1 /**
2  * \file bignum.h
3  *
4  * \brief Multi-precision integer library
5  */
6 /*
7  *  Copyright The Mbed TLS Contributors
8  *  SPDX-License-Identifier: Apache-2.0
9  *
10  *  Licensed under the Apache License, Version 2.0 (the "License"); you may
11  *  not use this file except in compliance with the License.
12  *  You may obtain a copy of the License at
13  *
14  *  http://www.apache.org/licenses/LICENSE-2.0
15  *
16  *  Unless required by applicable law or agreed to in writing, software
17  *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
18  *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
19  *  See the License for the specific language governing permissions and
20  *  limitations under the License.
21  */
22 #ifndef MBEDTLS_BIGNUM_H
23 #define MBEDTLS_BIGNUM_H
24 
25 #if !defined(MBEDTLS_CONFIG_FILE)
26 #include "mbedtls/config.h"
27 #else
28 #include MBEDTLS_CONFIG_FILE
29 #endif
30 
31 #include <stddef.h>
32 #include <stdint.h>
33 
34 #if defined(MBEDTLS_FS_IO)
35 #include <stdio.h>
36 #endif
37 
38 /** An error occurred while reading from or writing to a file. */
39 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR                     -0x0002
40 /** Bad input parameters to function. */
41 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA                    -0x0004
42 /** There is an invalid character in the digit string. */
43 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER                 -0x0006
44 /** The buffer is too small to write to. */
45 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL                  -0x0008
46 /** The input arguments are negative or result in illegal output. */
47 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE                    -0x000A
48 /** The input argument for division is zero, which is not allowed. */
49 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO                  -0x000C
50 /** The input arguments are not acceptable. */
51 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE                    -0x000E
52 /** Memory allocation failed. */
53 #define MBEDTLS_ERR_MPI_ALLOC_FAILED                      -0x0010
54 
55 #define MBEDTLS_MPI_CHK(f)       \
56     do                           \
57     {                            \
58         if( ( ret = (f) ) != 0 ) \
59             goto cleanup;        \
60     } while( 0 )
61 
62 /*
63  * Maximum size MPIs are allowed to grow to in number of limbs.
64  */
65 #define MBEDTLS_MPI_MAX_LIMBS                             10000
66 
67 #if !defined(MBEDTLS_MPI_WINDOW_SIZE)
68 /*
69  * Maximum window size used for modular exponentiation. Default: 6
70  * Minimum value: 1. Maximum value: 6.
71  *
72  * Result is an array of ( 2 ** MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
73  * for the sliding window calculation. (So 64 by default)
74  *
75  * Reduction in size, reduces speed.
76  */
77 #define MBEDTLS_MPI_WINDOW_SIZE                           6        /**< Maximum window size used. */
78 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */
79 
80 #if !defined(MBEDTLS_MPI_MAX_SIZE)
81 /*
82  * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
83  * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
84  *
85  * Note: Calculations can temporarily result in larger MPIs. So the number
86  * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
87  */
88 #define MBEDTLS_MPI_MAX_SIZE                              1024     /**< Maximum number of bytes for usable MPIs. */
89 #endif /* !MBEDTLS_MPI_MAX_SIZE */
90 
91 #define MBEDTLS_MPI_MAX_BITS                              ( 8 * MBEDTLS_MPI_MAX_SIZE )    /**< Maximum number of bits for usable MPIs. */
92 
93 /*
94  * When reading from files with mbedtls_mpi_read_file() and writing to files with
95  * mbedtls_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 MBEDTLS_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  *  MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
109  *                                LabelSize + 6
110  */
111 #define MBEDTLS_MPI_MAX_BITS_SCALE100          ( 100 * MBEDTLS_MPI_MAX_BITS )
112 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100                 332
113 #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 )
114 
115 /*
116  * Define the base integer type, architecture-wise.
117  *
118  * 32 or 64-bit integer types can be forced regardless of the underlying
119  * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
120  * respectively and undefining MBEDTLS_HAVE_ASM.
