]> git.zerfleddert.de Git - proxmark3-svn/blob - common/polarssl/bignum.c
projects / proxmark3-svn / blob
? search:
summary | shortlog | log | commit | commitdiff | tree
blame | history | raw | HEAD
Merge branch 'master' into master
[proxmark3-svn] / common / polarssl / bignum.c
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 "polarssl_config.h"
34
35 #if defined(POLARSSL_BIGNUM_C)
36
37 #include "bignum.h"
38 #include "bn_mul.h"
39
40 #include <stdlib.h>
41
42 #define ciL (sizeof(t_uint)) /* chars in limb */
43 #define biL (ciL << 3) /* bits in limb */
44 #define biH (ciL << 2) /* half limb size */
45
46 /*
47 * Convert between bits/chars and number of limbs
48 */
49 #define BITS_TO_LIMBS(i) (((i) + biL - 1) / biL)
50 #define CHARS_TO_LIMBS(i) (((i) + ciL - 1) / ciL)
51
52 /*
53 * Initialize one MPI
54 */
55 void mpi_init( mpi *X )
56 {
57 if( X == NULL )
58 return;
59
60 X->s = 1;
61 X->n = 0;
62 X->p = NULL;
63 }
64
65 /*
66 * Unallocate one MPI
67 */
68 void mpi_free( mpi *X )
69 {
70 if( X == NULL )
71 return;
72
73 if( X->p != NULL )
74 {
75 memset( X->p, 0, X->n * ciL );
76 free( X->p );
77 }
78
79 X->s = 1;
80 X->n = 0;
81 X->p = NULL;
82 }
83
84 /*
85 * Enlarge to the specified number of limbs
86 */
87 int mpi_grow( mpi *X, size_t nblimbs )
88 {
89 t_uint *p;
90
91 if( nblimbs > POLARSSL_MPI_MAX_LIMBS )
92 return( POLARSSL_ERR_MPI_MALLOC_FAILED );
93
94 if( X->n < nblimbs )
95 {
96 if( ( p = (t_uint *) malloc( nblimbs * ciL ) ) == NULL )
97 return( POLARSSL_ERR_MPI_MALLOC_FAILED );
98
99 memset( p, 0, nblimbs * ciL );
100
101 if( X->p != NULL )
102 {
103 memcpy( p, X->p, X->n * ciL );
104 memset( X->p, 0, X->n * ciL );
105 free( X->p );
106 }
107
108 X->n = nblimbs;
109 X->p = p;
110 }
111
112 return( 0 );
113 }
114
115 /*
116 * Copy the contents of Y into X
117 */
118 int mpi_copy( mpi *X, const mpi *Y )
119 {
120 int ret;
121 size_t i;
122
123 if( X == Y )
124 return( 0 );
125
126 for( i = Y->n - 1; i > 0; i-- )
127 if( Y->p[i] != 0 )
128 break;
129 i++;
130
131 X->s = Y->s;
132
133 MPI_CHK( mpi_grow( X, i ) );
134
135 memset( X->p, 0, X->n * ciL );
136 memcpy( X->p, Y->p, i * ciL );
137
138 cleanup:
139
140 return( ret );
141 }
142
143 /*
144 * Swap the contents of X and Y
145 */
146 void mpi_swap( mpi *X, mpi *Y )
147 {
148 mpi T;
149
150 memcpy( &T, X, sizeof( mpi ) );
151 memcpy( X, Y, sizeof( mpi ) );
152 memcpy( Y, &T, sizeof( mpi ) );
153 }
154
155 /*
156 * Set value from integer
157 */
158 int mpi_lset( mpi *X, t_sint z )
159 {
160 int ret;
161
162 MPI_CHK( mpi_grow( X, 1 ) );
163 memset( X->p, 0, X->n * ciL );
164
165 X->p[0] = ( z < 0 ) ? -z : z;
166 X->s = ( z < 0 ) ? -1 : 1;
167
168 cleanup:
169
170 return( ret );
171 }
172
173 /*
174 * Get a specific bit
175 */
176 int mpi_get_bit( const mpi *X, size_t pos )
177 {
178 if( X->n * biL <= pos )
179 return( 0 );
180
181 return ( X->p[pos / biL] >> ( pos % biL ) ) & 0x01;
182 }
183
184 /*
185 * Set a bit to a specific value of 0 or 1
186 */
187 int mpi_set_bit( mpi *X, size_t pos, unsigned char val )
188 {
189 int ret = 0;
190 size_t off = pos / biL;
191 size_t idx = pos % biL;
192
193 if( val != 0 && val != 1 )
194 return POLARSSL_ERR_MPI_BAD_INPUT_DATA;
195
196 if( X->n * biL <= pos )
197 {
198 if( val == 0 )
199 return ( 0 );
200
201 MPI_CHK( mpi_grow( X, off + 1 ) );
202 }
203
204 X->p[off] = ( X->p[off] & ~( 0x01 << idx ) ) | ( val << idx );
205
206 cleanup:
207
208 return( ret );
209 }
210
211 /*
212 * Return the number of least significant bits
213 */
214 size_t mpi_lsb( const mpi *X )
215 {
216 size_t i, j, count = 0;
217
218 for( i = 0; i < X->n; i++ )
219 for( j = 0; j < biL; j++, count++ )
220 if( ( ( X->p[i] >> j ) & 1 ) != 0 )
221 return( count );
222
223 return( 0 );
224 }
225
226 /*
227 * Return the number of most significant bits
228 */
229 size_t mpi_msb( const mpi *X )
230 {
231 size_t i, j;
232
233 for( i = X->n - 1; i > 0; i-- )
234 if( X->p[i] != 0 )
235 break;
236
237 for( j = biL; j > 0; j-- )
238 if( ( ( X->p[i] >> ( j - 1 ) ) & 1 ) != 0 )
239 break;
240
241 return( ( i * biL ) + j );
242 }
243
244 /*
245 * Return the total size in bytes
246 */
247 size_t mpi_size( const mpi *X )
248 {
249 return( ( mpi_msb( X ) + 7 ) >> 3 );
250 }
251
252 /*
253 * Convert an ASCII character to digit value
254 */
255 static int mpi_get_digit( t_uint *d, int radix, char c )
256 {
257 *d = 255;
258
259 if( c >= 0x30 && c <= 0x39 ) *d = c - 0x30;
260 if( c >= 0x41 && c <= 0x46 ) *d = c - 0x37;
261 if( c >= 0x61 && c <= 0x66 ) *d = c - 0x57;
262
263 if( *d >= (t_uint) radix )
264 return( POLARSSL_ERR_MPI_INVALID_CHARACTER );
265
266 return( 0 );
267 }
268
269 /*
270 * Import from an ASCII string
271 */
272 int mpi_read_string( mpi *X, int radix, const char *s )
273 {
274 int ret;
275 size_t i, j, slen, n;
276 t_uint d;
277 mpi T;
278
279 if( radix < 2 || radix > 16 )
280 return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
281
282 mpi_init( &T );
283
284 slen = strlen( s );
285
286 if( radix == 16 )
287 {
288 n = BITS_TO_LIMBS( slen << 2 );
289
290 MPI_CHK( mpi_grow( X, n ) );
291 MPI_CHK( mpi_lset( X, 0 ) );
292
293 for( i = slen, j = 0; i > 0; i--, j++ )
294 {
295 if( i == 1 && s[i - 1] == '-' )
296 {
297 X->s = -1;
298 break;
299 }
300
301 MPI_CHK( mpi_get_digit( &d, radix, s[i - 1] ) );
302 X->p[j / (2 * ciL)] |= d << ( (j % (2 * ciL)) << 2 );
303 }
304 }
305 else
306 {
307 MPI_CHK( mpi_lset( X, 0 ) );
308
309 for( i = 0; i < slen; i++ )
310 {
311 if( i == 0 && s[i] == '-' )
312 {
313 X->s = -1;
314 continue;
315 }
316
317 MPI_CHK( mpi_get_digit( &d, radix, s[i] ) );
318 MPI_CHK( mpi_mul_int( &T, X, radix ) );
319
320 if( X->s == 1 )
321 {
322 MPI_CHK( mpi_add_int( X, &T, d ) );
323 }
324 else
325 {
