Package dk.jonaslindstrom.ruffini.elliptic.structures

Class MontgomeryCurve<E,F extends Field<E>>

java.lang.Object

dk.jonaslindstrom.ruffini.elliptic.structures.MontgomeryCurve<E,F>

All Implemented Interfaces:

AdditiveGroup<AffinePoint<E>>, CommutativeMonoid<AffinePoint<E>>, Set<AffinePoint<E>>

Direct Known Subclasses:

Curve25519

public class MontgomeryCurve<E,F extends Field<E>>
extends Object
implements AdditiveGroup<AffinePoint<E>>

Curve on Montgomery form By² = x³ + Ax² + x. The field should have characteristics not equal to 2, A ≠ ∓ 2 and B ≠ 0.

Field Summary

Fields

Modifier and Type	Field	Description
protected final E	A
protected final E	B
protected final F	field

Constructor Summary

Constructors

Constructor	Description
MontgomeryCurve(F field, E A, E B)

Method Summary

Modifier and Type	Method	Description
AffinePoint<E>	add(AffinePoint<E> p, AffinePoint<E> q)	Return the result of a+b.
E	discriminant()
boolean	equals(AffinePoint<E> a, AffinePoint<E> b)	Returns true if and only if a = b as elements of this set.
E	getA()
E	getB()
Pair<ShortWeierstrassCurveAffine<E,F>,java.util.function.UnaryOperator<AffinePoint<E>>>	getCorrespondingWeierstrassCurve()
F	getField()
E	jInvariant()
AffinePoint<E>	negate(AffinePoint<E> p)	Return -a.
String	toString()
String	toString(AffinePoint<E> a)	Returns a human-readable string representation of an element in this set.
AffinePoint<E>	zero()	Return the zero element.

Methods inherited from class java.lang.Object

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

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.AdditiveGroup

doubling, isZero, scale, scale, subtract, sum

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.CommutativeMonoid

add, add

Field Details

A

protected final E A

B

protected final E B

field

protected final F extends Field<E> field

Constructor Details

MontgomeryCurve

public MontgomeryCurve(F field,
 E A,
 E B)

Method Details

getField

public F getField()

discriminant

public E discriminant()

jInvariant

public E jInvariant()

toString

public String toString(AffinePoint<E> a)

Description copied from interface: Set

Returns a human-readable string representation of an element in this set.

Specified by:

toString in interface Set<E>

equals

public boolean equals(AffinePoint<E> a,
 AffinePoint<E> b)

Description copied from interface: Set

Returns true if and only if a = b as elements of this set.

Specified by:

equals in interface Set<E>

add

public AffinePoint<E> add(AffinePoint<E> p,
 AffinePoint<E> q)

Description copied from interface: CommutativeMonoid

Return the result of a+b.

Specified by:

add in interface CommutativeMonoid<E>

negate

public AffinePoint<E> negate(AffinePoint<E> p)

Description copied from interface: AdditiveGroup

Return -a.

Specified by:

negate in interface AdditiveGroup<E>

zero

public AffinePoint<E> zero()

Description copied from interface: CommutativeMonoid

Return the zero element.

Specified by:

zero in interface CommutativeMonoid<E>

toString

public String toString()

Overrides:

toString in class Object

getA

public E getA()

getB

public E getB()

getCorrespondingWeierstrassCurve

public Pair<ShortWeierstrassCurveAffine<E,F>,java.util.function.UnaryOperator<AffinePoint<E>>> getCorrespondingWeierstrassCurve()