Author:

Keywords:

Science & Technology, Physical Sciences, Quantum Science & Technology, Physics, Multidisciplinary, Physics, Mathematical, Physics, Post-quantum cryptography, Elliptic curve isogeny, QUANTUM ALGORITHM, SUBEXPONENTIAL-TIME, GRAPHS, 0105 Mathematical Physics, 0206 Quantum Physics, 0802 Computation Theory and Mathematics, Mathematical Physics, 5108 Quantum physics

Abstract:

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. 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.