public Fp6 Mul(Fp6 o)
{
Fp2 a1 = a, b1 = b, c1 = c;
Fp2 a2 = o.a, b2 = o.b, c2 = o.c;
Fp2 a1a2 = a1.Mul(a2);
Fp2 b1b2 = b1.Mul(b2);
Fp2 c1c2 = c1.Mul(c2);
Fp2 ra = a1a2.Add(b1.Add(c1).Mul(b2.Add(c2)).Sub(b1b2).Sub(c1c2).MulByNonResidue());
Fp2 rb = a1.Add(b1).Mul(a2.Add(b2)).Sub(a1a2).Sub(b1b2).Add(c1c2.MulByNonResidue());
Fp2 rc = a1.Add(c1).Mul(a2.Add(c2)).Sub(a1a2).Add(b1b2).Sub(c1c2);
return(new Fp6(ra, rb, rc));
}
public Fp6 Squared()
{
Fp2 s0 = a.Squared();
Fp2 ab = a.Mul(b);
Fp2 s1 = ab.Dbl();
Fp2 s2 = a.Sub(b).Add(c).Squared();
Fp2 bc = b.Mul(c);
Fp2 s3 = bc.Dbl();
Fp2 s4 = c.Squared();
Fp2 ra = s0.Add(s3.MulByNonResidue());
Fp2 rb = s1.Add(s4.MulByNonResidue());
Fp2 rc = s1.Add(s2).Add(s3).Sub(s0).Sub(s4);
return(new Fp6(ra, rb, rc));
}
public Fp6 Inverse()
{
/* From "High-Speed Software Implementation of the Optimal Ate Pairing over Barreto-Naehrig Curves"; Algorithm 17 */
Fp2 t0 = a.Squared();
Fp2 t1 = b.Squared();
Fp2 t2 = c.Squared();
Fp2 t3 = a.Mul(b);
Fp2 t4 = a.Mul(c);
Fp2 t5 = b.Mul(c);
Fp2 c0 = t0.Sub(t5.MulByNonResidue());
Fp2 c1 = t2.MulByNonResidue().Sub(t3);
Fp2 c2 = t1.Sub(t4); // typo in paper referenced above. should be "-" as per Scott, but is "*"
Fp2 t6 = a.Mul(c0).Add((c.Mul(c1).Add(b.Mul(c2))).MulByNonResidue()).Inverse();
Fp2 ra = t6.Mul(c0);
Fp2 rb = t6.Mul(c1);
Fp2 rc = t6.Mul(c2);
return(new Fp6(ra, rb, rc));
}