Abstract group. More...

#include <algebra.h>

Inheritance diagram for AbstractGroup< T >:

Public Types
typedef T	Element

Public Member Functions
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 AbstractGroup< T >

Abstract group.

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 26 of file algebra.h.

Member Typedef Documentation

◆ Element

template<class T >

typedef T AbstractGroup< T >::Element

Definition at line 29 of file algebra.h.

Constructor & Destructor Documentation

◆ ~AbstractGroup()

template<class T >

virtual AbstractGroup< T >::~AbstractGroup ( )

inlinevirtual

Definition at line 31 of file algebra.h.

Member Function Documentation

◆ Equal()

template<class T >

virtual bool AbstractGroup< T >::Equal	(	const Element &	a,
		const Element &	b
	)		const

pure virtual

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

Implemented in EuclideanDomainOf< T >, EuclideanDomainOf< PolynomialMod2 >, QuotientRing< T >, QuotientRing< EuclideanDomainOf< PolynomialMod2 > >, GF2NP, RingOfPolynomialsOver< T >, GFP2_ONB< F >, ModularArithmetic, EC2N, and ECP.

◆ Identity()

template<class T >

virtual const Element & AbstractGroup< T >::Identity ( ) const

pure virtual

Provides the Identity element.

Returns: the Identity element

Implemented in EuclideanDomainOf< T >, EuclideanDomainOf< PolynomialMod2 >, QuotientRing< T >, QuotientRing< EuclideanDomainOf< PolynomialMod2 > >, EC2N, ECP, ModularArithmetic, RingOfPolynomialsOver< T >, and GFP2_ONB< F >.

◆ Add()

template<class T >

virtual const Element & AbstractGroup< T >::Add	(	const Element &	a,
		const Element &	b
	)		const

pure virtual

Adds elements in the group.

Parameters

a	first element
b	second element

Returns: the sum of a and b

Implemented in EuclideanDomainOf< T >, EuclideanDomainOf< PolynomialMod2 >, QuotientRing< T >, QuotientRing< EuclideanDomainOf< PolynomialMod2 > >, RingOfPolynomialsOver< T >, GFP2_ONB< F >, ModularArithmetic, EC2N, and ECP.

◆ Inverse()

template<class T >

virtual const Element & AbstractGroup< T >::Inverse ( const Element & a ) const

pure virtual

Inverts the element in the group.

Parameters

a	first element

Returns: the inverse of the element

Implemented in EuclideanDomainOf< T >, EuclideanDomainOf< PolynomialMod2 >, QuotientRing< T >, QuotientRing< EuclideanDomainOf< PolynomialMod2 > >, RingOfPolynomialsOver< T >, GFP2_ONB< F >, ModularArithmetic, EC2N, and ECP.

◆ InversionIsFast()

template<class T >

virtual bool AbstractGroup< T >::InversionIsFast ( ) const

inlinevirtual

Determine if inversion is fast.

Returns: true if inversion is fast, false otherwise

Reimplemented in EC2N, and ECP.

Definition at line 57 of file algebra.h.

◆ Double()

template<class T >

const T & AbstractGroup< T >::Double ( const Element & a ) const

virtual

Doubles an element in the group.

Parameters

a	the element

Returns: the element doubled

Reimplemented in EuclideanDomainOf< T >, EuclideanDomainOf< PolynomialMod2 >, QuotientRing< T >, QuotientRing< EuclideanDomainOf< PolynomialMod2 > >, RingOfPolynomialsOver< T >, GFP2_ONB< F >, ModularArithmetic, EC2N, and ECP.

Definition at line 15 of file algebra.cpp.

◆ Subtract()

template<class T >

const T & AbstractGroup< T >::Subtract	(	const Element &	a,
		const Element &	b
	)		const

virtual

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 in EuclideanDomainOf< T >, EuclideanDomainOf< PolynomialMod2 >, QuotientRing< T >, QuotientRing< EuclideanDomainOf< PolynomialMod2 > >, RingOfPolynomialsOver< T >, GFP2_ONB< F >, and ModularArithmetic.

Definition at line 20 of file algebra.cpp.

◆ Accumulate()

template<class T >

T & AbstractGroup< T >::Accumulate	(	Element &	a,
		const Element &	b
	)		const

virtual

TODO.

Parameters

a	first element
b	second element

Returns: TODO

Reimplemented in EuclideanDomainOf< T >, EuclideanDomainOf< PolynomialMod2 >, QuotientRing< T >, QuotientRing< EuclideanDomainOf< PolynomialMod2 > >, RingOfPolynomialsOver< T >, GFP2_ONB< F >, and ModularArithmetic.

Definition at line 27 of file algebra.cpp.

◆ Reduce()

template<class T >

T & AbstractGroup< T >::Reduce	(	Element &	a,
		const Element &	b
	)		const

virtual

Reduces an element in the congruence class.

Parameters

a	element to reduce
b	the congruence class

Returns: the reduced element

Reimplemented in EuclideanDomainOf< T >, EuclideanDomainOf< PolynomialMod2 >, QuotientRing< T >, QuotientRing< EuclideanDomainOf< PolynomialMod2 > >, RingOfPolynomialsOver< T >, GFP2_ONB< F >, and ModularArithmetic.

Definition at line 32 of file algebra.cpp.

◆ ScalarMultiply()

template<class T >

T AbstractGroup< T >::ScalarMultiply	(	const Element &	a,
		const Integer &	e
	)		const

virtual

Performs a scalar multiplication.

Parameters

a	multiplicand
e	multiplier

Returns: the product

Reimplemented in ECP.

Definition at line 90 of file algebra.cpp.

◆ CascadeScalarMultiply()

template<class T >

T AbstractGroup< T >::CascadeScalarMultiply	(	const Element &	x,
		const Integer &	e1,
		const Element &	y,
		const Integer &	e2
	)		const

virtual

TODO.

Parameters

x	first multiplicand
e1	the first multiplier
y	second multiplicand
e2	the second multiplier

Returns: TODO

Reimplemented in ECP.

Definition at line 97 of file algebra.cpp.

◆ SimultaneousMultiply()

template<class T >

void AbstractGroup< T >::SimultaneousMultiply	(	Element *	results,
		const Element &	base,
		const Integer *	exponents,
		unsigned int	exponentsCount
	)		const

virtual

Multiplies a base to multiple exponents in a group.

Parameters

results	an array of Elements
base	the base to raise to the exponents
exponents	an array of exponents
exponentsCount	the number of exponents in the array

SimultaneousMultiply() multiplies the base to each exponent in the exponents array and stores the result at the respective position in the results array.

SimultaneousMultiply() must be implemented in a derived class.

Precondition: COUNTOF(results) == exponentsCount; COUNTOF(exponents) == exponentsCount

Reimplemented in ECP.

Definition at line 256 of file algebra.cpp.

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

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ Element

Constructor & Destructor Documentation

◆ ~AbstractGroup()

Member Function Documentation

◆ Equal()

◆ Identity()

◆ Add()

◆ Inverse()

◆ InversionIsFast()

◆ Double()

◆ Subtract()

◆ Accumulate()

◆ Reduce()

◆ ScalarMultiply()

◆ CascadeScalarMultiply()

◆ SimultaneousMultiply()