( mpi *X, mpi *Y ) |
| 157 | { |
| 158 | mpi T; |
| 159 | |
| 160 | memcpy( &T, X, sizeof( mpi ) ); |
| 161 | memcpy( X, Y, sizeof( mpi ) ); |
| 162 | memcpy( Y, &T, sizeof( mpi ) ); |
| 163 | } |
| 164 | |
| 165 | /* |
| 166 | * Set value from integer |
| 167 | */ |
| 168 | int mpi_lset( mpi *X, int z ) |
| 169 | { |
| 170 | int ret; |
| 171 | |
| 172 | MPI_CHK( mpi_grow( X, 1 ) ); |
| 173 | memset( X->p, 0, X->n * ciL ); |
| 174 | |
| 175 | X->p[0] = ( z < 0 ) ? -z : z; |
| 176 | X->s = ( z < 0 ) ? -1 : 1; |
| 177 | |
| 178 | cleanup: |
| 179 | |
| 180 | return( ret ); |
| 181 | } |
| 182 | |
| 183 | /* |
| 184 | * Return the number of least significant bits |
| 185 | */ |
| 186 | int mpi_lsb( const mpi *X ) |
| 187 | { |
| 188 | int i, j, count = 0; |
| 189 | |
| 190 | for( i = 0; i < X->n; i++ ) |
| 191 | for( j = 0; j < (int) biL; j++, count++ ) |
| 192 | if( ( ( X->p[i] >> j ) & 1 ) != 0 ) |
| 193 | return( count ); |
| 194 | |
| 195 | return( 0 ); |
| 196 | } |
| 197 | |
| 198 | /* |
| 199 | * Return the number of most significant bits |
| 200 | */ |
| 201 | int mpi_msb( const mpi *X ) |
| 202 | { |
| 203 | int i, j; |
| 204 | |
| 205 | for( i = X->n - 1; i > 0; i-- ) |
| 206 | if( X->p[i] != 0 ) |
| 207 | break; |
| 208 | |
| 209 | for( j = biL - 1; j >= 0; j-- ) |
| 210 | if( ( ( X->p[i] >> j ) & 1 ) != 0 ) |
| 211 | break; |
| 212 | |
| 213 | return( ( i * biL ) + j + 1 ); |
| 214 | } |
| 215 | |
| 216 | /* |
| 217 | * Return the total size in bytes |
| 218 | */ |
| 219 | int mpi_size( const mpi *X ) |
| 220 | { |
| 221 | return( ( mpi_msb( X ) + 7 ) >> 3 ); |
| 222 | } |
| 223 | |
| 224 | /* |
| 225 | * Convert an ASCII character to digit value |
| 226 | */ |
| 227 | static int mpi_get_digit( t_int *d, int radix, char c ) |
| 228 | { |
| 229 | *d = 255; |
| 230 | |
| 231 | if( c >= 0x30 && c <= 0x39 ) *d = c - 0x30; |
| 232 | if( c >= 0x41 && c <= 0x46 ) *d = c - 0x37; |
| 233 | if( c >= 0x61 && c <= 0x66 ) *d = c - 0x57; |
| 234 | |
| 235 | if( *d >= (t_int) radix ) |
| 236 | return( POLARSSL_ERR_MPI_INVALID_CHARACTER ); |
| 237 | |
| 238 | return( 0 ); |
| 239 | } |
| 240 | |
| 241 | /* |
| 242 | * Import from an ASCII string |
| 243 | */ |
| 244 | int mpi_read_string( mpi *X, int radix, const char *s ) |
| 245 | { |
| 246 | int ret, i, j, n, slen; |
| 247 | t_int d; |
| 248 | mpi T; |
| 249 | |
| 250 | if( radix < 2 || radix > 16 ) |
| 251 | return( POLARSSL_ERR_MPI_BAD_INPUT_DATA ); |
| 252 | |
| 253 | mpi_init( &T, NULL ); |
| 254 | |
| 255 | slen = strlen( s ); |
| 256 | |
| 257 | if( radix == 16 ) |
| 258 | { |
| 259 | n = BITS_TO_LIMBS( slen << 2 ); |
| 260 | |
| 261 | MPI_CHK( mpi_grow( X, n ) ); |
| 262 | MPI_CHK( mpi_lset( X, 0 ) ); |
| 263 | |
| 264 | for( i = slen - 1, j = 0; i >= 0; i--, j++ ) |
| 265 | { |
| 266 | if( i == 0 && s[i] == '-' ) |
| 267 | { |
| 268 | X->s = -1; |
| 269 | break; |
| 270 | } |
| 271 | |
| 272 | MPI_CHK( mpi_get_digit( &d, radix, s[i] ) ); |
| 273 | X->p[j / (2 * ciL)] |= d << ( (j % (2 * ciL)) << 2 ); |
| 274 | } |
| 275 | } |
| 276 | else |
| 277 | { |
| 278 | MPI_CHK( mpi_lset( X, 0 ) ); |
| 279 | |
| 280 | for( i = 0; i < slen; i++ ) |
| 281 | { |
| 282 | if( i == 0 && s[i] == '-' ) |
| 283 | { |
| 284 | X->s = -1; |
| 285 | continue; |
| 286 | } |
| 287 | |
| 288 | MPI_CHK( mpi_get_digit( &d, radix, s[i] ) ); |
| 289 | MPI_CHK( mpi_mul_int( &T, X, radix ) ); |
| 290 | |
| 291 | if( X->s == 1 ) |
| 292 | { |
| 293 | MPI_CHK( mpi_add_int( X, &T, d ) ); |
| 294 | } |
| 295 | else |
| 296 | { |
| 297 | MPI_CHK( mpi_sub_int( X, &T, d ) ); |
| 298 | } |
| 299 | } |
| 300 | } |
| 301 | |
| 302 | cleanup: |
| 303 | |
| 304 | mpi_free( &T, NULL ); |
| 305 | |
| 306 | return( ret ); |
| 307 | } |
| 308 | |
| 309 | /* |
| 310 | * Helper to write the digits high-order first |
| 311 | */ |
| 312 | static int mpi_write_hlp( mpi *X, int radix, char **p ) |
| 313 | { |
| 314 | int ret; |
| 315 | t_int r; |
| 316 | |
| 317 | if( radix < 2 || radix > 16 ) |
| 318 | return( POLARSSL_ERR_MPI_BAD_INPUT_DATA ); |
| 319 | |
| 320 | MPI_CHK( mpi_mod_int( &r, X, radix ) ); |
| 321 | MPI_CHK( mpi_div_int( X, NULL, X, radix ) ); |
| 322 | |
| 323 | if( mpi_cmp_int( X, 0 ) != 0 ) |
| 324 | MPI_CHK( mpi_write_hlp( X, radix, p ) ); |
| 325 | |
| 326 | if( r < 10 ) |
| 327 | *(*p)++ = (char)( r + 0x30 ); |
| 328 | else |
| 329 | *(*p)++ = (char)( r + 0x37 ); |
| 330 | |
| 331 | cleanup: |
| 332 | |
| 333 | return( ret ); |
| 334 | } |
| 335 | |
| 336 | /* |
| 337 | * Export into an ASCII string |
| 338 | */ |
| 339 | int mpi_write_string( const mpi *X, int radix, char *s, int *slen ) |
| 340 | { |
| 341 | int ret = 0, n; |
| 342 | char *p; |
| 343 | mpi T; |
| 344 | |
| 345 | if( radix < 2 || radix > 16 ) |
| 346 | return( POLARSSL_ERR_MPI_BAD_INPUT_DATA ); |
| 347 | |
| 348 | n = mpi_msb( X ); |
| 349 | if( radix >= 4 ) n >>= 1; |
| 350 | if( radix >= 16 ) n >>= 1; |
| 351 | n += 3; |
| 352 | |
| 353 | if( *slen < n ) |
| 354 | { |
| 355 | *slen = n; |
| 356 | return( POLARSSL_ERR_MPI_BUFFER_TOO_SMALL ); |
| 357 | } |
| 358 | |
| 359 | p = s; |
| 360 | mpi_init( &T, NULL ); |
| 361 | |
| 362 | if( X->s == -1 ) |
| 363 | *p++ = '-'; |
| 364 | |
| 365 | if( radix == 16 ) |
| 366 | { |
| 367 | int c, i, j, k; |
| 368 | |
| 369 | for( i = X->n - 1, k = 0; i >= 0; i-- ) |
| 370 | { |
| 371 | for( j = ciL - 1; j >= 0; j-- ) |
| 372 | { |
| 373 | c = ( X->p[i] >> (j << 3) ) & 0xFF; |
| 374 | |
| 375 | if( c == 0 && k == 0 && (i + j) != 0 ) |
| 376 | continue; |
| 377 | |
| 378 | p += sprintf( p, "%02X", c ); |
| 379 | k = 1; |
| 380 | } |
| 381 | } |
