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1/**
2 * \file bignum.h
3 *
4 * \brief Multi-precision integer library
5 */
6/*
7 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
8 * SPDX-License-Identifier: GPL-2.0
9 *
10 * This program is free software; you can redistribute it and/or modify
11 * it under the terms of the GNU General Public License as published by
12 * the Free Software Foundation; either version 2 of the License, or
13 * (at your option) any later version.
14 *
15 * This program is distributed in the hope that it will be useful,
16 * but WITHOUT ANY WARRANTY; without even the implied warranty of
17 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18 * GNU General Public License for more details.
19 *
20 * You should have received a copy of the GNU General Public License along
21 * with this program; if not, write to the Free Software Foundation, Inc.,
22 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
23 *
24 * This file is part of mbed TLS (https://tls.mbed.org)
25 */
26#ifndef MBEDTLS_BIGNUM_H
27#define MBEDTLS_BIGNUM_H
28
29#if !defined(MBEDTLS_CONFIG_FILE)
30#include "config.h"
31#else
32#include MBEDTLS_CONFIG_FILE
33#endif
34
35#include <stddef.h>
36#include <stdint.h>
37
38#if defined(MBEDTLS_FS_IO)
39#include <stdio.h>
40#endif
41
42#define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002 /**< An error occurred while reading from or writing to a file. */
43#define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004 /**< Bad input parameters to function. */
44#define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006 /**< There is an invalid character in the digit string. */
45#define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008 /**< The buffer is too small to write to. */
46#define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A /**< The input arguments are negative or result in illegal output. */
47#define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C /**< The input argument for division is zero, which is not allowed. */
48#define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E /**< The input arguments are not acceptable. */
49#define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010 /**< Memory allocation failed. */
50
51#define MBEDTLS_MPI_CHK(f) do { if( ( ret = f ) != 0 ) goto cleanup; } while( 0 )
52
53/*
54 * Maximum size MPIs are allowed to grow to in number of limbs.
55 */
56#define MBEDTLS_MPI_MAX_LIMBS 10000
57
58#if !defined(MBEDTLS_MPI_WINDOW_SIZE)
59/*
60 * Maximum window size used for modular exponentiation. Default: 6
61 * Minimum value: 1. Maximum value: 6.
62 *
63 * Result is an array of ( 2 << MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
64 * for the sliding window calculation. (So 64 by default)
65 *
66 * Reduction in size, reduces speed.
67 */
68#define MBEDTLS_MPI_WINDOW_SIZE 6 /**< Maximum windows size used. */
69#endif /* !MBEDTLS_MPI_WINDOW_SIZE */
70
71#if !defined(MBEDTLS_MPI_MAX_SIZE)
72/*
73 * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
74 * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
75 *
76 * Note: Calculations can temporarily result in larger MPIs. So the number
77 * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
78 */
79#define MBEDTLS_MPI_MAX_SIZE 1024 /**< Maximum number of bytes for usable MPIs. */
80#endif /* !MBEDTLS_MPI_MAX_SIZE */
81
82#define MBEDTLS_MPI_MAX_BITS ( 8 * MBEDTLS_MPI_MAX_SIZE ) /**< Maximum number of bits for usable MPIs. */
83
84/*
85 * When reading from files with mbedtls_mpi_read_file() and writing to files with
86 * mbedtls_mpi_write_file() the buffer should have space
87 * for a (short) label, the MPI (in the provided radix), the newline
88 * characters and the '\0'.
89 *
90 * By default we assume at least a 10 char label, a minimum radix of 10
91 * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
92 * Autosized at compile time for at least a 10 char label, a minimum radix
93 * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
94 *
95 * This used to be statically sized to 1250 for a maximum of 4096 bit
96 * numbers (1234 decimal chars).
97 *
98 * Calculate using the formula:
99 * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
100 * LabelSize + 6
101 */
102#define MBEDTLS_MPI_MAX_BITS_SCALE100 ( 100 * MBEDTLS_MPI_MAX_BITS )
103#define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332
104#define MBEDTLS_MPI_RW_BUFFER_SIZE ( ((MBEDTLS_MPI_MAX_BITS_SCALE100 + MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6 )
105
106/*
107 * Define the base integer type, architecture-wise.
108 *
109 * 32 or 64-bit integer types can be forced regardless of the underlying
110 * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
111 * respectively and undefining MBEDTLS_HAVE_ASM.