326 MPI_CHK( mpi_sub_int( X, &T, d ) );
327 }
328 }
329 }
330
331 cleanup:
332
333 mpi_free( &T );
334
335 return( ret );
336 }
337
338 /*
339 * Helper to write the digits high-order first
340 */
341 static int mpi_write_hlp( mpi *X, int radix, char **p )
342 {
343 int ret;
344 t_uint r;
345
346 if( radix < 2 || radix > 16 )
347 return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
348
349 MPI_CHK( mpi_mod_int( &r, X, radix ) );
350 MPI_CHK( mpi_div_int( X, NULL, X, radix ) );
351
352 if( mpi_cmp_int( X, 0 ) != 0 )
353 MPI_CHK( mpi_write_hlp( X, radix, p ) );
354
355 if( r < 10 )
356 *(*p)++ = (char)( r + 0x30 );
357 else
358 *(*p)++ = (char)( r + 0x37 );
359
360 cleanup:
361
362 return( ret );
363 }
364
365 /*
366 * Export into an ASCII string
367 */
368 int mpi_write_string( const mpi *X, int radix, char *s, size_t *slen )
369 {
370 int ret = 0;
371 size_t n;
372 char *p;
373 mpi T;
374
375 if( radix < 2 || radix > 16 )
376 return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
377
378 n = mpi_msb( X );
379 if( radix >= 4 ) n >>= 1;
380 if( radix >= 16 ) n >>= 1;
381 n += 3;
382
383 if( *slen < n )
384 {
385 *slen = n;
386 return( POLARSSL_ERR_MPI_BUFFER_TOO_SMALL );
387 }
388
389 p = s;
390 mpi_init( &T );
391
392 if( X->s == -1 )
393 *p++ = '-';
394
395 if( radix == 16 )
396 {
397 int c;
398 size_t i, j, k;
399
400 for( i = X->n, k = 0; i > 0; i-- )
401 {
402 for( j = ciL; j > 0; j-- )
403 {
404 c = ( X->p[i - 1] >> ( ( j - 1 ) << 3) ) & 0xFF;
405
406 if( c == 0 && k == 0 && ( i + j + 3 ) != 0 )
407 continue;
408
409 *(p++) = "0123456789ABCDEF" [c / 16];
410 *(p++) = "0123456789ABCDEF" [c % 16];
411 k = 1;
412 }
413 }
414 }
415 else
416 {
417 MPI_CHK( mpi_copy( &T, X ) );
418
419 if( T.s == -1 )
420 T.s = 1;
421
422 MPI_CHK( mpi_write_hlp( &T, radix, &p ) );
423 }
424
425 *p++ = '\0';
426 *slen = p - s;
427
428 cleanup:
429
430 mpi_free( &T );
431
432 return( ret );
433 }
434
435 #if defined(POLARSSL_FS_IO)
436 /*
437 * Read X from an opened file
438 */
439 int mpi_read_file( mpi *X, int radix, FILE *fin )
440 {
441 t_uint d;
442 size_t slen;
443 char *p;
444 /*
445 * Buffer should have space for (short) label and decimal formatted MPI,
446 * newline characters and '\0'
447 */
448 char s[ POLARSSL_MPI_RW_BUFFER_SIZE ];
449
450 memset( s, 0, sizeof( s ) );
451 if( fgets( s, sizeof( s ) - 1, fin ) == NULL )
452 return( POLARSSL_ERR_MPI_FILE_IO_ERROR );
453
454 slen = strlen( s );
455 if( slen == sizeof( s ) - 2 )
456 return( POLARSSL_ERR_MPI_BUFFER_TOO_SMALL );
457
458 if( s[slen - 1] == '\n' ) { slen--; s[slen] = '\0'; }
459 if( s[slen - 1] == '\r' ) { slen--; s[slen] = '\0'; }
460
461 p = s + slen;
462 while( --p >= s )
463 if( mpi_get_digit( &d, radix, *p ) != 0 )
464 break;
465
466 return( mpi_read_string( X, radix, p + 1 ) );
467 }
468
469 /*
470 * Write X into an opened file (or stdout if fout == NULL)
471 */
472 int mpi_write_file( const char *p, const mpi *X, int radix, FILE *fout )
473 {
474 int ret;
475 size_t n, slen, plen;
476 /*
477 * Buffer should have space for (short) label and decimal formatted MPI,
478 * newline characters and '\0'
479 */
480 char s[ POLARSSL_MPI_RW_BUFFER_SIZE ];
481
482 n = sizeof( s );
483 memset( s, 0, n );
484 n -= 2;
485
486 MPI_CHK( mpi_write_string( X, radix, s, (size_t *) &n ) );
487
488 if( p == NULL ) p = "";
489
490 plen = strlen( p );
491 slen = strlen( s );
492 s[slen++] = '\r';
493 s[slen++] = '\n';
494
495 if( fout != NULL )
496 {
497 if( fwrite( p, 1, plen, fout ) != plen ||
498 fwrite( s, 1, slen, fout ) != slen )
499 return( POLARSSL_ERR_MPI_FILE_IO_ERROR );
500 }
501 else
502 printf( "%s%s", p, s );
503
504 cleanup:
505
506 return( ret );
507 }
508 #endif /* POLARSSL_FS_IO */
509
510 /*
511 * Import X from unsigned binary data, big endian
512 */
513 int mpi_read_binary( mpi *X, const unsigned char *buf, size_t buflen )
514 {
515 int ret;
516 size_t i, j, n;
517
518 for( n = 0; n < buflen; n++ )
519 if( buf[n] != 0 )
520 break;
521
522 MPI_CHK( mpi_grow( X, CHARS_TO_LIMBS( buflen - n ) ) );
523 MPI_CHK( mpi_lset( X, 0 ) );
524
525 for( i = buflen, j = 0; i > n; i--, j++ )
526 X->p[j / ciL] |= ((t_uint) buf[i - 1]) << ((j % ciL) << 3);
527
528 cleanup:
529
530 return( ret );
531 }
532
533 /*
534 * Export X into unsigned binary data, big endian
535 */
536 int mpi_write_binary( const mpi *X, unsigned char *buf, size_t buflen )
537 {
538 size_t i, j, n;
539
540 n = mpi_size( X );
541
542 if( buflen < n )
543 return( POLARSSL_ERR_MPI_BUFFER_TOO_SMALL );
544
545 memset( buf, 0, buflen );
546
547 for( i = buflen - 1, j = 0; n > 0; i--, j++, n-- )
548 buf[i] = (unsigned char)( X->p[j / ciL] >> ((j % ciL) << 3) );
549
550 return( 0 );
551 }
552
553 /*
554 * Left-shift: X <<= count
555 */
556 int mpi_shift_l( mpi *X, size_t count )
557 {
558 int ret;
559 size_t i, v0, t1;
560 t_uint r0 = 0, r1;
561
562 v0 = count / (biL );
563 t1 = count & (biL - 1);
564
565 i = mpi_msb( X ) + count;
566
567 if( X->n * biL < i )
568 MPI_CHK( mpi_grow( X, BITS_TO_LIMBS( i ) ) );
569
570 ret = 0;
571
572 /*
573 * shift by count / limb_size
574 */
575 if( v0 > 0 )
576 {
577 for( i = X->n; i > v0; i-- )
578 X->p[i - 1] = X->p[i - v0 - 1];
579
580 for( ; i > 0; i-- )
581 X->p[i - 1] = 0;
582 }
583
584 /*
585 * shift by count % limb_size
586 */
587 if( t1 > 0 )
588 {
589 for( i = v0; i < X->n; i++ )
590 {
591 r1 = X->p[i] >> (biL - t1);
592 X->p[i] <<= t1;
593 X->p[i] |= r0;
594 r0 = r1;
595 }
596 }
597
598 cleanup:
599
600 return( ret );
601 }
602
603 /*
604 * Right-shift: X >>= count
605 */
606 int mpi_shift_r( mpi *X, size_t count )
607 {
608 size_t i, v0, v1;
609 t_uint r0 = 0, r1;
610
611 v0 = count / biL;
612 v1 = count & (biL - 1);
613
614 if( v0 > X->n || ( v0 == X->n && v1 > 0 ) )
