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Paul Bakker5121ce52009-01-03 21:22:43 +00001/**
2 * \file bignum.h
Paul Bakkere0ccd0a2009-01-04 16:27:10 +00003 *
Darryl Greena40a1012018-01-05 15:33:17 +00004 * \brief Multi-precision integer library
5 */
6/*
Bence Szépkúti1e148272020-08-07 13:07:28 +02007 * Copyright The Mbed TLS Contributors
Manuel Pégourié-Gonnard37ff1402015-09-04 14:21:07 +02008 * 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.
Paul Bakker5121ce52009-01-03 21:22:43 +000021 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020022#ifndef MBEDTLS_BIGNUM_H
23#define MBEDTLS_BIGNUM_H
Mateusz Starzyk846f0212021-05-19 19:44:07 +020024#include "mbedtls/private_access.h"
Paul Bakker5121ce52009-01-03 21:22:43 +000025
Bence Szépkútic662b362021-05-27 11:25:03 +020026#include "mbedtls/build_info.h"
Paul Bakkercf0360a2012-01-20 10:08:14 +000027
Rich Evans00ab4702015-02-06 13:43:58 +000028#include <stddef.h>
Manuel Pégourié-Gonnardab229102015-04-15 11:53:16 +020029#include <stdint.h>
Rich Evans00ab4702015-02-06 13:43:58 +000030
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020031#if defined(MBEDTLS_FS_IO)
Manuel Pégourié-Gonnarde94e6e52015-01-19 15:01:53 +000032#include <stdio.h>
33#endif
34
Gilles Peskined2971572021-07-26 18:48:10 +020035/** An error occurred while reading from or writing to a file. */
36#define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002
37/** Bad input parameters to function. */
38#define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004
39/** There is an invalid character in the digit string. */
40#define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006
41/** The buffer is too small to write to. */
42#define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008
43/** The input arguments are negative or result in illegal output. */
44#define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A
45/** The input argument for division is zero, which is not allowed. */
46#define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C
47/** The input arguments are not acceptable. */
48#define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E
49/** Memory allocation failed. */
50#define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010
Paul Bakker5121ce52009-01-03 21:22:43 +000051
Hanno Becker1eeca412018-10-15 12:01:35 +010052#define MBEDTLS_MPI_CHK(f) \
53 do \
54 { \
Gilles Peskine449bd832023-01-11 14:50:10 +010055 if ((ret = (f)) != 0) \
56 goto cleanup; \
57 } while (0)
Paul Bakker5121ce52009-01-03 21:22:43 +000058
59/*
Paul Bakkerf9688572011-05-05 10:00:45 +000060 * Maximum size MPIs are allowed to grow to in number of limbs.
61 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020062#define MBEDTLS_MPI_MAX_LIMBS 10000
Paul Bakkerf9688572011-05-05 10:00:45 +000063
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020064#if !defined(MBEDTLS_MPI_WINDOW_SIZE)
Paul Bakkerf9688572011-05-05 10:00:45 +000065/*
Andrzej Kurek86f30ff2023-02-24 07:44:57 -050066 * Maximum window size used for modular exponentiation. Default: 2
Paul Bakkerb6d5f082011-11-25 11:52:11 +000067 * Minimum value: 1. Maximum value: 6.
68 *
Daniel Otte60861512020-09-07 13:07:14 +020069 * Result is an array of ( 2 ** MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
Paul Bakkerb6d5f082011-11-25 11:52:11 +000070 * for the sliding window calculation. (So 64 by default)
71 *
72 * Reduction in size, reduces speed.
73 */
Andrzej Kurek86f30ff2023-02-24 07:44:57 -050074#define MBEDTLS_MPI_WINDOW_SIZE 2 /**< Maximum window size used. */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020075#endif /* !MBEDTLS_MPI_WINDOW_SIZE */
Paul Bakkerb6d5f082011-11-25 11:52:11 +000076
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020077#if !defined(MBEDTLS_MPI_MAX_SIZE)
Paul Bakkerb6d5f082011-11-25 11:52:11 +000078/*
Paul Bakkerfe3256e2011-11-25 12:11:43 +000079 * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
Paul Bakkerf626e1d2013-01-21 12:10:00 +010080 * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
Paul Bakkerfe3256e2011-11-25 12:11:43 +000081 *
Hanno Beckerefeef6c2018-01-05 08:07:47 +000082 * Note: Calculations can temporarily result in larger MPIs. So the number
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020083 * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
Paul Bakkerfe3256e2011-11-25 12:11:43 +000084 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020085#define MBEDTLS_MPI_MAX_SIZE 1024 /**< Maximum number of bytes for usable MPIs. */
86#endif /* !MBEDTLS_MPI_MAX_SIZE */
Paul Bakker9bcf16c2013-06-24 19:31:17 +020087
Gilles Peskine449bd832023-01-11 14:50:10 +010088#define MBEDTLS_MPI_MAX_BITS (8 * MBEDTLS_MPI_MAX_SIZE) /**< Maximum number of bits for usable MPIs. */
Paul Bakkerfe3256e2011-11-25 12:11:43 +000089
90/*
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020091 * When reading from files with mbedtls_mpi_read_file() and writing to files with
92 * mbedtls_mpi_write_file() the buffer should have space
Paul Bakkercb37aa52011-11-30 16:00:20 +000093 * for a (short) label, the MPI (in the provided radix), the newline
94 * characters and the '\0'.
95 *
96 * By default we assume at least a 10 char label, a minimum radix of 10
97 * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
Paul Bakkerf9183102012-09-27 20:42:35 +000098 * Autosized at compile time for at least a 10 char label, a minimum radix
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020099 * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
Paul Bakkerf9183102012-09-27 20:42:35 +0000100 *
101 * This used to be statically sized to 1250 for a maximum of 4096 bit
102 * numbers (1234 decimal chars).
103 *
104 * Calculate using the formula:
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200105 * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
Paul Bakkerf9183102012-09-27 20:42:35 +0000106 * LabelSize + 6
Paul Bakkercb37aa52011-11-30 16:00:20 +0000107 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100108#define MBEDTLS_MPI_MAX_BITS_SCALE100 (100 * MBEDTLS_MPI_MAX_BITS)
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200109#define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332
Gilles Peskine449bd832023-01-11 14:50:10 +0100110#define MBEDTLS_MPI_RW_BUFFER_SIZE (((MBEDTLS_MPI_MAX_BITS_SCALE100 + \
111 MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / \
112 MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6)
Paul Bakkercb37aa52011-11-30 16:00:20 +0000113
114/*
Manuel Pégourié-Gonnard7b538892015-04-09 17:00:17 +0200115 * Define the base integer type, architecture-wise.
116 *
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100117 * 32 or 64-bit integer types can be forced regardless of the underlying
118 * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
119 * respectively and undefining MBEDTLS_HAVE_ASM.
