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The Bouncy Castle Crypto package is a Java implementation of cryptographic algorithms. This jar contains JCE provider and lightweight API for the Bouncy Castle Cryptography APIs for JDK 1.5 to JDK 1.8.
package org.bouncycastle.math.ec.custom.djb;
import org.bouncycastle.math.ec.ECCurve;
import org.bouncycastle.math.ec.ECFieldElement;
import org.bouncycastle.math.ec.ECPoint;
import org.bouncycastle.math.raw.Nat256;
public class Curve25519Point extends ECPoint.AbstractFp
{
Curve25519Point(ECCurve curve, ECFieldElement x, ECFieldElement y)
{
super(curve, x, y);
}
Curve25519Point(ECCurve curve, ECFieldElement x, ECFieldElement y, ECFieldElement[] zs)
{
super(curve, x, y, zs);
}
protected ECPoint detach()
{
return new Curve25519Point(null, getAffineXCoord(), getAffineYCoord());
}
public ECFieldElement getZCoord(int index)
{
if (index == 1)
{
return getJacobianModifiedW();
}
return super.getZCoord(index);
}
public ECPoint add(ECPoint b)
{
if (this.isInfinity())
{
return b;
}
if (b.isInfinity())
{
return this;
}
if (this == b)
{
return twice();
}
ECCurve curve = this.getCurve();
Curve25519FieldElement X1 = (Curve25519FieldElement)this.x, Y1 = (Curve25519FieldElement)this.y,
Z1 = (Curve25519FieldElement)this.zs[0];
Curve25519FieldElement X2 = (Curve25519FieldElement)b.getXCoord(), Y2 = (Curve25519FieldElement)b.getYCoord(),
Z2 = (Curve25519FieldElement)b.getZCoord(0);
int c;
int[] tt1 = Nat256.createExt();
int[] t2 = Nat256.create();
int[] t3 = Nat256.create();
int[] t4 = Nat256.create();
boolean Z1IsOne = Z1.isOne();
int[] U2, S2;
if (Z1IsOne)
{
U2 = X2.x;
S2 = Y2.x;
}
else
{
S2 = t3;
Curve25519Field.square(Z1.x, S2);
U2 = t2;
Curve25519Field.multiply(S2, X2.x, U2);
Curve25519Field.multiply(S2, Z1.x, S2);
Curve25519Field.multiply(S2, Y2.x, S2);
}
boolean Z2IsOne = Z2.isOne();
int[] U1, S1;
if (Z2IsOne)
{
U1 = X1.x;
S1 = Y1.x;
}
else
{
S1 = t4;
Curve25519Field.square(Z2.x, S1);
U1 = tt1;
Curve25519Field.multiply(S1, X1.x, U1);
Curve25519Field.multiply(S1, Z2.x, S1);
Curve25519Field.multiply(S1, Y1.x, S1);
}
int[] H = Nat256.create();
Curve25519Field.subtract(U1, U2, H);
int[] R = t2;
Curve25519Field.subtract(S1, S2, R);
// Check if b == this or b == -this
if (Nat256.isZero(H))
{
if (Nat256.isZero(R))
{
// this == b, i.e. this must be doubled
return this.twice();
}
// this == -b, i.e. the result is the point at infinity
return curve.getInfinity();
}
int[] HSquared = Nat256.create();
Curve25519Field.square(H, HSquared);
int[] G = Nat256.create();
Curve25519Field.multiply(HSquared, H, G);
int[] V = t3;
Curve25519Field.multiply(HSquared, U1, V);
Curve25519Field.negate(G, G);
Nat256.mul(S1, G, tt1);
c = Nat256.addBothTo(V, V, G);
Curve25519Field.reduce27(c, G);
Curve25519FieldElement X3 = new Curve25519FieldElement(t4);
Curve25519Field.square(R, X3.x);
Curve25519Field.subtract(X3.x, G, X3.x);
Curve25519FieldElement Y3 = new Curve25519FieldElement(G);
Curve25519Field.subtract(V, X3.x, Y3.x);
Curve25519Field.multiplyAddToExt(Y3.x, R, tt1);
Curve25519Field.reduce(tt1, Y3.x);
Curve25519FieldElement Z3 = new Curve25519FieldElement(H);
if (!Z1IsOne)
{
Curve25519Field.multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne)
{
Curve25519Field.multiply(Z3.x, Z2.x, Z3.x);
}
int[] Z3Squared = (Z1IsOne && Z2IsOne) ? HSquared : null;
