Crypto++  5.6.5 Free C++ class library of cryptographic schemes
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
 T element 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
 r the remainder q the quotient a the dividend d the 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
 a the element b the 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
 a the first element b the 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: