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Diffstat (limited to 'include/mbedtls/bignum.h')
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1 files changed, 1070 insertions, 0 deletions
diff --git a/include/mbedtls/bignum.h b/include/mbedtls/bignum.h new file mode 100644 index 000000000..877fbc7ce --- /dev/null +++ b/include/mbedtls/bignum.h @@ -0,0 +1,1070 @@ +/** + * \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 + +/** An error occurred while reading from or writing to a file. */ +#define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002 +/** Bad input parameters to function. */ +#define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004 +/** There is an invalid character in the digit string. */ +#define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006 +/** The buffer is too small to write to. */ +#define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008 +/** The input arguments are negative or result in illegal output. */ +#define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A +/** The input argument for division is zero, which is not allowed. */ +#define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C +/** The input arguments are not acceptable. */ +#define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E +/** Memory allocation failed. */ +#define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010 + +#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 */ + +/** \typedef mbedtls_mpi_uint + * \brief The type of machine digits in a bignum, called _limbs_. + * + * This is always an unsigned integer type with no padding bits. The size + * is platform-dependent. + */ + +/** \typedef mbedtls_mpi_sint + * \brief The signed type corresponding to #mbedtls_mpi_uint. + * + * This is always an signed integer type with no padding bits. The size + * is platform-dependent. + */ + +#ifdef __cplusplus +extern "C" { +#endif + +/** + * \brief MPI structure + */ +typedef struct mbedtls_mpi +{ + /** Sign: -1 if the mpi is negative, 1 otherwise. + * + * The number 0 must be represented with `s = +1`. Although many library + * functions treat all-limbs-zero as equivalent to a valid representation + * of 0 regardless of the sign bit, there are exceptions, so bignum + * functions and external callers must always set \c s to +1 for the + * number zero. + * + * Note that this implies that calloc() or `... = {0}` does not create + * a valid MPI representation. You must call mbedtls_mpi_init(). + */ + int MBEDTLS_PRIVATE(s); + + /** Total number of limbs in \c p. */ + size_t MBEDTLS_PRIVATE(n); + + /** Pointer to limbs. + * + * This may be \c NULL if \c n is 0. + */ + mbedtls_mpi_uint *MBEDTLS_PRIVATE(p); +} +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. Must be either 0 or 1: + * * \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). + * + * \warning If \p assign is neither 0 nor 1, the result of this function + * is indeterminate, and the resulting value in \p X might be + * neither its original value nor the value in \p Y. + * + * \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 swap The condition deciding whether to perform + * the swap or not. Must be either 0 or 1: + * * \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( swap ) mbedtls_mpi_swap( X, Y ); + * except that it avoids leaking any information about whether + * the swap was done or not (the above code may leak + * information through branch prediction and/or memory access + * patterns analysis). + * + * \warning If \p swap is neither 0 nor 1, the result of this function + * is indeterminate, and both \p X and \p Y might end up with + * values different to either of the original ones. + * + * \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 swap ); + +/** + * \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. This must not alias A or B. + * \param R The destination MPI for the remainder value. + * This may be \c NULL if the value of the + * remainder is not needed. This must not alias A or B. + * \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. This must not alias A. + * \param R The destination MPI for the remainder value. + * This may be \c NULL if the value of the + * remainder is not needed. This must not alias A. + * \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. + * This must not alias E or N. + * \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 prec_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 prec_RR for reuse on + * subsequent calls to this function. Otherwise, the function + * will assume that \p prec_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 *prec_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-adversarially (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 */ |