de.flexiprovider.common.math.finitefields
Class GF2nPolynomialField

java.lang.Object
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  +--de.flexiprovider.common.math.finitefields.GF2nField
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        +--de.flexiprovider.common.math.finitefields.GF2nPolynomialField

public class GF2nPolynomialField

extends GF2nField

This class implements the abstract class GF2nField for polynomial representation. It computes the field polynomial and the squaring matrix. GF2nField is used by GF2nPolynomialElement which implements the elements of this field.

Author:

Oliver Seiler

See Also:

GF2nField, GF2nPolynomialElement

Field Summary

(package private) GF2Polynomial[]

squaringMatrix Matrix used for fast squaring

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

fieldPolynomial, fields, matrices, mDegree

Constructor Summary

GF2nPolynomialField(int deg)
constructs an instance of the finite field with 2^deg elements and characteristic 2.

GF2nPolynomialField(int deg, boolean file)
constructs an instance of the finite field with 2^deg elements and characteristic 2.

GF2nPolynomialField(int deg, GF2Polynomial polynomial)
Creates a new GF2nField of degree i and uses the given polynomial as field polynomial.

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.
protected void	computeFieldPolynomial2() Computes the field polynomial.
int[]	getPc() Returns the degree of the middle coefficients of the used field pentanomial (x^n + x^(getPc()[2]) + x^(getPc()[1]) + x^(getPc()[0]) + 1).
protected GF2nElement	getRandomRoot(GF2Polynomial polynomial) Compute a random root of the given GF2Polynomial.
GF2Polynomial	getSquaringVector(int i) Return row vector i of the squaring matrix.
int	getTc() Returns the degree of the middle coefficient of the used field trinomial (x^n + x^(getTc()) + 1).
boolean	isPentanomial() Returns true if the field polynomial is a pentanomial.
boolean	isTrinomial() Returns true if the field polynomial is a trinomial.

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

squaringMatrix

GF2Polynomial[] squaringMatrix

Matrix used for fast squaring

Constructor Detail

GF2nPolynomialField

public GF2nPolynomialField(int deg)

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

Parameters:

deg - the extention degree of this field

GF2nPolynomialField

public GF2nPolynomialField(int deg,
                           boolean file)

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

Parameters:

deg - the degree of this field

file - true if you want to read the field polynomial from the file false if you want to use a random fielpolynomial (this can take very long for huge degrees)

GF2nPolynomialField

public GF2nPolynomialField(int deg,
                           GF2Polynomial polynomial)
                    throws PolynomialIsNotIrreducibleException

Creates a new GF2nField of degree i and uses the given polynomial as field polynomial. The polynomial is checked whether it is irreducible. This can take some time if i is huge!

Parameters:

deg - degree of the GF2nField

polynomial - the field polynomial to use

Throws:

PolynomialIsNotIrreducibleException - if the given polynomial is not irreducible in GF(2^i)

Method Detail

isTrinomial

public boolean isTrinomial()

Returns true if the field polynomial is a trinomial. The coefficient can be retrieved using getTc().

Returns:

true if the field polynomial is a trinomial

isPentanomial

public boolean isPentanomial()

Returns true if the field polynomial is a pentanomial. The coefficients can be retrieved using getPc().

Returns:

true if the field polynomial is a pentanomial

getTc

public int getTc()
          throws GFException

Returns the degree of the middle coefficient of the used field trinomial (x^n + x^(getTc()) + 1).

Returns:

the middle coefficient of the used field trinomial

Throws:

GFException - if the field polynomial is not a trinomial

getPc

public int[] getPc()
            throws GFException

Returns the degree of the middle coefficients of the used field pentanomial (x^n + x^(getPc()[2]) + x^(getPc()[1]) + x^(getPc()[0]) + 1).

Returns:

the middle coefficients of the used field pentanomial

Throws:

GFException - if the field polynomial is not a pentanomial

getSquaringVector

public GF2Polynomial getSquaringVector(int i)

Return row vector i of the squaring matrix.

Parameters:

i - the index of the row vector to return

Returns:

a copy of squaringMatrix[i]

See Also:

GF2nPolynomialElement.squareMatrix()

getRandomRoot

protected GF2nElement getRandomRoot(GF2Polynomial polynomial)

Compute a random root of the given GF2Polynomial.

Overrides:

getRandomRoot in class GF2nField

Parameters:

polynomial - the polynomial

Returns:

a random root of polynomial

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. This can take a long time for big degrees.

Overrides:

computeFieldPolynomial in class GF2nField

computeFieldPolynomial2

protected void computeFieldPolynomial2()

Computes the field polynomial. This can take a long time for big degrees.