615 return mpi_lset( X, 0 );
616
617 /*
618 * shift by count / limb_size
619 */
620 if( v0 > 0 )
621 {
622 for( i = 0; i < X->n - v0; i++ )
623 X->p[i] = X->p[i + v0];
624
625 for( ; i < X->n; i++ )
626 X->p[i] = 0;
627 }
628
629 /*
630 * shift by count % limb_size
631 */
632 if( v1 > 0 )
633 {
634 for( i = X->n; i > 0; i-- )
635 {
636 r1 = X->p[i - 1] << (biL - v1);
637 X->p[i - 1] >>= v1;
638 X->p[i - 1] |= r0;
639 r0 = r1;
640 }
641 }
642
643 return( 0 );
644 }
645
646 /*
647 * Compare unsigned values
648 */
649 int mpi_cmp_abs( const mpi *X, const mpi *Y )
650 {
651 size_t i, j;
652
653 for( i = X->n; i > 0; i-- )
654 if( X->p[i - 1] != 0 )
655 break;
656
657 for( j = Y->n; j > 0; j-- )
658 if( Y->p[j - 1] != 0 )
659 break;
660
661 if( i == 0 && j == 0 )
662 return( 0 );
663
664 if( i > j ) return( 1 );
665 if( j > i ) return( -1 );
666
667 for( ; i > 0; i-- )
668 {
669 if( X->p[i - 1] > Y->p[i - 1] ) return( 1 );
670 if( X->p[i - 1] < Y->p[i - 1] ) return( -1 );
671 }
672
673 return( 0 );
674 }
675
676 /*
677 * Compare signed values
678 */
679 int mpi_cmp_mpi( const mpi *X, const mpi *Y )
680 {
681 size_t i, j;
682
683 for( i = X->n; i > 0; i-- )
684 if( X->p[i - 1] != 0 )
685 break;
686
687 for( j = Y->n; j > 0; j-- )
688 if( Y->p[j - 1] != 0 )
689 break;
690
691 if( i == 0 && j == 0 )
692 return( 0 );
693
694 if( i > j ) return( X->s );
695 if( j > i ) return( -Y->s );
696
697 if( X->s > 0 && Y->s < 0 ) return( 1 );
698 if( Y->s > 0 && X->s < 0 ) return( -1 );
699
700 for( ; i > 0; i-- )
701 {
702 if( X->p[i - 1] > Y->p[i - 1] ) return( X->s );
703 if( X->p[i - 1] < Y->p[i - 1] ) return( -X->s );
704 }
705
706 return( 0 );
707 }
708
709 /*
710 * Compare signed values
711 */
712 int mpi_cmp_int( const mpi *X, t_sint z )
713 {
714 mpi Y;
715 t_uint p[1];
716
717 *p = ( z < 0 ) ? -z : z;
718 Y.s = ( z < 0 ) ? -1 : 1;
719 Y.n = 1;
720 Y.p = p;
721
722 return( mpi_cmp_mpi( X, &Y ) );
723 }
724
725 /*
726 * Unsigned addition: X = |A| + |B| (HAC 14.7)
727 */
728 int mpi_add_abs( mpi *X, const mpi *A, const mpi *B )
729 {
730 int ret;
731 size_t i, j;
732 t_uint *o, *p, c;
733
734 if( X == B )
735 {
736 const mpi *T = A; A = X; B = T;
737 }
738
739 if( X != A )
740 MPI_CHK( mpi_copy( X, A ) );
741
742 /*
743 * X should always be positive as a result of unsigned additions.
744 */
745 X->s = 1;
746
747 for( j = B->n; j > 0; j-- )
748 if( B->p[j - 1] != 0 )
749 break;
750
751 MPI_CHK( mpi_grow( X, j ) );
752
753 o = B->p; p = X->p; c = 0;
754
755 for( i = 0; i < j; i++, o++, p++ )
756 {
757 *p += c; c = ( *p < c );
758 *p += *o; c += ( *p < *o );
759 }
760
761 while( c != 0 )
762 {
763 if( i >= X->n )
764 {
765 MPI_CHK( mpi_grow( X, i + 1 ) );
766 p = X->p + i;
767 }
768
769 *p += c; c = ( *p < c ); i++; p++;
770 }
771
772 cleanup:
773
774 return( ret );
775 }
776
777 /*
778 * Helper for mpi substraction
779 */
780 static void mpi_sub_hlp( size_t n, t_uint *s, t_uint *d )
781 {
782 size_t i;
783 t_uint c, z;
784
785 for( i = c = 0; i < n; i++, s++, d++ )
786 {
787 z = ( *d < c ); *d -= c;
788 c = ( *d < *s ) + z; *d -= *s;
789 }
790
791 while( c != 0 )
792 {
793 z = ( *d < c ); *d -= c;
794 c = z; i++; d++;
795 }
796 }
797
798 /*
799 * Unsigned substraction: X = |A| - |B| (HAC 14.9)
800 */
801 int mpi_sub_abs( mpi *X, const mpi *A, const mpi *B )
802 {
803 mpi TB;
804 int ret;
805 size_t n;
806
807 if( mpi_cmp_abs( A, B ) < 0 )
808 return( POLARSSL_ERR_MPI_NEGATIVE_VALUE );
809
810 mpi_init( &TB );
811
812 if( X == B )
813 {
814 MPI_CHK( mpi_copy( &TB, B ) );
815 B = &TB;
816 }
817
818 if( X != A )
819 MPI_CHK( mpi_copy( X, A ) );
820
821 /*
822 * X should always be positive as a result of unsigned substractions.
823 */
824 X->s = 1;
825
826 ret = 0;
827
828 for( n = B->n; n > 0; n-- )
829 if( B->p[n - 1] != 0 )
830 break;
831
832 mpi_sub_hlp( n, B->p, X->p );
833
834 cleanup:
835
836 mpi_free( &TB );
837
838 return( ret );
839 }
840
841 /*
842 * Signed addition: X = A + B
843 */
844 int mpi_add_mpi( mpi *X, const mpi *A, const mpi *B )
845 {
846 int ret, s = A->s;
847
848 if( A->s * B->s < 0 )
849 {
850 if( mpi_cmp_abs( A, B ) >= 0 )
851 {
852 MPI_CHK( mpi_sub_abs( X, A, B ) );
853 X->s = s;
854 }
855 else
856 {
857 MPI_CHK( mpi_sub_abs( X, B, A ) );
858 X->s = -s;
859 }
860 }
861 else
862 {
863 MPI_CHK( mpi_add_abs( X, A, B ) );
864 X->s = s;
865 }
866
867 cleanup:
868
869 return( ret );
870 }
871
872 /*
873 * Signed substraction: X = A - B
874 */
875 int mpi_sub_mpi( mpi *X, const mpi *A, const mpi *B )
876 {
877 int ret, s = A->s;
878
879 if( A->s * B->s > 0 )
880 {
881 if( mpi_cmp_abs( A, B ) >= 0 )
882 {
883 MPI_CHK( mpi_sub_abs( X, A, B ) );
884 X->s = s;
885 }
886 else
887 {
888 MPI_CHK( mpi_sub_abs( X, B, A ) );
889 X->s = -s;
890 }
891 }
892 else
893 {
894 MPI_CHK( mpi_add_abs( X, A, B ) );
895 X->s = s;
896 }
897
898 cleanup:
899
900 return( ret );
901 }
902
903 /*
904 * Signed addition: X = A + b
905 */
906 int mpi_add_int( mpi *X, const mpi *A, t_sint b )
907 {
908 mpi _B;
909 t_uint p[1];
910
911 p[0] = ( b < 0 ) ? -b : b;
912 _B.s = ( b < 0 ) ? -1 : 1;
913 _B.n = 1;
914 _B.p = p;
915
916 return( mpi_add_mpi( X, A, &_B ) );
917 }
918
919 /*
920 * Signed substraction: X = A - b
921 */
922 int mpi_sub_int( mpi *X, const mpi *A, t_sint b )
923 {
924 mpi _B;
925 t_uint p[1];
926
927 p[0] = ( b < 0 ) ? -b : b;
928 _B.s = ( b < 0 ) ? -1 : 1;
929 _B.n = 1;
930 _B.p = p;
931
932 return( mpi_sub_mpi( X, A, &_B ) );
933 }
934
935 /*
936 * Helper for mpi multiplication
937 */
938 static
939 #if defined(__APPLE__) && defined(__arm__)
940 /*
941 * Apple LLVM version 4.2 (clang-425.0.24) (based on LLVM 3.2svn)
942 * appears to need this to prevent bad ARM code generation at -O3.
