/* f=f^e */
/* Note that this method requires a lot of RAM! Better to use compressed XTR method, see FP4.java */
public static FP12 GTPow(FP12 d, BIG e)
{
FP12 r;
if (USE_GS_GT)
{
FP12[] g = new FP12[4];
FP2 f = new FP2(new BIG(ROM.Fra), new BIG(ROM.Frb));
BIG q = new BIG(ROM.CURVE_Order);
BIG t = new BIG(0);
int i, np, nn;
BIG[] u = GS(e);
g[0] = new FP12(d);
for (i = 1; i < 4; i++)
{
g[i] = new FP12(0);
g[i].Copy(g[i - 1]);
g[i].Frob(f);
}
for (i = 0; i < 4; i++)
{
np = u[i].NBits();
t.Copy(BIG.ModNeg(u[i], q));
nn = t.NBits();
if (nn < np)
{
u[i].Copy(t);
g[i].Conj();
}
u[i].Norm();
}
r = FP12.Pow4(g, u);
}
else
{
r = d.Pow(e);
}
return(r);
}
/* 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);
}