protected BigInteger modInverse(BigInteger x) {
int bits = getFieldSize();
int len = (bits + 31) >> 5;
int[] p = Nat.fromBigInteger(bits, q);
int[] n = Nat.fromBigInteger(bits, x);
int[] z = Nat.create(len);
Mod.invert(p, n, z);
return Nat.toBigInteger(len, z);
}
public static void squareN(long[] x, int n, long[] z) {
// assert n > 0;
long[] tt = Nat.create64(5);
implSquare(x, tt);
reduce(tt, z);
while (--n > 0) {
implSquare(z, tt);
reduce(tt, z);
}
}
public ECPoint add(ECPoint b) {
if (this.isInfinity()) {
return b;
}
if (b.isInfinity()) {
return this;
}
if (this == b) {
return twice();
}
ECCurve curve = this.getCurve();
SecP521R1FieldElement X1 = (SecP521R1FieldElement) this.x, Y1 = (SecP521R1FieldElement) this.y;
SecP521R1FieldElement X2 = (SecP521R1FieldElement) b.getXCoord(),
Y2 = (SecP521R1FieldElement) b.getYCoord();
SecP521R1FieldElement Z1 = (SecP521R1FieldElement) this.zs[0];
SecP521R1FieldElement Z2 = (SecP521R1FieldElement) b.getZCoord(0);
int[] t1 = Nat.create(17);
int[] t2 = Nat.create(17);
int[] t3 = Nat.create(17);
int[] t4 = Nat.create(17);
boolean Z1IsOne = Z1.isOne();
int[] U2, S2;
if (Z1IsOne) {
U2 = X2.x;
S2 = Y2.x;
} else {
S2 = t3;
SecP521R1Field.square(Z1.x, S2);
U2 = t2;
SecP521R1Field.multiply(S2, X2.x, U2);
SecP521R1Field.multiply(S2, Z1.x, S2);
SecP521R1Field.multiply(S2, Y2.x, S2);
}
boolean Z2IsOne = Z2.isOne();
int[] U1, S1;
if (Z2IsOne) {
U1 = X1.x;
S1 = Y1.x;
} else {
S1 = t4;
SecP521R1Field.square(Z2.x, S1);
U1 = t1;
SecP521R1Field.multiply(S1, X1.x, U1);
SecP521R1Field.multiply(S1, Z2.x, S1);
SecP521R1Field.multiply(S1, Y1.x, S1);
}
int[] H = Nat.create(17);
SecP521R1Field.subtract(U1, U2, H);
int[] R = t2;
SecP521R1Field.subtract(S1, S2, R);
// Check if b == this or b == -this
if (Nat.isZero(17, H)) {
if (Nat.isZero(17, 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 = t3;
SecP521R1Field.square(H, HSquared);
int[] G = Nat.create(17);
SecP521R1Field.multiply(HSquared, H, G);
int[] V = t3;
SecP521R1Field.multiply(HSquared, U1, V);
SecP521R1Field.multiply(S1, G, t1);
SecP521R1FieldElement X3 = new SecP521R1FieldElement(t4);
SecP521R1Field.square(R, X3.x);
SecP521R1Field.add(X3.x, G, X3.x);
SecP521R1Field.subtract(X3.x, V, X3.x);
SecP521R1Field.subtract(X3.x, V, X3.x);
SecP521R1FieldElement Y3 = new SecP521R1FieldElement(G);
SecP521R1Field.subtract(V, X3.x, Y3.x);
SecP521R1Field.multiply(Y3.x, R, t2);
SecP521R1Field.subtract(t2, t1, Y3.x);
SecP521R1FieldElement Z3 = new SecP521R1FieldElement(H);
if (!Z1IsOne) {
SecP521R1Field.multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne) {
SecP521R1Field.multiply(Z3.x, Z2.x, Z3.x);
}
ECFieldElement[] zs = new ECFieldElement[] {Z3};
return new SecP521R1Point(curve, X3, Y3, zs, this.withCompression);
}
public ECPoint twice() {
if (this.isInfinity()) {
return this;
}
ECCurve curve = this.getCurve();
SecP521R1FieldElement Y1 = (SecP521R1FieldElement) this.y;
if (Y1.isZero()) {
return curve.getInfinity();
}
SecP521R1FieldElement X1 = (SecP521R1FieldElement) this.x,
Z1 = (SecP521R1FieldElement) this.zs[0];
int[] t1 = Nat.create(17);
int[] t2 = Nat.create(17);
int[] Y1Squared = Nat.create(17);
SecP521R1Field.square(Y1.x, Y1Squared);
int[] T = Nat.create(17);
SecP521R1Field.square(Y1Squared, T);
boolean Z1IsOne = Z1.isOne();
int[] Z1Squared = Z1.x;
if (!Z1IsOne) {
Z1Squared = t2;
SecP521R1Field.square(Z1.x, Z1Squared);
}
SecP521R1Field.subtract(X1.x, Z1Squared, t1);
int[] M = t2;
SecP521R1Field.add(X1.x, Z1Squared, M);
SecP521R1Field.multiply(M, t1, M);
Nat.addBothTo(17, M, M, M);
SecP521R1Field.reduce23(M);
int[] S = Y1Squared;
SecP521R1Field.multiply(Y1Squared, X1.x, S);
Nat.shiftUpBits(17, S, 2, 0);
SecP521R1Field.reduce23(S);
Nat.shiftUpBits(17, T, 3, 0, t1);
SecP521R1Field.reduce23(t1);
SecP521R1FieldElement X3 = new SecP521R1FieldElement(T);
SecP521R1Field.square(M, X3.x);
SecP521R1Field.subtract(X3.x, S, X3.x);
SecP521R1Field.subtract(X3.x, S, X3.x);
SecP521R1FieldElement Y3 = new SecP521R1FieldElement(S);
SecP521R1Field.subtract(S, X3.x, Y3.x);
SecP521R1Field.multiply(Y3.x, M, Y3.x);
SecP521R1Field.subtract(Y3.x, t1, Y3.x);
SecP521R1FieldElement Z3 = new SecP521R1FieldElement(M);
SecP521R1Field.twice(Y1.x, Z3.x);
if (!Z1IsOne) {
SecP521R1Field.multiply(Z3.x, Z1.x, Z3.x);
}
return new SecP521R1Point(curve, X3, Y3, new ECFieldElement[] {Z3}, this.withCompression);
}
public static void squareAddToExt(long[] x, long[] zz) {
long[] tt = Nat.create64(5);
implSquare(x, tt);
addExt(zz, tt, zz);
}
public static void square(long[] x, long[] z) {
long[] tt = Nat.create64(5);
implSquare(x, tt);
reduce(tt, z);
}