/**
* \file bignum.h
*
* \brief Multi-precision integer library
*/
/*
* Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
* SPDX-License-Identifier: Apache-2.0
*
* Licensed under the Apache License, Version 2.0 (the "License"); you may
* not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
* This file is part of mbed TLS (https://tls.mbed.org)
*/
#ifndef MBEDTLS_BIGNUM_H
#define MBEDTLS_BIGNUM_H
#if !defined(MBEDTLS_CONFIG_FILE)
#include "mbedtls/config.h"
#else
#include MBEDTLS_CONFIG_FILE
#endif
#include <stddef.h>
#include <stdint.h>
#if defined(MBEDTLS_FS_IO)
#include <stdio.h>
#endif
#define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002 /**< An error occurred while reading from or writing to a file. */
#define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004 /**< Bad input parameters to function. */
#define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006 /**< There is an invalid character in the digit string. */
#define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008 /**< The buffer is too small to write to. */
#define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A /**< The input arguments are negative or result in illegal output. */
#define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C /**< The input argument for division is zero, which is not allowed. */
#define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E /**< The input arguments are not acceptable. */
#define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010 /**< Memory allocation failed. */
#define MBEDTLS_MPI_CHK(f) \
do \
{ \
if( ( ret = (f) ) != 0 ) \
goto cleanup; \
} while( 0 )
/*
* Maximum size MPIs are allowed to grow to in number of limbs.
*/
#define MBEDTLS_MPI_MAX_LIMBS 10000
#if !defined(MBEDTLS_MPI_WINDOW_SIZE)
/*
* Maximum window size used for modular exponentiation. Default: 6
* Minimum value: 1. Maximum value: 6.
*
* Result is an array of ( 2 << MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
* for the sliding window calculation. (So 64 by default)
*
* Reduction in size, reduces speed.
*/
#define MBEDTLS_MPI_WINDOW_SIZE 6 /**< Maximum windows size used. */
#endif /* !MBEDTLS_MPI_WINDOW_SIZE */
#if !defined(MBEDTLS_MPI_MAX_SIZE)
/*
* Maximum size of MPIs allowed in bits and bytes for user-MPIs.
* ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
*
* Note: Calculations can temporarily result in larger MPIs. So the number
* of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
*/
#define MBEDTLS_MPI_MAX_SIZE 1024 /**< Maximum number of bytes for usable MPIs. */
#endif /* !MBEDTLS_MPI_MAX_SIZE */
#define MBEDTLS_MPI_MAX_BITS ( 8 * MBEDTLS_MPI_MAX_SIZE ) /**< Maximum number of bits for usable MPIs. */
/*
* When reading from files with mbedtls_mpi_read_file() and writing to files with
* mbedtls_mpi_write_file() the buffer should have space
* for a (short) label, the MPI (in the provided radix), the newline
* characters and the '\0'.
*
* By default we assume at least a 10 char label, a minimum radix of 10
* (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
* Autosized at compile time for at least a 10 char label, a minimum radix
* of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
*
* This used to be statically sized to 1250 for a maximum of 4096 bit
* numbers (1234 decimal chars).
*
* Calculate using the formula:
* MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
* LabelSize + 6
*/
#define MBEDTLS_MPI_MAX_BITS_SCALE100 ( 100 * MBEDTLS_MPI_MAX_BITS )
#define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332
#define MBEDTLS_MPI_RW_BUFFER_SIZE ( ((MBEDTLS_MPI_MAX_BITS_SCALE100 + MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6 )
/*
* Define the base integer type, architecture-wise.
*
* 32 or 64-bit integer types can be forced regardless of the underlying
* architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
* respectively and undefining MBEDTLS_HAVE_ASM.
*
* Double-width integers (e.g. 128-bit in 64-bit architectures) can be
* disabled by defining MBEDTLS_NO_UDBL_DIVISION.