120 *
Andres Amaya Garcia93db11a2017-07-20 12:11:19 +0100121 * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100122 * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
Paul Bakker5121ce52009-01-03 21:22:43 +0000123 */
Andres Amaya Garciaaa27dfe2017-05-04 11:05:55 +0100124#if !defined(MBEDTLS_HAVE_INT32)
125 #if defined(_MSC_VER) && defined(_M_AMD64)
Gilles Peskine449bd832023-01-11 14:50:10 +0100126/* Always choose 64-bit when using MSC */
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100127 #if !defined(MBEDTLS_HAVE_INT64)
128 #define MBEDTLS_HAVE_INT64
129 #endif /* !MBEDTLS_HAVE_INT64 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100130typedef int64_t mbedtls_mpi_sint;
131typedef uint64_t mbedtls_mpi_uint;
Agathiyan Bragadeesheed55c62023-07-19 11:08:02 +0100132#define MBEDTLS_MPI_UINT_MAX UINT64_MAX
Andres Amaya Garciaaa27dfe2017-05-04 11:05:55 +0100133 #elif defined(__GNUC__) && ( \
Gilles Peskine449bd832023-01-11 14:50:10 +0100134 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__))
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100140 #if !defined(MBEDTLS_HAVE_INT64)
141 #define MBEDTLS_HAVE_INT64
142 #endif /* MBEDTLS_HAVE_INT64 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100143typedef int64_t mbedtls_mpi_sint;
144typedef uint64_t mbedtls_mpi_uint;
Agathiyan Bragadeesheed55c62023-07-19 11:08:02 +0100145#define MBEDTLS_MPI_UINT_MAX UINT64_MAX
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100146 #if !defined(MBEDTLS_NO_UDBL_DIVISION)
Gilles Peskine449bd832023-01-11 14:50:10 +0100147/* mbedtls_t_udbl defined as 128-bit unsigned int */
148typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100149 #define MBEDTLS_HAVE_UDBL
150 #endif /* !MBEDTLS_NO_UDBL_DIVISION */
Ko-05cff952018-08-20 12:59:57 +0100151 #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
Gilles Peskine449bd832023-01-11 14:50:10 +0100152/*
153 * __ARMCC_VERSION is defined for both armcc and armclang and
154 * __aarch64__ is only defined by armclang when compiling 64-bit code
155 */
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100156 #if !defined(MBEDTLS_HAVE_INT64)
157 #define MBEDTLS_HAVE_INT64
158 #endif /* !MBEDTLS_HAVE_INT64 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100159typedef int64_t mbedtls_mpi_sint;
160typedef uint64_t mbedtls_mpi_uint;
Agathiyan Bragadeesheed55c62023-07-19 11:08:02 +0100161#define MBEDTLS_MPI_UINT_MAX UINT64_MAX
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100162 #if !defined(MBEDTLS_NO_UDBL_DIVISION)
Gilles Peskine449bd832023-01-11 14:50:10 +0100163/* mbedtls_t_udbl defined as 128-bit unsigned int */
164typedef __uint128_t mbedtls_t_udbl;
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100165 #define MBEDTLS_HAVE_UDBL
166 #endif /* !MBEDTLS_NO_UDBL_DIVISION */
167 #elif defined(MBEDTLS_HAVE_INT64)
Gilles Peskine449bd832023-01-11 14:50:10 +0100168/* Force 64-bit integers with unknown compiler */
169typedef int64_t mbedtls_mpi_sint;
170typedef uint64_t mbedtls_mpi_uint;
Agathiyan Bragadeesheed55c62023-07-19 11:08:02 +0100171#define MBEDTLS_MPI_UINT_MAX UINT64_MAX
Andres Amaya Garciaaa27dfe2017-05-04 11:05:55 +0100172 #endif
173#endif /* !MBEDTLS_HAVE_INT32 */
174
175#if !defined(MBEDTLS_HAVE_INT64)
Gilles Peskine449bd832023-01-11 14:50:10 +0100176/* Default to 32-bit compilation */
Andres Amaya Garciaaa27dfe2017-05-04 11:05:55 +0100177 #if !defined(MBEDTLS_HAVE_INT32)
178 #define MBEDTLS_HAVE_INT32
179 #endif /* !MBEDTLS_HAVE_INT32 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100180typedef int32_t mbedtls_mpi_sint;
181typedef uint32_t mbedtls_mpi_uint;
Agathiyan Bragadeesheed55c62023-07-19 11:08:02 +0100182#define MBEDTLS_MPI_UINT_MAX UINT32_MAX
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100183 #if !defined(MBEDTLS_NO_UDBL_DIVISION)
Gilles Peskine449bd832023-01-11 14:50:10 +0100184typedef uint64_t mbedtls_t_udbl;
Andres Amaya Garciadf1486a2017-07-20 17:33:09 +0100185 #define MBEDTLS_HAVE_UDBL
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100186 #endif /* !MBEDTLS_NO_UDBL_DIVISION */
Andres Amaya Garciaaa27dfe2017-05-04 11:05:55 +0100187#endif /* !MBEDTLS_HAVE_INT64 */
Paul Bakker5121ce52009-01-03 21:22:43 +0000188
Dave Rodgman85061b92023-09-06 08:41:05 +0100189/*
190 * Sanity check that exactly one of MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64 is defined,
191 * so that code elsewhere doesn't have to check.
192 */
193#if (!(defined(MBEDTLS_HAVE_INT32) || defined(MBEDTLS_HAVE_INT64))) || \
194 (defined(MBEDTLS_HAVE_INT32) && defined(MBEDTLS_HAVE_INT64))
195#error "Only 32-bit or 64-bit limbs are supported in bignum"
196#endif
197
Gilles Peskine6110a162022-11-15 21:22:27 +0100198/** \typedef mbedtls_mpi_uint
199 * \brief The type of machine digits in a bignum, called _limbs_.
200 *
201 * This is always an unsigned integer type with no padding bits. The size
202 * is platform-dependent.
203 */
204
205/** \typedef mbedtls_mpi_sint
206 * \brief The signed type corresponding to #mbedtls_mpi_uint.
207 *
208 * This is always an signed integer type with no padding bits. The size
209 * is platform-dependent.
210 */
211
Paul Bakker407a0da2013-06-27 14:29:21 +0200212#ifdef __cplusplus
213extern "C" {
214#endif
215
Paul Bakker5121ce52009-01-03 21:22:43 +0000216/**
217 * \brief MPI structure
218 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100219typedef struct mbedtls_mpi {
Dave Rodgman98e632f2023-07-11 15:59:14 +0100220 /** Pointer to limbs.
221 *
222 * This may be \c NULL if \c n is 0.
223 */
224 mbedtls_mpi_uint *MBEDTLS_PRIVATE(p);
225
Gilles Peskine12889572022-11-09 21:55:33 +0100226 /** Sign: -1 if the mpi is negative, 1 otherwise.
227 *
228 * The number 0 must be represented with `s = +1`. Although many library
229 * functions treat all-limbs-zero as equivalent to a valid representation
230 * of 0 regardless of the sign bit, there are exceptions, so bignum
231 * functions and external callers must always set \c s to +1 for the
232 * number zero.
233 *
234 * Note that this implies that calloc() or `... = {0}` does not create
235 * a valid MPI representation. You must call mbedtls_mpi_init().
236 */
Gilles Peskine053022f2023-06-29 19:26:48 +0200237 signed short MBEDTLS_PRIVATE(s);
Gilles Peskine12889572022-11-09 21:55:33 +0100238
239 /** Total number of limbs in \c p. */
Gilles Peskine053022f2023-06-29 19:26:48 +0200240 unsigned short MBEDTLS_PRIVATE(n);
Gilles Peskine24a305e2023-07-18 13:41:22 +0200241 /* Make sure that MBEDTLS_MPI_MAX_LIMBS fits in n.
242 * Use the same limit value on all platforms so that we don't have to
243 * think about different behavior on the rare platforms where
244 * unsigned short can store values larger than the minimum required by
245 * the C language, which is 65535.
246 */
Gilles Peskine053022f2023-06-29 19:26:48 +0200247#if MBEDTLS_MPI_MAX_LIMBS > 65535
248#error "MBEDTLS_MPI_MAX_LIMBS > 65535 is not supported"
249#endif
Paul Bakker5121ce52009-01-03 21:22:43 +0000250}
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200251mbedtls_mpi;
Paul Bakker5121ce52009-01-03 21:22:43 +0000252
Paul Bakker5121ce52009-01-03 21:22:43 +0000253/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000254 * \brief Initialize an MPI context.
255 *
256 * This makes the MPI ready to be set or freed,
Manuel Pégourié-Gonnardda61ed32015-04-30 10:28:51 +0200257 * but does not define a value for the MPI.
Paul Bakker6c591fa2011-05-05 11:49:20 +0000258 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000259 * \param X The MPI context to initialize. This must not be \c NULL.
Paul Bakker5121ce52009-01-03 21:22:43 +0000260 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100261void mbedtls_mpi_init(mbedtls_mpi *X);
Paul Bakker5121ce52009-01-03 21:22:43 +0000262
263/**
Hanno Becker8ce11a32018-12-19 16:18:52 +0000264 * \brief This function frees the components of an MPI context.
