4 * \brief Multi-precision integer library
7 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
8 * SPDX-License-Identifier: Apache-2.0
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
14 * http://www.apache.org/licenses/LICENSE-2.0
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.
22 * This file is part of mbed TLS (https://tls.mbed.org)
24 #ifndef MBEDTLS_BIGNUM_H
25 #define MBEDTLS_BIGNUM_H
27 #if !defined(MBEDTLS_CONFIG_FILE)
30 #include MBEDTLS_CONFIG_FILE
36 #if defined(MBEDTLS_FS_IO)
40 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002 /**< An error occurred while reading from or writing to a file. */
41 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004 /**< Bad input parameters to function. */
42 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006 /**< There is an invalid character in the digit string. */
43 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008 /**< The buffer is too small to write to. */
44 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A /**< The input arguments are negative or result in illegal output. */
45 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C /**< The input argument for division is zero, which is not allowed. */
46 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E /**< The input arguments are not acceptable. */
47 #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010 /**< Memory allocation failed. */
49 #define MBEDTLS_MPI_CHK(f) \
52 if( ( ret = (f) ) != 0 ) \
57 * Maximum size MPIs are allowed to grow to in number of limbs.
59 #define MBEDTLS_MPI_MAX_LIMBS 10000
61 #if !defined(MBEDTLS_MPI_WINDOW_SIZE)
63 * Maximum window size used for modular exponentiation. Default: 6
64 * Minimum value: 1. Maximum value: 6.
66 * Result is an array of ( 2 << MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
67 * for the sliding window calculation. (So 64 by default)
69 * Reduction in size, reduces speed.
71 #define MBEDTLS_MPI_WINDOW_SIZE 6 /**< Maximum windows size used. */
72 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */
74 #if !defined(MBEDTLS_MPI_MAX_SIZE)
76 * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
77 * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
79 * Note: Calculations can temporarily result in larger MPIs. So the number
80 * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
82 #define MBEDTLS_MPI_MAX_SIZE 1024 /**< Maximum number of bytes for usable MPIs. */
83 #endif /* !MBEDTLS_MPI_MAX_SIZE */
85 #define MBEDTLS_MPI_MAX_BITS ( 8 * MBEDTLS_MPI_MAX_SIZE ) /**< Maximum number of bits for usable MPIs. */
88 * When reading from files with mbedtls_mpi_read_file() and writing to files with
89 * mbedtls_mpi_write_file() the buffer should have space
90 * for a (short) label, the MPI (in the provided radix), the newline
91 * characters and the '\0'.
93 * By default we assume at least a 10 char label, a minimum radix of 10
94 * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
95 * Autosized at compile time for at least a 10 char label, a minimum radix
96 * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
98 * This used to be statically sized to 1250 for a maximum of 4096 bit
99 * numbers (1234 decimal chars).
101 * Calculate using the formula:
102 * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
105 #define MBEDTLS_MPI_MAX_BITS_SCALE100 ( 100 * MBEDTLS_MPI_MAX_BITS )
106 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332
107 #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 )
110 * Define the base integer type, architecture-wise.
112 * 32 or 64-bit integer types can be forced regardless of the underlying
113 * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
114 * respectively and undefining MBEDTLS_HAVE_ASM.
