org.spongycastle.pqc.math.linearalgebra

Class GoppaCode

java.lang.Object

org.spongycastle.pqc.math.linearalgebra.GoppaCode

public final class GoppaCode
extends java.lang.Object

This class describes decoding operations of an irreducible binary Goppa code. A check matrix H of the Goppa code and an irreducible Goppa polynomial are used the operations are worked over a finite field GF(2^m)

See Also:

GF2mField, PolynomialGF2mSmallM

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	GoppaCode.MaMaPe This class is a container for two instances of GF2Matrix and one instance of Permutation.
static class	GoppaCode.MatrixSet This class is a container for an instance of GF2Matrix and one int[].

Method Summary

Modifier and Type	Method and Description
static GoppaCode.MaMaPe	computeSystematicForm(GF2Matrix h, java.security.SecureRandom sr) Given a check matrix H, compute matrices S, M, and a random permutation P such that S*H*P = (Id|M).
static GF2Matrix	createCanonicalCheckMatrix(GF2mField field, PolynomialGF2mSmallM gp) Construct the check matrix of a Goppa code in canonical form from the irreducible Goppa polynomial over the finite field GF(2m).
static GF2Vector	syndromeDecode(GF2Vector syndVec, GF2mField field, PolynomialGF2mSmallM gp, PolynomialGF2mSmallM[] sqRootMatrix) Find an error vector e over GF(2) from an input syndrome s over GF(2m).

Methods inherited from class java.lang.Object

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

Method Detail

createCanonicalCheckMatrix

public static GF2Matrix createCanonicalCheckMatrix(GF2mField field,
                                                   PolynomialGF2mSmallM gp)

Construct the check matrix of a Goppa code in canonical form from the irreducible Goppa polynomial over the finite field GF(2^m).

Parameters:

field - the finite field

gp - the irreducible Goppa polynomial

computeSystematicForm

public static GoppaCode.MaMaPe computeSystematicForm(GF2Matrix h,
                                                     java.security.SecureRandom sr)

Given a check matrix H, compute matrices S, M, and a random permutation P such that S*H*P = (Id|M). Return S^-1, M, and P as GoppaCode.MaMaPe. The matrix (Id | M) is called the systematic form of H.

Parameters:

h - the check matrix

sr - a source of randomness

Returns:

the tuple (S^-1, M, P)

syndromeDecode

public static GF2Vector syndromeDecode(GF2Vector syndVec,
                                       GF2mField field,
                                       PolynomialGF2mSmallM gp,
                                       PolynomialGF2mSmallM[] sqRootMatrix)

Find an error vector e over GF(2) from an input syndrome s over GF(2^m).

Parameters:

syndVec - the syndrome

field - the finite field

gp - the irreducible Goppa polynomial

sqRootMatrix - the matrix for computing square roots in (GF(2^m))^t

Returns:

the error vector