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1/**
2 * \file bignum.h
3 *
4 * \brief Multi-precision integer library
5 *
6 * Copyright (C) 2006-2013, Brainspark B.V.
7 *
8 * This file is part of PolarSSL (http://www.polarssl.org)
9 * Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org>
10 *
11 * All rights reserved.
12 *
13 * This program is free software; you can redistribute it and/or modify
14 * it under the terms of the GNU General Public License as published by
15 * the Free Software Foundation; either version 2 of the License, or
16 * (at your option) any later version.
17 *
18 * This program is distributed in the hope that it will be useful,
19 * but WITHOUT ANY WARRANTY; without even the implied warranty of
20 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
21 * GNU General Public License for more details.
22 *
23 * You should have received a copy of the GNU General Public License along
24 * with this program; if not, write to the Free Software Foundation, Inc.,
25 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
26 */
27#ifndef POLARSSL_BIGNUM_H
28#define POLARSSL_BIGNUM_H
29
30#include <stdio.h>
31#include <string.h>
32
33#include "polarssl_config.h"
34
35#ifdef _MSC_VER
36#include <basetsd.h>
37#if (_MSC_VER <= 1200)
38typedef signed short int16_t;
39typedef unsigned short uint16_t;
40#else
41typedef INT16 int16_t;
42typedef UINT16 uint16_t;
43#endif
44typedef INT32 int32_t;
45typedef INT64 int64_t;
46typedef UINT32 uint32_t;
47typedef UINT64 uint64_t;
48#else
49#include <inttypes.h>
50#endif
51
52#define POLARSSL_ERR_MPI_FILE_IO_ERROR -0x0002 /**< An error occurred while reading from or writing to a file. */
53#define POLARSSL_ERR_MPI_BAD_INPUT_DATA -0x0004 /**< Bad input parameters to function. */
54#define POLARSSL_ERR_MPI_INVALID_CHARACTER -0x0006 /**< There is an invalid character in the digit string. */
55#define POLARSSL_ERR_MPI_BUFFER_TOO_SMALL -0x0008 /**< The buffer is too small to write to. */
56#define POLARSSL_ERR_MPI_NEGATIVE_VALUE -0x000A /**< The input arguments are negative or result in illegal output. */
57#define POLARSSL_ERR_MPI_DIVISION_BY_ZERO -0x000C /**< The input argument for division is zero, which is not allowed. */
58#define POLARSSL_ERR_MPI_NOT_ACCEPTABLE -0x000E /**< The input arguments are not acceptable. */
59#define POLARSSL_ERR_MPI_MALLOC_FAILED -0x0010 /**< Memory allocation failed. */
60
61#define MPI_CHK(f) if( ( ret = f ) != 0 ) goto cleanup
62
63/*
64 * Maximum size MPIs are allowed to grow to in number of limbs.
65 */
66#define POLARSSL_MPI_MAX_LIMBS 10000
67
68#if !defined(POLARSSL_CONFIG_OPTIONS)
69/*
70 * Maximum window size used for modular exponentiation. Default: 6
71 * Minimum value: 1. Maximum value: 6.
72 *
73 * Result is an array of ( 2 << POLARSSL_MPI_WINDOW_SIZE ) MPIs used
74 * for the sliding window calculation. (So 64 by default)
75 *
76 * Reduction in size, reduces speed.
77 */
78#define POLARSSL_MPI_WINDOW_SIZE 6 /**< Maximum windows size used. */
79
80/*
81 * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
82 * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
83 *
84 * Note: Calculations can results temporarily in larger MPIs. So the number
85 * of limbs required (POLARSSL_MPI_MAX_LIMBS) is higher.
86 */
87#define POLARSSL_MPI_MAX_SIZE 512 /**< Maximum number of bytes for usable MPIs. */
88
89#endif /* !POLARSSL_CONFIG_OPTIONS */
90
91#define POLARSSL_MPI_MAX_BITS ( 8 * POLARSSL_MPI_MAX_SIZE ) /**< Maximum number of bits for usable MPIs. */
92
93/*
94 * When reading from files with mpi_read_file() and writing to files with
95 * mpi_write_file() the buffer should have space
96 * for a (short) label, the MPI (in the provided radix), the newline
97 * characters and the '\0'.
98 *
99 * By default we assume at least a 10 char label, a minimum radix of 10
100 * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
101 * Autosized at compile time for at least a 10 char label, a minimum radix
102 * of 10 (decimal) for a number of POLARSSL_MPI_MAX_BITS size.
