Cryptology ePrint Archive: Report 2021/1295

Improved Quantum Hypercone Locality Sensitive Filtering in Lattice Sieving

Max Heiser

Abstract: The asymptotically fastest known method for solving SVP is via lattice sieving, an algorithm whose computational bottleneck is solving the Nearest Neighbor Search problem. The best known algorithm for solving this problem is Hypercone Locality Sensitive Filtering (LSF). The classical time complexity of a sieve using Hypercone LSF is \(2^{0.2925d+o(d)}\). The quantum time complexity is \(2^{0.2653d+o(d)}\), which is acquired by using Grover's algorithm to speed up part of the enumeration.

We present an improvement to the quantum algorithm, which improves the time complexity to \(2^{0.2571d+o(d)}\). Essentially, we provide a way to use Grover's algorithm to speed up another part of the process, providing a better tradeoff. This improvement affects the security of lattice-based encryption schemes, including NIST PQC Round 3 finalists.

Category / Keywords: public-key cryptography / lattice-based cryptography, SVP, sieving algorithms, cryptanalysis, lattice techniques

Date: received 27 Sep 2021

Contact author: heisermax at protonmail com

Available format(s): PDF | BibTeX Citation

Version: 20210927:130438 (All versions of this report)

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