112 *
113 * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
114 * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
115 */
116#if !defined(MBEDTLS_HAVE_INT32)
117 #if defined(_MSC_VER) && defined(_M_AMD64)
118 /* Always choose 64-bit when using MSC */
119 #if !defined(MBEDTLS_HAVE_INT64)
120 #define MBEDTLS_HAVE_INT64
121 #endif /* !MBEDTLS_HAVE_INT64 */
122 typedef int64_t mbedtls_mpi_sint;
123 typedef uint64_t mbedtls_mpi_uint;
124 #elif defined(__GNUC__) && ( \
125 defined(__amd64__) || defined(__x86_64__) || \
126 defined(__ppc64__) || defined(__powerpc64__) || \
127 defined(__ia64__) || defined(__alpha__) || \
128 ( defined(__sparc__) && defined(__arch64__) ) || \
129 defined(__s390x__) || defined(__mips64) )
130 #if !defined(MBEDTLS_HAVE_INT64)
131 #define MBEDTLS_HAVE_INT64
132 #endif /* MBEDTLS_HAVE_INT64 */
133 typedef int64_t mbedtls_mpi_sint;
134 typedef uint64_t mbedtls_mpi_uint;
135 #if !defined(MBEDTLS_NO_UDBL_DIVISION)
136 /* mbedtls_t_udbl defined as 128-bit unsigned int */
137 typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
138 #define MBEDTLS_HAVE_UDBL
139 #endif /* !MBEDTLS_NO_UDBL_DIVISION */
140 #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
141 /*
142 * __ARMCC_VERSION is defined for both armcc and armclang and
143 * __aarch64__ is only defined by armclang when compiling 64-bit code
144 */
145 #if !defined(MBEDTLS_HAVE_INT64)
146 #define MBEDTLS_HAVE_INT64
147 #endif /* !MBEDTLS_HAVE_INT64 */
148 typedef int64_t mbedtls_mpi_sint;
149 typedef uint64_t mbedtls_mpi_uint;
150 #if !defined(MBEDTLS_NO_UDBL_DIVISION)
151 /* mbedtls_t_udbl defined as 128-bit unsigned int */
152 typedef __uint128_t mbedtls_t_udbl;
153 #define MBEDTLS_HAVE_UDBL
154 #endif /* !MBEDTLS_NO_UDBL_DIVISION */
155 #elif defined(MBEDTLS_HAVE_INT64)
156 /* Force 64-bit integers with unknown compiler */
157 typedef int64_t mbedtls_mpi_sint;
158 typedef uint64_t mbedtls_mpi_uint;
159 #endif
160#endif /* !MBEDTLS_HAVE_INT32 */
161
162#if !defined(MBEDTLS_HAVE_INT64)
163 /* Default to 32-bit compilation */
164 #if !defined(MBEDTLS_HAVE_INT32)
165 #define MBEDTLS_HAVE_INT32
166 #endif /* !MBEDTLS_HAVE_INT32 */
167 typedef int32_t mbedtls_mpi_sint;
168 typedef uint32_t mbedtls_mpi_uint;
169 #if !defined(MBEDTLS_NO_UDBL_DIVISION)
170 typedef uint64_t mbedtls_t_udbl;
171 #define MBEDTLS_HAVE_UDBL
172 #endif /* !MBEDTLS_NO_UDBL_DIVISION */
173#endif /* !MBEDTLS_HAVE_INT64 */
174
175#ifdef __cplusplus
176extern "C" {
177#endif
178
179/**
180 * \brief MPI structure
181 */
182typedef struct mbedtls_mpi
183{
184 int s; /*!< integer sign */
185 size_t n; /*!< total # of limbs */
186 mbedtls_mpi_uint *p; /*!< pointer to limbs */
187}
188mbedtls_mpi;
189
190/**
191 * \brief Initialize one MPI (make internal references valid)
192 * This just makes it ready to be set or freed,
193 * but does not define a value for the MPI.
194 *
195 * \param X One MPI to initialize.
196 */
197void mbedtls_mpi_init( mbedtls_mpi *X );
198
199/**
200 * \brief Unallocate one MPI
201 *
202 * \param X One MPI to unallocate.
203 */
204void mbedtls_mpi_free( mbedtls_mpi *X );
205
206/**
207 * \brief Enlarge to the specified number of limbs
208 *
209 * This function does nothing if the MPI is already large enough.
210 *
211 * \param X MPI to grow
212 * \param nblimbs The target number of limbs
213 *
214 * \return 0 if successful,
215 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
216 */
217int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
218
219/**
220 * \brief Resize down, keeping at least the specified number of limbs
221 *
222 * If \c X is smaller than \c nblimbs, it is resized up
223 * instead.
