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80a47a2c TK |
1 | /* |
2 | * Multi-precision integer library | |
3 | * | |
67932e54 TK |
4 | * Copyright (C) 2006-2009, Paul Bakker <polarssl_maintainer at polarssl.org> |
5 | * All rights reserved. | |
80a47a2c | 6 | * |
67932e54 | 7 | * Joined copyright on original XySSL code with: Christophe Devine |
80a47a2c TK |
8 | * |
9 | * This program is free software; you can redistribute it and/or modify | |
10 | * it under the terms of the GNU General Public License as published by | |
11 | * the Free Software Foundation; either version 2 of the License, or | |
12 | * (at your option) any later version. | |
13 | * | |
14 | * This program is distributed in the hope that it will be useful, | |
15 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
16 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
17 | * GNU General Public License for more details. | |
18 | * | |
19 | * You should have received a copy of the GNU General Public License along | |
20 | * with this program; if not, write to the Free Software Foundation, Inc., | |
21 | * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. | |
22 | */ | |
23 | /* | |
24 | * This MPI implementation is based on: | |
25 | * | |
26 | * http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf | |
27 | * http://www.stillhq.com/extracted/gnupg-api/mpi/ | |
28 | * http://math.libtomcrypt.com/files/tommath.pdf | |
29 | */ | |
30 | ||
67932e54 TK |
31 | /* $Cambridge: exim/src/src/pdkim/bignum.c,v 1.3 2009/12/07 13:05:07 tom Exp $ */ |
32 | ||
80a47a2c TK |
33 | |
34 | #include "bignum.h" | |
35 | #include "bn_mul.h" | |
36 | ||
37 | #include <string.h> | |
38 | #include <stdlib.h> | |
39 | #include <stdarg.h> | |
40 | ||
41 | #define ciL ((int) sizeof(t_int)) /* chars in limb */ | |
42 | #define biL (ciL << 3) /* bits in limb */ | |
43 | #define biH (ciL << 2) /* half limb size */ | |
44 | ||
45 | /* | |
46 | * Convert between bits/chars and number of limbs | |
47 | */ | |
48 | #define BITS_TO_LIMBS(i) (((i) + biL - 1) / biL) | |
49 | #define CHARS_TO_LIMBS(i) (((i) + ciL - 1) / ciL) | |
50 | ||
51 | /* | |
52 | * Initialize one or more mpi | |
53 | */ | |
54 | void mpi_init( mpi *X, ... ) | |
55 | { | |
56 | va_list args; | |
57 | ||
58 | va_start( args, X ); | |
59 | ||
60 | while( X != NULL ) | |
61 | { | |
62 | X->s = 1; | |
63 | X->n = 0; | |
64 | X->p = NULL; | |
65 | ||
66 | X = va_arg( args, mpi* ); | |
67 | } | |
68 | ||
69 | va_end( args ); | |
70 | } | |
71 | ||
72 | /* | |
73 | * Unallocate one or more mpi | |
74 | */ | |
75 | void mpi_free( mpi *X, ... ) | |
76 | { | |
77 | va_list args; | |
78 | ||
79 | va_start( args, X ); | |
80 | ||
81 | while( X != NULL ) | |
82 | { | |
83 | if( X->p != NULL ) | |
84 | { | |
85 | memset( X->p, 0, X->n * ciL ); | |
86 | free( X->p ); | |
87 | } | |
88 | ||
89 | X->s = 1; | |
90 | X->n = 0; | |
91 | X->p = NULL; | |
92 | ||
93 | X = va_arg( args, mpi* ); | |
94 | } | |
95 | ||
96 | va_end( args ); | |
97 | } | |
98 | ||
99 | /* | |
100 | * Enlarge to the specified number of limbs | |
101 | */ | |
102 | int mpi_grow( mpi *X, int nblimbs ) | |
103 | { | |
104 | t_int *p; | |
105 | ||
106 | if( X->n < nblimbs ) | |
107 | { | |
108 | if( ( p = (t_int *) malloc( nblimbs * ciL ) ) == NULL ) | |
109 | return( 1 ); | |
110 | ||
111 | memset( p, 0, nblimbs * ciL ); | |
112 | ||
113 | if( X->p != NULL ) | |
114 | { | |
115 | memcpy( p, X->p, X->n * ciL ); | |
116 | memset( X->p, 0, X->n * ciL ); | |
117 | free( X->p ); | |
118 | } | |
119 | ||
120 | X->n = nblimbs; | |
121 | X->p = p; | |
122 | } | |
123 | ||
124 | return( 0 ); | |
125 | } | |
126 | ||
127 | /* | |
128 | * Copy the contents of Y into X | |
129 | */ | |
130 | int mpi_copy( mpi *X, mpi *Y ) | |
131 | { | |
132 | int ret, i; | |
133 | ||
134 | if( X == Y ) | |
135 | return( 0 ); | |
136 | ||
137 | for( i = Y->n - 1; i > 0; i-- ) | |
138 | if( Y->p[i] != 0 ) | |
139 | break; | |
140 | i++; | |
141 | ||
142 | X->s = Y->s; | |
143 | ||
144 | MPI_CHK( mpi_grow( X, i ) ); | |
145 | ||
146 | memset( X->p, 0, X->n * ciL ); | |
147 | memcpy( X->p, Y->p, i * ciL ); | |
148 | ||
149 | cleanup: | |
150 | ||
151 | return( ret ); | |
152 | } | |
153 | ||
154 | /* | |
155 | * Swap the contents of X and Y | |
156 | */ | |
157 | void mpi_swap( mpi *X, mpi *Y ) | |
158 | { | |
159 | mpi T; | |
160 | ||
161 | memcpy( &T, X, sizeof( mpi ) ); | |
162 | memcpy( X, Y, sizeof( mpi ) ); | |
163 | memcpy( Y, &T, sizeof( mpi ) ); | |
164 | } | |
165 | ||
166 | /* | |
167 | * Set value from integer | |
168 | */ | |
169 | int mpi_lset( mpi *X, int z ) | |
170 | { | |
171 | int ret; | |
172 | ||
173 | MPI_CHK( mpi_grow( X, 1 ) ); | |
174 | memset( X->p, 0, X->n * ciL ); | |
175 | ||
176 | X->p[0] = ( z < 0 ) ? -z : z; | |
177 | X->s = ( z < 0 ) ? -1 : 1; | |
178 | ||
179 | cleanup: | |
180 | ||
181 | return( ret ); | |
182 | } | |
183 | ||
184 | /* | |
185 | * Return the number of least significant bits | |
186 | */ | |
187 | int mpi_lsb( mpi *X ) | |
188 | { | |
189 | int i, j, count = 0; | |
190 | ||
191 | for( i = 0; i < X->n; i++ ) | |
192 | for( j = 0; j < (int) biL; j++, count++ ) | |
193 | if( ( ( X->p[i] >> j ) & 1 ) != 0 ) | |
194 | return( count ); | |
195 | ||
196 | return( 0 ); | |
197 | } | |
198 | ||
199 | /* | |
200 | * Return the number of most significant bits | |
201 | */ | |
202 | int mpi_msb( mpi *X ) | |
203 | { | |
204 | int i, j; | |
205 | ||
206 | for( i = X->n - 1; i > 0; i-- ) | |
207 | if( X->p[i] != 0 ) | |
208 | break; | |
209 | ||
210 | for( j = biL - 1; j >= 0; j-- ) | |
211 | if( ( ( X->p[i] >> j ) & 1 ) != 0 ) | |
212 | break; | |
213 | ||
214 | return( ( i * biL ) + j + 1 ); | |
215 | } | |
216 | ||
217 | /* | |
218 | * Return the total size in bytes | |
219 | */ | |
220 | int mpi_size( mpi *X ) | |
221 | { | |
222 | return( ( mpi_msb( X ) + 7 ) >> 3 ); | |
223 | } | |
224 | ||
225 | /* | |
226 | * Convert an ASCII character to digit value | |
227 | */ | |
228 | static int mpi_get_digit( t_int *d, int radix, char c ) | |
229 | { | |
230 | *d = 255; | |
231 | ||
