[Cryptography] Why is ECC secure?

[Bill Cox]

By the way, using the elliptic function addition laws
<https://en.wikipedia.org/wiki/Jacobi_elliptic_functions> on Wikipedia, I
get equations of equal speed to the Edwards curve addition laws.  It
computes the _same_ X coordinate.  The only difference is that this is done
on an ellipse.  I have not tested them in Python, yet.  I could have a
typo, or Wikipedia could, but it should work out.

I prefer this ellipse method of visualizing the Edwards addition law,
though I don't know how to add the twist:

x3 = (x1*y2*d2 + x2*y1*d1) / (1 - d*x1^2*x2^2)
y3 = (y1*y2 - x1*x2*d1*d2) / (1 - d*x1^2*x2^2)
d3 = (d1*d2 - d*x1*y1*x2*y2) / (1 - d*x1^2*x2^2)

A = x1*x2
B = A*A
N = 1 - d*C
C = y1*y2
D = d1*d2
E = A*C
F = x1*d2
G = x2*d1

X3 = y2*F + y1*G
Y3 = C - A*D
D3 = D - d*A*C

13 multiplies... identical to Edwards curve algorithm from Wikipedia.

Bill
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