Cryptology ePrint Archive: Report 2017/774

Computational problems in supersingular elliptic curve isogenies

Steven D. Galbraith and Frederik Vercauteren

Abstract: We give a brief survey of elliptic curve isogenies and the computational problems relevant for supersingular isogeny crypto. Supersingular isogeny cryptography is attracting attention due to the fact that there are no quantum attacks known against it that are significantly faster than classical attacks. However, the underlying computational problems have not been sufficiently studied by quantum algorithms 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.

Category / Keywords: public-key cryptography /

Date: received 14 Aug 2017, last revised 16 Oct 2017

Contact author: s galbraith at auckland ac nz

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Version: 20171016:095157 (All versions of this report)

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