Sieve, enumerate, slice, and lift:: Hybrid lattice algorithms for svp via cvpp

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Abstract

Motivated by recent results on solving large batches of closest vector problem (CVP) instances, we study how these techniques can be combined with lattice enumeration to obtain faster methods for solving the shortest vector problem (SVP) on high-dimensional lattices. Theoretically, under common heuristic assumptions we show how to solve SVP in dimension d with a cost proportional to running a sieve in dimension $$d - \varTheta (d / \log d)$$, resulting in a $$2^{\varTheta (d / \log d)}$$ speedup and memory reduction compared to running a full sieve. Combined with techniques from [Ducas, Eurocrypt 2018] we can asymptotically get a total of $$[\log (13/9) + o(1)] \cdot d / \log d$$ dimensions for free for solving SVP. Practically, the main obstacles for observing a speedup in moderate dimensions appear to be that the leading constant in the $$\varTheta (d / \log d)$$ term is rather small; that the overhead of the (batched) slicer may be large; and that competitive enumeration algorithms heavily rely on aggressive pruning techniques, which appear to be incompatible with our algorithms. These obstacles prevented this asymptotic speedup (compared to full sieving) from being observed in our experiments. However, it could be expected to become visible once optimized CVPP techniques are used in higher dimensional experiments.

Original languageEnglish
Title of host publicationProgress in Cryptology - AFRICACRYPT 2020 - 12th International Conference on Cryptology in Africa, Proceedings
EditorsAbderrahmane Nitaj, Amr Youssef
PublisherSpringer Gabler
Pages301-320
Number of pages20
ISBN (Print)9783030519377
DOIs
Publication statusPublished - 2020
Event12th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2020 - Cairo, Egypt
Duration: 20 Jul 202022 Jul 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12174 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference12th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2020
CountryEgypt
CityCairo
Period20/07/2022/07/20

Keywords

  • Closest vector problem (CVP)
  • Lattice enumeration
  • Lattice sieving
  • Randomized slicer
  • Shortest vector problem (SVP)

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