232 | if( c >= 0x30 && c <= 0x39 ) *d = c - 0x30; | |
233 | if( c >= 0x41 && c <= 0x46 ) *d = c - 0x37; | |
234 | if( c >= 0x61 && c <= 0x66 ) *d = c - 0x57; | |
235 | ||
236 | if( *d >= (t_int) radix ) | |
237 | return( POLARSSL_ERR_MPI_INVALID_CHARACTER ); | |
238 | ||
239 | return( 0 ); | |
240 | } | |
241 | ||
242 | /* | |
243 | * Import from an ASCII string | |
244 | */ | |
245 | int mpi_read_string( mpi *X, int radix, char *s ) | |
246 | { | |
247 | int ret, i, j, n; | |
248 | t_int d; | |
249 | mpi T; | |
250 | ||
251 | if( radix < 2 || radix > 16 ) | |
252 | return( POLARSSL_ERR_MPI_BAD_INPUT_DATA ); | |
253 | ||
254 | mpi_init( &T, NULL ); | |
255 | ||
256 | if( radix == 16 ) | |
257 | { | |
258 | n = BITS_TO_LIMBS( strlen( s ) << 2 ); | |
259 | ||
260 | MPI_CHK( mpi_grow( X, n ) ); | |
261 | MPI_CHK( mpi_lset( X, 0 ) ); | |
262 | ||
263 | for( i = strlen( s ) - 1, j = 0; i >= 0; i--, j++ ) | |
264 | { | |
265 | if( i == 0 && s[i] == '-' ) | |
266 | { | |
267 | X->s = -1; | |
268 | break; | |
269 | } | |
270 | ||
271 | MPI_CHK( mpi_get_digit( &d, radix, s[i] ) ); | |
272 | X->p[j / (2 * ciL)] |= d << ( (j % (2 * ciL)) << 2 ); | |
273 | } | |
274 | } | |
275 | else | |
276 | { | |
277 | MPI_CHK( mpi_lset( X, 0 ) ); | |
278 | ||
279 | for( i = 0; i < (int) strlen( s ); i++ ) | |
280 | { | |
281 | if( i == 0 && s[i] == '-' ) | |
282 | { | |
283 | X->s = -1; | |
284 | continue; | |
285 | } | |
286 | ||
287 | MPI_CHK( mpi_get_digit( &d, radix, s[i] ) ); | |
288 | MPI_CHK( mpi_mul_int( &T, X, radix ) ); | |
67932e54 TK |
289 | |
290 | if( X->s == 1 ) | |
291 | { | |
292 | MPI_CHK( mpi_add_int( X, &T, d ) ); | |
293 | } | |
294 | else | |
295 | { | |
296 | MPI_CHK( mpi_sub_int( X, &T, d ) ); | |
297 | } | |
80a47a2c TK |
298 | } |
299 | } | |
300 | ||
301 | cleanup: | |
302 | ||
303 | mpi_free( &T, NULL ); | |
304 | ||
305 | return( ret ); | |
306 | } | |
307 | ||
308 | /* | |
309 | * Helper to write the digits high-order first | |
310 | */ | |
311 | static int mpi_write_hlp( mpi *X, int radix, char **p ) | |
312 | { | |
313 | int ret; | |
314 | t_int r; | |
315 | ||
316 | if( radix < 2 || radix > 16 ) | |
317 | return( POLARSSL_ERR_MPI_BAD_INPUT_DATA ); | |
318 | ||
319 | MPI_CHK( mpi_mod_int( &r, X, radix ) ); | |
320 | MPI_CHK( mpi_div_int( X, NULL, X, radix ) ); | |
321 | ||
322 | if( mpi_cmp_int( X, 0 ) != 0 ) | |
323 | MPI_CHK( mpi_write_hlp( X, radix, p ) ); | |
324 | ||
325 | if( r < 10 ) | |
326 | *(*p)++ = (char)( r + 0x30 ); | |
327 | else | |
328 | *(*p)++ = (char)( r + 0x37 ); | |
329 | ||
330 | cleanup: | |
331 | ||
332 | return( ret ); | |
333 | } | |
334 | ||
335 | /* | |
336 | * Export into an ASCII string | |
337 | */ | |
338 | int mpi_write_string( mpi *X, int radix, char *s, int *slen ) | |
339 | { | |
340 | int ret = 0, n; | |
341 | char *p; | |
342 | mpi T; | |
343 | ||
344 | if( radix < 2 || radix > 16 ) | |
345 | return( POLARSSL_ERR_MPI_BAD_INPUT_DATA ); | |
346 | ||
347 | n = mpi_msb( X ); | |
348 | if( radix >= 4 ) n >>= 1; | |
349 | if( radix >= 16 ) n >>= 1; | |
350 | n += 3; | |
351 | ||
352 | if( *slen < n ) | |
353 | { | |
354 | *slen = n; | |
355 | return( POLARSSL_ERR_MPI_BUFFER_TOO_SMALL ); | |
356 | } | |
357 | ||
358 | p = s; | |
359 | mpi_init( &T, NULL ); | |
360 | ||
361 | if( X->s == -1 ) | |
362 | *p++ = '-'; | |
363 | ||
364 | if( radix == 16 ) | |
365 | { | |
366 | int c, i, j, k; | |
367 | ||
368 | for( i = X->n - 1, k = 0; i >= 0; i-- ) | |
369 | { | |
370 | for( j = ciL - 1; j >= 0; j-- ) | |
371 | { | |
372 | c = ( X->p[i] >> (j << 3) ) & 0xFF; | |
373 | ||
374 | if( c == 0 && k == 0 && (i + j) != 0 ) | |
375 | continue; | |
376 | ||
377 | p += sprintf( p, "%02X", c ); | |
378 | k = 1; | |
379 | } | |
380 | } | |
381 | } | |
382 | else | |
383 | { | |
384 | MPI_CHK( mpi_copy( &T, X ) ); | |
67932e54 TK |
385 | |
386 | if( T.s == -1 ) | |
387 | T.s = 1; | |
388 | ||
80a47a2c TK |
389 | MPI_CHK( mpi_write_hlp( &T, radix, &p ) ); |
390 | } | |
391 | ||
392 | *p++ = '\0'; | |
393 | *slen = p - s; | |
394 | ||
395 | cleanup: | |
396 | ||
397 | mpi_free( &T, NULL ); | |
398 | ||
399 | return( ret ); | |
400 | } | |
401 | ||
402 | /* | |
403 | * Read X from an opened file | |
404 | */ | |
405 | int mpi_read_file( mpi *X, int radix, FILE *fin ) | |
406 | { | |
407 | t_int d; | |
408 | int slen; | |
409 | char *p; | |
410 | char s[1024]; | |
411 | ||
412 | memset( s, 0, sizeof( s ) ); | |
413 | if( fgets( s, sizeof( s ) - 1, fin ) == NULL ) | |
414 | return( POLARSSL_ERR_MPI_FILE_IO_ERROR ); | |
415 | ||
416 | slen = strlen( s ); | |
417 | if( s[slen - 1] == '\n' ) { slen--; s[slen] = '\0'; } | |
418 | if( s[slen - 1] == '\r' ) { slen--; s[slen] = '\0'; } | |
419 | ||
420 | p = s + slen; | |
421 | while( --p >= s ) | |
422 | if( mpi_get_digit( &d, radix, *p ) != 0 ) | |
423 | break; | |
424 | ||
425 | return( mpi_read_string( X, radix, p + 1 ) ); | |
426 | } | |
427 | ||
428 | /* | |
429 | * Write X into an opened file (or stdout if fout == NULL) | |
430 | */ | |
1ba28e2b | 431 | int mpi_write_file( const char *p, mpi *X, int radix, FILE *fout ) |
80a47a2c TK |
432 | { |
433 | int n, ret; | |
434 | size_t slen; | |
435 | size_t plen; | |
436 | char s[1024]; | |
437 | ||
438 | n = sizeof( s ); | |
439 | memset( s, 0, n ); | |
440 | n -= 2; | |
441 | ||
442 | MPI_CHK( mpi_write_string( X, radix, s, (int *) &n ) ); | |
443 | ||
444 | if( p == NULL ) p = ""; | |
445 | ||
446 | plen = strlen( p ); | |
447 | slen = strlen( s ); | |
448 | s[slen++] = '\r'; | |
449 | s[slen++] = '\n'; | |
450 | ||
451 | if( fout != NULL ) | |
452 | { | |
453 | if( fwrite( p, 1, plen, fout ) != plen || | |
454 | fwrite( s, 1, slen, fout ) != slen ) | |
455 | return( POLARSSL_ERR_MPI_FILE_IO_ERROR ); | |
456 | } | |
457 | else | |
458 | printf( "%s%s", p, s ); | |
459 | ||
460 | cleanup: | |
461 | ||
462 | return( ret ); | |
463 | } | |
464 | ||
465 | /* | |
466 | * Import X from unsigned binary data, big endian | |
467 | */ | |
468 | int mpi_read_binary( mpi *X, unsigned char *buf, int buflen ) | |
469 | { | |
470 | int ret, i, j, n; | |
471 | ||
