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/**
* \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 "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) )
#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; /*!< integer sign */
size_t n; /*!< total # of limbs */
mbedtls_mpi_uint *p; /*!< pointer to limbs */
}
mbedtls_mpi;
/**
* \brief Initialize one MPI (make internal references valid)
* This just makes it ready to be set or freed,
* but does not define a value for the MPI.
*
* \param X One MPI to initialize.
*/
void mbedtls_mpi_init( mbedtls_mpi *X );
/**
* \brief Unallocate one MPI
*
* \param X One MPI to unallocate.
*/
void mbedtls_mpi_free( mbedtls_mpi *X );
/**
* \brief Enlarge to the specified number of limbs
*
* This function does nothing if the MPI is already large enough.
*
* \param X MPI to grow
* \param nblimbs The target number of limbs
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
/**
* \brief Resize down, keeping at least the specified number of limbs
*
* If \c X is smaller than \c nblimbs, it is resized up
* instead.
*
* \param X MPI to shrink
* \param nblimbs The minimum number of limbs to keep
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
* (this can only happen when resizing up).
*/
int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
/**
* \brief Copy the contents of Y into X
*
* \param X Destination MPI. It is enlarged if necessary.
* \param Y Source MPI.
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
/**
* \brief Swap the contents of X and Y
*
* \param X First MPI value
* \param Y Second MPI value
*/
void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y );
/**
* \brief Safe conditional assignement X = Y if assign is 1
*
* \param X MPI to conditionally assign to
* \param Y Value to be assigned
* \param assign 1: perform the assignment, 0: keep X's original value
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
*
* \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).
*/
int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
/**
* \brief Safe conditional swap X <-> Y if swap is 1
*
* \param X First mbedtls_mpi value
* \param Y Second mbedtls_mpi value
* \param assign 1: perform the swap, 0: keep X and Y's original values
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
*
* \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).
*/
int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
/**
* \brief Set value from integer
*
* \param X MPI to set
* \param z Value to use
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z );
/**
* \brief Get a specific bit from X
*
* \param X MPI to use
* \param pos Zero-based index of the bit in X
*
* \return Either a 0 or a 1
*/
int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
/**
* \brief Set a bit of X to a specific value of 0 or 1
*
* \note Will grow X if necessary to set a bit to 1 in a not yet
* existing limb. Will not grow if bit should be set to 0
*
* \param X MPI to use
* \param pos Zero-based index of the bit in X
* \param val The value to set the bit to (0 or 1)
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
* MBEDTLS_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1
*/
int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val );
/**
* \brief Return the number of zero-bits before the least significant
* '1' bit
*
* Note: Thus also the zero-based index of the least significant '1' bit
*
* \param X MPI to use
*/
size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
/**
* \brief Return the number of bits up to and including the most
* significant '1' bit'
*
* Note: Thus also the one-based index of the most significant '1' bit
*
* \param X MPI to use
*/
size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
/**
* \brief Return the total size in bytes
*
* \param X MPI to use
*/
size_t mbedtls_mpi_size( const mbedtls_mpi *X );
/**
* \brief Import from an ASCII string
*
* \param X Destination MPI
* \param radix Input numeric base
* \param s Null-terminated string buffer
*
* \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
*/
int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
/**
* \brief Export into an ASCII string
*
* \param X Source MPI
* \param radix Output numeric base
* \param buf Buffer to write the string to
* \param buflen Length of buf
* \param olen Length of the string written, including final NUL byte
*
* \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code.
* *olen is always updated to reflect the amount
* of data that has (or would have) been written.
*
* \note Call this function with buflen = 0 to obtain the
* minimum required buffer size in *olen.
*/
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 MPI from a line in an opened file
*
* \param X Destination MPI
* \param radix Input numeric base
* \param fin Input file handle
*
* \return 0 if successful, MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if
* the file read buffer is too small or a
* MBEDTLS_ERR_MPI_XXX error code
*
* \note On success, this function advances the file stream
* to the end of the current line or to EOF.
*
* The function returns 0 on an empty line.
*
* Leading whitespaces are ignored, as is a
* '0x' prefix for radix 16.
*
*/
int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
/**
* \brief Write X into an opened file, or stdout if fout is NULL
*
* \param p Prefix, can be NULL
* \param X Source MPI
* \param radix Output numeric base
* \param fout Output file handle (can be NULL)
*
* \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
*
* \note Set fout == NULL to print X on the console.