103 *
104 * This used to be statically sized to 1250 for a maximum of 4096 bit
105 * numbers (1234 decimal chars).
106 *
107 * Calculate using the formula:
108 * POLARSSL_MPI_RW_BUFFER_SIZE = ceil(POLARSSL_MPI_MAX_BITS / ln(10) * ln(2)) +
109 * LabelSize + 6
110 */
111#define POLARSSL_MPI_MAX_BITS_SCALE100 ( 100 * POLARSSL_MPI_MAX_BITS )
112#define LN_2_DIV_LN_10_SCALE100 332
113#define POLARSSL_MPI_RW_BUFFER_SIZE ( ((POLARSSL_MPI_MAX_BITS_SCALE100 + LN_2_DIV_LN_10_SCALE100 - 1) / LN_2_DIV_LN_10_SCALE100) + 10 + 6 )
114
115/*
116 * Define the base integer type, architecture-wise
117 */
118#if defined(POLARSSL_HAVE_INT8)
119typedef signed char t_sint;
120typedef unsigned char t_uint;
121typedef uint16_t t_udbl;
122#define POLARSSL_HAVE_UDBL
123#else
124#if defined(POLARSSL_HAVE_INT16)
125typedef int16_t t_sint;
126typedef uint16_t t_uint;
127typedef uint32_t t_udbl;
128#define POLARSSL_HAVE_UDBL
129#else
130 #if ( defined(_MSC_VER) && defined(_M_AMD64) )
131 typedef int64_t t_sint;
132 typedef uint64_t t_uint;
133 #else
134 #if ( defined(__GNUC__) && ( \
135 defined(__amd64__) || defined(__x86_64__) || \
136 defined(__ppc64__) || defined(__powerpc64__) || \
137 defined(__ia64__) || defined(__alpha__) || \
138 (defined(__sparc__) && defined(__arch64__)) || \
139 defined(__s390x__) ) )
140 typedef int64_t t_sint;
141 typedef uint64_t t_uint;
142 typedef unsigned int t_udbl __attribute__((mode(TI)));
143 #define POLARSSL_HAVE_UDBL
144 #else
145 typedef int32_t t_sint;
146 typedef uint32_t t_uint;
147 #if ( defined(_MSC_VER) && defined(_M_IX86) )
148 typedef uint64_t t_udbl;
149 #define POLARSSL_HAVE_UDBL
150 #else
151 #if defined( POLARSSL_HAVE_LONGLONG )
152 typedef unsigned long long t_udbl;
153 #define POLARSSL_HAVE_UDBL
154 #endif
155 #endif
156 #endif
157 #endif
158#endif /* POLARSSL_HAVE_INT16 */
159#endif /* POLARSSL_HAVE_INT8 */
160
161/**
162 * \brief MPI structure
163 */
164typedef struct
165{
166 int s; /*!< integer sign */
167 size_t n; /*!< total # of limbs */
168 t_uint *p; /*!< pointer to limbs */
169}
170mpi;
171
172#ifdef __cplusplus
173extern "C" {
174#endif
175
176/**
177 * \brief Initialize one MPI
178 *
179 * \param X One MPI to initialize.
180 */
181void mpi_init( mpi *X );
182
183/**
184 * \brief Unallocate one MPI
185 *
186 * \param X One MPI to unallocate.