472 | for( n = 0; n < buflen; n++ ) | |
473 | if( buf[n] != 0 ) | |
474 | break; | |
475 | ||
476 | MPI_CHK( mpi_grow( X, CHARS_TO_LIMBS( buflen - n ) ) ); | |
477 | MPI_CHK( mpi_lset( X, 0 ) ); | |
478 | ||
479 | for( i = buflen - 1, j = 0; i >= n; i--, j++ ) | |
480 | X->p[j / ciL] |= ((t_int) buf[i]) << ((j % ciL) << 3); | |
481 | ||
482 | cleanup: | |
483 | ||
484 | return( ret ); | |
485 | } | |
486 | ||
487 | /* | |
488 | * Export X into unsigned binary data, big endian | |
489 | */ | |
490 | int mpi_write_binary( mpi *X, unsigned char *buf, int buflen ) | |
491 | { | |
492 | int i, j, n; | |
493 | ||
494 | n = mpi_size( X ); | |
495 | ||
496 | if( buflen < n ) | |
497 | return( POLARSSL_ERR_MPI_BUFFER_TOO_SMALL ); | |
498 | ||
499 | memset( buf, 0, buflen ); | |
500 | ||
501 | for( i = buflen - 1, j = 0; n > 0; i--, j++, n-- ) | |
502 | buf[i] = (unsigned char)( X->p[j / ciL] >> ((j % ciL) << 3) ); | |
503 | ||
504 | return( 0 ); | |
505 | } | |
506 | ||
507 | /* | |
508 | * Left-shift: X <<= count | |
509 | */ | |
510 | int mpi_shift_l( mpi *X, int count ) | |
511 | { | |
512 | int ret, i, v0, t1; | |
513 | t_int r0 = 0, r1; | |
514 | ||
515 | v0 = count / (biL ); | |
516 | t1 = count & (biL - 1); | |
517 | ||
518 | i = mpi_msb( X ) + count; | |
519 | ||
520 | if( X->n * (int) biL < i ) | |
521 | MPI_CHK( mpi_grow( X, BITS_TO_LIMBS( i ) ) ); | |
522 | ||
523 | ret = 0; | |
524 | ||
525 | /* | |
526 | * shift by count / limb_size | |
527 | */ | |
528 | if( v0 > 0 ) | |
529 | { | |
530 | for( i = X->n - 1; i >= v0; i-- ) | |
531 | X->p[i] = X->p[i - v0]; | |
532 | ||
533 | for( ; i >= 0; i-- ) | |
534 | X->p[i] = 0; | |
535 | } | |
536 | ||
537 | /* | |
538 | * shift by count % limb_size | |
539 | */ | |
540 | if( t1 > 0 ) | |
541 | { | |
542 | for( i = v0; i < X->n; i++ ) | |
543 | { | |
544 | r1 = X->p[i] >> (biL - t1); | |
545 | X->p[i] <<= t1; | |
546 | X->p[i] |= r0; | |
547 | r0 = r1; | |
548 | } | |
549 | } | |
550 | ||
551 | cleanup: | |
552 | ||
553 | return( ret ); | |
554 | } | |
555 | ||
556 | /* | |
557 | * Right-shift: X >>= count | |
558 | */ | |
559 | int mpi_shift_r( mpi *X, int count ) | |
560 | { | |
561 | int i, v0, v1; | |
562 | t_int r0 = 0, r1; | |
563 | ||
564 | v0 = count / biL; | |
565 | v1 = count & (biL - 1); | |
566 | ||
567 | /* | |
568 | * shift by count / limb_size | |
569 | */ | |
570 | if( v0 > 0 ) | |
571 | { | |
572 | for( i = 0; i < X->n - v0; i++ ) | |
573 | X->p[i] = X->p[i + v0]; | |
574 | ||
575 | for( ; i < X->n; i++ ) | |
576 | X->p[i] = 0; | |
577 | } | |
578 | ||
579 | /* | |
580 | * shift by count % limb_size | |
581 | */ | |
582 | if( v1 > 0 ) | |
583 | { | |
584 | for( i = X->n - 1; i >= 0; i-- ) | |
585 | { | |
586 | r1 = X->p[i] << (biL - v1); | |
587 | X->p[i] >>= v1; | |
588 | X->p[i] |= r0; | |
589 | r0 = r1; | |
590 | } | |
591 | } | |
592 | ||
593 | return( 0 ); | |
594 | } | |
595 | ||
596 | /* | |
597 | * Compare unsigned values | |
598 | */ | |
599 | int mpi_cmp_abs( mpi *X, mpi *Y ) | |
600 | { | |
601 | int i, j; | |
602 | ||
603 | for( i = X->n - 1; i >= 0; i-- ) | |
604 | if( X->p[i] != 0 ) | |
605 | break; | |
606 | ||
607 | for( j = Y->n - 1; j >= 0; j-- ) | |
608 | if( Y->p[j] != 0 ) | |
609 | break; | |
610 | ||
611 | if( i < 0 && j < 0 ) | |
612 | return( 0 ); | |
613 | ||
614 | if( i > j ) return( 1 ); | |
615 | if( j > i ) return( -1 ); | |
616 | ||
617 | for( ; i >= 0; i-- ) | |
618 | { | |
619 | if( X->p[i] > Y->p[i] ) return( 1 ); | |
620 | if( X->p[i] < Y->p[i] ) return( -1 ); | |
621 | } | |
622 | ||
623 | return( 0 ); | |
624 | } | |
625 | ||
626 | /* | |
627 | * Compare signed values | |
628 | */ | |
629 | int mpi_cmp_mpi( mpi *X, mpi *Y ) | |
630 | { | |
631 | int i, j; | |
632 | ||
633 | for( i = X->n - 1; i >= 0; i-- ) | |
634 | if( X->p[i] != 0 ) | |
635 | break; | |
636 | ||
637 | for( j = Y->n - 1; j >= 0; j-- ) | |
638 | if( Y->p[j] != 0 ) | |
639 | break; | |
640 | ||
641 | if( i < 0 && j < 0 ) | |
642 | return( 0 ); | |
643 | ||
644 | if( i > j ) return( X->s ); | |
645 | if( j > i ) return( -X->s ); | |
646 | ||
647 | if( X->s > 0 && Y->s < 0 ) return( 1 ); | |
648 | if( Y->s > 0 && X->s < 0 ) return( -1 ); | |
649 | ||
650 | for( ; i >= 0; i-- ) | |
651 | { | |
652 | if( X->p[i] > Y->p[i] ) return( X->s ); | |
653 | if( X->p[i] < Y->p[i] ) return( -X->s ); | |
654 | } | |
655 | ||
656 | return( 0 ); | |
657 | } | |
658 | ||
659 | /* | |
660 | * Compare signed values | |
661 | */ | |
662 | int mpi_cmp_int( mpi *X, int z ) | |
663 | { | |
664 | mpi Y; | |
665 | t_int p[1]; | |
666 | ||
667 | *p = ( z < 0 ) ? -z : z; | |
668 | Y.s = ( z < 0 ) ? -1 : 1; | |
669 | Y.n = 1; | |
670 | Y.p = p; | |
671 | ||
672 | return( mpi_cmp_mpi( X, &Y ) ); | |
673 | } | |
674 | ||
675 | /* | |
676 | * Unsigned addition: X = |A| + |B| (HAC 14.7) | |
677 | */ | |
678 | int mpi_add_abs( mpi *X, mpi *A, mpi *B ) | |
679 | { | |
680 | int ret, i, j; | |
681 | t_int *o, *p, c; | |
682 | ||
683 | if( X == B ) | |
684 | { | |
685 | mpi *T = A; A = X; B = T; | |
686 | } | |
687 | ||
688 | if( X != A ) | |
689 | MPI_CHK( mpi_copy( X, A ) ); | |
690 | ||
67932e54 TK |
691 | /* |
692 | * X should always be positive as a result of unsigned additions. | |
693 | */ | |
694 | X->s = 1; | |
695 | ||
80a47a2c TK |
696 | for( j = B->n - 1; j >= 0; j-- ) |
697 | if( B->p[j] != 0 ) | |
698 | break; | |
699 | ||
700 | MPI_CHK( mpi_grow( X, j + 1 ) ); | |
701 | ||
702 | o = B->p; p = X->p; c = 0; | |
703 | ||
704 | for( i = 0; i <= j; i++, o++, p++ ) | |
705 | { | |
706 | *p += c; c = ( *p < c ); | |
707 | *p += *o; c += ( *p < *o ); | |
708 | } | |
709 | ||
710 | while( c != 0 ) | |
711 | { | |
712 | if( i >= X->n ) | |
713 | { | |
714 | MPI_CHK( mpi_grow( X, i + 1 ) ); | |
715 | p = X->p + i; | |
716 | } | |
717 | ||
718 | *p += c; c = ( *p < c ); i++; | |
719 | } | |
720 | ||
721 | cleanup: | |
722 | ||
723 | return( ret ); | |
724 | } | |
725 | ||
726 | /* | |
727 | * Helper for mpi substraction | |
728 | */ | |
729 | static void mpi_sub_hlp( int n, t_int *s, t_int *d ) | |
730 | { | |
731 | int i; | |
732 | t_int c, z; | |