121  *
122  * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
123  * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
124  */
125 #if !defined(MBEDTLS_HAVE_INT32)
126     #if defined(_MSC_VER) && defined(_M_AMD64)
127         /* Always choose 64-bit when using MSC */
128         #if !defined(MBEDTLS_HAVE_INT64)
129             #define MBEDTLS_HAVE_INT64
130         #endif /* !MBEDTLS_HAVE_INT64 */
131         typedef  int64_t mbedtls_mpi_sint;
132         typedef uint64_t mbedtls_mpi_uint;
133     #elif defined(__GNUC__) && (                         \
134         defined(__amd64__) || defined(__x86_64__)     || \
135         defined(__ppc64__) || defined(__powerpc64__)  || \
136         defined(__ia64__)  || defined(__alpha__)      || \
137         ( defined(__sparc__) && defined(__arch64__) ) || \
138         defined(__s390x__) || defined(__mips64)       || \
139         defined(__aarch64__) )
140         #if !defined(MBEDTLS_HAVE_INT64)
141             #define MBEDTLS_HAVE_INT64
142         #endif /* MBEDTLS_HAVE_INT64 */
143         typedef  int64_t mbedtls_mpi_sint;
144         typedef uint64_t mbedtls_mpi_uint;
145         #if !defined(MBEDTLS_NO_UDBL_DIVISION)
146             /* mbedtls_t_udbl defined as 128-bit unsigned int */
147             typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
148             #define MBEDTLS_HAVE_UDBL
149         #endif /* !MBEDTLS_NO_UDBL_DIVISION */
150     #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
151         /*
152          * __ARMCC_VERSION is defined for both armcc and armclang and
153          * __aarch64__ is only defined by armclang when compiling 64-bit code
154          */
155         #if !defined(MBEDTLS_HAVE_INT64)
156             #define MBEDTLS_HAVE_INT64
157         #endif /* !MBEDTLS_HAVE_INT64 */
158         typedef  int64_t mbedtls_mpi_sint;
159         typedef uint64_t mbedtls_mpi_uint;
160         #if !defined(MBEDTLS_NO_UDBL_DIVISION)
161             /* mbedtls_t_udbl defined as 128-bit unsigned int */
162             typedef __uint128_t mbedtls_t_udbl;
163             #define MBEDTLS_HAVE_UDBL
164         #endif /* !MBEDTLS_NO_UDBL_DIVISION */
165     #elif defined(MBEDTLS_HAVE_INT64)
166         /* Force 64-bit integers with unknown compiler */
167         typedef  int64_t mbedtls_mpi_sint;
168         typedef uint64_t mbedtls_mpi_uint;
169     #endif
170 #endif /* !MBEDTLS_HAVE_INT32 */
171 
172 #if !defined(MBEDTLS_HAVE_INT64)
173     /* Default to 32-bit compilation */
174     #if !defined(MBEDTLS_HAVE_INT32)
175         #define MBEDTLS_HAVE_INT32
176     #endif /* !MBEDTLS_HAVE_INT32 */
177     typedef  int32_t mbedtls_mpi_sint;
178     typedef uint32_t mbedtls_mpi_uint;
179     #if !defined(MBEDTLS_NO_UDBL_DIVISION)
180         typedef uint64_t mbedtls_t_udbl;
181         #define MBEDTLS_HAVE_UDBL
182     #endif /* !MBEDTLS_NO_UDBL_DIVISION */
183 #endif /* !MBEDTLS_HAVE_INT64 */
184 
185 #ifdef __cplusplus
186 extern "C" {
187 #endif
188 
189 /**
190  * \brief          MPI structure
191  */
192 typedef struct mbedtls_mpi
193 {
194     short s;            /*!<  Sign: -1 if the mpi is negative, 1 otherwise */
195     short use_mempool;
196     size_t n;           /*!<  total # of limbs  */
197     mbedtls_mpi_uint *p;          /*!<  pointer to limbs  */
198 }
199 mbedtls_mpi;
200 
201 extern void *mbedtls_mpi_mempool;
202 
203 /**
204  * \brief           Initialize an MPI context.
205  *
206  *                  This makes the MPI ready to be set or freed,
207  *                  but does not define a value for the MPI.
208  *
209  * \param X         The MPI context to initialize. This must not be \c NULL.
210  */
211 void mbedtls_mpi_init( mbedtls_mpi *X );
212 void mbedtls_mpi_init_mempool( mbedtls_mpi *X );
213 
214 /**
215  * \brief          This function frees the components of an MPI context.
216  *
217  * \param X        The MPI context to be cleared. This may be \c NULL,
218  *                 in which case this function is a no-op. If it is
219  *                 not \c NULL, it must point to an initialized MPI.
220  */
221 void mbedtls_mpi_free( mbedtls_mpi *X );
222 
223 /**
224  * \brief          Enlarge an MPI to the specified number of limbs.
225  *
226  * \note           This function does nothing if the MPI is
227  *                 already large enough.
228  *
229  * \param X        The MPI to grow. It must be initialized.
230  * \param nblimbs  The target number of limbs.
231  *
232  * \return         \c 0 if successful.
233  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
234  * \return         Another negative error code on other kinds of failure.
235  */
236 int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
237 
238 /**
239  * \brief          This function resizes an MPI downwards, keeping at least the
240  *                 specified number of limbs.
241  *
242  *                 If \c X is smaller than \c nblimbs, it is resized up
243  *                 instead.
244  *
245  * \param X        The MPI to shrink. This must point to an initialized MPI.
246  * \param nblimbs  The minimum number of limbs to keep.
247  *
248  * \return         \c 0 if successful.
249  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
250  *                 (this can only happen when resizing up).
251  * \return         Another negative error code on other kinds of failure.
252  */
253 int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
254 
255 /**
256  * \brief          Make a copy of an MPI.
257  *
258  * \param X        The destination MPI. This must point to an initialized MPI.
259  * \param Y        The source MPI. This must point to an initialized MPI.
260  *
261  * \note           The limb-buffer in the destination MPI is enlarged
262  *                 if necessary to hold the value in the source MPI.
263  *
264  * \return         \c 0 if successful.
265  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
266  * \return         Another negative error code on other kinds of failure.
267  */
268 int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
269 
270 /**
271  * \brief          Swap the contents of two MPIs.
