Cryptology ePrint Archive: Report 2021/570

Lattice sieving via quantum random walks

André Chailloux and Johanna Loyer

Abstract: Lattice-based cryptography is one of the leading proposals for post-quantum cryptography. The Shortest Vector Problem (SVP) is arguably the most important problem for the cryptanalysis of lattice-based cryptography, and many lattice-based schemes have security claims based on its hardness. The best quantum algorithm for the SVP is due to Laarhoven [Laa16 PhD] and runs in (heuristic) time $2^{0.2653d + o(d)}$. In this article, we present an improvement over Laarhoven's result and present an algorithm that has a (heuristic) running time of $2^{0.2570 d + o(d)}$ where $d$ is the lattice dimension. We also present time-memory trade-offs where we quantify the amount of quantum memory and quantum random access memory of our algorithm. The core idea is to replace Grover's algorithm used in [Laa16 PhD] in a key part of the sieving algorithm by a quantum random walk in which we add a layer of local sensitive filtering.

Category / Keywords: public-key cryptography / lattice-based cryptography, SVP, quantum random walks, sieving algorithms

Date: received 30 Apr 2021

Contact author: andre chailloux at inria fr , johanna loyer@inria fr

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Version: 20210503:201811 (All versions of this report)

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