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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) | |
38 | typedef signed short int16_t; | |
39 | typedef unsigned short uint16_t; | |
40 | #else | |
41 | typedef INT16 int16_t; | |
42 | typedef UINT16 uint16_t; | |
43 | #endif | |
44 | typedef INT32 int32_t; | |
45 | typedef INT64 int64_t; | |
46 | typedef UINT32 uint32_t; | |
47 | typedef 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) | |
119 | typedef signed char t_sint; | |
120 | typedef unsigned char t_uint; | |
121 | typedef uint16_t t_udbl; | |
122 | #define POLARSSL_HAVE_UDBL | |
123 | #else | |
124 | #if defined(POLARSSL_HAVE_INT16) | |
125 | typedef int16_t t_sint; | |
126 | typedef uint16_t t_uint; | |
127 | typedef 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 | */ | |
164 | typedef struct | |
165 | { | |
166 | int s; /*!< integer sign */ | |
167 | size_t n; /*!< total # of limbs */ | |
168 | t_uint *p; /*!< pointer to limbs */ | |
169 | } | |
170 | mpi; | |
171 | ||
172 | #ifdef __cplusplus | |
173 | extern "C" { | |
174 | #endif | |
175 | ||
176 | /** | |
177 | * \brief Initialize one MPI | |
178 | * | |
179 | * \param X One MPI to initialize. | |
180 | */ | |
181 | void mpi_init( mpi *X ); | |
182 | ||
183 | /** | |
184 | * \brief Unallocate one MPI | |
185 | * | |
186 | * \param X One MPI to unallocate. | |
187 | */ | |
188 | void 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 | */ | |
199 | int 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 | */ | |
210 | int 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 | */ | |
218 | void 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 | */ | |
229 | int 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 | */ | |
239 | int 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 | */ | |
255 | int 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 | */ | |
265 | size_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 | */ | |
275 | size_t mpi_msb( const mpi *X ); | |
276 | ||
277 | /** | |
278 | * \brief Return the total size in bytes | |
279 | * | |
280 | * \param X MPI to use | |
281 | */ | |
282 | size_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 | */ | |
293 | int 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 | */ | |
310 | int 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 | */ | |
324 | int 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 | */ | |
338 | int 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 | */ | |
351 | int 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 | */ | |
363 | int 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 | */ | |
374 | int 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 | */ | |
385 | int 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 | */ | |
397 | int 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 | */ | |
409 | int 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 | */ | |
421 | int 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 | */ | |
433 | int 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 | */ | |
445 | int 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 | */ | |
457 | int 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 | */ | |
469 | int 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 | */ | |
481 | int 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 | */ | |
493 | int 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 | */ | |
505 | int 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 | */ | |
519 | int 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 | */ | |
535 | int 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 | */ | |
551 | int 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 | */ | |
565 | int 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 | */ | |
579 | int 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 | */ | |
599 | int 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 | */ | |
612 | int 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 | */ | |
626 | int 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 | */ | |
640 | int 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 | */ | |
653 | int 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 | */ | |
670 | int 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 | */ | |
679 | int mpi_self_test( int verbose ); | |
680 | ||
681 | #ifdef __cplusplus | |
682 | } | |
683 | #endif | |
684 | ||
685 | #endif /* bignum.h */ |