943 */
944 __attribute__ ((noinline))
945 #endif
946 void mpi_mul_hlp( size_t i, t_uint *s, t_uint *d, t_uint b )
947 {
948 t_uint c = 0, t = 0;
949
950 #if defined(MULADDC_HUIT)
951 for( ; i >= 8; i -= 8 )
952 {
953 MULADDC_INIT
954 MULADDC_HUIT
955 MULADDC_STOP
956 }
957
958 for( ; i > 0; i-- )
959 {
960 MULADDC_INIT
961 MULADDC_CORE
962 MULADDC_STOP
963 }
964 #else
965 for( ; i >= 16; i -= 16 )
966 {
967 MULADDC_INIT
968 MULADDC_CORE MULADDC_CORE
969 MULADDC_CORE MULADDC_CORE
970 MULADDC_CORE MULADDC_CORE
971 MULADDC_CORE MULADDC_CORE
972
973 MULADDC_CORE MULADDC_CORE
974 MULADDC_CORE MULADDC_CORE
975 MULADDC_CORE MULADDC_CORE
976 MULADDC_CORE MULADDC_CORE
977 MULADDC_STOP
978 }
979
980 for( ; i >= 8; i -= 8 )
981 {
982 MULADDC_INIT
983 MULADDC_CORE MULADDC_CORE
984 MULADDC_CORE MULADDC_CORE
985
986 MULADDC_CORE MULADDC_CORE
987 MULADDC_CORE MULADDC_CORE
988 MULADDC_STOP
989 }
990
991 for( ; i > 0; i-- )
992 {
993 MULADDC_INIT
994 MULADDC_CORE
995 MULADDC_STOP
996 }
997 #endif
998
999 t++;
1000
1001 do {
1002 *d += c; c = ( *d < c ); d++;
1003 }
1004 while( c != 0 );
1005 }
1006
1007 /*
1008 * Baseline multiplication: X = A * B (HAC 14.12)
1009 */
1010 int mpi_mul_mpi( mpi *X, const mpi *A, const mpi *B )
1011 {
1012 int ret;
1013 size_t i, j;
1014 mpi TA, TB;
1015
1016 mpi_init( &TA ); mpi_init( &TB );
1017
1018 if( X == A ) { MPI_CHK( mpi_copy( &TA, A ) ); A = &TA; }
1019 if( X == B ) { MPI_CHK( mpi_copy( &TB, B ) ); B = &TB; }
1020
1021 for( i = A->n; i > 0; i-- )
1022 if( A->p[i - 1] != 0 )
1023 break;
1024
1025 for( j = B->n; j > 0; j-- )
1026 if( B->p[j - 1] != 0 )
1027 break;
1028
1029 MPI_CHK( mpi_grow( X, i + j ) );
1030 MPI_CHK( mpi_lset( X, 0 ) );
1031
1032 for( i++; j > 0; j-- )
1033 mpi_mul_hlp( i - 1, A->p, X->p + j - 1, B->p[j - 1] );
1034
1035 X->s = A->s * B->s;
1036
1037 cleanup:
1038
1039 mpi_free( &TB ); mpi_free( &TA );
1040
1041 return( ret );
1042 }
1043
1044 /*
1045 * Baseline multiplication: X = A * b
1046 */
1047 int mpi_mul_int( mpi *X, const mpi *A, t_sint b )
1048 {
1049 mpi _B;
1050 t_uint p[1];
1051
1052 _B.s = 1;
1053 _B.n = 1;
1054 _B.p = p;
1055 p[0] = b;
1056
1057 return( mpi_mul_mpi( X, A, &_B ) );
1058 }
1059
1060 /*
1061 * Division by mpi: A = Q * B + R (HAC 14.20)
1062 */
1063 int mpi_div_mpi( mpi *Q, mpi *R, const mpi *A, const mpi *B )
1064 {
1065 int ret;
1066 size_t i, n, t, k;
1067 mpi X, Y, Z, T1, T2;
1068
1069 if( mpi_cmp_int( B, 0 ) == 0 )
1070 return( POLARSSL_ERR_MPI_DIVISION_BY_ZERO );
1071
1072 mpi_init( &X ); mpi_init( &Y ); mpi_init( &Z );
1073 mpi_init( &T1 ); mpi_init( &T2 );
1074
1075 if( mpi_cmp_abs( A, B ) < 0 )
1076 {
1077 if( Q != NULL ) MPI_CHK( mpi_lset( Q, 0 ) );
1078 if( R != NULL ) MPI_CHK( mpi_copy( R, A ) );
1079 return( 0 );
1080 }
1081
1082 MPI_CHK( mpi_copy( &X, A ) );
1083 MPI_CHK( mpi_copy( &Y, B ) );
1084 X.s = Y.s = 1;
1085
1086 MPI_CHK( mpi_grow( &Z, A->n + 2 ) );
1087 MPI_CHK( mpi_lset( &Z, 0 ) );
1088 MPI_CHK( mpi_grow( &T1, 2 ) );
1089 MPI_CHK( mpi_grow( &T2, 3 ) );
1090
1091 k = mpi_msb( &Y ) % biL;
1092 if( k < biL - 1 )
1093 {
1094 k = biL - 1 - k;
1095 MPI_CHK( mpi_shift_l( &X, k ) );
1096 MPI_CHK( mpi_shift_l( &Y, k ) );
1097 }
1098 else k = 0;
1099
1100 n = X.n - 1;
1101 t = Y.n - 1;
1102 MPI_CHK( mpi_shift_l( &Y, biL * (n - t) ) );
1103
1104 while( mpi_cmp_mpi( &X, &Y ) >= 0 )
1105 {
1106 Z.p[n - t]++;
1107 mpi_sub_mpi( &X, &X, &Y );
1108 }
1109 mpi_shift_r( &Y, biL * (n - t) );
1110
1111 for( i = n; i > t ; i-- )
1112 {
1113 if( X.p[i] >= Y.p[t] )
1114 Z.p[i - t - 1] = ~0;
1115 else
1116 {
1117 #if defined(POLARSSL_HAVE_UDBL)
1118 t_udbl r;
1119
1120 r = (t_udbl) X.p[i] << biL;
1121 r |= (t_udbl) X.p[i - 1];
1122 r /= Y.p[t];
1123 if( r > ((t_udbl) 1 << biL) - 1)
1124 r = ((t_udbl) 1 << biL) - 1;
1125
1126 Z.p[i - t - 1] = (t_uint) r;
1127 #else
1128 /*
1129 * __udiv_qrnnd_c, from gmp/longlong.h
1130 */
1131 t_uint q0, q1, r0, r1;
1132 t_uint d0, d1, d, m;
1133
1134 d = Y.p[t];
1135 d0 = ( d << biH ) >> biH;
1136 d1 = ( d >> biH );
1137
1138 q1 = X.p[i] / d1;
1139 r1 = X.p[i] - d1 * q1;
1140 r1 <<= biH;
1141 r1 |= ( X.p[i - 1] >> biH );
1142
1143 m = q1 * d0;
1144 if( r1 < m )
1145 {
1146 q1--, r1 += d;
1147 while( r1 >= d && r1 < m )
1148 q1--, r1 += d;
1149 }
1150 r1 -= m;
1151
1152 q0 = r1 / d1;
1153 r0 = r1 - d1 * q0;
1154 r0 <<= biH;
1155 r0 |= ( X.p[i - 1] << biH ) >> biH;
1156
1157 m = q0 * d0;
1158 if( r0 < m )
1159 {
1160 q0--, r0 += d;
1161 while( r0 >= d && r0 < m )
1162 q0--, r0 += d;
1163 }
1164 r0 -= m;
1165
1166 Z.p[i - t - 1] = ( q1 << biH ) | q0;
1167 #endif
1168 }
1169
1170 Z.p[i - t - 1]++;
1171 do
1172 {
1173 Z.p[i - t - 1]--;
1174
1175 MPI_CHK( mpi_lset( &T1, 0 ) );
1176 T1.p[0] = (t < 1) ? 0 : Y.p[t - 1];
1177 T1.p[1] = Y.p[t];
1178 MPI_CHK( mpi_mul_int( &T1, &T1, Z.p[i - t - 1] ) );
1179
1180 MPI_CHK( mpi_lset( &T2, 0 ) );
1181 T2.p[0] = (i < 2) ? 0 : X.p[i - 2];
1182 T2.p[1] = (i < 1) ? 0 : X.p[i - 1];
1183 T2.p[2] = X.p[i];
1184 }
1185 while( mpi_cmp_mpi( &T1, &T2 ) > 0 );
1186
1187 MPI_CHK( mpi_mul_int( &T1, &Y, Z.p[i - t - 1] ) );
1188 MPI_CHK( mpi_shift_l( &T1, biL * (i - t - 1) ) );
1189 MPI_CHK( mpi_sub_mpi( &X, &X, &T1 ) );
1190
1191 if( mpi_cmp_int( &X, 0 ) < 0 )
1192 {
1193 MPI_CHK( mpi_copy( &T1, &Y ) );
1194 MPI_CHK( mpi_shift_l( &T1, biL * (i - t - 1) ) );
1195 MPI_CHK( mpi_add_mpi( &X, &X, &T1 ) );
1196 Z.p[i - t - 1]--;
1197 }
1198 }
1199
1200 if( Q != NULL )