116 * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
117 * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
119 #if !defined(MBEDTLS_HAVE_INT32)
120 #if defined(_MSC_VER) && defined(_M_AMD64)
121 /* Always choose 64-bit when using MSC */
122 #if !defined(MBEDTLS_HAVE_INT64)
123 #define MBEDTLS_HAVE_INT64
124 #endif /* !MBEDTLS_HAVE_INT64 */
125 typedef int64_t mbedtls_mpi_sint;
126 typedef uint64_t mbedtls_mpi_uint;
127 #elif defined(__GNUC__) && ( \
128 defined(__amd64__) || defined(__x86_64__) || \
129 defined(__ppc64__) || defined(__powerpc64__) || \
130 defined(__ia64__) || defined(__alpha__) || \
131 ( defined(__sparc__) && defined(__arch64__) ) || \
132 defined(__s390x__) || defined(__mips64) )
133 #if !defined(MBEDTLS_HAVE_INT64)
134 #define MBEDTLS_HAVE_INT64
135 #endif /* MBEDTLS_HAVE_INT64 */
136 typedef int64_t mbedtls_mpi_sint;
137 typedef uint64_t mbedtls_mpi_uint;
138 #if !defined(MBEDTLS_NO_UDBL_DIVISION)
139 /* mbedtls_t_udbl defined as 128-bit unsigned int */
140 typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
141 #define MBEDTLS_HAVE_UDBL
142 #endif /* !MBEDTLS_NO_UDBL_DIVISION */
143 #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
145 * __ARMCC_VERSION is defined for both armcc and armclang and
146 * __aarch64__ is only defined by armclang when compiling 64-bit code
148 #if !defined(MBEDTLS_HAVE_INT64)
149 #define MBEDTLS_HAVE_INT64
150 #endif /* !MBEDTLS_HAVE_INT64 */
151 typedef int64_t mbedtls_mpi_sint;
152 typedef uint64_t mbedtls_mpi_uint;
153 #if !defined(MBEDTLS_NO_UDBL_DIVISION)
154 /* mbedtls_t_udbl defined as 128-bit unsigned int */
155 typedef __uint128_t mbedtls_t_udbl;
156 #define MBEDTLS_HAVE_UDBL
157 #endif /* !MBEDTLS_NO_UDBL_DIVISION */
158 #elif defined(MBEDTLS_HAVE_INT64)
159 /* Force 64-bit integers with unknown compiler */
160 typedef int64_t mbedtls_mpi_sint;
161 typedef uint64_t mbedtls_mpi_uint;
163 #endif /* !MBEDTLS_HAVE_INT32 */
165 #if !defined(MBEDTLS_HAVE_INT64)
166 /* Default to 32-bit compilation */
167 #if !defined(MBEDTLS_HAVE_INT32)
168 #define MBEDTLS_HAVE_INT32
169 #endif /* !MBEDTLS_HAVE_INT32 */
170 typedef int32_t mbedtls_mpi_sint;
171 typedef uint32_t mbedtls_mpi_uint;
172 #if !defined(MBEDTLS_NO_UDBL_DIVISION)
173 typedef uint64_t mbedtls_t_udbl;
174 #define MBEDTLS_HAVE_UDBL
175 #endif /* !MBEDTLS_NO_UDBL_DIVISION */
176 #endif /* !MBEDTLS_HAVE_INT64 */
183 * \brief MPI structure
185 typedef struct mbedtls_mpi
187 int s; /*!< integer sign */
188 size_t n; /*!< total # of limbs */
189 mbedtls_mpi_uint *p; /*!< pointer to limbs */
194 * \brief Initialize an MPI context.
196 * This makes the MPI ready to be set or freed,
197 * but does not define a value for the MPI.
199 * \param X The MPI context to initialize. This must not be \c NULL.
201 void mbedtls_mpi_init( mbedtls_mpi *X );
204 * \brief This function frees the components of an MPI context.
206 * \param X The MPI context to be cleared. This may be \c NULL,
207 * in which case this function is a no-op. If it is
208 * not \c NULL, it must point to an initialized MPI.
210 void mbedtls_mpi_free( mbedtls_mpi *X );
213 * \brief Enlarge an MPI to the specified number of limbs.
215 * \note This function does nothing if the MPI is
216 * already large enough.
218 * \param X The MPI to grow. It must be initialized.
219 * \param nblimbs The target number of limbs.
221 * \return \c 0 if successful.
222 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
223 * \return Another negative error code on other kinds of failure.
225 int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
228 * \brief This function resizes an MPI downwards, keeping at least the
229 * specified number of limbs.
231 * If \c X is smaller than \c nblimbs, it is resized up
234 * \param X The MPI to shrink. This must point to an initialized MPI.
235 * \param nblimbs The minimum number of limbs to keep.
237 * \return \c 0 if successful.
238 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
239 * (this can only happen when resizing up).
240 * \return Another negative error code on other kinds of failure.
242 int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
245 * \brief Make a copy of an MPI.
247 * \param X The destination MPI. This must point to an initialized MPI.
248 * \param Y The source MPI. This must point to an initialized MPI.
250 * \note The limb-buffer in the destination MPI is enlarged
251 * if necessary to hold the value in the source MPI.
253 * \return \c 0 if successful.
254 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
255 * \return Another negative error code on other kinds of failure.
257 int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
260 * \brief Swap the contents of two MPIs.
262 * \param X The first MPI. It must be initialized.