| 382 | } |
| 383 | else |
| 384 | { |
| 385 | MPI_CHK( mpi_copy( &T, X ) ); |
| 386 | |
| 387 | if( T.s == -1 ) |
| 388 | T.s = 1; |
| 389 | |
| 390 | MPI_CHK( mpi_write_hlp( &T, radix, &p ) ); |
| 391 | } |
| 392 | |
| 393 | *p++ = '\0'; |
| 394 | *slen = p - s; |
| 395 | |
| 396 | cleanup: |
| 397 | |
| 398 | mpi_free( &T, NULL ); |
| 399 | |
| 400 | return( ret ); |
| 401 | } |
| 402 | |
| 403 | /* |
| 404 | * Read X from an opened file |
| 405 | */ |
| 406 | int mpi_read_file( mpi *X, int radix, FILE *fin ) |
| 407 | { |
| 408 | t_int d; |
| 409 | int slen; |
| 410 | char *p; |
| 411 | char s[1024]; |
| 412 | |
| 413 | memset( s, 0, sizeof( s ) ); |
| 414 | if( fgets( s, sizeof( s ) - 1, fin ) == NULL ) |
| 415 | return( POLARSSL_ERR_MPI_FILE_IO_ERROR ); |
| 416 | |
| 417 | slen = strlen( s ); |
| 418 | if( s[slen - 1] == '\n' ) { slen--; s[slen] = '\0'; } |
| 419 | if( s[slen - 1] == '\r' ) { slen--; s[slen] = '\0'; } |
| 420 | |
| 421 | p = s + slen; |
| 422 | while( --p >= s ) |
| 423 | if( mpi_get_digit( &d, radix, *p ) != 0 ) |
| 424 | break; |
| 425 | |
| 426 | return( mpi_read_string( X, radix, p + 1 ) ); |
| 427 | } |
| 428 | |
| 429 | /* |
| 430 | * Write X into an opened file (or stdout if fout == NULL) |
| 431 | */ |
| 432 | int mpi_write_file( const char *p, const mpi *X, int radix, FILE *fout ) |
| 433 | { |
| 434 | int n, ret; |
| 435 | size_t slen; |
| 436 | size_t plen; |
| 437 | char s[2048]; |
| 438 | |
| 439 | n = sizeof( s ); |
| 440 | memset( s, 0, n ); |
| 441 | n -= 2; |
| 442 | |
| 443 | MPI_CHK( mpi_write_string( X, radix, s, (int *) &n ) ); |
| 444 | |
| 445 | if( p == NULL ) p = ""; |
| 446 | |
| 447 | plen = strlen( p ); |
| 448 | slen = strlen( s ); |
| 449 | s[slen++] = '\r'; |
| 450 | s[slen++] = '\n'; |
| 451 | |
| 452 | if( fout != NULL ) |
| 453 | { |
| 454 | if( fwrite( p, 1, plen, fout ) != plen || |
| 455 | fwrite( s, 1, slen, fout ) != slen ) |
| 456 | return( POLARSSL_ERR_MPI_FILE_IO_ERROR ); |
| 457 | } |
| 458 | else |
| 459 | printf( "%s%s", p, s ); |
| 460 | |
| 461 | cleanup: |
| 462 | |
| 463 | return( ret ); |
| 464 | } |
| 465 | |
| 466 | /* |
| 467 | * Import X from unsigned binary data, big endian |
| 468 | */ |
| 469 | int mpi_read_binary( mpi *X, const unsigned char *buf, int buflen ) |
| 470 | { |
| 471 | int ret, i, j, n; |
| 472 | |
| 473 | for( n = 0; n < buflen; n++ ) |
| 474 | if( buf[n] != 0 ) |
| 475 | break; |
| 476 | |
| 477 | MPI_CHK( mpi_grow( X, CHARS_TO_LIMBS( buflen - n ) ) ); |
| 478 | MPI_CHK( mpi_lset( X, 0 ) ); |
| 479 | |
| 480 | for( i = buflen - 1, j = 0; i >= n; i--, j++ ) |
| 481 | X->p[j / ciL] |= ((t_int) buf[i]) << ((j % ciL) << 3); |
| 482 | |
| 483 | cleanup: |
| 484 | |
| 485 | return( ret ); |
| 486 | } |
| 487 | |
| 488 | /* |
| 489 | * Export X into unsigned binary data, big endian |
| 490 | */ |
| 491 | int mpi_write_binary( const mpi *X, unsigned char *buf, int buflen ) |
| 492 | { |
| 493 | int i, j, n; |
| 494 | |
| 495 | n = mpi_size( X ); |
| 496 | |
| 497 | if( buflen < n ) |
| 498 | return( POLARSSL_ERR_MPI_BUFFER_TOO_SMALL ); |
| 499 | |
| 500 | memset( buf, 0, buflen ); |
| 501 | |
| 502 | for( i = buflen - 1, j = 0; n > 0; i--, j++, n-- ) |
| 503 | buf[i] = (unsigned char)( X->p[j / ciL] >> ((j % ciL) << 3) ); |
| 504 | |
| 505 | return( 0 ); |
| 506 | } |
| 507 | |
| 508 | /* |
| 509 | * Left-shift: X <<= count |
| 510 | */ |
| 511 | int mpi_shift_l( mpi *X, int count ) |
| 512 | { |
| 513 | int ret, i, v0, t1; |
| 514 | t_int r0 = 0, r1; |
| 515 | |
| 516 | v0 = count / (biL ); |
| 517 | t1 = count & (biL - 1); |
| 518 | |
| 519 | i = mpi_msb( X ) + count; |
| 520 | |
| 521 | if( X->n * (int) biL < i ) |
| 522 | MPI_CHK( mpi_grow( X, BITS_TO_LIMBS( i ) ) ); |
| 523 | |
| 524 | ret = 0; |
| 525 | |
| 526 | /* |
| 527 | * shift by count / limb_size |
| 528 | */ |
| 529 | if( v0 > 0 ) |
| 530 | { |
| 531 | for( i = X->n - 1; i >= v0; i-- ) |
| 532 | X->p[i] = X->p[i - v0]; |
| 533 | |
| 534 | for( ; i >= 0; i-- ) |
| 535 | X->p[i] = 0; |
| 536 | } |
| 537 | |
| 538 | /* |
| 539 | * shift by count % limb_size |
| 540 | */ |
| 541 | if( t1 > 0 ) |
| 542 | { |
| 543 | for( i = v0; i < X->n; i++ ) |
| 544 | { |
| 545 | r1 = X->p[i] >> (biL - t1); |
| 546 | X->p[i] <<= t1; |
| 547 | X->p[i] |= r0; |
| 548 | r0 = r1; |
| 549 | } |
| 550 | } |
| 551 | |
| 552 | cleanup: |
| 553 | |
| 554 | return( ret ); |
| 555 | } |
| 556 | |
| 557 | /* |
| 558 | * Right-shift: X >>= count |
| 559 | */ |
| 560 | int mpi_shift_r( mpi *X, int count ) |
| 561 | { |
| 562 | int i, v0, v1; |
| 563 | t_int r0 = 0, r1; |
| 564 | |
| 565 | v0 = count / biL; |
| 566 | v1 = count & (biL - 1); |
| 567 | |
| 568 | /* |
| 569 | * shift by count / limb_size |
| 570 | */ |
| 571 | if( v0 > 0 ) |
| 572 | { |
| 573 | for( i = 0; i < X->n - v0; i++ ) |
| 574 | X->p[i] = X->p[i + v0]; |
| 575 | |
| 576 | for( ; i < X->n; i++ ) |
| 577 | X->p[i] = 0; |
| 578 | } |
| 579 | |
| 580 | /* |
| 581 | * shift by count % limb_size |
| 582 | */ |
| 583 | if( v1 > 0 ) |
| 584 | { |
| 585 | for( i = X->n - 1; i >= 0; i-- ) |
| 586 | { |
| 587 | r1 = X->p[i] << (biL - v1); |
| 588 | X->p[i] >>= v1; |
| 589 | X->p[i] |= r0; |
| 590 | r0 = r1; |
| 591 | } |
| 592 | } |
| 593 | |
| 594 | return( 0 ); |
| 595 | } |
| 596 | |
| 597 | /* |
| 598 | * Compare unsigned values |
| 599 | */ |
| 600 | int mpi_cmp_abs( const mpi *X, const mpi *Y ) |
| 601 | { |
| 602 | int i, j; |
| 603 | |
| 604 | for( i = X->n - 1; i >= 0; i-- ) |
| 605 | if( X->p[i] != 0 ) |
| 606 | break; |
| 607 | |
| 608 | for( j = Y->n - 1; j >= 0; j-- ) |
| 609 | if( Y->p[j] != 0 ) |
