Paper 2016/146
Improved Progressive BKZ Algorithms and their Precise Cost Estimation by Sharp Simulator
Yoshinori Aono, Yuntao Wang, Takuya Hayashi, and Tsuyoshi Takagi
Abstract
In this paper, we investigate a variant of the BKZ algorithm, called progressive BKZ, which performs BKZ reductions by starting with a small blocksize and gradually switching to larger blocks as the process continues. We discuss techniques to accelerate the speed of the progressive BKZ algorithm by optimizing the following parameters: blocksize, searching radius and probability for pruning of the local enumeration algorithm, and the constant in the geometric series assumption (GSA). We then propose a simulator for predicting the length of the Gram-Schmidt basis obtained from the BKZ reduction. We also present a model for estimating the computational cost of the proposed progressive BKZ by considering the efficient implementation of the local enumeration algorithm and the LLL algorithm. Finally, we compare the cost of the proposed progressive BKZ with that of other algorithms using instances from the Darmstadt SVP Challenge. The proposed algorithm is approximately 50 times faster than BKZ 2.0 (proposed by Chen-Nguyen) for solving the SVP Challenge up to 160 dimensions.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- A minor revision of an IACR publication in EUROCRYPT 2016
- Keywords
- Lattice basis reductionprogressive BKZGram-Schmidt orthogonal basisgeometric series assumption
- Contact author(s)
- aono @ nict go jp
- History
- 2016-05-07: last of 2 revisions
- 2016-02-18: received
- See all versions
- Short URL
- https://ia.cr/2016/146
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2016/146,
author = {Yoshinori Aono and Yuntao Wang and Takuya Hayashi and Tsuyoshi Takagi},
title = {Improved Progressive {BKZ} Algorithms and their Precise Cost Estimation by Sharp Simulator},
howpublished = {Cryptology {ePrint} Archive, Paper 2016/146},
year = {2016},
url = {https://eprint.iacr.org/2016/146}
}