263 * \param Y The second MPI. It must be initialized.
265 void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y );
268 * \brief Perform a safe conditional copy of MPI which doesn't
269 * reveal whether the condition was true or not.
271 * \param X The MPI to conditionally assign to. This must point
272 * to an initialized MPI.
273 * \param Y The MPI to be assigned from. This must point to an
275 * \param assign The condition deciding whether to perform the
276 * assignment or not. Possible values:
277 * * \c 1: Perform the assignment `X = Y`.
278 * * \c 0: Keep the original value of \p X.
280 * \note This function is equivalent to
281 * `if( assign ) mbedtls_mpi_copy( X, Y );`
282 * except that it avoids leaking any information about whether
283 * the assignment was done or not (the above code may leak
284 * information through branch prediction and/or memory access
285 * patterns analysis).
287 * \return \c 0 if successful.
288 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
289 * \return Another negative error code on other kinds of failure.
291 int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
294 * \brief Perform a safe conditional swap which doesn't
295 * reveal whether the condition was true or not.
297 * \param X The first MPI. This must be initialized.
298 * \param Y The second MPI. This must be initialized.
299 * \param assign The condition deciding whether to perform
300 * the swap or not. Possible values:
301 * * \c 1: Swap the values of \p X and \p Y.
302 * * \c 0: Keep the original values of \p X and \p Y.
304 * \note This function is equivalent to
305 * if( assign ) mbedtls_mpi_swap( X, Y );
306 * except that it avoids leaking any information about whether
307 * the assignment was done or not (the above code may leak
308 * information through branch prediction and/or memory access
309 * patterns analysis).
311 * \return \c 0 if successful.
312 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
313 * \return Another negative error code on other kinds of failure.
316 int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
319 * \brief Store integer value in MPI.
321 * \param X The MPI to set. This must be initialized.
322 * \param z The value to use.
324 * \return \c 0 if successful.
325 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
326 * \return Another negative error code on other kinds of failure.
328 int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z );
331 * \brief Get a specific bit from an MPI.
333 * \param X The MPI to query. This must be initialized.
334 * \param pos Zero-based index of the bit to query.
336 * \return \c 0 or \c 1 on success, depending on whether bit \c pos
337 * of \c X is unset or set.
338 * \return A negative error code on failure.
340 int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
343 * \brief Modify a specific bit in an MPI.
345 * \note This function will grow the target MPI if necessary to set a
346 * bit to \c 1 in a not yet existing limb. It will not grow if
347 * the bit should be set to \c 0.
349 * \param X The MPI to modify. This must be initialized.
350 * \param pos Zero-based index of the bit to modify.
351 * \param val The desired value of bit \c pos: \c 0 or \c 1.
353 * \return \c 0 if successful.
354 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
355 * \return Another negative error code on other kinds of failure.
357 int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val );
360 * \brief Return the number of bits of value \c 0 before the
361 * least significant bit of value \c 1.
363 * \note This is the same as the zero-based index of
364 * the least significant bit of value \c 1.
366 * \param X The MPI to query.
368 * \return The number of bits of value \c 0 before the least significant
369 * bit of value \c 1 in \p X.
371 size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
374 * \brief Return the number of bits up to and including the most
375 * significant bit of value \c 1.
377 * * \note This is same as the one-based index of the most
378 * significant bit of value \c 1.
380 * \param X The MPI to query. This must point to an initialized MPI.
382 * \return The number of bits up to and including the most
383 * significant bit of value \c 1.
385 size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
388 * \brief Return the total size of an MPI value in bytes.
390 * \param X The MPI to use. This must point to an initialized MPI.
392 * \note The value returned by this function may be less than
393 * the number of bytes used to store \p X internally.
394 * This happens if and only if there are trailing bytes
397 * \return The least number of bytes capable of storing
398 * the absolute value of \p X.
400 size_t mbedtls_mpi_size( const mbedtls_mpi *X );
403 * \brief Import an MPI from an ASCII string.
405 * \param X The destination MPI. This must point to an initialized MPI.
406 * \param radix The numeric base of the input string.
407 * \param s Null-terminated string buffer.
409 * \return \c 0 if successful.
410 * \return A negative error code on failure.
412 int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
415 * \brief Export an MPI to an ASCII string.
417 * \param X The source MPI. This must point to an initialized MPI.
