/* return this^e mod Modulus
* public FP pow(BIG e)
* {
* int bt;
* FP r=new FP(1);
* e.norm();
* x.norm();
* FP m=new FP(this);
* while (true)
* {
* bt=e.parity();
* e.fshr(1);
* if (bt==1) r.mul(m);
* if (e.iszilch()) break;
* m.sqr();
* }
* r.x.mod(p);
* return r;
* } */
/* return sqrt(this) mod Modulus */
public FP Sqrt()
{
Reduce();
BIG b = new BIG(ROM.Modulus);
if (MOD8 == 5)
{
b.Dec(5);
b.Norm();
b.Shr(3);
FP i = new FP(this);
i.x.Shl(1);
FP v = i.Pow(b);
i.Mul(v);
i.Mul(v);
i.x.Dec(1);
FP r = new FP(this);
r.Mul(v);
r.Mul(i);
r.Reduce();
return(r);
}
else
{
b.Inc(1);
b.Norm();
b.Shr(2);
return(Pow(b));
}
}
public FP Pow(BIG e)
{
sbyte[] w = new sbyte[1 + (BIG.NLEN * BIG.BASEBITS + 3) / 4];
FP[] tb = new FP[16];
BIG t = new BIG(e);
t.Norm();
int nb = 1 + (t.NBits() + 3) / 4;
for (int i = 0; i < nb; i++)
{
int lsbs = t.LastBits(4);
t.Dec(lsbs);
t.Norm();
w[i] = (sbyte)lsbs;
t.FShr(4);
}
tb[0] = new FP(1);
tb[1] = new FP(this);
for (int i = 2; i < 16; i++)
{
tb[i] = new FP(tb[i - 1]);
tb[i].Mul(this);
}
FP r = new FP(tb[w[nb - 1]]);
for (int i = nb - 2; i >= 0; i--)
{
r.Sqr();
r.Sqr();
r.Sqr();
r.Sqr();
r.Mul(tb[w[i]]);
}
r.Reduce();
return(r);
}
/* this*=s, where s is an FP */
public void PMul(FP s)
{
a.Mul(s);
b.Mul(s);
}