Cryptology ePrint Archive: Report 2016/146

Improved Progressive BKZ Algorithms and their Precise Cost Estimation by Sharp Simulator

Yoshinori Aono and Yuntao Wang and 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.

Category / Keywords: foundations / Lattice basis reduction, progressive BKZ, Gram-Schmidt orthogonal basis, geometric series assumption

Original Publication (with minor differences): IACR-EUROCRYPT-2016

Date: received 16 Feb 2016, last revised 6 May 2016

Contact author: aono at nict go jp

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Version: 20160507:021544 (All versions of this report)

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