733 | ||
734 | for( i = c = 0; i < n; i++, s++, d++ ) | |
735 | { | |
736 | z = ( *d < c ); *d -= c; | |
737 | c = ( *d < *s ) + z; *d -= *s; | |
738 | } | |
739 | ||
740 | while( c != 0 ) | |
741 | { | |
742 | z = ( *d < c ); *d -= c; | |
743 | c = z; i++; d++; | |
744 | } | |
745 | } | |
746 | ||
747 | /* | |
748 | * Unsigned substraction: X = |A| - |B| (HAC 14.9) | |
749 | */ | |
750 | int mpi_sub_abs( mpi *X, mpi *A, mpi *B ) | |
751 | { | |
752 | mpi TB; | |
753 | int ret, n; | |
754 | ||
755 | if( mpi_cmp_abs( A, B ) < 0 ) | |
756 | return( POLARSSL_ERR_MPI_NEGATIVE_VALUE ); | |
757 | ||
758 | mpi_init( &TB, NULL ); | |
759 | ||
760 | if( X == B ) | |
761 | { | |
762 | MPI_CHK( mpi_copy( &TB, B ) ); | |
763 | B = &TB; | |
764 | } | |
765 | ||
766 | if( X != A ) | |
767 | MPI_CHK( mpi_copy( X, A ) ); | |
768 | ||
67932e54 TK |
769 | /* |
770 | * X should always be positive as a result of unsigned substractions. | |
771 | */ | |
772 | X->s = 1; | |
773 | ||
80a47a2c TK |
774 | ret = 0; |
775 | ||
776 | for( n = B->n - 1; n >= 0; n-- ) | |
777 | if( B->p[n] != 0 ) | |
778 | break; | |
779 | ||
780 | mpi_sub_hlp( n + 1, B->p, X->p ); | |
781 | ||
782 | cleanup: | |
783 | ||
784 | mpi_free( &TB, NULL ); | |
785 | ||
786 | return( ret ); | |
787 | } | |
788 | ||
789 | /* | |
790 | * Signed addition: X = A + B | |
791 | */ | |
792 | int mpi_add_mpi( mpi *X, mpi *A, mpi *B ) | |
793 | { | |
794 | int ret, s = A->s; | |
795 | ||
796 | if( A->s * B->s < 0 ) | |
797 | { | |
798 | if( mpi_cmp_abs( A, B ) >= 0 ) | |
799 | { | |
800 | MPI_CHK( mpi_sub_abs( X, A, B ) ); | |
801 | X->s = s; | |
802 | } | |
803 | else | |
804 | { | |
805 | MPI_CHK( mpi_sub_abs( X, B, A ) ); | |
806 | X->s = -s; | |
807 | } | |
808 | } | |
809 | else | |
810 | { | |
811 | MPI_CHK( mpi_add_abs( X, A, B ) ); | |
812 | X->s = s; | |
813 | } | |
814 | ||
815 | cleanup: | |
816 | ||
817 | return( ret ); | |
818 | } | |
819 | ||
820 | /* | |
821 | * Signed substraction: X = A - B | |
822 | */ | |
823 | int mpi_sub_mpi( mpi *X, mpi *A, mpi *B ) | |
824 | { | |
825 | int ret, s = A->s; | |
826 | ||
827 | if( A->s * B->s > 0 ) | |
828 | { | |
829 | if( mpi_cmp_abs( A, B ) >= 0 ) | |
830 | { | |
831 | MPI_CHK( mpi_sub_abs( X, A, B ) ); | |
832 | X->s = s; | |
833 | } | |
834 | else | |
835 | { | |
836 | MPI_CHK( mpi_sub_abs( X, B, A ) ); | |
837 | X->s = -s; | |
838 | } | |
839 | } | |
840 | else | |
841 | { | |
842 | MPI_CHK( mpi_add_abs( X, A, B ) ); | |
843 | X->s = s; | |
844 | } | |
845 | ||
846 | cleanup: | |
847 | ||
848 | return( ret ); | |
849 | } | |
850 | ||
851 | /* | |
852 | * Signed addition: X = A + b | |
853 | */ | |
854 | int mpi_add_int( mpi *X, mpi *A, int b ) | |
855 | { | |
856 | mpi _B; | |
857 | t_int p[1]; | |
858 | ||
859 | p[0] = ( b < 0 ) ? -b : b; | |
860 | _B.s = ( b < 0 ) ? -1 : 1; | |
861 | _B.n = 1; | |
862 | _B.p = p; | |
863 | ||
864 | return( mpi_add_mpi( X, A, &_B ) ); | |
865 | } | |
866 | ||
867 | /* | |
868 | * Signed substraction: X = A - b | |
869 | */ | |
870 | int mpi_sub_int( mpi *X, mpi *A, int b ) | |
871 | { | |
872 | mpi _B; | |
873 | t_int p[1]; | |
874 | ||
875 | p[0] = ( b < 0 ) ? -b : b; | |
876 | _B.s = ( b < 0 ) ? -1 : 1; | |
877 | _B.n = 1; | |
878 | _B.p = p; | |
879 | ||
880 | return( mpi_sub_mpi( X, A, &_B ) ); | |
881 | } | |
882 | ||
883 | /* | |
884 | * Helper for mpi multiplication | |
885 | */ | |
886 | static void mpi_mul_hlp( int i, t_int *s, t_int *d, t_int b ) | |
887 | { | |
888 | t_int c = 0, t = 0; | |
889 | ||
890 | #if defined(MULADDC_HUIT) | |
891 | for( ; i >= 8; i -= 8 ) | |
892 | { | |
893 | MULADDC_INIT | |
894 | MULADDC_HUIT | |
895 | MULADDC_STOP | |
896 | } | |
897 | ||
898 | for( ; i > 0; i-- ) | |
899 | { | |
900 | MULADDC_INIT | |
901 | MULADDC_CORE | |
902 | MULADDC_STOP | |
903 | } | |
904 | #else | |
905 | for( ; i >= 16; i -= 16 ) | |
906 | { | |
907 | MULADDC_INIT | |
908 | MULADDC_CORE MULADDC_CORE | |
909 | MULADDC_CORE MULADDC_CORE | |
910 | MULADDC_CORE MULADDC_CORE | |
911 | MULADDC_CORE MULADDC_CORE | |
912 | ||
913 | MULADDC_CORE MULADDC_CORE | |
914 | MULADDC_CORE MULADDC_CORE | |
915 | MULADDC_CORE MULADDC_CORE | |
916 | MULADDC_CORE MULADDC_CORE | |
917 | MULADDC_STOP | |
918 | } | |
919 | ||
920 | for( ; i >= 8; i -= 8 ) | |
921 | { | |
922 | MULADDC_INIT | |
923 | MULADDC_CORE MULADDC_CORE | |
924 | MULADDC_CORE MULADDC_CORE | |
925 | ||
926 | MULADDC_CORE MULADDC_CORE | |
927 | MULADDC_CORE MULADDC_CORE | |
928 | MULADDC_STOP | |
929 | } | |
930 | ||
931 | for( ; i > 0; i-- ) | |
932 | { | |
933 | MULADDC_INIT | |
934 | MULADDC_CORE | |
935 | MULADDC_STOP | |
936 | } | |
937 | #endif | |
938 | ||
939 | t++; | |
940 | ||
941 | do { | |
942 | *d += c; c = ( *d < c ); d++; | |
943 | } | |
944 | while( c != 0 ); | |
945 | } | |
946 | ||
947 | /* | |
948 | * Baseline multiplication: X = A * B (HAC 14.12) | |
949 | */ | |
950 | int mpi_mul_mpi( mpi *X, mpi *A, mpi *B ) | |
951 | { | |
952 | int ret, i, j; | |
953 | mpi TA, TB; | |
954 | ||
955 | mpi_init( &TA, &TB, NULL ); | |
956 | ||
957 | if( X == A ) { MPI_CHK( mpi_copy( &TA, A ) ); A = &TA; } | |
958 | if( X == B ) { MPI_CHK( mpi_copy( &TB, B ) ); B = &TB; } | |
959 | ||
960 | for( i = A->n - 1; i >= 0; i-- ) | |
961 | if( A->p[i] != 0 ) | |
962 | break; | |
963 | ||
964 | for( j = B->n - 1; j >= 0; j-- ) | |
965 | if( B->p[j] != 0 ) | |
966 | break; | |
967 | ||
968 | MPI_CHK( mpi_grow( X, i + j + 2 ) ); | |
969 | MPI_CHK( mpi_lset( X, 0 ) ); | |
970 | ||
971 | for( i++; j >= 0; j-- ) | |
972 | mpi_mul_hlp( i, A->p, X->p + j, B->p[j] ); | |
973 | ||
974 | X->s = A->s * B->s; | |
975 | ||
976 | cleanup: | |
977 | ||
978 | mpi_free( &TB, &TA, NULL ); | |
979 | ||
980 | return( ret ); | |
981 | } | |
982 | ||
983 | /* | |
984 | * Baseline multiplication: X = A * b | |
985 | */ | |
986 | int mpi_mul_int( mpi *X, mpi *A, t_int b ) | |
987 | { | |
988 | mpi _B; | |
989 | t_int p[1]; | |
990 | ||
991 | _B.s = 1; | |
992 | _B.n = 1; | |
993 | _B.p = p; | |
994 | p[0] = b; | |
995 | ||
996 | return( mpi_mul_mpi( X, A, &_B ) ); | |
997 | } | |
998 | ||
999 | /* | |
