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#ifndef _IPXE_BIGINT_H
#define _IPXE_BIGINT_H
/** @file
*
* Big integer support
*/
FILE_LICENCE ( GPL2_OR_LATER_OR_UBDL );
#include <assert.h>
/**
* Define a big-integer type
*
* @v size Number of elements
* @ret bigint_t Big integer type
*/
#define bigint_t( size ) \
struct { \
bigint_element_t element[ (size) ]; \
}
/**
* Determine number of elements required for a big-integer type
*
* @v len Maximum length of big integer, in bytes
* @ret size Number of elements
*/
#define bigint_required_size( len ) \
( ( (len) + sizeof ( bigint_element_t ) - 1 ) / \
sizeof ( bigint_element_t ) )
/**
* Determine number of elements in big-integer type
*
* @v bigint Big integer
* @ret size Number of elements
*/
#define bigint_size( bigint ) \
( sizeof ( *(bigint) ) / sizeof ( (bigint)->element[0] ) )
/**
* Initialise big integer
*
* @v value Big integer to initialise
* @v data Raw data
* @v len Length of raw data
*/
#define bigint_init( value, data, len ) do { \
unsigned int size = bigint_size (value); \
assert ( (len) <= ( size * sizeof ( (value)->element[0] ) ) ); \
bigint_init_raw ( (value)->element, size, (data), (len) ); \
} while ( 0 )
/**
* Finalise big integer
*
* @v value Big integer to finalise
* @v out Output buffer
* @v len Length of output buffer
*/
#define bigint_done( value, out, len ) do { \
unsigned int size = bigint_size (value); \
bigint_done_raw ( (value)->element, size, (out), (len) ); \
} while ( 0 )
/**
* Add big integers
*
* @v addend Big integer to add
* @v value Big integer to be added to
* @ret carry Carry out
*/
#define bigint_add( addend, value ) ( { \
unsigned int size = bigint_size (addend); \
bigint_add_raw ( (addend)->element, (value)->element, size ); \
} )
/**
* Subtract big integers
*
* @v subtrahend Big integer to subtract
* @v value Big integer to be subtracted from
* @ret borrow Borrow out
*/
#define bigint_subtract( subtrahend, value ) ( { \
unsigned int size = bigint_size (subtrahend); \
bigint_subtract_raw ( (subtrahend)->element, (value)->element, \
size ); \
} )
/**
* Shift big integer left
*
* @v value Big integer
*/
#define bigint_shl( value ) do { \
unsigned int size = bigint_size (value); \
bigint_shl_raw ( (value)->element, size ); \
} while ( 0 )
/**
* Shift big integer right
*
* @v value Big integer
*/
#define bigint_shr( value ) do { \
unsigned int size = bigint_size (value); \
bigint_shr_raw ( (value)->element, size ); \
} while ( 0 )
/**
* Test if big integer is equal to zero
*
* @v value Big integer
* @v size Number of elements
* @ret is_zero Big integer is equal to zero
*/
#define bigint_is_zero( value ) ( { \
unsigned int size = bigint_size (value); \
bigint_is_zero_raw ( (value)->element, size ); } )
/**
* Compare big integers
*
* @v value Big integer
* @v reference Reference big integer
* @ret geq Big integer is greater than or equal to the reference
*/
#define bigint_is_geq( value, reference ) ( { \
unsigned int size = bigint_size (value); \
bigint_is_geq_raw ( (value)->element, (reference)->element, \
size ); } )
/**
* Test if bit is set in big integer
*
* @v value Big integer
* @v bit Bit to test
* @ret is_set Bit is set
*/
#define bigint_bit_is_set( value, bit ) ( { \
unsigned int size = bigint_size (value); \
bigint_bit_is_set_raw ( (value)->element, size, bit ); } )
/**
* Test if most significant bit is set in big integer
*
* @v value Big integer
* @ret is_set Most significant bit is set
*/
#define bigint_msb_is_set( value ) ( { \
unsigned int size = bigint_size (value); \
bigint_msb_is_set_raw ( (value)->element, size ); } )
/**
* Find highest bit set in big integer
*
* @v value Big integer
* @ret max_bit Highest bit set + 1 (or 0 if no bits set)
*/
#define bigint_max_set_bit( value ) ( { \
unsigned int size = bigint_size (value); \
bigint_max_set_bit_raw ( (value)->element, size ); } )
/**
* Grow big integer
*
* @v source Source big integer
* @v dest Destination big integer
*/
#define bigint_grow( source, dest ) do { \
unsigned int source_size = bigint_size (source); \
unsigned int dest_size = bigint_size (dest); \