*/
#if !defined(MBEDTLS_HAVE_INT32)
#if defined(_MSC_VER) && defined(_M_AMD64)
/* Always choose 64-bit when using MSC */
#if !defined(MBEDTLS_HAVE_INT64)
#define MBEDTLS_HAVE_INT64
#endif /* !MBEDTLS_HAVE_INT64 */
typedef int64_t mbedtls_mpi_sint;
typedef uint64_t mbedtls_mpi_uint;
#elif defined(__GNUC__) && ( \
defined(__amd64__) || defined(__x86_64__) || \
defined(__ppc64__) || defined(__powerpc64__) || \
defined(__ia64__) || defined(__alpha__) || \
( defined(__sparc__) && defined(__arch64__) ) || \
defined(__s390x__) || defined(__mips64) || \
defined(__aarch64__) )
#if !defined(MBEDTLS_HAVE_INT64)
#define MBEDTLS_HAVE_INT64
#endif /* MBEDTLS_HAVE_INT64 */
typedef int64_t mbedtls_mpi_sint;
typedef uint64_t mbedtls_mpi_uint;
#if !defined(MBEDTLS_NO_UDBL_DIVISION)
/* mbedtls_t_udbl defined as 128-bit unsigned int */
typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
#define MBEDTLS_HAVE_UDBL
#endif /* !MBEDTLS_NO_UDBL_DIVISION */
#elif defined(__ARMCC_VERSION) && defined(__aarch64__)
/*
* __ARMCC_VERSION is defined for both armcc and armclang and
* __aarch64__ is only defined by armclang when compiling 64-bit code
*/
#if !defined(MBEDTLS_HAVE_INT64)
#define MBEDTLS_HAVE_INT64
#endif /* !MBEDTLS_HAVE_INT64 */
typedef int64_t mbedtls_mpi_sint;
typedef uint64_t mbedtls_mpi_uint;
#if !defined(MBEDTLS_NO_UDBL_DIVISION)
/* mbedtls_t_udbl defined as 128-bit unsigned int */
typedef __uint128_t mbedtls_t_udbl;
#define MBEDTLS_HAVE_UDBL
#endif /* !MBEDTLS_NO_UDBL_DIVISION */
#elif defined(MBEDTLS_HAVE_INT64)
/* Force 64-bit integers with unknown compiler */
typedef int64_t mbedtls_mpi_sint;
typedef uint64_t mbedtls_mpi_uint;
#endif
#endif /* !MBEDTLS_HAVE_INT32 */
#if !defined(MBEDTLS_HAVE_INT64)
/* Default to 32-bit compilation */
#if !defined(MBEDTLS_HAVE_INT32)
#define MBEDTLS_HAVE_INT32
#endif /* !MBEDTLS_HAVE_INT32 */
typedef int32_t mbedtls_mpi_sint;
typedef uint32_t mbedtls_mpi_uint;
#if !defined(MBEDTLS_NO_UDBL_DIVISION)
typedef uint64_t mbedtls_t_udbl;
#define MBEDTLS_HAVE_UDBL
#endif /* !MBEDTLS_NO_UDBL_DIVISION */
#endif /* !MBEDTLS_HAVE_INT64 */
#ifdef __cplusplus
extern "C" {
#endif
/**
* \brief MPI structure
*/
typedef struct mbedtls_mpi
{
int s; /*!< Sign: -1 if the mpi is negative, 1 otherwise */
size_t n; /*!< total # of limbs */
mbedtls_mpi_uint *p; /*!< pointer to limbs */
}
mbedtls_mpi;
/**
* \brief Initialize an MPI context.
*
* This makes the MPI ready to be set or freed,
* but does not define a value for the MPI.
*
* \param X The MPI context to initialize. This must not be \c NULL.
*/
void mbedtls_mpi_init( mbedtls_mpi *X );
/**
* \brief This function frees the components of an MPI context.
*
* \param X The MPI context to be cleared. This may be \c NULL,
* in which case this function is a no-op. If it is
* not \c NULL, it must point to an initialized MPI.
*/
void mbedtls_mpi_free( mbedtls_mpi *X );
/**
* \brief Enlarge an MPI to the specified number of limbs.
*
* \note This function does nothing if the MPI is
* already large enough.
*
* \param X The MPI to grow. It must be initialized.
* \param nblimbs The target number of limbs.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
/**
* \brief This function resizes an MPI downwards, keeping at least the
* specified number of limbs.
*
* If \c X is smaller than \c nblimbs, it is resized up
* instead.
*
* \param X The MPI to shrink. This must point to an initialized MPI.
* \param nblimbs The minimum number of limbs to keep.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
* (this can only happen when resizing up).
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
/**
* \brief Make a copy of an MPI.
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param Y The source MPI. This must point to an initialized MPI.
*
* \note The limb-buffer in the destination MPI is enlarged
* if necessary to hold the value in the source MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
/**
* \brief Swap the contents of two MPIs.
*
* \param X The first MPI. It must be initialized.
* \param Y The second MPI. It must be initialized.
*/
void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y );
/**
* \brief Perform a safe conditional copy of MPI which doesn't
* reveal whether the condition was true or not.