| 610 | break; |
| 611 | |
| 612 | if( i < 0 && j < 0 ) |
| 613 | return( 0 ); |
| 614 | |
| 615 | if( i > j ) return( 1 ); |
| 616 | if( j > i ) return( -1 ); |
| 617 | |
| 618 | for( ; i >= 0; i-- ) |
| 619 | { |
| 620 | if( X->p[i] > Y->p[i] ) return( 1 ); |
| 621 | if( X->p[i] < Y->p[i] ) return( -1 ); |
| 622 | } |
| 623 | |
| 624 | return( 0 ); |
| 625 | } |
| 626 | |
| 627 | /* |
| 628 | * Compare signed values |
| 629 | */ |
| 630 | int mpi_cmp_mpi( const mpi *X, const mpi *Y ) |
| 631 | { |
| 632 | int i, j; |
| 633 | |
| 634 | for( i = X->n - 1; i >= 0; i-- ) |
| 635 | if( X->p[i] != 0 ) |
| 636 | break; |
| 637 | |
| 638 | for( j = Y->n - 1; j >= 0; j-- ) |
| 639 | if( Y->p[j] != 0 ) |
| 640 | break; |
| 641 | |
| 642 | if( i < 0 && j < 0 ) |
| 643 | return( 0 ); |
| 644 | |
| 645 | if( i > j ) return( X->s ); |
| 646 | if( j > i ) return( -X->s ); |
| 647 | |
| 648 | if( X->s > 0 && Y->s < 0 ) return( 1 ); |
| 649 | if( Y->s > 0 && X->s < 0 ) return( -1 ); |
| 650 | |
| 651 | for( ; i >= 0; i-- ) |
| 652 | { |
| 653 | if( X->p[i] > Y->p[i] ) return( X->s ); |
| 654 | if( X->p[i] < Y->p[i] ) return( -X->s ); |
| 655 | } |
| 656 | |
| 657 | return( 0 ); |
| 658 | } |
| 659 | |
| 660 | /* |
| 661 | * Compare signed values |
| 662 | */ |
| 663 | int mpi_cmp_int( const mpi *X, int z ) |
| 664 | { |
| 665 | mpi Y; |
| 666 | t_int p[1]; |
| 667 | |
| 668 | *p = ( z < 0 ) ? -z : z; |
| 669 | Y.s = ( z < 0 ) ? -1 : 1; |
| 670 | Y.n = 1; |
| 671 | Y.p = p; |
| 672 | |
| 673 | return( mpi_cmp_mpi( X, &Y ) ); |
| 674 | } |
| 675 | |
| 676 | /* |
| 677 | * Unsigned addition: X = |A| + |B| (HAC 14.7) |
| 678 | */ |
| 679 | int mpi_add_abs( mpi *X, const mpi *A, const mpi *B ) |
| 680 | { |
| 681 | int ret, i, j; |
| 682 | t_int *o, *p, c; |
| 683 | |
| 684 | if( X == B ) |
| 685 | { |
| 686 | const mpi *T = A; A = X; B = T; |
| 687 | } |
| 688 | |
| 689 | if( X != A ) |
| 690 | MPI_CHK( mpi_copy( X, A ) ); |
| 691 | |
| 692 | /* |
| 693 | * X should always be positive as a result of unsigned additions. |
| 694 | */ |
| 695 | X->s = 1; |
| 696 | |
| 697 | for( j = B->n - 1; j >= 0; j-- ) |
| 698 | if( B->p[j] != 0 ) |
| 699 | break; |
| 700 | |
| 701 | MPI_CHK( mpi_grow( X, j + 1 ) ); |
| 702 | |
| 703 | o = B->p; p = X->p; c = 0; |
| 704 | |
| 705 | for( i = 0; i <= j; i++, o++, p++ ) |
| 706 | { |
| 707 | *p += c; c = ( *p < c ); |
| 708 | *p += *o; c += ( *p < *o ); |
| 709 | } |
| 710 | |
| 711 | while( c != 0 ) |
| 712 | { |
| 713 | if( i >= X->n ) |
| 714 | { |
| 715 | MPI_CHK( mpi_grow( X, i + 1 ) ); |
| 716 | p = X->p + i; |
| 717 | } |
| 718 | |
| 719 | *p += c; c = ( *p < c ); i++; |
| 720 | } |
| 721 | |
| 722 | cleanup: |
| 723 | |
| 724 | return( ret ); |
| 725 | } |
| 726 | |
| 727 | /* |
| 728 | * Helper for mpi substraction |
| 729 | */ |
| 730 | static void mpi_sub_hlp( int n, t_int *s, t_int *d ) |
| 731 | { |
| 732 | int i; |
| 733 | t_int c, z; |
| 734 | |
| 735 | for( i = c = 0; i < n; i++, s++, d++ ) |
| 736 | { |
| 737 | z = ( *d < c ); *d -= c; |
| 738 | c = ( *d < *s ) + z; *d -= *s; |
| 739 | } |
| 740 | |
| 741 | while( c != 0 ) |
| 742 | { |
| 743 | z = ( *d < c ); *d -= c; |
| 744 | c = z; i++; d++; |
| 745 | } |
| 746 | } |
| 747 | |
| 748 | /* |
| 749 | * Unsigned substraction: X = |A| - |B| (HAC 14.9) |
| 750 | */ |
| 751 | int mpi_sub_abs( mpi *X, const mpi *A, const mpi *B ) |
| 752 | { |
| 753 | mpi TB; |
| 754 | int ret, n; |
| 755 | |
| 756 | if( mpi_cmp_abs( A, B ) < 0 ) |
| 757 | return( POLARSSL_ERR_MPI_NEGATIVE_VALUE ); |
| 758 | |
| 759 | mpi_init( &TB, NULL ); |
| 760 | |
| 761 | if( X == B ) |
| 762 | { |
| 763 | MPI_CHK( mpi_copy( &TB, B ) ); |
| 764 | B = &TB; |
| 765 | } |
| 766 | |
| 767 | if( X != A ) |
| 768 | MPI_CHK( mpi_copy( X, A ) ); |
| 769 | |
| 770 | /* |
| 771 | * X should always be positive as a result of unsigned substractions. |
| 772 | */ |
| 773 | X->s = 1; |
| 774 | |
| 775 | ret = 0; |
| 776 | |
| 777 | for( n = B->n - 1; n >= 0; n-- ) |
| 778 | if( B->p[n] != 0 ) |
| 779 | break; |
| 780 | |
| 781 | mpi_sub_hlp( n + 1, B->p, X->p ); |
| 782 | |
| 783 | cleanup: |
| 784 | |
| 785 | mpi_free( &TB, NULL ); |
| 786 | |
| 787 | return( ret ); |
| 788 | } |
| 789 | |
| 790 | /* |
| 791 | * Signed addition: X = A + B |
| 792 | */ |
| 793 | int mpi_add_mpi( mpi *X, const mpi *A, const mpi *B ) |
| 794 | { |
| 795 | int ret, s = A->s; |
| 796 | |
| 797 | if( A->s * B->s < 0 ) |
| 798 | { |
| 799 | if( mpi_cmp_abs( A, B ) >= 0 ) |
| 800 | { |
| 801 | MPI_CHK( mpi_sub_abs( X, A, B ) ); |
| 802 | X->s = s; |
| 803 | } |
| 804 | else |
| 805 | { |
| 806 | MPI_CHK( mpi_sub_abs( X, B, A ) ); |
| 807 | X->s = -s; |
| 808 | } |
| 809 | } |
| 810 | else |
| 811 | { |
| 812 | MPI_CHK( mpi_add_abs( X, A, B ) ); |
| 813 | X->s = s; |
| 814 | } |
| 815 | |
| 816 | cleanup: |
| 817 | |
| 818 | return( ret ); |
| 819 | } |
| 820 | |
| 821 | /* |
| 822 | * Signed substraction: X = A - B |
| 823 | */ |
| 824 | int mpi_sub_mpi( mpi *X, const mpi *A, const mpi *B ) |
| 825 | { |
| 826 | int ret, s = A->s; |
| 827 | |
| 828 | if( A->s * B->s > 0 ) |
| 829 | { |
| 830 | if( mpi_cmp_abs( A, B ) >= 0 ) |
| 831 | { |
| 832 | MPI_CHK( mpi_sub_abs( X, A, B ) ); |
| 833 | X->s = s; |
| 834 | } |
| 835 | else |
| 836 | { |
| 837 | MPI_CHK( mpi_sub_abs( X, B, A ) ); |
| 838 | X->s = -s; |
| 839 | } |
| 840 | } |
| 841 | else |
| 842 | { |
| 843 | MPI_CHK( mpi_add_abs( X, A, B ) ); |
| 844 | X->s = s; |
| 845 | } |
| 846 | |
| 847 | cleanup: |
| 848 | |
| 849 | return( ret ); |
| 850 | } |
| 851 | |
| 852 | /* |
| 853 | * Signed addition: X = A + b |