224 *
225 * \param X MPI to shrink
226 * \param nblimbs The minimum number of limbs to keep
227 *
228 * \return 0 if successful,
229 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
230 * (this can only happen when resizing up).
231 */
232int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
233
234/**
235 * \brief Copy the contents of Y into X
236 *
237 * \param X Destination MPI. It is enlarged if necessary.
238 * \param Y Source MPI.
239 *
240 * \return 0 if successful,
241 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
242 */
243int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
244
245/**
246 * \brief Swap the contents of X and Y
247 *
248 * \param X First MPI value
249 * \param Y Second MPI value
250 */
251void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y );
252
253/**
254 * \brief Safe conditional assignement X = Y if assign is 1
255 *
256 * \param X MPI to conditionally assign to
257 * \param Y Value to be assigned
258 * \param assign 1: perform the assignment, 0: keep X's original value
259 *
260 * \return 0 if successful,
261 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
262 *
263 * \note This function is equivalent to
264 * if( assign ) mbedtls_mpi_copy( X, Y );
265 * except that it avoids leaking any information about whether
266 * the assignment was done or not (the above code may leak
267 * information through branch prediction and/or memory access
268 * patterns analysis).
269 */
270int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
271
272/**
273 * \brief Safe conditional swap X <-> Y if swap is 1
274 *
275 * \param X First mbedtls_mpi value
276 * \param Y Second mbedtls_mpi value
277 * \param assign 1: perform the swap, 0: keep X and Y's original values
278 *
279 * \return 0 if successful,
280 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
281 *
282 * \note This function is equivalent to
283 * if( assign ) mbedtls_mpi_swap( X, Y );
284 * except that it avoids leaking any information about whether
285 * the assignment was done or not (the above code may leak
286 * information through branch prediction and/or memory access
287 * patterns analysis).
288 */
289int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
290
291/**
292 * \brief Set value from integer
293 *
294 * \param X MPI to set
295 * \param z Value to use
296 *
297 * \return 0 if successful,
298 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
299 */
300int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z );
301
302/**
303 * \brief Get a specific bit from X
304 *
305 * \param X MPI to use
306 * \param pos Zero-based index of the bit in X
307 *
308 * \return Either a 0 or a 1
309 */
310int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
311
312/**
313 * \brief Set a bit of X to a specific value of 0 or 1
314 *
315 * \note Will grow X if necessary to set a bit to 1 in a not yet
316 * existing limb. Will not grow if bit should be set to 0
317 *
318 * \param X MPI to use
319 * \param pos Zero-based index of the bit in X
320 * \param val The value to set the bit to (0 or 1)
321 *
322 * \return 0 if successful,
323 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
324 * MBEDTLS_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1
325 */
326int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val );
327
328/**
329 * \brief Return the number of zero-bits before the least significant
330 * '1' bit
331 *
332 * Note: Thus also the zero-based index of the least significant '1' bit
333 *
334 * \param X MPI to use
335 */
336size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
337
338/**
339 * \brief Return the number of bits up to and including the most
340 * significant '1' bit'
341 *
342 * Note: Thus also the one-based index of the most significant '1' bit
343 *
344 * \param X MPI to use
345 */
346size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
347
348/**
349 * \brief Return the total size in bytes
350 *
351 * \param X MPI to use
352 */
353size_t mbedtls_mpi_size( const mbedtls_mpi *X );
354
355/**
356 * \brief Import from an ASCII string
357 *
358 * \param X Destination MPI
359 * \param radix Input numeric base
360 * \param s Null-terminated string buffer
361 *
362 * \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
363 */
364int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
365
366/**
367 * \brief Export into an ASCII string
368 *
369 * \param X Source MPI
370 * \param radix Output numeric base
371 * \param buf Buffer to write the string to
372 * \param buflen Length of buf
373 * \param olen Length of the string written, including final NUL byte
374 *
375 * \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code.
376 * *olen is always updated to reflect the amount
377 * of data that has (or would have) been written.
378 *
379 * \note Call this function with buflen = 0 to obtain the
380 * minimum required buffer size in *olen.
381 */
382int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
383 char *buf, size_t buflen, size_t *olen );
384
385#if defined(MBEDTLS_FS_IO)
386/**
387 * \brief Read MPI from a line in an opened file
388 *
389 * \param X Destination MPI
390 * \param radix Input numeric base
391 * \param fin Input file handle
392 *
393 * \return 0 if successful, MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if
394 * the file read buffer is too small or a
395 * MBEDTLS_ERR_MPI_XXX error code
396 *
397 * \note On success, this function advances the file stream
398 * to the end of the current line or to EOF.
399 *
400 * The function returns 0 on an empty line.