272  *
273  * \param X        The first MPI. It must be initialized.
274  * \param Y        The second MPI. It must be initialized.
275  */
276 void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y );
277 
278 /**
279  * \brief          Perform a safe conditional copy of MPI which doesn't
280  *                 reveal whether the condition was true or not.
281  *
282  * \param X        The MPI to conditionally assign to. This must point
283  *                 to an initialized MPI.
284  * \param Y        The MPI to be assigned from. This must point to an
285  *                 initialized MPI.
286  * \param assign   The condition deciding whether to perform the
287  *                 assignment or not. Possible values:
288  *                 * \c 1: Perform the assignment `X = Y`.
289  *                 * \c 0: Keep the original value of \p X.
290  *
291  * \note           This function is equivalent to
292  *                      `if( assign ) mbedtls_mpi_copy( X, Y );`
293  *                 except that it avoids leaking any information about whether
294  *                 the assignment was done or not (the above code may leak
295  *                 information through branch prediction and/or memory access
296  *                 patterns analysis).
297  *
298  * \return         \c 0 if successful.
299  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
300  * \return         Another negative error code on other kinds of failure.
301  */
302 int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
303 
304 /**
305  * \brief          Perform a safe conditional swap which doesn't
306  *                 reveal whether the condition was true or not.
307  *
308  * \param X        The first MPI. This must be initialized.
309  * \param Y        The second MPI. This must be initialized.
310  * \param assign   The condition deciding whether to perform
311  *                 the swap or not. Possible values:
312  *                 * \c 1: Swap the values of \p X and \p Y.
313  *                 * \c 0: Keep the original values of \p X and \p Y.
314  *
315  * \note           This function is equivalent to
316  *                      if( assign ) mbedtls_mpi_swap( X, Y );
317  *                 except that it avoids leaking any information about whether
318  *                 the assignment was done or not (the above code may leak
319  *                 information through branch prediction and/or memory access
320  *                 patterns analysis).
321  *
322  * \return         \c 0 if successful.
323  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
324  * \return         Another negative error code on other kinds of failure.
325  *
326  */
327 int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
328 
329 /**
330  * \brief          Store integer value in MPI.
331  *
332  * \param X        The MPI to set. This must be initialized.
333  * \param z        The value to use.
334  *
335  * \return         \c 0 if successful.
336  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
337  * \return         Another negative error code on other kinds of failure.
338  */
339 int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z );
340 
341 /**
342  * \brief          Get a specific bit from an MPI.
343  *
344  * \param X        The MPI to query. This must be initialized.
345  * \param pos      Zero-based index of the bit to query.
346  *
347  * \return         \c 0 or \c 1 on success, depending on whether bit \c pos
348  *                 of \c X is unset or set.
349  * \return         A negative error code on failure.
350  */
351 int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
352 
353 /**
354  * \brief          Modify a specific bit in an MPI.
355  *
356  * \note           This function will grow the target MPI if necessary to set a
357  *                 bit to \c 1 in a not yet existing limb. It will not grow if
358  *                 the bit should be set to \c 0.
359  *
360  * \param X        The MPI to modify. This must be initialized.
361  * \param pos      Zero-based index of the bit to modify.
362  * \param val      The desired value of bit \c pos: \c 0 or \c 1.
363  *
364  * \return         \c 0 if successful.
365  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
366  * \return         Another negative error code on other kinds of failure.
367  */
368 int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val );
369 
370 /**
371  * \brief          Return the number of bits of value \c 0 before the
372  *                 least significant bit of value \c 1.
373  *
374  * \note           This is the same as the zero-based index of
375  *                 the least significant bit of value \c 1.
376  *
377  * \param X        The MPI to query.
378  *
379  * \return         The number of bits of value \c 0 before the least significant
380  *                 bit of value \c 1 in \p X.
381  */
382 size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
383 
384 /**
385  * \brief          Return the number of bits up to and including the most
386  *                 significant bit of value \c 1.
387  *
388  * * \note         This is same as the one-based index of the most
389  *                 significant bit of value \c 1.
390  *
391  * \param X        The MPI to query. This must point to an initialized MPI.
392  *
393  * \return         The number of bits up to and including the most
394  *                 significant bit of value \c 1.
395  */
396 size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
397 
398 /**
399  * \brief          Return the total size of an MPI value in bytes.
400  *
401  * \param X        The MPI to use. This must point to an initialized MPI.
402  *
403  * \note           The value returned by this function may be less than
404  *                 the number of bytes used to store \p X internally.
405  *                 This happens if and only if there are trailing bytes
406  *                 of value zero.
407  *
408  * \return         The least number of bytes capable of storing
409  *                 the absolute value of \p X.
410  */
411 size_t mbedtls_mpi_size( const mbedtls_mpi *X );
412 
413 /**
414  * \brief          Import an MPI from an ASCII string.
415  *
416  * \param X        The destination MPI. This must point to an initialized MPI.
417  * \param radix    The numeric base of the input string.
418  * \param s        Null-terminated string buffer.
419  *
420  * \return         \c 0 if successful.
421  * \return         A negative error code on failure.
