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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
Dave Rodgman16799db2023-11-02 19:47:20 +00008 * SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
Paul Bakker5121ce52009-01-03 21:22:43 +00009 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020010#ifndef MBEDTLS_BIGNUM_H
11#define MBEDTLS_BIGNUM_H
Mateusz Starzyk846f0212021-05-19 19:44:07 +020012#include "mbedtls/private_access.h"
Paul Bakker5121ce52009-01-03 21:22:43 +000013
Bence Szépkútic662b362021-05-27 11:25:03 +020014#include "mbedtls/build_info.h"
Paul Bakkercf0360a2012-01-20 10:08:14 +000015
Rich Evans00ab4702015-02-06 13:43:58 +000016#include <stddef.h>
Manuel Pégourié-Gonnardab229102015-04-15 11:53:16 +020017#include <stdint.h>
Rich Evans00ab4702015-02-06 13:43:58 +000018
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020019#if defined(MBEDTLS_FS_IO)
Manuel Pégourié-Gonnarde94e6e52015-01-19 15:01:53 +000020#include <stdio.h>
21#endif
22
Gilles Peskined2971572021-07-26 18:48:10 +020023/** An error occurred while reading from or writing to a file. */
24#define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002
25/** Bad input parameters to function. */
26#define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004
27/** There is an invalid character in the digit string. */
28#define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006
29/** The buffer is too small to write to. */
30#define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008
31/** The input arguments are negative or result in illegal output. */
32#define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A
33/** The input argument for division is zero, which is not allowed. */
34#define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C
35/** The input arguments are not acceptable. */
36#define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E
37/** Memory allocation failed. */
38#define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010
Paul Bakker5121ce52009-01-03 21:22:43 +000039
Hanno Becker1eeca412018-10-15 12:01:35 +010040#define MBEDTLS_MPI_CHK(f) \
41 do \
42 { \
Gilles Peskine449bd832023-01-11 14:50:10 +010043 if ((ret = (f)) != 0) \
44 goto cleanup; \
45 } while (0)
Paul Bakker5121ce52009-01-03 21:22:43 +000046
Janos Follathe0849642024-08-12 17:26:24 +010047/* Constants to identify whether a value is public or secret. If a parameter is marked as secret by
48 * this constant, the function must be constant time with respect to the parameter.
49 *
50 * This is only needed for functions with the _optionally_safe postfix. All other functions have
51 * fixed behavior that can't be changed at runtime and are constant time with respect to their
52 * parameters as prescribed by their documentation or by conventions in their module's documentation.
Manuel Pégourié-Gonnard75ed5872024-06-18 12:52:45 +020053 *
54 * Parameters should be named X_public where X is the name of the
55 * corresponding input parameter.
56 *
57 * Implementation should always check using
58 * if (X_public == MBEDTLS_MPI_IS_PUBLIC) {
59 * // unsafe path
60 * } else {
61 * // safe path
62 * }
63 * not the other way round, in order to prevent misuse. (This is, if a value
64 * other than the two below is passed, default to the safe path.) */
65#define MBEDTLS_MPI_IS_PUBLIC 0x2a2a
66#define MBEDTLS_MPI_IS_SECRET 0
67
Paul Bakker5121ce52009-01-03 21:22:43 +000068/*
Paul Bakkerf9688572011-05-05 10:00:45 +000069 * Maximum size MPIs are allowed to grow to in number of limbs.
70 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020071#define MBEDTLS_MPI_MAX_LIMBS 10000
Paul Bakkerf9688572011-05-05 10:00:45 +000072
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020073#if !defined(MBEDTLS_MPI_WINDOW_SIZE)
Paul Bakkerf9688572011-05-05 10:00:45 +000074/*
Janos Follath6bd5cae2024-02-21 11:27:31 +000075 * Maximum window size used for modular exponentiation. Default: 3
Paul Bakkerb6d5f082011-11-25 11:52:11 +000076 * Minimum value: 1. Maximum value: 6.
77 *
Daniel Otte60861512020-09-07 13:07:14 +020078 * Result is an array of ( 2 ** MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
Janos Follath6bd5cae2024-02-21 11:27:31 +000079 * for the sliding window calculation. (So 8 by default)
Paul Bakkerb6d5f082011-11-25 11:52:11 +000080 *
81 * Reduction in size, reduces speed.
82 */
Janos Follath1609d572024-02-14 14:58:39 +000083#define MBEDTLS_MPI_WINDOW_SIZE 3 /**< Maximum window size used. */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020084#endif /* !MBEDTLS_MPI_WINDOW_SIZE */
Paul Bakkerb6d5f082011-11-25 11:52:11 +000085
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020086#if !defined(MBEDTLS_MPI_MAX_SIZE)
Paul Bakkerb6d5f082011-11-25 11:52:11 +000087/*
Paul Bakkerfe3256e2011-11-25 12:11:43 +000088 * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
Paul Bakkerf626e1d2013-01-21 12:10:00 +010089 * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
Paul Bakkerfe3256e2011-11-25 12:11:43 +000090 *
Hanno Beckerefeef6c2018-01-05 08:07:47 +000091 * Note: Calculations can temporarily result in larger MPIs. So the number
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020092 * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
Paul Bakkerfe3256e2011-11-25 12:11:43 +000093 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020094#define MBEDTLS_MPI_MAX_SIZE 1024 /**< Maximum number of bytes for usable MPIs. */
95#endif /* !MBEDTLS_MPI_MAX_SIZE */
Paul Bakker9bcf16c2013-06-24 19:31:17 +020096
Gilles Peskine449bd832023-01-11 14:50:10 +010097#define MBEDTLS_MPI_MAX_BITS (8 * MBEDTLS_MPI_MAX_SIZE) /**< Maximum number of bits for usable MPIs. */
Paul Bakkerfe3256e2011-11-25 12:11:43 +000098
99/*
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200100 * When reading from files with mbedtls_mpi_read_file() and writing to files with
101 * mbedtls_mpi_write_file() the buffer should have space
Paul Bakkercb37aa52011-11-30 16:00:20 +0000102 * for a (short) label, the MPI (in the provided radix), the newline
103 * characters and the '\0'.
104 *
105 * By default we assume at least a 10 char label, a minimum radix of 10
106 * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
Paul Bakkerf9183102012-09-27 20:42:35 +0000107 * Autosized at compile time for at least a 10 char label, a minimum radix
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200108 * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
Paul Bakkerf9183102012-09-27 20:42:35 +0000109 *
110 * This used to be statically sized to 1250 for a maximum of 4096 bit
111 * numbers (1234 decimal chars).
112 *
113 * Calculate using the formula:
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200114 * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
Paul Bakkerf9183102012-09-27 20:42:35 +0000115 * LabelSize + 6
Paul Bakkercb37aa52011-11-30 16:00:20 +0000116 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100117#define MBEDTLS_MPI_MAX_BITS_SCALE100 (100 * MBEDTLS_MPI_MAX_BITS)
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200118#define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332
Gilles Peskine449bd832023-01-11 14:50:10 +0100119#define MBEDTLS_MPI_RW_BUFFER_SIZE (((MBEDTLS_MPI_MAX_BITS_SCALE100 + \
120 MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / \
121 MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6)
Paul Bakkercb37aa52011-11-30 16:00:20 +0000122
123/*
Manuel Pégourié-Gonnard7b538892015-04-09 17:00:17 +0200124 * Define the base integer type, architecture-wise.
125 *
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100126 * 32 or 64-bit integer types can be forced regardless of the underlying
127 * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
128 * respectively and undefining MBEDTLS_HAVE_ASM.
