/* this=this^p using Frobenius */
public void Frob(FP2 f)
{
FP2 f2 = new FP2(f);
FP2 f3 = new FP2(f);
f2.Sqr();
f3.Mul(f2);
a.Frob(f3);
b.Frob(f3);
c.Frob(f3);
b.PMul(f);
c.PMul(f2);
}
/* this=1/this */
public void Inverse()
{
// norm();
FP2 t1 = new FP2(a);
FP2 t2 = new FP2(b);
t1.Sqr();
t2.Sqr();
t2.Mul_Ip();
t2.Norm();
t1.Sub(t2);
t1.Inverse();
a.Mul(t1);
t1.Neg();
t1.Norm();
b.Mul(t1);
}
/* sqrt(a+ib) = sqrt(a+sqrt(a*a-n*b*b)/2)+ib/(2*sqrt(a+sqrt(a*a-n*b*b)/2)) */
/* returns true if this is QR */
public bool Sqrt()
{
if (IsZilch())
{
return(true);
}
FP2 wa = new FP2(a);
FP2 ws = new FP2(b);
FP2 wt = new FP2(a);
if (ws.IsZilch())
{
if (wt.Sqrt())
{
a.Copy(wt);
b.Zero();
}
else
{
wt.Div_Ip();
wt.Sqrt();
b.Copy(wt);
a.Zero();
}
return(true);
}
ws.Sqr();
wa.Sqr();
ws.Mul_Ip();
ws.Norm();
wa.Sub(ws);
ws.Copy(wa);
if (!ws.Sqrt())
{
return(false);
}
wa.Copy(wt);
wa.Add(ws);
wa.Norm();
wa.Div2();
if (!wa.Sqrt())
{
wa.Copy(wt);
wa.Sub(ws);
wa.Norm();
wa.Div2();
if (!wa.Sqrt())
{
return(false);
}
}
wt.Copy(b);
ws.Copy(wa);
ws.Add(wa);
ws.Inverse();
wt.Mul(ws);
a.Copy(wa);
b.Copy(wt);
return(true);
}
/* Line function */
public static FP12 Line(ECP2 A, ECP2 B, FP Qx, FP Qy)
{
//System.out.println("Into line");
FP4 a, b, c; // Edits here
// c=new FP4(0);
if (A == B)
{
// Doubling
FP2 XX = new FP2(A.GetX()); //X
FP2 YY = new FP2(A.GetY()); //Y
FP2 ZZ = new FP2(A.GetZ()); //Z
FP2 YZ = new FP2(YY); //Y
YZ.Mul(ZZ); //YZ
XX.Sqr(); //X^2
YY.Sqr(); //Y^2
ZZ.Sqr(); //Z^2
YZ.IMul(4);
YZ.Neg();
YZ.Norm(); //-2YZ
YZ.PMul(Qy); //-2YZ.Ys
XX.IMul(6); //3X^2
XX.PMul(Qx); //3X^2.Xs
int sb = 3 * ROM.CURVE_B_I;
ZZ.IMul(sb);
if (ECP.SEXTIC_TWIST == ECP.D_TYPE)
{
ZZ.Div_Ip2();
}
if (ECP.SEXTIC_TWIST == ECP.M_TYPE)
{
ZZ.Mul_Ip();
ZZ.Add(ZZ);
YZ.Mul_Ip();
YZ.Norm();
}
ZZ.Norm(); // 3b.Z^2
YY.Add(YY);
ZZ.Sub(YY);
ZZ.Norm(); // 3b.Z^2-Y^2
a = new FP4(YZ, ZZ); // -2YZ.Ys | 3b.Z^2-Y^2 | 3X^2.Xs
if (ECP.SEXTIC_TWIST == ECP.D_TYPE)
{
b = new FP4(XX); // L(0,1) | L(0,0) | L(1,0)
c = new FP4(0);
}
if (ECP.SEXTIC_TWIST == ECP.M_TYPE)
{
b = new FP4(0);
c = new FP4(XX);
c.Times_I();
}
A.Dbl();
}
else
{
// Addition - assume B is affine
FP2 X1 = new FP2(A.GetX()); // X1
FP2 Y1 = new FP2(A.GetY()); // Y1
FP2 T1 = new FP2(A.GetZ()); // Z1
FP2 T2 = new FP2(A.GetZ()); // Z1
T1.Mul(B.GetY()); // T1=Z1.Y2
T2.Mul(B.GetX()); // T2=Z1.X2
X1.Sub(T2);
X1.Norm(); // X1=X1-Z1.X2
Y1.Sub(T1);
Y1.Norm(); // Y1=Y1-Z1.Y2
T1.Copy(X1); // T1=X1-Z1.X2
X1.PMul(Qy); // X1=(X1-Z1.X2).Ys
if (ECP.SEXTIC_TWIST == ECP.M_TYPE)
{
X1.Mul_Ip();
X1.Norm();
}
T1.Mul(B.GetY()); // T1=(X1-Z1.X2).Y2
T2.Copy(Y1); // T2=Y1-Z1.Y2
T2.Mul(B.GetX()); // T2=(Y1-Z1.Y2).X2
T2.Sub(T1);
T2.Norm(); // T2=(Y1-Z1.Y2).X2 - (X1-Z1.X2).Y2
Y1.PMul(Qx);
Y1.Neg();
Y1.Norm(); // Y1=-(Y1-Z1.Y2).Xs
a = new FP4(X1, T2); // (X1-Z1.X2).Ys | (Y1-Z1.Y2).X2 - (X1-Z1.X2).Y2 | - (Y1-Z1.Y2).Xs
if (ECP.SEXTIC_TWIST == ECP.D_TYPE)
{
b = new FP4(Y1);
c = new FP4(0);
}
if (ECP.SEXTIC_TWIST == ECP.M_TYPE)
{
b = new FP4(0);
c = new FP4(Y1);
c.Times_I();
}
A.Add(B);
}
//System.out.println("Out of line");
return(new FP12(a, b, c));
}