422  */
423 int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
424 
425 /**
426  * \brief          Export an MPI to an ASCII string.
427  *
428  * \param X        The source MPI. This must point to an initialized MPI.
429  * \param radix    The numeric base of the output string.
430  * \param buf      The buffer to write the string to. This must be writable
431  *                 buffer of length \p buflen Bytes.
432  * \param buflen   The available size in Bytes of \p buf.
433  * \param olen     The address at which to store the length of the string
434  *                 written, including the  final \c NULL byte. This must
435  *                 not be \c NULL.
436  *
437  * \note           You can call this function with `buflen == 0` to obtain the
438  *                 minimum required buffer size in `*olen`.
439  *
440  * \return         \c 0 if successful.
441  * \return         #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer \p buf
442  *                 is too small to hold the value of \p X in the desired base.
443  *                 In this case, `*olen` is nonetheless updated to contain the
444  *                 size of \p buf required for a successful call.
445  * \return         Another negative error code on different kinds of failure.
446  */
447 int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
448                               char *buf, size_t buflen, size_t *olen );
449 
450 #if defined(MBEDTLS_FS_IO)
451 /**
452  * \brief          Read an MPI from a line in an opened file.
453  *
454  * \param X        The destination MPI. This must point to an initialized MPI.
455  * \param radix    The numeric base of the string representation used
456  *                 in the source line.
457  * \param fin      The input file handle to use. This must not be \c NULL.
458  *
459  * \note           On success, this function advances the file stream
460  *                 to the end of the current line or to EOF.
461  *
462  *                 The function returns \c 0 on an empty line.
463  *
464  *                 Leading whitespaces are ignored, as is a
465  *                 '0x' prefix for radix \c 16.
466  *
467  * \return         \c 0 if successful.
468  * \return         #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer
469  *                 is too small.
470  * \return         Another negative error code on failure.
471  */
472 int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
473 
474 /**
475  * \brief          Export an MPI into an opened file.
476  *
477  * \param p        A string prefix to emit prior to the MPI data.
478  *                 For example, this might be a label, or "0x" when
479  *                 printing in base \c 16. This may be \c NULL if no prefix
480  *                 is needed.
481  * \param X        The source MPI. This must point to an initialized MPI.
482  * \param radix    The numeric base to be used in the emitted string.
483  * \param fout     The output file handle. This may be \c NULL, in which case
484  *                 the output is written to \c stdout.
485  *
486  * \return         \c 0 if successful.
487  * \return         A negative error code on failure.
488  */
489 int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X,
490                             int radix, FILE *fout );
491 #endif /* MBEDTLS_FS_IO */
492 
493 /**
494  * \brief          Import an MPI from unsigned big endian binary data.
495  *
496  * \param X        The destination MPI. This must point to an initialized MPI.
497  * \param buf      The input buffer. This must be a readable buffer of length
498  *                 \p buflen Bytes.
499  * \param buflen   The length of the input buffer \p p in Bytes.
500  *
501  * \return         \c 0 if successful.
502  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
503  * \return         Another negative error code on different kinds of failure.
504  */
505 int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf,
506                              size_t buflen );
507 
508 /**
509  * \brief          Import X from unsigned binary data, little endian
510  *
511  * \param X        The destination MPI. This must point to an initialized MPI.
512  * \param buf      The input buffer. This must be a readable buffer of length
513  *                 \p buflen Bytes.
514  * \param buflen   The length of the input buffer \p p in Bytes.
515  *
516  * \return         \c 0 if successful.
517  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
518  * \return         Another negative error code on different kinds of failure.
519  */
520 int mbedtls_mpi_read_binary_le( mbedtls_mpi *X,
521                                 const unsigned char *buf, size_t buflen );
522 
523 /**
524  * \brief          Export X into unsigned binary data, big endian.
525  *                 Always fills the whole buffer, which will start with zeros
526  *                 if the number is smaller.
527  *
528  * \param X        The source MPI. This must point to an initialized MPI.
529  * \param buf      The output buffer. This must be a writable buffer of length
530  *                 \p buflen Bytes.
531  * \param buflen   The size of the output buffer \p buf in Bytes.
532  *
533  * \return         \c 0 if successful.
534  * \return         #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
535  *                 large enough to hold the value of \p X.
536  * \return         Another negative error code on different kinds of failure.
537  */
538 int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf,
539                               size_t buflen );
540 
541 /**
542  * \brief          Export X into unsigned binary data, little endian.
543  *                 Always fills the whole buffer, which will end with zeros
544  *                 if the number is smaller.
545  *
546  * \param X        The source MPI. This must point to an initialized MPI.
547  * \param buf      The output buffer. This must be a writable buffer of length
548  *                 \p buflen Bytes.
549  * \param buflen   The size of the output buffer \p buf in Bytes.
550  *
551  * \return         \c 0 if successful.
552  * \return         #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
553  *                 large enough to hold the value of \p X.
554  * \return         Another negative error code on different kinds of failure.
555  */
556 int mbedtls_mpi_write_binary_le( const mbedtls_mpi *X,
557                                  unsigned char *buf, size_t buflen );
558 
559 /**
560  * \brief          Perform a left-shift on an MPI: X <<= count
561  *
562  * \param X        The MPI to shift. This must point to an initialized MPI.