Paul Bakker6c591fa2011-05-05 11:49:20 +0000265 *
Hanno Beckere1185042018-12-13 14:31:46 +0000266 * \param X The MPI context to be cleared. This may be \c NULL,
Hanno Becker8282c2f2018-12-12 13:36:46 +0000267 * in which case this function is a no-op. If it is
268 * not \c NULL, it must point to an initialized MPI.
Paul Bakker5121ce52009-01-03 21:22:43 +0000269 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100270void mbedtls_mpi_free(mbedtls_mpi *X);
Paul Bakker5121ce52009-01-03 21:22:43 +0000271
272/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000273 * \brief Enlarge an MPI to the specified number of limbs.
Paul Bakker5121ce52009-01-03 21:22:43 +0000274 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000275 * \note This function does nothing if the MPI is
276 * already large enough.
Gilles Peskine70ad8392018-03-21 16:28:41 +0100277 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000278 * \param X The MPI to grow. It must be initialized.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000279 * \param nblimbs The target number of limbs.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000280 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000281 * \return \c 0 if successful.
282 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
283 * \return Another negative error code on other kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000284 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100285int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs);
Paul Bakker5121ce52009-01-03 21:22:43 +0000286
287/**
Hanno Beckere1185042018-12-13 14:31:46 +0000288 * \brief This function resizes an MPI downwards, keeping at least the
289 * specified number of limbs.
Manuel Pégourié-Gonnard58681632013-11-21 10:39:37 +0100290 *
Gilles Peskine70ad8392018-03-21 16:28:41 +0100291 * If \c X is smaller than \c nblimbs, it is resized up
292 * instead.
293 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000294 * \param X The MPI to shrink. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000295 * \param nblimbs The minimum number of limbs to keep.
Manuel Pégourié-Gonnard58681632013-11-21 10:39:37 +0100296 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000297 * \return \c 0 if successful.
298 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
Gilles Peskine70ad8392018-03-21 16:28:41 +0100299 * (this can only happen when resizing up).
Hanno Beckerc23483e2018-12-10 17:21:19 +0000300 * \return Another negative error code on other kinds of failure.
Manuel Pégourié-Gonnard58681632013-11-21 10:39:37 +0100301 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100302int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs);
Manuel Pégourié-Gonnard58681632013-11-21 10:39:37 +0100303
304/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000305 * \brief Make a copy of an MPI.
Paul Bakker5121ce52009-01-03 21:22:43 +0000306 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000307 * \param X The destination MPI. This must point to an initialized MPI.
308 * \param Y The source MPI. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000309 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000310 * \note The limb-buffer in the destination MPI is enlarged
311 * if necessary to hold the value in the source MPI.
312 *
313 * \return \c 0 if successful.
314 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
315 * \return Another negative error code on other kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000316 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100317int mbedtls_mpi_copy(mbedtls_mpi *X, const mbedtls_mpi *Y);
Paul Bakker5121ce52009-01-03 21:22:43 +0000318
319/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000320 * \brief Swap the contents of two MPIs.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000321 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000322 * \param X The first MPI. It must be initialized.
323 * \param Y The second MPI. It must be initialized.
Paul Bakker5121ce52009-01-03 21:22:43 +0000324 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100325void mbedtls_mpi_swap(mbedtls_mpi *X, mbedtls_mpi *Y);
Paul Bakker5121ce52009-01-03 21:22:43 +0000326
327/**
Hanno Beckere1185042018-12-13 14:31:46 +0000328 * \brief Perform a safe conditional copy of MPI which doesn't
329 * reveal whether the condition was true or not.
Manuel Pégourié-Gonnard71c2c212013-11-21 16:56:39 +0100330 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000331 * \param X The MPI to conditionally assign to. This must point
332 * to an initialized MPI.
333 * \param Y The MPI to be assigned from. This must point to an
334 * initialized MPI.
Hanno Beckere1185042018-12-13 14:31:46 +0000335 * \param assign The condition deciding whether to perform the
Tom Cosgrove583816c2022-08-18 14:09:18 +0100336 * assignment or not. Must be either 0 or 1:
Hanno Beckerc23483e2018-12-10 17:21:19 +0000337 * * \c 1: Perform the assignment `X = Y`.
338 * * \c 0: Keep the original value of \p X.
Manuel Pégourié-Gonnard71c2c212013-11-21 16:56:39 +0100339 *
340 * \note This function is equivalent to
Hanno Beckerc23483e2018-12-10 17:21:19 +0000341 * `if( assign ) mbedtls_mpi_copy( X, Y );`
Manuel Pégourié-Gonnard71c2c212013-11-21 16:56:39 +0100342 * except that it avoids leaking any information about whether
343 * the assignment was done or not (the above code may leak
Manuel Pégourié-Gonnardd7283502013-11-21 20:00:38 +0100344 * information through branch prediction and/or memory access
345 * patterns analysis).
Hanno Beckerc23483e2018-12-10 17:21:19 +0000346 *
Tom Cosgrove583816c2022-08-18 14:09:18 +0100347 * \warning If \p assign is neither 0 nor 1, the result of this function
348 * is indeterminate, and the resulting value in \p X might be
349 * neither its original value nor the value in \p Y.
350 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000351 * \return \c 0 if successful.
352 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
353 * \return Another negative error code on other kinds of failure.
Manuel Pégourié-Gonnard71c2c212013-11-21 16:56:39 +0100354 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100355int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign);
Manuel Pégourié-Gonnard71c2c212013-11-21 16:56:39 +0100356
357/**
Hanno Beckere1185042018-12-13 14:31:46 +0000358 * \brief Perform a safe conditional swap which doesn't
359 * reveal whether the condition was true or not.
Manuel Pégourié-Gonnarda60fe892013-12-04 21:41:50 +0100360 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000361 * \param X The first MPI. This must be initialized.
362 * \param Y The second MPI. This must be initialized.
Tom Cosgrove583816c2022-08-18 14:09:18 +0100363 * \param swap The condition deciding whether to perform
364 * the swap or not. Must be either 0 or 1:
Hanno Beckerc23483e2018-12-10 17:21:19 +0000365 * * \c 1: Swap the values of \p X and \p Y.
366 * * \c 0: Keep the original values of \p X and \p Y.
Manuel Pégourié-Gonnarda60fe892013-12-04 21:41:50 +0100367 *
368 * \note This function is equivalent to
Tom Cosgrove583816c2022-08-18 14:09:18 +0100369 * if( swap ) mbedtls_mpi_swap( X, Y );
Manuel Pégourié-Gonnarda60fe892013-12-04 21:41:50 +0100370 * except that it avoids leaking any information about whether
Tom Cosgrove583816c2022-08-18 14:09:18 +0100371 * the swap was done or not (the above code may leak
Manuel Pégourié-Gonnarda60fe892013-12-04 21:41:50 +0100372 * information through branch prediction and/or memory access
373 * patterns analysis).
Hanno Beckerc23483e2018-12-10 17:21:19 +0000374 *
Tom Cosgrove583816c2022-08-18 14:09:18 +0100375 * \warning If \p swap is neither 0 nor 1, the result of this function
376 * is indeterminate, and both \p X and \p Y might end up with
377 * values different to either of the original ones.
378 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000379 * \return \c 0 if successful.
380 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
381 * \return Another negative error code on other kinds of failure.
382 *
Manuel Pégourié-Gonnarda60fe892013-12-04 21:41:50 +0100383 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100384int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap);
Manuel Pégourié-Gonnarda60fe892013-12-04 21:41:50 +0100385
386/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000387 * \brief Store integer value in MPI.
Paul Bakker5121ce52009-01-03 21:22:43 +0000388 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000389 * \param X The MPI to set. This must be initialized.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000390 * \param z The value to use.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000391 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000392 * \return \c 0 if successful.
