| /** |
| * \file bignum.h |
| * |
| * \brief Multi-precision integer library |
| */ |
| /* |
| * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved |
| * SPDX-License-Identifier: Apache-2.0 |
| * |
| * Licensed under the Apache License, Version 2.0 (the "License"); you may |
| * not use this file except in compliance with the License. |
| * You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT |
| * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| * |
| * This file is part of mbed TLS (https://tls.mbed.org) |
| */ |
| #ifndef MBEDTLS_BIGNUM_H |
| #define MBEDTLS_BIGNUM_H |
| |
| #if !defined(MBEDTLS_CONFIG_FILE) |
| #include "config.h" |
| #else |
| #include MBEDTLS_CONFIG_FILE |
| #endif |
| |
| #include <stddef.h> |
| #include <stdint.h> |
| |
| #if defined(MBEDTLS_FS_IO) |
| #include <stdio.h> |
| #endif |
| |
| #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002 /**< An error occurred while reading from or writing to a file. */ |
| #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004 /**< Bad input parameters to function. */ |
| #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006 /**< There is an invalid character in the digit string. */ |
| #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008 /**< The buffer is too small to write to. */ |
| #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A /**< The input arguments are negative or result in illegal output. */ |
| #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C /**< The input argument for division is zero, which is not allowed. */ |
| #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E /**< The input arguments are not acceptable. */ |
| #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010 /**< Memory allocation failed. */ |
| |
| #define MBEDTLS_MPI_CHK(f) do { if( ( ret = f ) != 0 ) goto cleanup; } while( 0 ) |
| |
| /* |
| * Maximum size MPIs are allowed to grow to in number of limbs. |
| */ |
| #define MBEDTLS_MPI_MAX_LIMBS 10000 |
| |
| #if !defined(MBEDTLS_MPI_WINDOW_SIZE) |
| /* |
| * Maximum window size used for modular exponentiation. Default: 6 |
| * Minimum value: 1. Maximum value: 6. |
| * |
| * Result is an array of ( 2 << MBEDTLS_MPI_WINDOW_SIZE ) MPIs used |
| * for the sliding window calculation. (So 64 by default) |
| * |
| * Reduction in size, reduces speed. |
| */ |
| #define MBEDTLS_MPI_WINDOW_SIZE 6 /**< Maximum windows size used. */ |
| #endif /* !MBEDTLS_MPI_WINDOW_SIZE */ |
| |
| #if !defined(MBEDTLS_MPI_MAX_SIZE) |
| /* |
| * Maximum size of MPIs allowed in bits and bytes for user-MPIs. |
| * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits ) |
| * |
| * Note: Calculations can temporarily result in larger MPIs. So the number |
| * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher. |
| */ |
| #define MBEDTLS_MPI_MAX_SIZE 1024 /**< Maximum number of bytes for usable MPIs. */ |
| #endif /* !MBEDTLS_MPI_MAX_SIZE */ |
| |
| #define MBEDTLS_MPI_MAX_BITS ( 8 * MBEDTLS_MPI_MAX_SIZE ) /**< Maximum number of bits for usable MPIs. */ |
| |
| /* |
| * When reading from files with mbedtls_mpi_read_file() and writing to files with |
| * mbedtls_mpi_write_file() the buffer should have space |
| * for a (short) label, the MPI (in the provided radix), the newline |
| * characters and the '\0'. |
| * |
| * By default we assume at least a 10 char label, a minimum radix of 10 |
| * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars). |
| * Autosized at compile time for at least a 10 char label, a minimum radix |
| * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size. |
| * |
| * This used to be statically sized to 1250 for a maximum of 4096 bit |
| * numbers (1234 decimal chars). |
| * |
| * Calculate using the formula: |
| * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) + |
| * LabelSize + 6 |
| */ |
| #define MBEDTLS_MPI_MAX_BITS_SCALE100 ( 100 * MBEDTLS_MPI_MAX_BITS ) |
| #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332 |
| #define MBEDTLS_MPI_RW_BUFFER_SIZE ( ((MBEDTLS_MPI_MAX_BITS_SCALE100 + MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6 ) |
| |
| /* |
| * Define the base integer type, architecture-wise. |
| * |
| * 32 or 64-bit integer types can be forced regardless of the underlying |
| * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64 |
| * respectively and undefining MBEDTLS_HAVE_ASM. |
| * |
| * Double-width integers (e.g. 128-bit in 64-bit architectures) can be |
| * disabled by defining MBEDTLS_NO_UDBL_DIVISION. |
| */ |
| #if !defined(MBEDTLS_HAVE_INT32) |
| #if defined(_MSC_VER) && defined(_M_AMD64) |
| /* Always choose 64-bit when using MSC */ |
| #if !defined(MBEDTLS_HAVE_INT64) |
| #define MBEDTLS_HAVE_INT64 |
| #endif /* !MBEDTLS_HAVE_INT64 */ |
| typedef int64_t mbedtls_mpi_sint; |
| typedef uint64_t mbedtls_mpi_uint; |
| #elif defined(__GNUC__) && ( \ |
| defined(__amd64__) || defined(__x86_64__) || \ |
| defined(__ppc64__) || defined(__powerpc64__) || \ |
| defined(__ia64__) || defined(__alpha__) || \ |
| ( defined(__sparc__) && defined(__arch64__) ) || \ |
| defined(__s390x__) || defined(__mips64) ) |
| #if !defined(MBEDTLS_HAVE_INT64) |
| #define MBEDTLS_HAVE_INT64 |
| #endif /* MBEDTLS_HAVE_INT64 */ |
| typedef int64_t mbedtls_mpi_sint; |
| typedef uint64_t mbedtls_mpi_uint; |
| #if !defined(MBEDTLS_NO_UDBL_DIVISION) |
| /* mbedtls_t_udbl defined as 128-bit unsigned int */ |
| typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI))); |
| #define MBEDTLS_HAVE_UDBL |
| #endif /* !MBEDTLS_NO_UDBL_DIVISION */ |
| #elif defined(__ARMCC_VERSION) && defined(__aarch64__) |
| /* |
| * __ARMCC_VERSION is defined for both armcc and armclang and |
| * __aarch64__ is only defined by armclang when compiling 64-bit code |
| */ |
| #if !defined(MBEDTLS_HAVE_INT64) |
| #define MBEDTLS_HAVE_INT64 |
| #endif /* !MBEDTLS_HAVE_INT64 */ |
| typedef int64_t mbedtls_mpi_sint; |
| typedef uint64_t mbedtls_mpi_uint; |
| #if !defined(MBEDTLS_NO_UDBL_DIVISION) |
| /* mbedtls_t_udbl defined as 128-bit unsigned int */ |
| typedef __uint128_t mbedtls_t_udbl; |
| #define MBEDTLS_HAVE_UDBL |
| #endif /* !MBEDTLS_NO_UDBL_DIVISION */ |
| #elif defined(MBEDTLS_HAVE_INT64) |
| /* Force 64-bit integers with unknown compiler */ |
| typedef int64_t mbedtls_mpi_sint; |
| typedef uint64_t mbedtls_mpi_uint; |
| #endif |
| #endif /* !MBEDTLS_HAVE_INT32 */ |
| |
| #if !defined(MBEDTLS_HAVE_INT64) |
| /* Default to 32-bit compilation */ |
| #if !defined(MBEDTLS_HAVE_INT32) |
| #define MBEDTLS_HAVE_INT32 |
| #endif /* !MBEDTLS_HAVE_INT32 */ |
| typedef int32_t mbedtls_mpi_sint; |
| typedef uint32_t mbedtls_mpi_uint; |
| #if !defined(MBEDTLS_NO_UDBL_DIVISION) |
| typedef uint64_t mbedtls_t_udbl; |
| #define MBEDTLS_HAVE_UDBL |
| #endif /* !MBEDTLS_NO_UDBL_DIVISION */ |
| #endif /* !MBEDTLS_HAVE_INT64 */ |
| |
| #ifdef __cplusplus |
| extern "C" { |
| #endif |
| |
| /** |
| * \brief MPI structure |
| */ |
| typedef struct mbedtls_mpi |
| { |
| int s; /*!< integer sign */ |
| size_t n; /*!< total # of limbs */ |
| mbedtls_mpi_uint *p; /*!< pointer to limbs */ |
| } |
| mbedtls_mpi; |
| |
| /** |
| * \brief Initialize one MPI (make internal references valid) |
| * This just makes it ready to be set or freed, |
| * but does not define a value for the MPI. |
| * |
| * \param X One MPI to initialize. |
| */ |
| void mbedtls_mpi_init( mbedtls_mpi *X ); |
| |
| /** |
| * \brief Unallocate one MPI |
| * |
| * \param X One MPI to unallocate. |
| */ |
| void mbedtls_mpi_free( mbedtls_mpi *X ); |
| |
| /** |
| * \brief Enlarge to the specified number of limbs |
| * |
| * This function does nothing if the MPI is already large enough. |
| * |
| * \param X MPI to grow |
| * \param nblimbs The target number of limbs |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| */ |
| int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs ); |
| |
| /** |
| * \brief Resize down, keeping at least the specified number of limbs |
| * |
| * If \c X is smaller than \c nblimbs, it is resized up |
| * instead. |
| * |
| * \param X MPI to shrink |
| * \param nblimbs The minimum number of limbs to keep |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| * (this can only happen when resizing up). |
| */ |
| int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs ); |
| |
| /** |
| * \brief Copy the contents of Y into X |
| * |
| * \param X Destination MPI. It is enlarged if necessary. |
| * \param Y Source MPI. |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| */ |
