A Complete Analysis of the BKZ Lattice Reduction Algorithm

Jianwei Li; Phong Q.  Nguyen

Paper 2020/1237

A Complete Analysis of the BKZ Lattice Reduction Algorithm

Jianwei Li and Phong Q. Nguyen

Abstract

We present the first rigorous dynamic analysis of BKZ, the most widely used lattice reduction algorithm besides LLL. Previous analyses were either heuristic or only applied to variants of BKZ. Namely, we provide guarantees on the quality of the current lattice basis during execution. Our analysis extends to a generic BKZ algorithm where the SVP-oracle is replaced by an approximate oracle and/or the basis update is not necessarily performed by LLL. Interestingly, it also provides currently the best and simplest bounds for both the output quality and the running time. As an application, we observe that in certain approximation regimes, it is more efficient to use BKZ with an approximate rather than exact SVP-oracle.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: Lattice Reduction BKZ Dynamical Systems and Enumeration
Contact author(s): lijianweisk @ sina com
History: 2022-03-05: last of 3 revisions; 2020-10-09: received; See all versions
Short URL: https://ia.cr/2020/1237
License: CC BY

BibTeX

@misc{cryptoeprint:2020/1237,
      author = {Jianwei Li and Phong Q.  Nguyen},
      title = {A Complete Analysis of the BKZ Lattice Reduction Algorithm},
      howpublished = {Cryptology ePrint Archive, Paper 2020/1237},
      year = {2020},
      note = {\url{https://eprint.iacr.org/2020/1237}},
      url = {https://eprint.iacr.org/2020/1237}
}