393 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
394 * \return Another negative error code on other kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000395 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100396int mbedtls_mpi_lset(mbedtls_mpi *X, mbedtls_mpi_sint z);
Paul Bakker5121ce52009-01-03 21:22:43 +0000397
Paul Bakker9a736322012-11-14 12:39:52 +0000398/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000399 * \brief Get a specific bit from an MPI.
Paul Bakker2f5947e2011-05-18 15:47:11 +0000400 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000401 * \param X The MPI to query. This must be initialized.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000402 * \param pos Zero-based index of the bit to query.
Paul Bakker2f5947e2011-05-18 15:47:11 +0000403 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000404 * \return \c 0 or \c 1 on success, depending on whether bit \c pos
Hanno Becker8282c2f2018-12-12 13:36:46 +0000405 * of \c X is unset or set.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000406 * \return A negative error code on failure.
Paul Bakker2f5947e2011-05-18 15:47:11 +0000407 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100408int mbedtls_mpi_get_bit(const mbedtls_mpi *X, size_t pos);
Paul Bakker2f5947e2011-05-18 15:47:11 +0000409
Paul Bakker9a736322012-11-14 12:39:52 +0000410/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000411 * \brief Modify a specific bit in an MPI.
Paul Bakker2f5947e2011-05-18 15:47:11 +0000412 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000413 * \note This function will grow the target MPI if necessary to set a
414 * bit to \c 1 in a not yet existing limb. It will not grow if
415 * the bit should be set to \c 0.
Paul Bakker2f5947e2011-05-18 15:47:11 +0000416 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000417 * \param X The MPI to modify. This must be initialized.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000418 * \param pos Zero-based index of the bit to modify.
419 * \param val The desired value of bit \c pos: \c 0 or \c 1.
Paul Bakker2f5947e2011-05-18 15:47:11 +0000420 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000421 * \return \c 0 if successful.
422 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
423 * \return Another negative error code on other kinds of failure.
Paul Bakker2f5947e2011-05-18 15:47:11 +0000424 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100425int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val);
Paul Bakker2f5947e2011-05-18 15:47:11 +0000426
Paul Bakker5121ce52009-01-03 21:22:43 +0000427/**
Hanno Beckere1185042018-12-13 14:31:46 +0000428 * \brief Return the number of bits of value \c 0 before the
429 * least significant bit of value \c 1.
Paul Bakker6b906e52012-05-08 12:01:43 +0000430 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000431 * \note This is the same as the zero-based index of
Hanno Beckere1185042018-12-13 14:31:46 +0000432 * the least significant bit of value \c 1.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000433 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000434 * \param X The MPI to query.
435 *
Hanno Beckere1185042018-12-13 14:31:46 +0000436 * \return The number of bits of value \c 0 before the least significant
437 * bit of value \c 1 in \p X.
Paul Bakker5121ce52009-01-03 21:22:43 +0000438 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100439size_t mbedtls_mpi_lsb(const mbedtls_mpi *X);
Paul Bakker5121ce52009-01-03 21:22:43 +0000440
441/**
Paul Bakker6b906e52012-05-08 12:01:43 +0000442 * \brief Return the number of bits up to and including the most
Hanno Beckere1185042018-12-13 14:31:46 +0000443 * significant bit of value \c 1.
Paul Bakker6b906e52012-05-08 12:01:43 +0000444 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000445 * * \note This is same as the one-based index of the most
Hanno Beckere1185042018-12-13 14:31:46 +0000446 * significant bit of value \c 1.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000447 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000448 * \param X The MPI to query. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000449 *
450 * \return The number of bits up to and including the most
Hanno Beckere1185042018-12-13 14:31:46 +0000451 * significant bit of value \c 1.
Paul Bakker5121ce52009-01-03 21:22:43 +0000452 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100453size_t mbedtls_mpi_bitlen(const mbedtls_mpi *X);
Paul Bakker5121ce52009-01-03 21:22:43 +0000454
455/**
Hanno Beckere1185042018-12-13 14:31:46 +0000456 * \brief Return the total size of an MPI value in bytes.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000457 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000458 * \param X The MPI to use. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000459 *
460 * \note The value returned by this function may be less than
461 * the number of bytes used to store \p X internally.
Hanno Beckere1185042018-12-13 14:31:46 +0000462 * This happens if and only if there are trailing bytes
463 * of value zero.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000464 *
465 * \return The least number of bytes capable of storing
466 * the absolute value of \p X.
Paul Bakker5121ce52009-01-03 21:22:43 +0000467 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100468size_t mbedtls_mpi_size(const mbedtls_mpi *X);
Paul Bakker5121ce52009-01-03 21:22:43 +0000469
470/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000471 * \brief Import an MPI from an ASCII string.
Paul Bakker5121ce52009-01-03 21:22:43 +0000472 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000473 * \param X The destination MPI. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000474 * \param radix The numeric base of the input string.
475 * \param s Null-terminated string buffer.
Paul Bakker5121ce52009-01-03 21:22:43 +0000476 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000477 * \return \c 0 if successful.
478 * \return A negative error code on failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000479 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100480int mbedtls_mpi_read_string(mbedtls_mpi *X, int radix, const char *s);
Paul Bakker5121ce52009-01-03 21:22:43 +0000481
482/**
Hanno Beckere1185042018-12-13 14:31:46 +0000483 * \brief Export an MPI to an ASCII string.
Paul Bakker5121ce52009-01-03 21:22:43 +0000484 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000485 * \param X The source MPI. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000486 * \param radix The numeric base of the output string.
Hanno Beckere1185042018-12-13 14:31:46 +0000487 * \param buf The buffer to write the string to. This must be writable
Hanno Beckerd7310122018-12-18 18:11:42 +0000488 * buffer of length \p buflen Bytes.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000489 * \param buflen The available size in Bytes of \p buf.
Hanno Beckere1185042018-12-13 14:31:46 +0000490 * \param olen The address at which to store the length of the string
491 * written, including the final \c NULL byte. This must
492 * not be \c NULL.
Paul Bakker5121ce52009-01-03 21:22:43 +0000493 *
Hanno Beckere1185042018-12-13 14:31:46 +0000494 * \note You can call this function with `buflen == 0` to obtain the
Hanno Beckerc23483e2018-12-10 17:21:19 +0000495 * minimum required buffer size in `*olen`.
Paul Bakker5121ce52009-01-03 21:22:43 +0000496 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000497 * \return \c 0 if successful.
498 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer \p buf
499 * is too small to hold the value of \p X in the desired base.
500 * In this case, `*olen` is nonetheless updated to contain the
501 * size of \p buf required for a successful call.
502 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000503 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100504int mbedtls_mpi_write_string(const mbedtls_mpi *X, int radix,
505 char *buf, size_t buflen, size_t *olen);
Paul Bakker5121ce52009-01-03 21:22:43 +0000506
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200507#if defined(MBEDTLS_FS_IO)
Paul Bakker5121ce52009-01-03 21:22:43 +0000508/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000509 * \brief Read an MPI from a line in an opened file.
Paul Bakker5121ce52009-01-03 21:22:43 +0000510 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000511 * \param X The destination MPI. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000512 * \param radix The numeric base of the string representation used
513 * in the source line.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000514 * \param fin The input file handle to use. This must not be \c NULL.
Hanno Beckerb2034b72017-04-26 11:46:46 +0100515 *
516 * \note On success, this function advances the file stream
517 * to the end of the current line or to EOF.
518 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000519 * The function returns \c 0 on an empty line.
Hanno Beckerb2034b72017-04-26 11:46:46 +0100520 *
521 * Leading whitespaces are ignored, as is a
Hanno Beckerc23483e2018-12-10 17:21:19 +0000522 * '0x' prefix for radix \c 16.
Hanno Beckerb2034b72017-04-26 11:46:46 +0100523 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000524 * \return \c 0 if successful.
525 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer
526 * is too small.
527 * \return Another negative error code on failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000528 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100529int mbedtls_mpi_read_file(mbedtls_mpi *X, int radix, FILE *fin);
Paul Bakker5121ce52009-01-03 21:22:43 +0000530
531/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000532 * \brief Export an MPI into an opened file.
