public ECPoint twicePlus(ECPoint b) {
if (this.isInfinity()) {
return b;
}
if (b.isInfinity()) {
return twice();
}
ECCurve curve = this.getCurve();
ECFieldElement X1 = this.x;
if (X1.isZero()) {
// A point with X == 0 is it's own additive inverse
return b;
}
// NOTE: twicePlus() only optimized for lambda-affine argument
ECFieldElement X2 = b.getRawXCoord(), Z2 = b.getZCoord(0);
if (X2.isZero() || !Z2.isOne()) {
return twice().add(b);
}
ECFieldElement L1 = this.y, Z1 = this.zs[0];
ECFieldElement L2 = b.getRawYCoord();
ECFieldElement X1Sq = X1.square();
ECFieldElement L1Sq = L1.square();
ECFieldElement Z1Sq = Z1.square();
ECFieldElement L1Z1 = L1.multiply(Z1);
// ECFieldElement T = curve.getA().multiply(Z1Sq).add(L1Sq).add(L1Z1);
ECFieldElement T = L1Sq.add(L1Z1);
ECFieldElement L2plus1 = L2.addOne();
// ECFieldElement A =
// curve.getA().add(L2plus1).multiply(Z1Sq).add(L1Sq).multiplyPlusProduct(T, X1Sq, Z1Sq);
ECFieldElement A = L2plus1.multiply(Z1Sq).add(L1Sq).multiplyPlusProduct(T, X1Sq, Z1Sq);
ECFieldElement X2Z1Sq = X2.multiply(Z1Sq);
ECFieldElement B = X2Z1Sq.add(T).square();
if (B.isZero()) {
if (A.isZero()) {
return b.twice();
}
return curve.getInfinity();
}
if (A.isZero()) {
// return new SecT283K1Point(curve, A, curve.getB().sqrt(), withCompression);
return new SecT283K1Point(curve, A, curve.getB(), withCompression);
}
ECFieldElement X3 = A.square().multiply(X2Z1Sq);
ECFieldElement Z3 = A.multiply(B).multiply(Z1Sq);
ECFieldElement L3 = A.add(B).square().multiplyPlusProduct(T, L2plus1, Z3);
return new SecT283K1Point(curve, X3, L3, new ECFieldElement[] {Z3}, this.withCompression);
}
public ECPoint twice() {
if (this.isInfinity()) {
return this;
}
ECCurve curve = this.getCurve();
ECFieldElement X1 = this.x;
if (X1.isZero()) {
// A point with X == 0 is it's own additive inverse
return curve.getInfinity();
}
ECFieldElement L1 = this.y, Z1 = this.zs[0];
boolean Z1IsOne = Z1.isOne();
ECFieldElement Z1Sq = Z1IsOne ? Z1 : Z1.square();
ECFieldElement T;
if (Z1IsOne) {
T = L1.square().add(L1);
} else {
T = L1.add(Z1).multiply(L1);
}
if (T.isZero()) {
// return new SecT283K1Point(curve, T, curve.getB().sqrt(), withCompression);
return new SecT283K1Point(curve, T, curve.getB(), withCompression);
}
ECFieldElement X3 = T.square();
ECFieldElement Z3 = Z1IsOne ? T : T.multiply(Z1Sq);
ECFieldElement t1 = L1.add(X1).square();
ECFieldElement t2 = Z1IsOne ? Z1 : Z1Sq.square();
ECFieldElement L3 = t1.add(T).add(Z1Sq).multiply(t1).add(t2).add(X3).add(Z3);
return new SecT283K1Point(curve, X3, L3, new ECFieldElement[] {Z3}, this.withCompression);
}
public ECPoint negate() {
if (this.isInfinity()) {
return this;
}
ECFieldElement X = this.x;
if (X.isZero()) {
return this;
}
// L is actually Lambda (X + Y/X) here
ECFieldElement L = this.y, Z = this.zs[0];
return new SecT283K1Point(curve, X, L.add(Z), new ECFieldElement[] {Z}, this.withCompression);
}
public ECFieldElement getYCoord() {
ECFieldElement X = x, L = y;
if (this.isInfinity() || X.isZero()) {
return L;
}
// Y is actually Lambda (X + Y/X) here; convert to affine value on the fly
ECFieldElement Y = L.add(X).multiply(X);
ECFieldElement Z = zs[0];
if (!Z.isOne()) {
Y = Y.divide(Z);
}
return Y;
}
public ECPoint add(ECPoint b) {
if (this.isInfinity()) {
return b;
}
if (b.isInfinity()) {
return this;
}
ECCurve curve = this.getCurve();
ECFieldElement X1 = this.x;
ECFieldElement X2 = b.getRawXCoord();
if (X1.isZero()) {
if (X2.isZero()) {
return curve.getInfinity();
}
return b.add(this);
}
ECFieldElement L1 = this.y, Z1 = this.zs[0];
ECFieldElement L2 = b.getRawYCoord(), Z2 = b.getZCoord(0);
boolean Z1IsOne = Z1.isOne();
ECFieldElement U2 = X2, S2 = L2;
if (!Z1IsOne) {
U2 = U2.multiply(Z1);
S2 = S2.multiply(Z1);
}
boolean Z2IsOne = Z2.isOne();
ECFieldElement U1 = X1, S1 = L1;
if (!Z2IsOne) {
U1 = U1.multiply(Z2);
S1 = S1.multiply(Z2);
}
ECFieldElement A = S1.add(S2);
ECFieldElement B = U1.add(U2);
if (B.isZero()) {
if (A.isZero()) {
return twice();
}
return curve.getInfinity();
}
ECFieldElement X3, L3, Z3;
if (X2.isZero()) {
// TODO This can probably be optimized quite a bit
ECPoint p = this.normalize();
X1 = p.getXCoord();
ECFieldElement Y1 = p.getYCoord();
ECFieldElement Y2 = L2;
ECFieldElement L = Y1.add(Y2).divide(X1);
// X3 = L.square().add(L).add(X1).add(curve.getA());
X3 = L.square().add(L).add(X1);
if (X3.isZero()) {
// return new SecT283K1Point(curve, X3, curve.getB().sqrt(),
// this.withCompression);
return new SecT283K1Point(curve, X3, curve.getB(), this.withCompression);
}
ECFieldElement Y3 = L.multiply(X1.add(X3)).add(X3).add(Y1);
L3 = Y3.divide(X3).add(X3);
Z3 = curve.fromBigInteger(ECConstants.ONE);
} else {
B = B.square();
ECFieldElement AU1 = A.multiply(U1);
ECFieldElement AU2 = A.multiply(U2);
X3 = AU1.multiply(AU2);
if (X3.isZero()) {
// return new SecT283K1Point(curve, X3, curve.getB().sqrt(),
// this.withCompression);
return new SecT283K1Point(curve, X3, curve.getB(), this.withCompression);
}
ECFieldElement ABZ2 = A.multiply(B);
if (!Z2IsOne) {
ABZ2 = ABZ2.multiply(Z2);
}
L3 = AU2.add(B).squarePlusProduct(ABZ2, L1.add(Z1));
Z3 = ABZ2;
if (!Z1IsOne) {
Z3 = Z3.multiply(Z1);
}
}
return new SecT283K1Point(curve, X3, L3, new ECFieldElement[] {Z3}, this.withCompression);
}