563  * \param count    The number of bits to shift by.
564  *
565  * \return         \c 0 if successful.
566  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
567  * \return         Another negative error code on different kinds of failure.
568  */
569 int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
570 
571 /**
572  * \brief          Perform a right-shift on an MPI: X >>= count
573  *
574  * \param X        The MPI to shift. This must point to an initialized MPI.
575  * \param count    The number of bits to shift by.
576  *
577  * \return         \c 0 if successful.
578  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
579  * \return         Another negative error code on different kinds of failure.
580  */
581 int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count );
582 
583 /**
584  * \brief          Compare the absolute values of two MPIs.
585  *
586  * \param X        The left-hand MPI. This must point to an initialized MPI.
587  * \param Y        The right-hand MPI. This must point to an initialized MPI.
588  *
589  * \return         \c 1 if `|X|` is greater than `|Y|`.
590  * \return         \c -1 if `|X|` is lesser than `|Y|`.
591  * \return         \c 0 if `|X|` is equal to `|Y|`.
592  */
593 int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
594 
595 /**
596  * \brief          Compare two MPIs.
597  *
598  * \param X        The left-hand MPI. This must point to an initialized MPI.
599  * \param Y        The right-hand MPI. This must point to an initialized MPI.
600  *
601  * \return         \c 1 if \p X is greater than \p Y.
602  * \return         \c -1 if \p X is lesser than \p Y.
603  * \return         \c 0 if \p X is equal to \p Y.
604  */
605 int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
606 
607 /**
608  * \brief          Check if an MPI is less than the other in constant time.
609  *
610  * \param X        The left-hand MPI. This must point to an initialized MPI
611  *                 with the same allocated length as Y.
612  * \param Y        The right-hand MPI. This must point to an initialized MPI
613  *                 with the same allocated length as X.
614  * \param ret      The result of the comparison:
615  *                 \c 1 if \p X is less than \p Y.
616  *                 \c 0 if \p X is greater than or equal to \p Y.
617  *
618  * \return         0 on success.
619  * \return         MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the allocated length of
620  *                 the two input MPIs is not the same.
621  */
622 int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y,
623         unsigned *ret );
624 
625 /**
626  * \brief          Compare an MPI with an integer.
627  *
628  * \param X        The left-hand MPI. This must point to an initialized MPI.
629  * \param z        The integer value to compare \p X to.
630  *
631  * \return         \c 1 if \p X is greater than \p z.
632  * \return         \c -1 if \p X is lesser than \p z.
633  * \return         \c 0 if \p X is equal to \p z.
634  */
635 int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z );
636 
637 /**
638  * \brief          Perform an unsigned addition of MPIs: X = |A| + |B|
639  *
640  * \param X        The destination MPI. This must point to an initialized MPI.
641  * \param A        The first summand. This must point to an initialized MPI.
642  * \param B        The second summand. This must point to an initialized MPI.
643  *
644  * \return         \c 0 if successful.
645  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
646  * \return         Another negative error code on different kinds of failure.
647  */
648 int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A,
649                          const mbedtls_mpi *B );
650 
651 /**
652  * \brief          Perform an unsigned subtraction of MPIs: X = |A| - |B|
653  *
654  * \param X        The destination MPI. This must point to an initialized MPI.
655  * \param A        The minuend. This must point to an initialized MPI.
656  * \param B        The subtrahend. This must point to an initialized MPI.
657  *
658  * \return         \c 0 if successful.
659  * \return         #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is greater than \p A.
660  * \return         Another negative error code on different kinds of failure.
661  *
662  */
663 int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A,
664                          const mbedtls_mpi *B );
665 
666 /**
667  * \brief          Perform a signed addition of MPIs: X = A + B
668  *
669  * \param X        The destination MPI. This must point to an initialized MPI.
670  * \param A        The first summand. This must point to an initialized MPI.
671  * \param B        The second summand. This must point to an initialized MPI.
672  *
673  * \return         \c 0 if successful.
674  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
675  * \return         Another negative error code on different kinds of failure.
676  */
677 int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
678                          const mbedtls_mpi *B );
679 
680 /**
681  * \brief          Perform a signed subtraction of MPIs: X = A - B
682  *
683  * \param X        The destination MPI. This must point to an initialized MPI.
684  * \param A        The minuend. This must point to an initialized MPI.
685  * \param B        The subtrahend. This must point to an initialized MPI.
686  *
687  * \return         \c 0 if successful.
688  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
689  * \return         Another negative error code on different kinds of failure.
690  */
691 int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
692                          const mbedtls_mpi *B );
693 
694 /**
695  * \brief          Perform a signed addition of an MPI and an integer: X = A + b
696  *
697  * \param X        The destination MPI. This must point to an initialized MPI.
698  * \param A        The first summand. This must point to an initialized MPI.
699  * \param b        The second summand.
700  *
701  * \return         \c 0 if successful.
702  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
703  * \return         Another negative error code on different kinds of failure.
