Crypto++  5.6.3
Free C++ class library of cryptographic schemes
Public Types | Public Member Functions | List of all members
AbstractEuclideanDomain< T > Class Template Referenceabstract

Abstract Euclidean domain. More...

+ Inheritance diagram for AbstractEuclideanDomain< T >:

Public Types

typedef T Element
 
- Public Types inherited from AbstractRing< T >
typedef T Element
 
- Public Types inherited from AbstractGroup< T >
typedef T Element
 

Public Member Functions

virtual void DivisionAlgorithm (Element &r, Element &q, const Element &a, const Element &d) const =0
 Performs the division algorithm on two elements in the ring. More...
 
virtual const Element & Mod (const Element &a, const Element &b) const =0
 Performs a modular reduction in the ring. More...
 
virtual const Element & Gcd (const Element &a, const Element &b) const
 Calculates the greatest common denominator in the ring. More...
 
- Public Member Functions inherited from AbstractRing< T >
 AbstractRing ()
 Construct an AbstractRing.
 
 AbstractRing (const AbstractRing &source)
 Copy construct an AbstractRing. More...
 
AbstractRingoperator= (const AbstractRing &source)
 Assign an AbstractRing. More...
 
virtual bool IsUnit (const Element &a) const =0
 Determines whether an element is a unit in the group. More...
 
virtual const Element & MultiplicativeIdentity () const =0
 Retrieves the multiplicative identity. More...
 
virtual const Element & Multiply (const Element &a, const Element &b) const =0
 Multiplies elements in the group. More...
 
virtual const Element & MultiplicativeInverse (const Element &a) const =0
 Calculate the multiplicative inverse of an element in the group. More...
 
virtual const Element & Square (const Element &a) const
 Square an element in the group. More...
 
virtual const Element & Divide (const Element &a, const Element &b) const
 Divides elements in the group. More...
 
virtual Element Exponentiate (const Element &a, const Integer &e) const
 Raises a base to an exponent in the group. More...
 
virtual Element CascadeExponentiate (const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
 TODO. More...
 
virtual void SimultaneousExponentiate (Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
 Exponentiates a base to multiple exponents in the Ring. More...
 
virtual const AbstractGroup< T > & MultiplicativeGroup () const
 Retrieves the multiplicative group. More...
 
- Public Member Functions inherited from AbstractGroup< T >
virtual bool Equal (const Element &a, const Element &b) const =0
 Compare two elements for equality. More...
 
virtual const Element & Identity () const =0
 Provides the Identity element. More...
 
virtual const Element & Add (const Element &a, const Element &b) const =0
 Adds elements in the group. More...
 
virtual const Element & Inverse (const Element &a) const =0
 Inverts the element in the group. More...
 
virtual bool InversionIsFast () const
 Determine if inversion is fast. More...
 
virtual const Element & Double (const Element &a) const
 Doubles an element in the group. More...
 
virtual const Element & Subtract (const Element &a, const Element &b) const
 Subtracts elements in the group. More...
 
virtual Element & Accumulate (Element &a, const Element &b) const
 TODO. More...
 
virtual Element & Reduce (Element &a, const Element &b) const
 Reduces an element in the congruence class. More...
 
virtual Element ScalarMultiply (const Element &a, const Integer &e) const
 Performs a scalar multiplication. More...
 
virtual Element CascadeScalarMultiply (const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
 TODO. More...
 
virtual void SimultaneousMultiply (Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
 Multiplies a base to multiple exponents in a group. More...
 

Detailed Description

template<class T>
class AbstractEuclideanDomain< T >

Abstract Euclidean domain.

Template Parameters
Telement class or type

const Element& returned by member functions are references to internal data members. Since each object may have only one such data member for holding results, the following code will produce incorrect results:

    abcd = group.Add(group.Add(a,b), group.Add(c,d));

But this should be fine:

    abcd = group.Add(a, group.Add(b, group.Add(c,d));

Definition at line 276 of file algebra.h.

Member Function Documentation

template<class T>
virtual void AbstractEuclideanDomain< T >::DivisionAlgorithm ( Element &  r,
Element &  q,
const Element &  a,
const Element &  d 
) const
pure virtual

Performs the division algorithm on two elements in the ring.

Parameters
rthe remainder
qthe quotient
athe dividend
dthe divisor

Implemented in RingOfPolynomialsOver< T >, EuclideanDomainOf< T >, and EuclideanDomainOf< PolynomialMod2 >.

template<class T >
const T & AbstractEuclideanDomain< T >::Mod ( const Element &  a,
const Element &  b 
) const
pure virtual

Performs a modular reduction in the ring.

Parameters
athe element
bthe modulus
Returns
the result of ab.

Implemented in RingOfPolynomialsOver< T >, EuclideanDomainOf< T >, and EuclideanDomainOf< PolynomialMod2 >.

Definition at line 49 of file algebra.cpp.

template<class T >
const T & AbstractEuclideanDomain< T >::Gcd ( const Element &  a,
const Element &  b 
) const
virtual

Calculates the greatest common denominator in the ring.

Parameters
athe first element
bthe second element
Returns
the the greatest common denominator of a and b.

Definition at line 56 of file algebra.cpp.


The documentation for this class was generated from the following files: