Computational problems in supersingular elliptic curve isogenies

Abstract

We present an overview of supersingular isogeny cryptography and how it fits into the broad theme of post-quantum public-key crypto. The paper also gives a brief tutorial of elliptic curve isogenies and the computational problems relevant for supersingular isogeny crypto. Supersingular isogeny crypto is attracting attention due to the fact that the best attacks, both classical and quantum, require exponential time. However, the underlying computational problems have not been sufficiently studied by quantum algorithm researchers, especially since there are significant mathematical preliminaries needed to fully understand isogeny crypto. The main goal of the paper is to advertise various related computational problems and to explain the relationships between them, in a way that is accessible to experts in quantum algorithms.