/* this=this^e */
public FP4 Pow(BIG e)
{
Norm();
e.Norm();
FP4 w = new FP4(this);
BIG z = new BIG(e);
FP4 r = new FP4(1);
while (true)
{
int bt = z.Parity();
z.FShr(1);
if (bt == 1)
{
r.Mul(w);
}
if (z.IsZilch())
{
break;
}
w.Sqr();
}
r.Reduce();
return(r);
}
/* this=1/this */
public void Inverse()
{
FP4 f0 = new FP4(a);
FP4 f1 = new FP4(b);
FP4 f2 = new FP4(a);
FP4 f3 = new FP4(0);
Norm();
f0.Sqr();
f1.Mul(c);
f1.Times_I();
f0.Sub(f1);
f0.Norm();
f1.Copy(c);
f1.Sqr();
f1.Times_I();
f2.Mul(b);
f1.Sub(f2);
f1.Norm();
f2.Copy(b);
f2.Sqr();
f3.Copy(a);
f3.Mul(c);
f2.Sub(f3);
f2.Norm();
f3.Copy(b);
f3.Mul(f2);
f3.Times_I();
a.Mul(f0);
f3.Add(a);
c.Mul(f1);
c.Times_I();
f3.Add(c);
f3.Norm();
f3.Inverse();
a.Copy(f0);
a.Mul(f3);
b.Copy(f1);
b.Mul(f3);
c.Copy(f2);
c.Mul(f3);
}
/* Chung-Hasan SQR2 method from http://cacr.uwaterloo.ca/techreports/2006/cacr2006-24.pdf */
public void Sqr()
{
//System.out.println("Into sqr");
FP4 A = new FP4(a);
FP4 B = new FP4(b);
FP4 C = new FP4(c);
FP4 D = new FP4(a);
A.Sqr();
B.Mul(c);
B.Add(B);
B.Norm();
C.Sqr();
D.Mul(b);
D.Add(D);
c.Add(a);
c.Add(b);
c.Norm();
c.Sqr();
a.Copy(A);
A.Add(B);
A.Norm();
A.Add(C);
A.Add(D);
A.Norm();
A.Neg();
B.Times_I();
C.Times_I();
a.Add(B);
b.Copy(C);
b.Add(D);
c.Add(A);
//System.out.println("Out of sqr");
Norm();
}
/* Special case of multiplication arises from special form of ATE pairing line function */
public void SMul(FP12 y, int type)
{
//System.out.println("Into smul");
if (type == ECP.D_TYPE)
{
FP4 z0 = new FP4(a);
FP4 z2 = new FP4(b);
FP4 z3 = new FP4(b);
FP4 t0 = new FP4(0);
FP4 t1 = new FP4(y.a);
z0.Mul(y.a);
z2.PMul(y.b.Real());
b.Add(a);
t1.Real().Add(y.b.Real());
t1.Norm();
b.Norm();
b.Mul(t1);
z3.Add(c);
z3.Norm();
z3.PMul(y.b.Real());
t0.Copy(z0);
t0.Neg();
t1.Copy(z2);
t1.Neg();
b.Add(t0);
b.Add(t1);
z3.Add(t1);
z2.Add(t0);
t0.Copy(a);
t0.Add(c);
t0.Norm();
z3.Norm();
t0.Mul(y.a);
c.Copy(z2);
c.Add(t0);
z3.Times_I();
a.Copy(z0);
a.Add(z3);
}
if (type == ECP.M_TYPE)
{
FP4 z0 = new FP4(a);
FP4 z1 = new FP4(0);
FP4 z2 = new FP4(0);
FP4 z3 = new FP4(0);
FP4 t0 = new FP4(a);
FP4 t1 = new FP4(0);
z0.Mul(y.a);
t0.Add(b);
t0.Norm();
z1.Copy(t0);
z1.Mul(y.a);
t0.Copy(b);
t0.Add(c);
t0.Norm();
z3.Copy(t0); //z3.mul(y.c);
z3.PMul(y.c.GetB());
z3.Times_I();
t0.Copy(z0);
t0.Neg();
z1.Add(t0);
b.Copy(z1);
z2.Copy(t0);
t0.Copy(a);
t0.Add(c);
t1.Copy(y.a);
t1.Add(y.c);
t0.Norm();
t1.Norm();
t0.Mul(t1);
z2.Add(t0);
t0.Copy(c);
t0.PMul(y.c.GetB());
t0.Times_I();
t1.Copy(t0);
t1.Neg();
c.Copy(z2);
c.Add(t1);
z3.Add(t1);
t0.Times_I();
b.Add(t0);
z3.Norm();
z3.Times_I();
a.Copy(z0);
a.Add(z3);
}
Norm();
//System.out.println("Out of smul");
}
/* FP12 full multiplication this=this*y */
public void mul(FP12 y)
{
//System.out.println("Into mul");
FP4 z0 = new FP4(a);
FP4 z1 = new FP4(0);
FP4 z2 = new FP4(b);
FP4 z3 = new FP4(0);
FP4 t0 = new FP4(a);
FP4 t1 = new FP4(y.a);
z0.Mul(y.a);
z2.Mul(y.b);
t0.Add(b);
t1.Add(y.b);
t0.Norm();
t1.Norm();
z1.Copy(t0);
z1.Mul(t1);
t0.Copy(b);
t0.Add(c);
t1.Copy(y.b);
t1.Add(y.c);
t0.Norm();
t1.Norm();
z3.Copy(t0);
z3.Mul(t1);
t0.Copy(z0);
t0.Neg();
t1.Copy(z2);
t1.Neg();
z1.Add(t0);
//z1.norm();
b.Copy(z1);
b.Add(t1);
z3.Add(t1);
z2.Add(t0);
t0.Copy(a);
t0.Add(c);
t1.Copy(y.a);
t1.Add(y.c);
t0.Norm();
t1.Norm();
t0.Mul(t1);
z2.Add(t0);
t0.Copy(c);
t0.Mul(y.c);
t1.Copy(t0);
t1.Neg();
// z2.norm();
// z3.norm();
// b.norm();
c.Copy(z2);
c.Add(t1);
z3.Add(t1);
t0.Times_I();
b.Add(t0);
z3.Norm();
z3.Times_I();
a.Copy(z0);
a.Add(z3);
Norm();
//System.out.println("Out of mul");
}
