[Cryptography] Edwards curves are just ellipses - and why ECC works

[Bill Cox]

On Sun, Oct 4, 2015 at 8:29 AM, Bill Cox <waywardgeek at gmail.com> wrote:

> By the way, I also just showed that the Y coordinate in the Edward's
> addition law is simply cn/dn from the ancient addition law.  This means I
> can simplify the ancient law as follows:
>

I found slides from a talk by DjB that shows that this is already known:

"Edwards x is sn;
Edwards y is cn/dn."

I'm sure the other formula must also be well known, that G(a, b, d) =
sn(F(a;d) + F(b;d), d) being equivalent to the addition laws.  Of course
this is only valid when F(a), F(b), and F(a) + F(b) are all positive (or
all negative).  The other variable for cn is required to traverse the whole
ellipse.

Bill
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