bigint_grow_raw ( (source)->element, source_size, \
(dest)->element, dest_size ); \
} while ( 0 )
/**
* Shrink big integer
*
* @v source Source big integer
* @v dest Destination big integer
*/
#define bigint_shrink( source, dest ) do { \
unsigned int source_size = bigint_size (source); \
unsigned int dest_size = bigint_size (dest); \
bigint_shrink_raw ( (source)->element, source_size, \
(dest)->element, dest_size ); \
} while ( 0 )
/**
* Copy big integer
*
* @v source Source big integer
* @v dest Destination big integer
*/
#define bigint_copy( source, dest ) do { \
build_assert ( sizeof ( *(source) ) == sizeof ( *(dest) ) ); \
bigint_shrink ( (source), (dest) ); \
} while ( 0 )
/**
* Conditionally swap big integers (in constant time)
*
* @v first Big integer to be conditionally swapped
* @v second Big integer to be conditionally swapped
* @v swap Swap first and second big integers
*/
#define bigint_swap( first, second, swap ) do { \
unsigned int size = bigint_size (first); \
bigint_swap_raw ( (first)->element, (second)->element, size, \
(swap) ); \
} while ( 0 )
/**
* Multiply big integers
*
* @v multiplicand Big integer to be multiplied
* @v multiplier Big integer to be multiplied
* @v result Big integer to hold result
*/
#define bigint_multiply( multiplicand, multiplier, result ) do { \
unsigned int multiplicand_size = bigint_size (multiplicand); \
unsigned int multiplier_size = bigint_size (multiplier); \
bigint_multiply_raw ( (multiplicand)->element, \
multiplicand_size, (multiplier)->element, \
multiplier_size, (result)->element ); \
} while ( 0 )
/**
* Reduce big integer
*
* @v modulus Big integer modulus
* @v value Big integer to be reduced
*/
#define bigint_reduce( modulus, value ) do { \
unsigned int size = bigint_size (modulus); \
bigint_reduce_raw ( (modulus)->element, \
(value)->element, size ); \
} while ( 0 )
/**
* Compute inverse of odd big integer modulo any power of two
*
* @v invertend Odd big integer to be inverted
* @v inverse Big integer to hold result
*/
#define bigint_mod_invert( invertend, inverse ) do { \
unsigned int size = bigint_size ( inverse ); \
bigint_mod_invert_raw ( (invertend)->element, \
(inverse)->element, size ); \
} while ( 0 )
/**
* Perform Montgomery reduction (REDC) of a big integer product
*
* @v modulus Big integer modulus
* @v modinv Big integer inverse of the modulus modulo 2^k
* @v mont Big integer Montgomery product
* @v result Big integer to hold result
*
* Note that the Montgomery product will be overwritten.
*/
#define bigint_montgomery( modulus, modinv, mont, result ) do { \
unsigned int size = bigint_size (modulus); \
bigint_montgomery_raw ( (modulus)->element, (modinv)->element, \
(mont)->element, (result)->element, \
size ); \
} while ( 0 )
/**
* Perform modular multiplication of big integers
*
* @v multiplicand Big integer to be multiplied
* @v multiplier Big integer to be multiplied
* @v modulus Big integer modulus
* @v result Big integer to hold result
* @v tmp Temporary working space
*/
#define bigint_mod_multiply( multiplicand, multiplier, modulus, \
result, tmp ) do { \
unsigned int size = bigint_size (multiplicand); \
bigint_mod_multiply_raw ( (multiplicand)->element, \
(multiplier)->element, \
(modulus)->element, \
(result)->element, size, tmp ); \
} while ( 0 )
/**
* Calculate temporary working space required for moduluar multiplication
*
* @v modulus Big integer modulus
* @ret len Length of temporary working space
*/
#define bigint_mod_multiply_tmp_len( modulus ) ( { \
unsigned int size = bigint_size (modulus); \
sizeof ( struct { \
bigint_t ( size * 2 ) temp_result; \
bigint_t ( size * 2 ) temp_modulus; \
} ); } )
/**
* Perform modular exponentiation of big integers
*
* @v base Big integer base
* @v modulus Big integer modulus
* @v exponent Big integer exponent
* @v result Big integer to hold result
* @v tmp Temporary working space
*/
#define bigint_mod_exp( base, modulus, exponent, result, tmp ) do { \
unsigned int size = bigint_size (base); \
unsigned int exponent_size = bigint_size (exponent); \
bigint_mod_exp_raw ( (base)->element, (modulus)->element, \