| 854 | */ |
| 855 | int mpi_add_int( mpi *X, const mpi *A, int b ) |
| 856 | { |
| 857 | mpi _B; |
| 858 | t_int p[1]; |
| 859 | |
| 860 | p[0] = ( b < 0 ) ? -b : b; |
| 861 | _B.s = ( b < 0 ) ? -1 : 1; |
| 862 | _B.n = 1; |
| 863 | _B.p = p; |
| 864 | |
| 865 | return( mpi_add_mpi( X, A, &_B ) ); |
| 866 | } |
| 867 | |
| 868 | /* |
| 869 | * Signed substraction: X = A - b |
| 870 | */ |
| 871 | int mpi_sub_int( mpi *X, const mpi *A, int b ) |
| 872 | { |
| 873 | mpi _B; |
| 874 | t_int p[1]; |
| 875 | |
| 876 | p[0] = ( b < 0 ) ? -b : b; |
| 877 | _B.s = ( b < 0 ) ? -1 : 1; |
| 878 | _B.n = 1; |
| 879 | _B.p = p; |
| 880 | |
| 881 | return( mpi_sub_mpi( X, A, &_B ) ); |
| 882 | } |
| 883 | |
| 884 | /* |
| 885 | * Helper for mpi multiplication |
| 886 | */ |
| 887 | static void mpi_mul_hlp( int i, t_int *s, t_int *d, t_int b ) |
| 888 | { |
| 889 | t_int c = 0, t = 0; |
| 890 | |
| 891 | #if defined(MULADDC_HUIT) |
| 892 | for( ; i >= 8; i -= 8 ) |
| 893 | { |
| 894 | MULADDC_INIT |
| 895 | MULADDC_HUIT |
| 896 | MULADDC_STOP |
| 897 | } |
| 898 | |
| 899 | for( ; i > 0; i-- ) |
| 900 | { |
| 901 | MULADDC_INIT |
| 902 | MULADDC_CORE |
| 903 | MULADDC_STOP |
| 904 | } |
| 905 | #else |
| 906 | for( ; i >= 16; i -= 16 ) |
| 907 | { |
| 908 | MULADDC_INIT |
| 909 | MULADDC_CORE MULADDC_CORE |
| 910 | MULADDC_CORE MULADDC_CORE |
| 911 | MULADDC_CORE MULADDC_CORE |
| 912 | MULADDC_CORE MULADDC_CORE |
| 913 | |
| 914 | MULADDC_CORE MULADDC_CORE |
| 915 | MULADDC_CORE MULADDC_CORE |
| 916 | MULADDC_CORE MULADDC_CORE |
| 917 | MULADDC_CORE MULADDC_CORE |
| 918 | MULADDC_STOP |
| 919 | } |
| 920 | |
| 921 | for( ; i >= 8; i -= 8 ) |
| 922 | { |
| 923 | MULADDC_INIT |
| 924 | MULADDC_CORE MULADDC_CORE |
| 925 | MULADDC_CORE MULADDC_CORE |
| 926 | |
| 927 | MULADDC_CORE MULADDC_CORE |
| 928 | MULADDC_CORE MULADDC_CORE |
| 929 | MULADDC_STOP |
| 930 | } |
| 931 | |
| 932 | for( ; i > 0; i-- ) |
| 933 | { |
| 934 | MULADDC_INIT |
| 935 | MULADDC_CORE |
| 936 | MULADDC_STOP |
| 937 | } |
| 938 | #endif |
| 939 | |
| 940 | t++; |
| 941 | |
| 942 | do { |
| 943 | *d += c; c = ( *d < c ); d++; |
| 944 | } |
| 945 | while( c != 0 ); |
| 946 | } |
| 947 | |
| 948 | /* |
| 949 | * Baseline multiplication: X = A * B (HAC 14.12) |
| 950 | */ |
| 951 | int mpi_mul_mpi( mpi *X, const mpi *A, const mpi *B ) |
| 952 | { |
| 953 | int ret, i, j; |
| 954 | mpi TA, TB; |
| 955 | |
| 956 | mpi_init( &TA, &TB, NULL ); |
| 957 | |
| 958 | if( X == A ) { MPI_CHK( mpi_copy( &TA, A ) ); A = &TA; } |
| 959 | if( X == B ) { MPI_CHK( mpi_copy( &TB, B ) ); B = &TB; } |
| 960 | |
| 961 | for( i = A->n - 1; i >= 0; i-- ) |
| 962 | if( A->p[i] != 0 ) |
| 963 | break; |
| 964 | |
| 965 | for( j = B->n - 1; j >= 0; j-- ) |
| 966 | if( B->p[j] != 0 ) |
| 967 | break; |
| 968 | |
| 969 | MPI_CHK( mpi_grow( X, i + j + 2 ) ); |
| 970 | MPI_CHK( mpi_lset( X, 0 ) ); |
| 971 | |
| 972 | for( i++; j >= 0; j-- ) |
| 973 | mpi_mul_hlp( i, A->p, X->p + j, B->p[j] ); |
| 974 | |
| 975 | X->s = A->s * B->s; |
| 976 | |
| 977 | cleanup: |
| 978 | |
| 979 | mpi_free( &TB, &TA, NULL ); |
| 980 | |
| 981 | return( ret ); |
| 982 | } |
| 983 | |
| 984 | /* |
| 985 | * Baseline multiplication: X = A * b |
| 986 | */ |
| 987 | int mpi_mul_int( mpi *X, const mpi *A, t_int b ) |
| 988 | { |
| 989 | mpi _B; |
| 990 | t_int p[1]; |
| 991 | |
| 992 | _B.s = 1; |
| 993 | _B.n = 1; |
| 994 | _B.p = p; |
| 995 | p[0] = b; |
| 996 | |
| 997 | return( mpi_mul_mpi( X, A, &_B ) ); |
| 998 | } |
| 999 | |
| 1000 | /* |
| 1001 | * Division by mpi: A = Q * B + R (HAC 14.20) |
| 1002 | */ |
| 1003 | int mpi_div_mpi( mpi *Q, mpi *R, const mpi *A, const mpi *B ) |
| 1004 | { |
| 1005 | int ret, i, n, t, k; |
| 1006 | mpi X, Y, Z, T1, T2; |
| 1007 | |
| 1008 | if( mpi_cmp_int( B, 0 ) == 0 ) |
| 1009 | return( POLARSSL_ERR_MPI_DIVISION_BY_ZERO ); |
| 1010 | |
| 1011 | mpi_init( &X, &Y, &Z, &T1, &T2, NULL ); |
| 1012 | |
| 1013 | if( mpi_cmp_abs( A, B ) < 0 ) |
| 1014 | { |
| 1015 | if( Q != NULL ) MPI_CHK( mpi_lset( Q, 0 ) ); |
| 1016 | if( R != NULL ) MPI_CHK( mpi_copy( R, A ) ); |
| 1017 | return( 0 ); |
| 1018 | } |
| 1019 | |
| 1020 | MPI_CHK( mpi_copy( &X, A ) ); |
| 1021 | MPI_CHK( mpi_copy( &Y, B ) ); |
| 1022 | X.s = Y.s = 1; |
| 1023 | |
| 1024 | MPI_CHK( mpi_grow( &Z, A->n + 2 ) ); |
| 1025 | MPI_CHK( mpi_lset( &Z, 0 ) ); |
| 1026 | MPI_CHK( mpi_grow( &T1, 2 ) ); |
| 1027 | MPI_CHK( mpi_grow( &T2, 3 ) ); |
| 1028 | |
| 1029 | k = mpi_msb( &Y ) % biL; |
| 1030 | if( k < (int) biL - 1 ) |
| 1031 | { |
| 1032 | k = biL - 1 - k; |
| 1033 | MPI_CHK( mpi_shift_l( &X, k ) ); |
| 1034 | MPI_CHK( mpi_shift_l( &Y, k ) ); |
| 1035 | } |
| 1036 | else k = 0; |
| 1037 | |
| 1038 | n = X.n - 1; |
| 1039 | t = Y.n - 1; |
| 1040 | mpi_shift_l( &Y, biL * (n - t) ); |
| 1041 | |
| 1042 | while( mpi_cmp_mpi( &X, &Y ) >= 0 ) |
| 1043 | { |
| 1044 | Z.p[n - t]++; |
| 1045 | mpi_sub_mpi( &X, &X, &Y ); |
| 1046 | } |
| 1047 | mpi_shift_r( &Y, biL * (n - t) ); |
| 1048 | |
| 1049 | for( i = n; i > t ; i-- ) |
| 1050 | { |
| 1051 | if( X.p[i] >= Y.p[t] ) |
| 1052 | Z.p[i - t - 1] = ~0; |
| 1053 | else |
| 1054 | { |
| 1055 | #if defined(POLARSSL_HAVE_LONGLONG) |
| 1056 | t_dbl r; |
| 1057 | |
| 1058 | r = (t_dbl) X.p[i] << biL; |
| 1059 | r |= (t_dbl) X.p[i - 1]; |
| 1060 | r /= Y.p[t]; |
| 1061 | if( r > ((t_dbl) 1 << biL) - 1) |
| 1062 | r = ((t_dbl) 1 << biL) - 1; |
| 1063 | |
| 1064 | Z.p[i - t - 1] = (t_int) r; |
| 1065 | #else |
| 1066 | /* |
| 1067 | * __udiv_qrnnd_c, from gmp/longlong.h |
| 1068 | */ |
| 1069 | t_int q0, q1, r0, r1; |
