Crypto++  8.8 Free C++ class library of cryptographic schemes
GFP2_ONB< F > Class Template Reference

GF(p^2), optimal normal basis. More...

Inheritance diagram for GFP2_ONB< F >:

Public Types

typedef F BaseField

Public Types inherited from AbstractRing< GFP2Element >
typedef GFP2Element Element

Public Types inherited from AbstractGroup< GFP2Element >
typedef GFP2Element Element

Public Member Functions

GFP2_ONB (const Integer &p)

const IntegerGetModulus () const

GFP2Element ConvertIn (const Integer &a) const

GFP2Element ConvertIn (const GFP2Element &a) const

GFP2Element ConvertOut (const GFP2Element &a) const

bool Equal (const GFP2Element &a, const GFP2Element &b) const
Compare two elements for equality. More...

const ElementIdentity () const
Provides the Identity element. More...

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

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

const ElementDouble (const Element &a) const

const ElementSubtract (const Element &a, const Element &b) const

ElementAccumulate (Element &a, const Element &b) const

ElementReduce (Element &a, const Element &b) const

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

const ElementMultiplicativeIdentity () const
Retrieves the multiplicative identity. More...

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

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

const ElementSquare (const Element &a) const

Element Exponentiate (const Element &a, const Integer &e) const

const ElementPthPower (const Element &a) const

void RaiseToPthPower (Element &a) const

const ElementSpecialOperation1 (const Element &a) const

const ElementSpecialOperation2 (const Element &x, const Element &y, const Element &z) const

Public Member Functions inherited from AbstractRing< GFP2Element >
AbstractRing ()
Construct an AbstractRing.

AbstractRing (const AbstractRing &source)
Copy construct an AbstractRing. More...

AbstractRingoperator= (const AbstractRing &source)
Assign an AbstractRing. More...

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

virtual const ElementDivide (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< GFP2Element > & MultiplicativeGroup () const
Retrieves the multiplicative group. More...

Public Member Functions inherited from AbstractGroup< GFP2Element >
virtual bool InversionIsFast () const
Determine if inversion is fast. More...

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

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

virtual ElementAccumulate (Element &a, const Element &b) const
TODO. More...

virtual ElementReduce (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 F> class GFP2_ONB< F >

GF(p^2), optimal normal basis.

Definition at line 46 of file xtr.h.

◆ Equal()

template<class F >
 bool GFP2_ONB< F >::Equal ( const GFP2Element & a, const GFP2Element & 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< GFP2Element >.

Definition at line 71 of file xtr.h.

◆ Identity()

template<class F >
 const Element& GFP2_ONB< F >::Identity ( ) const
inlinevirtual

Provides the Identity element.

Returns
the Identity element

Implements AbstractGroup< GFP2Element >.

Definition at line 76 of file xtr.h.

template<class F >
 const Element& GFP2_ONB< F >::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< GFP2Element >.

Definition at line 81 of file xtr.h.

◆ Inverse()

template<class F >
 const Element& GFP2_ONB< F >::Inverse ( const Element & a ) const
inlinevirtual

Inverts the element in the group.

Parameters
 a first element
Returns
the inverse of the element

Implements AbstractGroup< GFP2Element >.

Definition at line 88 of file xtr.h.

◆ IsUnit()

template<class F >
 bool GFP2_ONB< F >::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< GFP2Element >.

Definition at line 123 of file xtr.h.

◆ MultiplicativeIdentity()

template<class F >
 const Element& GFP2_ONB< F >::MultiplicativeIdentity ( ) const
inlinevirtual

Retrieves the multiplicative identity.

Returns
the multiplicative identity

Implements AbstractRing< GFP2Element >.

Definition at line 128 of file xtr.h.

◆ Multiply()

template<class F >
 const Element& GFP2_ONB< F >::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< GFP2Element >.

Definition at line 134 of file xtr.h.

◆ MultiplicativeInverse()

template<class F >
 const Element& GFP2_ONB< F >::MultiplicativeInverse ( const Element & a ) const
inlinevirtual

Calculate the multiplicative inverse of an element in the group.

Parameters
 a the element

Implements AbstractRing< GFP2Element >.

Definition at line 148 of file xtr.h.

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