401 *
402 * Leading whitespaces are ignored, as is a
403 * '0x' prefix for radix 16.
404 *
405 */
406int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
407
408/**
409 * \brief Write X into an opened file, or stdout if fout is NULL
410 *
411 * \param p Prefix, can be NULL
412 * \param X Source MPI
413 * \param radix Output numeric base
414 * \param fout Output file handle (can be NULL)
415 *
416 * \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
417 *
418 * \note Set fout == NULL to print X on the console.
419 */
420int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout );
421#endif /* MBEDTLS_FS_IO */
422
423/**
424 * \brief Import X from unsigned binary data, big endian
425 *
426 * \param X Destination MPI
427 * \param buf Input buffer
428 * \param buflen Input buffer size
429 *
430 * \return 0 if successful,
431 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
432 */
433int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen );
434
435/**
436 * \brief Export X into unsigned binary data, big endian.
437 * Always fills the whole buffer, which will start with zeros
438 * if the number is smaller.
439 *
440 * \param X Source MPI
441 * \param buf Output buffer
442 * \param buflen Output buffer size
443 *
444 * \return 0 if successful,
445 * MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough
446 */
447int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf, size_t buflen );
448
449/**
450 * \brief Left-shift: X <<= count
451 *
452 * \param X MPI to shift
453 * \param count Amount to shift
454 *
455 * \return 0 if successful,
456 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
457 */
458int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
459
460/**
461 * \brief Right-shift: X >>= count
462 *
463 * \param X MPI to shift
464 * \param count Amount to shift
465 *
466 * \return 0 if successful,
467 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
468 */
469int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count );
470
471/**
472 * \brief Compare unsigned values
473 *
474 * \param X Left-hand MPI
475 * \param Y Right-hand MPI
476 *
477 * \return 1 if |X| is greater than |Y|,
478 * -1 if |X| is lesser than |Y| or
479 * 0 if |X| is equal to |Y|
480 */
481int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
482
483/**
484 * \brief Compare signed values
485 *
486 * \param X Left-hand MPI
487 * \param Y Right-hand MPI
488 *
489 * \return 1 if X is greater than Y,
490 * -1 if X is lesser than Y or
491 * 0 if X is equal to Y
492 */
493int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
494
495/**
496 * \brief Compare signed values
497 *
498 * \param X Left-hand MPI
499 * \param z The integer value to compare to
500 *
501 * \return 1 if X is greater than z,
502 * -1 if X is lesser than z or
503 * 0 if X is equal to z
504 */
505int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z );
506
507/**
508 * \brief Unsigned addition: X = |A| + |B|
509 *
510 * \param X Destination MPI
511 * \param A Left-hand MPI
512 * \param B Right-hand MPI
513 *
514 * \return 0 if successful,
515 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
516 */
517int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
518
519/**
520 * \brief Unsigned subtraction: X = |A| - |B|
521 *
522 * \param X Destination MPI
523 * \param A Left-hand MPI
524 * \param B Right-hand MPI
525 *
526 * \return 0 if successful,
527 * MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B is greater than A
528 */
529int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
530
531/**
532 * \brief Signed addition: X = A + B
533 *
534 * \param X Destination MPI
535 * \param A Left-hand MPI
536 * \param B Right-hand MPI
537 *
538 * \return 0 if successful,
539 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
540 */
541int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
542
543/**
544 * \brief Signed subtraction: X = A - B
545 *
546 * \param X Destination MPI
547 * \param A Left-hand MPI
548 * \param B Right-hand MPI
549 *
550 * \return 0 if successful,
551 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
552 */
553int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
554
555/**
556 * \brief Signed addition: X = A + b
557 *
558 * \param X Destination MPI
559 * \param A Left-hand MPI
560 * \param b The integer value to add
561 *
562 * \return 0 if successful,
563 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
564 */
565int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b );
566
567/**
568 * \brief Signed subtraction: X = A - b
569 *
570 * \param X Destination MPI
571 * \param A Left-hand MPI
572 * \param b The integer value to subtract
573 *
574 * \return 0 if successful,
575 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
576 */
577int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b );
578
579/**
580 * \brief Baseline multiplication: X = A * B
581 *
582 * \param X Destination MPI
583 * \param A Left-hand MPI
584 * \param B Right-hand MPI
585 *
586 * \return 0 if successful,
587 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
588 */
589int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
590
591/**
592 * \brief Baseline multiplication: X = A * b
593 *
594 * \param X Destination MPI
595 * \param A Left-hand MPI
596 * \param b The unsigned integer value to multiply with
597 *
598 * \note b is unsigned
599 *
600 * \return 0 if successful,
601 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
602 */
603int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b );
604
605/**
606 * \brief Division by mbedtls_mpi: A = Q * B + R
607 *
608 * \param Q Destination MPI for the quotient
609 * \param R Destination MPI for the rest value
610 * \param A Left-hand MPI
611 * \param B Right-hand MPI
612 *
613 * \return 0 if successful,
614 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
615 * MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0
616 *
617 * \note Either Q or R can be NULL.
