bigint.h

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#ifndef _IPXE_BIGINT_H
#define _IPXE_BIGINT_H
 
/** @file
 *
 * Big integer support
 */
 
FILE_LICENCE ( GPL2_OR_LATER_OR_UBDL );
FILE_SECBOOT ( PERMITTED );
 
#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) ? ( ( (len) + sizeof ( bigint_element_t ) - 1 ) /       \
                    sizeof ( bigint_element_t ) ) : 1 )
 
/**
 * 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] ) )
 
/**
 * Transcribe big integer (for debugging)
 *
 * @v value             Big integer to be transcribed
 * @ret string          Big integer in string form (may be abbreviated)
 */
#define bigint_ntoa( value ) ( {                                        \
        unsigned int size = bigint_size (value);                        \
        bigint_ntoa_raw ( (value)->element, size );                     \
        } )
 
/**
 * 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
 * @ret out             Bit shifted out
 */
#define bigint_shl( value ) ( {                                         \
        unsigned int size = bigint_size (value);                        \
        bigint_shl_raw ( (value)->element, size );                      \
        } )
 
/**
 * Shift big integer right
 *
 * @v value             Big integer
 * @ret out             Bit shifted out
 */
#define bigint_shr( value ) ( {                                         \
        unsigned int size = bigint_size (value);                        \
        bigint_shr_raw ( (value)->element, size );                      \
        } )
 
/**
 * 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 ); } )
 
/**
 * Set bit in big integer
 *
 * @v value             Big integer
 * @v bit               Bit to set
 */
#define bigint_set_bit( value, bit ) do {                               \
        unsigned int size = bigint_size (value);                        \
        bigint_set_bit_raw ( (value)->element, size, bit );             \
        } while ( 0 )
 
/**
 * Clear bit in big integer
 *
 * @v value             Big integer
 * @v bit               Bit to set
 */
#define bigint_clear_bit( value, bit ) do {                             \
        unsigned int size = bigint_size (value);                        \
        bigint_clear_bit_raw ( (value)->element, size, bit );           \
        } while ( 0 )
 
/**
 * 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 R^2 modulo N
 *
 * @v modulus           Big integer modulus
 * @v result            Big integer to hold result
 */
#define bigint_reduce( modulus, result ) do {                           \
        unsigned int size = bigint_size (modulus);                      \
        bigint_reduce_raw ( (modulus)->element, (result)->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 relaxed Montgomery reduction (REDC) of a big integer
 *
 * @v modulus           Big integer odd modulus
 * @v value             Big integer to be reduced
 * @v result            Big integer to hold result
 * @ret carry           Carry out
 */
#define bigint_montgomery_relaxed( modulus, value, result ) ( {         \
        unsigned int size = bigint_size (modulus);                      \
        bigint_montgomery_relaxed_raw ( (modulus)->element,             \
                                        (value)->element,               \
                                        (result)->element, size );      \
        } )
 
/**
 * Perform classic Montgomery reduction (REDC) of a big integer
 *
 * @v modulus           Big integer odd modulus
 * @v value             Big integer to be reduced
 * @v result            Big integer to hold result
 */
#define bigint_montgomery( modulus, value, result ) do {                \
        unsigned int size = bigint_size (modulus);                      \
        bigint_montgomery_raw ( (modulus)->element, (value)->element,   \
                                (result)->element, size );              \
        } while ( 0 )
 
/**
 * Perform generalised exponentiation via a Montgomery ladder
 *
 * @v result            Big integer result (initialised to identity element)
 * @v multiple          Big integer multiple (initialised to generator)
 * @v exponent          Big integer exponent
 * @v op                Montgomery ladder commutative operation
 * @v ctx               Operation context (if needed)
 * @v tmp               Temporary working space (if needed)
 */
#define bigint_ladder( result, multiple, exponent, op, ctx, tmp ) do {  \
        unsigned int size = bigint_size (result);                       \
        unsigned int exponent_size = bigint_size (exponent);            \
        bigint_ladder_raw ( (result)->element, (multiple)->element,     \
                            size, (exponent)->element, exponent_size,   \
                            (op), (ctx), (tmp) );                       \
        } while ( 0 )
 
/**
 * 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>
 
/**
 * A big integer Montgomery ladder commutative operation
 *
 * @v operand           Element 0 of first input operand (may overlap result)
 * @v result            Element 0 of second input operand and result
 * @v size              Number of elements in operands and result
 * @v ctx               Operation context (if needed)
 * @v tmp               Temporary working space (if needed)
 */
typedef void ( bigint_ladder_op_t ) ( const bigint_element_t *operand0,
                                      bigint_element_t *result0,
                                      unsigned int size, const void *ctx,
                                      void *tmp );
 
/**
 * Set bit in big integer
 *
 * @v value0            Element 0 of big integer
 * @v size              Number of elements
 * @v bit               Bit to set
 */
static inline __attribute__ (( always_inline )) void
bigint_set_bit_raw ( bigint_element_t *value0, unsigned int size,
                     unsigned int bit ) {
        bigint_t ( size ) __attribute__ (( may_alias )) *value =
                ( ( void * ) value0 );
        unsigned int index = ( bit / ( 8 * sizeof ( value->element[0] ) ) );
        unsigned int subindex = ( bit % ( 8 * sizeof ( value->element[0] ) ) );
 
        value->element[index] |= ( 1UL << subindex );
}
 
/**
 * Clear bit in big integer
 *
 * @v value0            Element 0 of big integer
 * @v size              Number of elements
 * @v bit               Bit to clear
 */
static inline __attribute__ (( always_inline )) void
bigint_clear_bit_raw ( bigint_element_t *value0, unsigned int size,
                       unsigned int bit ) {
        bigint_t ( size ) __attribute__ (( may_alias )) *value =
                ( ( void * ) value0 );
        unsigned int index = ( bit / ( 8 * sizeof ( value->element[0] ) ) );
        unsigned int subindex = ( bit % ( 8 * sizeof ( value->element[0] ) ) );
 
        value->element[index] &= ~( 1UL << subindex );
}
 
/**
 * 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 ) ) );
}
 
const char * bigint_ntoa_raw ( const bigint_element_t *value0,
                               unsigned int size );
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 );
int bigint_shl_raw ( bigint_element_t *value0, unsigned int size );
int 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 ( const bigint_element_t *modulus0,
                         bigint_element_t *result0, unsigned int size );
void bigint_mod_invert_raw ( const bigint_element_t *invertend0,
                             bigint_element_t *inverse0, unsigned int size );
int bigint_montgomery_relaxed_raw ( const bigint_element_t *modulus0,
                                    bigint_element_t *value0,
                                    bigint_element_t *result0,
                                    unsigned int size );
void bigint_montgomery_raw ( const bigint_element_t *modulus0,
                             bigint_element_t *value0,
                             bigint_element_t *result0, unsigned int size );
void bigint_ladder_raw ( bigint_element_t *result0,
                         bigint_element_t *multiple0, unsigned int size,
                         const bigint_element_t *exponent0,
                         unsigned int exponent_size, bigint_ladder_op_t *op,
                         const void *ctx, void *tmp );
void bigint_mod_exp_ladder ( const bigint_element_t *multiplier0,
                             bigint_element_t *result0, unsigned int size,
                             const void *ctx, 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 */