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 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
const Element & | Subtract (const Element &a, const Element &b) const
Element & | Accumulate (Element &a, const Element &b) const
Element & | Reduce (Element &a, const Element &b) const
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
Element | Exponentiate (const Element &a, const Integer &e) const
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.
| AbstractRing (const AbstractRing &source)
| Copy construct an AbstractRing. More...
AbstractRing & | operator= (const AbstractRing &source)
| Assign an AbstractRing. 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 | 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 Function Documentation

## Equal()

template<class F >

bool GFP2_ONB< F >::Equal | ( | const GFP2Element & | a,
|  | const GFP2Element & | b
| ) |  | const

inline 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`

Implements AbstractGroup< GFP2Element >.

Definition at line 71 of file xtr.h.

## Identity()

template<class F >

const Element& GFP2_ONB< F >::Identity | ( |  | ) | const

inline virtual

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

inline virtual

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

inline virtual

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

inline virtual

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

inline virtual

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

inline virtual

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

inline virtual

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:

- xtr.h