[curves] Introduction to ECC

[Brad Klee]

Hi Jan,

I think you probably want to hear from an expert, but maybe you will find
worthwhile a few comments from another perspective:

1. If you even mention magic in your business pitch-- this is an
advertisement, right?--your potential customers will wonder if you really
have the most powerful magicians on your team. If no, then some potential
customers will run away from you.

2. Mentioning magic also raises suspicion. What assurance do we have that
your suggested website is nothing mendacious? To make the trust situation
more difficult, we can see that trustica is affiliated with brmlab, a
self-declared "hacker" entity based in Prague [1,2].

These points aside, a few more:

3. The supremacy of particular normal form is part of a history leading up
to the computer age, and not really part of the computer age itself. With
computer-based mathematics, we can rely less and less upon simplifying
assumptions. Why do we need to start with Weierstrass formalism?

4. If you look at the [curves] archives, many of the recent topics regard
Curve25519 and Ed25519. Why not use this curve as an example? Can you make
a nice transformation video between these curves?

5. Your mention of Riemann-Roch is confusing. When discussing genus, it's
really more practical and helpful to just give readers the simple Singular
algorithm for calculating the genus of an algebraic plane curve [3] (thanks
again TU Eindhoven!).

4. The citations are superfluous and lacking. LMFDB is also standardized on
the Weierstrass model, so why not cite them? If you search their collection
of Q-Curves for "[2,2,-1,1,3]" or "[-3,21/4]" they will return
"y^2+y=x^3-3*x+5" and "P=(1/4,13/8)" [4].

Regards,

Brad

[1] https://myip.ms/view/dns/571223/ns.trustica.cz
[2] https://wiki.hackerspaces.org/Brmlab
[3] https://www.win.tue.nl/~aeb/2WF02/genus.pdf
[4] http://www.lmfdb.org/EllipticCurve/Q/10179/b/1

Original Post: https://moderncrypto.org/mail-archive/curves/2018/000975.html
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