Cryptology ePrint Archive: Report 2019/1161

Quantum speedups for lattice sieves are tenuous at best

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

Abstract: Quantum variants of lattice sieve algorithms are often 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 used in lattice sieves. We design quantum circuits for near neighbour 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. We find that quantum search may provide a small speedup in dimensions of cryptanalytic interest, but only under exceedingly optimistic physical and algorithmic assumptions.

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

Date: received 6 Oct 2019

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

Available format(s): PDF | BibTeX Citation

Version: 20191007:082623 (All versions of this report)

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