Paul Bakker5121ce52009-01-03 21:22:43 +0000533 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000534 * \param p A string prefix to emit prior to the MPI data.
535 * For example, this might be a label, or "0x" when
Hanno Beckere1185042018-12-13 14:31:46 +0000536 * printing in base \c 16. This may be \c NULL if no prefix
Hanno Beckerc23483e2018-12-10 17:21:19 +0000537 * is needed.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000538 * \param X The source MPI. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000539 * \param radix The numeric base to be used in the emitted string.
Hanno Beckere1185042018-12-13 14:31:46 +0000540 * \param fout The output file handle. This may be \c NULL, in which case
541 * the output is written to \c stdout.
Paul Bakker5121ce52009-01-03 21:22:43 +0000542 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000543 * \return \c 0 if successful.
544 * \return A negative error code on failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000545 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100546int mbedtls_mpi_write_file(const char *p, const mbedtls_mpi *X,
547 int radix, FILE *fout);
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200548#endif /* MBEDTLS_FS_IO */
Paul Bakker5121ce52009-01-03 21:22:43 +0000549
550/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000551 * \brief Import an MPI from unsigned big endian binary data.
Paul Bakker5121ce52009-01-03 21:22:43 +0000552 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000553 * \param X The destination MPI. This must point to an initialized MPI.
Hanno Beckere1185042018-12-13 14:31:46 +0000554 * \param buf The input buffer. This must be a readable buffer of length
Hanno Beckerc23483e2018-12-10 17:21:19 +0000555 * \p buflen Bytes.
Andrzej Kurek69ed8c42022-02-17 10:06:44 -0500556 * \param buflen The length of the input buffer \p buf in Bytes.
Paul Bakker5121ce52009-01-03 21:22:43 +0000557 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000558 * \return \c 0 if successful.
559 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
560 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000561 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100562int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *buf,
563 size_t buflen);
Paul Bakker5121ce52009-01-03 21:22:43 +0000564
565/**
Janos Follatha778a942019-02-13 10:28:28 +0000566 * \brief Import X from unsigned binary data, little endian
567 *
568 * \param X The destination MPI. This must point to an initialized MPI.
569 * \param buf The input buffer. This must be a readable buffer of length
570 * \p buflen Bytes.
Andrzej Kurek69ed8c42022-02-17 10:06:44 -0500571 * \param buflen The length of the input buffer \p buf in Bytes.
Janos Follatha778a942019-02-13 10:28:28 +0000572 *
573 * \return \c 0 if successful.
574 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
575 * \return Another negative error code on different kinds of failure.
576 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100577int mbedtls_mpi_read_binary_le(mbedtls_mpi *X,
578 const unsigned char *buf, size_t buflen);
Janos Follatha778a942019-02-13 10:28:28 +0000579
580/**
581 * \brief Export X into unsigned binary data, big endian.
582 * Always fills the whole buffer, which will start with zeros
583 * if the number is smaller.
Paul Bakker5121ce52009-01-03 21:22:43 +0000584 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000585 * \param X The source MPI. This must point to an initialized MPI.
Hanno Beckere1185042018-12-13 14:31:46 +0000586 * \param buf The output buffer. This must be a writable buffer of length
Hanno Beckerc23483e2018-12-10 17:21:19 +0000587 * \p buflen Bytes.
588 * \param buflen The size of the output buffer \p buf in Bytes.
Paul Bakker5121ce52009-01-03 21:22:43 +0000589 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000590 * \return \c 0 if successful.
591 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
Hanno Beckere1185042018-12-13 14:31:46 +0000592 * large enough to hold the value of \p X.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000593 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000594 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100595int mbedtls_mpi_write_binary(const mbedtls_mpi *X, unsigned char *buf,
596 size_t buflen);
Paul Bakker5121ce52009-01-03 21:22:43 +0000597
598/**
Janos Follathe344d0f2019-02-19 16:17:40 +0000599 * \brief Export X into unsigned binary data, little endian.
600 * Always fills the whole buffer, which will end with zeros
601 * if the number is smaller.
602 *
603 * \param X The source MPI. This must point to an initialized MPI.
604 * \param buf The output buffer. This must be a writable buffer of length
605 * \p buflen Bytes.
606 * \param buflen The size of the output buffer \p buf in Bytes.
607 *
608 * \return \c 0 if successful.
609 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
610 * large enough to hold the value of \p X.
611 * \return Another negative error code on different kinds of failure.
612 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100613int mbedtls_mpi_write_binary_le(const mbedtls_mpi *X,
614 unsigned char *buf, size_t buflen);
Janos Follathe344d0f2019-02-19 16:17:40 +0000615
616/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000617 * \brief Perform a left-shift on an MPI: X <<= count
Paul Bakker5121ce52009-01-03 21:22:43 +0000618 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000619 * \param X The MPI to shift. This must point to an initialized MPI.
Minos Galanakis2056d092023-05-02 14:53:58 +0100620 * The MPI pointed by \p X may be resized to fit
621 * the resulting number.
Hanno Beckere1185042018-12-13 14:31:46 +0000622 * \param count The number of bits to shift by.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000623 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000624 * \return \c 0 if successful.
625 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
626 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000627 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100628int mbedtls_mpi_shift_l(mbedtls_mpi *X, size_t count);
Paul Bakker5121ce52009-01-03 21:22:43 +0000629
630/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000631 * \brief Perform a right-shift on an MPI: X >>= count
Paul Bakker5121ce52009-01-03 21:22:43 +0000632 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000633 * \param X The MPI to shift. This must point to an initialized MPI.
Hanno Beckere1185042018-12-13 14:31:46 +0000634 * \param count The number of bits to shift by.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000635 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000636 * \return \c 0 if successful.
637 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
638 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000639 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100640int mbedtls_mpi_shift_r(mbedtls_mpi *X, size_t count);
Paul Bakker5121ce52009-01-03 21:22:43 +0000641
642/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000643 * \brief Compare the absolute values of two MPIs.
Paul Bakker5121ce52009-01-03 21:22:43 +0000644 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000645 * \param X The left-hand MPI. This must point to an initialized MPI.
646 * \param Y The right-hand MPI. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000647 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000648 * \return \c 1 if `|X|` is greater than `|Y|`.
649 * \return \c -1 if `|X|` is lesser than `|Y|`.
Hanno Beckere1185042018-12-13 14:31:46 +0000650 * \return \c 0 if `|X|` is equal to `|Y|`.
Paul Bakker5121ce52009-01-03 21:22:43 +0000651 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100652int mbedtls_mpi_cmp_abs(const mbedtls_mpi *X, const mbedtls_mpi *Y);
Paul Bakker5121ce52009-01-03 21:22:43 +0000653
654/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000655 * \brief Compare two MPIs.
Paul Bakker5121ce52009-01-03 21:22:43 +0000656 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000657 * \param X The left-hand MPI. This must point to an initialized MPI.
658 * \param Y The right-hand MPI. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000659 *
Hanno Beckere1185042018-12-13 14:31:46 +0000660 * \return \c 1 if \p X is greater than \p Y.
661 * \return \c -1 if \p X is lesser than \p Y.
662 * \return \c 0 if \p X is equal to \p Y.
Paul Bakker5121ce52009-01-03 21:22:43 +0000663 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100664int mbedtls_mpi_cmp_mpi(const mbedtls_mpi *X, const mbedtls_mpi *Y);
Paul Bakker5121ce52009-01-03 21:22:43 +0000665
666/**
Janos Follath0e5532d2019-10-11 14:21:53 +0100667 * \brief Check if an MPI is less than the other in constant time.
Janos Follathee6abce2019-09-05 14:47:19 +0100668 *
669 * \param X The left-hand MPI. This must point to an initialized MPI
670 * with the same allocated length as Y.
671 * \param Y The right-hand MPI. This must point to an initialized MPI
672 * with the same allocated length as X.
