public static Fp12 FinalExponentiation(Fp12 el)
{
// first chunk
Fp12 w = new Fp12(el.a, el.b.Negate()); // el.b = -el.b
Fp12 x = el.Inverse();
Fp12 y = w.Mul(x);
Fp12 z = y.FrobeniusMap(2);
Fp12 pre = z.Mul(y);
// last chunk
Fp12 a = pre.NegExp(Parameters.PAIRING_FINAL_EXPONENT_Z);
Fp12 b = a.CyclotomicSquared();
Fp12 c = b.CyclotomicSquared();
Fp12 d = c.Mul(b);
Fp12 e = d.NegExp(Parameters.PAIRING_FINAL_EXPONENT_Z);
Fp12 f = e.CyclotomicSquared();
Fp12 g = f.NegExp(Parameters.PAIRING_FINAL_EXPONENT_Z);
Fp12 h = d.UnitaryInverse();
Fp12 i = g.UnitaryInverse();
Fp12 j = i.Mul(e);
Fp12 k = j.Mul(h);
Fp12 l = k.Mul(b);
Fp12 m = k.Mul(e);
Fp12 n = m.Mul(pre);
Fp12 o = l.FrobeniusMap(1);
Fp12 p = o.Mul(n);
Fp12 q = k.FrobeniusMap(2);
Fp12 r = q.Mul(p);
Fp12 s = pre.UnitaryInverse();
Fp12 t = s.Mul(l);
Fp12 u = t.FrobeniusMap(3);
Fp12 v = u.Mul(r);
return(v);
}
public void Run()
{
foreach (Pair pair in pairs)
{
Fp12 miller = pair.MillerLoop();
if (!miller.Equals(Fp12._1)) // run mul code only if necessary
{
product = product.Mul(miller);
}
}
// finalize
product = FinalExponentiation(product);
}
private static Fp12 MillerLoop(BN128G1 g1, BN128G2 g2)
{
// convert to affine coordinates
g1 = g1.ToAffineBN128G1();
g2 = g2.ToAffineBN128G2();
// calculate Ell coefficients
List <EllCoeffs> coeffs = CalcEllCoeffs(g2);
Fp12 f = Fp12._1;
int idx = 0;
EllCoeffs c;
// for each bit except most significant one
for (int i = LOOP_COUNT.BitLength - 2; i >= 0; i--)
{
c = coeffs[idx++];
f = f.Squared();
f = f.MulBy024(c.ell0, g1.y.Mul(c.ellVW), g1.x.Mul(c.ellVV));
if (LOOP_COUNT.TestBit(i))
{
c = coeffs[idx++];
f = f.MulBy024(c.ell0, g1.y.Mul(c.ellVW), g1.x.Mul(c.ellVV));
}
}
c = coeffs[idx++];
f = f.MulBy024(c.ell0, g1.y.Mul(c.ellVW), g1.x.Mul(c.ellVV));
c = coeffs[idx];
f = f.MulBy024(c.ell0, g1.y.Mul(c.ellVW), g1.x.Mul(c.ellVV));
return(f);
}