129 *
Andres Amaya Garcia93db11a2017-07-20 12:11:19 +0100130 * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100131 * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
Paul Bakker5121ce52009-01-03 21:22:43 +0000132 */
Andres Amaya Garciaaa27dfe2017-05-04 11:05:55 +0100133#if !defined(MBEDTLS_HAVE_INT32)
134 #if defined(_MSC_VER) && defined(_M_AMD64)
Gilles Peskine449bd832023-01-11 14:50:10 +0100135/* Always choose 64-bit when using MSC */
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100136 #if !defined(MBEDTLS_HAVE_INT64)
137 #define MBEDTLS_HAVE_INT64
138 #endif /* !MBEDTLS_HAVE_INT64 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100139typedef int64_t mbedtls_mpi_sint;
140typedef uint64_t mbedtls_mpi_uint;
Agathiyan Bragadeesheed55c62023-07-19 11:08:02 +0100141#define MBEDTLS_MPI_UINT_MAX UINT64_MAX
Andres Amaya Garciaaa27dfe2017-05-04 11:05:55 +0100142 #elif defined(__GNUC__) && ( \
Gilles Peskine449bd832023-01-11 14:50:10 +0100143 defined(__amd64__) || defined(__x86_64__) || \
144 defined(__ppc64__) || defined(__powerpc64__) || \
145 defined(__ia64__) || defined(__alpha__) || \
146 (defined(__sparc__) && defined(__arch64__)) || \
147 defined(__s390x__) || defined(__mips64) || \
148 defined(__aarch64__))
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100149 #if !defined(MBEDTLS_HAVE_INT64)
150 #define MBEDTLS_HAVE_INT64
151 #endif /* MBEDTLS_HAVE_INT64 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100152typedef int64_t mbedtls_mpi_sint;
153typedef uint64_t mbedtls_mpi_uint;
Agathiyan Bragadeesheed55c62023-07-19 11:08:02 +0100154#define MBEDTLS_MPI_UINT_MAX UINT64_MAX
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100155 #if !defined(MBEDTLS_NO_UDBL_DIVISION)
Gilles Peskine449bd832023-01-11 14:50:10 +0100156/* mbedtls_t_udbl defined as 128-bit unsigned int */
157typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100158 #define MBEDTLS_HAVE_UDBL
159 #endif /* !MBEDTLS_NO_UDBL_DIVISION */
Ko-05cff952018-08-20 12:59:57 +0100160 #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
Gilles Peskine449bd832023-01-11 14:50:10 +0100161/*
162 * __ARMCC_VERSION is defined for both armcc and armclang and
163 * __aarch64__ is only defined by armclang when compiling 64-bit code
164 */
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100165 #if !defined(MBEDTLS_HAVE_INT64)
166 #define MBEDTLS_HAVE_INT64
167 #endif /* !MBEDTLS_HAVE_INT64 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100168typedef int64_t mbedtls_mpi_sint;
169typedef uint64_t mbedtls_mpi_uint;
Agathiyan Bragadeesheed55c62023-07-19 11:08:02 +0100170#define MBEDTLS_MPI_UINT_MAX UINT64_MAX
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100171 #if !defined(MBEDTLS_NO_UDBL_DIVISION)
Gilles Peskine449bd832023-01-11 14:50:10 +0100172/* mbedtls_t_udbl defined as 128-bit unsigned int */
173typedef __uint128_t mbedtls_t_udbl;
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100174 #define MBEDTLS_HAVE_UDBL
175 #endif /* !MBEDTLS_NO_UDBL_DIVISION */
176 #elif defined(MBEDTLS_HAVE_INT64)
Gilles Peskine449bd832023-01-11 14:50:10 +0100177/* Force 64-bit integers with unknown compiler */
178typedef int64_t mbedtls_mpi_sint;
179typedef uint64_t mbedtls_mpi_uint;
Agathiyan Bragadeesheed55c62023-07-19 11:08:02 +0100180#define MBEDTLS_MPI_UINT_MAX UINT64_MAX
Andres Amaya Garciaaa27dfe2017-05-04 11:05:55 +0100181 #endif
182#endif /* !MBEDTLS_HAVE_INT32 */
183
184#if !defined(MBEDTLS_HAVE_INT64)
Gilles Peskine449bd832023-01-11 14:50:10 +0100185/* Default to 32-bit compilation */
Andres Amaya Garciaaa27dfe2017-05-04 11:05:55 +0100186 #if !defined(MBEDTLS_HAVE_INT32)
187 #define MBEDTLS_HAVE_INT32
188 #endif /* !MBEDTLS_HAVE_INT32 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100189typedef int32_t mbedtls_mpi_sint;
190typedef uint32_t mbedtls_mpi_uint;
Agathiyan Bragadeesheed55c62023-07-19 11:08:02 +0100191#define MBEDTLS_MPI_UINT_MAX UINT32_MAX
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100192 #if !defined(MBEDTLS_NO_UDBL_DIVISION)
Gilles Peskine449bd832023-01-11 14:50:10 +0100193typedef uint64_t mbedtls_t_udbl;
Andres Amaya Garciadf1486a2017-07-20 17:33:09 +0100194 #define MBEDTLS_HAVE_UDBL
Andres Amaya Garciad7fce002017-07-20 11:49:32 +0100195 #endif /* !MBEDTLS_NO_UDBL_DIVISION */
Andres Amaya Garciaaa27dfe2017-05-04 11:05:55 +0100196#endif /* !MBEDTLS_HAVE_INT64 */
Paul Bakker5121ce52009-01-03 21:22:43 +0000197
Dave Rodgman85061b92023-09-06 08:41:05 +0100198/*
199 * Sanity check that exactly one of MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64 is defined,
200 * so that code elsewhere doesn't have to check.
201 */
202#if (!(defined(MBEDTLS_HAVE_INT32) || defined(MBEDTLS_HAVE_INT64))) || \
203 (defined(MBEDTLS_HAVE_INT32) && defined(MBEDTLS_HAVE_INT64))
204#error "Only 32-bit or 64-bit limbs are supported in bignum"
205#endif
206
Gilles Peskine6110a162022-11-15 21:22:27 +0100207/** \typedef mbedtls_mpi_uint
208 * \brief The type of machine digits in a bignum, called _limbs_.
209 *
210 * This is always an unsigned integer type with no padding bits. The size
211 * is platform-dependent.
212 */
213
214/** \typedef mbedtls_mpi_sint
215 * \brief The signed type corresponding to #mbedtls_mpi_uint.
216 *
217 * This is always an signed integer type with no padding bits. The size
218 * is platform-dependent.
219 */
220
Paul Bakker407a0da2013-06-27 14:29:21 +0200221#ifdef __cplusplus
222extern "C" {
223#endif
224
Paul Bakker5121ce52009-01-03 21:22:43 +0000225/**
226 * \brief MPI structure
227 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100228typedef struct mbedtls_mpi {
Dave Rodgman98e632f2023-07-11 15:59:14 +0100229 /** Pointer to limbs.
230 *
231 * This may be \c NULL if \c n is 0.
232 */
233 mbedtls_mpi_uint *MBEDTLS_PRIVATE(p);
234
Gilles Peskine12889572022-11-09 21:55:33 +0100235 /** Sign: -1 if the mpi is negative, 1 otherwise.
236 *
237 * The number 0 must be represented with `s = +1`. Although many library
238 * functions treat all-limbs-zero as equivalent to a valid representation
239 * of 0 regardless of the sign bit, there are exceptions, so bignum
240 * functions and external callers must always set \c s to +1 for the
241 * number zero.
242 *
243 * Note that this implies that calloc() or `... = {0}` does not create
244 * a valid MPI representation. You must call mbedtls_mpi_init().
245 */
Gilles Peskine053022f2023-06-29 19:26:48 +0200246 signed short MBEDTLS_PRIVATE(s);
Gilles Peskine12889572022-11-09 21:55:33 +0100247
248 /** Total number of limbs in \c p. */
Gilles Peskine053022f2023-06-29 19:26:48 +0200249 unsigned short MBEDTLS_PRIVATE(n);
Gilles Peskine24a305e2023-07-18 13:41:22 +0200250 /* Make sure that MBEDTLS_MPI_MAX_LIMBS fits in n.
251 * Use the same limit value on all platforms so that we don't have to
252 * think about different behavior on the rare platforms where
253 * unsigned short can store values larger than the minimum required by
254 * the C language, which is 65535.
255 */
Gilles Peskine053022f2023-06-29 19:26:48 +0200256#if MBEDTLS_MPI_MAX_LIMBS > 65535
257#error "MBEDTLS_MPI_MAX_LIMBS > 65535 is not supported"
258#endif
Paul Bakker5121ce52009-01-03 21:22:43 +0000259}
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200260mbedtls_mpi;
Paul Bakker5121ce52009-01-03 21:22:43 +0000261
Paul Bakker5121ce52009-01-03 21:22:43 +0000262/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000263 * \brief Initialize an MPI context.
264 *
265 * This makes the MPI ready to be set or freed,
Manuel Pégourié-Gonnardda61ed32015-04-30 10:28:51 +0200266 * but does not define a value for the MPI.
Paul Bakker6c591fa2011-05-05 11:49:20 +0000267 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000268 * \param X The MPI context to initialize. This must not be \c NULL.
