/** * \file bignum.h * * \brief Multi-precision integer library * * Copyright (C) 2006-2014, ARM Limited, All Rights Reserved * * This file is part of mbed TLS (http://www.polarssl.org) * Lead Maintainer: Paul Bakker * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License along * with this program; if not, write to the Free Software Foundation, Inc., * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */ #ifndef POLARSSL_BIGNUM_H #define POLARSSL_BIGNUM_H #include #include #if !defined(POLARSSL_CONFIG_FILE) #include "config.h" #else #include POLARSSL_CONFIG_FILE #endif #if defined(_MSC_VER) && !defined(EFIX64) && !defined(EFI32) #include #if (_MSC_VER <= 1200) typedef signed short int16_t; typedef unsigned short uint16_t; #else typedef INT16 int16_t; typedef UINT16 uint16_t; #endif typedef INT32 int32_t; typedef INT64 int64_t; typedef UINT32 uint32_t; typedef UINT64 uint64_t; #else #include #endif /* _MSC_VER && !EFIX64 && !EFI32 */ #define POLARSSL_ERR_MPI_FILE_IO_ERROR -0x0002 /**< An error occurred while reading from or writing to a file. */ #define POLARSSL_ERR_MPI_BAD_INPUT_DATA -0x0004 /**< Bad input parameters to function. */ #define POLARSSL_ERR_MPI_INVALID_CHARACTER -0x0006 /**< There is an invalid character in the digit string. */ #define POLARSSL_ERR_MPI_BUFFER_TOO_SMALL -0x0008 /**< The buffer is too small to write to. */ #define POLARSSL_ERR_MPI_NEGATIVE_VALUE -0x000A /**< The input arguments are negative or result in illegal output. */ #define POLARSSL_ERR_MPI_DIVISION_BY_ZERO -0x000C /**< The input argument for division is zero, which is not allowed. */ #define POLARSSL_ERR_MPI_NOT_ACCEPTABLE -0x000E /**< The input arguments are not acceptable. */ #define POLARSSL_ERR_MPI_MALLOC_FAILED -0x0010 /**< Memory allocation failed. */ #define 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 POLARSSL_MPI_MAX_LIMBS 10000 #if !defined(POLARSSL_MPI_WINDOW_SIZE) /* * Maximum window size used for modular exponentiation. Default: 6 * Minimum value: 1. Maximum value: 6. * * Result is an array of ( 2 << POLARSSL_MPI_WINDOW_SIZE ) MPIs used * for the sliding window calculation. (So 64 by default) * * Reduction in size, reduces speed. */ #define POLARSSL_MPI_WINDOW_SIZE 6 /**< Maximum windows size used. */ #endif /* !POLARSSL_MPI_WINDOW_SIZE */ #if !defined(POLARSSL_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 results temporarily in larger MPIs. So the number * of limbs required (POLARSSL_MPI_MAX_LIMBS) is higher. */ #define POLARSSL_MPI_MAX_SIZE 1024 /**< Maximum number of bytes for usable MPIs. */ #endif /* !POLARSSL_MPI_MAX_SIZE */ #define POLARSSL_MPI_MAX_BITS ( 8 * POLARSSL_MPI_MAX_SIZE ) /**< Maximum number of bits for usable MPIs. */ /* * When reading from files with mpi_read_file() and writing to files with * 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 POLARSSL_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: * POLARSSL_MPI_RW_BUFFER_SIZE = ceil(POLARSSL_MPI_MAX_BITS / ln(10) * ln(2)) + * LabelSize + 6 */ #define POLARSSL_MPI_MAX_BITS_SCALE100 ( 100 * POLARSSL_MPI_MAX_BITS ) #define LN_2_DIV_LN_10_SCALE100 332 #define POLARSSL_MPI_RW_BUFFER_SIZE ( ((POLARSSL_MPI_MAX_BITS_SCALE100 + LN_2_DIV_LN_10_SCALE100 - 1) / LN_2_DIV_LN_10_SCALE100) + 10 + 6 ) /* * Define the base integer type, architecture-wise */ #if defined(POLARSSL_HAVE_INT8) typedef signed char t_sint; typedef unsigned char t_uint; typedef uint16_t t_udbl; #define POLARSSL_HAVE_UDBL #else #if defined(POLARSSL_HAVE_INT16) typedef int16_t t_sint; typedef uint16_t t_uint; typedef uint32_t t_udbl; #define POLARSSL_HAVE_UDBL #else /* * 32-bit integers can be forced on 64-bit arches (eg. for testing purposes) * by defining POLARSSL_HAVE_INT32 and undefining POLARSSL_HAVE_ASM */ #if ( ! defined(POLARSSL_HAVE_INT32) && \ defined(_MSC_VER) && defined(_M_AMD64) ) #define POLARSSL_HAVE_INT64 typedef int64_t t_sint; typedef uint64_t t_uint; #else #if ( ! defined(POLARSSL_HAVE_INT32) && \ defined(__GNUC__) && ( \ defined(__amd64__) || defined(__x86_64__) || \ defined(__ppc64__) || defined(__powerpc64__) || \ defined(__ia64__) || defined(__alpha__) || \ (defined(__sparc__) && defined(__arch64__)) || \ defined(__s390x__) ) ) #define POLARSSL_HAVE_INT64 typedef int64_t t_sint; typedef uint64_t t_uint; typedef unsigned int t_udbl __attribute__((mode(TI))); #define POLARSSL_HAVE_UDBL #else #define POLARSSL_HAVE_INT32 typedef int32_t t_sint; typedef uint32_t t_uint; #if ( defined(_MSC_VER) && defined(_M_IX86) ) typedef uint64_t t_udbl; #define POLARSSL_HAVE_UDBL #else #if defined( POLARSSL_HAVE_LONGLONG ) typedef unsigned long long t_udbl; #define POLARSSL_HAVE_UDBL #endif #endif #endif /* !POLARSSL_HAVE_INT32 && __GNUC__ && 64-bit platform */ #endif /* !POLARSSL_HAVE_INT32 && _MSC_VER && _M_AMD64 */ #endif /* POLARSSL_HAVE_INT16 */ #endif /* POLARSSL_HAVE_INT8 */ #ifdef __cplusplus extern "C" { #endif /** * \brief MPI structure */ typedef struct { int s; /*!