1000 | * Division by mpi: A = Q * B + R (HAC 14.20) | |
1001 | */ | |
1002 | int mpi_div_mpi( mpi *Q, mpi *R, mpi *A, mpi *B ) | |
1003 | { | |
1004 | int ret, i, n, t, k; | |
1005 | mpi X, Y, Z, T1, T2; | |
1006 | ||
1007 | if( mpi_cmp_int( B, 0 ) == 0 ) | |
1008 | return( POLARSSL_ERR_MPI_DIVISION_BY_ZERO ); | |
1009 | ||
1010 | mpi_init( &X, &Y, &Z, &T1, &T2, NULL ); | |
1011 | ||
1012 | if( mpi_cmp_abs( A, B ) < 0 ) | |
1013 | { | |
1014 | if( Q != NULL ) MPI_CHK( mpi_lset( Q, 0 ) ); | |
1015 | if( R != NULL ) MPI_CHK( mpi_copy( R, A ) ); | |
1016 | return( 0 ); | |
1017 | } | |
1018 | ||
1019 | MPI_CHK( mpi_copy( &X, A ) ); | |
1020 | MPI_CHK( mpi_copy( &Y, B ) ); | |
1021 | X.s = Y.s = 1; | |
1022 | ||
1023 | MPI_CHK( mpi_grow( &Z, A->n + 2 ) ); | |
1024 | MPI_CHK( mpi_lset( &Z, 0 ) ); | |
1025 | MPI_CHK( mpi_grow( &T1, 2 ) ); | |
1026 | MPI_CHK( mpi_grow( &T2, 3 ) ); | |
1027 | ||
1028 | k = mpi_msb( &Y ) % biL; | |
1029 | if( k < (int) biL - 1 ) | |
1030 | { | |
1031 | k = biL - 1 - k; | |
1032 | MPI_CHK( mpi_shift_l( &X, k ) ); | |
1033 | MPI_CHK( mpi_shift_l( &Y, k ) ); | |
1034 | } | |
1035 | else k = 0; | |
1036 | ||
1037 | n = X.n - 1; | |
1038 | t = Y.n - 1; | |
1039 | mpi_shift_l( &Y, biL * (n - t) ); | |
1040 | ||
1041 | while( mpi_cmp_mpi( &X, &Y ) >= 0 ) | |
1042 | { | |
1043 | Z.p[n - t]++; | |
1044 | mpi_sub_mpi( &X, &X, &Y ); | |
1045 | } | |
1046 | mpi_shift_r( &Y, biL * (n - t) ); | |
1047 | ||
1048 | for( i = n; i > t ; i-- ) | |
1049 | { | |
1050 | if( X.p[i] >= Y.p[t] ) | |
1051 | Z.p[i - t - 1] = ~0; | |
1052 | else | |
1053 | { | |
1054 | #if defined(POLARSSL_HAVE_LONGLONG) | |
1055 | t_dbl r; | |
1056 | ||
1057 | r = (t_dbl) X.p[i] << biL; | |
1058 | r |= (t_dbl) X.p[i - 1]; | |
1059 | r /= Y.p[t]; | |
1060 | if( r > ((t_dbl) 1 << biL) - 1) | |
1061 | r = ((t_dbl) 1 << biL) - 1; | |
1062 | ||
1063 | Z.p[i - t - 1] = (t_int) r; | |
1064 | #else | |
1065 | /* | |
1066 | * __udiv_qrnnd_c, from gmp/longlong.h | |
1067 | */ | |
1068 | t_int q0, q1, r0, r1; | |
1069 | t_int d0, d1, d, m; | |
1070 | ||
1071 | d = Y.p[t]; | |
1072 | d0 = ( d << biH ) >> biH; | |
1073 | d1 = ( d >> biH ); | |
1074 | ||
1075 | q1 = X.p[i] / d1; | |
1076 | r1 = X.p[i] - d1 * q1; | |
1077 | r1 <<= biH; | |
1078 | r1 |= ( X.p[i - 1] >> biH ); | |
1079 | ||
1080 | m = q1 * d0; | |
1081 | if( r1 < m ) | |
1082 | { | |
1083 | q1--, r1 += d; | |
1084 | while( r1 >= d && r1 < m ) | |
1085 | q1--, r1 += d; | |
1086 | } | |
1087 | r1 -= m; | |
1088 | ||
1089 | q0 = r1 / d1; | |
1090 | r0 = r1 - d1 * q0; | |
1091 | r0 <<= biH; | |
1092 | r0 |= ( X.p[i - 1] << biH ) >> biH; | |
1093 | ||
1094 | m = q0 * d0; | |
1095 | if( r0 < m ) | |
1096 | { | |
1097 | q0--, r0 += d; | |
1098 | while( r0 >= d && r0 < m ) | |
1099 | q0--, r0 += d; | |
1100 | } | |
1101 | r0 -= m; | |
1102 | ||
1103 | Z.p[i - t - 1] = ( q1 << biH ) | q0; | |
1104 | #endif | |
1105 | } | |
1106 | ||
1107 | Z.p[i - t - 1]++; | |
1108 | do | |
1109 | { | |
1110 | Z.p[i - t - 1]--; | |
1111 | ||
1112 | MPI_CHK( mpi_lset( &T1, 0 ) ); | |
1113 | T1.p[0] = (t < 1) ? 0 : Y.p[t - 1]; | |
1114 | T1.p[1] = Y.p[t]; | |
1115 | MPI_CHK( mpi_mul_int( &T1, &T1, Z.p[i - t - 1] ) ); | |
1116 | ||
1117 | MPI_CHK( mpi_lset( &T2, 0 ) ); | |
1118 | T2.p[0] = (i < 2) ? 0 : X.p[i - 2]; | |
1119 | T2.p[1] = (i < 1) ? 0 : X.p[i - 1]; | |
1120 | T2.p[2] = X.p[i]; | |
1121 | } | |
1122 | while( mpi_cmp_mpi( &T1, &T2 ) > 0 ); | |
1123 | ||
1124 | MPI_CHK( mpi_mul_int( &T1, &Y, Z.p[i - t - 1] ) ); | |
1125 | MPI_CHK( mpi_shift_l( &T1, biL * (i - t - 1) ) ); | |
1126 | MPI_CHK( mpi_sub_mpi( &X, &X, &T1 ) ); | |
1127 | ||
1128 | if( mpi_cmp_int( &X, 0 ) < 0 ) | |
1129 | { | |
1130 | MPI_CHK( mpi_copy( &T1, &Y ) ); | |
1131 | MPI_CHK( mpi_shift_l( &T1, biL * (i - t - 1) ) ); | |
1132 | MPI_CHK( mpi_add_mpi( &X, &X, &T1 ) ); | |
1133 | Z.p[i - t - 1]--; | |
1134 | } | |
1135 | } | |
1136 | ||
1137 | if( Q != NULL ) | |
1138 | { | |
1139 | mpi_copy( Q, &Z ); | |
1140 | Q->s = A->s * B->s; | |
1141 | } | |
1142 | ||
1143 | if( R != NULL ) | |
1144 | { | |
1145 | mpi_shift_r( &X, k ); | |
1146 | mpi_copy( R, &X ); | |
1147 | ||
1148 | R->s = A->s; | |
1149 | if( mpi_cmp_int( R, 0 ) == 0 ) | |
1150 | R->s = 1; | |
1151 | } | |
1152 | ||
1153 | cleanup: | |
1154 | ||
1155 | mpi_free( &X, &Y, &Z, &T1, &T2, NULL ); | |
1156 | ||
1157 | return( ret ); | |
1158 | } | |
1159 | ||
1160 | /* | |
1161 | * Division by int: A = Q * b + R | |
1162 | * | |
1163 | * Returns 0 if successful | |
1164 | * 1 if memory allocation failed | |
1165 | * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0 | |
1166 | */ | |
1167 | int mpi_div_int( mpi *Q, mpi *R, mpi *A, int b ) | |
1168 | { | |
1169 | mpi _B; | |
1170 | t_int p[1]; | |
1171 | ||
1172 | p[0] = ( b < 0 ) ? -b : b; | |
1173 | _B.s = ( b < 0 ) ? -1 : 1; | |
1174 | _B.n = 1; | |
1175 | _B.p = p; | |
1176 | ||
1177 | return( mpi_div_mpi( Q, R, A, &_B ) ); | |
1178 | } | |
1179 | ||
1180 | /* | |
1181 | * Modulo: R = A mod B | |
1182 | */ | |
1183 | int mpi_mod_mpi( mpi *R, mpi *A, mpi *B ) | |
1184 | { | |
1185 | int ret; | |
1186 | ||
67932e54 TK |
1187 | if( mpi_cmp_int( B, 0 ) < 0 ) |
1188 | return POLARSSL_ERR_MPI_NEGATIVE_VALUE; | |
1189 | ||
80a47a2c TK |
1190 | MPI_CHK( mpi_div_mpi( NULL, R, A, B ) ); |
1191 | ||
1192 | while( mpi_cmp_int( R, 0 ) < 0 ) | |
1193 | MPI_CHK( mpi_add_mpi( R, R, B ) ); | |
1194 | ||
1195 | while( mpi_cmp_mpi( R, B ) >= 0 ) | |
1196 | MPI_CHK( mpi_sub_mpi( R, R, B ) ); | |
1197 | ||
1198 | cleanup: | |
1199 | ||
1200 | return( ret ); | |
1201 | } | |
1202 | ||
1203 | /* | |
1204 | * Modulo: r = A mod b | |
1205 | */ | |
1206 | int mpi_mod_int( t_int *r, mpi *A, int b ) | |
1207 | { | |
1208 | int i; | |
1209 | t_int x, y, z; | |
1210 | ||
1211 | if( b == 0 ) | |
1212 | return( POLARSSL_ERR_MPI_DIVISION_BY_ZERO ); | |
1213 | ||
1214 | if( b < 0 ) | |
67932e54 | 1215 | return POLARSSL_ERR_MPI_NEGATIVE_VALUE; |
80a47a2c TK |
1216 | |
1217 | /* | |
1218 | * handle trivial cases | |
1219 | */ | |
1220 | if( b == 1 ) | |
1221 | { | |
1222 | *r = 0; | |
1223 | return( 0 ); | |