1201 {
1202 mpi_copy( Q, &Z );
1203 Q->s = A->s * B->s;
1204 }
1205
1206 if( R != NULL )
1207 {
1208 mpi_shift_r( &X, k );
1209 X.s = A->s;
1210 mpi_copy( R, &X );
1211
1212 if( mpi_cmp_int( R, 0 ) == 0 )
1213 R->s = 1;
1214 }
1215
1216 cleanup:
1217
1218 mpi_free( &X ); mpi_free( &Y ); mpi_free( &Z );
1219 mpi_free( &T1 ); mpi_free( &T2 );
1220
1221 return( ret );
1222 }
1223
1224 /*
1225 * Division by int: A = Q * b + R
1226 */
1227 int mpi_div_int( mpi *Q, mpi *R, const mpi *A, t_sint b )
1228 {
1229 mpi _B;
1230 t_uint p[1];
1231
1232 p[0] = ( b < 0 ) ? -b : b;
1233 _B.s = ( b < 0 ) ? -1 : 1;
1234 _B.n = 1;
1235 _B.p = p;
1236
1237 return( mpi_div_mpi( Q, R, A, &_B ) );
1238 }
1239
1240 /*
1241 * Modulo: R = A mod B
1242 */
1243 int mpi_mod_mpi( mpi *R, const mpi *A, const mpi *B )
1244 {
1245 int ret;
1246
1247 if( mpi_cmp_int( B, 0 ) < 0 )
1248 return POLARSSL_ERR_MPI_NEGATIVE_VALUE;
1249
1250 MPI_CHK( mpi_div_mpi( NULL, R, A, B ) );
1251
1252 while( mpi_cmp_int( R, 0 ) < 0 )
1253 MPI_CHK( mpi_add_mpi( R, R, B ) );
1254
1255 while( mpi_cmp_mpi( R, B ) >= 0 )
1256 MPI_CHK( mpi_sub_mpi( R, R, B ) );
1257
1258 cleanup:
1259
1260 return( ret );
1261 }
1262
1263 /*
1264 * Modulo: r = A mod b
1265 */
1266 int mpi_mod_int( t_uint *r, const mpi *A, t_sint b )
1267 {
1268 size_t i;
1269 t_uint x, y, z;
1270
1271 if( b == 0 )
1272 return( POLARSSL_ERR_MPI_DIVISION_BY_ZERO );
1273
1274 if( b < 0 )
1275 return POLARSSL_ERR_MPI_NEGATIVE_VALUE;
1276
1277 /*
1278 * handle trivial cases
1279 */
1280 if( b == 1 )
1281 {
1282 *r = 0;
1283 return( 0 );
1284 }
1285
1286 if( b == 2 )
1287 {
1288 *r = A->p[0] & 1;
1289 return( 0 );
1290 }
1291
1292 /*
1293 * general case
1294 */
1295 for( i = A->n, y = 0; i > 0; i-- )
1296 {
1297 x = A->p[i - 1];
1298 y = ( y << biH ) | ( x >> biH );
1299 z = y / b;
1300 y -= z * b;
1301
1302 x <<= biH;
1303 y = ( y << biH ) | ( x >> biH );
1304 z = y / b;
1305 y -= z * b;
1306 }
1307
1308 /*
1309 * If A is negative, then the current y represents a negative value.
1310 * Flipping it to the positive side.
1311 */
1312 if( A->s < 0 && y != 0 )
1313 y = b - y;
1314
1315 *r = y;
1316
1317 return( 0 );
1318 }
1319
1320 /*
1321 * Fast Montgomery initialization (thanks to Tom St Denis)
1322 */
1323 static void mpi_montg_init( t_uint *mm, const mpi *N )
1324 {
1325 t_uint x, m0 = N->p[0];
1326
1327 x = m0;
1328 x += ( ( m0 + 2 ) & 4 ) << 1;
1329 x *= ( 2 - ( m0 * x ) );
1330
1331 if( biL >= 16 ) x *= ( 2 - ( m0 * x ) );
1332 if( biL >= 32 ) x *= ( 2 - ( m0 * x ) );
1333 if( biL >= 64 ) x *= ( 2 - ( m0 * x ) );
1334
1335 *mm = ~x + 1;
1336 }
1337
1338 /*
1339 * Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36)
1340 */
1341 static void mpi_montmul( mpi *A, const mpi *B, const mpi *N, t_uint mm, const mpi *T )
1342 {
1343 size_t i, n, m;
1344 t_uint u0, u1, *d;
1345
1346 memset( T->p, 0, T->n * ciL );
1347
1348 d = T->p;
1349 n = N->n;
1350 m = ( B->n < n ) ? B->n : n;
1351
1352 for( i = 0; i < n; i++ )
1353 {
1354 /*
1355 * T = (T + u0*B + u1*N) / 2^biL
1356 */
1357 u0 = A->p[i];
1358 u1 = ( d[0] + u0 * B->p[0] ) * mm;
1359
1360 mpi_mul_hlp( m, B->p, d, u0 );
1361 mpi_mul_hlp( n, N->p, d, u1 );
1362
1363 *d++ = u0; d[n + 1] = 0;
1364 }
1365
1366 memcpy( A->p, d, (n + 1) * ciL );
1367
1368 if( mpi_cmp_abs( A, N ) >= 0 )
1369 mpi_sub_hlp( n, N->p, A->p );
1370 else
1371 /* prevent timing attacks */
1372 mpi_sub_hlp( n, A->p, T->p );
1373 }
1374
1375 /*
1376 * Montgomery reduction: A = A * R^-1 mod N
1377 */
1378 static void mpi_montred( mpi *A, const mpi *N, t_uint mm, const mpi *T )
1379 {
1380 t_uint z = 1;
1381 mpi U;
1382
1383 U.n = U.s = (int) z;
1384 U.p = &z;
1385
1386 mpi_montmul( A, &U, N, mm, T );
1387 }
1388
1389 /*
1390 * Sliding-window exponentiation: X = A^E mod N (HAC 14.85)
1391 */
1392 int mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR )
1393 {
1394 int ret;
1395 size_t wbits, wsize, one = 1;
1396 size_t i, j, nblimbs;
1397 size_t bufsize, nbits;
1398 t_uint ei, mm, state;
1399 mpi RR, T, W[ 2 << POLARSSL_MPI_WINDOW_SIZE ], Apos;
1400 int neg;
1401
1402 if( mpi_cmp_int( N, 0 ) < 0 || ( N->p[0] & 1 ) == 0 )
1403 return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
1404
1405 if( mpi_cmp_int( E, 0 ) < 0 )
1406 return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
1407
1408 /*
1409 * Init temps and window size
1410 */
1411 mpi_montg_init( &mm, N );
1412 mpi_init( &RR ); mpi_init( &T );
1413 memset( W, 0, sizeof( W ) );
1414
1415 i = mpi_msb( E );
1416
1417 wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 :
1418 ( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1;
1419
1420 if( wsize > POLARSSL_MPI_WINDOW_SIZE )
1421 wsize = POLARSSL_MPI_WINDOW_SIZE;
1422
1423 j = N->n + 1;
1424 MPI_CHK( mpi_grow( X, j ) );
1425 MPI_CHK( mpi_grow( &W[1], j ) );
1426 MPI_CHK( mpi_grow( &T, j * 2 ) );
1427
1428 /*
1429 * Compensate for negative A (and correct at the end)
1430 */
1431 neg = ( A->s == -1 );
1432
1433 mpi_init( &Apos );
1434 if( neg )
1435 {
1436 MPI_CHK( mpi_copy( &Apos, A ) );
1437 Apos.s = 1;
1438 A = &Apos;
1439 }
1440
1441 /*
1442 * If 1st call, pre-compute R^2 mod N
1443 */
1444 if( _RR == NULL || _RR->p == NULL )
1445 {
1446 MPI_CHK( mpi_lset( &RR, 1 ) );
1447 MPI_CHK( mpi_shift_l( &RR, N->n * 2 * biL ) );
1448 MPI_CHK( mpi_mod_mpi( &RR, &RR, N ) );
1449
1450 if( _RR != NULL )
1451 memcpy( _RR, &RR, sizeof( mpi ) );