418 * \param radix The numeric base of the output string.
419 * \param buf The buffer to write the string to. This must be writable
420 * buffer of length \p buflen Bytes.
421 * \param buflen The available size in Bytes of \p buf.
422 * \param olen The address at which to store the length of the string
423 * written, including the final \c NULL byte. This must
426 * \note You can call this function with `buflen == 0` to obtain the
427 * minimum required buffer size in `*olen`.
429 * \return \c 0 if successful.
430 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer \p buf
431 * is too small to hold the value of \p X in the desired base.
432 * In this case, `*olen` is nonetheless updated to contain the
433 * size of \p buf required for a successful call.
434 * \return Another negative error code on different kinds of failure.
436 int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
437 char *buf, size_t buflen, size_t *olen );
439 #if defined(MBEDTLS_FS_IO)
441 * \brief Read an MPI from a line in an opened file.
443 * \param X The destination MPI. This must point to an initialized MPI.
444 * \param radix The numeric base of the string representation used
445 * in the source line.
446 * \param fin The input file handle to use. This must not be \c NULL.
448 * \note On success, this function advances the file stream
449 * to the end of the current line or to EOF.
451 * The function returns \c 0 on an empty line.
453 * Leading whitespaces are ignored, as is a
454 * '0x' prefix for radix \c 16.
456 * \return \c 0 if successful.
457 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer
459 * \return Another negative error code on failure.
461 int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
464 * \brief Export an MPI into an opened file.
466 * \param p A string prefix to emit prior to the MPI data.
467 * For example, this might be a label, or "0x" when
468 * printing in base \c 16. This may be \c NULL if no prefix
470 * \param X The source MPI. This must point to an initialized MPI.
471 * \param radix The numeric base to be used in the emitted string.
472 * \param fout The output file handle. This may be \c NULL, in which case
473 * the output is written to \c stdout.
475 * \return \c 0 if successful.
476 * \return A negative error code on failure.
478 int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X,
479 int radix, FILE *fout );
480 #endif /* MBEDTLS_FS_IO */
483 * \brief Import an MPI from unsigned big endian binary data.
485 * \param X The destination MPI. This must point to an initialized MPI.
486 * \param buf The input buffer. This must be a readable buffer of length
488 * \param buflen The length of the input buffer \p p in Bytes.
490 * \return \c 0 if successful.
491 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
492 * \return Another negative error code on different kinds of failure.
494 int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf,
498 * \brief Import X from unsigned binary data, little endian
500 * \param X The destination MPI. This must point to an initialized MPI.
501 * \param buf The input buffer. This must be a readable buffer of length
503 * \param buflen The length of the input buffer \p p in Bytes.
505 * \return \c 0 if successful.
506 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
507 * \return Another negative error code on different kinds of failure.
509 int mbedtls_mpi_read_binary_le( mbedtls_mpi *X,
510 const unsigned char *buf, size_t buflen );
513 * \brief Export X into unsigned binary data, big endian.
514 * Always fills the whole buffer, which will start with zeros
515 * if the number is smaller.
517 * \param X The source MPI. This must point to an initialized MPI.
518 * \param buf The output buffer. This must be a writable buffer of length
520 * \param buflen The size of the output buffer \p buf in Bytes.
522 * \return \c 0 if successful.
523 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
524 * large enough to hold the value of \p X.
525 * \return Another negative error code on different kinds of failure.
527 int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf,
531 * \brief Export X into unsigned binary data, little endian.
532 * Always fills the whole buffer, which will end with zeros
533 * if the number is smaller.
535 * \param X The source MPI. This must point to an initialized MPI.
536 * \param buf The output buffer. This must be a writable buffer of length
538 * \param buflen The size of the output buffer \p buf in Bytes.
540 * \return \c 0 if successful.
541 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
542 * large enough to hold the value of \p X.
543 * \return Another negative error code on different kinds of failure.
545 int mbedtls_mpi_write_binary_le( const mbedtls_mpi *X,
546 unsigned char *buf, size_t buflen );
549 * \brief Perform a left-shift on an MPI: X <<= count
551 * \param X The MPI to shift. This must point to an initialized MPI.
552 * \param count The number of bits to shift by.
554 * \return \c 0 if successful.
555 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
556 * \return Another negative error code on different kinds of failure.