673 * \param ret The result of the comparison:
Janos Follath0e5532d2019-10-11 14:21:53 +0100674 * \c 1 if \p X is less than \p Y.
675 * \c 0 if \p X is greater than or equal to \p Y.
Janos Follathee6abce2019-09-05 14:47:19 +0100676 *
677 * \return 0 on success.
678 * \return MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the allocated length of
679 * the two input MPIs is not the same.
680 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100681int mbedtls_mpi_lt_mpi_ct(const mbedtls_mpi *X, const mbedtls_mpi *Y,
682 unsigned *ret);
Janos Follathee6abce2019-09-05 14:47:19 +0100683
684/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000685 * \brief Compare an MPI with an integer.
Paul Bakker5121ce52009-01-03 21:22:43 +0000686 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000687 * \param X The left-hand MPI. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000688 * \param z The integer value to compare \p X to.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000689 *
Hanno Beckere1185042018-12-13 14:31:46 +0000690 * \return \c 1 if \p X is greater than \p z.
691 * \return \c -1 if \p X is lesser than \p z.
692 * \return \c 0 if \p X is equal to \p z.
Paul Bakker5121ce52009-01-03 21:22:43 +0000693 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100694int mbedtls_mpi_cmp_int(const mbedtls_mpi *X, mbedtls_mpi_sint z);
Paul Bakker5121ce52009-01-03 21:22:43 +0000695
696/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000697 * \brief Perform an unsigned addition of MPIs: X = |A| + |B|
Paul Bakker5121ce52009-01-03 21:22:43 +0000698 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000699 * \param X The destination MPI. This must point to an initialized MPI.
700 * \param A The first summand. This must point to an initialized MPI.
701 * \param B The second summand. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000702 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000703 * \return \c 0 if successful.
704 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
705 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000706 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100707int mbedtls_mpi_add_abs(mbedtls_mpi *X, const mbedtls_mpi *A,
708 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000709
710/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000711 * \brief Perform an unsigned subtraction of MPIs: X = |A| - |B|
Paul Bakker5121ce52009-01-03 21:22:43 +0000712 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000713 * \param X The destination MPI. This must point to an initialized MPI.
714 * \param A The minuend. This must point to an initialized MPI.
715 * \param B The subtrahend. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000716 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000717 * \return \c 0 if successful.
718 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is greater than \p A.
719 * \return Another negative error code on different kinds of failure.
720 *
Paul Bakker5121ce52009-01-03 21:22:43 +0000721 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100722int mbedtls_mpi_sub_abs(mbedtls_mpi *X, const mbedtls_mpi *A,
723 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000724
725/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000726 * \brief Perform a signed addition of MPIs: X = A + B
Paul Bakker5121ce52009-01-03 21:22:43 +0000727 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000728 * \param X The destination MPI. This must point to an initialized MPI.
729 * \param A The first summand. This must point to an initialized MPI.
730 * \param B The second summand. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000731 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000732 * \return \c 0 if successful.
733 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
734 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000735 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100736int mbedtls_mpi_add_mpi(mbedtls_mpi *X, const mbedtls_mpi *A,
737 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000738
739/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000740 * \brief Perform a signed subtraction of MPIs: X = A - B
Paul Bakker5121ce52009-01-03 21:22:43 +0000741 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000742 * \param X The destination MPI. This must point to an initialized MPI.
743 * \param A The minuend. This must point to an initialized MPI.
744 * \param B The subtrahend. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000745 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000746 * \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.
Paul Bakker5121ce52009-01-03 21:22:43 +0000749 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100750int mbedtls_mpi_sub_mpi(mbedtls_mpi *X, const mbedtls_mpi *A,
751 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000752
753/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000754 * \brief Perform a signed addition of an MPI and an integer: X = A + b
Paul Bakker5121ce52009-01-03 21:22:43 +0000755 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000756 * \param X The destination MPI. This must point to an initialized MPI.
757 * \param A The first summand. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000758 * \param b The second summand.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000759 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000760 * \return \c 0 if successful.
761 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
762 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000763 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100764int mbedtls_mpi_add_int(mbedtls_mpi *X, const mbedtls_mpi *A,
765 mbedtls_mpi_sint b);
Paul Bakker5121ce52009-01-03 21:22:43 +0000766
767/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000768 * \brief Perform a signed subtraction of an MPI and an integer:
769 * X = A - b
Paul Bakker5121ce52009-01-03 21:22:43 +0000770 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000771 * \param X The destination MPI. This must point to an initialized MPI.
772 * \param A The minuend. This must point to an initialized MPI.
Hanno Becker01c3c102018-12-17 23:04:51 +0000773 * \param b The subtrahend.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000774 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000775 * \return \c 0 if successful.
776 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
777 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000778 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100779int mbedtls_mpi_sub_int(mbedtls_mpi *X, const mbedtls_mpi *A,
780 mbedtls_mpi_sint b);
Paul Bakker5121ce52009-01-03 21:22:43 +0000781
782/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000783 * \brief Perform a multiplication of two MPIs: X = A * B
Paul Bakker5121ce52009-01-03 21:22:43 +0000784 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000785 * \param X The destination MPI. This must point to an initialized MPI.
786 * \param A The first factor. This must point to an initialized MPI.
787 * \param B The second factor. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000788 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000789 * \return \c 0 if successful.
790 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
791 * \return Another negative error code on different kinds of failure.
792 *
Paul Bakker5121ce52009-01-03 21:22:43 +0000793 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100794int mbedtls_mpi_mul_mpi(mbedtls_mpi *X, const mbedtls_mpi *A,
795 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000796
797/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000798 * \brief Perform a multiplication of an MPI with an unsigned integer:
799 * X = A * b
Paul Bakker5121ce52009-01-03 21:22:43 +0000800 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000801 * \param X The destination MPI. This must point to an initialized MPI.
802 * \param A The first factor. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000803 * \param b The second factor.
Manuel Pégourié-Gonnard35f1d7f2015-03-19 12:42:40 +0000804 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000805 * \return \c 0 if successful.
806 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
807 * \return Another negative error code on different kinds of failure.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000808 *
Paul Bakker5121ce52009-01-03 21:22:43 +0000809 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100810int mbedtls_mpi_mul_int(mbedtls_mpi *X, const mbedtls_mpi *A,
811 mbedtls_mpi_uint b);
Paul Bakker5121ce52009-01-03 21:22:43 +0000812
813/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000814 * \brief Perform a division with remainder of two MPIs:
815 * A = Q * B + R
Paul Bakker5121ce52009-01-03 21:22:43 +0000816 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000817 * \param Q The destination MPI for the quotient.
Hanno Beckerd01ff492018-12-18 23:10:28 +0000818 * This may be \c NULL if the value of the
Glenn Strauss0750d082022-11-08 02:25:01 -0500819 * quotient is not needed. This must not alias A or B.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000820 * \param R The destination MPI for the remainder value.
Hanno Beckerd01ff492018-12-18 23:10:28 +0000821 * This may be \c NULL if the value of the
Glenn Strauss0750d082022-11-08 02:25:01 -0500822 * remainder is not needed. This must not alias A or B.
823 * \param A The dividend. This must point to an initialized MPI.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000824 * \param B The divisor. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000825 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000826 * \return \c 0 if successful.
827 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
Hanno Beckere1185042018-12-13 14:31:46 +0000828 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000829 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000830 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100831int mbedtls_mpi_div_mpi(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
832 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000833
834/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000835 * \brief Perform a division with remainder of an MPI by an integer:
836 * A = Q * b + R
Paul Bakker5121ce52009-01-03 21:22:43 +0000837 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000838 * \param Q The destination MPI for the quotient.
Hanno Beckerd01ff492018-12-18 23:10:28 +0000839 * This may be \c NULL if the value of the
Glenn Strauss0750d082022-11-08 02:25:01 -0500840 * quotient is not needed. This must not alias A.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000841 * \param R The destination MPI for the remainder value.
