Development of a dual version of DeepBKZ and its application to solving the LWE challenge

Masaya Yasuda, Junpei Yamaguchi, Michiko Ooka, Satoshi Nakamura

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

Lattice basis reduction is a strong tool in cryptanalysis. In 2017, DeepBKZ was proposed as a new variant of BKZ, and it calls LLL with deep insertions (DeepLLL) as a subroutine alternative to LLL. In this paper, we develop a dual version of DeepBKZ (which we call “Dual-DeepBKZ”), to reduce the dual basis of an input basis. For Dual-DeepBKZ, we develop a dual version of DeepLLL, and then combine it with the dual enumeration by Micciancio and Walter. It never computes the dual basis of an input basis, and it is as efficient as the primal DeepBKZ. We also demonstrate that Dual-DeepBKZ solves several instances in the TU Darmstadt LWE challenge. We use Dual-DeepBKZ in the bounded distance decoding (BDD) approach for solving an LWE instance. Our experiments show that Dual-DeepBKZ reduces the cost of Liu-Nguyen’s BDD enumeration more effectively than BKZ. For the LWE instance of (n, α) = (40, 0.015) (resp., (n, α) = (60, 0.005)), our results are about 2.2 times (resp., 4.0 times) faster than Xu et al.’s results, for which they used BKZ in the fplll library and the BDD enumeration with extreme pruning while we used linear pruning in our experiments.

Original languageEnglish
Title of host publicationProgress in Cryptology - AFRICACRYPT 2018 - 10th International Conference on Cryptology in Africa, Proceedings
EditorsAbderrahmane Nitaj, Tajjeeddine Rachidi, Antoine Joux
PublisherSpringer Verlag
Pages162-182
Number of pages21
ISBN (Print)9783319893389
DOIs
Publication statusPublished - 2018
Event10th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2018 - Marrakesh, Morocco
Duration: May 7 2018May 9 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10831 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2018
CountryMorocco
CityMarrakesh
Period5/7/185/9/18

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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