1224 | } | |
1225 | ||
1226 | if( b == 2 ) | |
1227 | { | |
1228 | *r = A->p[0] & 1; | |
1229 | return( 0 ); | |
1230 | } | |
1231 | ||
1232 | /* | |
1233 | * general case | |
1234 | */ | |
1235 | for( i = A->n - 1, y = 0; i >= 0; i-- ) | |
1236 | { | |
1237 | x = A->p[i]; | |
1238 | y = ( y << biH ) | ( x >> biH ); | |
1239 | z = y / b; | |
1240 | y -= z * b; | |
1241 | ||
1242 | x <<= biH; | |
1243 | y = ( y << biH ) | ( x >> biH ); | |
1244 | z = y / b; | |
1245 | y -= z * b; | |
1246 | } | |
1247 | ||
67932e54 TK |
1248 | /* |
1249 | * If A is negative, then the current y represents a negative value. | |
1250 | * Flipping it to the positive side. | |
1251 | */ | |
1252 | if( A->s < 0 && y != 0 ) | |
1253 | y = b - y; | |
1254 | ||
80a47a2c TK |
1255 | *r = y; |
1256 | ||
1257 | return( 0 ); | |
1258 | } | |
1259 | ||
1260 | /* | |
1261 | * Fast Montgomery initialization (thanks to Tom St Denis) | |
1262 | */ | |
1263 | static void mpi_montg_init( t_int *mm, mpi *N ) | |
1264 | { | |
1265 | t_int x, m0 = N->p[0]; | |
1266 | ||
1267 | x = m0; | |
1268 | x += ( ( m0 + 2 ) & 4 ) << 1; | |
1269 | x *= ( 2 - ( m0 * x ) ); | |
1270 | ||
1271 | if( biL >= 16 ) x *= ( 2 - ( m0 * x ) ); | |
1272 | if( biL >= 32 ) x *= ( 2 - ( m0 * x ) ); | |
1273 | if( biL >= 64 ) x *= ( 2 - ( m0 * x ) ); | |
1274 | ||
1275 | *mm = ~x + 1; | |
1276 | } | |
1277 | ||
1278 | /* | |
1279 | * Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36) | |
1280 | */ | |
1281 | static void mpi_montmul( mpi *A, mpi *B, mpi *N, t_int mm, mpi *T ) | |
1282 | { | |
1283 | int i, n, m; | |
1284 | t_int u0, u1, *d; | |
1285 | ||
1286 | memset( T->p, 0, T->n * ciL ); | |
1287 | ||
1288 | d = T->p; | |
1289 | n = N->n; | |
1290 | m = ( B->n < n ) ? B->n : n; | |
1291 | ||
1292 | for( i = 0; i < n; i++ ) | |
1293 | { | |
1294 | /* | |
1295 | * T = (T + u0*B + u1*N) / 2^biL | |
1296 | */ | |
1297 | u0 = A->p[i]; | |
1298 | u1 = ( d[0] + u0 * B->p[0] ) * mm; | |
1299 | ||
1300 | mpi_mul_hlp( m, B->p, d, u0 ); | |
1301 | mpi_mul_hlp( n, N->p, d, u1 ); | |
1302 | ||
1303 | *d++ = u0; d[n + 1] = 0; | |
1304 | } | |
1305 | ||
1306 | memcpy( A->p, d, (n + 1) * ciL ); | |
1307 | ||
1308 | if( mpi_cmp_abs( A, N ) >= 0 ) | |
1309 | mpi_sub_hlp( n, N->p, A->p ); | |
1310 | else | |
1311 | /* prevent timing attacks */ | |
1312 | mpi_sub_hlp( n, A->p, T->p ); | |
1313 | } | |
1314 | ||
1315 | /* | |
1316 | * Montgomery reduction: A = A * R^-1 mod N | |
1317 | */ | |
1318 | static void mpi_montred( mpi *A, mpi *N, t_int mm, mpi *T ) | |
1319 | { | |
1320 | t_int z = 1; | |
1321 | mpi U; | |
1322 | ||
1323 | U.n = U.s = z; | |
1324 | U.p = &z; | |
1325 | ||
1326 | mpi_montmul( A, &U, N, mm, T ); | |
1327 | } | |
1328 | ||
1329 | /* | |
1330 | * Sliding-window exponentiation: X = A^E mod N (HAC 14.85) | |
1331 | */ | |
1332 | int mpi_exp_mod( mpi *X, mpi *A, mpi *E, mpi *N, mpi *_RR ) | |
1333 | { | |
1334 | int ret, i, j, wsize, wbits; | |
1335 | int bufsize, nblimbs, nbits; | |
1336 | t_int ei, mm, state; | |
1337 | mpi RR, T, W[64]; | |
1338 | ||
1339 | if( mpi_cmp_int( N, 0 ) < 0 || ( N->p[0] & 1 ) == 0 ) | |
1340 | return( POLARSSL_ERR_MPI_BAD_INPUT_DATA ); | |
1341 | ||
1342 | /* | |
1343 | * Init temps and window size | |
1344 | */ | |
1345 | mpi_montg_init( &mm, N ); | |
1346 | mpi_init( &RR, &T, NULL ); | |
1347 | memset( W, 0, sizeof( W ) ); | |
1348 | ||
1349 | i = mpi_msb( E ); | |
1350 | ||
1351 | wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 : | |
1352 | ( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1; | |
1353 | ||
1354 | j = N->n + 1; | |
1355 | MPI_CHK( mpi_grow( X, j ) ); | |
1356 | MPI_CHK( mpi_grow( &W[1], j ) ); | |
1357 | MPI_CHK( mpi_grow( &T, j * 2 ) ); | |
1358 | ||
1359 | /* | |
1360 | * If 1st call, pre-compute R^2 mod N | |
1361 | */ | |
1362 | if( _RR == NULL || _RR->p == NULL ) | |
1363 | { | |
1364 | MPI_CHK( mpi_lset( &RR, 1 ) ); | |
1365 | MPI_CHK( mpi_shift_l( &RR, N->n * 2 * biL ) ); | |
1366 | MPI_CHK( mpi_mod_mpi( &RR, &RR, N ) ); | |
1367 | ||
1368 | if( _RR != NULL ) | |
1369 | memcpy( _RR, &RR, sizeof( mpi ) ); | |
1370 | } | |
1371 | else | |
1372 | memcpy( &RR, _RR, sizeof( mpi ) ); | |
1373 | ||
1374 | /* | |
1375 | * W[1] = A * R^2 * R^-1 mod N = A * R mod N | |
1376 | */ | |
1377 | if( mpi_cmp_mpi( A, N ) >= 0 ) | |
1378 | mpi_mod_mpi( &W[1], A, N ); | |
1379 | else mpi_copy( &W[1], A ); | |
1380 | ||
1381 | mpi_montmul( &W[1], &RR, N, mm, &T ); | |
1382 | ||
1383 | /* | |
1384 | * X = R^2 * R^-1 mod N = R mod N | |
1385 | */ | |
1386 | MPI_CHK( mpi_copy( X, &RR ) ); | |
1387 | mpi_montred( X, N, mm, &T ); | |
1388 | ||
1389 | if( wsize > 1 ) | |
1390 | { | |
1391 | /* | |
1392 | * W[1 << (wsize - 1)] = W[1] ^ (wsize - 1) | |
1393 | */ | |
1394 | j = 1 << (wsize - 1); | |
1395 | ||
1396 | MPI_CHK( mpi_grow( &W[j], N->n + 1 ) ); | |
1397 | MPI_CHK( mpi_copy( &W[j], &W[1] ) ); | |
1398 | ||
1399 | for( i = 0; i < wsize - 1; i++ ) | |
1400 | mpi_montmul( &W[j], &W[j], N, mm, &T ); | |
1401 | ||
1402 | /* | |
1403 | * W[i] = W[i - 1] * W[1] | |
1404 | */ | |
1405 | for( i = j + 1; i < (1 << wsize); i++ ) | |
1406 | { | |
1407 | MPI_CHK( mpi_grow( &W[i], N->n + 1 ) ); | |
1408 | MPI_CHK( mpi_copy( &W[i], &W[i - 1] ) ); | |
1409 | ||
1410 | mpi_montmul( &W[i], &W[1], N, mm, &T ); | |
1411 | } | |
1412 | } | |
1413 | ||
1414 | nblimbs = E->n; | |
1415 | bufsize = 0; | |
1416 | nbits = 0; | |
1417 | wbits = 0; | |
1418 | state = 0; | |
1419 | ||
1420 | while( 1 ) | |
1421 | { | |
1422 | if( bufsize == 0 ) | |
1423 | { | |
1424 | if( nblimbs-- == 0 ) | |
1425 | break; | |
1426 | ||
1427 | bufsize = sizeof( t_int ) << 3; | |
1428 | } | |
1429 | ||
1430 | bufsize--; | |
1431 | ||
1432 | ei = (E->p[nblimbs] >> bufsize) & 1; | |
1433 | ||
1434 | /* | |
1435 | * skip leading 0s | |
1436 | */ | |
1437 | if( ei == 0 && state == 0 ) | |
1438 | continue; | |
1439 | ||
1440 | if( ei == 0 && state == 1 ) | |
1441 | { | |
1442 | /* | |
1443 | * out of window, square X | |
1444 | */ | |
1445 | mpi_montmul( X, X, N, mm, &T ); | |
1446 | continue; | |
1447 | } | |
1448 | ||
1449 | /* | |
