org.spongycastle.pqc.math.linearalgebra

Class GF2nField

java.lang.Object

org.spongycastle.pqc.math.linearalgebra.GF2nField

Direct Known Subclasses:

GF2nONBField, GF2nPolynomialField

public abstract class GF2nField
extends java.lang.Object

This abstract class defines the finite field GF(2ⁿ). It holds the extension degree n, the characteristic, the irreducible fieldpolynomial and conversion matrices. GF2nField is implemented by the classes GF2nPolynomialField and GF2nONBField.

See Also:

GF2nONBField, GF2nPolynomialField

Field Summary

Fields

Modifier and Type	Field and Description
protected GF2Polynomial	fieldPolynomial the irreducible fieldPolynomial stored in normal order (also for ONB)
protected java.util.Vector	fields holds a list of GF2nFields to which elements have been converted and thus a COB-Matrix exists
protected java.util.Vector	matrices the COB matrices
protected int	mDegree the degree of this field

Constructor Summary

Constructors

Constructor and Description
GF2nField()

Method Summary

Methods

Modifier and Type	Method and Description
protected abstract void	computeCOBMatrix(GF2nField B1) Computes the change-of-basis matrix for basis conversion according to 1363.
protected abstract void	computeFieldPolynomial() Computes the fieldpolynomial.
GF2nElement	convert(GF2nElement elem, GF2nField basis) Converts the given element in representation according to this field to a new element in representation according to B1 using the change-of-basis matrix calculated by computeCOBMatrix.
boolean	equals(java.lang.Object other) Decides whether the given object other is the same as this field.
int	getDegree() Returns the degree n of this field.
GF2Polynomial	getFieldPolynomial() Returns the fieldpolynomial as a new Bitstring.
protected abstract GF2nElement	getRandomRoot(GF2Polynomial B0FieldPolynomial) Computes a random root from the given irreducible fieldpolynomial according to IEEE 1363 algorithm A.5.6.
int	hashCode()
protected GF2Polynomial[]	invertMatrix(GF2Polynomial[] matrix) Inverts the given matrix represented as bitstrings.

Methods inherited from class java.lang.Object

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

Field Detail

mDegree

protected int mDegree

the degree of this field

fieldPolynomial

protected GF2Polynomial fieldPolynomial

the irreducible fieldPolynomial stored in normal order (also for ONB)

fields

protected java.util.Vector fields

holds a list of GF2nFields to which elements have been converted and thus a COB-Matrix exists

matrices

protected java.util.Vector matrices

the COB matrices

Constructor Detail

GF2nField

public GF2nField()

Method Detail

getDegree

public final int getDegree()

Returns the degree n of this field.

Returns:

the degree n of this field

getFieldPolynomial

public final GF2Polynomial getFieldPolynomial()

Returns the fieldpolynomial as a new Bitstring.

Returns:

a copy of the fieldpolynomial as a new Bitstring

equals

public final boolean equals(java.lang.Object other)

Decides whether the given object other is the same as this field.

Overrides:

equals in class java.lang.Object

Parameters:

other - another object

Returns:

(this == other)

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object

Returns:

the hash code of this field

getRandomRoot

protected abstract GF2nElement getRandomRoot(GF2Polynomial B0FieldPolynomial)

Computes a random root from the given irreducible fieldpolynomial according to IEEE 1363 algorithm A.5.6. This cal take very long for big degrees.

Parameters:

B0FieldPolynomial - the fieldpolynomial if the other basis as a Bitstring

Returns:

a random root of BOFieldPolynomial in representation according to this field

See Also:

"P1363 A.5.6, p103f"

computeCOBMatrix

protected abstract 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.

Parameters:

B1 - the GF2nField to convert to

See Also:

"P1363 A.7.3, p111ff"

computeFieldPolynomial

protected abstract void computeFieldPolynomial()

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

invertMatrix

protected final GF2Polynomial[] invertMatrix(GF2Polynomial[] matrix)

Inverts the given matrix represented as bitstrings.

Parameters:

matrix - the matrix to invert as a Bitstring[]

Returns:

matrix^(-1)

convert

public final GF2nElement convert(GF2nElement elem,
                  GF2nField basis)
                          throws java.lang.RuntimeException

Converts the given element in representation according to this field to a new element in representation according to B1 using the change-of-basis matrix calculated by computeCOBMatrix.

Parameters:

elem - the GF2nElement to convert

basis - the basis to convert elem to

Returns:

elem converted to a new element representation according to basis

Throws:

DifferentFieldsException - if elem cannot be converted according to basis.

java.lang.RuntimeException

See Also:

computeCOBMatrix(org.spongycastle.pqc.math.linearalgebra.GF2nField), getRandomRoot(org.spongycastle.pqc.math.linearalgebra.GF2Polynomial), GF2nPolynomial, "P1363 A.7 p109ff"