| 1070 | t_int d0, d1, d, m; |
| 1071 | |
| 1072 | d = Y.p[t]; |
| 1073 | d0 = ( d << biH ) >> biH; |
| 1074 | d1 = ( d >> biH ); |
| 1075 | |
| 1076 | q1 = X.p[i] / d1; |
| 1077 | r1 = X.p[i] - d1 * q1; |
| 1078 | r1 <<= biH; |
| 1079 | r1 |= ( X.p[i - 1] >> biH ); |
| 1080 | |
| 1081 | m = q1 * d0; |
| 1082 | if( r1 < m ) |
| 1083 | { |
| 1084 | q1--, r1 += d; |
| 1085 | while( r1 >= d && r1 < m ) |
| 1086 | q1--, r1 += d; |
| 1087 | } |
| 1088 | r1 -= m; |
| 1089 | |
| 1090 | q0 = r1 / d1; |
| 1091 | r0 = r1 - d1 * q0; |
| 1092 | r0 <<= biH; |
| 1093 | r0 |= ( X.p[i - 1] << biH ) >> biH; |
| 1094 | |
| 1095 | m = q0 * d0; |
| 1096 | if( r0 < m ) |
| 1097 | { |
| 1098 | q0--, r0 += d; |
| 1099 | while( r0 >= d && r0 < m ) |
| 1100 | q0--, r0 += d; |
| 1101 | } |
| 1102 | r0 -= m; |
| 1103 | |
| 1104 | Z.p[i - t - 1] = ( q1 << biH ) | q0; |
| 1105 | #endif |
| 1106 | } |
| 1107 | |
| 1108 | Z.p[i - t - 1]++; |
| 1109 | do |
| 1110 | { |
| 1111 | Z.p[i - t - 1]--; |
| 1112 | |
| 1113 | MPI_CHK( mpi_lset( &T1, 0 ) ); |
| 1114 | T1.p[0] = (t < 1) ? 0 : Y.p[t - 1]; |
| 1115 | T1.p[1] = Y.p[t]; |
| 1116 | MPI_CHK( mpi_mul_int( &T1, &T1, Z.p[i - t - 1] ) ); |
| 1117 | |
| 1118 | MPI_CHK( mpi_lset( &T2, 0 ) ); |
| 1119 | T2.p[0] = (i < 2) ? 0 : X.p[i - 2]; |
| 1120 | T2.p[1] = (i < 1) ? 0 : X.p[i - 1]; |
| 1121 | T2.p[2] = X.p[i]; |
| 1122 | } |
| 1123 | while( mpi_cmp_mpi( &T1, &T2 ) > 0 ); |
| 1124 | |
| 1125 | MPI_CHK( mpi_mul_int( &T1, &Y, Z.p[i - t - 1] ) ); |
| 1126 | MPI_CHK( mpi_shift_l( &T1, biL * (i - t - 1) ) ); |
| 1127 | MPI_CHK( mpi_sub_mpi( &X, &X, &T1 ) ); |
| 1128 | |
| 1129 | if( mpi_cmp_int( &X, 0 ) < 0 ) |
| 1130 | { |
| 1131 | MPI_CHK( mpi_copy( &T1, &Y ) ); |
| 1132 | MPI_CHK( mpi_shift_l( &T1, biL * (i - t - 1) ) ); |
| 1133 | MPI_CHK( mpi_add_mpi( &X, &X, &T1 ) ); |
| 1134 | Z.p[i - t - 1]--; |
| 1135 | } |
| 1136 | } |
| 1137 | |
| 1138 | if( Q != NULL ) |
| 1139 | { |
| 1140 | mpi_copy( Q, &Z ); |
| 1141 | Q->s = A->s * B->s; |
| 1142 | } |
| 1143 | |
| 1144 | if( R != NULL ) |
| 1145 | { |
| 1146 | mpi_shift_r( &X, k ); |
| 1147 | mpi_copy( R, &X ); |
| 1148 | |
| 1149 | R->s = A->s; |
| 1150 | if( mpi_cmp_int( R, 0 ) == 0 ) |
| 1151 | R->s = 1; |
| 1152 | } |
| 1153 | |
| 1154 | cleanup: |
| 1155 | |
| 1156 | mpi_free( &X, &Y, &Z, &T1, &T2, NULL ); |
| 1157 | |
| 1158 | return( ret ); |
| 1159 | } |
| 1160 | |
| 1161 | /* |
| 1162 | * Division by int: A = Q * b + R |
| 1163 | * |
| 1164 | * Returns 0 if successful |
| 1165 | * 1 if memory allocation failed |
| 1166 | * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0 |
| 1167 | */ |
| 1168 | int mpi_div_int( mpi *Q, mpi *R, const mpi *A, int b ) |
| 1169 | { |
| 1170 | mpi _B; |
| 1171 | t_int p[1]; |
| 1172 | |
| 1173 | p[0] = ( b < 0 ) ? -b : b; |
| 1174 | _B.s = ( b < 0 ) ? -1 : 1; |
| 1175 | _B.n = 1; |
| 1176 | _B.p = p; |
| 1177 | |
| 1178 | return( mpi_div_mpi( Q, R, A, &_B ) ); |
| 1179 | } |
| 1180 | |
| 1181 | /* |
| 1182 | * Modulo: R = A mod B |
| 1183 | */ |
| 1184 | int mpi_mod_mpi( mpi *R, const mpi *A, const mpi *B ) |
| 1185 | { |
| 1186 | int ret; |
| 1187 | |
| 1188 | if( mpi_cmp_int( B, 0 ) < 0 ) |
| 1189 | return POLARSSL_ERR_MPI_NEGATIVE_VALUE; |
| 1190 | |
| 1191 | MPI_CHK( mpi_div_mpi( NULL, R, A, B ) ); |
| 1192 | |
| 1193 | while( mpi_cmp_int( R, 0 ) < 0 ) |
| 1194 | MPI_CHK( mpi_add_mpi( R, R, B ) ); |
| 1195 | |
| 1196 | while( mpi_cmp_mpi( R, B ) >= 0 ) |
| 1197 | MPI_CHK( mpi_sub_mpi( R, R, B ) ); |
| 1198 | |
| 1199 | cleanup: |
| 1200 | |
| 1201 | return( ret ); |
| 1202 | } |
| 1203 | |
| 1204 | /* |
| 1205 | * Modulo: r = A mod b |
| 1206 | */ |
| 1207 | int mpi_mod_int( t_int *r, const mpi *A, int b ) |
| 1208 | { |
| 1209 | int i; |
| 1210 | t_int x, y, z; |
| 1211 | |
| 1212 | if( b == 0 ) |
| 1213 | return( POLARSSL_ERR_MPI_DIVISION_BY_ZERO ); |
| 1214 | |
| 1215 | if( b < 0 ) |
| 1216 | return POLARSSL_ERR_MPI_NEGATIVE_VALUE; |
| 1217 | |
| 1218 | /* |
| 1219 | * handle trivial cases |
| 1220 | */ |
| 1221 | if( b == 1 ) |
| 1222 | { |
| 1223 | *r = 0; |
| 1224 | return( 0 ); |
| 1225 | } |
| 1226 | |
| 1227 | if( b == 2 ) |
| 1228 | { |
| 1229 | *r = A->p[0] & 1; |
| 1230 | return( 0 ); |
| 1231 | } |
| 1232 | |
| 1233 | /* |
| 1234 | * general case |
| 1235 | */ |
| 1236 | for( i = A->n - 1, y = 0; i >= 0; i-- ) |
| 1237 | { |
| 1238 | x = A->p[i]; |
| 1239 | y = ( y << biH ) | ( x >> biH ); |
| 1240 | z = y / b; |
| 1241 | y -= z * b; |
| 1242 | |
| 1243 | x <<= biH; |
| 1244 | y = ( y << biH ) | ( x >> biH ); |
| 1245 | z = y / b; |
| 1246 | y -= z * b; |
| 1247 | } |
| 1248 | |
| 1249 | /* |
| 1250 | * If A is negative, then the current y represents a negative value. |
| 1251 | * Flipping it to the positive side. |
| 1252 | */ |
| 1253 | if( A->s < 0 && y != 0 ) |
| 1254 | y = b - y; |
| 1255 | |
| 1256 | *r = y; |
| 1257 | |
| 1258 | return( 0 ); |
| 1259 | } |
| 1260 | |
| 1261 | /* |
| 1262 | * Fast Montgomery initialization (thanks to Tom St Denis) |
| 1263 | */ |
| 1264 | static void mpi_montg_init( t_int *mm, const mpi *N ) |
| 1265 | { |
| 1266 | t_int x, m0 = N->p[0]; |
| 1267 | |
| 1268 | x = m0; |
| 1269 | x += ( ( m0 + 2 ) & 4 ) << 1; |
| 1270 | x *= ( 2 - ( m0 * x ) ); |
| 1271 | |
| 1272 | if( biL >= 16 ) x *= ( 2 - ( m0 * x ) ); |
| 1273 | if( biL >= 32 ) x *= ( 2 - ( m0 * x ) ); |
| 1274 | if( biL >= 64 ) x *= ( 2 - ( m0 * x ) ); |
| 1275 | |
| 1276 | *mm = ~x + 1; |
| 1277 | } |
| 1278 | |
| 1279 | /* |
| 1280 | * Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36) |
| 1281 | */ |
| 1282 | static void mpi_montmul( mpi *A, const mpi *B, const mpi *N, t_int mm, const mpi *T ) |
