Cryptology ePrint Archive: Report 2017/774

Computational problems in supersingular elliptic curve isogenies

Steven D. Galbraith and Frederik Vercauteren

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.

This is a post-peer-review, pre-copyedit version of an article to be published as a "perspective paper" in the journal Quantum Information Processing.

Category / Keywords: public-key cryptography /

Original Publication (with minor differences): Quantum Information Processing

Date: received 14 Aug 2017, last revised 28 Aug 2018

Contact author: s galbraith at auckland ac nz

Available format(s): PDF | BibTeX Citation

Version: 20180829:051700 (All versions of this report)

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