de.flexiprovider.common.math.finitefields
Class GF2nONBField

java.lang.Object
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  +--de.flexiprovider.common.math.finitefields.GF2nField
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        +--de.flexiprovider.common.math.finitefields.GF2nONBField

public class GF2nONBField

extends GF2nField

This class implements the abstract class GF2nField for ONB representation. It computes the fieldpolynomial, multiplication matrix and one of its roots mONBRoot, (see for example Certicoms Whitepapers). GF2nField is used by GF2nONBElement which implements the elements of this field.

Author:

Birgit Henhapl, Oliver Seiler

See Also:

GF2nField, GF2nONBElement

Field Summary

(package private) int[][]

mMult holds the multiplication matrix

Fields inherited from class de.flexiprovider.common.math.finitefields.GF2nField

fieldPolynomial, fields, matrices, mDegree

Constructor Summary

GF2nONBField(int deg)
constructs an instance of the finite field with 2^deg elements and characteristic 2.

Method Summary

protected void	computeCOBMatrix(GF2nField B1) Computes the change-of-basis matrix for basis conversion according to 1363.
protected void	computeFieldPolynomial() Computes the field polynomial for a ONB according to IEEE 1363 A.7.2 (p110f).
(package private) int	getONBBit()
(package private) int	getONBLength()
protected GF2nElement	getRandomRoot(GF2Polynomial polynomial) Computes a random root of the given polynomial.
(package private) int[][]	invMatrix(int[][] a) Compute the inverse of a matrix a.

Methods inherited from class de.flexiprovider.common.math.finitefields.GF2nField

convert, equals, getDegree, getFieldPolynomial, hashCode, invertMatrix

Methods inherited from class java.lang.Object

, clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

Field Detail

mMult

int[][] mMult

holds the multiplication matrix

Constructor Detail

GF2nONBField

public GF2nONBField(int deg)
             throws NoSuchBasisException

constructs an instance of the finite field with 2^deg elements and characteristic 2.

Parameters:

deg - - the extention degree of this field

Throws:

NoSuchBasisException - if an ONB-implementation other than type 1 or type 2 is requested.

Method Detail

getONBLength

int getONBLength()

getONBBit

int getONBBit()

getRandomRoot

protected GF2nElement getRandomRoot(GF2Polynomial polynomial)

Computes a random root of the given polynomial.

Overrides:

getRandomRoot in class GF2nField

Parameters:

polynomial - a polynomial

Returns:

a random root of the polynomial

See Also:

"P1363 A.5.6, p103f"

computeCOBMatrix

protected void computeCOBMatrix(GF2nField B1)

Computes the change-of-basis matrix for basis conversion according to 1363. The result is stored in the lists fields and matrices.

Overrides:

computeCOBMatrix in class GF2nField

Parameters:

B1 - the GF2nField to convert to

See Also:

"P1363 A.7.3, p111ff"

computeFieldPolynomial

protected void computeFieldPolynomial()

Computes the field polynomial for a ONB according to IEEE 1363 A.7.2 (p110f).

Overrides:

computeFieldPolynomial in class GF2nField

See Also:

"P1363 A.7.2, p110f"

invMatrix

int[][] invMatrix(int[][] a)

Compute the inverse of a matrix a.

Parameters:

a - the matrix

Returns:

a^-1