| int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y ); |
| |
| /** |
| * \brief Swap the contents of X and Y |
| * |
| * \param X First MPI value |
| * \param Y Second MPI value |
| */ |
| void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y ); |
| |
| /** |
| * \brief Safe conditional assignement X = Y if assign is 1 |
| * |
| * \param X MPI to conditionally assign to |
| * \param Y Value to be assigned |
| * \param assign 1: perform the assignment, 0: keep X's original value |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| * |
| * \note This function is equivalent to |
| * if( assign ) mbedtls_mpi_copy( X, Y ); |
| * except that it avoids leaking any information about whether |
| * the assignment was done or not (the above code may leak |
| * information through branch prediction and/or memory access |
| * patterns analysis). |
| */ |
| int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign ); |
| |
| /** |
| * \brief Safe conditional swap X <-> Y if swap is 1 |
| * |
| * \param X First mbedtls_mpi value |
| * \param Y Second mbedtls_mpi value |
| * \param assign 1: perform the swap, 0: keep X and Y's original values |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| * |
| * \note This function is equivalent to |
| * if( assign ) mbedtls_mpi_swap( X, Y ); |
| * except that it avoids leaking any information about whether |
| * the assignment was done or not (the above code may leak |
| * information through branch prediction and/or memory access |
| * patterns analysis). |
| */ |
| int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign ); |
| |
| /** |
| * \brief Set value from integer |
| * |
| * \param X MPI to set |
| * \param z Value to use |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| */ |
| int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z ); |
| |
| /** |
| * \brief Get a specific bit from X |
| * |
| * \param X MPI to use |
| * \param pos Zero-based index of the bit in X |
| * |
| * \return Either a 0 or a 1 |
| */ |
| int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos ); |
| |
| /** |
| * \brief Set a bit of X to a specific value of 0 or 1 |
| * |
| * \note Will grow X if necessary to set a bit to 1 in a not yet |
| * existing limb. Will not grow if bit should be set to 0 |
| * |
| * \param X MPI to use |
| * \param pos Zero-based index of the bit in X |
| * \param val The value to set the bit to (0 or 1) |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| * MBEDTLS_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1 |
| */ |
| int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val ); |
| |
| /** |
| * \brief Return the number of zero-bits before the least significant |
| * '1' bit |
| * |
| * Note: Thus also the zero-based index of the least significant '1' bit |
| * |
| * \param X MPI to use |
| */ |
| size_t mbedtls_mpi_lsb( const mbedtls_mpi *X ); |
| |
| /** |
| * \brief Return the number of bits up to and including the most |
| * significant '1' bit' |
| * |
| * Note: Thus also the one-based index of the most significant '1' bit |
| * |
| * \param X MPI to use |
| */ |
| size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X ); |
| |
| /** |
| * \brief Return the total size in bytes |
| * |
| * \param X MPI to use |
| */ |
| size_t mbedtls_mpi_size( const mbedtls_mpi *X ); |
| |
| /** |
| * \brief Import from an ASCII string |
| * |
| * \param X Destination MPI |
| * \param radix Input numeric base |
| * \param s Null-terminated string buffer |
| * |
| * \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code |
| */ |
| int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s ); |
| |
| /** |
| * \brief Export into an ASCII string |
| * |
| * \param X Source MPI |
| * \param radix Output numeric base |
| * \param buf Buffer to write the string to |
| * \param buflen Length of buf |
| * \param olen Length of the string written, including final NUL byte |
| * |
| * \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code. |
| * *olen is always updated to reflect the amount |
| * of data that has (or would have) been written. |
| * |
| * \note Call this function with buflen = 0 to obtain the |
| * minimum required buffer size in *olen. |
| */ |