| 1283 | { |
| 1284 | int i, n, m; |
| 1285 | t_int u0, u1, *d; |
| 1286 | |
| 1287 | memset( T->p, 0, T->n * ciL ); |
| 1288 | |
| 1289 | d = T->p; |
| 1290 | n = N->n; |
| 1291 | m = ( B->n < n ) ? B->n : n; |
| 1292 | |
| 1293 | for( i = 0; i < n; i++ ) |
| 1294 | { |
| 1295 | /* |
| 1296 | * T = (T + u0*B + u1*N) / 2^biL |
| 1297 | */ |
| 1298 | u0 = A->p[i]; |
| 1299 | u1 = ( d[0] + u0 * B->p[0] ) * mm; |
| 1300 | |
| 1301 | mpi_mul_hlp( m, B->p, d, u0 ); |
| 1302 | mpi_mul_hlp( n, N->p, d, u1 ); |
| 1303 | |
| 1304 | *d++ = u0; d[n + 1] = 0; |
| 1305 | } |
| 1306 | |
| 1307 | memcpy( A->p, d, (n + 1) * ciL ); |
| 1308 | |
| 1309 | if( mpi_cmp_abs( A, N ) >= 0 ) |
| 1310 | mpi_sub_hlp( n, N->p, A->p ); |
| 1311 | else |
| 1312 | /* prevent timing attacks */ |
| 1313 | mpi_sub_hlp( n, A->p, T->p ); |
| 1314 | } |
| 1315 | |
| 1316 | /* |
| 1317 | * Montgomery reduction: A = A * R^-1 mod N |
| 1318 | */ |
| 1319 | static void mpi_montred( mpi *A, const mpi *N, t_int mm, const mpi *T ) |
| 1320 | { |
| 1321 | t_int z = 1; |
| 1322 | mpi U; |
| 1323 | |
| 1324 | U.n = U.s = z; |
| 1325 | U.p = &z; |
| 1326 | |
| 1327 | mpi_montmul( A, &U, N, mm, T ); |
| 1328 | } |
| 1329 | |
| 1330 | /* |
| 1331 | * Sliding-window exponentiation: X = A^E mod N (HAC 14.85) |
| 1332 | */ |
| 1333 | int mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR ) |
| 1334 | { |
| 1335 | int ret, i, j, wsize, wbits; |
| 1336 | int bufsize, nblimbs, nbits; |
| 1337 | t_int ei, mm, state; |
| 1338 | mpi RR, T, W[64]; |
| 1339 | |
| 1340 | if( mpi_cmp_int( N, 0 ) < 0 || ( N->p[0] & 1 ) == 0 ) |
| 1341 | return( POLARSSL_ERR_MPI_BAD_INPUT_DATA ); |
| 1342 | |
| 1343 | /* |
| 1344 | * Init temps and window size |
| 1345 | */ |
| 1346 | mpi_montg_init( &mm, N ); |
| 1347 | mpi_init( &RR, &T, NULL ); |
| 1348 | memset( W, 0, sizeof( W ) ); |
| 1349 | |
| 1350 | i = mpi_msb( E ); |
| 1351 | |
| 1352 | wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 : |
| 1353 | ( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1; |
| 1354 | |
| 1355 | j = N->n + 1; |
| 1356 | MPI_CHK( mpi_grow( X, j ) ); |
| 1357 | MPI_CHK( mpi_grow( &W[1], j ) ); |
| 1358 | MPI_CHK( mpi_grow( &T, j * 2 ) ); |
| 1359 | |
| 1360 | /* |
| 1361 | * If 1st call, pre-compute R^2 mod N |
| 1362 | */ |
| 1363 | if( _RR == NULL || _RR->p == NULL ) |
| 1364 | { |
| 1365 | MPI_CHK( mpi_lset( &RR, 1 ) ); |
| 1366 | MPI_CHK( mpi_shift_l( &RR, N->n * 2 * biL ) ); |
| 1367 | MPI_CHK( mpi_mod_mpi( &RR, &RR, N ) ); |
| 1368 | |
| 1369 | if( _RR != NULL ) |
| 1370 | memcpy( _RR, &RR, sizeof( mpi ) ); |
| 1371 | } |
| 1372 | else |
| 1373 | memcpy( &RR, _RR, sizeof( mpi ) ); |
| 1374 | |
| 1375 | /* |
| 1376 | * W[1] = A * R^2 * R^-1 mod N = A * R mod N |
| 1377 | */ |
| 1378 | if( mpi_cmp_mpi( A, N ) >= 0 ) |
| 1379 | mpi_mod_mpi( &W[1], A, N ); |
| 1380 | else mpi_copy( &W[1], A ); |
| 1381 | |
| 1382 | mpi_montmul( &W[1], &RR, N, mm, &T ); |
| 1383 | |
| 1384 | /* |
| 1385 | * X = R^2 * R^-1 mod N = R mod N |
| 1386 | */ |
| 1387 | MPI_CHK( mpi_copy( X, &RR ) ); |
| 1388 | mpi_montred( X, N, mm, &T ); |
| 1389 | |
| 1390 | if( wsize > 1 ) |
| 1391 | { |
| 1392 | /* |
| 1393 | * W[1 << (wsize - 1)] = W[1] ^ (wsize - 1) |
| 1394 | */ |
| 1395 | j = 1 << (wsize - 1); |
| 1396 | |
| 1397 | MPI_CHK( mpi_grow( &W[j], N->n + 1 ) ); |
| 1398 | MPI_CHK( mpi_copy( &W[j], &W[1] ) ); |
| 1399 | |
| 1400 | for( i = 0; i < wsize - 1; i++ ) |
| 1401 | mpi_montmul( &W[j], &W[j], N, mm, &T ); |
| 1402 | |
| 1403 | /* |
| 1404 | * W[i] = W[i - 1] * W[1] |
| 1405 | */ |
| 1406 | for( i = j + 1; i < (1 << wsize); i++ ) |
| 1407 | { |
| 1408 | MPI_CHK( mpi_grow( &W[i], N->n + 1 ) ); |
| 1409 | MPI_CHK( mpi_copy( &W[i], &W[i - 1] ) ); |
| 1410 | |
| 1411 | mpi_montmul( &W[i], &W[1], N, mm, &T ); |
| 1412 | } |
| 1413 | } |
| 1414 | |
| 1415 | nblimbs = E->n; |
| 1416 | bufsize = 0; |
| 1417 | nbits = 0; |
| 1418 | wbits = 0; |
| 1419 | state = 0; |
| 1420 | |
| 1421 | while( 1 ) |
| 1422 | { |
| 1423 | if( bufsize == 0 ) |
| 1424 | { |
| 1425 | if( nblimbs-- == 0 ) |
| 1426 | break; |
| 1427 | |
| 1428 | bufsize = sizeof( t_int ) << 3; |
| 1429 | } |
| 1430 | |
| 1431 | bufsize--; |
| 1432 | |
| 1433 | ei = (E->p[nblimbs] >> bufsize) & 1; |
| 1434 | |
| 1435 | /* |
| 1436 | * skip leading 0s |
| 1437 | */ |
| 1438 | if( ei == 0 && state == 0 ) |
| 1439 | continue; |
| 1440 | |
| 1441 | if( ei == 0 && state == 1 ) |
| 1442 | { |
| 1443 | /* |
| 1444 | * out of window, square X |
| 1445 | */ |
| 1446 | mpi_montmul( X, X, N, mm, &T ); |
| 1447 | continue; |
| 1448 | } |
| 1449 | |
| 1450 | /* |
| 1451 | * add ei to current window |
| 1452 | */ |
| 1453 | state = 2; |
| 1454 | |
| 1455 | nbits++; |
| 1456 | wbits |= (ei << (wsize - nbits)); |
| 1457 | |
| 1458 | if( nbits == wsize ) |
| 1459 | { |
| 1460 | /* |
| 1461 | * X = X^wsize R^-1 mod N |
| 1462 | */ |
| 1463 | for( i = 0; i < wsize; i++ ) |
| 1464 | mpi_montmul( X, X, N, mm, &T ); |
| 1465 | |
| 1466 | /* |
| 1467 | * X = X * W[wbits] R^-1 mod N |
| 1468 | */ |
| 1469 | mpi_montmul( X, &W[wbits], N, mm, &T ); |
| 1470 | |
| 1471 | state--; |
| 1472 | nbits = 0; |
| 1473 | wbits = 0; |
| 1474 | } |
| 1475 | } |
| 1476 | |
| 1477 | /* |
| 1478 | * process the remaining bits |
| 1479 | */ |
| 1480 | for( i = 0; i < nbits; i++ ) |
| 1481 | { |
| 1482 | mpi_montmul( X, X, N, mm, &T ); |
| 1483 | |
| 1484 | wbits <<= 1; |
| 1485 | |
| 1486 | if( (wbits & (1 << wsize)) != 0 ) |
| 1487 | mpi_montmul( X, &W[1], N, mm, &T ); |
| 1488 | } |
| 1489 | |
| 1490 | /* |
