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1 | /** |
2 | * \file bignum.h | |
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 | #ifndef POLARSSL_BIGNUM_H | |
27 | #define POLARSSL_BIGNUM_H | |
28 | ||
29 | #include <stdio.h> | |
30 | ||
31 | #define POLARSSL_ERR_MPI_FILE_IO_ERROR 0x0002 | |
32 | #define POLARSSL_ERR_MPI_BAD_INPUT_DATA 0x0004 | |
33 | #define POLARSSL_ERR_MPI_INVALID_CHARACTER 0x0006 | |
34 | #define POLARSSL_ERR_MPI_BUFFER_TOO_SMALL 0x0008 | |
35 | #define POLARSSL_ERR_MPI_NEGATIVE_VALUE 0x000A | |
36 | #define POLARSSL_ERR_MPI_DIVISION_BY_ZERO 0x000C | |
37 | #define POLARSSL_ERR_MPI_NOT_ACCEPTABLE 0x000E | |
38 | ||
39 | #define MPI_CHK(f) if( ( ret = f ) != 0 ) goto cleanup | |
40 | ||
41 | /* | |
42 | * Define the base integer type, architecture-wise | |
43 | */ | |
44 | #if defined(POLARSSL_HAVE_INT8) | |
45 | typedef unsigned char t_int; | |
46 | typedef unsigned short t_dbl; | |
47 | #else | |
48 | #if defined(POLARSSL_HAVE_INT16) | |
49 | typedef unsigned short t_int; | |
50 | typedef unsigned long t_dbl; | |
51 | #else | |
52 | typedef unsigned long t_int; | |
53 | #if defined(_MSC_VER) && defined(_M_IX86) | |
54 | typedef unsigned __int64 t_dbl; | |
55 | #else | |
56 | #if defined(__amd64__) || defined(__x86_64__) || \ | |
57 | defined(__ppc64__) || defined(__powerpc64__) || \ | |
58 | defined(__ia64__) || defined(__alpha__) | |
59 | typedef unsigned int t_dbl __attribute__((mode(TI))); | |
60 | #else | |
61 | #if defined(POLARSSL_HAVE_LONGLONG) | |
62 | typedef unsigned long long t_dbl; | |
63 | #endif | |
64 | #endif | |
65 | #endif | |
66 | #endif | |
67 | #endif | |
68 | ||
69 | /** | |
70 | * \brief MPI structure | |
71 | */ | |
72 | typedef struct | |
73 | { | |
74 | int s; /*!< integer sign */ | |
75 | int n; /*!< total # of limbs */ | |
76 | t_int *p; /*!< pointer to limbs */ | |
77 | } | |
78 | mpi; | |
79 | ||
80 | #ifdef __cplusplus | |
81 | extern "C" { | |
82 | #endif | |
83 | ||
84 | /** | |
85 | * \brief Initialize one or more mpi | |
86 | */ | |
87 | void mpi_init( mpi *X, ... ); | |
88 | ||
89 | /** | |
90 | * \brief Unallocate one or more mpi | |
91 | */ | |
92 | void mpi_free( mpi *X, ... ); | |
93 | ||
94 | /** | |
95 | * \brief Enlarge to the specified number of limbs | |
96 | * | |
97 | * \param X MPI to grow | |
98 | * \param nblimbs The target number of limbs | |
99 | * | |
100 | * \return 0 if successful, | |
101 | * 1 if memory allocation failed | |
102 | */ | |
103 | int mpi_grow( mpi *X, int nblimbs ); | |
104 | ||
105 | /** | |
106 | * \brief Copy the contents of Y into X | |
107 | * | |
108 | * \param X Destination MPI | |
109 | * \param Y Source MPI | |
110 | * | |
111 | * \return 0 if successful, | |
112 | * 1 if memory allocation failed | |
113 | */ | |
114 | int mpi_copy( mpi *X, const mpi *Y ); | |
115 | ||
116 | /** | |
117 | * \brief Swap the contents of X and Y | |
118 | * | |
119 | * \param X First MPI value | |
120 | * \param Y Second MPI value | |
121 | */ | |
122 | void mpi_swap( mpi *X, mpi *Y ); | |
123 | ||
124 | /** | |
125 | * \brief Set value from integer | |
126 | * | |
127 | * \param X MPI to set | |
128 | * \param z Value to use | |
129 | * | |
130 | * \return 0 if successful, | |