*
* \param X The MPI to conditionally assign to. This must point
* to an initialized MPI.
* \param Y The MPI to be assigned from. This must point to an
* initialized MPI.
* \param assign The condition deciding whether to perform the
* assignment or not. Possible values:
* * \c 1: Perform the assignment `X = Y`.
* * \c 0: Keep the original value of \p X.
*
* \note This function is equivalent to
* `if( assign ) mbedtls_mpi_copy( X, Y );`
* except that it avoids leaking any information about whether
* the assignment was done or not (the above code may leak
* information through branch prediction and/or memory access
* patterns analysis).
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
/**
* \brief Perform a safe conditional swap which doesn't
* reveal whether the condition was true or not.
*
* \param X The first MPI. This must be initialized.
* \param Y The second MPI. This must be initialized.
* \param assign The condition deciding whether to perform
* the swap or not. Possible values:
* * \c 1: Swap the values of \p X and \p Y.
* * \c 0: Keep the original values of \p X and \p Y.
*
* \note This function is equivalent to
* if( assign ) mbedtls_mpi_swap( X, Y );
* except that it avoids leaking any information about whether
* the assignment was done or not (the above code may leak
* information through branch prediction and/or memory access
* patterns analysis).
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on other kinds of failure.
*
*/
int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
/**
* \brief Store integer value in MPI.
*
* \param X The MPI to set. This must be initialized.
* \param z The value to use.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z );
/**
* \brief Get a specific bit from an MPI.
*
* \param X The MPI to query. This must be initialized.
* \param pos Zero-based index of the bit to query.
*
* \return \c 0 or \c 1 on success, depending on whether bit \c pos
* of \c X is unset or set.
* \return A negative error code on failure.
*/
int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
/**
* \brief Modify a specific bit in an MPI.
*
* \note This function will grow the target MPI if necessary to set a
* bit to \c 1 in a not yet existing limb. It will not grow if
* the bit should be set to \c 0.
*
* \param X The MPI to modify. This must be initialized.
* \param pos Zero-based index of the bit to modify.
* \param val The desired value of bit \c pos: \c 0 or \c 1.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val );
/**
* \brief Return the number of bits of value \c 0 before the
* least significant bit of value \c 1.
*
* \note This is the same as the zero-based index of
* the least significant bit of value \c 1.
*
* \param X The MPI to query.
*
* \return The number of bits of value \c 0 before the least significant
* bit of value \c 1 in \p X.
*/
size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
/**
* \brief Return the number of bits up to and including the most
* significant bit of value \c 1.
*
* * \note This is same as the one-based index of the most
* significant bit of value \c 1.
*
* \param X The MPI to query. This must point to an initialized MPI.
*
* \return The number of bits up to and including the most
* significant bit of value \c 1.
*/
size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
/**
* \brief Return the total size of an MPI value in bytes.
*
* \param X The MPI to use. This must point to an initialized MPI.
*
* \note The value returned by this function may be less than
* the number of bytes used to store \p X internally.
* This happens if and only if there are trailing bytes
* of value zero.
*
* \return The least number of bytes capable of storing
* the absolute value of \p X.
*/
size_t mbedtls_mpi_size( const mbedtls_mpi *X );
/**
* \brief Import an MPI from an ASCII string.
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param radix The numeric base of the input string.
* \param s Null-terminated string buffer.
*
* \return \c 0 if successful.
* \return A negative error code on failure.
*/
int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
/**
* \brief Export an MPI to an ASCII string.
*
* \param X The source MPI. This must point to an initialized MPI.
* \param radix The numeric base of the output string.
* \param buf The buffer to write the string to. This must be writable
* buffer of length \p buflen Bytes.
* \param buflen The available size in Bytes of \p buf.
* \param olen The address at which to store the length of the string
* written, including the final \c NULL byte. This must
* not be \c NULL.
*
* \note You can call this function with `buflen == 0` to obtain the
* minimum required buffer size in `*olen`.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer \p buf
* is too small to hold the value of \p X in the desired base.
* In this case, `*olen` is nonetheless updated to contain the
* size of \p buf required for a successful call.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
char *buf, size_t buflen, size_t *olen );
#if defined(MBEDTLS_FS_IO)
/**
* \brief Read an MPI from a line in an opened file.
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param radix The numeric base of the string representation used
* in the source line.
* \param fin The input file handle to use. This must not be \c NULL.
*
* \note On success, this function advances the file stream
* to the end of the current line or to EOF.
