/* test group membership */
/* with GT-Strong curve, now only check that m!=1, conj(m)*m==1, and m.m^{p^4}=m^{p^2} */
public static bool GTmember(FP12 m)
{
if (m.isunity())
{
return(false);
}
FP12 r = new FP12(m);
r.conj();
r.mul(m);
if (!r.isunity())
{
return(false);
}
FP2 f = new FP2(new BIG(ROM.CURVE_Fra), new BIG(ROM.CURVE_Frb));
r.copy(m);
r.frob(f);
r.frob(f);
FP12 w = new FP12(r);
w.frob(f);
w.frob(f);
w.mul(m);
if (!ROM.GT_STRONG)
{
if (!w.Equals(r))
{
return(false);
}
BIG x = new BIG(ROM.CURVE_Bnx);
r.copy(m);
w = r.pow(x);
w = w.pow(x);
r.copy(w);
r.sqr();
r.mul(w);
r.sqr();
w.copy(m);
w.frob(f);
}
return(w.Equals(r));
}