| /** |
| * \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 */ |