*
* The function returns \c 0 on an empty line.
*
* Leading whitespaces are ignored, as is a
* '0x' prefix for radix \c 16.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer
* is too small.
* \return Another negative error code on failure.
*/
int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
/**
* \brief Export an MPI into an opened file.
*
* \param p A string prefix to emit prior to the MPI data.
* For example, this might be a label, or "0x" when
* printing in base \c 16. This may be \c NULL if no prefix
* is needed.
* \param X The source MPI. This must point to an initialized MPI.
* \param radix The numeric base to be used in the emitted string.
* \param fout The output file handle. This may be \c NULL, in which case
* the output is written to \c stdout.
*
* \return \c 0 if successful.
* \return A negative error code on failure.
*/
int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X,
int radix, FILE *fout );
#endif /* MBEDTLS_FS_IO */
/**
* \brief Import an MPI from unsigned big endian binary data.
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param buf The input buffer. This must be a readable buffer of length
* \p buflen Bytes.
* \param buflen The length of the input buffer \p p in Bytes.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf,
size_t buflen );
/**
* \brief Import X from unsigned binary data, little endian
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param buf The input buffer. This must be a readable buffer of length
* \p buflen Bytes.
* \param buflen The length of the input buffer \p p in Bytes.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_read_binary_le( mbedtls_mpi *X,
const unsigned char *buf, size_t buflen );
/**
* \brief Export X into unsigned binary data, big endian.
* Always fills the whole buffer, which will start with zeros
* if the number is smaller.
*
* \param X The source MPI. This must point to an initialized MPI.
* \param buf The output buffer. This must be a writable buffer of length
* \p buflen Bytes.
* \param buflen The size of the output buffer \p buf in Bytes.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
* large enough to hold the value of \p X.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf,
size_t buflen );
/**
* \brief Export X into unsigned binary data, little endian.
* Always fills the whole buffer, which will end with zeros
* if the number is smaller.
*
* \param X The source MPI. This must point to an initialized MPI.
* \param buf The output buffer. This must be a writable buffer of length
* \p buflen Bytes.
* \param buflen The size of the output buffer \p buf in Bytes.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
* large enough to hold the value of \p X.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_write_binary_le( const mbedtls_mpi *X,
unsigned char *buf, size_t buflen );
/**
* \brief Perform a left-shift on an MPI: X <<= count
*
* \param X The MPI to shift. This must point to an initialized MPI.
* \param count The number of bits to shift by.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
/**
* \brief Perform a right-shift on an MPI: X >>= count
*
* \param X The MPI to shift. This must point to an initialized MPI.
* \param count The number of bits to shift by.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count );
/**
* \brief Compare the absolute values of two MPIs.
*
* \param X The left-hand MPI. This must point to an initialized MPI.
* \param Y The right-hand MPI. This must point to an initialized MPI.
*
* \return \c 1 if `|X|` is greater than `|Y|`.
* \return \c -1 if `|X|` is lesser than `|Y|`.
* \return \c 0 if `|X|` is equal to `|Y|`.
*/
int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
/**
* \brief Compare two MPIs.
*
* \param X The left-hand MPI. This must point to an initialized MPI.
* \param Y The right-hand MPI. This must point to an initialized MPI.
*
* \return \c 1 if \p X is greater than \p Y.
* \return \c -1 if \p X is lesser than \p Y.
* \return \c 0 if \p X is equal to \p Y.
*/
int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
/**
* \brief Check if an MPI is less than the other in constant time.
*
* \param X The left-hand MPI. This must point to an initialized MPI
* with the same allocated length as Y.
* \param Y The right-hand MPI. This must point to an initialized MPI
* with the same allocated length as X.
* \param ret The result of the comparison:
* \c 1 if \p X is less than \p Y.
* \c 0 if \p X is greater than or equal to \p Y.
*
* \return 0 on success.
* \return MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the allocated length of
* the two input MPIs is not the same.
*/
int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y,
unsigned *ret );
/**
* \brief Compare an MPI with an integer.
*
* \param X The left-hand MPI. This must point to an initialized MPI.
* \param z The integer value to compare \p X to.
*
* \return \c 1 if \p X is greater than \p z.
* \return \c -1 if \p X is lesser than \p z.
* \return \c 0 if \p X is equal to \p z.
*/
int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z );
/**
* \brief Perform an unsigned addition of MPIs: X = |A| + |B|
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The first summand. This must point to an initialized MPI.
