Cryptology ePrint Archive: Report 2019/1161

Estimating quantum speedups for lattice sieves

Martin R. Albrecht and Vlad Gheorghiu and Eamonn W. Postlethwaite and John M. Schanck

Abstract: Quantum variants of lattice sieve algorithms are routinely used to assess the security of lattice based cryptographic constructions. In this work we provide a heuristic, non-asymptotic, analysis of the cost of several algorithms for near neighbour search on high dimensional spheres. These algorithms are key components of lattice sieves. We design quantum circuits for near neighbour search algorithms and provide software that numerically optimises algorithm parameters according to various cost metrics. Using this software we estimate the cost of classical and quantum near neighbour search on spheres. For the most performant near neighbour search algorithm that we analyse we find a small quantum speedup in dimensions of cryptanalytic interest. Achieving this speedup requires several optimistic physical and algorithmic assumptions.

Category / Keywords: public-key cryptography / lattice sieves, quantum computing, cryptanalysis, post-quantum

Date: received 6 Oct 2019, last revised 20 May 2020

Contact author: eamonn postlethwaite 2016 at rhul ac uk,vlad gheorghiu@uwaterloo ca,jschanck@uwaterloo ca,martin albrecht@royalholloway ac uk

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Version: 20200520:144758 (All versions of this report)

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