Package dk.jonaslindstrom.ruffini.elliptic.structures

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

java.lang.Object

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

All Implemented Interfaces:

AdditiveGroup<EdwardsPoint<E>>, CommutativeMonoid<EdwardsPoint<E>>, Set<EdwardsPoint<E>>

public class EdwardsCurve<E,F extends Field<E>>
extends Object
implements AdditiveGroup<EdwardsPoint<E>>

Instances of this class represents a curve over a field over elements of type E satisfying the equation x² + y² = 1 + d x² y².

Constructor Summary

Constructors

Constructor	Description
EdwardsCurve(F field, E d)

Method Summary

Modifier and Type	Method	Description
EdwardsPoint<E>	add(EdwardsPoint<E> a, EdwardsPoint<E> b)	Return the result of a+b.
boolean	equals(EdwardsPoint<E> a, EdwardsPoint<E> b)	Returns true if and only if a = b as elements of this set.
Pair<MontgomeryCurve<E,F>,java.util.function.Function<EdwardsPoint<E>,AffinePoint<E>>>	getCorrespondingMontgomeryCurve()	Return an elliptic curve in Montgomery form which is birationally equivalent to this curve and a mapping from points on this curve to points on the Montgomery curve.
EdwardsPoint<E>	negate(EdwardsPoint<E> a)	Return -a.
String	toString(EdwardsPoint<E> a)	Returns a human-readable string representation of an element in this set.
EdwardsPoint<E>	zero()	Return the zero element.

Methods inherited from class java.lang.Object

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

Constructor Details

EdwardsCurve

public EdwardsCurve(F field,
 E d)

Method Details

toString

public String toString(EdwardsPoint<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(EdwardsPoint<E> a,
 EdwardsPoint<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 EdwardsPoint<E> add(EdwardsPoint<E> a,
 EdwardsPoint<E> b)

Description copied from interface: CommutativeMonoid

Return the result of a+b.

Specified by:

add in interface CommutativeMonoid<E>

negate

public EdwardsPoint<E> negate(EdwardsPoint<E> a)

Description copied from interface: AdditiveGroup

Return -a.

Specified by:

negate in interface AdditiveGroup<E>

zero

public EdwardsPoint<E> zero()

Description copied from interface: CommutativeMonoid

Return the zero element.

Specified by:

zero in interface CommutativeMonoid<E>

getCorrespondingMontgomeryCurve

public Pair<MontgomeryCurve<E,F>,java.util.function.Function<EdwardsPoint<E>,AffinePoint<E>>> getCorrespondingMontgomeryCurve()

Return an elliptic curve in Montgomery form which is birationally equivalent to this curve and a mapping from points on this curve to points on the Montgomery curve.