| 1491 | * X = A^E * R * R^-1 mod N = A^E mod N |
| 1492 | */ |
| 1493 | mpi_montred( X, N, mm, &T ); |
| 1494 | |
| 1495 | cleanup: |
| 1496 | |
| 1497 | for( i = (1 << (wsize - 1)); i < (1 << wsize); i++ ) |
| 1498 | mpi_free( &W[i], NULL ); |
| 1499 | |
| 1500 | if( _RR != NULL ) |
| 1501 | mpi_free( &W[1], &T, NULL ); |
| 1502 | else mpi_free( &W[1], &T, &RR, NULL ); |
| 1503 | |
| 1504 | return( ret ); |
| 1505 | } |
| 1506 | |
| 1507 | /* |
| 1508 | * Greatest common divisor: G = gcd(A, B) (HAC 14.54) |
| 1509 | */ |
| 1510 | int mpi_gcd( mpi *G, const mpi *A, const mpi *B ) |
| 1511 | { |
| 1512 | int ret, lz, lzt; |
| 1513 | mpi TG, TA, TB; |
| 1514 | |
| 1515 | mpi_init( &TG, &TA, &TB, NULL ); |
| 1516 | |
| 1517 | MPI_CHK( mpi_copy( &TA, A ) ); |
| 1518 | MPI_CHK( mpi_copy( &TB, B ) ); |
| 1519 | |
| 1520 | lz = mpi_lsb( &TA ); |
| 1521 | lzt = mpi_lsb( &TB ); |
| 1522 | |
| 1523 | if ( lzt < lz ) |
| 1524 | lz = lzt; |
| 1525 | |
| 1526 | MPI_CHK( mpi_shift_r( &TA, lz ) ); |
| 1527 | MPI_CHK( mpi_shift_r( &TB, lz ) ); |
| 1528 | |
| 1529 | TA.s = TB.s = 1; |
| 1530 | |
| 1531 | while( mpi_cmp_int( &TA, 0 ) != 0 ) |
| 1532 | { |
| 1533 | MPI_CHK( mpi_shift_r( &TA, mpi_lsb( &TA ) ) ); |
| 1534 | MPI_CHK( mpi_shift_r( &TB, mpi_lsb( &TB ) ) ); |
| 1535 | |
| 1536 | if( mpi_cmp_mpi( &TA, &TB ) >= 0 ) |
| 1537 | { |
| 1538 | MPI_CHK( mpi_sub_abs( &TA, &TA, &TB ) ); |
| 1539 | MPI_CHK( mpi_shift_r( &TA, 1 ) ); |
| 1540 | } |
| 1541 | else |
| 1542 | { |
| 1543 | MPI_CHK( mpi_sub_abs( &TB, &TB, &TA ) ); |
| 1544 | MPI_CHK( mpi_shift_r( &TB, 1 ) ); |
| 1545 | } |
| 1546 | } |
| 1547 | |
| 1548 | MPI_CHK( mpi_shift_l( &TB, lz ) ); |
| 1549 | MPI_CHK( mpi_copy( G, &TB ) ); |
| 1550 | |
| 1551 | cleanup: |
| 1552 | |
| 1553 | mpi_free( &TB, &TA, &TG, NULL ); |
| 1554 | |
| 1555 | return( ret ); |
| 1556 | } |
| 1557 | |
| 1558 | #if defined(POLARSSL_GENPRIME) |
| 1559 | |
| 1560 | /* |
| 1561 | * Modular inverse: X = A^-1 mod N (HAC 14.61 / 14.64) |
| 1562 | */ |
| 1563 | int mpi_inv_mod( mpi *X, const mpi *A, const mpi *N ) |
| 1564 | { |
| 1565 | int ret; |
| 1566 | mpi G, TA, TU, U1, U2, TB, TV, V1, V2; |
| 1567 | |
| 1568 | if( mpi_cmp_int( N, 0 ) <= 0 ) |
| 1569 | return( POLARSSL_ERR_MPI_BAD_INPUT_DATA ); |
| 1570 | |
| 1571 | mpi_init( &TA, &TU, &U1, &U2, &G, |
| 1572 | &TB, &TV, &V1, &V2, NULL ); |
| 1573 | |
| 1574 | MPI_CHK( mpi_gcd( &G, A, N ) ); |
| 1575 | |
| 1576 | if( mpi_cmp_int( &G, 1 ) != 0 ) |
| 1577 | { |
| 1578 | ret = POLARSSL_ERR_MPI_NOT_ACCEPTABLE; |
| 1579 | goto cleanup; |
| 1580 | } |
| 1581 | |
| 1582 | MPI_CHK( mpi_mod_mpi( &TA, A, N ) ); |
| 1583 | MPI_CHK( mpi_copy( &TU, &TA ) ); |
| 1584 | MPI_CHK( mpi_copy( &TB, N ) ); |
| 1585 | MPI_CHK( mpi_copy( &TV, N ) ); |
| 1586 | |
| 1587 | MPI_CHK( mpi_lset( &U1, 1 ) ); |
| 1588 | MPI_CHK( mpi_lset( &U2, 0 ) ); |
| 1589 | MPI_CHK( mpi_lset( &V1, 0 ) ); |
| 1590 | MPI_CHK( mpi_lset( &V2, 1 ) ); |
| 1591 | |
| 1592 | do |
| 1593 | { |
| 1594 | while( ( TU.p[0] & 1 ) == 0 ) |
| 1595 | { |
| 1596 | MPI_CHK( mpi_shift_r( &TU, 1 ) ); |
| 1597 | |
| 1598 | if( ( U1.p[0] & 1 ) != 0 || ( U2.p[0] & 1 ) != 0 ) |
| 1599 | { |
| 1600 | MPI_CHK( mpi_add_mpi( &U1, &U1, &TB ) ); |
| 1601 | MPI_CHK( mpi_sub_mpi( &U2, &U2, &TA ) ); |
| 1602 | } |
| 1603 | |
| 1604 | MPI_CHK( mpi_shift_r( &U1, 1 ) ); |
| 1605 | MPI_CHK( mpi_shift_r( &U2, 1 ) ); |
| 1606 | } |
| 1607 | |
| 1608 | while( ( TV.p[0] & 1 ) == 0 ) |
| 1609 | { |
| 1610 | MPI_CHK( mpi_shift_r( &TV, 1 ) ); |
| 1611 | |
| 1612 | if( ( V1.p[0] & 1 ) != 0 || ( V2.p[0] & 1 ) != 0 ) |
| 1613 | { |
| 1614 | MPI_CHK( mpi_add_mpi( &V1, &V1, &TB ) ); |
| 1615 | MPI_CHK( mpi_sub_mpi( &V2, &V2, &TA ) ); |
| 1616 | } |
| 1617 | |
| 1618 | MPI_CHK( mpi_shift_r( &V1, 1 ) ); |
| 1619 | MPI_CHK( mpi_shift_r( &V2, 1 ) ); |
| 1620 | } |
| 1621 | |
| 1622 | if( mpi_cmp_mpi( &TU, &TV ) >= 0 ) |
| 1623 | { |
| 1624 | MPI_CHK( mpi_sub_mpi( &TU, &TU, &TV ) ); |
| 1625 | MPI_CHK( mpi_sub_mpi( &U1, &U1, &V1 ) ); |
| 1626 | MPI_CHK( mpi_sub_mpi( &U2, &U2, &V2 ) ); |
| 1627 | } |
| 1628 | else |
| 1629 | { |
| 1630 | MPI_CHK( mpi_sub_mpi( &TV, &TV, &TU ) ); |
| 1631 | MPI_CHK( mpi_sub_mpi( &V1, &V1, &U1 ) ); |
| 1632 | MPI_CHK( mpi_sub_mpi( &V2, &V2, &U2 ) ); |
| 1633 | } |
| 1634 | } |
| 1635 | while( mpi_cmp_int( &TU, 0 ) != 0 ); |
| 1636 | |
| 1637 | while( mpi_cmp_int( &V1, 0 ) < 0 ) |
| 1638 | MPI_CHK( mpi_add_mpi( &V1, &V1, N ) ); |
| 1639 | |
| 1640 | while( mpi_cmp_mpi( &V1, N ) >= 0 ) |
| 1641 | MPI_CHK( mpi_sub_mpi( &V1, &V1, N ) ); |
| 1642 | |
| 1643 | MPI_CHK( mpi_copy( X, &V1 ) ); |
| 1644 | |
| 1645 | cleanup: |
| 1646 | |
| 1647 | mpi_free( &V2, &V1, &TV, &TB, &G, |
| 1648 | &U2, &U1, &TU, &TA, NULL ); |
| 1649 | |
| 1650 | return( ret ); |
| 1651 | } |
| 1652 | |
| 1653 | static const int small_prime[] = |
| 1654 | { |
| 1655 | 3, 5, 7, 11, 13, 17, 19, 23, |
| 1656 | 29, 31, 37, 41, 43, 47, 53, 59, |
| 1657 | 61, 67, 71, 73, 79, 83, 89, 97, |
| 1658 | 101, 103, 107, 109, 113, 127, 131, 137, |
| 1659 | 139, 149, 151, 157, 163, 167, 173, 179, |
| 1660 | 181, 191, 193, 197, 199, 211, 223, 227, |
| 1661 | 229, 233, 239, 241, 251, 257, 263, 269, |
| 1662 | 271, 277, 281, 283, 293, 307, 311, 313, |
| 1663 | 317, 331, 337, 347, 349, 353, 359, 367, |
| 1664 | 373, 379, 383, 389, 397, 401, 409, 419, |
| 1665 | 421, 431, 433, 439, 443, 449, 457, 461, |
| 1666 | 463, 467, 479, 487, 491, 499, 503, 509, |
| 1667 | 521, 523, 541, 547, 557, 563, 569, 571, |
| 1668 | 577, 587, 593, 599, 601, 607, 613, 617, |
| 1669 | 619, 631, 641, 643, 647, 653, 659, 661, |
| 1670 | 673, 677, 683, 691, 701, 709, 719, 727, |