// TODO If the result will only be used in a subsequent addition, we don't need W3
Curve25519FieldElement W3 = calculateJacobianModifiedW((Curve25519FieldElement)Z3, Z3Squared);
ECFieldElement[] zs = new ECFieldElement[]{ Z3, W3 };
return new Curve25519Point(curve, X3, Y3, zs);
}
public ECPoint twice()
{
if (this.isInfinity())
{
return this;
}
ECCurve curve = this.getCurve();
ECFieldElement Y1 = this.y;
if (Y1.isZero())
{
return curve.getInfinity();
}
return twiceJacobianModified(true);
}
public ECPoint twicePlus(ECPoint b)
{
if (this == b)
{
return threeTimes();
}
if (this.isInfinity())
{
return b;
}
if (b.isInfinity())
{
return twice();
}
ECFieldElement Y1 = this.y;
if (Y1.isZero())
{
return b;
}
return twiceJacobianModified(false).add(b);
}
public ECPoint threeTimes()
{
if (this.isInfinity())
{
return this;
}
ECFieldElement Y1 = this.y;
if (Y1.isZero())
{
return this;
}
return twiceJacobianModified(false).add(this);
}
public ECPoint negate()
{
if (this.isInfinity())
{
return this;
}
return new Curve25519Point(this.getCurve(), this.x, this.y.negate(), this.zs);
}
protected Curve25519FieldElement calculateJacobianModifiedW(Curve25519FieldElement Z, int[] ZSquared)
{
Curve25519FieldElement a4 = (Curve25519FieldElement)this.getCurve().getA();
if (Z.isOne())
{
return a4;
}
Curve25519FieldElement W = new Curve25519FieldElement();
if (ZSquared == null)
{
ZSquared = W.x;
Curve25519Field.square(Z.x, ZSquared);
}
Curve25519Field.square(ZSquared, W.x);
Curve25519Field.multiply(W.x, a4.x, W.x);
return W;
}
protected Curve25519FieldElement getJacobianModifiedW()
{
Curve25519FieldElement W = (Curve25519FieldElement)this.zs[1];
if (W == null)
{
// NOTE: Rarely, twicePlus will result in the need for a lazy W1 calculation here
this.zs[1] = W = calculateJacobianModifiedW((Curve25519FieldElement)this.zs[0], null);
}
return W;
}
protected Curve25519Point twiceJacobianModified(boolean calculateW)
{
Curve25519FieldElement X1 = (Curve25519FieldElement)this.x, Y1 = (Curve25519FieldElement)this.y,
Z1 = (Curve25519FieldElement)this.zs[0], W1 = getJacobianModifiedW();
int c;
int[] M = Nat256.create();
Curve25519Field.square(X1.x, M);
c = Nat256.addBothTo(M, M, M);
c += Nat256.addTo(W1.x, M);
Curve25519Field.reduce27(c, M);
int[] _2Y1 = Nat256.create();
Curve25519Field.twice(Y1.x, _2Y1);
int[] _2Y1Squared = Nat256.create();
Curve25519Field.multiply(_2Y1, Y1.x, _2Y1Squared);
int[] S = Nat256.create();
Curve25519Field.multiply(_2Y1Squared, X1.x, S);
Curve25519Field.twice(S, S);
int[] _8T = Nat256.create();
Curve25519Field.square(_2Y1Squared, _8T);
Curve25519Field.twice(_8T, _8T);
Curve25519FieldElement X3 = new Curve25519FieldElement(_2Y1Squared);
Curve25519Field.square(M, X3.x);
Curve25519Field.subtract(X3.x, S, X3.x);
Curve25519Field.subtract(X3.x, S, X3.x);
Curve25519FieldElement Y3 = new Curve25519FieldElement(S);
Curve25519Field.subtract(S, X3.x, Y3.x);
Curve25519Field.multiply(Y3.x, M, Y3.x);
Curve25519Field.subtract(Y3.x, _8T, Y3.x);
Curve25519FieldElement Z3 = new Curve25519FieldElement(_2Y1);
if (!Nat256.isOne(Z1.x))
{
Curve25519Field.multiply(Z3.x, Z1.x, Z3.x);
}
Curve25519FieldElement W3 = null;
if (calculateW)
{
W3 = new Curve25519FieldElement(_8T);
Curve25519Field.multiply(W3.x, W1.x, W3.x);
Curve25519Field.twice(W3.x, W3.x);
}
return new Curve25519Point(this.getCurve(), X3, Y3, new ECFieldElement[]{ Z3, W3 });
}
}