Paul Bakker5121ce52009-01-03 21:22:43 +0000269 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100270void mbedtls_mpi_init(mbedtls_mpi *X);
Paul Bakker5121ce52009-01-03 21:22:43 +0000271
272/**
Hanno Becker8ce11a32018-12-19 16:18:52 +0000273 * \brief This function frees the components of an MPI context.
Paul Bakker6c591fa2011-05-05 11:49:20 +0000274 *
Hanno Beckere1185042018-12-13 14:31:46 +0000275 * \param X The MPI context to be cleared. This may be \c NULL,
Hanno Becker8282c2f2018-12-12 13:36:46 +0000276 * in which case this function is a no-op. If it is
277 * not \c NULL, it must point to an initialized MPI.
Paul Bakker5121ce52009-01-03 21:22:43 +0000278 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100279void mbedtls_mpi_free(mbedtls_mpi *X);
Paul Bakker5121ce52009-01-03 21:22:43 +0000280
281/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000282 * \brief Enlarge an MPI to the specified number of limbs.
Paul Bakker5121ce52009-01-03 21:22:43 +0000283 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000284 * \note This function does nothing if the MPI is
285 * already large enough.
Gilles Peskine70ad8392018-03-21 16:28:41 +0100286 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000287 * \param X The MPI to grow. It must be initialized.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000288 * \param nblimbs The target number of limbs.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000289 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000290 * \return \c 0 if successful.
291 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
292 * \return Another negative error code on other kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000293 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100294int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs);
Paul Bakker5121ce52009-01-03 21:22:43 +0000295
296/**
Hanno Beckere1185042018-12-13 14:31:46 +0000297 * \brief This function resizes an MPI downwards, keeping at least the
298 * specified number of limbs.
Manuel Pégourié-Gonnard58681632013-11-21 10:39:37 +0100299 *
Gilles Peskine70ad8392018-03-21 16:28:41 +0100300 * If \c X is smaller than \c nblimbs, it is resized up
301 * instead.
302 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000303 * \param X The MPI to shrink. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000304 * \param nblimbs The minimum number of limbs to keep.
Manuel Pégourié-Gonnard58681632013-11-21 10:39:37 +0100305 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000306 * \return \c 0 if successful.
307 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
Gilles Peskine70ad8392018-03-21 16:28:41 +0100308 * (this can only happen when resizing up).
Hanno Beckerc23483e2018-12-10 17:21:19 +0000309 * \return Another negative error code on other kinds of failure.
Manuel Pégourié-Gonnard58681632013-11-21 10:39:37 +0100310 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100311int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs);
Manuel Pégourié-Gonnard58681632013-11-21 10:39:37 +0100312
313/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000314 * \brief Make a copy of an MPI.
Paul Bakker5121ce52009-01-03 21:22:43 +0000315 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000316 * \param X The destination MPI. This must point to an initialized MPI.
317 * \param Y The source MPI. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000318 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000319 * \note The limb-buffer in the destination MPI is enlarged
320 * if necessary to hold the value in the source MPI.
321 *
322 * \return \c 0 if successful.
323 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
324 * \return Another negative error code on other kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000325 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100326int mbedtls_mpi_copy(mbedtls_mpi *X, const mbedtls_mpi *Y);
Paul Bakker5121ce52009-01-03 21:22:43 +0000327
328/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000329 * \brief Swap the contents of two MPIs.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000330 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000331 * \param X The first MPI. It must be initialized.
332 * \param Y The second MPI. It must be initialized.
Paul Bakker5121ce52009-01-03 21:22:43 +0000333 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100334void mbedtls_mpi_swap(mbedtls_mpi *X, mbedtls_mpi *Y);
Paul Bakker5121ce52009-01-03 21:22:43 +0000335
336/**
Hanno Beckere1185042018-12-13 14:31:46 +0000337 * \brief Perform a safe conditional copy of MPI which doesn't
338 * reveal whether the condition was true or not.
Manuel Pégourié-Gonnard71c2c212013-11-21 16:56:39 +0100339 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000340 * \param X The MPI to conditionally assign to. This must point
341 * to an initialized MPI.
342 * \param Y The MPI to be assigned from. This must point to an
343 * initialized MPI.
Hanno Beckere1185042018-12-13 14:31:46 +0000344 * \param assign The condition deciding whether to perform the
Tom Cosgrove583816c2022-08-18 14:09:18 +0100345 * assignment or not. Must be either 0 or 1:
Hanno Beckerc23483e2018-12-10 17:21:19 +0000346 * * \c 1: Perform the assignment `X = Y`.
347 * * \c 0: Keep the original value of \p X.
Manuel Pégourié-Gonnard71c2c212013-11-21 16:56:39 +0100348 *
349 * \note This function is equivalent to
Hanno Beckerc23483e2018-12-10 17:21:19 +0000350 * `if( assign ) mbedtls_mpi_copy( X, Y );`
Manuel Pégourié-Gonnard71c2c212013-11-21 16:56:39 +0100351 * except that it avoids leaking any information about whether
352 * the assignment was done or not (the above code may leak
Manuel Pégourié-Gonnardd7283502013-11-21 20:00:38 +0100353 * information through branch prediction and/or memory access
354 * patterns analysis).
Hanno Beckerc23483e2018-12-10 17:21:19 +0000355 *
Tom Cosgrove583816c2022-08-18 14:09:18 +0100356 * \warning If \p assign is neither 0 nor 1, the result of this function
357 * is indeterminate, and the resulting value in \p X might be
358 * neither its original value nor the value in \p Y.
359 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000360 * \return \c 0 if successful.
361 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
362 * \return Another negative error code on other kinds of failure.
Manuel Pégourié-Gonnard71c2c212013-11-21 16:56:39 +0100363 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100364int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign);
Manuel Pégourié-Gonnard71c2c212013-11-21 16:56:39 +0100365
366/**
Hanno Beckere1185042018-12-13 14:31:46 +0000367 * \brief Perform a safe conditional swap which doesn't
368 * reveal whether the condition was true or not.
Manuel Pégourié-Gonnarda60fe892013-12-04 21:41:50 +0100369 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000370 * \param X The first MPI. This must be initialized.
371 * \param Y The second MPI. This must be initialized.
Tom Cosgrove583816c2022-08-18 14:09:18 +0100372 * \param swap The condition deciding whether to perform
373 * the swap or not. Must be either 0 or 1:
Hanno Beckerc23483e2018-12-10 17:21:19 +0000374 * * \c 1: Swap the values of \p X and \p Y.
375 * * \c 0: Keep the original values of \p X and \p Y.
Manuel Pégourié-Gonnarda60fe892013-12-04 21:41:50 +0100376 *
377 * \note This function is equivalent to
Tom Cosgrove583816c2022-08-18 14:09:18 +0100378 * if( swap ) mbedtls_mpi_swap( X, Y );
Manuel Pégourié-Gonnarda60fe892013-12-04 21:41:50 +0100379 * except that it avoids leaking any information about whether
Tom Cosgrove583816c2022-08-18 14:09:18 +0100380 * the swap was done or not (the above code may leak
Manuel Pégourié-Gonnarda60fe892013-12-04 21:41:50 +0100381 * information through branch prediction and/or memory access
382 * patterns analysis).
Hanno Beckerc23483e2018-12-10 17:21:19 +0000383 *
Tom Cosgrove583816c2022-08-18 14:09:18 +0100384 * \warning If \p swap is neither 0 nor 1, the result of this function
385 * is indeterminate, and both \p X and \p Y might end up with
386 * values different to either of the original ones.
387 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000388 * \return \c 0 if successful.
389 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
390 * \return Another negative error code on other kinds of failure.
391 *
Manuel Pégourié-Gonnarda60fe892013-12-04 21:41:50 +0100392 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100393int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap);
Manuel Pégourié-Gonnarda60fe892013-12-04 21:41:50 +0100394
395/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000396 * \brief Store integer value in MPI.
Paul Bakker5121ce52009-01-03 21:22:43 +0000397 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000398 * \param X The MPI to set. This must be initialized.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000399 * \param z The value to use.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000400 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000401 * \return \c 0 if successful.
402 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
403 * \return Another negative error code on other kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000404 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100405int mbedtls_mpi_lset(mbedtls_mpi *X, mbedtls_mpi_sint z);
Paul Bakker5121ce52009-01-03 21:22:43 +0000406
Paul Bakker9a736322012-11-14 12:39:52 +0000407/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000408 * \brief Get a specific bit from an MPI.