704  */
705 int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A,
706                          mbedtls_mpi_sint b );
707 
708 /**
709  * \brief          Perform a signed subtraction of an MPI and an integer:
710  *                 X = A - b
711  *
712  * \param X        The destination MPI. This must point to an initialized MPI.
713  * \param A        The minuend. This must point to an initialized MPI.
714  * \param b        The subtrahend.
715  *
716  * \return         \c 0 if successful.
717  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
718  * \return         Another negative error code on different kinds of failure.
719  */
720 int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A,
721                          mbedtls_mpi_sint b );
722 
723 /**
724  * \brief          Perform a multiplication of two MPIs: X = A * B
725  *
726  * \param X        The destination MPI. This must point to an initialized MPI.
727  * \param A        The first factor. This must point to an initialized MPI.
728  * \param B        The second factor. This must point to an initialized MPI.
729  *
730  * \return         \c 0 if successful.
731  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
732  * \return         Another negative error code on different kinds of failure.
733  *
734  */
735 int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
736                          const mbedtls_mpi *B );
737 
738 /**
739  * \brief          Perform a multiplication of an MPI with an unsigned integer:
740  *                 X = A * b
741  *
742  * \param X        The destination MPI. This must point to an initialized MPI.
743  * \param A        The first factor. This must point to an initialized MPI.
744  * \param b        The second factor.
745  *
746  * \return         \c 0 if successful.
747  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
748  * \return         Another negative error code on different kinds of failure.
749  *
750  */
751 int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A,
752                          mbedtls_mpi_uint b );
753 
754 /**
755  * \brief          Perform a division with remainder of two MPIs:
756  *                 A = Q * B + R
757  *
758  * \param Q        The destination MPI for the quotient.
759  *                 This may be \c NULL if the value of the
760  *                 quotient is not needed.
761  * \param R        The destination MPI for the remainder value.
762  *                 This may be \c NULL if the value of the
763  *                 remainder is not needed.
764  * \param A        The dividend. This must point to an initialized MPi.
765  * \param B        The divisor. This must point to an initialized MPI.
766  *
767  * \return         \c 0 if successful.
768  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
769  * \return         #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero.
770  * \return         Another negative error code on different kinds of failure.
771  */
772 int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
773                          const mbedtls_mpi *B );
774 
775 /**
776  * \brief          Perform a division with remainder of an MPI by an integer:
777  *                 A = Q * b + R
778  *
779  * \param Q        The destination MPI for the quotient.
780  *                 This may be \c NULL if the value of the
781  *                 quotient is not needed.
782  * \param R        The destination MPI for the remainder value.
783  *                 This may be \c NULL if the value of the
784  *                 remainder is not needed.
785  * \param A        The dividend. This must point to an initialized MPi.
786  * \param b        The divisor.
787  *
788  * \return         \c 0 if successful.
789  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
790  * \return         #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero.
791  * \return         Another negative error code on different kinds of failure.
792  */
793 int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
794                          mbedtls_mpi_sint b );
795 
796 /**
797  * \brief          Perform a modular reduction. R = A mod B
798  *
799  * \param R        The destination MPI for the residue value.
800  *                 This must point to an initialized MPI.
801  * \param A        The MPI to compute the residue of.
802  *                 This must point to an initialized MPI.
803  * \param B        The base of the modular reduction.
804  *                 This must point to an initialized MPI.
805  *
806  * \return         \c 0 if successful.
807  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
808  * \return         #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero.
809  * \return         #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is negative.
810  * \return         Another negative error code on different kinds of failure.
811  *
812  */
813 int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A,
814                          const mbedtls_mpi *B );
815 
816 /**
817  * \brief          Perform a modular reduction with respect to an integer.
818  *                 r = A mod b
819  *
820  * \param r        The address at which to store the residue.
821  *                 This must not be \c NULL.
822  * \param A        The MPI to compute the residue of.
823  *                 This must point to an initialized MPi.
824  * \param b        The integer base of the modular reduction.
825  *
826  * \return         \c 0 if successful.
827  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
828  * \return         #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero.
829  * \return         #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p b is negative.
830  * \return         Another negative error code on different kinds of failure.
831  */
832 int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A,
833                          mbedtls_mpi_sint b );
834 
835 /**
836  * \brief          Perform a sliding-window exponentiation: X = A^E mod N
837  *
838  * \param X        The destination MPI. This must point to an initialized MPI.
839  * \param A        The base of the exponentiation.
840  *                 This must point to an initialized MPI.
841  * \param E        The exponent MPI. This must point to an initialized MPI.
842  * \param N        The base for the modular reduction. This must point to an
843  *                 initialized MPI.
844  * \param prec_RR  A helper MPI depending solely on \p N which can be used to
845  *                 speed-up multiple modular exponentiations for the same value
846  *                 of \p N. This may be \c NULL. If it is not \c NULL, it must
847  *                 point to an initialized MPI. If it hasn't been used after
848  *                 the call to mbedtls_mpi_init(), this function will compute
849  *                 the helper value and store it in \p prec_RR for reuse on
850  *                 subsequent calls to this function. Otherwise, the function
851  *                 will assume that \p prec_RR holds the helper value set by a
852  *                 previous call to mbedtls_mpi_exp_mod(), and reuse it.
