[curves] Climbing the elliptic learning curve (was: Re: Finalizing XEdDSA)

Trevor Perrin trevp at trevp.net
Tue Nov 8 16:00:12 PST 2016

On Mon, Nov 7, 2016 at 12:51 AM, Ben Smith <hyperelliptic at gmail.com> wrote:
> Here's a rather longish explanation that might be helpful (I hope).
> It's sort of a geometric complement to Mike's reply on curve shapes.
> It should really be a link to a blog post, I suppose---but in the
> absence of a blog, I'm posting it here.
> What I'm aiming to do here is
> * Connect the Edwards equation with a Weierstrass equation (actually a
> Montgomery curve);
> * Show how the usual magic birational map appears in a more natural way;
> * Resolve Ron's apparent degree-3-vs-degree-4 incompatibility; and
> * Explain how we can ignore the whole resolution-of-singularities
> issue by simply never having singularities in the first place.
> (If the geometric language goes over your head, don't worry; there
> will be variables and equations the whole time to to show what I mean.

Thanks to you and Mike, that's awesome!

I wonder what the easiest path is to *learn* the geometric language
that you and Mike are using, to the point of following along here?

A lot of crypto-interested people can roughly understand RSA and DH,
and would like to understand ECC, but get lost with terms like
(skimming recent mails):

singularities / nonsingular
projective (plane, closure, line)

Are there gentle references you'd suggest?


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