Crypto++  8.2 Free C++ class library of cryptographic schemes
EuclideanDomainOf< T > Class Template Reference

Euclidean domain. More... Inheritance diagram for EuclideanDomainOf< T >:

Public Types

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

Public Member Functions

bool Equal (const Element &a, const Element &b) const
Compare two elements for equality. More...

const Element & Identity () const
Provides the Identity element. More...

const Element & Add (const Element &a, const Element &b) const
Adds elements in the group. More...

Element & Accumulate (Element &a, const Element &b) const
TODO. More...

const Element & Inverse (const Element &a) const
Inverts the element in the group. More...

const Element & Subtract (const Element &a, const Element &b) const
Subtracts elements in the group. More...

Element & Reduce (Element &a, const Element &b) const
Reduces an element in the congruence class. More...

const Element & Double (const Element &a) const
Doubles an element in the group. More...

const Element & MultiplicativeIdentity () const
Retrieves the multiplicative identity. More...

const Element & Multiply (const Element &a, const Element &b) const
Multiplies elements in the group. More...

const Element & Square (const Element &a) const
Square an element in the group. More...

bool IsUnit (const Element &a) const
Determines whether an element is a unit in the group. More...

const Element & MultiplicativeInverse (const Element &a) const
Calculate the multiplicative inverse of an element in the group. More...

const Element & Divide (const Element &a, const Element &b) const
Divides elements in the group. More...

const Element & Mod (const Element &a, const Element &b) const
Performs a modular reduction in the ring. More...

void DivisionAlgorithm (Element &r, Element &q, const Element &a, const Element &d) const
Performs the division algorithm on two elements in the ring. More...

bool operator== (const EuclideanDomainOf< T > &rhs) const Public Member Functions inherited from AbstractEuclideanDomain< T >
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 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 InversionIsFast () const
Determine if inversion is fast. 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 EuclideanDomainOf< T >

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 315 of file algebra.h.

◆ Equal()

template<class T>
 bool EuclideanDomainOf< T >::Equal ( const Element & a, const Element & b ) const
inlinevirtual

Compare two elements for equality.

Parameters
 a first element b second element
Returns
true if the elements are equal, false otherwise

Equal() tests the elements for equality using `a==b`

Implements AbstractGroup< T >.

Definition at line 322 of file algebra.h.

◆ Identity()

template<class T>
 const Element& EuclideanDomainOf< T >::Identity ( ) const
inlinevirtual

Provides the Identity element.

Returns
the Identity element

Implements AbstractGroup< T >.

Definition at line 325 of file algebra.h.

template<class T>
 const Element& EuclideanDomainOf< T >::Add ( const Element & a, const Element & b ) const
inlinevirtual

Parameters
 a first element b second element
Returns
the sum of `a` and `b`

Implements AbstractGroup< T >.

Definition at line 328 of file algebra.h.

◆ Accumulate()

template<class T>
 Element& EuclideanDomainOf< T >::Accumulate ( Element & a, const Element & b ) const
inlinevirtual

TODO.

Parameters
 a first element b second element
Returns
TODO

Reimplemented from AbstractGroup< T >.

Definition at line 331 of file algebra.h.

◆ Inverse()

template<class T>
 const Element& EuclideanDomainOf< T >::Inverse ( const Element & a ) const
inlinevirtual

Inverts the element in the group.

Parameters
 a first element
Returns
the inverse of the element

Implements AbstractGroup< T >.

Definition at line 334 of file algebra.h.

◆ Subtract()

template<class T>
 const Element& EuclideanDomainOf< T >::Subtract ( const Element & a, const Element & b ) const
inlinevirtual

Subtracts elements in the group.

Parameters
 a first element b second element
Returns
the difference of `a` and `b`. The element `a` must provide a Subtract member function.

Reimplemented from AbstractGroup< T >.

Definition at line 337 of file algebra.h.

◆ Reduce()

template<class T>
 Element& EuclideanDomainOf< T >::Reduce ( Element & a, const Element & b ) const
inlinevirtual

Reduces an element in the congruence class.

Parameters
 a element to reduce b the congruence class
Returns
the reduced element

Reimplemented from AbstractGroup< T >.

Definition at line 340 of file algebra.h.

◆ Double()

template<class T>
 const Element& EuclideanDomainOf< T >::Double ( const Element & a ) const
inlinevirtual

Doubles an element in the group.

Parameters
 a the element
Returns
the element doubled

Reimplemented from AbstractGroup< T >.

Definition at line 343 of file algebra.h.

◆ MultiplicativeIdentity()

template<class T>
 const Element& EuclideanDomainOf< T >::MultiplicativeIdentity ( ) const
inlinevirtual

Retrieves the multiplicative identity.

Returns
the multiplicative identity

Implements AbstractRing< T >.

Definition at line 346 of file algebra.h.

◆ Multiply()

template<class T>
 const Element& EuclideanDomainOf< T >::Multiply ( const Element & a, const Element & b ) const
inlinevirtual

Multiplies elements in the group.

Parameters
 a the multiplicand b the multiplier
Returns
the product of a and b

Implements AbstractRing< T >.

Definition at line 349 of file algebra.h.

◆ Square()

template<class T>
 const Element& EuclideanDomainOf< T >::Square ( const Element & a ) const
inlinevirtual

Square an element in the group.

Parameters
 a the element
Returns
the element squared

Reimplemented from AbstractRing< T >.

Definition at line 352 of file algebra.h.

◆ IsUnit()

template<class T>
 bool EuclideanDomainOf< T >::IsUnit ( const Element & a ) const
inlinevirtual

Determines whether an element is a unit in the group.

Parameters
 a the element
Returns
true if the element is a unit after reduction, false otherwise.

Implements AbstractRing< T >.

Definition at line 355 of file algebra.h.

◆ MultiplicativeInverse()

template<class T>
 const Element& EuclideanDomainOf< T >::MultiplicativeInverse ( const Element & a ) const
inlinevirtual

Calculate the multiplicative inverse of an element in the group.

Parameters
 a the element

Implements AbstractRing< T >.

Definition at line 358 of file algebra.h.

◆ Divide()

template<class T>
 const Element& EuclideanDomainOf< T >::Divide ( const Element & a, const Element & b ) const
inlinevirtual

Divides elements in the group.

Parameters
 a the dividend b the divisor
Returns
the quotient

Reimplemented from AbstractRing< T >.

Definition at line 361 of file algebra.h.

◆ Mod()

template<class T>
 const Element& EuclideanDomainOf< T >::Mod ( const Element & a, const Element & b ) const
inlinevirtual

Performs a modular reduction in the ring.

Parameters
 a the element b the modulus
Returns
the result of `ab`.

Implements AbstractEuclideanDomain< T >.

Definition at line 364 of file algebra.h.

◆ DivisionAlgorithm()

template<class T>
 void EuclideanDomainOf< T >::DivisionAlgorithm ( Element & r, Element & q, const Element & a, const Element & d ) const
inlinevirtual

Performs the division algorithm on two elements in the ring.

Parameters
 r the remainder q the quotient a the dividend d the divisor

Implements AbstractEuclideanDomain< T >.

Definition at line 367 of file algebra.h.

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