131 | * 1 if memory allocation failed | |
132 | */ | |
133 | int mpi_lset( mpi *X, int z ); | |
134 | ||
135 | /** | |
136 | * \brief Return the number of least significant bits | |
137 | * | |
138 | * \param X MPI to use | |
139 | */ | |
140 | int mpi_lsb( const mpi *X ); | |
141 | ||
142 | /** | |
143 | * \brief Return the number of most significant bits | |
144 | * | |
145 | * \param X MPI to use | |
146 | */ | |
147 | int mpi_msb( const mpi *X ); | |
148 | ||
149 | /** | |
150 | * \brief Return the total size in bytes | |
151 | * | |
152 | * \param X MPI to use | |
153 | */ | |
154 | int mpi_size( const mpi *X ); | |
155 | ||
156 | /** | |
157 | * \brief Import from an ASCII string | |
158 | * | |
159 | * \param X Destination MPI | |
160 | * \param radix Input numeric base | |
161 | * \param s Null-terminated string buffer | |
162 | * | |
163 | * \return 0 if successful, or an POLARSSL_ERR_MPI_XXX error code | |
164 | */ | |
165 | int mpi_read_string( mpi *X, int radix, const char *s ); | |
166 | ||
167 | /** | |
168 | * \brief Export into an ASCII string | |
169 | * | |
170 | * \param X Source MPI | |
171 | * \param radix Output numeric base | |
172 | * \param s String buffer | |
173 | * \param slen String buffer size | |
174 | * | |
175 | * \return 0 if successful, or an POLARSSL_ERR_MPI_XXX error code. | |
176 | * *slen is always updated to reflect the amount | |
177 | * of data that has (or would have) been written. | |
178 | * | |
179 | * \note Call this function with *slen = 0 to obtain the | |
180 | * minimum required buffer size in *slen. | |
181 | */ | |
182 | int mpi_write_string( const mpi *X, int radix, char *s, int *slen ); | |
183 | ||
184 | /** | |
185 | * \brief Read X from an opened file | |
186 | * | |
187 | * \param X Destination MPI | |
188 | * \param radix Input numeric base | |
189 | * \param fin Input file handle | |
190 | * | |
191 | * \return 0 if successful, or an POLARSSL_ERR_MPI_XXX error code | |
192 | */ | |
193 | int mpi_read_file( mpi *X, int radix, FILE *fin ); | |
194 | ||
195 | /** | |
196 | * \brief Write X into an opened file, or stdout if fout is NULL | |
197 | * | |
198 | * \param p Prefix, can be NULL | |
199 | * \param X Source MPI | |
200 | * \param radix Output numeric base | |
201 | * \param fout Output file handle (can be NULL) | |
202 | * | |
203 | * \return 0 if successful, or an POLARSSL_ERR_MPI_XXX error code | |
204 | * | |
205 | * \note Set fout == NULL to print X on the console. | |
206 | */ | |
207 | int mpi_write_file( const char *p, const mpi *X, int radix, FILE *fout ); | |
208 | ||
209 | /** | |
210 | * \brief Import X from unsigned binary data, big endian | |
211 | * | |
212 | * \param X Destination MPI | |
213 | * \param buf Input buffer | |
214 | * \param buflen Input buffer size | |
215 | * | |
216 | * \return 0 if successful, | |
217 | * 1 if memory allocation failed | |
218 | */ | |
219 | int mpi_read_binary( mpi *X, const unsigned char *buf, int buflen ); | |
220 | ||
221 | /** | |
222 | * \brief Export X into unsigned binary data, big endian | |
223 | * | |
224 | * \param X Source MPI | |
225 | * \param buf Output buffer | |
226 | * \param buflen Output buffer size | |
227 | * | |
228 | * \return 0 if successful, | |
229 | * POLARSSL_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough | |
230 | */ | |
231 | int mpi_write_binary( const mpi *X, unsigned char *buf, int buflen ); | |
232 | ||
233 | /** | |
234 | * \brief Left-shift: X <<= count | |
235 | * | |
236 | * \param X MPI to shift | |
237 | * \param count Amount to shift | |
238 | * | |
239 | * \return 0 if successful, | |
240 | * 1 if memory allocation failed | |
241 | */ | |
242 | int mpi_shift_l( mpi *X, int count ); | |
243 | ||
244 | /** | |
245 | * \brief Right-shift: X >>= count | |
246 | * | |
247 | * \param X MPI to shift | |
248 | * \param count Amount to shift | |
249 | * | |
250 | * \return 0 if successful, | |
251 | * 1 if memory allocation failed | |
252 | */ | |
253 | int mpi_shift_r( mpi *X, int count ); | |
254 | ||
255 | /** | |
256 | * \brief Compare unsigned values | |
257 | * | |
258 | * \param X Left-hand MPI | |
259 | * \param Y Right-hand MPI | |
260 | * | |
261 | * \return 1 if |X| is greater than |Y|, | |
262 | * -1 if |X| is lesser than |Y| or | |
263 | * 0 if |X| is equal to |Y| | |
264 | */ | |
265 | int mpi_cmp_abs( const mpi *X, const mpi *Y ); | |
266 | ||
267 | /** | |
268 | * \brief Compare signed values | |
269 | * | |
270 | * \param X Left-hand MPI | |
271 | * \param Y Right-hand MPI | |
272 | * | |
273 | * \return 1 if X is greater than Y, | |
274 | * -1 if X is lesser than Y or | |
275 | * 0 if X is equal to Y | |
276 | */ | |
277 | int mpi_cmp_mpi( const mpi *X, const mpi *Y ); | |
278 | ||
279 | /** | |
280 | * \brief Compare signed values | |
281 | * | |
282 | * \param X Left-hand MPI | |
283 | * \param z The integer value to compare to | |
284 | * | |
285 | * \return 1 if X is greater than z, | |
286 | * -1 if X is lesser than z or | |
287 | * 0 if X is equal to z | |
288 | */ | |
289 | int mpi_cmp_int( const mpi *X, int z ); | |
290 | ||
291 | /** | |
292 | * \brief Unsigned addition: X = |A| + |B| | |
293 | * | |
294 | * \param X Destination MPI | |
295 | * \param A Left-hand MPI | |
296 | * \param B Right-hand MPI | |
297 | * | |
298 | * \return 0 if successful, | |
299 | * 1 if memory allocation failed | |
300 | */ | |
301 | int mpi_add_abs( mpi *X, const mpi *A, const mpi *B ); | |
302 | ||
303 | /** | |
304 | * \brief Unsigned substraction: X = |A| - |B| | |
305 | * | |
306 | * \param X Destination MPI | |
307 | * \param A Left-hand MPI | |
308 | * \param B Right-hand MPI | |
309 | * | |
310 | * \return 0 if successful, | |
311 | * POLARSSL_ERR_MPI_NEGATIVE_VALUE if B is greater than A | |
312 | */ | |
313 | int mpi_sub_abs( mpi *X, const mpi *A, const mpi *B ); | |
314 | ||
315 | /** | |
316 | * \brief Signed addition: X = A + B | |
317 | * | |
318 | * \param X Destination MPI | |
319 | * \param A Left-hand MPI | |
320 | * \param B Right-hand MPI | |
321 | * | |
322 | * \return 0 if successful, | |
323 | * 1 if memory allocation failed | |
324 | */ | |
325 | int mpi_add_mpi( mpi *X, const mpi *A, const mpi *B ); | |
326 | ||
327 | /** | |
328 | * \brief Signed substraction: X = A - B | |
329 | * | |
330 | * \param X Destination MPI | |
331 | * \param A Left-hand MPI | |
332 | * \param B Right-hand MPI | |
333 | * | |
334 | * \return 0 if successful, | |
335 | * 1 if memory allocation failed | |
336 | */ | |