< integer sign */ size_t n; /*!< total # of limbs */ t_uint *p; /*!< pointer to limbs */ } mpi; /** * \brief Initialize one MPI * * \param X One MPI to initialize. */ void mpi_init( mpi *X ); /** * \brief Unallocate one MPI * * \param X One MPI to unallocate. */ void mpi_free( mpi *X ); /** * \brief Enlarge to the specified number of limbs * * \param X MPI to grow * \param nblimbs The target number of limbs * * \return 0 if successful, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_grow( mpi *X, size_t nblimbs ); /** * \brief Resize down, keeping at least the specified number of limbs * * \param X MPI to shrink * \param nblimbs The minimum number of limbs to keep * * \return 0 if successful, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_shrink( mpi *X, size_t nblimbs ); /** * \brief Copy the contents of Y into X * * \param X Destination MPI * \param Y Source MPI * * \return 0 if successful, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_copy( mpi *X, const mpi *Y ); /** * \brief Swap the contents of X and Y * * \param X First MPI value * \param Y Second MPI value */ void mpi_swap( mpi *X, 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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, * * \note This function is equivalent to * if( assign ) 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 mpi_safe_cond_assign( mpi *X, const mpi *Y, unsigned char assign ); /** * \brief Safe conditional swap X <-> Y if swap is 1 * * \param X First mpi value * \param Y Second mpi value * \param assign 1: perform the swap, 0: keep X and Y's original values * * \return 0 if successful, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, * * \note This function is equivalent to * if( assign ) 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 mpi_safe_cond_swap( mpi *X, mpi *Y, unsigned char assign ); /** * \brief Set value from integer * * \param X MPI to set * \param z Value to use * * \return 0 if successful, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_lset( mpi *X, t_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 mpi_get_bit( const 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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, * POLARSSL_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1 */ int mpi_set_bit( 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 mpi_lsb( const 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 mpi_msb( const mpi *X ); /** * \brief Return the total size in bytes * * \param X MPI to use */ size_t mpi_size( const 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 POLARSSL_ERR_MPI_XXX error code */ int mpi_read_string( mpi *X, int radix, const char *s ); /** * \brief Export into an ASCII string * * \param X Source MPI * \param radix Output numeric base * \param s String buffer * \param slen String buffer size * * \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code. * *slen is always updated to reflect the amount * of data that has (or would have) been written. * * \note Call this function with *slen = 0 to obtain the * minimum required buffer size in *slen. */ int mpi_write_string( const mpi *X, int radix, char *s, size_t *slen ); #if defined(POLARSSL_FS_IO) /** * \brief Read X from an opened file * * \param X Destination MPI * \param radix Input numeric base * \param fin Input file handle * * \return 0 if successful, POLARSSL_ERR_MPI_BUFFER_TOO_SMALL if * the file read buffer is too small or a * POLARSSL_ERR_MPI_XXX error code */ int mpi_read_file( 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 POLARSSL_ERR_MPI_XXX error code * * \note Set fout == NULL to print X on the console. */ int mpi_write_file( const char *p, const mpi *X, int radix, FILE *fout ); #endif /* POLARSSL_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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_read_binary( 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, * POLARSSL_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough */ int mpi_write_binary( const 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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_shift_l( mpi *X, size_t count ); /** * \brief Right-shift: X >>= count * * \param X MPI to shift * \param count Amount to shift * * \return 0 if successful, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_shift_r( 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 mpi_cmp_abs( const mpi *X, const 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 mpi_cmp_mpi( const mpi *X, const 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 mpi_cmp_int( const mpi *X, t_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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_add_abs( mpi *X, const mpi *A, const 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, * POLARSSL_ERR_MPI_NEGATIVE_VALUE if B is greater than A */ int mpi_sub_abs( mpi *X, const mpi *A, const 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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_add_mpi( mpi *X, const mpi *A, const 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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_sub_mpi( mpi *X, const mpi *A, const 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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_add_int( mpi *X, const mpi *A, t_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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_sub_int( mpi *X, const mpi *A, t_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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_mul_mpi( mpi *X, const mpi *A, const mpi *B ); /** * \brief Baseline multiplication: X = A * b * Note: despite the functon signature, b is treated as a * t_uint. Negative values of b are treated as large positive * values. * * \param X Destination MPI * \param A Left-hand MPI * \param b The integer value to multiply with * * \return 0 if successful, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_mul_int( mpi *X, const mpi *A, t_sint b ); /** * \brief Division by 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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0 * * \note Either Q or R can be NULL. */ int mpi_div_mpi( mpi *Q, mpi *R, const mpi *A, const 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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0 * * \note Either Q or R can be NULL. */ int mpi_div_int( mpi *Q, mpi *R, const mpi *A, t_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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0, * POLARSSL_ERR_MPI_NEGATIVE_VALUE if B < 0 */ int mpi_mod_mpi( mpi *R, const mpi *A, const mpi *B ); /** * \brief Modulo: r = A mod b * * \param r Destination t_uint * \param A Left-hand MPI * \param b Integer to divide by * * \return 0 if successful, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0, * POLARSSL_ERR_MPI_NEGATIVE_VALUE if b < 0 */ int mpi_mod_int( t_uint *r, const mpi *A, t_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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, * POLARSSL_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 mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, 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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_fill_random( 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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int mpi_gcd( mpi *G, const mpi *A, const 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, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, * POLARSSL_ERR_MPI_BAD_INPUT_DATA if N is negative or nil POLARSSL_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N */ int mpi_inv_mod( mpi *X, const mpi *A, const mpi *N ); /** * \brief Miller-Rabin primality test * * \param X MPI to check * \param f_rng RNG function * \param p_rng RNG parameter * * \return 0 if successful (probably prime), * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, * POLARSSL_ERR_MPI_NOT_ACCEPTABLE if X is not prime */ int mpi_is_prime( mpi *X, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ); /** * \brief Prime number generation * * \param X Destination MPI * \param nbits Required size of X in bits * ( 3 <= nbits <= POLARSSL_MPI_MAX_BITS ) * \param dh_flag If 1, then (X-1)/2 will be prime too * \param f_rng RNG function * \param p_rng RNG parameter * * \return 0 if successful (probably prime), * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, * POLARSSL_ERR_MPI_BAD_INPUT_DATA if nbits is < 3 */ int mpi_gen_prime( mpi *X, size_t nbits, int dh_flag, 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 mpi_self_test( int verbose ); #ifdef __cplusplus } #endif #endif /* bignum.h */