Paul Bakker2f5947e2011-05-18 15:47:11 +0000409 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000410 * \param X The MPI to query. This must be initialized.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000411 * \param pos Zero-based index of the bit to query.
Paul Bakker2f5947e2011-05-18 15:47:11 +0000412 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000413 * \return \c 0 or \c 1 on success, depending on whether bit \c pos
Hanno Becker8282c2f2018-12-12 13:36:46 +0000414 * of \c X is unset or set.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000415 * \return A negative error code on failure.
Paul Bakker2f5947e2011-05-18 15:47:11 +0000416 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100417int mbedtls_mpi_get_bit(const mbedtls_mpi *X, size_t pos);
Paul Bakker2f5947e2011-05-18 15:47:11 +0000418
Paul Bakker9a736322012-11-14 12:39:52 +0000419/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000420 * \brief Modify a specific bit in an MPI.
Paul Bakker2f5947e2011-05-18 15:47:11 +0000421 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000422 * \note This function will grow the target MPI if necessary to set a
423 * bit to \c 1 in a not yet existing limb. It will not grow if
424 * the bit should be set to \c 0.
Paul Bakker2f5947e2011-05-18 15:47:11 +0000425 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000426 * \param X The MPI to modify. This must be initialized.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000427 * \param pos Zero-based index of the bit to modify.
428 * \param val The desired value of bit \c pos: \c 0 or \c 1.
Paul Bakker2f5947e2011-05-18 15:47:11 +0000429 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000430 * \return \c 0 if successful.
431 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
432 * \return Another negative error code on other kinds of failure.
Paul Bakker2f5947e2011-05-18 15:47:11 +0000433 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100434int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val);
Paul Bakker2f5947e2011-05-18 15:47:11 +0000435
Paul Bakker5121ce52009-01-03 21:22:43 +0000436/**
Hanno Beckere1185042018-12-13 14:31:46 +0000437 * \brief Return the number of bits of value \c 0 before the
438 * least significant bit of value \c 1.
Paul Bakker6b906e52012-05-08 12:01:43 +0000439 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000440 * \note This is the same as the zero-based index of
Hanno Beckere1185042018-12-13 14:31:46 +0000441 * the least significant bit of value \c 1.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000442 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000443 * \param X The MPI to query.
444 *
Hanno Beckere1185042018-12-13 14:31:46 +0000445 * \return The number of bits of value \c 0 before the least significant
446 * bit of value \c 1 in \p X.
Paul Bakker5121ce52009-01-03 21:22:43 +0000447 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100448size_t mbedtls_mpi_lsb(const mbedtls_mpi *X);
Paul Bakker5121ce52009-01-03 21:22:43 +0000449
450/**
Paul Bakker6b906e52012-05-08 12:01:43 +0000451 * \brief Return the number of bits up to and including the most
Hanno Beckere1185042018-12-13 14:31:46 +0000452 * significant bit of value \c 1.
Paul Bakker6b906e52012-05-08 12:01:43 +0000453 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000454 * * \note This is same as the one-based index of the most
Hanno Beckere1185042018-12-13 14:31:46 +0000455 * significant bit of value \c 1.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000456 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000457 * \param X The MPI to query. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000458 *
459 * \return The number of bits up to and including the most
Hanno Beckere1185042018-12-13 14:31:46 +0000460 * significant bit of value \c 1.
Paul Bakker5121ce52009-01-03 21:22:43 +0000461 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100462size_t mbedtls_mpi_bitlen(const mbedtls_mpi *X);
Paul Bakker5121ce52009-01-03 21:22:43 +0000463
464/**
Hanno Beckere1185042018-12-13 14:31:46 +0000465 * \brief Return the total size of an MPI value in bytes.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000466 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000467 * \param X The MPI to use. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000468 *
469 * \note The value returned by this function may be less than
470 * the number of bytes used to store \p X internally.
Hanno Beckere1185042018-12-13 14:31:46 +0000471 * This happens if and only if there are trailing bytes
472 * of value zero.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000473 *
474 * \return The least number of bytes capable of storing
475 * the absolute value of \p X.
Paul Bakker5121ce52009-01-03 21:22:43 +0000476 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100477size_t mbedtls_mpi_size(const mbedtls_mpi *X);
Paul Bakker5121ce52009-01-03 21:22:43 +0000478
479/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000480 * \brief Import an MPI from an ASCII string.
Paul Bakker5121ce52009-01-03 21:22:43 +0000481 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000482 * \param X The destination MPI. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000483 * \param radix The numeric base of the input string.
484 * \param s Null-terminated string buffer.
Paul Bakker5121ce52009-01-03 21:22:43 +0000485 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000486 * \return \c 0 if successful.
487 * \return A negative error code on failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000488 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100489int mbedtls_mpi_read_string(mbedtls_mpi *X, int radix, const char *s);
Paul Bakker5121ce52009-01-03 21:22:43 +0000490
491/**
Hanno Beckere1185042018-12-13 14:31:46 +0000492 * \brief Export an MPI to an ASCII string.
Paul Bakker5121ce52009-01-03 21:22:43 +0000493 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000494 * \param X The source MPI. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000495 * \param radix The numeric base of the output string.
Hanno Beckere1185042018-12-13 14:31:46 +0000496 * \param buf The buffer to write the string to. This must be writable
Hanno Beckerd7310122018-12-18 18:11:42 +0000497 * buffer of length \p buflen Bytes.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000498 * \param buflen The available size in Bytes of \p buf.
Hanno Beckere1185042018-12-13 14:31:46 +0000499 * \param olen The address at which to store the length of the string
500 * written, including the final \c NULL byte. This must
501 * not be \c NULL.
Paul Bakker5121ce52009-01-03 21:22:43 +0000502 *
Hanno Beckere1185042018-12-13 14:31:46 +0000503 * \note You can call this function with `buflen == 0` to obtain the
Hanno Beckerc23483e2018-12-10 17:21:19 +0000504 * minimum required buffer size in `*olen`.
Paul Bakker5121ce52009-01-03 21:22:43 +0000505 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000506 * \return \c 0 if successful.
507 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer \p buf
508 * is too small to hold the value of \p X in the desired base.
509 * In this case, `*olen` is nonetheless updated to contain the
510 * size of \p buf required for a successful call.
511 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000512 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100513int mbedtls_mpi_write_string(const mbedtls_mpi *X, int radix,
514 char *buf, size_t buflen, size_t *olen);
Paul Bakker5121ce52009-01-03 21:22:43 +0000515
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200516#if defined(MBEDTLS_FS_IO)
Paul Bakker5121ce52009-01-03 21:22:43 +0000517/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000518 * \brief Read an MPI from a line in an opened file.
Paul Bakker5121ce52009-01-03 21:22:43 +0000519 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000520 * \param X The destination MPI. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000521 * \param radix The numeric base of the string representation used
522 * in the source line.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000523 * \param fin The input file handle to use. This must not be \c NULL.
Hanno Beckerb2034b72017-04-26 11:46:46 +0100524 *
525 * \note On success, this function advances the file stream
526 * to the end of the current line or to EOF.
527 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000528 * The function returns \c 0 on an empty line.
Hanno Beckerb2034b72017-04-26 11:46:46 +0100529 *
530 * Leading whitespaces are ignored, as is a
Hanno Beckerc23483e2018-12-10 17:21:19 +0000531 * '0x' prefix for radix \c 16.
Hanno Beckerb2034b72017-04-26 11:46:46 +0100532 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000533 * \return \c 0 if successful.
534 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer
535 * is too small.
536 * \return Another negative error code on failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000537 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100538int mbedtls_mpi_read_file(mbedtls_mpi *X, int radix, FILE *fin);
Paul Bakker5121ce52009-01-03 21:22:43 +0000539
540/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000541 * \brief Export an MPI into an opened file.
Paul Bakker5121ce52009-01-03 21:22:43 +0000542 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000543 * \param p A string prefix to emit prior to the MPI data.
544 * For example, this might be a label, or "0x" when
Hanno Beckere1185042018-12-13 14:31:46 +0000545 * printing in base \c 16. This may be \c NULL if no prefix
Hanno Beckerc23483e2018-12-10 17:21:19 +0000546 * is needed.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000547 * \param X The source MPI. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000548 * \param radix The numeric base to be used in the emitted string.
Hanno Beckere1185042018-12-13 14:31:46 +0000549 * \param fout The output file handle. This may be \c NULL, in which case
550 * the output is written to \c stdout.