187 */
188void mpi_free( mpi *X );
189
190/**
191 * \brief Enlarge to the specified number of limbs
192 *
193 * \param X MPI to grow
194 * \param nblimbs The target number of limbs
195 *
196 * \return 0 if successful,
197 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
198 */
199int mpi_grow( mpi *X, size_t nblimbs );
200
201/**
202 * \brief Copy the contents of Y into X
203 *
204 * \param X Destination MPI
205 * \param Y Source MPI
206 *
207 * \return 0 if successful,
208 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
209 */
210int mpi_copy( mpi *X, const mpi *Y );
211
212/**
213 * \brief Swap the contents of X and Y
214 *
215 * \param X First MPI value
216 * \param Y Second MPI value
217 */
218void mpi_swap( mpi *X, mpi *Y );
219
220/**
221 * \brief Set value from integer
222 *
223 * \param X MPI to set
224 * \param z Value to use
225 *
226 * \return 0 if successful,
227 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
228 */
229int mpi_lset( mpi *X, t_sint z );
230
231/**
232 * \brief Get a specific bit from X
233 *
234 * \param X MPI to use
235 * \param pos Zero-based index of the bit in X
236 *
237 * \return Either a 0 or a 1
238 */
239int mpi_get_bit( const mpi *X, size_t pos );
240
241/**
242 * \brief Set a bit of X to a specific value of 0 or 1
243 *
244 * \note Will grow X if necessary to set a bit to 1 in a not yet
245 * existing limb. Will not grow if bit should be set to 0
246 *
247 * \param X MPI to use
248 * \param pos Zero-based index of the bit in X
249 * \param val The value to set the bit to (0 or 1)
250 *
251 * \return 0 if successful,
252 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
253 * POLARSSL_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1
254 */
255int mpi_set_bit( mpi *X, size_t pos, unsigned char val );
256
257/**
258 * \brief Return the number of zero-bits before the least significant
259 * '1' bit
260 *
261 * Note: Thus also the zero-based index of the least significant '1' bit
262 *
263 * \param X MPI to use
264 */
265size_t mpi_lsb( const mpi *X );
266
267/**
268 * \brief Return the number of bits up to and including the most
269 * significant '1' bit'
270 *
271 * Note: Thus also the one-based index of the most significant '1' bit
272 *
273 * \param X MPI to use
274 */
275size_t mpi_msb( const mpi *X );
276
277/**
278 * \brief Return the total size in bytes
279 *
280 * \param X MPI to use
281 */
282size_t mpi_size( const mpi *X );
283
284/**
285 * \brief Import from an ASCII string
286 *
287 * \param X Destination MPI
288 * \param radix Input numeric base
289 * \param s Null-terminated string buffer
290 *
291 * \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code
292 */
293int mpi_read_string( mpi *X, int radix, const char *s );
294
295/**
296 * \brief Export into an ASCII string
297 *
298 * \param X Source MPI
299 * \param radix Output numeric base
300 * \param s String buffer
301 * \param slen String buffer size
302 *
303 * \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code.
304 * *slen is always updated to reflect the amount
305 * of data that has (or would have) been written.
306 *
307 * \note Call this function with *slen = 0 to obtain the
308 * minimum required buffer size in *slen.
309 */
310int mpi_write_string( const mpi *X, int radix, char *s, size_t *slen );
311
312#if defined(POLARSSL_FS_IO)
313/**
314 * \brief Read X from an opened file
315 *
316 * \param X Destination MPI
317 * \param radix Input numeric base
318 * \param fin Input file handle
319 *
320 * \return 0 if successful, POLARSSL_ERR_MPI_BUFFER_TOO_SMALL if
321 * the file read buffer is too small or a
322 * POLARSSL_ERR_MPI_XXX error code
323 */
324int mpi_read_file( mpi *X, int radix, FILE *fin );
325
326/**
327 * \brief Write X into an opened file, or stdout if fout is NULL
328 *
329 * \param p Prefix, can be NULL
330 * \param X Source MPI
331 * \param radix Output numeric base
332 * \param fout Output file handle (can be NULL)
333 *
334 * \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code
335 *
336 * \note Set fout == NULL to print X on the console.
337 */
338int mpi_write_file( const char *p, const mpi *X, int radix, FILE *fout );
339#endif /* POLARSSL_FS_IO */
340
341/**
342 * \brief Import X from unsigned binary data, big endian
343 *
344 * \param X Destination MPI
345 * \param buf Input buffer
346 * \param buflen Input buffer size
347 *
348 * \return 0 if successful,
349 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
350 */
351int mpi_read_binary( mpi *X, const unsigned char *buf, size_t buflen );
352
353/**
354 * \brief Export X into unsigned binary data, big endian
355 *
356 * \param X Source MPI
357 * \param buf Output buffer
358 * \param buflen Output buffer size
359 *
360 * \return 0 if successful,
361 * POLARSSL_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough
362 */
363int mpi_write_binary( const mpi *X, unsigned char *buf, size_t buflen );
