On Mon, Nov 7, 2016 at 12:51 AM, Ben Smith <hyperellip...@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): twist torsion homogenous isogenies birational singularities / nonsingular affine projective (plane, closure, line) genus embedding Are there gentle references you'd suggest? Trevor _______________________________________________ Curves mailing list Curves@moderncrypto.org https://moderncrypto.org/mailman/listinfo/curves