Hanno Beckerd01ff492018-12-18 23:10:28 +0000842 * This may be \c NULL if the value of the
Glenn Strauss0750d082022-11-08 02:25:01 -0500843 * remainder is not needed. This must not alias A.
Hanno Becker8ce11a32018-12-19 16:18:52 +0000844 * \param A The dividend. This must point to an initialized MPi.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000845 * \param b The divisor.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000846 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000847 * \return \c 0 if successful.
848 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
Hanno Beckere1185042018-12-13 14:31:46 +0000849 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000850 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000851 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100852int mbedtls_mpi_div_int(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
853 mbedtls_mpi_sint b);
Paul Bakker5121ce52009-01-03 21:22:43 +0000854
855/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000856 * \brief Perform a modular reduction. R = A mod B
Paul Bakker5121ce52009-01-03 21:22:43 +0000857 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000858 * \param R The destination MPI for the residue value.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000859 * This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000860 * \param A The MPI to compute the residue of.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000861 * This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000862 * \param B The base of the modular reduction.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000863 * This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000864 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000865 * \return \c 0 if successful.
866 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
Hanno Beckere1185042018-12-13 14:31:46 +0000867 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero.
868 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is negative.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000869 * \return Another negative error code on different kinds of failure.
870 *
Paul Bakker5121ce52009-01-03 21:22:43 +0000871 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100872int mbedtls_mpi_mod_mpi(mbedtls_mpi *R, const mbedtls_mpi *A,
873 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000874
875/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000876 * \brief Perform a modular reduction with respect to an integer.
877 * r = A mod b
Paul Bakker5121ce52009-01-03 21:22:43 +0000878 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000879 * \param r The address at which to store the residue.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000880 * This must not be \c NULL.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000881 * \param A The MPI to compute the residue of.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000882 * This must point to an initialized MPi.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000883 * \param b The integer base of the modular reduction.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000884 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000885 * \return \c 0 if successful.
886 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
Hanno Beckere1185042018-12-13 14:31:46 +0000887 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero.
888 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p b is negative.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000889 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000890 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100891int mbedtls_mpi_mod_int(mbedtls_mpi_uint *r, const mbedtls_mpi *A,
892 mbedtls_mpi_sint b);
Paul Bakker5121ce52009-01-03 21:22:43 +0000893
894/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000895 * \brief Perform a sliding-window exponentiation: X = A^E mod N
Paul Bakker5121ce52009-01-03 21:22:43 +0000896 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000897 * \param X The destination MPI. This must point to an initialized MPI.
Glenn Strauss0750d082022-11-08 02:25:01 -0500898 * This must not alias E or N.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000899 * \param A The base of the exponentiation.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000900 * This must point to an initialized MPI.
901 * \param E The exponent MPI. This must point to an initialized MPI.
902 * \param N The base for the modular reduction. This must point to an
Hanno Beckerc23483e2018-12-10 17:21:19 +0000903 * initialized MPI.
Yuto Takano538a0cb2021-07-14 10:20:09 +0100904 * \param prec_RR A helper MPI depending solely on \p N which can be used to
Hanno Beckerc23483e2018-12-10 17:21:19 +0000905 * speed-up multiple modular exponentiations for the same value
Hanno Beckere1185042018-12-13 14:31:46 +0000906 * of \p N. This may be \c NULL. If it is not \c NULL, it must
Hanno Becker8ce11a32018-12-19 16:18:52 +0000907 * point to an initialized MPI. If it hasn't been used after
Hanno Beckere1185042018-12-13 14:31:46 +0000908 * the call to mbedtls_mpi_init(), this function will compute
Yuto Takano538a0cb2021-07-14 10:20:09 +0100909 * the helper value and store it in \p prec_RR for reuse on
Hanno Beckere1185042018-12-13 14:31:46 +0000910 * subsequent calls to this function. Otherwise, the function
Yuto Takano538a0cb2021-07-14 10:20:09 +0100911 * will assume that \p prec_RR holds the helper value set by a
Hanno Beckere1185042018-12-13 14:31:46 +0000912 * previous call to mbedtls_mpi_exp_mod(), and reuse it.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000913 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000914 * \return \c 0 if successful.
915 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
916 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \c N is negative or
917 * even, or if \c E is negative.
918 * \return Another negative error code on different kinds of failures.
Paul Bakker5121ce52009-01-03 21:22:43 +0000919 *
Paul Bakker5121ce52009-01-03 21:22:43 +0000920 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100921int mbedtls_mpi_exp_mod(mbedtls_mpi *X, const mbedtls_mpi *A,
922 const mbedtls_mpi *E, const mbedtls_mpi *N,
923 mbedtls_mpi *prec_RR);
Paul Bakker5121ce52009-01-03 21:22:43 +0000924
925/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000926 * \brief Fill an MPI with a number of random bytes.
Paul Bakker287781a2011-03-26 13:18:49 +0000927 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000928 * \param X The destination MPI. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000929 * \param size The number of random bytes to generate.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000930 * \param f_rng The RNG function to use. This must not be \c NULL.
Hanno Beckere1185042018-12-13 14:31:46 +0000931 * \param p_rng The RNG parameter to be passed to \p f_rng. This may be
932 * \c NULL if \p f_rng doesn't need a context argument.
Paul Bakker287781a2011-03-26 13:18:49 +0000933 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000934 * \return \c 0 if successful.
935 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
936 * \return Another negative error code on failure.
Hanno Becker15f2b3e2017-10-17 15:17:05 +0100937 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000938 * \note The bytes obtained from the RNG are interpreted
Hanno Becker15f2b3e2017-10-17 15:17:05 +0100939 * as a big-endian representation of an MPI; this can
940 * be relevant in applications like deterministic ECDSA.
Paul Bakker287781a2011-03-26 13:18:49 +0000941 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100942int mbedtls_mpi_fill_random(mbedtls_mpi *X, size_t size,
943 int (*f_rng)(void *, unsigned char *, size_t),
944 void *p_rng);
Paul Bakker287781a2011-03-26 13:18:49 +0000945
Gilles Peskine02ac93a2021-03-29 22:02:55 +0200946/** Generate a random number uniformly in a range.
947 *
948 * This function generates a random number between \p min inclusive and
949 * \p N exclusive.
950 *
951 * The procedure complies with RFC 6979 §3.3 (deterministic ECDSA)
952 * when the RNG is a suitably parametrized instance of HMAC_DRBG
953 * and \p min is \c 1.
954 *
955 * \note There are `N - min` possible outputs. The lower bound
956 * \p min can be reached, but the upper bound \p N cannot.
957 *
958 * \param X The destination MPI. This must point to an initialized MPI.
959 * \param min The minimum value to return.
960 * It must be nonnegative.
961 * \param N The upper bound of the range, exclusive.
962 * In other words, this is one plus the maximum value to return.
963 * \p N must be strictly larger than \p min.
964 * \param f_rng The RNG function to use. This must not be \c NULL.
965 * \param p_rng The RNG parameter to be passed to \p f_rng.
966 *
967 * \return \c 0 if successful.
968 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
Gilles Peskine1e918f42021-03-29 22:14:51 +0200969 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p min or \p N is invalid
970 * or if they are incompatible.
Gilles Peskine7ed7c5a2021-04-13 21:28:38 +0200971 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if the implementation was
972 * unable to find a suitable value within a limited number
973 * of attempts. This has a negligible probability if \p N
974 * is significantly larger than \p min, which is the case
975 * for all usual cryptographic applications.
Gilles Peskine02ac93a2021-03-29 22:02:55 +0200976 * \return Another negative error code on failure.
977 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100978int mbedtls_mpi_random(mbedtls_mpi *X,
979 mbedtls_mpi_sint min,
980 const mbedtls_mpi *N,
981 int (*f_rng)(void *, unsigned char *, size_t),
982 void *p_rng);
Gilles Peskine02ac93a2021-03-29 22:02:55 +0200983
Paul Bakker287781a2011-03-26 13:18:49 +0000984/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000985 * \brief Compute the greatest common divisor: G = gcd(A, B)
Paul Bakker5121ce52009-01-03 21:22:43 +0000986 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000987 * \param G The destination MPI. This must point to an initialized MPI.
