[Cryptography] Why is ECC secure?

[Bill Cox]

I simplified some of the math above.  For d == -1 (it's only slightly more
complex for d != 1), the equation to integrate in the path from the origin
to the elliptic curve point simplifies to:

    sqrt(2)/sqrt(1 - x^4)

The line integral simplifies to:

    Sqrt[2] EllipticF[ArcSin[x], -1]

Evaluating this equation at the first four points where the generator has x
= 0.4:

path integral over 0 .. 1 = 1.85407, which is Sqrt[2] EllipticK[-1]

x               y               path integral ratio
0.4             0.8509629434    0.567149
0.7699820705 0.5252257314 1.1343       2.0000035264
0.9884198756 0.1079220526 1.70145       3.0000052896
0.9175950827 -0.2928953491 2.26859       3.9999894208

Now, if I could just figure out how to evaluate
sqrt(2)*EllipticF(arcsin(x), -1) mod p :)
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