public FP4 ComPow(BIG e, BIG r)
{
FP12 g1 = new FP12(0);
FP12 g2 = new FP12(0);
FP2 f = new FP2(new BIG(ROM.Fra), new BIG(ROM.Frb));
BIG q = new BIG(ROM.Modulus);
BIG m = new BIG(q);
m.Mod(r);
BIG a = new BIG(e);
a.Mod(m);
BIG b = new BIG(e);
b.Div(m);
g1.Copy(this);
g2.Copy(this);
FP4 c = g1.Trace();
if (b.IsZilch())
{
c = c.Xtr_Pow(e);
return(c);
}
g2.Frob(f);
FP4 cp = g2.Trace();
g1.Conj();
g2.mul(g1);
FP4 cpm1 = g2.Trace();
g2.mul(g1);
FP4 cpm2 = g2.Trace();
c = c.Xtr_Pow2(cp, cpm1, cpm2, a, b);
return(c);
}
/* final exponentiation - keep separate for multi-pairings and to avoid thrashing stack */
public static FP12 FExp(FP12 m)
{
FP2 f = new FP2(new BIG(ROM.Fra), new BIG(ROM.Frb));
BIG x = new BIG(ROM.CURVE_Bnx);
FP12 r = new FP12(m);
/* Easy part of final exp */
FP12 lv = new FP12(r);
lv.Inverse();
r.Conj();
r.mul(lv);
lv.Copy(r);
r.Frob(f);
r.Frob(f);
r.mul(lv);
/* Hard part of final exp */
if (ECP.CURVE_PAIRING_TYPE == ECP.BN)
{
FP12 x0, x1, x2, x3, x4, x5;
lv.Copy(r);
lv.Frob(f);
x0 = new FP12(lv);
x0.Frob(f);
lv.mul(r);
x0.mul(lv);
x0.Frob(f);
x1 = new FP12(r);
x1.Conj();
x4 = r.Pow(x);
if (ECP.SIGN_OF_X == ECP.POSITIVEX)
{
x4.Conj();
}
x3 = new FP12(x4);
x3.Frob(f);
x2 = x4.Pow(x);
if (ECP.SIGN_OF_X == ECP.POSITIVEX)
{
x2.Conj();
}
x5 = new FP12(x2);
x5.Conj();
lv = x2.Pow(x);
if (ECP.SIGN_OF_X == ECP.POSITIVEX)
{
lv.Conj();
}
x2.Frob(f);
r.Copy(x2);
r.Conj();
x4.mul(r);
x2.Frob(f);
r.Copy(lv);
r.Frob(f);
lv.mul(r);
lv.USqr();
lv.mul(x4);
lv.mul(x5);
r.Copy(x3);
r.mul(x5);
r.mul(lv);
lv.mul(x2);
r.USqr();
r.mul(lv);
r.USqr();
lv.Copy(r);
lv.mul(x1);
r.mul(x0);
lv.USqr();
r.mul(lv);
r.Reduce();
}
else
{
FP12 y0, y1, y2, y3;
// Ghamman & Fouotsa Method
y0 = new FP12(r);
y0.USqr();
y1 = y0.Pow(x);
if (ECP.SIGN_OF_X == ECP.NEGATIVEX)
{
y1.Conj();
}
x.FShr(1);
y2 = y1.Pow(x);
if (ECP.SIGN_OF_X == ECP.NEGATIVEX)
{
y2.Conj();
}
x.FShl(1);
y3 = new FP12(r);
y3.Conj();
y1.mul(y3);
y1.Conj();
y1.mul(y2);
y2 = y1.Pow(x);
if (ECP.SIGN_OF_X == ECP.NEGATIVEX)
{
y2.Conj();
}
y3 = y2.Pow(x);
if (ECP.SIGN_OF_X == ECP.NEGATIVEX)
{
y3.Conj();
}
y1.Conj();
y3.mul(y1);
y1.Conj();
y1.Frob(f);
y1.Frob(f);
y1.Frob(f);
y2.Frob(f);
y2.Frob(f);
y1.mul(y2);
y2 = y3.Pow(x);
if (ECP.SIGN_OF_X == ECP.NEGATIVEX)
{
y2.Conj();
}
y2.mul(y0);
y2.mul(r);
y1.mul(y2);
y2.Copy(y3);
y2.Frob(f);
y1.mul(y2);
r.Copy(y1);
r.Reduce();
}
return(r);
}