618 */
619int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B );
620
621/**
622 * \brief Division by int: A = Q * b + R
623 *
624 * \param Q Destination MPI for the quotient
625 * \param R Destination MPI for the rest value
626 * \param A Left-hand MPI
627 * \param b Integer to divide by
628 *
629 * \return 0 if successful,
630 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
631 * MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0
632 *
633 * \note Either Q or R can be NULL.
634 */
635int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_sint b );
636
637/**
638 * \brief Modulo: R = A mod B
639 *
640 * \param R Destination MPI for the rest value
641 * \param A Left-hand MPI
642 * \param B Right-hand MPI
643 *
644 * \return 0 if successful,
645 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
646 * MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0,
647 * MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B < 0
648 */
649int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B );
650
651/**
652 * \brief Modulo: r = A mod b
653 *
654 * \param r Destination mbedtls_mpi_uint
655 * \param A Left-hand MPI
656 * \param b Integer to divide by
657 *
658 * \return 0 if successful,
659 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
660 * MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0,
661 * MBEDTLS_ERR_MPI_NEGATIVE_VALUE if b < 0
662 */
663int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b );
664
665/**
666 * \brief Sliding-window exponentiation: X = A^E mod N
667 *
668 * \param X Destination MPI
669 * \param A Left-hand MPI
670 * \param E Exponent MPI
671 * \param N Modular MPI
672 * \param _RR Speed-up MPI used for recalculations
673 *
674 * \return 0 if successful,
675 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
676 * MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is negative or even or
677 * if E is negative
678 *
679 * \note _RR is used to avoid re-computing R*R mod N across
680 * multiple calls, which speeds up things a bit. It can
681 * be set to NULL if the extra performance is unneeded.
682 */
683int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR );
684
685/**
686 * \brief Fill an MPI X with size bytes of random
687 *
688 * \param X Destination MPI
689 * \param size Size in bytes
690 * \param f_rng RNG function
691 * \param p_rng RNG parameter
692 *
693 * \return 0 if successful,
694 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
695 *
696 * \note The bytes obtained from the PRNG are interpreted
697 * as a big-endian representation of an MPI; this can
698 * be relevant in applications like deterministic ECDSA.
699 */
700int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
701 int (*f_rng)(void *, unsigned char *, size_t),
702 void *p_rng );
703
704/**
705 * \brief Greatest common divisor: G = gcd(A, B)
706 *
707 * \param G Destination MPI
708 * \param A Left-hand MPI
709 * \param B Right-hand MPI
710 *
711 * \return 0 if successful,
712 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
713 */
714int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B );
715
716/**
717 * \brief Modular inverse: X = A^-1 mod N
718 *
719 * \param X Destination MPI
720 * \param A Left-hand MPI
721 * \param N Right-hand MPI
722 *
723 * \return 0 if successful,
724 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
725 * MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is <= 1,
726 MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N.
727 */
728int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N );
729
730/**
731 * \brief Miller-Rabin primality test
732 *
733 * \param X MPI to check
734 * \param f_rng RNG function
735 * \param p_rng RNG parameter
736 *
737 * \return 0 if successful (probably prime),
738 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
739 * MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime
740 */
741int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
742 int (*f_rng)(void *, unsigned char *, size_t),
743 void *p_rng );
744
745/**
746 * \brief Prime number generation
747 *
748 * \param X Destination MPI
749 * \param nbits Required size of X in bits
750 * ( 3 <= nbits <= MBEDTLS_MPI_MAX_BITS )
751 * \param dh_flag If 1, then (X-1)/2 will be prime too
752 * \param f_rng RNG function
753 * \param p_rng RNG parameter
754 *
755 * \return 0 if successful (probably prime),
756 * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
757 * MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
758 */
759int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int dh_flag,
760 int (*f_rng)(void *, unsigned char *, size_t),
761 void *p_rng );
762
763/**
764 * \brief Checkup routine
765 *
766 * \return 0 if successful, or 1 if the test failed
767 */
768int mbedtls_mpi_self_test( int verbose );
769
770#ifdef __cplusplus
771}
772#endif
773
774#endif /* bignum.h */
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