* \param B The second summand. This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A,
const mbedtls_mpi *B );
/**
* \brief Perform an unsigned subtraction of MPIs: X = |A| - |B|
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The minuend. This must point to an initialized MPI.
* \param B The subtrahend. This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is greater than \p A.
* \return Another negative error code on different kinds of failure.
*
*/
int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A,
const mbedtls_mpi *B );
/**
* \brief Perform a signed addition of MPIs: X = A + B
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The first summand. This must point to an initialized MPI.
* \param B The second summand. This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
const mbedtls_mpi *B );
/**
* \brief Perform a signed subtraction of MPIs: X = A - B
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The minuend. This must point to an initialized MPI.
* \param B The subtrahend. This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
const mbedtls_mpi *B );
/**
* \brief Perform a signed addition of an MPI and an integer: X = A + b
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The first summand. This must point to an initialized MPI.
* \param b The second summand.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A,
mbedtls_mpi_sint b );
/**
* \brief Perform a signed subtraction of an MPI and an integer:
* X = A - b
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The minuend. This must point to an initialized MPI.
* \param b The subtrahend.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A,
mbedtls_mpi_sint b );
/**
* \brief Perform a multiplication of two MPIs: X = A * B
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The first factor. This must point to an initialized MPI.
* \param B The second factor. This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*
*/
int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
const mbedtls_mpi *B );
/**
* \brief Perform a multiplication of an MPI with an unsigned integer:
* X = A * b
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The first factor. This must point to an initialized MPI.
* \param b The second factor.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*
*/
int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A,
mbedtls_mpi_uint b );
/**
* \brief Perform a division with remainder of two MPIs:
* A = Q * B + R
*
* \param Q The destination MPI for the quotient.
* This may be \c NULL if the value of the
* quotient is not needed.
* \param R The destination MPI for the remainder value.
* This may be \c NULL if the value of the
* remainder is not needed.
* \param A The dividend. This must point to an initialized MPi.
* \param B The divisor. This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
const mbedtls_mpi *B );
/**
* \brief Perform a division with remainder of an MPI by an integer:
* A = Q * b + R
*
* \param Q The destination MPI for the quotient.
* This may be \c NULL if the value of the
* quotient is not needed.
* \param R The destination MPI for the remainder value.
* This may be \c NULL if the value of the
* remainder is not needed.
* \param A The dividend. This must point to an initialized MPi.
* \param b The divisor.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
mbedtls_mpi_sint b );
/**
* \brief Perform a modular reduction. R = A mod B
*
* \param R The destination MPI for the residue value.
* This must point to an initialized MPI.
* \param A The MPI to compute the residue of.
* This must point to an initialized MPI.
* \param B The base of the modular reduction.
* This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero.
* \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is negative.
* \return Another negative error code on different kinds of failure.
*
*/
int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A,
const mbedtls_mpi *B );
/**
* \brief Perform a modular reduction with respect to an integer.
* r = A mod b
*
* \param r The address at which to store the residue.
* This must not be \c NULL.
* \param A The MPI to compute the residue of.
* This must point to an initialized MPi.
* \param b The integer base of the modular reduction.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero.
* \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p b is negative.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A,
mbedtls_mpi_sint b );
/**
* \brief Perform a sliding-window exponentiation: X = A^E mod N
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The base of the exponentiation.
* This must point to an initialized MPI.
* \param E The exponent MPI. This must point to an initialized MPI.
* \param N The base for the modular reduction. This must point to an
* initialized MPI.
* \param _RR A helper MPI depending solely on \p N which can be used to
* speed-up multiple modular exponentiations for the same value
* of \p N. This may be \c NULL. If it is not \c NULL, it must
* point to an initialized MPI. If it hasn't been used after
* the call to mbedtls_mpi_init(), this function will compute
* the helper value and store it in \p _RR for reuse on
* subsequent calls to this function. Otherwise, the function
* will assume that \p _RR holds the helper value set by a
* previous call to mbedtls_mpi_exp_mod(), and reuse it.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \c N is negative or
* even, or if \c E is negative.
* \return Another negative error code on different kinds of failures.
*
*/
int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
const mbedtls_mpi *E, const mbedtls_mpi *N,
mbedtls_mpi *_RR );
/**
* \brief Fill an MPI with a number of random bytes.
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param size The number of random bytes to generate.
* \param f_rng The RNG function to use. This must not be \c NULL.
* \param p_rng The RNG parameter to be passed to \p f_rng. This may be
* \c NULL if \p f_rng doesn't need a context argument.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on failure.
