Crypto++  5.6.5
Free C++ class library of cryptographic schemes
Public Types | Public Member Functions | List of all members
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
 Doubles an element in the group. More...
 
const ElementSubtract (const Element &a, const Element &b) const
 Subtracts elements in the group. More...
 
ElementAccumulate (Element &a, const Element &b) const
 TODO. More...
 
ElementReduce (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 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
 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 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 ElementDivide (const Element &a, const Element &b) const
 Divides elements 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 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 48 of file xtr.h.

Member Function Documentation

template<class F>
bool GFP2_ONB< F >::Equal ( const GFP2Element a,
const GFP2Element b 
) const
inlinevirtual

Compare two elements for equality.

Parameters
afirst element
bsecond 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 73 of file xtr.h.

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 78 of file xtr.h.

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

Adds elements in the group.

Parameters
afirst element
bsecond element
Returns
the sum of a and b

Implements AbstractGroup< GFP2Element >.

Definition at line 83 of file xtr.h.

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

Inverts the element in the group.

Parameters
afirst element
Returns
the inverse of the element

Implements AbstractGroup< GFP2Element >.

Definition at line 90 of file xtr.h.

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

Doubles an element in the group.

Parameters
athe element
Returns
the element doubled

Reimplemented from AbstractGroup< GFP2Element >.

Definition at line 97 of file xtr.h.

template<class F>
const Element& GFP2_ONB< F >::Subtract ( const Element a,
const Element b 
) const
inlinevirtual

Subtracts elements in the group.

Parameters
afirst element
bsecond element
Returns
the difference of a and b. The element a must provide a Subtract member function.

Reimplemented from AbstractGroup< GFP2Element >.

Definition at line 104 of file xtr.h.

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

TODO.

Parameters
afirst element
bsecond element
Returns
TODO

Reimplemented from AbstractGroup< GFP2Element >.

Definition at line 111 of file xtr.h.

template<class F>
Element& GFP2_ONB< F >::Reduce ( Element a,
const Element b 
) const
inlinevirtual

Reduces an element in the congruence class.

Parameters
aelement to reduce
bthe congruence class
Returns
the reduced element

Reimplemented from AbstractGroup< GFP2Element >.

Definition at line 118 of file xtr.h.

template<class F>
bool GFP2_ONB< F >::IsUnit ( const Element a) const
inlinevirtual

Determines whether an element is a unit in the group.

Parameters
athe element
Returns
true if the element is a unit after reduction, false otherwise.

Implements AbstractRing< GFP2Element >.

Definition at line 125 of file xtr.h.

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 130 of file xtr.h.

template<class F>
const Element& GFP2_ONB< F >::Multiply ( const Element a,
const Element b 
) const
inlinevirtual

Multiplies elements in the group.

Parameters
athe multiplicand
bthe multiplier
Returns
the product of a and b

Implements AbstractRing< GFP2Element >.

Definition at line 136 of file xtr.h.

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
athe element

Implements AbstractRing< GFP2Element >.

Definition at line 150 of file xtr.h.

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

Square an element in the group.

Parameters
athe element
Returns
the element squared

Reimplemented from AbstractRing< GFP2Element >.

Definition at line 155 of file xtr.h.

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
athe base
ethe exponent
Returns
the exponentiation

Reimplemented from AbstractRing< GFP2Element >.

Definition at line 163 of file xtr.h.


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