988 * \param A The first operand. This must point to an initialized MPI.
Hanno Becker01c3c102018-12-17 23:04:51 +0000989 * \param B The second operand. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000990 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000991 * \return \c 0 if successful.
992 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
993 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000994 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100995int mbedtls_mpi_gcd(mbedtls_mpi *G, const mbedtls_mpi *A,
996 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000997
998/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000999 * \brief Compute the modular inverse: X = A^-1 mod N
Paul Bakker5121ce52009-01-03 21:22:43 +00001000 *
Hanno Becker8282c2f2018-12-12 13:36:46 +00001001 * \param X The destination MPI. This must point to an initialized MPI.
1002 * \param A The MPI to calculate the modular inverse of. This must point
Hanno Beckerc23483e2018-12-10 17:21:19 +00001003 * to an initialized MPI.
Hanno Becker8282c2f2018-12-12 13:36:46 +00001004 * \param N The base of the modular inversion. This must point to an
Hanno Beckerc23483e2018-12-10 17:21:19 +00001005 * initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +00001006 *
Hanno Beckerc23483e2018-12-10 17:21:19 +00001007 * \return \c 0 if successful.
1008 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
Hanno Beckere1185042018-12-13 14:31:46 +00001009 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p N is less than
1010 * or equal to one.
Andrzej Kurek69ed8c42022-02-17 10:06:44 -05001011 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p A has no modular
1012 * inverse with respect to \p N.
Paul Bakker5121ce52009-01-03 21:22:43 +00001013 */
Gilles Peskine449bd832023-01-11 14:50:10 +01001014int mbedtls_mpi_inv_mod(mbedtls_mpi *X, const mbedtls_mpi *A,
1015 const mbedtls_mpi *N);
Paul Bakker5121ce52009-01-03 21:22:43 +00001016
Paul Bakker5121ce52009-01-03 21:22:43 +00001017/**
Janos Follatha0b67c22018-09-18 14:48:23 +01001018 * \brief Miller-Rabin primality test.
1019 *
1020 * \warning If \p X is potentially generated by an adversary, for example
1021 * when validating cryptographic parameters that you didn't
1022 * generate yourself and that are supposed to be prime, then
1023 * \p rounds should be at least the half of the security
1024 * strength of the cryptographic algorithm. On the other hand,
Tom Cosgrove1e211442022-05-26 11:51:00 +01001025 * if \p X is chosen uniformly or non-adversarially (as is the
Janos Follatha0b67c22018-09-18 14:48:23 +01001026 * case when mbedtls_mpi_gen_prime calls this function), then
1027 * \p rounds can be much lower.
1028 *
Hanno Beckerc23483e2018-12-10 17:21:19 +00001029 * \param X The MPI to check for primality.
Hanno Becker8282c2f2018-12-12 13:36:46 +00001030 * This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +00001031 * \param rounds The number of bases to perform the Miller-Rabin primality
1032 * test for. The probability of returning 0 on a composite is
David Horstmannd855b462023-02-23 18:39:16 +00001033 * at most 2<sup>-2*\p rounds </sup>.
Hanno Becker8282c2f2018-12-12 13:36:46 +00001034 * \param f_rng The RNG function to use. This must not be \c NULL.
Hanno Beckerc23483e2018-12-10 17:21:19 +00001035 * \param p_rng The RNG parameter to be passed to \p f_rng.
Hanno Beckere1185042018-12-13 14:31:46 +00001036 * This may be \c NULL if \p f_rng doesn't use
1037 * a context parameter.
Janos Follatha0b67c22018-09-18 14:48:23 +01001038 *
Hanno Beckerc23483e2018-12-10 17:21:19 +00001039 * \return \c 0 if successful, i.e. \p X is probably prime.
1040 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
1041 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime.
1042 * \return Another negative error code on other kinds of failure.
Janos Follatha0b67c22018-09-18 14:48:23 +01001043 */
Gilles Peskine449bd832023-01-11 14:50:10 +01001044int mbedtls_mpi_is_prime_ext(const mbedtls_mpi *X, int rounds,
1045 int (*f_rng)(void *, unsigned char *, size_t),
1046 void *p_rng);
Janos Follatha0b67c22018-09-18 14:48:23 +01001047/**
Janos Follath7c025a92018-08-14 11:08:41 +01001048 * \brief Flags for mbedtls_mpi_gen_prime()
1049 *
1050 * Each of these flags is a constraint on the result X returned by
1051 * mbedtls_mpi_gen_prime().
1052 */
1053typedef enum {
Janos Follathf301d232018-08-14 13:34:01 +01001054 MBEDTLS_MPI_GEN_PRIME_FLAG_DH = 0x0001, /**< (X-1)/2 is prime too */
1055 MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR = 0x0002, /**< lower error rate from 2<sup>-80</sup> to 2<sup>-128</sup> */
Janos Follath7c025a92018-08-14 11:08:41 +01001056} mbedtls_mpi_gen_prime_flag_t;
1057
1058/**
Hanno Beckerc23483e2018-12-10 17:21:19 +00001059 * \brief Generate a prime number.
Paul Bakker5121ce52009-01-03 21:22:43 +00001060 *
Hanno Beckerc23483e2018-12-10 17:21:19 +00001061 * \param X The destination MPI to store the generated prime in.
Hanno Becker8282c2f2018-12-12 13:36:46 +00001062 * This must point to an initialized MPi.
Hanno Beckerc23483e2018-12-10 17:21:19 +00001063 * \param nbits The required size of the destination MPI in bits.
Hanno Beckerd01ff492018-12-18 23:10:28 +00001064 * This must be between \c 3 and #MBEDTLS_MPI_MAX_BITS.
Hanno Beckerc23483e2018-12-10 17:21:19 +00001065 * \param flags A mask of flags of type #mbedtls_mpi_gen_prime_flag_t.
Hanno Becker8282c2f2018-12-12 13:36:46 +00001066 * \param f_rng The RNG function to use. This must not be \c NULL.
Hanno Beckerc23483e2018-12-10 17:21:19 +00001067 * \param p_rng The RNG parameter to be passed to \p f_rng.
Hanno Beckere1185042018-12-13 14:31:46 +00001068 * This may be \c NULL if \p f_rng doesn't use
1069 * a context parameter.
Paul Bakker5121ce52009-01-03 21:22:43 +00001070 *
Hanno Beckere1185042018-12-13 14:31:46 +00001071 * \return \c 0 if successful, in which case \p X holds a
Hanno Beckerc23483e2018-12-10 17:21:19 +00001072 * probably prime number.
1073 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
1074 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `nbits` is not between
1075 * \c 3 and #MBEDTLS_MPI_MAX_BITS.
Paul Bakker5121ce52009-01-03 21:22:43 +00001076 */
Gilles Peskine449bd832023-01-11 14:50:10 +01001077int mbedtls_mpi_gen_prime(mbedtls_mpi *X, size_t nbits, int flags,
1078 int (*f_rng)(void *, unsigned char *, size_t),
1079 void *p_rng);
Paul Bakker5121ce52009-01-03 21:22:43 +00001080
Ron Eldorfa8f6352017-06-20 15:48:46 +03001081#if defined(MBEDTLS_SELF_TEST)
1082
Paul Bakker5121ce52009-01-03 21:22:43 +00001083/**
1084 * \brief Checkup routine
1085 *
1086 * \return 0 if successful, or 1 if the test failed
1087 */
Gilles Peskine449bd832023-01-11 14:50:10 +01001088int mbedtls_mpi_self_test(int verbose);
Paul Bakker5121ce52009-01-03 21:22:43 +00001089
Ron Eldorfa8f6352017-06-20 15:48:46 +03001090#endif /* MBEDTLS_SELF_TEST */
1091
Paul Bakker5121ce52009-01-03 21:22:43 +00001092#ifdef __cplusplus
1093}
1094#endif
1095
1096#endif /* bignum.h */