1450 | * add ei to current window | |
1451 | */ | |
1452 | state = 2; | |
1453 | ||
1454 | nbits++; | |
1455 | wbits |= (ei << (wsize - nbits)); | |
1456 | ||
1457 | if( nbits == wsize ) | |
1458 | { | |
1459 | /* | |
1460 | * X = X^wsize R^-1 mod N | |
1461 | */ | |
1462 | for( i = 0; i < wsize; i++ ) | |
1463 | mpi_montmul( X, X, N, mm, &T ); | |
1464 | ||
1465 | /* | |
1466 | * X = X * W[wbits] R^-1 mod N | |
1467 | */ | |
1468 | mpi_montmul( X, &W[wbits], N, mm, &T ); | |
1469 | ||
1470 | state--; | |
1471 | nbits = 0; | |
1472 | wbits = 0; | |
1473 | } | |
1474 | } | |
1475 | ||
1476 | /* | |
1477 | * process the remaining bits | |
1478 | */ | |
1479 | for( i = 0; i < nbits; i++ ) | |
1480 | { | |
1481 | mpi_montmul( X, X, N, mm, &T ); | |
1482 | ||
1483 | wbits <<= 1; | |
1484 | ||
1485 | if( (wbits & (1 << wsize)) != 0 ) | |
1486 | mpi_montmul( X, &W[1], N, mm, &T ); | |
1487 | } | |
1488 | ||
1489 | /* | |
1490 | * X = A^E * R * R^-1 mod N = A^E mod N | |
1491 | */ | |
1492 | mpi_montred( X, N, mm, &T ); | |
1493 | ||
1494 | cleanup: | |
1495 | ||
1496 | for( i = (1 << (wsize - 1)); i < (1 << wsize); i++ ) | |
1497 | mpi_free( &W[i], NULL ); | |
1498 | ||
1499 | if( _RR != NULL ) | |
1500 | mpi_free( &W[1], &T, NULL ); | |
1501 | else mpi_free( &W[1], &T, &RR, NULL ); | |
1502 | ||
1503 | return( ret ); | |
1504 | } | |
1505 | ||
1506 | /* | |
1507 | * Greatest common divisor: G = gcd(A, B) (HAC 14.54) | |
1508 | */ | |
1509 | int mpi_gcd( mpi *G, mpi *A, mpi *B ) | |
1510 | { | |
67932e54 | 1511 | int ret, lz, lzt; |
80a47a2c TK |
1512 | mpi TG, TA, TB; |
1513 | ||
1514 | mpi_init( &TG, &TA, &TB, NULL ); | |
1515 | ||
80a47a2c TK |
1516 | MPI_CHK( mpi_copy( &TA, A ) ); |
1517 | MPI_CHK( mpi_copy( &TB, B ) ); | |
1518 | ||
67932e54 TK |
1519 | lz = mpi_lsb( &TA ); |
1520 | lzt = mpi_lsb( &TB ); | |
1521 | ||
1522 | if ( lzt < lz ) | |
1523 | lz = lzt; | |
1524 | ||
1525 | MPI_CHK( mpi_shift_r( &TA, lz ) ); | |
1526 | MPI_CHK( mpi_shift_r( &TB, lz ) ); | |
1527 | ||
80a47a2c TK |
1528 | TA.s = TB.s = 1; |
1529 | ||
1530 | while( mpi_cmp_int( &TA, 0 ) != 0 ) | |
1531 | { | |
67932e54 TK |
1532 | MPI_CHK( mpi_shift_r( &TA, mpi_lsb( &TA ) ) ); |
1533 | MPI_CHK( mpi_shift_r( &TB, mpi_lsb( &TB ) ) ); | |
80a47a2c TK |
1534 | |
1535 | if( mpi_cmp_mpi( &TA, &TB ) >= 0 ) | |
1536 | { | |
1537 | MPI_CHK( mpi_sub_abs( &TA, &TA, &TB ) ); | |
1538 | MPI_CHK( mpi_shift_r( &TA, 1 ) ); | |
1539 | } | |
1540 | else | |
1541 | { | |
1542 | MPI_CHK( mpi_sub_abs( &TB, &TB, &TA ) ); | |
1543 | MPI_CHK( mpi_shift_r( &TB, 1 ) ); | |
1544 | } | |
1545 | } | |
1546 | ||
67932e54 TK |
1547 | MPI_CHK( mpi_shift_l( &TB, lz ) ); |
1548 | MPI_CHK( mpi_copy( G, &TB ) ); | |
80a47a2c TK |
1549 | |
1550 | cleanup: | |
1551 | ||
1552 | mpi_free( &TB, &TA, &TG, NULL ); | |
1553 | ||
1554 | return( ret ); | |
1555 | } | |
1556 | ||
67932e54 TK |
1557 | #if defined(POLARSSL_GENPRIME) |
1558 | ||
80a47a2c TK |
1559 | /* |
1560 | * Modular inverse: X = A^-1 mod N (HAC 14.61 / 14.64) | |
1561 | */ | |
1562 | int mpi_inv_mod( mpi *X, mpi *A, mpi *N ) | |
1563 | { | |
1564 | int ret; | |
1565 | mpi G, TA, TU, U1, U2, TB, TV, V1, V2; | |
1566 | ||
1567 | if( mpi_cmp_int( N, 0 ) <= 0 ) | |
1568 | return( POLARSSL_ERR_MPI_BAD_INPUT_DATA ); | |
1569 | ||
1570 | mpi_init( &TA, &TU, &U1, &U2, &G, | |
1571 | &TB, &TV, &V1, &V2, NULL ); | |
1572 | ||
1573 | MPI_CHK( mpi_gcd( &G, A, N ) ); | |
1574 | ||
1575 | if( mpi_cmp_int( &G, 1 ) != 0 ) | |
1576 | { | |
1577 | ret = POLARSSL_ERR_MPI_NOT_ACCEPTABLE; | |
1578 | goto cleanup; | |
1579 | } | |
1580 | ||
1581 | MPI_CHK( mpi_mod_mpi( &TA, A, N ) ); | |
1582 | MPI_CHK( mpi_copy( &TU, &TA ) ); | |
1583 | MPI_CHK( mpi_copy( &TB, N ) ); | |
1584 | MPI_CHK( mpi_copy( &TV, N ) ); | |
1585 | ||
1586 | MPI_CHK( mpi_lset( &U1, 1 ) ); | |
1587 | MPI_CHK( mpi_lset( &U2, 0 ) ); | |
1588 | MPI_CHK( mpi_lset( &V1, 0 ) ); | |
1589 | MPI_CHK( mpi_lset( &V2, 1 ) ); | |
1590 | ||
1591 | do | |
1592 | { | |
1593 | while( ( TU.p[0] & 1 ) == 0 ) | |
1594 | { | |
1595 | MPI_CHK( mpi_shift_r( &TU, 1 ) ); | |
1596 | ||
1597 | if( ( U1.p[0] & 1 ) != 0 || ( U2.p[0] & 1 ) != 0 ) | |
1598 | { | |
1599 | MPI_CHK( mpi_add_mpi( &U1, &U1, &TB ) ); | |
1600 | MPI_CHK( mpi_sub_mpi( &U2, &U2, &TA ) ); | |
1601 | } | |
1602 | ||
1603 | MPI_CHK( mpi_shift_r( &U1, 1 ) ); | |
1604 | MPI_CHK( mpi_shift_r( &U2, 1 ) ); | |
1605 | } | |
1606 | ||
1607 | while( ( TV.p[0] & 1 ) == 0 ) | |
1608 | { | |
1609 | MPI_CHK( mpi_shift_r( &TV, 1 ) ); | |
1610 | ||
1611 | if( ( V1.p[0] & 1 ) != 0 || ( V2.p[0] & 1 ) != 0 ) | |
1612 | { | |
1613 | MPI_CHK( mpi_add_mpi( &V1, &V1, &TB ) ); | |
1614 | MPI_CHK( mpi_sub_mpi( &V2, &V2, &TA ) ); | |
1615 | } | |
1616 | ||
1617 | MPI_CHK( mpi_shift_r( &V1, 1 ) ); | |
1618 | MPI_CHK( mpi_shift_r( &V2, 1 ) ); | |
1619 | } | |
1620 | ||
1621 | if( mpi_cmp_mpi( &TU, &TV ) >= 0 ) | |
1622 | { | |
1623 | MPI_CHK( mpi_sub_mpi( &TU, &TU, &TV ) ); | |
1624 | MPI_CHK( mpi_sub_mpi( &U1, &U1, &V1 ) ); | |
1625 | MPI_CHK( mpi_sub_mpi( &U2, &U2, &V2 ) ); | |
1626 | } | |
1627 | else | |
1628 | { | |
1629 | MPI_CHK( mpi_sub_mpi( &TV, &TV, &TU ) ); | |
1630 | MPI_CHK( mpi_sub_mpi( &V1, &V1, &U1 ) ); | |
1631 | MPI_CHK( mpi_sub_mpi( &V2, &V2, &U2 ) ); | |
1632 | } | |
1633 | } | |
1634 | while( mpi_cmp_int( &TU, 0 ) != 0 ); | |
1635 | ||
1636 | while( mpi_cmp_int( &V1, 0 ) < 0 ) | |
1637 | MPI_CHK( mpi_add_mpi( &V1, &V1, N ) ); | |
1638 | ||
1639 | while( mpi_cmp_mpi( &V1, N ) >= 0 ) | |
1640 | MPI_CHK( mpi_sub_mpi( &V1, &V1, N ) ); | |
1641 | ||
1642 | MPI_CHK( mpi_copy( X, &V1 ) ); | |
1643 | ||
1644 | cleanup: | |
1645 | ||
1646 | mpi_free( &V2, &V1, &TV, &TB, &G, | |
1647 | &U2, &U1, &TU, &TA, NULL ); | |
1648 | ||
1649 | return( ret ); | |
1650 | } | |
1651 | ||
1652 | static const int small_prime[] = | |
1653 | { | |
1654 | 3, 5, 7, 11, 13, 17, 19, 23, | |
1655 | 29, 31, 37, 41, 43, 47, 53, 59, | |
1656 | 61, 67, 71, 73, 79, 83, 89, 97, | |
1657 | 101, 103, 107, 109, 113, 127, 131, 137, | |
1658 | 139, 149, 151, 157, 163, 167, 173, 179, | |
1659 | 181, 191, 193, 197, 199, 211, 223, 227, | |