853  *
854  * \return         \c 0 if successful.
855  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
856  * \return         #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \c N is negative or
857  *                 even, or if \c E is negative.
858  * \return         Another negative error code on different kinds of failures.
859  *
860  */
861 int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
862                          const mbedtls_mpi *E, const mbedtls_mpi *N,
863                          mbedtls_mpi *prec_RR );
864 
865 /**
866  * \brief          Fill an MPI with a number of random bytes.
867  *
868  * \param X        The destination MPI. This must point to an initialized MPI.
869  * \param size     The number of random bytes to generate.
870  * \param f_rng    The RNG function to use. This must not be \c NULL.
871  * \param p_rng    The RNG parameter to be passed to \p f_rng. This may be
872  *                 \c NULL if \p f_rng doesn't need a context argument.
873  *
874  * \return         \c 0 if successful.
875  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
876  * \return         Another negative error code on failure.
877  *
878  * \note           The bytes obtained from the RNG are interpreted
879  *                 as a big-endian representation of an MPI; this can
880  *                 be relevant in applications like deterministic ECDSA.
881  */
882 int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
883                      int (*f_rng)(void *, unsigned char *, size_t),
884                      void *p_rng );
885 
886 /** Generate a random number uniformly in a range.
887  *
888  * This function generates a random number between \p min inclusive and
889  * \p N exclusive.
890  *
891  * The procedure complies with RFC 6979 §3.3 (deterministic ECDSA)
892  * when the RNG is a suitably parametrized instance of HMAC_DRBG
893  * and \p min is \c 1.
894  *
895  * \note           There are `N - min` possible outputs. The lower bound
896  *                 \p min can be reached, but the upper bound \p N cannot.
897  *
898  * \param X        The destination MPI. This must point to an initialized MPI.
899  * \param min      The minimum value to return.
900  *                 It must be nonnegative.
901  * \param N        The upper bound of the range, exclusive.
902  *                 In other words, this is one plus the maximum value to return.
903  *                 \p N must be strictly larger than \p min.
904  * \param f_rng    The RNG function to use. This must not be \c NULL.
905  * \param p_rng    The RNG parameter to be passed to \p f_rng.
906  *
907  * \return         \c 0 if successful.
908  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
909  * \return         #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p min or \p N is invalid
910  *                 or if they are incompatible.
911  * \return         #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if the implementation was
912  *                 unable to find a suitable value within a limited number
913  *                 of attempts. This has a negligible probability if \p N
914  *                 is significantly larger than \p min, which is the case
915  *                 for all usual cryptographic applications.
916  * \return         Another negative error code on failure.
917  */
918 int mbedtls_mpi_random( mbedtls_mpi *X,
919                         mbedtls_mpi_sint min,
920                         const mbedtls_mpi *N,
921                         int (*f_rng)(void *, unsigned char *, size_t),
922                         void *p_rng );
923 
924 /**
925  * \brief          Compute the greatest common divisor: G = gcd(A, B)
926  *
927  * \param G        The destination MPI. This must point to an initialized MPI.
928  * \param A        The first operand. This must point to an initialized MPI.
929  * \param B        The second operand. This must point to an initialized MPI.
930  *
931  * \return         \c 0 if successful.
932  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
933  * \return         Another negative error code on different kinds of failure.
934  */
935 int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A,
936                      const mbedtls_mpi *B );
937 
938 /**
939  * \brief          Compute the modular inverse: X = A^-1 mod N
940  *
941  * \param X        The destination MPI. This must point to an initialized MPI.
942  * \param A        The MPI to calculate the modular inverse of. This must point
943  *                 to an initialized MPI.
944  * \param N        The base of the modular inversion. This must point to an
945  *                 initialized MPI.
946  *
947  * \return         \c 0 if successful.
948  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
949  * \return         #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p N is less than
950  *                 or equal to one.
951  * \return         #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p has no modular inverse
952  *                 with respect to \p N.
953  */
954 int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
955                          const mbedtls_mpi *N );
956 
957 #if !defined(MBEDTLS_DEPRECATED_REMOVED)
958 #if defined(MBEDTLS_DEPRECATED_WARNING)
959 #define MBEDTLS_DEPRECATED      __attribute__((deprecated))
960 #else
961 #define MBEDTLS_DEPRECATED
962 #endif
963 /**
964  * \brief          Perform a Miller-Rabin primality test with error
965  *                 probability of 2<sup>-80</sup>.
966  *
967  * \deprecated     Superseded by mbedtls_mpi_is_prime_ext() which allows
968  *                 specifying the number of Miller-Rabin rounds.
969  *
970  * \param X        The MPI to check for primality.
971  *                 This must point to an initialized MPI.
972  * \param f_rng    The RNG function to use. This must not be \c NULL.
973  * \param p_rng    The RNG parameter to be passed to \p f_rng.
974  *                 This may be \c NULL if \p f_rng doesn't use a
975  *                 context parameter.
976  *
977  * \return         \c 0 if successful, i.e. \p X is probably prime.
978  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
979  * \return         #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime.
980  * \return         Another negative error code on other kinds of failure.
