pigweed / third_party / github / ARMmbed / mbedtls / 2c9e54a063533b1a88adf13cd271bea4bc1be650 / . / include / mbedtls / bignum.h

/** | |

* \file bignum.h | |

* | |

* \brief Multi-precision integer library | |

*/ | |

/* | |

* Copyright The Mbed TLS Contributors | |

* 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. | |

*/ | |

#ifndef MBEDTLS_BIGNUM_H | |

#define MBEDTLS_BIGNUM_H | |

#include "mbedtls/private_access.h" | |

#include "mbedtls/build_info.h" | |

#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 window 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 MBEDTLS_PRIVATE(s); /*!< Sign: -1 if the mpi is negative, 1 otherwise */ | |

size_t MBEDTLS_PRIVATE(n); /*!< total # of limbs */ | |

mbedtls_mpi_uint *MBEDTLS_PRIVATE(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 ); | |

/** Generate a random number uniformly in a range. | |

* | |

* This function generates a random number between \p min inclusive and | |

* \p N exclusive. | |

* | |

* The procedure complies with RFC 6979 ยง3.3 (deterministic ECDSA) | |

* when the RNG is a suitably parametrized instance of HMAC_DRBG | |

* and \p min is \c 1. | |

* | |

* \note There are `N - min` possible outputs. The lower bound | |

* \p min can be reached, but the upper bound \p N cannot. | |

* | |

* \param X The destination MPI. This must point to an initialized MPI. | |

* \param min The minimum value to return. | |

* It must be nonnegative. | |

* \param N The upper bound of the range, exclusive. | |

* In other words, this is one plus the maximum value to return. | |

* \p N must be strictly larger than \p min. | |

* \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. | |

* | |

* \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 min or \p N is invalid | |

* or if they are incompatible. | |

* \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if the implementation was | |

* unable to find a suitable value within a limited number | |

* of attempts. This has a negligible probability if \p N | |

* is significantly larger than \p min, which is the case | |

* for all usual cryptographic applications. | |

* \return Another negative error code on failure. | |

*/ | |

int mbedtls_mpi_random( mbedtls_mpi *X, | |

mbedtls_mpi_sint min, | |

const mbedtls_mpi *N, | |

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 ); | |

/** | |

* \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 */ |