1660 | 229, 233, 239, 241, 251, 257, 263, 269, | |
1661 | 271, 277, 281, 283, 293, 307, 311, 313, | |
1662 | 317, 331, 337, 347, 349, 353, 359, 367, | |
1663 | 373, 379, 383, 389, 397, 401, 409, 419, | |
1664 | 421, 431, 433, 439, 443, 449, 457, 461, | |
1665 | 463, 467, 479, 487, 491, 499, 503, 509, | |
1666 | 521, 523, 541, 547, 557, 563, 569, 571, | |
1667 | 577, 587, 593, 599, 601, 607, 613, 617, | |
1668 | 619, 631, 641, 643, 647, 653, 659, 661, | |
1669 | 673, 677, 683, 691, 701, 709, 719, 727, | |
1670 | 733, 739, 743, 751, 757, 761, 769, 773, | |
1671 | 787, 797, 809, 811, 821, 823, 827, 829, | |
1672 | 839, 853, 857, 859, 863, 877, 881, 883, | |
1673 | 887, 907, 911, 919, 929, 937, 941, 947, | |
1674 | 953, 967, 971, 977, 983, 991, 997, -103 | |
1675 | }; | |
1676 | ||
1677 | /* | |
1678 | * Miller-Rabin primality test (HAC 4.24) | |
1679 | */ | |
1680 | int mpi_is_prime( mpi *X, int (*f_rng)(void *), void *p_rng ) | |
1681 | { | |
1682 | int ret, i, j, n, s, xs; | |
1683 | mpi W, R, T, A, RR; | |
1684 | unsigned char *p; | |
1685 | ||
67932e54 TK |
1686 | if( mpi_cmp_int( X, 0 ) == 0 || |
1687 | mpi_cmp_int( X, 1 ) == 0 ) | |
1688 | return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE ); | |
1689 | ||
1690 | if( mpi_cmp_int( X, 2 ) == 0 ) | |
80a47a2c TK |
1691 | return( 0 ); |
1692 | ||
1693 | mpi_init( &W, &R, &T, &A, &RR, NULL ); | |
1694 | ||
1695 | xs = X->s; X->s = 1; | |
1696 | ||
1697 | /* | |
1698 | * test trivial factors first | |
1699 | */ | |
1700 | if( ( X->p[0] & 1 ) == 0 ) | |
1701 | return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE ); | |
1702 | ||
1703 | for( i = 0; small_prime[i] > 0; i++ ) | |
1704 | { | |
1705 | t_int r; | |
1706 | ||
1707 | if( mpi_cmp_int( X, small_prime[i] ) <= 0 ) | |
1708 | return( 0 ); | |
1709 | ||
1710 | MPI_CHK( mpi_mod_int( &r, X, small_prime[i] ) ); | |
1711 | ||
1712 | if( r == 0 ) | |
1713 | return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE ); | |
1714 | } | |
1715 | ||
1716 | /* | |
1717 | * W = |X| - 1 | |
1718 | * R = W >> lsb( W ) | |
1719 | */ | |
1720 | s = mpi_lsb( &W ); | |
1721 | MPI_CHK( mpi_sub_int( &W, X, 1 ) ); | |
1722 | MPI_CHK( mpi_copy( &R, &W ) ); | |
1723 | MPI_CHK( mpi_shift_r( &R, s ) ); | |
1724 | ||
1725 | i = mpi_msb( X ); | |
1726 | /* | |
1727 | * HAC, table 4.4 | |
1728 | */ | |
1729 | n = ( ( i >= 1300 ) ? 2 : ( i >= 850 ) ? 3 : | |
1730 | ( i >= 650 ) ? 4 : ( i >= 350 ) ? 8 : | |
1731 | ( i >= 250 ) ? 12 : ( i >= 150 ) ? 18 : 27 ); | |
1732 | ||
1733 | for( i = 0; i < n; i++ ) | |
1734 | { | |
1735 | /* | |
1736 | * pick a random A, 1 < A < |X| - 1 | |
1737 | */ | |
1738 | MPI_CHK( mpi_grow( &A, X->n ) ); | |
1739 | ||
1740 | p = (unsigned char *) A.p; | |
1741 | for( j = 0; j < A.n * ciL; j++ ) | |
1742 | *p++ = (unsigned char) f_rng( p_rng ); | |
1743 | ||
1744 | j = mpi_msb( &A ) - mpi_msb( &W ); | |
1745 | MPI_CHK( mpi_shift_r( &A, j + 1 ) ); | |
1746 | A.p[0] |= 3; | |
1747 | ||
1748 | /* | |
1749 | * A = A^R mod |X| | |
1750 | */ | |
1751 | MPI_CHK( mpi_exp_mod( &A, &A, &R, X, &RR ) ); | |
1752 | ||
1753 | if( mpi_cmp_mpi( &A, &W ) == 0 || | |
1754 | mpi_cmp_int( &A, 1 ) == 0 ) | |
1755 | continue; | |
1756 | ||
1757 | j = 1; | |
1758 | while( j < s && mpi_cmp_mpi( &A, &W ) != 0 ) | |
1759 | { | |
1760 | /* | |
1761 | * A = A * A mod |X| | |
1762 | */ | |
1763 | MPI_CHK( mpi_mul_mpi( &T, &A, &A ) ); | |
1764 | MPI_CHK( mpi_mod_mpi( &A, &T, X ) ); | |
1765 | ||
1766 | if( mpi_cmp_int( &A, 1 ) == 0 ) | |
1767 | break; | |
1768 | ||
1769 | j++; | |
1770 | } | |
1771 | ||
1772 | /* | |
1773 | * not prime if A != |X| - 1 or A == 1 | |
1774 | */ | |
1775 | if( mpi_cmp_mpi( &A, &W ) != 0 || | |
1776 | mpi_cmp_int( &A, 1 ) == 0 ) | |
1777 | { | |
1778 | ret = POLARSSL_ERR_MPI_NOT_ACCEPTABLE; | |
1779 | break; | |
1780 | } | |
1781 | } | |
1782 | ||
1783 | cleanup: | |
1784 | ||
1785 | X->s = xs; | |
1786 | ||
1787 | mpi_free( &RR, &A, &T, &R, &W, NULL ); | |
1788 | ||
1789 | return( ret ); | |
1790 | } | |
1791 | ||
1792 | /* | |
1793 | * Prime number generation | |
1794 | */ | |
1795 | int mpi_gen_prime( mpi *X, int nbits, int dh_flag, | |
1796 | int (*f_rng)(void *), void *p_rng ) | |
1797 | { | |
1798 | int ret, k, n; | |
1799 | unsigned char *p; | |
1800 | mpi Y; | |
1801 | ||
1802 | if( nbits < 3 ) | |
1803 | return( POLARSSL_ERR_MPI_BAD_INPUT_DATA ); | |
1804 | ||
1805 | mpi_init( &Y, NULL ); | |
1806 | ||
1807 | n = BITS_TO_LIMBS( nbits ); | |
1808 | ||
1809 | MPI_CHK( mpi_grow( X, n ) ); | |
1810 | MPI_CHK( mpi_lset( X, 0 ) ); | |
1811 | ||
1812 | p = (unsigned char *) X->p; | |
1813 | for( k = 0; k < X->n * ciL; k++ ) | |
1814 | *p++ = (unsigned char) f_rng( p_rng ); | |
1815 | ||
1816 | k = mpi_msb( X ); | |
1817 | if( k < nbits ) MPI_CHK( mpi_shift_l( X, nbits - k ) ); | |
1818 | if( k > nbits ) MPI_CHK( mpi_shift_r( X, k - nbits ) ); | |
1819 | ||
1820 | X->p[0] |= 3; | |
1821 | ||
1822 | if( dh_flag == 0 ) | |
1823 | { | |
1824 | while( ( ret = mpi_is_prime( X, f_rng, p_rng ) ) != 0 ) | |
1825 | { | |
1826 | if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE ) | |
1827 | goto cleanup; | |
1828 | ||
1829 | MPI_CHK( mpi_add_int( X, X, 2 ) ); | |
1830 | } | |
1831 | } | |
1832 | else | |
1833 | { | |
1834 | MPI_CHK( mpi_sub_int( &Y, X, 1 ) ); | |
1835 | MPI_CHK( mpi_shift_r( &Y, 1 ) ); | |
1836 | ||
1837 | while( 1 ) | |
1838 | { | |
1839 | if( ( ret = mpi_is_prime( X, f_rng, p_rng ) ) == 0 ) | |
1840 | { | |
1841 | if( ( ret = mpi_is_prime( &Y, f_rng, p_rng ) ) == 0 ) | |
1842 | break; | |
1843 | ||
1844 | if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE ) | |
1845 | goto cleanup; | |
1846 | } | |
1847 | ||
1848 | if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE ) | |
1849 | goto cleanup; | |
1850 | ||
1851 | MPI_CHK( mpi_add_int( &Y, X, 1 ) ); | |
1852 | MPI_CHK( mpi_add_int( X, X, 2 ) ); | |
1853 | MPI_CHK( mpi_shift_r( &Y, 1 ) ); | |
1854 | } | |
1855 | } | |
1856 | ||
1857 | cleanup: | |
1858 | ||
1859 | mpi_free( &Y, NULL ); | |
1860 | ||
1861 | return( ret ); | |
1862 | } | |
67932e54 TK |
1863 | |
1864 | #endif |