981  */
982 MBEDTLS_DEPRECATED int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
983                           int (*f_rng)(void *, unsigned char *, size_t),
984                           void *p_rng );
985 #undef MBEDTLS_DEPRECATED
986 #endif /* !MBEDTLS_DEPRECATED_REMOVED */
987 
988 /**
989  * \brief          Miller-Rabin primality test.
990  *
991  * \warning        If \p X is potentially generated by an adversary, for example
992  *                 when validating cryptographic parameters that you didn't
993  *                 generate yourself and that are supposed to be prime, then
994  *                 \p rounds should be at least the half of the security
995  *                 strength of the cryptographic algorithm. On the other hand,
996  *                 if \p X is chosen uniformly or non-adversarially (as is the
997  *                 case when mbedtls_mpi_gen_prime calls this function), then
998  *                 \p rounds can be much lower.
999  *
1000  * \param X        The MPI to check for primality.
1001  *                 This must point to an initialized MPI.
1002  * \param rounds   The number of bases to perform the Miller-Rabin primality
1003  *                 test for. The probability of returning 0 on a composite is
1004  *                 at most 2<sup>-2*\p rounds</sup>.
1005  * \param f_rng    The RNG function to use. This must not be \c NULL.
1006  * \param p_rng    The RNG parameter to be passed to \p f_rng.
1007  *                 This may be \c NULL if \p f_rng doesn't use
1008  *                 a context parameter.
1009  *
1010  * \return         \c 0 if successful, i.e. \p X is probably prime.
1011  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
1012  * \return         #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime.
1013  * \return         Another negative error code on other kinds of failure.
1014  */
1015 int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds,
1016                               int (*f_rng)(void *, unsigned char *, size_t),
1017                               void *p_rng );
1018 /**
1019  * \brief Flags for mbedtls_mpi_gen_prime()
1020  *
1021  * Each of these flags is a constraint on the result X returned by
1022  * mbedtls_mpi_gen_prime().
1023  */
1024 typedef enum {
1025     MBEDTLS_MPI_GEN_PRIME_FLAG_DH =      0x0001, /**< (X-1)/2 is prime too */
1026     MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR = 0x0002, /**< lower error rate from 2<sup>-80</sup> to 2<sup>-128</sup> */
1027 } mbedtls_mpi_gen_prime_flag_t;
1028 
1029 /**
1030  * \brief          Generate a prime number.
1031  *
1032  * \param X        The destination MPI to store the generated prime in.
1033  *                 This must point to an initialized MPi.
1034  * \param nbits    The required size of the destination MPI in bits.
1035  *                 This must be between \c 3 and #MBEDTLS_MPI_MAX_BITS.
1036  * \param flags    A mask of flags of type #mbedtls_mpi_gen_prime_flag_t.
1037  * \param f_rng    The RNG function to use. This must not be \c NULL.
1038  * \param p_rng    The RNG parameter to be passed to \p f_rng.
1039  *                 This may be \c NULL if \p f_rng doesn't use
1040  *                 a context parameter.
1041  *
1042  * \return         \c 0 if successful, in which case \p X holds a
1043  *                 probably prime number.
1044  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
1045  * \return         #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `nbits` is not between
1046  *                 \c 3 and #MBEDTLS_MPI_MAX_BITS.
1047  */
1048 int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags,
1049                    int (*f_rng)(void *, unsigned char *, size_t),
1050                    void *p_rng );
1051 
1052 /**
1053  * \brief          Montgomery initialization
1054  *
1055  * \param mm       The -1/m mod N result
1056  * \param N        The modulus
1057  */
1058 void mbedtls_mpi_montg_init( mbedtls_mpi_uint *mm, const mbedtls_mpi *N );
1059 
1060 /**
1061  * \brief          Montgomery multiplication: A = A * B * R^-1 mod N
1062  * \A              Parameter and result
1063  * \B              Parameter
1064  * \N              Modulus
1065  * \mm             Parameter from mbedtls_mpi_montg_init()
1066  * \T              Temporary variable, should be as twice as big as N + 2
1067  */
1068 void mbedtls_mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B,
1069                           const mbedtls_mpi *N, mbedtls_mpi_uint mm,
1070                           const mbedtls_mpi *T );
1071 
1072 /**
1073  * \brief          Montgomery reduction: A = A * R^-1 mod N
1074  * \A              Parameter and result
1075  * \N              Modulus
1076  * \mm             Parameter from mbedtls_mpi_montg_init()
1077  * \T              Temporary variable, should be as twice as big as N + 2
1078  */
1079 void mbedtls_mpi_montred( mbedtls_mpi *A, const mbedtls_mpi *N,
1080                           mbedtls_mpi_uint mm, const mbedtls_mpi *T );
1081 
1082 #if defined(MBEDTLS_SELF_TEST)
1083 
1084 /**
1085  * \brief          Checkup routine
1086  *
1087  * \return         0 if successful, or 1 if the test failed
1088  */
1089 int mbedtls_mpi_self_test( int verbose );
1090 
1091 #endif /* MBEDTLS_SELF_TEST */
1092 
1093 #ifdef __cplusplus
1094 }
1095 #endif
1096 
1097 #endif /* bignum.h */
1098