GF(2^n) with Polynomial Basis. More...

#include <gf2n.h>

Inheritance diagram for GF2NP:

Public Member Functions
	GF2NP (const PolynomialMod2 &modulus)

virtual GF2NP *	Clone () const

virtual void	DEREncode (BufferedTransformation &bt) const

void	DEREncodeElement (BufferedTransformation &out, const Element &a) const

void	BERDecodeElement (BufferedTransformation &in, Element &a) const

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

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

unsigned int	MaxElementBitLength () const

unsigned int	MaxElementByteLength () const

Element	SquareRoot (const Element &a) const

Element	HalfTrace (const Element &a) const

Element	SolveQuadraticEquation (const Element &a) const

Public Member Functions inherited from QuotientRing< EuclideanDomainOf< PolynomialMod2 > >
	QuotientRing (const EuclideanDomain &domain, const Element &modulus)

const EuclideanDomain &	GetDomain () const

const Element &	GetModulus () const

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...

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

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

bool	operator== (const QuotientRing< EuclideanDomainOf< PolynomialMod2 > > &rhs) const

Public Member Functions inherited from AbstractRing< T::Element >
	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< 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...

Additional Inherited Members
Public Types inherited from QuotientRing< EuclideanDomainOf< PolynomialMod2 > >
typedef EuclideanDomainOf< PolynomialMod2 >	EuclideanDomain

typedef T::Element	Element

Public Types inherited from AbstractRing< T::Element >
typedef T	Element

Public Types inherited from AbstractGroup< T >
typedef T	Element

Detailed Description

GF(2^n) with Polynomial Basis.

Definition at line 296 of file gf2n.h.

Member Function Documentation

◆ Clone()

virtual GF2NP * GF2NP::Clone ( ) const

inlinevirtual

Definition at line 301 of file gf2n.h.

◆ DEREncode()

virtual void GF2NP::DEREncode ( BufferedTransformation & bt ) const

inlinevirtual

Definition at line 302 of file gf2n.h.

◆ Equal()

bool GF2NP::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 308 of file gf2n.h.

◆ IsUnit()

bool GF2NP::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::Element >.

Definition at line 311 of file gf2n.h.

◆ MaxElementBitLength()

unsigned int GF2NP::MaxElementBitLength ( ) const

inline

Definition at line 314 of file gf2n.h.

◆ MaxElementByteLength()

unsigned int GF2NP::MaxElementByteLength ( ) const

inline

Definition at line 317 of file gf2n.h.

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

gf2n.h

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ Clone()

◆ DEREncode()

◆ Equal()

◆ IsUnit()

◆ MaxElementBitLength()

◆ MaxElementByteLength()