blob: 74deecf5cce9e3610a265c5d6975ff68244d8408 [file] [log] [blame]
 /** * \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" #if !defined(MBEDTLS_CONFIG_FILE) #include "mbedtls/config.h" #else #include MBEDTLS_CONFIG_FILE #endif #include #include #if defined(MBEDTLS_FS_IO) #include #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 §3.3 (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 2-2*\p rounds. * \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 2-80 to 2-128 */ } 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 */