use of com.github.zhenwei.core.math.ec.ECFieldElement in project LinLong-Java by zhenwei1108.
the class SecT409R1Point method getCompressionYTilde.
protected boolean getCompressionYTilde() {
ECFieldElement X = this.getRawXCoord();
if (X.isZero()) {
return false;
}
ECFieldElement Y = this.getRawYCoord();
// Y is actually Lambda (X + Y/X) here
return Y.testBitZero() != X.testBitZero();
}
use of com.github.zhenwei.core.math.ec.ECFieldElement in project LinLong-Java by zhenwei1108.
the class SecT571K1Point method twicePlus.
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 its 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 = L1Sq.add(L1Z1);
ECFieldElement L2plus1 = L2.addOne();
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 SecT571K1Point(curve, A, curve.getB());
}
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 SecT571K1Point(curve, X3, L3, new ECFieldElement[] { Z3 });
}
use of com.github.zhenwei.core.math.ec.ECFieldElement in project LinLong-Java by zhenwei1108.
the class SecT571K1Point method getYCoord.
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;
}
use of com.github.zhenwei.core.math.ec.ECFieldElement in project LinLong-Java by zhenwei1108.
the class SecT571K1Point method getCompressionYTilde.
protected boolean getCompressionYTilde() {
ECFieldElement X = this.getRawXCoord();
if (X.isZero()) {
return false;
}
ECFieldElement Y = this.getRawYCoord();
// Y is actually Lambda (X + Y/X) here
return Y.testBitZero() != X.testBitZero();
}
use of com.github.zhenwei.core.math.ec.ECFieldElement in project LinLong-Java by zhenwei1108.
the class SecT571K1Point method add.
public ECPoint add(ECPoint b) {
if (this.isInfinity()) {
return b;
}
if (b.isInfinity()) {
return this;
}
ECCurve curve = this.getCurve();
SecT571FieldElement X1 = (SecT571FieldElement) this.x;
SecT571FieldElement X2 = (SecT571FieldElement) b.getRawXCoord();
if (X1.isZero()) {
if (X2.isZero()) {
return curve.getInfinity();
}
return b.add(this);
}
SecT571FieldElement L1 = (SecT571FieldElement) this.y, Z1 = (SecT571FieldElement) this.zs[0];
SecT571FieldElement L2 = (SecT571FieldElement) b.getRawYCoord(), Z2 = (SecT571FieldElement) b.getZCoord(0);
long[] t1 = Nat576.create64();
long[] t2 = Nat576.create64();
long[] t3 = Nat576.create64();
long[] t4 = Nat576.create64();
long[] Z1Precomp = Z1.isOne() ? null : SecT571Field.precompMultiplicand(Z1.x);
long[] U2, S2;
if (Z1Precomp == null) {
U2 = X2.x;
S2 = L2.x;
} else {
SecT571Field.multiplyPrecomp(X2.x, Z1Precomp, U2 = t2);
SecT571Field.multiplyPrecomp(L2.x, Z1Precomp, S2 = t4);
}
long[] Z2Precomp = Z2.isOne() ? null : SecT571Field.precompMultiplicand(Z2.x);
long[] U1, S1;
if (Z2Precomp == null) {
U1 = X1.x;
S1 = L1.x;
} else {
SecT571Field.multiplyPrecomp(X1.x, Z2Precomp, U1 = t1);
SecT571Field.multiplyPrecomp(L1.x, Z2Precomp, S1 = t3);
}
long[] A = t3;
SecT571Field.add(S1, S2, A);
long[] B = t4;
SecT571Field.add(U1, U2, B);
if (Nat576.isZero64(B)) {
if (Nat576.isZero64(A)) {
return twice();
}
return curve.getInfinity();
}
SecT571FieldElement X3, L3, Z3;
if (X2.isZero()) {
// TODO This can probably be optimized quite a bit
ECPoint p = this.normalize();
X1 = (SecT571FieldElement) p.getXCoord();
ECFieldElement Y1 = p.getYCoord();
ECFieldElement Y2 = L2;
ECFieldElement L = Y1.add(Y2).divide(X1);
X3 = (SecT571FieldElement) L.square().add(L).add(X1);
if (X3.isZero()) {
return new SecT571K1Point(curve, X3, curve.getB());
}
ECFieldElement Y3 = L.multiply(X1.add(X3)).add(X3).add(Y1);
L3 = (SecT571FieldElement) Y3.divide(X3).add(X3);
Z3 = (SecT571FieldElement) curve.fromBigInteger(ECConstants.ONE);
} else {
SecT571Field.square(B, B);
long[] APrecomp = SecT571Field.precompMultiplicand(A);
long[] AU1 = t1;
long[] AU2 = t2;
SecT571Field.multiplyPrecomp(U1, APrecomp, AU1);
SecT571Field.multiplyPrecomp(U2, APrecomp, AU2);
X3 = new SecT571FieldElement(t1);
SecT571Field.multiply(AU1, AU2, X3.x);
if (X3.isZero()) {
return new SecT571K1Point(curve, X3, curve.getB());
}
Z3 = new SecT571FieldElement(t3);
SecT571Field.multiplyPrecomp(B, APrecomp, Z3.x);
if (Z2Precomp != null) {
SecT571Field.multiplyPrecomp(Z3.x, Z2Precomp, Z3.x);
}
long[] tt = Nat576.createExt64();
SecT571Field.add(AU2, B, t4);
SecT571Field.squareAddToExt(t4, tt);
SecT571Field.add(L1.x, Z1.x, t4);
SecT571Field.multiplyAddToExt(t4, Z3.x, tt);
L3 = new SecT571FieldElement(t4);
SecT571Field.reduce(tt, L3.x);
if (Z1Precomp != null) {
SecT571Field.multiplyPrecomp(Z3.x, Z1Precomp, Z3.x);
}
}
return new SecT571K1Point(curve, X3, L3, new ECFieldElement[] { Z3 });
}
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