On Nov 8, 2016, at 4:00 PM, Trevor Perrin <[email protected]> wrote: > On Mon, Nov 7, 2016 at 12:51 AM, Ben Smith <[email protected]> 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
order cofactor characteristic trace of frobenius Another thing that has been driving me nuts for years is Theorem 2.1 in the Curve25519 paper. I understand what it *says* but I still don’t understand what it *means*. rg _______________________________________________ Curves mailing list [email protected] https://moderncrypto.org/mailman/listinfo/curves