| int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix, |
| char *buf, size_t buflen, size_t *olen ); |
| |
| #if defined(MBEDTLS_FS_IO) |
| /** |
| * \brief Read MPI from a line in an opened file |
| * |
| * \param X Destination MPI |
| * \param radix Input numeric base |
| * \param fin Input file handle |
| * |
| * \return 0 if successful, MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if |
| * the file read buffer is too small or a |
| * MBEDTLS_ERR_MPI_XXX error code |
| * |
| * \note On success, this function advances the file stream |
| * to the end of the current line or to EOF. |
| * |
| * The function returns 0 on an empty line. |
| * |
| * Leading whitespaces are ignored, as is a |
| * '0x' prefix for radix 16. |
| * |
| */ |
| int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin ); |
| |
| /** |
| * \brief Write X into an opened file, or stdout if fout is NULL |
| * |
| * \param p Prefix, can be NULL |
| * \param X Source MPI |
| * \param radix Output numeric base |
| * \param fout Output file handle (can be NULL) |
| * |
| * \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code |
| * |
| * \note Set fout == NULL to print X on the console. |
| */ |
| int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout ); |
| #endif /* MBEDTLS_FS_IO */ |
| |
| /** |
| * \brief Import X from unsigned binary data, big endian |
| * |
| * \param X Destination MPI |
| * \param buf Input buffer |
| * \param buflen Input buffer size |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| */ |
| int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen ); |
| |
| /** |
| * \brief Export X into unsigned binary data, big endian. |
| * Always fills the whole buffer, which will start with zeros |
| * if the number is smaller. |
| * |
| * \param X Source MPI |
| * \param buf Output buffer |
| * \param buflen Output buffer size |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough |
| */ |
| int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf, size_t buflen ); |
| |
| /** |
| * \brief Left-shift: X <<= count |
| * |
| * \param X MPI to shift |
| * \param count Amount to shift |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| */ |
| int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count ); |
| |
| /** |
| * \brief Right-shift: X >>= count |
| * |
| * \param X MPI to shift |
| * \param count Amount to shift |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| */ |
| int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count ); |
| |
| /** |
| * \brief Compare unsigned values |
| * |
| * \param X Left-hand MPI |
| * \param Y Right-hand MPI |
| * |
| * \return 1 if |X| is greater than |Y|, |
| * -1 if |X| is lesser than |Y| or |
| * 0 if |X| is equal to |Y| |
| */ |
| int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y ); |
| |
| /** |
| * \brief Compare signed values |
| * |
| * \param X Left-hand MPI |
| * \param Y Right-hand MPI |
| * |
| * \return 1 if X is greater than Y, |
| * -1 if X is lesser than Y or |
| * 0 if X is equal to Y |
| */ |
| int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y ); |
| |
| /** |
| * \brief Compare signed values |
| * |
| * \param X Left-hand MPI |
| * \param z The integer value to compare to |
| * |
| * \return 1 if X is greater than z, |
| * -1 if X is lesser than z or |
| * 0 if X is equal to z |
| */ |
| int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z ); |
| |
| /** |
| * \brief Unsigned addition: X = |A| + |B| |
| * |
| * \param X Destination MPI |
| * \param A Left-hand MPI |
| * \param B Right-hand MPI |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| */ |
| int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| |
| /** |
| * \brief Unsigned subtraction: X = |A| - |B| |
| * |
| * \param X Destination MPI |
| * \param A Left-hand MPI |
| * \param B Right-hand MPI |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B is greater than A |
| */ |
| int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| |
| /** |
| * \brief Signed addition: X = A + B |
| * |
| * \param X Destination MPI |
| * \param A Left-hand MPI |
| * \param B Right-hand MPI |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| */ |
| int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| |
| /** |
