LMath::SpecialModExp method.
If this is you, you can safely skip this section and are finished the documentation unless you want to look at the references.
Currently this class uses methods in the LInteger and
LMath classes. Later versions of this library
will probably be modified so that the class only calls methods
in LMisc and BMath. This should make
porting the methods to other languages much easier. The interface
will change somewhat once this happens, though. The basic purpose of
the class will remain the same, however: To save information
required to do fast modular multiplication in a given base.
When this section refers to the "base of the calling instance"
it, technically, means the cardinality of the residue class of
the Montgomery representtaion. This will equal the value of the
LInteger the class was created with.
unsigned int* Monty::TScratch;
Let N be the
base the calling instance was created
to do modular operations in. Then
TScratch is a buffer for numbers with up to one
more than two times the number of digits as N.
LInteger
Monty::Monty(const LInteger& N);
Creates an object which saves information for converting magnitudes
to and from the Montgomery representation for the
residue class of N, and for doing
arithmetic with these residues.
inline void Monty::MontyReduceTScratch();
Replaces the magnitude in TScratch by the product of
R^{-1} for the calling instance
and the magnitude in TScratch before the method was
called.
(See Montgomery (1985) for defintions)
inline void Monty::MontyMultiply(const unsigned int* a,
const unsigned int* b,
unsigned int* result);
If a and b are the Montgomery representations
of some integers x and y, then this method
will put the Montgomery representation
of the product of x and y
into result. a
and b must have the same number of digits as the
base the calling instance was created for, and at least one of
the two must already be less than this base. The result will have the
same number of digits as the base the calling instance was
created for.
inline void Monty::MontySquare(const unsigned int* a, unsigned int* result);
If a is the Montgomery representation
of some integer x then this method
will put the Montgomery representation
of the square of x
into result. a
must have the same number of digits as the
base the calling instance was created
for, and must
be less than this base. The result
will have the
same number of digits as the base
the calling instance was created for.
inline void Monty::ConvertToMonty(unsigned int* a);
Converts the magnitude pointed to by a to its
Montgomery representation in the base the calling instance
was created for.
a must point to a magnitude having
the same number of digits as the base of the calling instance.
inline void Monty::ConvertFromMonty(unsigned int* a);
Converts the Montgomery representation a points to
back to an integer.
a must point to a magnitude having
the same number of digits as the base of the calling instance.