[curves] Introduction to ECC

Brad Klee bradklee at gmail.com
Mon Mar 12 19:40:41 PDT 2018

Hi Cecilia,

Great post, and you are right about hacker hysteria. Maybe you miss my
sense of humour though. It's certainly //not an attack// of hacker culture
that serves the children. I hope that students in Brazil will do crazy
experiments like tearing apart a computer mouse to accomplish a digital
pendulum experiment [1,2]. Even better if observing energy-dependence of
the oscillation period somehow leads into a discussion of elliptic curve
cryptography. Do many computer hackers in Brazil know how to produce the
Jacobian Elliptic functions from Edwards's psi function? That is a topic we
are already starting to help with [3]! Before you start a lawsuit against
me, please realize that it will be more difficult for me to give away these
interesting secrets if I'm incarcerated. Hopefully that isn't your goal

Let's avoid silly personal arguments, continue technical discussion, and
stay on the topic of curves, especially over finite fields. Hey look at
this, someone drew Cayley graphs isomorphic by a bi-rational shear
transformation [4,5]. The difficult part is not calculating inverses,
rather dealing with case exceptions and points at infinity. From whatever
I've managed to figure out, calculations on the Jacobi Quartic probably
need projective coordinates(?). Unfortunately, I don't have anyone telling
me the answers, and this trustica introduction only deals with Weierstrass
normal form. What about pairing calculations? Thanks again Craig Costello,
for making these detailed notes freely available [6]. Learning more soon.



PS. Don't sell Brazil short, a great country, especially for music, but
they never should have put Caetano Veloso in jail [7]!

[1] https://arxiv.org/pdf/0901.4319.pdf
[2] https://arxiv.org/pdf/1605.09102.pdf ( due for a rewrite )
[3] http://demonstrations.wolfram.com/EdwardssSolutionOfPendulumOscillation/
[4] https://moderncrypto.org/mail-archive/curves/2017/000951.html
[5] https://ptpb.pw/AfTT.png
[6] http://www.craigcostello.com.au/pairings/PairingsForBeginners.pdf
[7] Caetano Veloso, "It's a long way", Transa, 1972.
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