337 | int mpi_sub_mpi( mpi *X, const mpi *A, const mpi *B ); | |
338 | ||
339 | /** | |
340 | * \brief Signed addition: X = A + b | |
341 | * | |
342 | * \param X Destination MPI | |
343 | * \param A Left-hand MPI | |
344 | * \param b The integer value to add | |
345 | * | |
346 | * \return 0 if successful, | |
347 | * 1 if memory allocation failed | |
348 | */ | |
349 | int mpi_add_int( mpi *X, const mpi *A, int b ); | |
350 | ||
351 | /** | |
352 | * \brief Signed substraction: X = A - b | |
353 | * | |
354 | * \param X Destination MPI | |
355 | * \param A Left-hand MPI | |
356 | * \param b The integer value to subtract | |
357 | * | |
358 | * \return 0 if successful, | |
359 | * 1 if memory allocation failed | |
360 | */ | |
361 | int mpi_sub_int( mpi *X, const mpi *A, int b ); | |
362 | ||
363 | /** | |
364 | * \brief Baseline multiplication: X = A * B | |
365 | * | |
366 | * \param X Destination MPI | |
367 | * \param A Left-hand MPI | |
368 | * \param B Right-hand MPI | |
369 | * | |
370 | * \return 0 if successful, | |
371 | * 1 if memory allocation failed | |
372 | */ | |
373 | int mpi_mul_mpi( mpi *X, const mpi *A, const mpi *B ); | |
374 | ||
375 | /** | |
376 | * \brief Baseline multiplication: X = A * b | |
377 | * Note: b is an unsigned integer type, thus | |
378 | * Negative values of b are ignored. | |
379 | * | |
380 | * \param X Destination MPI | |
381 | * \param A Left-hand MPI | |
382 | * \param b The integer value to multiply with | |
383 | * | |
384 | * \return 0 if successful, | |
385 | * 1 if memory allocation failed | |
386 | */ | |
387 | int mpi_mul_int( mpi *X, const mpi *A, t_int b ); | |
388 | ||
389 | /** | |
390 | * \brief Division by mpi: A = Q * B + R | |
391 | * | |
392 | * \param Q Destination MPI for the quotient | |
393 | * \param R Destination MPI for the rest value | |
394 | * \param A Left-hand MPI | |
395 | * \param B Right-hand MPI | |
396 | * | |
397 | * \return 0 if successful, | |
398 | * 1 if memory allocation failed, | |
399 | * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0 | |
400 | * | |
401 | * \note Either Q or R can be NULL. | |
402 | */ | |
403 | int mpi_div_mpi( mpi *Q, mpi *R, const mpi *A, const mpi *B ); | |
404 | ||
405 | /** | |
406 | * \brief Division by int: A = Q * b + R | |
407 | * | |
408 | * \param Q Destination MPI for the quotient | |
409 | * \param R Destination MPI for the rest value | |
410 | * \param A Left-hand MPI | |
411 | * \param b Integer to divide by | |
412 | * | |
413 | * \return 0 if successful, | |
414 | * 1 if memory allocation failed, | |
415 | * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0 | |
416 | * | |
417 | * \note Either Q or R can be NULL. | |
418 | */ | |
419 | int mpi_div_int( mpi *Q, mpi *R, const mpi *A, int b ); | |
420 | ||
421 | /** | |
422 | * \brief Modulo: R = A mod B | |
423 | * | |
424 | * \param R Destination MPI for the rest value | |
425 | * \param A Left-hand MPI | |
426 | * \param B Right-hand MPI | |
427 | * | |
428 | * \return 0 if successful, | |
429 | * 1 if memory allocation failed, | |
430 | * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0, | |
431 | * POLARSSL_ERR_MPI_NEGATIVE_VALUE if B < 0 | |
432 | */ | |
433 | int mpi_mod_mpi( mpi *R, const mpi *A, const mpi *B ); | |