*/
int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout );
#endif /* MBEDTLS_FS_IO */
/**
* \brief Import X from unsigned binary data, big endian
*
* \param X Destination MPI
* \param buf Input buffer
* \param buflen Input buffer size
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
int mbedtls_mpi_read_binary( 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 Source MPI
* \param buf Output buffer
* \param buflen Output buffer size
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough
*/
int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf, size_t buflen );
/**
* \brief Left-shift: X <<= count
*
* \param X MPI to shift
* \param count Amount to shift
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
/**
* \brief Right-shift: X >>= count
*
* \param X MPI to shift
* \param count Amount to shift
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count );
/**
* \brief Compare unsigned values
*
* \param X Left-hand MPI
* \param Y Right-hand MPI
*
* \return 1 if |X| is greater than |Y|,
* -1 if |X| is lesser than |Y| or
* 0 if |X| is equal to |Y|
*/
int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
/**
* \brief Compare signed values
*
* \param X Left-hand MPI
* \param Y Right-hand MPI
*
* \return 1 if X is greater than Y,
* -1 if X is lesser than Y or
* 0 if X is equal to Y
*/
int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
/**
* \brief Compare signed values
*
* \param X Left-hand MPI
* \param z The integer value to compare to
*
* \return 1 if X is greater than z,
* -1 if X is lesser than z or
* 0 if X is equal to z
*/
int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z );
/**
* \brief Unsigned addition: X = |A| + |B|
*
* \param X Destination MPI
* \param A Left-hand MPI
* \param B Right-hand MPI
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
/**
* \brief Unsigned subtraction: X = |A| - |B|
*
* \param X Destination MPI
* \param A Left-hand MPI
* \param B Right-hand MPI
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B is greater than A
*/
int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
/**
* \brief Signed addition: X = A + B
*
* \param X Destination MPI
* \param A Left-hand MPI
* \param B Right-hand MPI
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
/**
* \brief Signed subtraction: X = A - B
*
* \param X Destination MPI
* \param A Left-hand MPI
* \param B Right-hand MPI
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
/**
* \brief Signed addition: X = A + b
*
* \param X Destination MPI
* \param A Left-hand MPI
* \param b The integer value to add
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b );
/**
* \brief Signed subtraction: X = A - b
*
* \param X Destination MPI
* \param A Left-hand MPI
* \param b The integer value to subtract
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b );
/**
* \brief Baseline multiplication: X = A * B
*
* \param X Destination MPI
* \param A Left-hand MPI
* \param B Right-hand MPI
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
/**
* \brief Baseline multiplication: X = A * b
*
* \param X Destination MPI
* \param A Left-hand MPI
* \param b The unsigned integer value to multiply with
*
* \note b is unsigned
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b );
/**
* \brief Division by mbedtls_mpi: A = Q * B + R
*
* \param Q Destination MPI for the quotient
* \param R Destination MPI for the rest value
* \param A Left-hand MPI
* \param B Right-hand MPI
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
* MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0
*
* \note Either Q or R can be NULL.
*/
int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B );
/**
* \brief Division by int: A = Q * b + R
*
* \param Q Destination MPI for the quotient
* \param R Destination MPI for the rest value
* \param A Left-hand MPI
* \param b Integer to divide by
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
* MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0
*
* \note Either Q or R can be NULL.
*/
int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_sint b );
/**
* \brief Modulo: R = A mod B
*
* \param R Destination MPI for the rest value
* \param A Left-hand MPI
* \param B Right-hand MPI
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
* MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0,
* MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B < 0
*/
int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B );
/**
* \brief Modulo: r = A mod b
*
* \param r Destination mbedtls_mpi_uint
* \param A Left-hand MPI
* \param b Integer to divide by
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
* MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0,
* MBEDTLS_ERR_MPI_NEGATIVE_VALUE if b < 0
*/
int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b );
/**
* \brief Sliding-window exponentiation: X = A^E mod N
*
* \param X Destination MPI
* \param A Left-hand MPI
* \param E Exponent MPI
* \param N Modular MPI
* \param _RR Speed-up MPI used for recalculations
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
* MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is negative or even or
* if E is negative
*
* \note _RR is used to avoid re-computing R*R mod N across
* multiple calls, which speeds up things a bit. It can
* be set to NULL if the extra performance is unneeded.
*/
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 X with size bytes of random
*
* \param X Destination MPI
* \param size Size in bytes
* \param f_rng RNG function
* \param p_rng RNG parameter
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*
* \note The bytes obtained from the PRNG 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 Greatest common divisor: G = gcd(A, B)
*
* \param G Destination MPI
* \param A Left-hand MPI
* \param B Right-hand MPI
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B );
/**
* \brief Modular inverse: X = A^-1 mod N
*
* \param X Destination MPI
* \param A Left-hand MPI
* \param N Right-hand MPI
*
* \return 0 if successful,
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
* MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is <= 1,
MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod 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 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 MPI to check
* \param f_rng RNG function
* \param p_rng RNG parameter
*
* \return 0 if successful (probably prime),
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
* MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime
*/
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 MPI to check
* \param rounds Number of bases to perform 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 RNG function
* \param p_rng RNG parameter
*
* \return 0 if successful (probably prime),
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
* MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime
*/
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 Prime number generation
*
* \param X Destination MPI
* \param nbits Required size of X in bits
* ( 3 <= nbits <= MBEDTLS_MPI_MAX_BITS )
* \param flags Mask of flags of type #mbedtls_mpi_gen_prime_flag_t
* \param f_rng RNG function
* \param p_rng RNG parameter
*
* \return 0 if successful (probably prime),
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
* MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
*/
int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng );
/**
* \brief Checkup routine
*
* \return 0 if successful, or 1 if the test failed
*/
int mbedtls_mpi_self_test( int verbose );
#ifdef __cplusplus
}
#endif
#endif /* bignum.h */