364
365/**
366 * \brief Left-shift: X <<= count
367 *
368 * \param X MPI to shift
369 * \param count Amount to shift
370 *
371 * \return 0 if successful,
372 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
373 */
374int mpi_shift_l( mpi *X, size_t count );
375
376/**
377 * \brief Right-shift: X >>= count
378 *
379 * \param X MPI to shift
380 * \param count Amount to shift
381 *
382 * \return 0 if successful,
383 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
384 */
385int mpi_shift_r( mpi *X, size_t count );
386
387/**
388 * \brief Compare unsigned values
389 *
390 * \param X Left-hand MPI
391 * \param Y Right-hand MPI
392 *
393 * \return 1 if |X| is greater than |Y|,
394 * -1 if |X| is lesser than |Y| or
395 * 0 if |X| is equal to |Y|
396 */
397int mpi_cmp_abs( const mpi *X, const mpi *Y );
398
399/**
400 * \brief Compare signed values
401 *
402 * \param X Left-hand MPI
403 * \param Y Right-hand MPI
404 *
405 * \return 1 if X is greater than Y,
406 * -1 if X is lesser than Y or
407 * 0 if X is equal to Y
408 */
409int mpi_cmp_mpi( const mpi *X, const mpi *Y );
410
411/**
412 * \brief Compare signed values
413 *
414 * \param X Left-hand MPI
415 * \param z The integer value to compare to
416 *
417 * \return 1 if X is greater than z,
418 * -1 if X is lesser than z or
419 * 0 if X is equal to z
420 */
421int mpi_cmp_int( const mpi *X, t_sint z );
422
423/**
424 * \brief Unsigned addition: X = |A| + |B|
425 *
426 * \param X Destination MPI
427 * \param A Left-hand MPI
428 * \param B Right-hand MPI
429 *
430 * \return 0 if successful,
431 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
432 */
433int mpi_add_abs( mpi *X, const mpi *A, const mpi *B );
434
435/**
436 * \brief Unsigned substraction: X = |A| - |B|
437 *
438 * \param X Destination MPI
439 * \param A Left-hand MPI
440 * \param B Right-hand MPI
441 *
442 * \return 0 if successful,
443 * POLARSSL_ERR_MPI_NEGATIVE_VALUE if B is greater than A
444 */
445int mpi_sub_abs( mpi *X, const mpi *A, const mpi *B );
446
447/**
448 * \brief Signed addition: X = A + B
449 *
450 * \param X Destination MPI
451 * \param A Left-hand MPI
452 * \param B Right-hand MPI
453 *
454 * \return 0 if successful,
455 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
456 */
457int mpi_add_mpi( mpi *X, const mpi *A, const mpi *B );
458
459/**
460 * \brief Signed substraction: X = A - B
461 *
462 * \param X Destination MPI
463 * \param A Left-hand MPI
464 * \param B Right-hand MPI
465 *
466 * \return 0 if successful,
467 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
468 */
469int mpi_sub_mpi( mpi *X, const mpi *A, const mpi *B );
470
471/**
472 * \brief Signed addition: X = A + b
473 *
474 * \param X Destination MPI
475 * \param A Left-hand MPI
476 * \param b The integer value to add
477 *
478 * \return 0 if successful,
479 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
480 */
481int mpi_add_int( mpi *X, const mpi *A, t_sint b );
482
483/**
484 * \brief Signed substraction: X = A - b
485 *
486 * \param X Destination MPI
487 * \param A Left-hand MPI
488 * \param b The integer value to subtract
489 *
490 * \return 0 if successful,
491 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
492 */
493int mpi_sub_int( mpi *X, const mpi *A, t_sint b );
494
495/**
496 * \brief Baseline multiplication: X = A * B
497 *
498 * \param X Destination MPI
499 * \param A Left-hand MPI
500 * \param B Right-hand MPI
501 *
502 * \return 0 if successful,
503 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
504 */
505int mpi_mul_mpi( mpi *X, const mpi *A, const mpi *B );
506
507/**
508 * \brief Baseline multiplication: X = A * b
509 * Note: b is an unsigned integer type, thus
510 * Negative values of b are ignored.
511 *
512 * \param X Destination MPI
513 * \param A Left-hand MPI
514 * \param b The integer value to multiply with
515 *
516 * \return 0 if successful,
517 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
518 */
519int mpi_mul_int( mpi *X, const mpi *A, t_sint b );
520
521/**
522 * \brief Division by mpi: A = Q * B + R
523 *
524 * \param Q Destination MPI for the quotient
525 * \param R Destination MPI for the rest value
526 * \param A Left-hand MPI
527 * \param B Right-hand MPI
528 *
529 * \return 0 if successful,
530 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
531 * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0
532 *
533 * \note Either Q or R can be NULL.
534 */
535int mpi_div_mpi( mpi *Q, mpi *R, const mpi *A, const mpi *B );
536
537/**
538 * \brief Division by int: A = Q * b + R
539 *
540 * \param Q Destination MPI for the quotient
541 * \param R Destination MPI for the rest value
542 * \param A Left-hand MPI
543 * \param b Integer to divide by
544 *
545 * \return 0 if successful,
546 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
547 * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0
548 *
549 * \note Either Q or R can be NULL.
