Reports@SCM, Vol 6, No 1 (2021)

Random walks on supersingular isogeny graphs

Enric Florit Zacarías


We survey several aspects of supersingular elliptic curves and their isogeny graphs. Isogeny graphs have obtained attention for the last _fteen years due to their uses in quantum-resistant cryptographic protocols. Studying them involves looking at elliptic curves, quaternion algebras, and random walks on (almost) regular graphs, among other topics. In particular, we give the tools necessary to state the Ramanujan property, connecting supersingular curves in characteristic p with modular forms of level p. We also explain the hash function of Charles, Lauter and Goren as an example of application.

Keywords: isogenies, Ramanujan graphs, random walks.

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ISSN: 2385-4227 (electronic edition)