1452 }
1453 else
1454 memcpy( &RR, _RR, sizeof( mpi ) );
1455
1456 /*
1457 * W[1] = A * R^2 * R^-1 mod N = A * R mod N
1458 */
1459 if( mpi_cmp_mpi( A, N ) >= 0 )
1460 mpi_mod_mpi( &W[1], A, N );
1461 else mpi_copy( &W[1], A );
1462
1463 mpi_montmul( &W[1], &RR, N, mm, &T );
1464
1465 /*
1466 * X = R^2 * R^-1 mod N = R mod N
1467 */
1468 MPI_CHK( mpi_copy( X, &RR ) );
1469 mpi_montred( X, N, mm, &T );
1470
1471 if( wsize > 1 )
1472 {
1473 /*
1474 * W[1 << (wsize - 1)] = W[1] ^ (wsize - 1)
1475 */
1476 j = one << (wsize - 1);
1477
1478 MPI_CHK( mpi_grow( &W[j], N->n + 1 ) );
1479 MPI_CHK( mpi_copy( &W[j], &W[1] ) );
1480
1481 for( i = 0; i < wsize - 1; i++ )
1482 mpi_montmul( &W[j], &W[j], N, mm, &T );
1483
1484 /*
1485 * W[i] = W[i - 1] * W[1]
1486 */
1487 for( i = j + 1; i < (one << wsize); i++ )
1488 {
1489 MPI_CHK( mpi_grow( &W[i], N->n + 1 ) );
1490 MPI_CHK( mpi_copy( &W[i], &W[i - 1] ) );
1491
1492 mpi_montmul( &W[i], &W[1], N, mm, &T );
1493 }
1494 }
1495
1496 nblimbs = E->n;
1497 bufsize = 0;
1498 nbits = 0;
1499 wbits = 0;
1500 state = 0;
1501
1502 while( 1 )
1503 {
1504 if( bufsize == 0 )
1505 {
1506 if( nblimbs-- == 0 )
1507 break;
1508
1509 bufsize = sizeof( t_uint ) << 3;
1510 }
1511
1512 bufsize--;
1513
1514 ei = (E->p[nblimbs] >> bufsize) & 1;
1515
1516 /*
1517 * skip leading 0s
1518 */
1519 if( ei == 0 && state == 0 )
1520 continue;
1521
1522 if( ei == 0 && state == 1 )
1523 {
1524 /*
1525 * out of window, square X
1526 */
1527 mpi_montmul( X, X, N, mm, &T );
1528 continue;
1529 }
1530
1531 /*
1532 * add ei to current window
1533 */
1534 state = 2;
1535
1536 nbits++;
1537 wbits |= (ei << (wsize - nbits));
1538
1539 if( nbits == wsize )
1540 {
1541 /*
1542 * X = X^wsize R^-1 mod N
1543 */
1544 for( i = 0; i < wsize; i++ )
1545 mpi_montmul( X, X, N, mm, &T );
1546
1547 /*
1548 * X = X * W[wbits] R^-1 mod N
1549 */
1550 mpi_montmul( X, &W[wbits], N, mm, &T );
1551
1552 state--;
1553 nbits = 0;
1554 wbits = 0;
1555 }
1556 }
1557
1558 /*
1559 * process the remaining bits
1560 */
1561 for( i = 0; i < nbits; i++ )
1562 {
1563 mpi_montmul( X, X, N, mm, &T );
1564
1565 wbits <<= 1;
1566
1567 if( (wbits & (one << wsize)) != 0 )
1568 mpi_montmul( X, &W[1], N, mm, &T );
1569 }
1570
1571 /*
1572 * X = A^E * R * R^-1 mod N = A^E mod N
1573 */
1574 mpi_montred( X, N, mm, &T );
1575
1576 if( neg )
1577 {
1578 X->s = -1;
1579 mpi_add_mpi( X, N, X );
1580 }
1581
1582 cleanup:
1583
1584 for( i = (one << (wsize - 1)); i < (one << wsize); i++ )
1585 mpi_free( &W[i] );
1586
1587 mpi_free( &W[1] ); mpi_free( &T ); mpi_free( &Apos );
1588
1589 if( _RR == NULL )
1590 mpi_free( &RR );
1591
1592 return( ret );
1593 }
1594
1595 /*
1596 * Greatest common divisor: G = gcd(A, B) (HAC 14.54)
1597 */
1598 int mpi_gcd( mpi *G, const mpi *A, const mpi *B )
1599 {
1600 int ret;
1601 size_t lz, lzt;
1602 mpi TG, TA, TB;
1603
1604 mpi_init( &TG ); mpi_init( &TA ); mpi_init( &TB );
1605
1606 MPI_CHK( mpi_copy( &TA, A ) );
1607 MPI_CHK( mpi_copy( &TB, B ) );
1608
1609 lz = mpi_lsb( &TA );
1610 lzt = mpi_lsb( &TB );
1611
1612 if ( lzt < lz )
1613 lz = lzt;
1614
1615 MPI_CHK( mpi_shift_r( &TA, lz ) );
1616 MPI_CHK( mpi_shift_r( &TB, lz ) );
1617
1618 TA.s = TB.s = 1;
1619
1620 while( mpi_cmp_int( &TA, 0 ) != 0 )
1621 {
1622 MPI_CHK( mpi_shift_r( &TA, mpi_lsb( &TA ) ) );
1623 MPI_CHK( mpi_shift_r( &TB, mpi_lsb( &TB ) ) );
1624
1625 if( mpi_cmp_mpi( &TA, &TB ) >= 0 )
1626 {
1627 MPI_CHK( mpi_sub_abs( &TA, &TA, &TB ) );
1628 MPI_CHK( mpi_shift_r( &TA, 1 ) );
1629 }
1630 else
1631 {
1632 MPI_CHK( mpi_sub_abs( &TB, &TB, &TA ) );
1633 MPI_CHK( mpi_shift_r( &TB, 1 ) );
1634 }
1635 }
1636
1637 MPI_CHK( mpi_shift_l( &TB, lz ) );
1638 MPI_CHK( mpi_copy( G, &TB ) );
1639
1640 cleanup:
1641
1642 mpi_free( &TG ); mpi_free( &TA ); mpi_free( &TB );
1643
1644 return( ret );
1645 }
1646
1647 int mpi_fill_random( mpi *X, size_t size,
1648 int (*f_rng)(void *, unsigned char *, size_t),
1649 void *p_rng )
1650 {
1651 int ret;
1652
1653 MPI_CHK( mpi_grow( X, CHARS_TO_LIMBS( size ) ) );
1654 MPI_CHK( mpi_lset( X, 0 ) );
1655
1656 MPI_CHK( f_rng( p_rng, (unsigned char *) X->p, size ) );
1657
1658 cleanup:
1659 return( ret );
1660 }
1661
1662 /*
1663 * Modular inverse: X = A^-1 mod N (HAC 14.61 / 14.64)
1664 */
1665 int mpi_inv_mod( mpi *X, const mpi *A, const mpi *N )
1666 {
1667 int ret;
1668 mpi G, TA, TU, U1, U2, TB, TV, V1, V2;
1669
1670 if( mpi_cmp_int( N, 0 ) <= 0 )
1671 return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
1672
1673 mpi_init( &TA ); mpi_init( &TU ); mpi_init( &U1 ); mpi_init( &U2 );
1674 mpi_init( &G ); mpi_init( &TB ); mpi_init( &TV );
1675 mpi_init( &V1 ); mpi_init( &V2 );
1676
1677 MPI_CHK( mpi_gcd( &G, A, N ) );
1678
1679 if( mpi_cmp_int( &G, 1 ) != 0 )
1680 {
1681 ret = POLARSSL_ERR_MPI_NOT_ACCEPTABLE;
1682 goto cleanup;
1683 }
1684
1685 MPI_CHK( mpi_mod_mpi( &TA, A, N ) );
1686 MPI_CHK( mpi_copy( &TU, &TA ) );
1687 MPI_CHK( mpi_copy( &TB, N ) );
1688 MPI_CHK( mpi_copy( &TV, N ) );
1689
1690 MPI_CHK( mpi_lset( &U1, 1 ) );
1691 MPI_CHK( mpi_lset( &U2, 0 ) );
1692 MPI_CHK( mpi_lset( &V1, 0 ) );
1693 MPI_CHK( mpi_lset( &V2, 1 ) );
1694
1695 do
1696 {
1697 while( ( TU.p[0] & 1 ) == 0 )
1698 {
1699 MPI_CHK( mpi_shift_r( &TU, 1 ) );
1700
1701 if( ( U1.p[0] & 1 ) != 0 || ( U2.p[0] & 1 ) != 0 )
1702 {
1703 MPI_CHK( mpi_add_mpi( &U1, &U1, &TB ) );
1704 MPI_CHK( mpi_sub_mpi( &U2, &U2, &TA ) );
1705 }
