3 ms·
I wish I had known about this when I was writing my dissertation. This looks reasonably complete for a lot of the mathematical diagrams in cryptography. It wou
by throwawaymath 8y ago
I wish I had known about this when I was writing my dissertation.
This looks reasonably complete for a lot of the mathematical diagrams in cryptography. It would be nice if the supersingular isogeny support included more diagrams than just the Diffie Hellman key exchange protocol, but they’re a relatively recent are of study so it makes sense. But there are a lot of isogeny diagrams (such as endomorphisms, volcanoes and random walks) beyond SIDH.
For example, Luca De Feo’s 2017 article on isogeny mathematics in cryptography [1] (pages 10,11,13,18,21,27,28,32,35) and the 2011 Feo-Jao-Plut paper introducing isogeny key exchange [2] (pages 4,6,8,9,10) both have very beautiful, full-color diagrams to walk through very complex concepts. Luca De Feo has a tendency to put the TeX of his papers and slides on GitHub [3], so I’ve reused some of his diagrammatic code before :). I recall spending hours on some diagrams to make them look as nice as these.
Lattice-based constructions sometimes need good diagrammatic code as well, but thankfully you can mostly get by without it (even though lattice depictions can be pretty, as one of De Feo’s GitHub packages shows) - for instance, note the relative lack of diagrams in Peikert’s well-known survey on lattice cryptography [4].
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1. https://arxiv.org/abs/1711.04062 https://arxiv.org/abs/1711.04062
2. https://eprint.iacr.org/2011/506.pdf https://eprint.iacr.org/2011/506.pdf
3. https://github.com/defeo https://github.com/defeo
4. https://web.eecs.umich.edu/~cpeikert/pubs/lattice-survey.pdf https://web.eecs.umich.edu/~cpeikert/pubs/lattice-survey.pdf