Paul Bakker5121ce52009-01-03 21:22:43 +0000551 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000552 * \return \c 0 if successful.
553 * \return A negative error code on failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000554 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100555int mbedtls_mpi_write_file(const char *p, const mbedtls_mpi *X,
556 int radix, FILE *fout);
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200557#endif /* MBEDTLS_FS_IO */
Paul Bakker5121ce52009-01-03 21:22:43 +0000558
559/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000560 * \brief Import an MPI from unsigned big endian binary data.
Paul Bakker5121ce52009-01-03 21:22:43 +0000561 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000562 * \param X The destination MPI. This must point to an initialized MPI.
Hanno Beckere1185042018-12-13 14:31:46 +0000563 * \param buf The input buffer. This must be a readable buffer of length
Hanno Beckerc23483e2018-12-10 17:21:19 +0000564 * \p buflen Bytes.
Andrzej Kurek69ed8c42022-02-17 10:06:44 -0500565 * \param buflen The length of the input buffer \p buf in Bytes.
Paul Bakker5121ce52009-01-03 21:22:43 +0000566 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000567 * \return \c 0 if successful.
568 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
569 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000570 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100571int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *buf,
572 size_t buflen);
Paul Bakker5121ce52009-01-03 21:22:43 +0000573
574/**
Janos Follatha778a942019-02-13 10:28:28 +0000575 * \brief Import X from unsigned binary data, little endian
576 *
577 * \param X The destination MPI. This must point to an initialized MPI.
578 * \param buf The input buffer. This must be a readable buffer of length
579 * \p buflen Bytes.
Andrzej Kurek69ed8c42022-02-17 10:06:44 -0500580 * \param buflen The length of the input buffer \p buf in Bytes.
Janos Follatha778a942019-02-13 10:28:28 +0000581 *
582 * \return \c 0 if successful.
583 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
584 * \return Another negative error code on different kinds of failure.
585 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100586int mbedtls_mpi_read_binary_le(mbedtls_mpi *X,
587 const unsigned char *buf, size_t buflen);
Janos Follatha778a942019-02-13 10:28:28 +0000588
589/**
590 * \brief Export X into unsigned binary data, big endian.
591 * Always fills the whole buffer, which will start with zeros
592 * if the number is smaller.
Paul Bakker5121ce52009-01-03 21:22:43 +0000593 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000594 * \param X The source MPI. This must point to an initialized MPI.
Hanno Beckere1185042018-12-13 14:31:46 +0000595 * \param buf The output buffer. This must be a writable buffer of length
Hanno Beckerc23483e2018-12-10 17:21:19 +0000596 * \p buflen Bytes.
597 * \param buflen The size of the output buffer \p buf in Bytes.
Paul Bakker5121ce52009-01-03 21:22:43 +0000598 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000599 * \return \c 0 if successful.
600 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
Hanno Beckere1185042018-12-13 14:31:46 +0000601 * large enough to hold the value of \p X.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000602 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000603 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100604int mbedtls_mpi_write_binary(const mbedtls_mpi *X, unsigned char *buf,
605 size_t buflen);
Paul Bakker5121ce52009-01-03 21:22:43 +0000606
607/**
Janos Follathe344d0f2019-02-19 16:17:40 +0000608 * \brief Export X into unsigned binary data, little endian.
609 * Always fills the whole buffer, which will end with zeros
610 * if the number is smaller.
611 *
612 * \param X The source MPI. This must point to an initialized MPI.
613 * \param buf The output buffer. This must be a writable buffer of length
614 * \p buflen Bytes.
615 * \param buflen The size of the output buffer \p buf in Bytes.
616 *
617 * \return \c 0 if successful.
618 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
619 * large enough to hold the value of \p X.
620 * \return Another negative error code on different kinds of failure.
621 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100622int mbedtls_mpi_write_binary_le(const mbedtls_mpi *X,
623 unsigned char *buf, size_t buflen);
Janos Follathe344d0f2019-02-19 16:17:40 +0000624
625/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000626 * \brief Perform a left-shift on an MPI: X <<= count
Paul Bakker5121ce52009-01-03 21:22:43 +0000627 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000628 * \param X The MPI to shift. This must point to an initialized MPI.
Minos Galanakis2056d092023-05-02 14:53:58 +0100629 * The MPI pointed by \p X may be resized to fit
630 * the resulting number.
Hanno Beckere1185042018-12-13 14:31:46 +0000631 * \param count The number of bits to shift by.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000632 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000633 * \return \c 0 if successful.
634 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
635 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000636 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100637int mbedtls_mpi_shift_l(mbedtls_mpi *X, size_t count);
Paul Bakker5121ce52009-01-03 21:22:43 +0000638
639/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000640 * \brief Perform a right-shift on an MPI: X >>= count
Paul Bakker5121ce52009-01-03 21:22:43 +0000641 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000642 * \param X The MPI to shift. This must point to an initialized MPI.
Hanno Beckere1185042018-12-13 14:31:46 +0000643 * \param count The number of bits to shift by.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000644 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000645 * \return \c 0 if successful.
646 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
647 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000648 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100649int mbedtls_mpi_shift_r(mbedtls_mpi *X, size_t count);
Paul Bakker5121ce52009-01-03 21:22:43 +0000650
651/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000652 * \brief Compare the absolute values of two MPIs.
Paul Bakker5121ce52009-01-03 21:22:43 +0000653 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000654 * \param X The left-hand MPI. This must point to an initialized MPI.
655 * \param Y The right-hand MPI. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000656 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000657 * \return \c 1 if `|X|` is greater than `|Y|`.
658 * \return \c -1 if `|X|` is lesser than `|Y|`.
Hanno Beckere1185042018-12-13 14:31:46 +0000659 * \return \c 0 if `|X|` is equal to `|Y|`.
Paul Bakker5121ce52009-01-03 21:22:43 +0000660 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100661int mbedtls_mpi_cmp_abs(const mbedtls_mpi *X, const mbedtls_mpi *Y);
Paul Bakker5121ce52009-01-03 21:22:43 +0000662
663/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000664 * \brief Compare two MPIs.
Paul Bakker5121ce52009-01-03 21:22:43 +0000665 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000666 * \param X The left-hand MPI. This must point to an initialized MPI.
667 * \param Y The right-hand MPI. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000668 *
Hanno Beckere1185042018-12-13 14:31:46 +0000669 * \return \c 1 if \p X is greater than \p Y.
670 * \return \c -1 if \p X is lesser than \p Y.
671 * \return \c 0 if \p X is equal to \p Y.
Paul Bakker5121ce52009-01-03 21:22:43 +0000672 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100673int mbedtls_mpi_cmp_mpi(const mbedtls_mpi *X, const mbedtls_mpi *Y);
Paul Bakker5121ce52009-01-03 21:22:43 +0000674
675/**
Janos Follath0e5532d2019-10-11 14:21:53 +0100676 * \brief Check if an MPI is less than the other in constant time.
Janos Follathee6abce2019-09-05 14:47:19 +0100677 *
678 * \param X The left-hand MPI. This must point to an initialized MPI
679 * with the same allocated length as Y.
680 * \param Y The right-hand MPI. This must point to an initialized MPI
681 * with the same allocated length as X.
682 * \param ret The result of the comparison:
Janos Follath0e5532d2019-10-11 14:21:53 +0100683 * \c 1 if \p X is less than \p Y.
684 * \c 0 if \p X is greater than or equal to \p Y.
Janos Follathee6abce2019-09-05 14:47:19 +0100685 *
686 * \return 0 on success.
687 * \return MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the allocated length of
688 * the two input MPIs is not the same.
689 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100690int mbedtls_mpi_lt_mpi_ct(const mbedtls_mpi *X, const mbedtls_mpi *Y,
691 unsigned *ret);
Janos Follathee6abce2019-09-05 14:47:19 +0100692
693/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000694 * \brief Compare an MPI with an integer.
Paul Bakker5121ce52009-01-03 21:22:43 +0000695 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000696 * \param X The left-hand MPI. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000697 * \param z The integer value to compare \p X to.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000698 *
Hanno Beckere1185042018-12-13 14:31:46 +0000699 * \return \c 1 if \p X is greater than \p z.
700 * \return \c -1 if \p X is lesser than \p z.
701 * \return \c 0 if \p X is equal to \p z.
