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

#include <xtr.h>

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

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

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

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

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

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

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

bool	IsUnit (const Element &a) const
	Determines whether an element is a unit 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 &	MultiplicativeInverse (const Element &a) const
	Calculate the multiplicative inverse of an element in the group. More...

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

Element	Exponentiate (const Element &a, const Integer &e) const
	Raises a base to an exponent in the group. More...

const Element &	PthPower (const Element &a) const

void	RaiseToPthPower (Element &a) const

const Element &	SpecialOperation1 (const Element &a) const

const Element &	SpecialOperation2 (const Element &x, const Element &y, const Element &z) const

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

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

AbstractRing &	operator= (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< GFP2Element > &	MultiplicativeGroup () const
	Retrieves the multiplicative group. More...

Public Member Functions inherited from AbstractGroup< GFP2Element >
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 F>
class GFP2_ONB< F >

GF(p^2), optimal normal basis.

Definition at line 46 of file xtr.h.

Member Typedef Documentation

◆ BaseField

template<class F >

typedef F GFP2_ONB< F >::BaseField

Definition at line 49 of file xtr.h.

Constructor & Destructor Documentation

◆ GFP2_ONB()

template<class F >

GFP2_ONB< F >::GFP2_ONB ( const Integer & p )

inline

Definition at line 51 of file xtr.h.

Member Function Documentation

◆ GetModulus()

template<class F >

const Integer & GFP2_ONB< F >::GetModulus ( ) const

inline

Definition at line 57 of file xtr.h.

◆ ConvertIn() [1/2]

template<class F >

GFP2Element GFP2_ONB< F >::ConvertIn ( const Integer & a ) const

inline

Definition at line 59 of file xtr.h.

◆ ConvertIn() [2/2]

template<class F >

GFP2Element GFP2_ONB< F >::ConvertIn ( const GFP2Element & a ) const

inline

Definition at line 65 of file xtr.h.

◆ ConvertOut()

template<class F >

GFP2Element GFP2_ONB< F >::ConvertOut ( const GFP2Element & a ) const

inline

Definition at line 68 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.

◆ Add()

template<class F >

const Element & GFP2_ONB< F >::Add	(	const Element &	a,
		const Element &	b
	)		const

inlinevirtual

Adds elements in the group.

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.

◆ Double()

template<class F >

const Element & GFP2_ONB< F >::Double ( const Element & a ) const

inlinevirtual

Doubles an element in the group.

Parameters

a	the element

Returns: the element doubled

Reimplemented from AbstractGroup< GFP2Element >.

Definition at line 95 of file xtr.h.

◆ Subtract()

template<class F >

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

Definition at line 102 of file xtr.h.

◆ Accumulate()

template<class F >

Element & GFP2_ONB< F >::Accumulate	(	Element &	a,
		const Element &	b
	)		const

inlinevirtual

TODO.

Parameters

a	first element
b	second element

Returns: TODO

Reimplemented from AbstractGroup< GFP2Element >.

Definition at line 109 of file xtr.h.

◆ Reduce()

template<class F >

Element & GFP2_ONB< F >::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< GFP2Element >.

Definition at line 116 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.

◆ Square()

template<class F >

const Element & GFP2_ONB< F >::Square ( const Element & a ) const

inlinevirtual

Square an element in the group.

Parameters

a	the element

Returns: the element squared

Reimplemented from AbstractRing< GFP2Element >.

Definition at line 153 of file xtr.h.

◆ Exponentiate()

template<class F >

Element GFP2_ONB< F >::Exponentiate	(	const Element &	a,
		const Integer &	e
	)		const

inlinevirtual

Raises a base to an exponent in the group.

Parameters

a	the base
e	the exponent

Returns: the exponentiation

Reimplemented from AbstractRing< GFP2Element >.

Definition at line 161 of file xtr.h.

◆ PthPower()

template<class F >

const Element & GFP2_ONB< F >::PthPower ( const Element & a ) const

inline

Definition at line 169 of file xtr.h.

◆ RaiseToPthPower()

template<class F >

void GFP2_ONB< F >::RaiseToPthPower ( Element & a ) const

inline

Definition at line 176 of file xtr.h.

◆ SpecialOperation1()

template<class F >

const Element & GFP2_ONB< F >::SpecialOperation1 ( const Element & a ) const

inline

Definition at line 182 of file xtr.h.

◆ SpecialOperation2()

template<class F >

const Element & GFP2_ONB< F >::SpecialOperation2	(	const Element &	x,
		const Element &	y,
		const Element &	z
	)		const

inline

Definition at line 194 of file xtr.h.

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

xtr.h

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ BaseField

Constructor & Destructor Documentation

◆ GFP2_ONB()

Member Function Documentation

◆ GetModulus()

◆ ConvertIn() [1/2]

◆ ConvertIn() [2/2]

◆ ConvertOut()

◆ Equal()

◆ Identity()

◆ Add()

◆ Inverse()

◆ Double()

◆ Subtract()

◆ Accumulate()

◆ Reduce()

◆ IsUnit()

◆ MultiplicativeIdentity()

◆ Multiply()

◆ MultiplicativeInverse()

◆ Square()

◆ Exponentiate()

◆ PthPower()

◆ RaiseToPthPower()

◆ SpecialOperation1()

◆ SpecialOperation2()