Class EllipticCurveGroup

java.lang.Object
org.apfloat.jscience.EllipticCurveGroup
All Implemented Interfaces:
Serializable, Immutable, Realtime, ValueType, XMLSerializable, GroupAdditive<EllipticCurveGroup>, Structure<EllipticCurveGroup>
public class EllipticCurveGroup extends Object implements GroupAdditive<EllipticCurveGroup>, Realtime, XMLSerializable, Serializable
This class represents a point on an elliptic curve defined over the integers modulo a modulus. All arithmetic is done in Weierstrass form.

This class sets the modulus using ModuloApintField.setModulus(Apint).

Since:
1.15.0
Version:
1.15.0
Author:
Mikko Tommila
See Also:

  • Field Details

  • Constructor Details

    • EllipticCurveGroup

      public EllipticCurveGroup(Apint x, Apint y)
      Constructs a new point on the elliptic curve. Uses Weierstrass coordinates.
      Parameters:
      x - The x-coordinate.
      y - The y-coordinate.

  • Method Details

    • fromMontgomeryPoint

      public static EllipticCurveGroup fromMontgomeryPoint(Apint x, Apint y)
      Construct a point from Montgomery curve coordinates. The Montgomery curve parameters must be first set with setMontgomeryParameters(Apint, Apint, Apint).
      Parameters:
      x - The Montgomery curve x-coordinate.
      y - The Montgomery curve y-coordinate.
      Returns:
      The point in Weierstrass coordinates.

    • fromEdwardsPoint

      public static EllipticCurveGroup fromEdwardsPoint(Apint x, Apint y)
      Construct a point from twisted Edwards curve coordinates. The Edwards curve parameters must be first set with setEdwardsParameters(Apint, Apint, Apint).
      Parameters:
      x - The Edwards curve x-coordinate.
      y - The Edwards curve y-coordinate.
      Returns:
      The point in Weierstrass coordinates.

    • setWeierstrassParameters

      public static void setWeierstrassParameters(Apint a, Apint b, Apint p)
      Set the curve parameters in Weierstrass form. The elliptic curve specified in the Weierstrass form is
      y2 = x3 + a x + b

      For example, Curve25519 can be set with

      setWeierstrassParameters(new Apint(486662), new Apint(1), ApintMath.pow(new Apint(2), 255).subtract(new Apint(19)))

      Parameters:
      a - The curve parameter a.
      b - The curve parameter b.
      p - The modulus.

    • setMontgomeryParameters

      public static void setMontgomeryParameters(Apint b, Apint a, Apint p)
      Set the curve parameters in Montgomery form. The elliptic curve specified in the Montgomery form is
      B y2 = x3 + A x2 + x For example, Curve25519 can be set with

      setMontgomeryParameters(new Apint(1), new Apint(486662), ApintMath.pow(new Apint(2), 255).subtract(new Apint(19)))

      Parameters:
      b - The curve parameter B.
      a - The curve parameter A.
      p - The modulus.

    • setEdwardsParameters

      public static void setEdwardsParameters(Apint a, Apint d, Apint p)
      Set the curve parameters in twisted Edwards form. The elliptic curve specified in the twisted Edwards form is
      a x2 + y2 = 1 + d x2 y2 For example, Curve448 can be set with

      setEdwardsParameters(new Apint(1), new Apint(-39081), ApintMath.pow(new Apint(2), 448).subtract(ApintMath.pow(new Apint(2), 224).subtract(new Apint(1))))

      Parameters:
      a - The curve parameter a.
      d - The curve parameter d.
      p - The modulus.

    • getA

      public static Apint getA()
      Returns the curve parameter a in Weierstrass form.
      Returns:
      The curve parameter a.
      See Also:

    • getB

      public static Apint getB()
      Returns the curve parameter b in Weierstrass form.
      Returns:
      The curve parameter b.
      See Also:

    • getJInvariant

      public static Apint getJInvariant()
      Returns the j-invariant of the curve.
      Returns:
      The j-invariant of the curve.

    • getX

      public Apint getX()
      Returns the x-coordinate of this point.
      Returns:
      The x-coordinate.

    • getY

      public Apint getY()
      Returns the y-coordinate of this point.
      Returns:
      The y-coordinate.

    • plus

      public EllipticCurveGroup plus(EllipticCurveGroup that)
      Specified by:
      plus in interface GroupAdditive<EllipticCurveGroup>

    • times

      public EllipticCurveGroup times(Apint that)
      Returns this elliptic curve point multiplied by a scalar.
      Parameters:
      that - The multiplier.
      Returns:
      The resulting elliptic curve point.

    • opposite

      public EllipticCurveGroup opposite()
      Specified by:
      opposite in interface GroupAdditive<EllipticCurveGroup>

    • copy

      public EllipticCurveGroup copy()
      Specified by:
      copy in interface ValueType

    • toText

      public Text toText()
      Specified by:
      toText in interface Realtime

    • toString

      public String toString()
      Overrides:
      toString in class Object

    • hashCode

      public int hashCode()
      Overrides:
      hashCode in class Object

    • equals

      public boolean equals(Object obj)
      Overrides:
      equals in class Object