(exponent)->element, (result)->element, \
size, exponent_size, tmp ); \
} while ( 0 )
/**
* Calculate temporary working space required for moduluar exponentiation
*
* @v modulus Big integer modulus
* @ret len Length of temporary working space
*/
#define bigint_mod_exp_tmp_len( modulus ) ( { \
unsigned int size = bigint_size (modulus); \
sizeof ( struct { \
bigint_t ( size ) temp[4]; \
} ); } )
#include <bits/bigint.h>
/**
* Test if bit is set in big integer
*
* @v value0 Element 0 of big integer
* @v size Number of elements
* @v bit Bit to test
* @ret is_set Bit is set
*/
static inline __attribute__ (( always_inline )) int
bigint_bit_is_set_raw ( const bigint_element_t *value0, unsigned int size,
unsigned int bit ) {
const bigint_t ( size ) __attribute__ (( may_alias )) *value =
( ( const void * ) value0 );
unsigned int index = ( bit / ( 8 * sizeof ( value->element[0] ) ) );
unsigned int subindex = ( bit % ( 8 * sizeof ( value->element[0] ) ) );
return ( !! ( value->element[index] & ( 1UL << subindex ) ) );
}
/**
* Test if most significant bit is set in big integer
*
* @v value0 Element 0 of big integer
* @v size Number of elements
* @ret is_set Most significant bit is set
*/
static inline __attribute__ (( always_inline )) int
bigint_msb_is_set_raw ( const bigint_element_t *value0, unsigned int size ) {
const bigint_t ( size ) __attribute__ (( may_alias )) *value =
( ( const void * ) value0 );
unsigned int index = ( size - 1 );
unsigned int subindex = ( ( 8 * sizeof ( value->element[0] ) ) - 1 );
return ( !! ( value->element[index] & ( 1UL << subindex ) ) );
}
void bigint_init_raw ( bigint_element_t *value0, unsigned int size,
const void *data, size_t len );
void bigint_done_raw ( const bigint_element_t *value0, unsigned int size,
void *out, size_t len );
int bigint_add_raw ( const bigint_element_t *addend0,
bigint_element_t *value0, unsigned int size );
int bigint_subtract_raw ( const bigint_element_t *subtrahend0,
bigint_element_t *value0, unsigned int size );
void bigint_shl_raw ( bigint_element_t *value0, unsigned int size );
void bigint_shr_raw ( bigint_element_t *value0, unsigned int size );
int bigint_is_zero_raw ( const bigint_element_t *value0, unsigned int size );
int bigint_is_geq_raw ( const bigint_element_t *value0,
const bigint_element_t *reference0,
unsigned int size );
int bigint_bit_is_set_raw ( const bigint_element_t *value0, unsigned int size,
unsigned int bit );
int bigint_max_set_bit_raw ( const bigint_element_t *value0,
unsigned int size );
void bigint_grow_raw ( const bigint_element_t *source0,
unsigned int source_size, bigint_element_t *dest0,
unsigned int dest_size );
void bigint_shrink_raw ( const bigint_element_t *source0,
unsigned int source_size, bigint_element_t *dest0,
unsigned int dest_size );
void bigint_swap_raw ( bigint_element_t *first0, bigint_element_t *second0,
unsigned int size, int swap );
void bigint_multiply_one ( const bigint_element_t multiplicand,
const bigint_element_t multiplier,
bigint_element_t *result,
bigint_element_t *carry );
void bigint_multiply_raw ( const bigint_element_t *multiplicand0,
unsigned int multiplicand_size,
const bigint_element_t *multiplier0,
unsigned int multiplier_size,
bigint_element_t *result0 );
void bigint_reduce_raw ( bigint_element_t *modulus0, bigint_element_t *value0,
unsigned int size );
void bigint_mod_invert_raw ( const bigint_element_t *invertend0,
bigint_element_t *inverse0, unsigned int size );
void bigint_montgomery_raw ( const bigint_element_t *modulus0,
const bigint_element_t *modinv0,
bigint_element_t *mont0,
bigint_element_t *result0, unsigned int size );
void bigint_mod_multiply_raw ( const bigint_element_t *multiplicand0,
const bigint_element_t *multiplier0,
const bigint_element_t *modulus0,
bigint_element_t *result0,
unsigned int size, void *tmp );
void bigint_mod_exp_raw ( const bigint_element_t *base0,
const bigint_element_t *modulus0,
const bigint_element_t *exponent0,
bigint_element_t *result0,
unsigned int size, unsigned int exponent_size,
void *tmp );
#endif /* _IPXE_BIGINT_H */
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