| * \brief Signed subtraction: X = A - B |
| * |
| * \param X Destination MPI |
| * \param A Left-hand MPI |
| * \param B Right-hand MPI |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| */ |
| int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| |
| /** |
| * \brief Signed addition: X = A + b |
| * |
| * \param X Destination MPI |
| * \param A Left-hand MPI |
| * \param b The integer value to add |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| */ |
| int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b ); |
| |
| /** |
| * \brief Signed subtraction: X = A - b |
| * |
| * \param X Destination MPI |
| * \param A Left-hand MPI |
| * \param b The integer value to subtract |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| */ |
| int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b ); |
| |
| /** |
| * \brief Baseline multiplication: X = A * B |
| * |
| * \param X Destination MPI |
| * \param A Left-hand MPI |
| * \param B Right-hand MPI |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| */ |
| int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| |
| /** |
| * \brief Baseline multiplication: X = A * b |
| * |
| * \param X Destination MPI |
| * \param A Left-hand MPI |
| * \param b The unsigned integer value to multiply with |
| * |
| * \note b is unsigned |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| */ |
| int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b ); |
| |
| /** |
| * \brief Division by mbedtls_mpi: A = Q * B + R |
| * |
| * \param Q Destination MPI for the quotient |
| * \param R Destination MPI for the rest value |
| * \param A Left-hand MPI |
| * \param B Right-hand MPI |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| * MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0 |
| * |
| * \note Either Q or R can be NULL. |
| */ |
| int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| |
| /** |
| * \brief Division by int: A = Q * b + R |
| * |
| * \param Q Destination MPI for the quotient |
| * \param R Destination MPI for the rest value |
| * \param A Left-hand MPI |
| * \param b Integer to divide by |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| * MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0 |
| * |
| * \note Either Q or R can be NULL. |
| */ |
| int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_sint b ); |
| |
| /** |
| * \brief Modulo: R = A mod B |
| * |
| * \param R Destination MPI for the rest value |
| * \param A Left-hand MPI |
| * \param B Right-hand MPI |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| * MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0, |
| * MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B < 0 |
| */ |
| int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| |
| /** |
| * \brief Modulo: r = A mod b |
| * |
| * \param r Destination mbedtls_mpi_uint |
| * \param A Left-hand MPI |
| * \param b Integer to divide by |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| * MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0, |
| * MBEDTLS_ERR_MPI_NEGATIVE_VALUE if b < 0 |
| */ |
| int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b ); |
| |
| /** |
| * \brief Sliding-window exponentiation: X = A^E mod N |
| * |
| * \param X Destination MPI |
| * \param A Left-hand MPI |
| * \param E Exponent MPI |
| * \param N Modular MPI |
| * \param _RR Speed-up MPI used for recalculations |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| * MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is negative or even or |
| * if E is negative |
| * |
| * \note _RR is used to avoid re-computing R*R mod N across |
| * multiple calls, which speeds up things a bit. It can |
| * be set to NULL if the extra performance is unneeded. |
| */ |
| int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR ); |
| |
| /** |
| * \brief Fill an MPI X with size bytes of random |
| * |
| * \param X Destination MPI |
| * \param size Size in bytes |
| * \param f_rng RNG function |
| * \param p_rng RNG parameter |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| * |
| * \note The bytes obtained from the PRNG are interpreted |
| * as a big-endian representation of an MPI; this can |
| * be relevant in applications like deterministic ECDSA. |
