de.flexiprovider.common.math.finitefields
Class GF2nElement

java.lang.Object
  |
  +--de.flexiprovider.common.math.finitefields.GF2nElement

All Implemented Interfaces:

GFElement

Direct Known Subclasses:

GF2nONBElement, GF2nPolynomialElement

public abstract class GF2nElement

extends java.lang.Object

implements GFElement

This abstract class implements an element of the finite field GF(2)ⁿ in either optimal normal basis representation (ONB) or in polynomial representation. It is extended by the classes GF2nONBElement and GF2nPolynomialElement .

Author:

Birgit Henhapl, Martin Döring, Oliver Seiler

See Also:

GF2nPolynomialElement, GF2nONBElement, GF2nONBField

Field Summary

protected int	mDegree holds the extension degree n of this element's corresponding field.
protected GF2nField	mField holds a pointer to this element's corresponding field.

Constructor Summary

GF2nElement()

Method Summary

(package private) abstract void	assignOne() Assigns the value 1 to this element.
(package private) abstract void	assignZero() Assign the value 0 to this element.
abstract java.lang.Object	clone()
GF2nElement	convert(GF2nField basis) Performs a basis transformation of this element to the given GF2nField basis.
GF2nField	getField() Returns the field of this element.
abstract GF2nElement	increase() Returns this element + 1.
abstract void	increaseThis() Increases this element by one.
abstract GF2nElement	solveQuadraticEquation() Solves a quadratic equation. Let z2 + z = this.
abstract GF2nElement	square() Returns this element to the power of 2.
abstract GF2nElement	squareRoot() Compute the square root of this element and return the result in a new GF2nElement.
abstract void	squareRootThis() Compute the square root of this element.
abstract void	squareThis() Squares this element.
GFElement	subtract(GFElement minuend) Compute the difference of this element and minuend.
void	subtractFromThis(GFElement minuend) Compute the difference of this element and minuend, overwriting this element.
(package private) abstract boolean	testBit(int index) Checks whether the indexed bit of the bit representation is set
abstract boolean	testRightmostBit() Returns whether the rightmost bit of the bit representation is set.
abstract int	trace() Returns the trace of this element.

Methods inherited from class java.lang.Object

, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface de.flexiprovider.common.math.finitefields.GFElement

add, addToThis, equals, hashCode, invert, isOne, isZero, multiply, multiplyThisBy, toByteArray, toFlexiBigInt, toString, toString

Field Detail

mField

protected GF2nField mField

holds a pointer to this element's corresponding field.

mDegree

protected int mDegree

holds the extension degree n of this element's corresponding field.

Constructor Detail

GF2nElement

public GF2nElement()

Method Detail

clone

public abstract java.lang.Object clone()

Specified by:

clone in interface GFElement

Overrides:

clone in class java.lang.Object

Returns:

a copy of this GF2nElement

assignZero

abstract void assignZero()

Assign the value 0 to this element.

assignOne

abstract void assignOne()

Assigns the value 1 to this element.

testRightmostBit

public abstract boolean testRightmostBit()

Returns whether the rightmost bit of the bit representation is set. This is needed for data conversion according to 1363.

Returns:

true if the rightmost bit of this element is set

testBit

abstract boolean testBit(int index)

Checks whether the indexed bit of the bit representation is set

Parameters:

index - the index of the bit to test

Returns:

true if the indexed bit is set

getField

public final GF2nField getField()

Returns the field of this element.

Returns:

the field of this element

increase

public abstract GF2nElement increase()

Returns this element + 1.

Returns:

this + 1

increaseThis

public abstract void increaseThis()

Increases this element by one.

subtract

public final GFElement subtract(GFElement minuend)
                         throws DifferentFieldsException

Compute the difference of this element and minuend.

Specified by:

subtract in interface GFElement

Parameters:

minuend - the minuend

Returns:

this - minuend (newly created)

Throws:

DifferentFieldsException - if the elements are of different fields.

subtractFromThis

public final void subtractFromThis(GFElement minuend)

Compute the difference of this element and minuend, overwriting this element.

Specified by:

subtractFromThis in interface GFElement

Parameters:

minuend - the minuend

Throws:

DifferentFieldsException - if the elements are of different fields.

square

public abstract GF2nElement square()

Returns this element to the power of 2.

Returns:

this²

squareThis

public abstract void squareThis()

Squares this element.

squareRoot

public abstract GF2nElement squareRoot()

Compute the square root of this element and return the result in a new GF2nElement.

Returns:

this^1/2 (newly created)

squareRootThis

public abstract void squareRootThis()

Compute the square root of this element.

convert

public final GF2nElement convert(GF2nField basis)
                          throws DifferentFieldsException

Performs a basis transformation of this element to the given GF2nField basis.

Parameters:

basis - the GF2nField representation to transform this element to

Returns:

this element in the representation of basis

Throws:

DifferentFieldsException - if this cannot be converted according to basis.

trace

public abstract int trace()

Returns the trace of this element.

Returns:

the trace of this element

solveQuadraticEquation

public abstract GF2nElement solveQuadraticEquation()
                                            throws NoSolutionException

Solves a quadratic equation.
Let z² + z = this. Then this method returns z.

Returns:

z with z² + z = this

Throws:

NoSolutionException - if z² + z = this does not have a solution