*
* \note The bytes obtained from the RNG are interpreted
* as a big-endian representation of an MPI; this can
* be relevant in applications like deterministic ECDSA.
*/
int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng );
/**
* \brief Compute the greatest common divisor: G = gcd(A, B)
*
* \param G The destination MPI. This must point to an initialized MPI.
* \param A The first operand. This must point to an initialized MPI.
* \param B The second operand. This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A,
const mbedtls_mpi *B );
/**
* \brief Compute the modular inverse: X = A^-1 mod N
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The MPI to calculate the modular inverse of. This must point
* to an initialized MPI.
* \param N The base of the modular inversion. This must point to an
* initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p N is less than
* or equal to one.
* \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p has no modular inverse
* with respect to \p N.
*/
int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
const mbedtls_mpi *N );
#if !defined(MBEDTLS_DEPRECATED_REMOVED)
#if defined(MBEDTLS_DEPRECATED_WARNING)
#define MBEDTLS_DEPRECATED __attribute__((deprecated))
#else
#define MBEDTLS_DEPRECATED
#endif
/**
* \brief Perform a Miller-Rabin primality test with error
* probability of 2<sup>-80</sup>.
*
* \deprecated Superseded by mbedtls_mpi_is_prime_ext() which allows
* specifying the number of Miller-Rabin rounds.
*
* \param X The MPI to check for primality.
* This must point to an initialized MPI.
* \param f_rng The RNG function to use. This must not be \c NULL.
* \param p_rng The RNG parameter to be passed to \p f_rng.
* This may be \c NULL if \p f_rng doesn't use a
* context parameter.
*
* \return \c 0 if successful, i.e. \p X is probably prime.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime.
* \return Another negative error code on other kinds of failure.
*/
MBEDTLS_DEPRECATED int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng );
#undef MBEDTLS_DEPRECATED
#endif /* !MBEDTLS_DEPRECATED_REMOVED */
/**
* \brief Miller-Rabin primality test.
*
* \warning If \p X is potentially generated by an adversary, for example
* when validating cryptographic parameters that you didn't
* generate yourself and that are supposed to be prime, then
* \p rounds should be at least the half of the security
* strength of the cryptographic algorithm. On the other hand,
* if \p X is chosen uniformly or non-adversially (as is the
* case when mbedtls_mpi_gen_prime calls this function), then
* \p rounds can be much lower.
*
* \param X The MPI to check for primality.
* This must point to an initialized MPI.
* \param rounds The number of bases to perform the Miller-Rabin primality
* test for. The probability of returning 0 on a composite is
* at most 2<sup>-2*\p rounds</sup>.
* \param f_rng The RNG function to use. This must not be \c NULL.
* \param p_rng The RNG parameter to be passed to \p f_rng.
* This may be \c NULL if \p f_rng doesn't use
* a context parameter.
*
* \return \c 0 if successful, i.e. \p X is probably prime.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime.
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng );
/**
* \brief Flags for mbedtls_mpi_gen_prime()
*
* Each of these flags is a constraint on the result X returned by
* mbedtls_mpi_gen_prime().
*/
typedef enum {
MBEDTLS_MPI_GEN_PRIME_FLAG_DH = 0x0001, /**< (X-1)/2 is prime too */
MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR = 0x0002, /**< lower error rate from 2<sup>-80</sup> to 2<sup>-128</sup> */
} mbedtls_mpi_gen_prime_flag_t;
/**
* \brief Generate a prime number.
*
* \param X The destination MPI to store the generated prime in.
* This must point to an initialized MPi.
* \param nbits The required size of the destination MPI in bits.
* This must be between \c 3 and #MBEDTLS_MPI_MAX_BITS.
* \param flags A mask of flags of type #mbedtls_mpi_gen_prime_flag_t.
* \param f_rng The RNG function to use. This must not be \c NULL.
* \param p_rng The RNG parameter to be passed to \p f_rng.
* This may be \c NULL if \p f_rng doesn't use
* a context parameter.
*
* \return \c 0 if successful, in which case \p X holds a
* probably prime number.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `nbits` is not between
* \c 3 and #MBEDTLS_MPI_MAX_BITS.
*/
int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng );
#if defined(MBEDTLS_SELF_TEST)
/**
* \brief Checkup routine
*
* \return 0 if successful, or 1 if the test failed
*/
int mbedtls_mpi_self_test( int verbose );
#endif /* MBEDTLS_SELF_TEST */
#ifdef __cplusplus
}
#endif
#endif /* bignum.h */