550 */
551int mpi_div_int( mpi *Q, mpi *R, const mpi *A, t_sint b );
552
553/**
554 * \brief Modulo: R = A mod B
555 *
556 * \param R Destination MPI for the rest value
557 * \param A Left-hand MPI
558 * \param B Right-hand MPI
559 *
560 * \return 0 if successful,
561 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
562 * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0,
563 * POLARSSL_ERR_MPI_NEGATIVE_VALUE if B < 0
564 */
565int mpi_mod_mpi( mpi *R, const mpi *A, const mpi *B );
566
567/**
568 * \brief Modulo: r = A mod b
569 *
570 * \param r Destination t_uint
571 * \param A Left-hand MPI
572 * \param b Integer to divide by
573 *
574 * \return 0 if successful,
575 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
576 * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0,
577 * POLARSSL_ERR_MPI_NEGATIVE_VALUE if b < 0
578 */
579int mpi_mod_int( t_uint *r, const mpi *A, t_sint b );
580
581/**
582 * \brief Sliding-window exponentiation: X = A^E mod N
583 *
584 * \param X Destination MPI
585 * \param A Left-hand MPI
586 * \param E Exponent MPI
587 * \param N Modular MPI
588 * \param _RR Speed-up MPI used for recalculations
589 *
590 * \return 0 if successful,
591 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
592 * POLARSSL_ERR_MPI_BAD_INPUT_DATA if N is negative or even or if
593 * E is negative
594 *
595 * \note _RR is used to avoid re-computing R*R mod N across
596 * multiple calls, which speeds up things a bit. It can
597 * be set to NULL if the extra performance is unneeded.
598 */
599int mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR );
600
601/**
602 * \brief Fill an MPI X with size bytes of random
603 *
604 * \param X Destination MPI
605 * \param size Size in bytes
606 * \param f_rng RNG function
607 * \param p_rng RNG parameter
608 *
609 * \return 0 if successful,
610 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
611 */
612int mpi_fill_random( mpi *X, size_t size,
613 int (*f_rng)(void *, unsigned char *, size_t),
614 void *p_rng );
615
616/**
617 * \brief Greatest common divisor: G = gcd(A, B)
618 *
619 * \param G Destination MPI
620 * \param A Left-hand MPI
621 * \param B Right-hand MPI
622 *
623 * \return 0 if successful,
624 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
625 */
626int mpi_gcd( mpi *G, const mpi *A, const mpi *B );
627
628/**
629 * \brief Modular inverse: X = A^-1 mod N
630 *
631 * \param X Destination MPI
632 * \param A Left-hand MPI
633 * \param N Right-hand MPI
634 *
635 * \return 0 if successful,
636 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
637 * POLARSSL_ERR_MPI_BAD_INPUT_DATA if N is negative or nil
638 POLARSSL_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N
639 */
640int mpi_inv_mod( mpi *X, const mpi *A, const mpi *N );
641
642/**
643 * \brief Miller-Rabin primality test
644 *
645 * \param X MPI to check
646 * \param f_rng RNG function
647 * \param p_rng RNG parameter
648 *
649 * \return 0 if successful (probably prime),
650 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
651 * POLARSSL_ERR_MPI_NOT_ACCEPTABLE if X is not prime
652 */
653int mpi_is_prime( mpi *X,
654 int (*f_rng)(void *, unsigned char *, size_t),
655 void *p_rng );
656
657/**
658 * \brief Prime number generation
659 *
660 * \param X Destination MPI
661 * \param nbits Required size of X in bits ( 3 <= nbits <= POLARSSL_MPI_MAX_BITS )
662 * \param dh_flag If 1, then (X-1)/2 will be prime too
663 * \param f_rng RNG function
664 * \param p_rng RNG parameter
665 *
666 * \return 0 if successful (probably prime),
667 * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
668 * POLARSSL_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
669 */
670int mpi_gen_prime( mpi *X, size_t nbits, int dh_flag,
671 int (*f_rng)(void *, unsigned char *, size_t),
672 void *p_rng );
673
674/**
675 * \brief Checkup routine
676 *
677 * \return 0 if successful, or 1 if the test failed
678 */
679int mpi_self_test( int verbose );
680
681#ifdef __cplusplus
682}
683#endif
684
685#endif /* bignum.h */
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