| 1671 | 733, 739, 743, 751, 757, 761, 769, 773, |
| 1672 | 787, 797, 809, 811, 821, 823, 827, 829, |
| 1673 | 839, 853, 857, 859, 863, 877, 881, 883, |
| 1674 | 887, 907, 911, 919, 929, 937, 941, 947, |
| 1675 | 953, 967, 971, 977, 983, 991, 997, -103 |
| 1676 | }; |
| 1677 | |
| 1678 | /* |
| 1679 | * Miller-Rabin primality test (HAC 4.24) |
| 1680 | */ |
| 1681 | int mpi_is_prime( mpi *X, int (*f_rng)(void *), void *p_rng ) |
| 1682 | { |
| 1683 | int ret, i, j, n, s, xs; |
| 1684 | mpi W, R, T, A, RR; |
| 1685 | unsigned char *p; |
| 1686 | |
| 1687 | if( mpi_cmp_int( X, 0 ) == 0 || |
| 1688 | mpi_cmp_int( X, 1 ) == 0 ) |
| 1689 | return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE ); |
| 1690 | |
| 1691 | if( mpi_cmp_int( X, 2 ) == 0 ) |
| 1692 | return( 0 ); |
| 1693 | |
| 1694 | mpi_init( &W, &R, &T, &A, &RR, NULL ); |
| 1695 | |
| 1696 | xs = X->s; X->s = 1; |
| 1697 | |
| 1698 | /* |
| 1699 | * test trivial factors first |
| 1700 | */ |
| 1701 | if( ( X->p[0] & 1 ) == 0 ) |
| 1702 | return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE ); |
| 1703 | |
| 1704 | for( i = 0; small_prime[i] > 0; i++ ) |
| 1705 | { |
| 1706 | t_int r; |
| 1707 | |
| 1708 | if( mpi_cmp_int( X, small_prime[i] ) <= 0 ) |
| 1709 | return( 0 ); |
| 1710 | |
| 1711 | MPI_CHK( mpi_mod_int( &r, X, small_prime[i] ) ); |
| 1712 | |
| 1713 | if( r == 0 ) |
| 1714 | return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE ); |
| 1715 | } |
| 1716 | |
| 1717 | /* |
| 1718 | * W = |X| - 1 |
| 1719 | * R = W >> lsb( W ) |
| 1720 | */ |
| 1721 | MPI_CHK( mpi_sub_int( &W, X, 1 ) ); |
| 1722 | s = mpi_lsb( &W ); |
| 1723 | MPI_CHK( mpi_copy( &R, &W ) ); |
| 1724 | MPI_CHK( mpi_shift_r( &R, s ) ); |
| 1725 | |
| 1726 | i = mpi_msb( X ); |
| 1727 | /* |
| 1728 | * HAC, table 4.4 |
| 1729 | */ |
| 1730 | n = ( ( i >= 1300 ) ? 2 : ( i >= 850 ) ? 3 : |
| 1731 | ( i >= 650 ) ? 4 : ( i >= 350 ) ? 8 : |
| 1732 | ( i >= 250 ) ? 12 : ( i >= 150 ) ? 18 : 27 ); |
| 1733 | |
| 1734 | for( i = 0; i < n; i++ ) |
| 1735 | { |
| 1736 | /* |
| 1737 | * pick a random A, 1 < A < |X| - 1 |
| 1738 | */ |
| 1739 | MPI_CHK( mpi_grow( &A, X->n ) ); |
| 1740 | |
| 1741 | p = (unsigned char *) A.p; |
| 1742 | for( j = 0; j < A.n * ciL; j++ ) |
| 1743 | *p++ = (unsigned char) f_rng( p_rng ); |
| 1744 | |
| 1745 | j = mpi_msb( &A ) - mpi_msb( &W ); |
| 1746 | MPI_CHK( mpi_shift_r( &A, j + 1 ) ); |
| 1747 | A.p[0] |= 3; |
| 1748 | |
| 1749 | /* |
| 1750 | * A = A^R mod |X| |
| 1751 | */ |
| 1752 | MPI_CHK( mpi_exp_mod( &A, &A, &R, X, &RR ) ); |
| 1753 | |
| 1754 | if( mpi_cmp_mpi( &A, &W ) == 0 || |
| 1755 | mpi_cmp_int( &A, 1 ) == 0 ) |
| 1756 | continue; |
| 1757 | |
| 1758 | j = 1; |
| 1759 | while( j < s && mpi_cmp_mpi( &A, &W ) != 0 ) |
| 1760 | { |
| 1761 | /* |
| 1762 | * A = A * A mod |X| |
| 1763 | */ |
| 1764 | MPI_CHK( mpi_mul_mpi( &T, &A, &A ) ); |
| 1765 | MPI_CHK( mpi_mod_mpi( &A, &T, X ) ); |
| 1766 | |
| 1767 | if( mpi_cmp_int( &A, 1 ) == 0 ) |
| 1768 | break; |
| 1769 | |
| 1770 | j++; |
| 1771 | } |
| 1772 | |
| 1773 | /* |
| 1774 | * not prime if A != |X| - 1 or A == 1 |
| 1775 | */ |
| 1776 | if( mpi_cmp_mpi( &A, &W ) != 0 || |
| 1777 | mpi_cmp_int( &A, 1 ) == 0 ) |
| 1778 | { |
| 1779 | ret = POLARSSL_ERR_MPI_NOT_ACCEPTABLE; |
| 1780 | break; |
| 1781 | } |
| 1782 | } |
| 1783 | |
| 1784 | cleanup: |
| 1785 | |
| 1786 | X->s = xs; |
| 1787 | |
| 1788 | mpi_free( &RR, &A, &T, &R, &W, NULL ); |
| 1789 | |
| 1790 | return( ret ); |
| 1791 | } |
| 1792 | |
| 1793 | /* |
| 1794 | * Prime number generation |
| 1795 | */ |
| 1796 | int mpi_gen_prime( mpi *X, int nbits, int dh_flag, |
| 1797 | int (*f_rng)(void *), void *p_rng ) |
| 1798 | { |
| 1799 | int ret, k, n; |
| 1800 | unsigned char *p; |
| 1801 | mpi Y; |
| 1802 | |
| 1803 | if( nbits < 3 ) |
| 1804 | return( POLARSSL_ERR_MPI_BAD_INPUT_DATA ); |
| 1805 | |
| 1806 | mpi_init( &Y, NULL ); |
| 1807 | |
| 1808 | n = BITS_TO_LIMBS( nbits ); |
| 1809 | |
| 1810 | MPI_CHK( mpi_grow( X, n ) ); |
| 1811 | MPI_CHK( mpi_lset( X, 0 ) ); |
| 1812 | |
| 1813 | p = (unsigned char *) X->p; |
| 1814 | for( k = 0; k < X->n * ciL; k++ ) |
| 1815 | *p++ = (unsigned char) f_rng( p_rng ); |
| 1816 | |
| 1817 | k = mpi_msb( X ); |
| 1818 | if( k < nbits ) MPI_CHK( mpi_shift_l( X, nbits - k ) ); |
| 1819 | if( k > nbits ) MPI_CHK( mpi_shift_r( X, k - nbits ) ); |
| 1820 | |
| 1821 | X->p[0] |= 3; |
| 1822 | |
| 1823 | if( dh_flag == 0 ) |
| 1824 | { |
| 1825 | while( ( ret = mpi_is_prime( X, f_rng, p_rng ) ) != 0 ) |
| 1826 | { |
| 1827 | if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE ) |
| 1828 | goto cleanup; |
| 1829 | |
| 1830 | MPI_CHK( mpi_add_int( X, X, 2 ) ); |
| 1831 | } |
| 1832 | } |
| 1833 | else |
| 1834 | { |
| 1835 | MPI_CHK( mpi_sub_int( &Y, X, 1 ) ); |
| 1836 | MPI_CHK( mpi_shift_r( &Y, 1 ) ); |
| 1837 | |
| 1838 | while( 1 ) |
| 1839 | { |
| 1840 | if( ( ret = mpi_is_prime( X, f_rng, p_rng ) ) == 0 ) |
| 1841 | { |
| 1842 | if( ( ret = mpi_is_prime( &Y, f_rng, p_rng ) ) == 0 ) |
| 1843 | break; |
| 1844 | |
| 1845 | if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE ) |
| 1846 | goto cleanup; |
| 1847 | } |
| 1848 | |
| 1849 | if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE ) |
| 1850 | goto cleanup; |
| 1851 | |
| 1852 | MPI_CHK( mpi_add_int( &Y, X, 1 ) ); |
| 1853 | MPI_CHK( mpi_add_int( X, X, 2 ) ); |
| 1854 | MPI_CHK( mpi_shift_r( &Y, 1 ) ); |
| 1855 | } |
| 1856 | } |
| 1857 | |
| 1858 | cleanup: |
| 1859 | |
| 1860 | mpi_free( &Y, NULL ); |
| 1861 | |
| 1862 | return( ret ); |
| 1863 | } |
| 1864 | |
| 1865 | #endif |