net.i2p.crypto.eddsa.math

Class GroupElement

java.lang.Object

net.i2p.crypto.eddsa.math.GroupElement

All Implemented Interfaces:

java.io.Serializable

public class GroupElement
extends java.lang.Object
implements java.io.Serializable

A point (x,y) on an EdDSA curve.

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	GroupElement.Representation

Constructor Summary

Constructors

Constructor and Description
GroupElement(Curve curve, byte[] s)
GroupElement(Curve curve, GroupElement.Representation repr, FieldElement X, FieldElement Y, FieldElement Z, FieldElement T)

Method Summary

Methods

Modifier and Type	Method and Description
GroupElement	add(GroupElement q) GroupElement addition using the twisted Edwards addition law with extended coordinates (Hisil2008).
static GroupElement	cached(Curve curve, FieldElement YpX, FieldElement YmX, FieldElement Z, FieldElement T2d)
GroupElement	dbl() r = 2 * p
GroupElement	doubleScalarMultiplyVariableTime(GroupElement A, byte[] a, byte[] b) r = a * A + b * B where a = a[0]+256*a[1]+...+256^31 a[31], b = b[0]+256*b[1]+...+256^31 b[31] and B is this point.
boolean	equals(java.lang.Object obj)
int	hashCode()
boolean	isOnCurve() Verify that a point is on its curve.
boolean	isOnCurve(Curve curve) Verify that a point is on the curve.
GroupElement	negate()
static GroupElement	p1p1(Curve curve, FieldElement X, FieldElement Y, FieldElement Z, FieldElement T)
static GroupElement	p2(Curve curve, FieldElement X, FieldElement Y, FieldElement Z)
static GroupElement	p3(Curve curve, FieldElement X, FieldElement Y, FieldElement Z, FieldElement T)
static GroupElement	precomp(Curve curve, FieldElement ypx, FieldElement ymx, FieldElement xy2d)
void	precompute(boolean precomputeSingle) Precompute the tables for scalarMultiply(byte[]) and doubleScalarMultiplyVariableTime(net.i2p.crypto.eddsa.math.GroupElement, byte[], byte[]).
GroupElement	scalarMultiply(byte[] a) h = a * B where a = a[0]+256*a[1]+...+256^31 a[31] and B is this point.
GroupElement	sub(GroupElement q) GroupElement subtraction using the twisted Edwards addition law with extended coordinates (Hisil2008).
byte[]	toByteArray()
GroupElement	toCached()
GroupElement	toP2()
GroupElement	toP3()
java.lang.String	toString()

Methods inherited from class java.lang.Object

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

Constructor Detail

GroupElement

public GroupElement(Curve curve,
            GroupElement.Representation repr,
            FieldElement X,
            FieldElement Y,
            FieldElement Z,
            FieldElement T)

GroupElement

public GroupElement(Curve curve,
            byte[] s)

Method Detail

p2

public static GroupElement p2(Curve curve,
              FieldElement X,
              FieldElement Y,
              FieldElement Z)

p3

public static GroupElement p3(Curve curve,
              FieldElement X,
              FieldElement Y,
              FieldElement Z,
              FieldElement T)

p1p1

public static GroupElement p1p1(Curve curve,
                FieldElement X,
                FieldElement Y,
                FieldElement Z,
                FieldElement T)

precomp

public static GroupElement precomp(Curve curve,
                   FieldElement ypx,
                   FieldElement ymx,
                   FieldElement xy2d)

cached

public static GroupElement cached(Curve curve,
                  FieldElement YpX,
                  FieldElement YmX,
                  FieldElement Z,
                  FieldElement T2d)

toByteArray

public byte[] toByteArray()

toP2

public GroupElement toP2()

toP3

public GroupElement toP3()

toCached

public GroupElement toCached()

precompute

public void precompute(boolean precomputeSingle)

Precompute the tables for scalarMultiply(byte[]) and doubleScalarMultiplyVariableTime(net.i2p.crypto.eddsa.math.GroupElement, byte[], byte[]).

Parameters:

precomputeSingle - should the matrix for scalarMultiply() be precomputed?

dbl

public GroupElement dbl()

r = 2 * p

Returns:

The P1P1 representation

add

public GroupElement add(GroupElement q)

GroupElement addition using the twisted Edwards addition law with extended coordinates (Hisil2008).
r = p + q

Parameters:

q - the CACHED representation of the GroupElement to add.

Returns:

the P1P1 representation of the result.

sub

public GroupElement sub(GroupElement q)

GroupElement subtraction using the twisted Edwards addition law with extended coordinates (Hisil2008).
r = p - q

Parameters:

q - the PRECOMP representation of the GroupElement to subtract.

Returns:

the P1P1 representation of the result.

negate

public GroupElement negate()

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object

equals

public boolean equals(java.lang.Object obj)

Overrides:

equals in class java.lang.Object

scalarMultiply

public GroupElement scalarMultiply(byte[] a)

h = a * B where a = a[0]+256*a[1]+...+256^31 a[31] and B is this point. If its lookup table has not been precomputed, it will be at the start of the method (and cached for later calls). Constant time. Preconditions: (TODO: Check this applies here) a[31] <= 127

Parameters:

a - = a[0]+256*a[1]+...+256^31 a[31]

Returns:

doubleScalarMultiplyVariableTime

public GroupElement doubleScalarMultiplyVariableTime(GroupElement A,
                                            byte[] a,
                                            byte[] b)

r = a * A + b * B where a = a[0]+256*a[1]+...+256^31 a[31], b = b[0]+256*b[1]+...+256^31 b[31] and B is this point. A must have been previously precomputed.

Parameters:

A - in P3 representation.

a - = a[0]+256*a[1]+...+256^31 a[31]

b - = b[0]+256*b[1]+...+256^31 b[31]

Returns:

isOnCurve

public boolean isOnCurve()

Verify that a point is on its curve.

Parameters:

P - The point to check.

Returns:

true if the point lies on its curve.

isOnCurve

public boolean isOnCurve(Curve curve)

Verify that a point is on the curve.

Parameters:

curve - The curve to check.

Returns:

true if the point lies on the curve.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object