1706
1707 MPI_CHK( mpi_shift_r( &U1, 1 ) );
1708 MPI_CHK( mpi_shift_r( &U2, 1 ) );
1709 }
1710
1711 while( ( TV.p[0] & 1 ) == 0 )
1712 {
1713 MPI_CHK( mpi_shift_r( &TV, 1 ) );
1714
1715 if( ( V1.p[0] & 1 ) != 0 || ( V2.p[0] & 1 ) != 0 )
1716 {
1717 MPI_CHK( mpi_add_mpi( &V1, &V1, &TB ) );
1718 MPI_CHK( mpi_sub_mpi( &V2, &V2, &TA ) );
1719 }
1720
1721 MPI_CHK( mpi_shift_r( &V1, 1 ) );
1722 MPI_CHK( mpi_shift_r( &V2, 1 ) );
1723 }
1724
1725 if( mpi_cmp_mpi( &TU, &TV ) >= 0 )
1726 {
1727 MPI_CHK( mpi_sub_mpi( &TU, &TU, &TV ) );
1728 MPI_CHK( mpi_sub_mpi( &U1, &U1, &V1 ) );
1729 MPI_CHK( mpi_sub_mpi( &U2, &U2, &V2 ) );
1730 }
1731 else
1732 {
1733 MPI_CHK( mpi_sub_mpi( &TV, &TV, &TU ) );
1734 MPI_CHK( mpi_sub_mpi( &V1, &V1, &U1 ) );
1735 MPI_CHK( mpi_sub_mpi( &V2, &V2, &U2 ) );
1736 }
1737 }
1738 while( mpi_cmp_int( &TU, 0 ) != 0 );
1739
1740 while( mpi_cmp_int( &V1, 0 ) < 0 )
1741 MPI_CHK( mpi_add_mpi( &V1, &V1, N ) );
1742
1743 while( mpi_cmp_mpi( &V1, N ) >= 0 )
1744 MPI_CHK( mpi_sub_mpi( &V1, &V1, N ) );
1745
1746 MPI_CHK( mpi_copy( X, &V1 ) );
1747
1748 cleanup:
1749
1750 mpi_free( &TA ); mpi_free( &TU ); mpi_free( &U1 ); mpi_free( &U2 );
1751 mpi_free( &G ); mpi_free( &TB ); mpi_free( &TV );
1752 mpi_free( &V1 ); mpi_free( &V2 );
1753
1754 return( ret );
1755 }
1756
1757 #if defined(POLARSSL_GENPRIME)
1758
1759 static const int small_prime[] =
1760 {
1761 3, 5, 7, 11, 13, 17, 19, 23,
1762 29, 31, 37, 41, 43, 47, 53, 59,
1763 61, 67, 71, 73, 79, 83, 89, 97,
1764 101, 103, 107, 109, 113, 127, 131, 137,
1765 139, 149, 151, 157, 163, 167, 173, 179,
1766 181, 191, 193, 197, 199, 211, 223, 227,
1767 229, 233, 239, 241, 251, 257, 263, 269,
1768 271, 277, 281, 283, 293, 307, 311, 313,
1769 317, 331, 337, 347, 349, 353, 359, 367,
1770 373, 379, 383, 389, 397, 401, 409, 419,
1771 421, 431, 433, 439, 443, 449, 457, 461,
1772 463, 467, 479, 487, 491, 499, 503, 509,
1773 521, 523, 541, 547, 557, 563, 569, 571,
1774 577, 587, 593, 599, 601, 607, 613, 617,
1775 619, 631, 641, 643, 647, 653, 659, 661,
1776 673, 677, 683, 691, 701, 709, 719, 727,
1777 733, 739, 743, 751, 757, 761, 769, 773,
1778 787, 797, 809, 811, 821, 823, 827, 829,
1779 839, 853, 857, 859, 863, 877, 881, 883,
1780 887, 907, 911, 919, 929, 937, 941, 947,
1781 953, 967, 971, 977, 983, 991, 997, -103
1782 };
1783
1784 /*
1785 * Miller-Rabin primality test (HAC 4.24)
1786 */
1787 int mpi_is_prime( mpi *X,
1788 int (*f_rng)(void *, unsigned char *, size_t),
1789 void *p_rng )
1790 {
1791 int ret, xs;
1792 size_t i, j, n, s;
1793 mpi W, R, T, A, RR;
1794
1795 if( mpi_cmp_int( X, 0 ) == 0 ||
1796 mpi_cmp_int( X, 1 ) == 0 )
1797 return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE );
1798
1799 if( mpi_cmp_int( X, 2 ) == 0 )
1800 return( 0 );
1801
1802 mpi_init( &W ); mpi_init( &R ); mpi_init( &T ); mpi_init( &A );
1803 mpi_init( &RR );
1804
1805 xs = X->s; X->s = 1;
1806
1807 /*
1808 * test trivial factors first
1809 */
1810 if( ( X->p[0] & 1 ) == 0 )
1811 return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE );
1812
1813 for( i = 0; small_prime[i] > 0; i++ )
1814 {
1815 t_uint r;
1816
1817 if( mpi_cmp_int( X, small_prime[i] ) <= 0 )
1818 return( 0 );
1819
1820 MPI_CHK( mpi_mod_int( &r, X, small_prime[i] ) );
1821
1822 if( r == 0 )
1823 return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE );
1824 }
1825
1826 /*
1827 * W = |X| - 1
1828 * R = W >> lsb( W )
1829 */
1830 MPI_CHK( mpi_sub_int( &W, X, 1 ) );
1831 s = mpi_lsb( &W );
1832 MPI_CHK( mpi_copy( &R, &W ) );
1833 MPI_CHK( mpi_shift_r( &R, s ) );
1834
1835 i = mpi_msb( X );
1836 /*
1837 * HAC, table 4.4
1838 */
1839 n = ( ( i >= 1300 ) ? 2 : ( i >= 850 ) ? 3 :
1840 ( i >= 650 ) ? 4 : ( i >= 350 ) ? 8 :
1841 ( i >= 250 ) ? 12 : ( i >= 150 ) ? 18 : 27 );
1842
1843 for( i = 0; i < n; i++ )
1844 {
1845 /*
1846 * pick a random A, 1 < A < |X| - 1
1847 */
1848 MPI_CHK( mpi_fill_random( &A, X->n * ciL, f_rng, p_rng ) );
1849
1850 if( mpi_cmp_mpi( &A, &W ) >= 0 )
1851 {
1852 j = mpi_msb( &A ) - mpi_msb( &W );
1853 MPI_CHK( mpi_shift_r( &A, j + 1 ) );
1854 }
1855 A.p[0] |= 3;
1856
1857 /*
1858 * A = A^R mod |X|
1859 */
1860 MPI_CHK( mpi_exp_mod( &A, &A, &R, X, &RR ) );
1861
1862 if( mpi_cmp_mpi( &A, &W ) == 0 ||
1863 mpi_cmp_int( &A, 1 ) == 0 )
1864 continue;
1865
1866 j = 1;
1867 while( j < s && mpi_cmp_mpi( &A, &W ) != 0 )
1868 {
1869 /*
1870 * A = A * A mod |X|
1871 */
1872 MPI_CHK( mpi_mul_mpi( &T, &A, &A ) );
1873 MPI_CHK( mpi_mod_mpi( &A, &T, X ) );
1874
1875 if( mpi_cmp_int( &A, 1 ) == 0 )
1876 break;
1877
1878 j++;
1879 }
1880
1881 /*
1882 * not prime if A != |X| - 1 or A == 1
1883 */
1884 if( mpi_cmp_mpi( &A, &W ) != 0 ||
1885 mpi_cmp_int( &A, 1 ) == 0 )
1886 {
1887 ret = POLARSSL_ERR_MPI_NOT_ACCEPTABLE;
1888 break;
1889 }
1890 }
1891
1892 cleanup:
1893
1894 X->s = xs;
1895
1896 mpi_free( &W ); mpi_free( &R ); mpi_free( &T ); mpi_free( &A );
1897 mpi_free( &RR );
1898
1899 return( ret );
1900 }
1901
1902 /*
1903 * Prime number generation
1904 */
1905 int mpi_gen_prime( mpi *X, size_t nbits, int dh_flag,
1906 int (*f_rng)(void *, unsigned char *, size_t),
1907 void *p_rng )
1908 {
1909 int ret;
1910 size_t k, n;
1911 mpi Y;
1912
1913 if( nbits < 3 || nbits > POLARSSL_MPI_MAX_BITS )
1914 return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
1915
1916 mpi_init( &Y );
1917
1918 n = BITS_TO_LIMBS( nbits );
1919
1920 MPI_CHK( mpi_fill_random( X, n * ciL, f_rng, p_rng ) );