| */ |
| int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size, |
| int (*f_rng)(void *, unsigned char *, size_t), |
| void *p_rng ); |
| |
| /** |
| * \brief Greatest common divisor: G = gcd(A, B) |
| * |
| * \param G Destination MPI |
| * \param A Left-hand MPI |
| * \param B Right-hand MPI |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| */ |
| int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| |
| /** |
| * \brief Modular inverse: X = A^-1 mod N |
| * |
| * \param X Destination MPI |
| * \param A Left-hand MPI |
| * \param N Right-hand MPI |
| * |
| * \return 0 if successful, |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| * MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is <= 1, |
| MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N. |
| */ |
| int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N ); |
| |
| #if !defined(MBEDTLS_DEPRECATED_REMOVED) |
| #if defined(MBEDTLS_DEPRECATED_WARNING) |
| #define MBEDTLS_DEPRECATED __attribute__((deprecated)) |
| #else |
| #define MBEDTLS_DEPRECATED |
| #endif |
| /** |
| * \brief Miller-Rabin primality test with error probability of |
| * 2<sup>-80</sup> |
| * |
| * \deprecated Superseded by mbedtls_mpi_is_prime_ext() which allows |
| * specifying the number of Miller-Rabin rounds. |
| * |
| * \param X MPI to check |
| * \param f_rng RNG function |
| * \param p_rng RNG parameter |
| * |
| * \return 0 if successful (probably prime), |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| * MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime |
| */ |
| MBEDTLS_DEPRECATED int mbedtls_mpi_is_prime( const mbedtls_mpi *X, |
| int (*f_rng)(void *, unsigned char *, size_t), |
| void *p_rng ); |
| #undef MBEDTLS_DEPRECATED |
| #endif /* !MBEDTLS_DEPRECATED_REMOVED */ |
| |
| /** |
| * \brief Miller-Rabin primality test. |
| * |
| * \warning If \p X is potentially generated by an adversary, for example |
| * when validating cryptographic parameters that you didn't |
| * generate yourself and that are supposed to be prime, then |
| * \p rounds should be at least the half of the security |
| * strength of the cryptographic algorithm. On the other hand, |
| * if \p X is chosen uniformly or non-adversially (as is the |
| * case when mbedtls_mpi_gen_prime calls this function), then |
| * \p rounds can be much lower. |
| * |
| * \param X MPI to check |
| * \param rounds Number of bases to perform Miller-Rabin primality test for. |
| * The probability of returning 0 on a composite is at most |
| * 2<sup>-2*\p rounds</sup>. |
| * \param f_rng RNG function |
| * \param p_rng RNG parameter |
| * |
| * \return 0 if successful (probably prime), |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| * MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime |
| */ |
| int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds, |
| int (*f_rng)(void *, unsigned char *, size_t), |
| void *p_rng ); |
| /** |
| * \brief Flags for mbedtls_mpi_gen_prime() |
| * |
| * Each of these flags is a constraint on the result X returned by |
| * mbedtls_mpi_gen_prime(). |
| */ |
| typedef enum { |
| MBEDTLS_MPI_GEN_PRIME_FLAG_DH = 0x0001, /**< (X-1)/2 is prime too */ |
| MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR = 0x0002, /**< lower error rate from 2<sup>-80</sup> to 2<sup>-128</sup> */ |
| } mbedtls_mpi_gen_prime_flag_t; |
| |
| /** |
| * \brief Prime number generation |
| * |
| * \param X Destination MPI |
| * \param nbits Required size of X in bits |
| * ( 3 <= nbits <= MBEDTLS_MPI_MAX_BITS ) |
| * \param flags Mask of flags of type #mbedtls_mpi_gen_prime_flag_t |
| * \param f_rng RNG function |
| * \param p_rng RNG parameter |
| * |
| * \return 0 if successful (probably prime), |
| * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| * MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3 |
| */ |
| int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags, |
| int (*f_rng)(void *, unsigned char *, size_t), |
| void *p_rng ); |
| |
| /** |
| * \brief Checkup routine |
| * |
| * \return 0 if successful, or 1 if the test failed |
| */ |
| int mbedtls_mpi_self_test( int verbose ); |
| |
| #ifdef __cplusplus |
| } |
| #endif |
| |
| #endif /* bignum.h */ |