Random walks on supersingular isogeny graphs

Authors

  • Enric Florit Zacarías Universitat de Barcelona

Keywords:

isogenies, Ramanujan graphs, random walks.

Abstract

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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How to Cite

Florit Zacarías, E. (2021). Random walks on supersingular isogeny graphs. Reports@SCM, 6(1), 23–34. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/149355

Issue

Vol. 6 No. 1 (2021)

Section

Articles

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