On Nov 1, 2016, at 2:40 PM, Trevor Perrin <tr...@trevp.net> wrote: > It would be be great if there were better surveys on modern ECC and > engineering issues. If someone wanted to suggest a reading list / > bibliography that would be a nice contribution (but also a bunch of > work).
I decided it would be a useful exercise for me to undertake to write such a survey (even if I couldn’t actually finish it), and right away I ran into a snag. I was trying to reconcile all the different forms of elliptic curve formulas commonly found in the literature, and found the following promising-looking lead on mathworld: http://mathworld.wolfram.com/EllipticCurve.html Ax^3 + Bx^2y + Cxy^2 + Dy^3 + Ex^2 + Fxy + Gy^2 + hHx + Iy + J = 0 This is consistent (AFAICT) with the definition given in section 4.4.2.a of Cohen and Frey. But then there are Edwards curves, which have a x^2y^2 term in them. How do those fit in? In fact, as I started thinking about this I realized that Edwards curves are really weird because they’re quartic and not cubic (aren’t they?) and all elliptic curves are supposed to be cubic (aren’t they?) How can a fourth-order polynomial be birationally equivalent to a third-order polynomial? I tried taking a look at some of the proofs that Edwards curves are birationally equivalent to Montgomery curves but they went way over my head. Is there a more elementary way of understanding this? Thanks, rg _______________________________________________ Curves mailing list Curves@moderncrypto.org https://moderncrypto.org/mailman/listinfo/curves