1921
1922 k = mpi_msb( X );
1923 if( k < nbits ) MPI_CHK( mpi_shift_l( X, nbits - k ) );
1924 if( k > nbits ) MPI_CHK( mpi_shift_r( X, k - nbits ) );
1925
1926 X->p[0] |= 3;
1927
1928 if( dh_flag == 0 )
1929 {
1930 while( ( ret = mpi_is_prime( X, f_rng, p_rng ) ) != 0 )
1931 {
1932 if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE )
1933 goto cleanup;
1934
1935 MPI_CHK( mpi_add_int( X, X, 2 ) );
1936 }
1937 }
1938 else
1939 {
1940 MPI_CHK( mpi_sub_int( &Y, X, 1 ) );
1941 MPI_CHK( mpi_shift_r( &Y, 1 ) );
1942
1943 while( 1 )
1944 {
1945 if( ( ret = mpi_is_prime( X, f_rng, p_rng ) ) == 0 )
1946 {
1947 if( ( ret = mpi_is_prime( &Y, f_rng, p_rng ) ) == 0 )
1948 break;
1949
1950 if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE )
1951 goto cleanup;
1952 }
1953
1954 if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE )
1955 goto cleanup;
1956
1957 MPI_CHK( mpi_add_int( &Y, X, 1 ) );
1958 MPI_CHK( mpi_add_int( X, X, 2 ) );
1959 MPI_CHK( mpi_shift_r( &Y, 1 ) );
1960 }
1961 }
1962
1963 cleanup:
1964
1965 mpi_free( &Y );
1966
1967 return( ret );
1968 }
1969
1970 #endif
1971
1972 #if defined(POLARSSL_SELF_TEST)
1973
1974 #define GCD_PAIR_COUNT 3
1975
1976 static const int gcd_pairs[GCD_PAIR_COUNT][3] =
1977 {
1978 { 693, 609, 21 },
1979 { 1764, 868, 28 },
1980 { 768454923, 542167814, 1 }
1981 };
1982
1983 /*
1984 * Checkup routine
1985 */
1986 int mpi_self_test( int verbose )
1987 {
1988 int ret, i;
1989 mpi A, E, N, X, Y, U, V;
1990
1991 mpi_init( &A ); mpi_init( &E ); mpi_init( &N ); mpi_init( &X );
1992 mpi_init( &Y ); mpi_init( &U ); mpi_init( &V );
1993
1994 MPI_CHK( mpi_read_string( &A, 16,
1995 "EFE021C2645FD1DC586E69184AF4A31E" \
1996 "D5F53E93B5F123FA41680867BA110131" \
1997 "944FE7952E2517337780CB0DB80E61AA" \
1998 "E7C8DDC6C5C6AADEB34EB38A2F40D5E6" ) );
1999
2000 MPI_CHK( mpi_read_string( &E, 16,
2001 "B2E7EFD37075B9F03FF989C7C5051C20" \
2002 "34D2A323810251127E7BF8625A4F49A5" \
2003 "F3E27F4DA8BD59C47D6DAABA4C8127BD" \
2004 "5B5C25763222FEFCCFC38B832366C29E" ) );
2005
2006 MPI_CHK( mpi_read_string( &N, 16,
2007 "0066A198186C18C10B2F5ED9B522752A" \
2008 "9830B69916E535C8F047518A889A43A5" \
2009 "94B6BED27A168D31D4A52F88925AA8F5" ) );
2010
2011 MPI_CHK( mpi_mul_mpi( &X, &A, &N ) );
2012
2013 MPI_CHK( mpi_read_string( &U, 16,
2014 "602AB7ECA597A3D6B56FF9829A5E8B85" \
2015 "9E857EA95A03512E2BAE7391688D264A" \
2016 "A5663B0341DB9CCFD2C4C5F421FEC814" \
2017 "8001B72E848A38CAE1C65F78E56ABDEF" \
2018 "E12D3C039B8A02D6BE593F0BBBDA56F1" \
2019 "ECF677152EF804370C1A305CAF3B5BF1" \
2020 "30879B56C61DE584A0F53A2447A51E" ) );
2021
2022 if( verbose != 0 )
2023 printf( " MPI test #1 (mul_mpi): " );
2024
2025 if( mpi_cmp_mpi( &X, &U ) != 0 )
2026 {
2027 if( verbose != 0 )
2028 printf( "failed\n" );
2029
2030 return( 1 );
2031 }
2032
2033 if( verbose != 0 )
2034 printf( "passed\n" );
2035
2036 MPI_CHK( mpi_div_mpi( &X, &Y, &A, &N ) );
2037
2038 MPI_CHK( mpi_read_string( &U, 16,
2039 "256567336059E52CAE22925474705F39A94" ) );
2040
2041 MPI_CHK( mpi_read_string( &V, 16,
2042 "6613F26162223DF488E9CD48CC132C7A" \
2043 "0AC93C701B001B092E4E5B9F73BCD27B" \
2044 "9EE50D0657C77F374E903CDFA4C642" ) );
2045
2046 if( verbose != 0 )
2047 printf( " MPI test #2 (div_mpi): " );
2048
2049 if( mpi_cmp_mpi( &X, &U ) != 0 ||
2050 mpi_cmp_mpi( &Y, &V ) != 0 )
2051 {
2052 if( verbose != 0 )
2053 printf( "failed\n" );
2054
2055 return( 1 );
2056 }
2057
2058 if( verbose != 0 )
2059 printf( "passed\n" );
2060
2061 MPI_CHK( mpi_exp_mod( &X, &A, &E, &N, NULL ) );
2062
2063 MPI_CHK( mpi_read_string( &U, 16,
2064 "36E139AEA55215609D2816998ED020BB" \
2065 "BD96C37890F65171D948E9BC7CBAA4D9" \
2066 "325D24D6A3C12710F10A09FA08AB87" ) );
2067
2068 if( verbose != 0 )
2069 printf( " MPI test #3 (exp_mod): " );
2070
2071 if( mpi_cmp_mpi( &X, &U ) != 0 )
2072 {
2073 if( verbose != 0 )
2074 printf( "failed\n" );
2075
2076 return( 1 );
2077 }
2078
2079 if( verbose != 0 )
2080 printf( "passed\n" );
2081
2082 #if defined(POLARSSL_GENPRIME)
2083 MPI_CHK( mpi_inv_mod( &X, &A, &N ) );
2084
2085 MPI_CHK( mpi_read_string( &U, 16,
2086 "003A0AAEDD7E784FC07D8F9EC6E3BFD5" \
2087 "C3DBA76456363A10869622EAC2DD84EC" \
2088 "C5B8A74DAC4D09E03B5E0BE779F2DF61" ) );
2089
2090 if( verbose != 0 )
2091 printf( " MPI test #4 (inv_mod): " );
2092
2093 if( mpi_cmp_mpi( &X, &U ) != 0 )
2094 {
2095 if( verbose != 0 )
2096 printf( "failed\n" );
2097
2098 return( 1 );
2099 }
2100
2101 if( verbose != 0 )
2102 printf( "passed\n" );
2103 #endif
2104
2105 if( verbose != 0 )
2106 printf( " MPI test #5 (simple gcd): " );
2107
2108 for ( i = 0; i < GCD_PAIR_COUNT; i++)
2109 {
2110 MPI_CHK( mpi_lset( &X, gcd_pairs[i][0] ) );
2111 MPI_CHK( mpi_lset( &Y, gcd_pairs[i][1] ) );
2112
2113 MPI_CHK( mpi_gcd( &A, &X, &Y ) );
2114
2115 if( mpi_cmp_int( &A, gcd_pairs[i][2] ) != 0 )
2116 {
2117 if( verbose != 0 )
2118 printf( "failed at %d\n", i );
2119
2120 return( 1 );
2121 }
2122 }
2123
2124 if( verbose != 0 )
2125 printf( "passed\n" );
2126
2127 cleanup:
2128
2129 if( ret != 0 && verbose != 0 )
2130 printf( "Unexpected error, return code = %08X\n", ret );
2131
2132 mpi_free( &A ); mpi_free( &E ); mpi_free( &N ); mpi_free( &X );
2133 mpi_free( &Y ); mpi_free( &U ); mpi_free( &V );
2134
2135 if( verbose != 0 )
2136 printf( "\n" );
2137
2138 return( ret );
2139 }
2140
2141 #endif
2142
2143 #endif
Proxmark3 GIT tracking
Impressum, Datenschutz