Paul Bakker5121ce52009-01-03 21:22:43 +0000702 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100703int mbedtls_mpi_cmp_int(const mbedtls_mpi *X, mbedtls_mpi_sint z);
Paul Bakker5121ce52009-01-03 21:22:43 +0000704
705/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000706 * \brief Perform an unsigned addition of MPIs: X = |A| + |B|
Paul Bakker5121ce52009-01-03 21:22:43 +0000707 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000708 * \param X The destination MPI. This must point to an initialized MPI.
709 * \param A The first summand. This must point to an initialized MPI.
710 * \param B The second summand. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000711 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000712 * \return \c 0 if successful.
713 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
714 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000715 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100716int mbedtls_mpi_add_abs(mbedtls_mpi *X, const mbedtls_mpi *A,
717 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000718
719/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000720 * \brief Perform an unsigned subtraction of MPIs: X = |A| - |B|
Paul Bakker5121ce52009-01-03 21:22:43 +0000721 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000722 * \param X The destination MPI. This must point to an initialized MPI.
723 * \param A The minuend. This must point to an initialized MPI.
724 * \param B The subtrahend. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000725 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000726 * \return \c 0 if successful.
727 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is greater than \p A.
728 * \return Another negative error code on different kinds of failure.
729 *
Paul Bakker5121ce52009-01-03 21:22:43 +0000730 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100731int mbedtls_mpi_sub_abs(mbedtls_mpi *X, const mbedtls_mpi *A,
732 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000733
734/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000735 * \brief Perform a signed addition of MPIs: X = A + B
Paul Bakker5121ce52009-01-03 21:22:43 +0000736 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000737 * \param X The destination MPI. This must point to an initialized MPI.
738 * \param A The first summand. This must point to an initialized MPI.
739 * \param B The second summand. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000740 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000741 * \return \c 0 if successful.
742 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
743 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000744 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100745int mbedtls_mpi_add_mpi(mbedtls_mpi *X, const mbedtls_mpi *A,
746 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000747
748/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000749 * \brief Perform a signed subtraction of MPIs: X = A - B
Paul Bakker5121ce52009-01-03 21:22:43 +0000750 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000751 * \param X The destination MPI. This must point to an initialized MPI.
752 * \param A The minuend. This must point to an initialized MPI.
753 * \param B The subtrahend. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000754 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000755 * \return \c 0 if successful.
756 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
757 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000758 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100759int mbedtls_mpi_sub_mpi(mbedtls_mpi *X, const mbedtls_mpi *A,
760 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000761
762/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000763 * \brief Perform a signed addition of an MPI and an integer: X = A + b
Paul Bakker5121ce52009-01-03 21:22:43 +0000764 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000765 * \param X The destination MPI. This must point to an initialized MPI.
766 * \param A The first summand. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000767 * \param b The second summand.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000768 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000769 * \return \c 0 if successful.
770 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
771 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000772 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100773int mbedtls_mpi_add_int(mbedtls_mpi *X, const mbedtls_mpi *A,
774 mbedtls_mpi_sint b);
Paul Bakker5121ce52009-01-03 21:22:43 +0000775
776/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000777 * \brief Perform a signed subtraction of an MPI and an integer:
778 * X = A - b
Paul Bakker5121ce52009-01-03 21:22:43 +0000779 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000780 * \param X The destination MPI. This must point to an initialized MPI.
781 * \param A The minuend. This must point to an initialized MPI.
Hanno Becker01c3c102018-12-17 23:04:51 +0000782 * \param b The subtrahend.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000783 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000784 * \return \c 0 if successful.
785 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
786 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000787 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100788int mbedtls_mpi_sub_int(mbedtls_mpi *X, const mbedtls_mpi *A,
789 mbedtls_mpi_sint b);
Paul Bakker5121ce52009-01-03 21:22:43 +0000790
791/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000792 * \brief Perform a multiplication of two MPIs: X = A * B
Paul Bakker5121ce52009-01-03 21:22:43 +0000793 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000794 * \param X The destination MPI. This must point to an initialized MPI.
795 * \param A The first factor. This must point to an initialized MPI.
796 * \param B The second factor. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000797 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000798 * \return \c 0 if successful.
799 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
800 * \return Another negative error code on different kinds of failure.
801 *
Paul Bakker5121ce52009-01-03 21:22:43 +0000802 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100803int mbedtls_mpi_mul_mpi(mbedtls_mpi *X, const mbedtls_mpi *A,
804 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000805
806/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000807 * \brief Perform a multiplication of an MPI with an unsigned integer:
808 * X = A * b
Paul Bakker5121ce52009-01-03 21:22:43 +0000809 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000810 * \param X The destination MPI. This must point to an initialized MPI.
811 * \param A The first factor. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000812 * \param b The second factor.
Manuel Pégourié-Gonnard35f1d7f2015-03-19 12:42:40 +0000813 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000814 * \return \c 0 if successful.
815 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
816 * \return Another negative error code on different kinds of failure.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000817 *
Paul Bakker5121ce52009-01-03 21:22:43 +0000818 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100819int mbedtls_mpi_mul_int(mbedtls_mpi *X, const mbedtls_mpi *A,
820 mbedtls_mpi_uint b);
Paul Bakker5121ce52009-01-03 21:22:43 +0000821
822/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000823 * \brief Perform a division with remainder of two MPIs:
824 * A = Q * B + R
Paul Bakker5121ce52009-01-03 21:22:43 +0000825 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000826 * \param Q The destination MPI for the quotient.
Hanno Beckerd01ff492018-12-18 23:10:28 +0000827 * This may be \c NULL if the value of the
Glenn Strauss0750d082022-11-08 02:25:01 -0500828 * quotient is not needed. This must not alias A or B.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000829 * \param R The destination MPI for the remainder value.
Hanno Beckerd01ff492018-12-18 23:10:28 +0000830 * This may be \c NULL if the value of the
Glenn Strauss0750d082022-11-08 02:25:01 -0500831 * remainder is not needed. This must not alias A or B.
832 * \param A The dividend. This must point to an initialized MPI.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000833 * \param B The divisor. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000834 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000835 * \return \c 0 if successful.
836 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
Hanno Beckere1185042018-12-13 14:31:46 +0000837 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000838 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000839 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100840int mbedtls_mpi_div_mpi(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
841 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000842
843/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000844 * \brief Perform a division with remainder of an MPI by an integer:
845 * A = Q * b + R
Paul Bakker5121ce52009-01-03 21:22:43 +0000846 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000847 * \param Q The destination MPI for the quotient.
Hanno Beckerd01ff492018-12-18 23:10:28 +0000848 * This may be \c NULL if the value of the
Glenn Strauss0750d082022-11-08 02:25:01 -0500849 * quotient is not needed. This must not alias A.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000850 * \param R The destination MPI for the remainder value.
Hanno Beckerd01ff492018-12-18 23:10:28 +0000851 * This may be \c NULL if the value of the
Glenn Strauss0750d082022-11-08 02:25:01 -0500852 * remainder is not needed. This must not alias A.
Hanno Becker8ce11a32018-12-19 16:18:52 +0000853 * \param A The dividend. This must point to an initialized MPi.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000854 * \param b The divisor.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000855 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000856 * \return \c 0 if successful.
857 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
Hanno Beckere1185042018-12-13 14:31:46 +0000858 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000859 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000860 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100861int mbedtls_mpi_div_int(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
862 mbedtls_mpi_sint b);
Paul Bakker5121ce52009-01-03 21:22:43 +0000863
864/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000865 * \brief Perform a modular reduction. R = A mod B
Paul Bakker5121ce52009-01-03 21:22:43 +0000866 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000867 * \param R The destination MPI for the residue value.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000868 * This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000869 * \param A The MPI to compute the residue of.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000870 * This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000871 * \param B The base of the modular reduction.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000872 * This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000873 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000874 * \return \c 0 if successful.
875 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
Hanno Beckere1185042018-12-13 14:31:46 +0000876 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero.
877 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is negative.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000878 * \return Another negative error code on different kinds of failure.
879 *
Paul Bakker5121ce52009-01-03 21:22:43 +0000880 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100881int mbedtls_mpi_mod_mpi(mbedtls_mpi *R, const mbedtls_mpi *A,
882 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +0000883
884/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000885 * \brief Perform a modular reduction with respect to an integer.
886 * r = A mod b
Paul Bakker5121ce52009-01-03 21:22:43 +0000887 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000888 * \param r The address at which to store the residue.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000889 * This must not be \c NULL.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000890 * \param A The MPI to compute the residue of.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000891 * This must point to an initialized MPi.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000892 * \param b The integer base of the modular reduction.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000893 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000894 * \return \c 0 if successful.
