de.flexiprovider.common.math.ellipticcurves
Class EllipticCurveGF2n

java.lang.Object
  |
  +--de.flexiprovider.common.math.ellipticcurves.EllipticCurve
        |
        +--de.flexiprovider.common.math.ellipticcurves.EllipticCurveGF2n

public class EllipticCurveGF2n

extends EllipticCurve

This class provides features for elliptic curves over finite fields with characteristic 2 (GF(2ⁿ). The equation for such a curve is:
E: y² + xy = x³ + ax² + b.
The parameters a and b are stored in GF2nElements mA and mB.

Author:

Birgit Henhapl

See Also:

EllipticCurve, Point

Fields inherited from class de.flexiprovider.common.math.ellipticcurves.EllipticCurve

mA, mB, mQ

Constructor Summary

EllipticCurveGF2n(GF2nElement a, GF2nElement b, FlexiBigInt q)
Constructs an elliptic curve E with the specified parameters a and b in short Weierstrass normal form in projective representation over the field with the specified size.

EllipticCurveGF2n(GF2nElement a, GF2nElement b, GF2nField gf2n)
Constructs an elliptic curve E with the specified parameters a and b in short Weierstrass normal form in projective representation over the given field.

EllipticCurveGF2n(GF2nElement a, GF2nElement b, int deg)
Constructs an elliptic curve E with the specified parameters a and b in short Weierstrass normal form in projective representation over the field with the specified characteristic 2^deg.

Method Summary

java.lang.String

toString()

Methods inherited from class de.flexiprovider.common.math.ellipticcurves.EllipticCurve

equals, getA, getB, getQ, hashCode

Methods inherited from class java.lang.Object

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

Constructor Detail

EllipticCurveGF2n

public EllipticCurveGF2n(GF2nElement a,
                         GF2nElement b,
                         int deg)

Constructs an elliptic curve E with the specified parameters a and b in short Weierstrass normal form in projective representation over the field with the specified characteristic 2^deg.

Parameters:

a - curve parameter a

b - curve parameter b

deg - extension degree of the underlying field

See Also:

GF2nElement

EllipticCurveGF2n

public EllipticCurveGF2n(GF2nElement a,
                         GF2nElement b,
                         FlexiBigInt q)

Constructs an elliptic curve E with the specified parameters a and b in short Weierstrass normal form in projective representation over the field with the specified size.

Parameters:

a - curve parameter a

b - curve parameter b

q - size of the underlying field

See Also:

GF2nElement

EllipticCurveGF2n

public EllipticCurveGF2n(GF2nElement a,
                         GF2nElement b,
                         GF2nField gf2n)

Constructs an elliptic curve E with the specified parameters a and b in short Weierstrass normal form in projective representation over the given field.

Parameters:

a - curve parameter a

b - curve parameter b

gf2n - the underlying field

See Also:

GF2nElement

Method Detail

toString

public java.lang.String toString()

Overrides:

toString in class EllipticCurve

Returns:

a human readable form of this elliptic curve