434 | ||
435 | /** | |
436 | * \brief Modulo: r = A mod b | |
437 | * | |
438 | * \param r Destination t_int | |
439 | * \param A Left-hand MPI | |
440 | * \param b Integer to divide by | |
441 | * | |
442 | * \return 0 if successful, | |
443 | * 1 if memory allocation failed, | |
444 | * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0, | |
445 | * POLARSSL_ERR_MPI_NEGATIVE_VALUE if b < 0 | |
446 | */ | |
447 | int mpi_mod_int( t_int *r, const mpi *A, int b ); | |
448 | ||
449 | /** | |
450 | * \brief Sliding-window exponentiation: X = A^E mod N | |
451 | * | |
452 | * \param X Destination MPI | |
453 | * \param A Left-hand MPI | |
454 | * \param E Exponent MPI | |
455 | * \param N Modular MPI | |
456 | * \param _RR Speed-up MPI used for recalculations | |
457 | * | |
458 | * \return 0 if successful, | |
459 | * 1 if memory allocation failed, | |
460 | * POLARSSL_ERR_MPI_BAD_INPUT_DATA if N is negative or even | |
461 | * | |
462 | * \note _RR is used to avoid re-computing R*R mod N across | |
463 | * multiple calls, which speeds up things a bit. It can | |
464 | * be set to NULL if the extra performance is unneeded. | |
465 | */ | |
466 | int mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR ); | |
467 | ||
468 | /** | |
469 | * \brief Greatest common divisor: G = gcd(A, B) | |
470 | * | |
471 | * \param G Destination MPI | |
472 | * \param A Left-hand MPI | |
473 | * \param B Right-hand MPI | |
474 | * | |
475 | * \return 0 if successful, | |
476 | * 1 if memory allocation failed | |
477 | */ | |
478 | int mpi_gcd( mpi *G, const mpi *A, const mpi *B ); | |
479 | ||
480 | /** | |
481 | * \brief Modular inverse: X = A^-1 mod N | |
482 | * | |
483 | * \param X Destination MPI | |
484 | * \param A Left-hand MPI | |
485 | * \param N Right-hand MPI | |
486 | * | |
487 | * \return 0 if successful, | |
488 | * 1 if memory allocation failed, | |
489 | * POLARSSL_ERR_MPI_BAD_INPUT_DATA if N is negative or nil | |
490 | POLARSSL_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N | |
491 | */ | |
492 | int mpi_inv_mod( mpi *X, const mpi *A, const mpi *N ); | |
493 | ||
494 | /** | |
495 | * \brief Miller-Rabin primality test | |
496 | * | |
497 | * \param X MPI to check | |
498 | * \param f_rng RNG function | |
499 | * \param p_rng RNG parameter | |
500 | * | |
501 | * \return 0 if successful (probably prime), | |
502 | * 1 if memory allocation failed, | |
503 | * POLARSSL_ERR_MPI_NOT_ACCEPTABLE if X is not prime | |
504 | */ | |
505 | int mpi_is_prime( mpi *X, int (*f_rng)(void *), void *p_rng ); | |
506 | ||
507 | /** | |
508 | * \brief Prime number generation | |
509 | * | |
510 | * \param X Destination MPI | |
511 | * \param nbits Required size of X in bits | |
512 | * \param dh_flag If 1, then (X-1)/2 will be prime too | |
513 | * \param f_rng RNG function | |
514 | * \param p_rng RNG parameter | |
515 | * | |
516 | * \return 0 if successful (probably prime), | |
517 | * 1 if memory allocation failed, | |
518 | * POLARSSL_ERR_MPI_BAD_INPUT_DATA if nbits is < 3 | |
519 | */ | |
520 | int mpi_gen_prime( mpi *X, int nbits, int dh_flag, | |
521 | int (*f_rng)(void *), void *p_rng ); | |
522 | ||
523 | #ifdef __cplusplus | |
524 | } | |
525 | #endif | |
526 | ||
527 | #endif /* bignum.h */ |