895 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
Hanno Beckere1185042018-12-13 14:31:46 +0000896 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero.
897 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p b is negative.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000898 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +0000899 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100900int mbedtls_mpi_mod_int(mbedtls_mpi_uint *r, const mbedtls_mpi *A,
901 mbedtls_mpi_sint b);
Paul Bakker5121ce52009-01-03 21:22:43 +0000902
903/**
Manuel Pégourié-Gonnard75ed5872024-06-18 12:52:45 +0200904 * \brief Perform a modular exponentiation: X = A^E mod N
905 *
906 * \param X The destination MPI. This must point to an initialized MPI.
907 * This must not alias E or N.
908 * \param A The base of the exponentiation.
909 * This must point to an initialized MPI.
910 * \param E The exponent MPI. This must point to an initialized MPI.
911 * \param N The base for the modular reduction. This must point to an
912 * initialized MPI.
913 * \param prec_RR A helper MPI depending solely on \p N which can be used to
914 * speed-up multiple modular exponentiations for the same value
915 * of \p N. This may be \c NULL. If it is not \c NULL, it must
916 * point to an initialized MPI. If it hasn't been used after
917 * the call to mbedtls_mpi_init(), this function will compute
918 * the helper value and store it in \p prec_RR for reuse on
919 * subsequent calls to this function. Otherwise, the function
920 * will assume that \p prec_RR holds the helper value set by a
921 * previous call to mbedtls_mpi_exp_mod(), and reuse it.
922 *
923 * \return \c 0 if successful.
924 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
925 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \c N is negative or
926 * even, or if \c E is negative.
927 * \return Another negative error code on different kinds of failures.
928 *
929 */
930int mbedtls_mpi_exp_mod_optionally_safe(mbedtls_mpi *X, const mbedtls_mpi *A,
931 const mbedtls_mpi *E, const mbedtls_mpi *N,
932 mbedtls_mpi *prec_RR, int E_public);
933
934/**
935 * \brief Perform a modular exponentiation: X = A^E mod N
Paul Bakker5121ce52009-01-03 21:22:43 +0000936 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000937 * \param X The destination MPI. This must point to an initialized MPI.
Glenn Strauss0750d082022-11-08 02:25:01 -0500938 * This must not alias E or N.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000939 * \param A The base of the exponentiation.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000940 * This must point to an initialized MPI.
941 * \param E The exponent MPI. This must point to an initialized MPI.
942 * \param N The base for the modular reduction. This must point to an
Hanno Beckerc23483e2018-12-10 17:21:19 +0000943 * initialized MPI.
Yuto Takano538a0cb2021-07-14 10:20:09 +0100944 * \param prec_RR A helper MPI depending solely on \p N which can be used to
Hanno Beckerc23483e2018-12-10 17:21:19 +0000945 * speed-up multiple modular exponentiations for the same value
Hanno Beckere1185042018-12-13 14:31:46 +0000946 * of \p N. This may be \c NULL. If it is not \c NULL, it must
Hanno Becker8ce11a32018-12-19 16:18:52 +0000947 * point to an initialized MPI. If it hasn't been used after
Hanno Beckere1185042018-12-13 14:31:46 +0000948 * the call to mbedtls_mpi_init(), this function will compute
Yuto Takano538a0cb2021-07-14 10:20:09 +0100949 * the helper value and store it in \p prec_RR for reuse on
Hanno Beckere1185042018-12-13 14:31:46 +0000950 * subsequent calls to this function. Otherwise, the function
Yuto Takano538a0cb2021-07-14 10:20:09 +0100951 * will assume that \p prec_RR holds the helper value set by a
Hanno Beckere1185042018-12-13 14:31:46 +0000952 * previous call to mbedtls_mpi_exp_mod(), and reuse it.
Paul Bakker13e2dfe2009-07-28 07:18:38 +0000953 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000954 * \return \c 0 if successful.
955 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
956 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \c N is negative or
957 * even, or if \c E is negative.
958 * \return Another negative error code on different kinds of failures.
Paul Bakker5121ce52009-01-03 21:22:43 +0000959 *
Paul Bakker5121ce52009-01-03 21:22:43 +0000960 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100961int mbedtls_mpi_exp_mod(mbedtls_mpi *X, const mbedtls_mpi *A,
962 const mbedtls_mpi *E, const mbedtls_mpi *N,
963 mbedtls_mpi *prec_RR);
Paul Bakker5121ce52009-01-03 21:22:43 +0000964
965/**
Hanno Beckerc23483e2018-12-10 17:21:19 +0000966 * \brief Fill an MPI with a number of random bytes.
Paul Bakker287781a2011-03-26 13:18:49 +0000967 *
Hanno Becker8282c2f2018-12-12 13:36:46 +0000968 * \param X The destination MPI. This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +0000969 * \param size The number of random bytes to generate.
Hanno Becker8282c2f2018-12-12 13:36:46 +0000970 * \param f_rng The RNG function to use. This must not be \c NULL.
Hanno Beckere1185042018-12-13 14:31:46 +0000971 * \param p_rng The RNG parameter to be passed to \p f_rng. This may be
972 * \c NULL if \p f_rng doesn't need a context argument.
Paul Bakker287781a2011-03-26 13:18:49 +0000973 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000974 * \return \c 0 if successful.
975 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
976 * \return Another negative error code on failure.
Hanno Becker15f2b3e2017-10-17 15:17:05 +0100977 *
Hanno Beckerc23483e2018-12-10 17:21:19 +0000978 * \note The bytes obtained from the RNG are interpreted
Hanno Becker15f2b3e2017-10-17 15:17:05 +0100979 * as a big-endian representation of an MPI; this can
980 * be relevant in applications like deterministic ECDSA.
Paul Bakker287781a2011-03-26 13:18:49 +0000981 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100982int mbedtls_mpi_fill_random(mbedtls_mpi *X, size_t size,
983 int (*f_rng)(void *, unsigned char *, size_t),
984 void *p_rng);
Paul Bakker287781a2011-03-26 13:18:49 +0000985
Gilles Peskine02ac93a2021-03-29 22:02:55 +0200986/** Generate a random number uniformly in a range.
987 *
988 * This function generates a random number between \p min inclusive and
989 * \p N exclusive.
990 *
991 * The procedure complies with RFC 6979 §3.3 (deterministic ECDSA)
992 * when the RNG is a suitably parametrized instance of HMAC_DRBG
993 * and \p min is \c 1.
994 *
995 * \note There are `N - min` possible outputs. The lower bound
996 * \p min can be reached, but the upper bound \p N cannot.
997 *
998 * \param X The destination MPI. This must point to an initialized MPI.
999 * \param min The minimum value to return.
1000 * It must be nonnegative.
1001 * \param N The upper bound of the range, exclusive.
1002 * In other words, this is one plus the maximum value to return.
1003 * \p N must be strictly larger than \p min.
1004 * \param f_rng The RNG function to use. This must not be \c NULL.
1005 * \param p_rng The RNG parameter to be passed to \p f_rng.
1006 *
1007 * \return \c 0 if successful.
1008 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
Gilles Peskine1e918f42021-03-29 22:14:51 +02001009 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p min or \p N is invalid
1010 * or if they are incompatible.
Gilles Peskine7ed7c5a2021-04-13 21:28:38 +02001011 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if the implementation was
1012 * unable to find a suitable value within a limited number
1013 * of attempts. This has a negligible probability if \p N
1014 * is significantly larger than \p min, which is the case
1015 * for all usual cryptographic applications.
Gilles Peskine02ac93a2021-03-29 22:02:55 +02001016 * \return Another negative error code on failure.
1017 */
Gilles Peskine449bd832023-01-11 14:50:10 +01001018int mbedtls_mpi_random(mbedtls_mpi *X,
1019 mbedtls_mpi_sint min,
1020 const mbedtls_mpi *N,
1021 int (*f_rng)(void *, unsigned char *, size_t),
1022 void *p_rng);
Gilles Peskine02ac93a2021-03-29 22:02:55 +02001023
Paul Bakker287781a2011-03-26 13:18:49 +00001024/**
Hanno Beckerc23483e2018-12-10 17:21:19 +00001025 * \brief Compute the greatest common divisor: G = gcd(A, B)
Paul Bakker5121ce52009-01-03 21:22:43 +00001026 *
Hanno Becker8282c2f2018-12-12 13:36:46 +00001027 * \param G The destination MPI. This must point to an initialized MPI.