558 int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
561 * \brief Perform a right-shift on an MPI: X >>= count
563 * \param X The MPI to shift. This must point to an initialized MPI.
564 * \param count The number of bits to shift by.
566 * \return \c 0 if successful.
567 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
568 * \return Another negative error code on different kinds of failure.
570 int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count );
573 * \brief Compare the absolute values of two MPIs.
575 * \param X The left-hand MPI. This must point to an initialized MPI.
576 * \param Y The right-hand MPI. This must point to an initialized MPI.
578 * \return \c 1 if `|X|` is greater than `|Y|`.
579 * \return \c -1 if `|X|` is lesser than `|Y|`.
580 * \return \c 0 if `|X|` is equal to `|Y|`.
582 int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
585 * \brief Compare two MPIs.
587 * \param X The left-hand MPI. This must point to an initialized MPI.
588 * \param Y The right-hand MPI. This must point to an initialized MPI.
590 * \return \c 1 if \p X is greater than \p Y.
591 * \return \c -1 if \p X is lesser than \p Y.
592 * \return \c 0 if \p X is equal to \p Y.
594 int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
597 * \brief Compare an MPI with an integer.
599 * \param X The left-hand MPI. This must point to an initialized MPI.
600 * \param z The integer value to compare \p X to.
602 * \return \c 1 if \p X is greater than \p z.
603 * \return \c -1 if \p X is lesser than \p z.
604 * \return \c 0 if \p X is equal to \p z.
606 int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z );
609 * \brief Perform an unsigned addition of MPIs: X = |A| + |B|
611 * \param X The destination MPI. This must point to an initialized MPI.
612 * \param A The first summand. This must point to an initialized MPI.
613 * \param B The second summand. This must point to an initialized MPI.
615 * \return \c 0 if successful.
616 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
617 * \return Another negative error code on different kinds of failure.
619 int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A,
620 const mbedtls_mpi *B );
623 * \brief Perform an unsigned subtraction of MPIs: X = |A| - |B|
625 * \param X The destination MPI. This must point to an initialized MPI.
626 * \param A The minuend. This must point to an initialized MPI.
627 * \param B The subtrahend. This must point to an initialized MPI.
629 * \return \c 0 if successful.
630 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is greater than \p A.
631 * \return Another negative error code on different kinds of failure.
634 int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A,
635 const mbedtls_mpi *B );
638 * \brief Perform a signed addition of MPIs: X = A + B
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.
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.
648 int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
649 const mbedtls_mpi *B );
652 * \brief Perform a signed subtraction of MPIs: X = A - B
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.
658 * \return \c 0 if successful.
659 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
660 * \return Another negative error code on different kinds of failure.
662 int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
663 const mbedtls_mpi *B );
666 * \brief Perform a signed addition of an MPI and an integer: X = A + b
668 * \param X The destination MPI. This must point to an initialized MPI.
669 * \param A The first summand. This must point to an initialized MPI.
670 * \param b The second summand.
672 * \return \c 0 if successful.
673 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
674 * \return Another negative error code on different kinds of failure.
676 int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A,
677 mbedtls_mpi_sint b );
680 * \brief Perform a signed subtraction of an MPI and an integer:
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.
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.
691 int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A,
692 mbedtls_mpi_sint b );
695 * \brief Perform a multiplication of two MPIs: X = A * B
697 * \param X The destination MPI. This must point to an initialized MPI.
698 * \param A The first factor. This must point to an initialized MPI.
699 * \param B The second factor. This must point to an initialized MPI.
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.
706 int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
707 const mbedtls_mpi *B );
710 * \brief Perform a multiplication of an MPI with an unsigned integer:
713 * \param X The destination MPI. This must point to an initialized MPI.
714 * \param A The first factor. This must point to an initialized MPI.
715 * \param b The second factor.
717 * \return \c 0 if successful.
718 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
719 * \return Another negative error code on different kinds of failure.
722 int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A,
723 mbedtls_mpi_uint b );
726 * \brief Perform a division with remainder of two MPIs:
729 * \param Q The destination MPI for the quotient.
730 * This may be \c NULL if the value of the
731 * quotient is not needed.
732 * \param R The destination MPI for the remainder value.
733 * This may be \c NULL if the value of the
734 * remainder is not needed.
735 * \param A The dividend. This must point to an initialized MPi.
736 * \param B The divisor. This must point to an initialized MPI.
