public Fp2 FrobeniusMap(int power)
{
Fp ra = a;
Fp rb = FROBENIUS_COEFFS_B[power % 2].Mul(b);
return(new Fp2(ra, rb));
}
public static Fp2 Create(byte[] aa, byte[] bb)
{
Fp a = Fp.Create(aa);
Fp b = Fp.Create(bb);
return(new Fp2(a, b));
}
public static Fp2 Create(BigInteger aa, BigInteger bb)
{
Fp a = Fp.Create(aa);
Fp b = Fp.Create(bb);
return(new Fp2(a, b));
}
public Fp2 Mul(Fp2 o)
{
Fp aa = a.Mul(o.a);
Fp bb = b.Mul(o.b);
Fp ra = bb.Mul(Fp.NON_RESIDUE).Add(aa); // ra = a1 * a2 + NON_RESIDUE * b1 * b2
Fp rb = a.Add(b).Mul(o.a.Add(o.b)).Sub(aa).Sub(bb); // rb = (a1 + b1)(a2 + b2) - a1 * a2 - b1 * b2
return(new Fp2(ra, rb));
}
public Fp2 Squared()
{
Fp ab = a.Mul(b);
Fp ra = a.Add(b).Mul(b.Mul(Fp.NON_RESIDUE).Add(a))
.Sub(ab)
.Sub(ab.Mul(Fp.NON_RESIDUE)); // ra = (a + b)(a + NON_RESIDUE * b) - ab - NON_RESIDUE * b
Fp rb = ab.Dbl();
return(new Fp2(ra, rb));
}
public Fp2 Inverse()
{
Fp t0 = a.Squared();
Fp t1 = b.Squared();
Fp t2 = t0.Sub(Fp.NON_RESIDUE.Mul(t1));
Fp t3 = t2.Inverse();
Fp ra = a.Mul(t3); // ra = a * t3
Fp rb = b.Mul(t3).Negate(); // rb = -(b * t3)
return(new Fp2(ra, rb));
}
public Fp2(Fp a, Fp b)
{
this.a = a;
this.b = b;
}