1028 * \param A The first operand. This must point to an initialized MPI.
Hanno Becker01c3c102018-12-17 23:04:51 +00001029 * \param B The second operand. This must point to an initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +00001030 *
Hanno Beckerc23483e2018-12-10 17:21:19 +00001031 * \return \c 0 if successful.
1032 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
1033 * \return Another negative error code on different kinds of failure.
Paul Bakker5121ce52009-01-03 21:22:43 +00001034 */
Gilles Peskine449bd832023-01-11 14:50:10 +01001035int mbedtls_mpi_gcd(mbedtls_mpi *G, const mbedtls_mpi *A,
1036 const mbedtls_mpi *B);
Paul Bakker5121ce52009-01-03 21:22:43 +00001037
1038/**
Hanno Beckerc23483e2018-12-10 17:21:19 +00001039 * \brief Compute the modular inverse: X = A^-1 mod N
Paul Bakker5121ce52009-01-03 21:22:43 +00001040 *
Hanno Becker8282c2f2018-12-12 13:36:46 +00001041 * \param X The destination MPI. This must point to an initialized MPI.
1042 * \param A The MPI to calculate the modular inverse of. This must point
Hanno Beckerc23483e2018-12-10 17:21:19 +00001043 * to an initialized MPI.
Hanno Becker8282c2f2018-12-12 13:36:46 +00001044 * \param N The base of the modular inversion. This must point to an
Hanno Beckerc23483e2018-12-10 17:21:19 +00001045 * initialized MPI.
Paul Bakker13e2dfe2009-07-28 07:18:38 +00001046 *
Hanno Beckerc23483e2018-12-10 17:21:19 +00001047 * \return \c 0 if successful.
1048 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
Hanno Beckere1185042018-12-13 14:31:46 +00001049 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p N is less than
1050 * or equal to one.
Andrzej Kurek69ed8c42022-02-17 10:06:44 -05001051 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p A has no modular
1052 * inverse with respect to \p N.
Paul Bakker5121ce52009-01-03 21:22:43 +00001053 */
Gilles Peskine449bd832023-01-11 14:50:10 +01001054int mbedtls_mpi_inv_mod(mbedtls_mpi *X, const mbedtls_mpi *A,
1055 const mbedtls_mpi *N);
Paul Bakker5121ce52009-01-03 21:22:43 +00001056
Paul Bakker5121ce52009-01-03 21:22:43 +00001057/**
Janos Follatha0b67c22018-09-18 14:48:23 +01001058 * \brief Miller-Rabin primality test.
1059 *
1060 * \warning If \p X is potentially generated by an adversary, for example
1061 * when validating cryptographic parameters that you didn't
1062 * generate yourself and that are supposed to be prime, then
1063 * \p rounds should be at least the half of the security
1064 * strength of the cryptographic algorithm. On the other hand,
Tom Cosgrove1e211442022-05-26 11:51:00 +01001065 * if \p X is chosen uniformly or non-adversarially (as is the
Janos Follatha0b67c22018-09-18 14:48:23 +01001066 * case when mbedtls_mpi_gen_prime calls this function), then
1067 * \p rounds can be much lower.
1068 *
Hanno Beckerc23483e2018-12-10 17:21:19 +00001069 * \param X The MPI to check for primality.
Hanno Becker8282c2f2018-12-12 13:36:46 +00001070 * This must point to an initialized MPI.
Hanno Beckerc23483e2018-12-10 17:21:19 +00001071 * \param rounds The number of bases to perform the Miller-Rabin primality
1072 * test for. The probability of returning 0 on a composite is
David Horstmannd855b462023-02-23 18:39:16 +00001073 * at most 2<sup>-2*\p rounds </sup>.
Hanno Becker8282c2f2018-12-12 13:36:46 +00001074 * \param f_rng The RNG function to use. This must not be \c NULL.
Hanno Beckerc23483e2018-12-10 17:21:19 +00001075 * \param p_rng The RNG parameter to be passed to \p f_rng.
Hanno Beckere1185042018-12-13 14:31:46 +00001076 * This may be \c NULL if \p f_rng doesn't use
1077 * a context parameter.
Janos Follatha0b67c22018-09-18 14:48:23 +01001078 *
Hanno Beckerc23483e2018-12-10 17:21:19 +00001079 * \return \c 0 if successful, i.e. \p X is probably prime.
1080 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
1081 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime.
1082 * \return Another negative error code on other kinds of failure.
Janos Follatha0b67c22018-09-18 14:48:23 +01001083 */
Gilles Peskine449bd832023-01-11 14:50:10 +01001084int mbedtls_mpi_is_prime_ext(const mbedtls_mpi *X, int rounds,
1085 int (*f_rng)(void *, unsigned char *, size_t),
1086 void *p_rng);
Janos Follatha0b67c22018-09-18 14:48:23 +01001087/**
Janos Follath7c025a92018-08-14 11:08:41 +01001088 * \brief Flags for mbedtls_mpi_gen_prime()
1089 *
1090 * Each of these flags is a constraint on the result X returned by
1091 * mbedtls_mpi_gen_prime().
1092 */
1093typedef enum {
Janos Follathf301d232018-08-14 13:34:01 +01001094 MBEDTLS_MPI_GEN_PRIME_FLAG_DH = 0x0001, /**< (X-1)/2 is prime too */
1095 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 +01001096} mbedtls_mpi_gen_prime_flag_t;
1097
1098/**
Hanno Beckerc23483e2018-12-10 17:21:19 +00001099 * \brief Generate a prime number.
Paul Bakker5121ce52009-01-03 21:22:43 +00001100 *
Hanno Beckerc23483e2018-12-10 17:21:19 +00001101 * \param X The destination MPI to store the generated prime in.
Hanno Becker8282c2f2018-12-12 13:36:46 +00001102 * This must point to an initialized MPi.
Hanno Beckerc23483e2018-12-10 17:21:19 +00001103 * \param nbits The required size of the destination MPI in bits.
Hanno Beckerd01ff492018-12-18 23:10:28 +00001104 * This must be between \c 3 and #MBEDTLS_MPI_MAX_BITS.
Hanno Beckerc23483e2018-12-10 17:21:19 +00001105 * \param flags A mask of flags of type #mbedtls_mpi_gen_prime_flag_t.
Hanno Becker8282c2f2018-12-12 13:36:46 +00001106 * \param f_rng The RNG function to use. This must not be \c NULL.
Hanno Beckerc23483e2018-12-10 17:21:19 +00001107 * \param p_rng The RNG parameter to be passed to \p f_rng.
Hanno Beckere1185042018-12-13 14:31:46 +00001108 * This may be \c NULL if \p f_rng doesn't use
1109 * a context parameter.
Paul Bakker5121ce52009-01-03 21:22:43 +00001110 *
Hanno Beckere1185042018-12-13 14:31:46 +00001111 * \return \c 0 if successful, in which case \p X holds a
Hanno Beckerc23483e2018-12-10 17:21:19 +00001112 * probably prime number.
1113 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
1114 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `nbits` is not between
1115 * \c 3 and #MBEDTLS_MPI_MAX_BITS.
Paul Bakker5121ce52009-01-03 21:22:43 +00001116 */
Gilles Peskine449bd832023-01-11 14:50:10 +01001117int mbedtls_mpi_gen_prime(mbedtls_mpi *X, size_t nbits, int flags,
1118 int (*f_rng)(void *, unsigned char *, size_t),
1119 void *p_rng);
Paul Bakker5121ce52009-01-03 21:22:43 +00001120
Ron Eldorfa8f6352017-06-20 15:48:46 +03001121#if defined(MBEDTLS_SELF_TEST)
1122
Paul Bakker5121ce52009-01-03 21:22:43 +00001123/**
1124 * \brief Checkup routine
1125 *
1126 * \return 0 if successful, or 1 if the test failed
1127 */
Gilles Peskine449bd832023-01-11 14:50:10 +01001128int mbedtls_mpi_self_test(int verbose);
Paul Bakker5121ce52009-01-03 21:22:43 +00001129
Ron Eldorfa8f6352017-06-20 15:48:46 +03001130#endif /* MBEDTLS_SELF_TEST */
1131
Paul Bakker5121ce52009-01-03 21:22:43 +00001132#ifdef __cplusplus
1133}
1134#endif
1135
1136#endif /* bignum.h */