private static Precomputed FlippedMillerLoopMixedAddition(BN128G2 base_val, BN128G2 addend)
{
Fp2 x1 = addend.x, y1 = addend.y, z1 = addend.z;
Fp2 x2 = base_val.x, y2 = base_val.y;
Fp2 d = x1.Sub(x2.Mul(z1)); // d = x1 - x2 * z1
Fp2 e = y1.Sub(y2.Mul(z1)); // e = y1 - y2 * z1
Fp2 f = d.Squared(); // f = d^2
Fp2 g = e.Squared(); // g = e^2
Fp2 h = d.Mul(f); // h = d * f
Fp2 i = x1.Mul(f); // i = x1 * f
Fp2 j = h.Add(z1.Mul(g)).Sub(i.Dbl()); // j = h + z1 * g - 2 * i
Fp2 x3 = d.Mul(j); // x3 = d * j
Fp2 y3 = e.Mul(i.Sub(j)).Sub(h.Mul(y1)); // y3 = e * (i - j) - h * y1)
Fp2 z3 = z1.Mul(h); // z3 = Z1*H
Fp2 ell0 = Parameters.TWIST.Mul(e.Mul(x2).Sub(d.Mul(y2))); // ell_0 = TWIST * (e * x2 - d * y2)
Fp2 ellVV = e.Negate(); // ell_VV = -e
Fp2 ellVW = d; // ell_VW = d
return(Precomputed.Of(
new BN128G2(x3, y3, z3),
new EllCoeffs(ell0, ellVW, ellVV)
));
}
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));
}