738 * \return \c 0 if successful.
739 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
740 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero.
741 * \return Another negative error code on different kinds of failure.
743 int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
744 const mbedtls_mpi *B );
747 * \brief Perform a division with remainder of an MPI by an integer:
750 * \param Q The destination MPI for the quotient.
751 * This may be \c NULL if the value of the
752 * quotient is not needed.
753 * \param R The destination MPI for the remainder value.
754 * This may be \c NULL if the value of the
755 * remainder is not needed.
756 * \param A The dividend. This must point to an initialized MPi.
757 * \param b The divisor.
759 * \return \c 0 if successful.
760 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
761 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero.
762 * \return Another negative error code on different kinds of failure.
764 int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
765 mbedtls_mpi_sint b );
768 * \brief Perform a modular reduction. R = A mod B
770 * \param R The destination MPI for the residue value.
771 * This must point to an initialized MPI.
772 * \param A The MPI to compute the residue of.
773 * This must point to an initialized MPI.
774 * \param B The base of the modular reduction.
775 * This must point to an initialized MPI.
777 * \return \c 0 if successful.
778 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
779 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero.
780 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is negative.
781 * \return Another negative error code on different kinds of failure.
784 int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A,
785 const mbedtls_mpi *B );
788 * \brief Perform a modular reduction with respect to an integer.
791 * \param r The address at which to store the residue.
792 * This must not be \c NULL.
793 * \param A The MPI to compute the residue of.
794 * This must point to an initialized MPi.
795 * \param b The integer base of the modular reduction.
797 * \return \c 0 if successful.
798 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
799 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero.
800 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p b is negative.
801 * \return Another negative error code on different kinds of failure.
803 int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A,
804 mbedtls_mpi_sint b );
807 * \brief Perform a sliding-window exponentiation: X = A^E mod N
809 * \param X The destination MPI. This must point to an initialized MPI.
810 * \param A The base of the exponentiation.
811 * This must point to an initialized MPI.
812 * \param E The exponent MPI. This must point to an initialized MPI.
813 * \param N The base for the modular reduction. This must point to an
815 * \param _RR A helper MPI depending solely on \p N which can be used to
816 * speed-up multiple modular exponentiations for the same value
817 * of \p N. This may be \c NULL. If it is not \c NULL, it must
818 * point to an initialized MPI. If it hasn't been used after
819 * the call to mbedtls_mpi_init(), this function will compute
820 * the helper value and store it in \p _RR for reuse on
821 * subsequent calls to this function. Otherwise, the function
822 * will assume that \p _RR holds the helper value set by a
823 * previous call to mbedtls_mpi_exp_mod(), and reuse it.
825 * \return \c 0 if successful.
826 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
827 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \c N is negative or
828 * even, or if \c E is negative.
829 * \return Another negative error code on different kinds of failures.
832 int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
833 const mbedtls_mpi *E, const mbedtls_mpi *N,
837 * \brief Fill an MPI with a number of random bytes.
839 * \param X The destination MPI. This must point to an initialized MPI.
840 * \param size The number of random bytes to generate.
841 * \param f_rng The RNG function to use. This must not be \c NULL.
842 * \param p_rng The RNG parameter to be passed to \p f_rng. This may be
843 * \c NULL if \p f_rng doesn't need a context argument.
845 * \return \c 0 if successful.
846 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
847 * \return Another negative error code on failure.
849 * \note The bytes obtained from the RNG are interpreted
850 * as a big-endian representation of an MPI; this can
851 * be relevant in applications like deterministic ECDSA.
853 int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
854 int (*f_rng)(void *, unsigned char *, size_t),
858 * \brief Compute the greatest common divisor: G = gcd(A, B)
860 * \param G The destination MPI. This must point to an initialized MPI.
861 * \param A The first operand. This must point to an initialized MPI.
862 * \param B The second operand. This must point to an initialized MPI.
864 * \return \c 0 if successful.
865 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
866 * \return Another negative error code on different kinds of failure.
868 int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A,
869 const mbedtls_mpi *B );
872 * \brief Compute the modular inverse: X = A^-1 mod N
874 * \param X The destination MPI. This must point to an initialized MPI.
875 * \param A The MPI to calculate the modular inverse of. This must point
876 * to an initialized MPI.
