Analysis of DeepBKZ reduction for finding short lattice vectors

Masaya Yasuda, Satoshi Nakamura, Junpei Yamaguchi

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Lattice basis reduction is a mandatory tool for solving lattice problems such as the shortest vector problem. The Lenstra–Lenstra–Lovász reduction algorithm (LLL) is the most famous, and its typical improvements are the block Korkine–Zolotarev algorithm and LLL with deep insertions (DeepLLL), both proposed by Schnorr and Euchner. In BKZ with blocksize β, LLL is called many times to reduce a lattice basis before enumeration to find a shortest non-zero vector in every block lattice of dimension β. Recently, “DeepBKZ” was proposed as a mathematical improvement of BKZ, in which DeepLLL is called as a subroutine alternative to LLL. In this paper, we analyze the output quality of DeepBKZ in both theory and practice. Specifically, we give provable upper bounds specific to DeepBKZ. We also develop “DeepBKZ 2.0”, an improvement of DeepBKZ like BKZ 2.0, and show experimental results that it finds shorter lattice vectors than BKZ 2.0 in practice.

Original languageEnglish
Pages (from-to)2077-2100
Number of pages24
JournalDesigns, Codes, and Cryptography
Issue number10
Publication statusPublished - Oct 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics
  • Computer Science Applications


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