877 * \param N The base of the modular inversion. This must point to an
880 * \return \c 0 if successful.
881 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
882 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p N is less than
884 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p has no modular inverse
885 * with respect to \p N.
887 int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
888 const mbedtls_mpi *N );
890 #if !defined(MBEDTLS_DEPRECATED_REMOVED)
891 #if defined(MBEDTLS_DEPRECATED_WARNING)
892 #define MBEDTLS_DEPRECATED __attribute__((deprecated))
894 #define MBEDTLS_DEPRECATED
897 * \brief Perform a Miller-Rabin primality test with error
898 * probability of 2<sup>-80</sup>.
900 * \deprecated Superseded by mbedtls_mpi_is_prime_ext() which allows
901 * specifying the number of Miller-Rabin rounds.
903 * \param X The MPI to check for primality.
904 * This must point to an initialized MPI.
905 * \param f_rng The RNG function to use. This must not be \c NULL.
906 * \param p_rng The RNG parameter to be passed to \p f_rng.
907 * This may be \c NULL if \p f_rng doesn't use a
910 * \return \c 0 if successful, i.e. \p X is probably prime.
911 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
912 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime.
913 * \return Another negative error code on other kinds of failure.
915 MBEDTLS_DEPRECATED int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
916 int (*f_rng)(void *, unsigned char *, size_t),
918 #undef MBEDTLS_DEPRECATED
919 #endif /* !MBEDTLS_DEPRECATED_REMOVED */
922 * \brief Miller-Rabin primality test.
924 * \warning If \p X is potentially generated by an adversary, for example
925 * when validating cryptographic parameters that you didn't
926 * generate yourself and that are supposed to be prime, then
927 * \p rounds should be at least the half of the security
928 * strength of the cryptographic algorithm. On the other hand,
929 * if \p X is chosen uniformly or non-adversially (as is the
930 * case when mbedtls_mpi_gen_prime calls this function), then
931 * \p rounds can be much lower.
933 * \param X The MPI to check for primality.
934 * This must point to an initialized MPI.
935 * \param rounds The number of bases to perform the Miller-Rabin primality
936 * test for. The probability of returning 0 on a composite is
937 * at most 2<sup>-2*\p rounds</sup>.
938 * \param f_rng The RNG function to use. This must not be \c NULL.
939 * \param p_rng The RNG parameter to be passed to \p f_rng.
940 * This may be \c NULL if \p f_rng doesn't use
941 * a context parameter.
943 * \return \c 0 if successful, i.e. \p X is probably prime.
944 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
945 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime.
946 * \return Another negative error code on other kinds of failure.
948 int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds,
949 int (*f_rng)(void *, unsigned char *, size_t),
952 * \brief Flags for mbedtls_mpi_gen_prime()
954 * Each of these flags is a constraint on the result X returned by
955 * mbedtls_mpi_gen_prime().
958 MBEDTLS_MPI_GEN_PRIME_FLAG_DH = 0x0001, /**< (X-1)/2 is prime too */
959 MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR = 0x0002, /**< lower error rate from 2<sup>-80</sup> to 2<sup>-128</sup> */
960 } mbedtls_mpi_gen_prime_flag_t;
963 * \brief Generate a prime number.
965 * \param X The destination MPI to store the generated prime in.
966 * This must point to an initialized MPi.
967 * \param nbits The required size of the destination MPI in bits.
968 * This must be between \c 3 and #MBEDTLS_MPI_MAX_BITS.
969 * \param flags A mask of flags of type #mbedtls_mpi_gen_prime_flag_t.
970 * \param f_rng The RNG function to use. This must not be \c NULL.
971 * \param p_rng The RNG parameter to be passed to \p f_rng.
972 * This may be \c NULL if \p f_rng doesn't use
973 * a context parameter.
975 * \return \c 0 if successful, in which case \p X holds a
976 * probably prime number.
977 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
978 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `nbits` is not between
979 * \c 3 and #MBEDTLS_MPI_MAX_BITS.
981 int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags,
982 int (*f_rng)(void *, unsigned char *, size_t),
985 #if defined(MBEDTLS_SELF_TEST)
988 * \brief Checkup routine
990 * \return 0 if successful, or 1 if the test failed
992 int mbedtls_mpi_self_test( int verbose );
994 #endif /* MBEDTLS_SELF_TEST */
1000 #endif /* bignum.h */