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A New Random Sampling Method and Its Application in Improving Progressive BKZ Algorithm

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Abstract

Random sampling algorithm was proposed firstly by Schnorr in 2003 to find short lattice vectors, as an alternative to enumeration. The follow-up developments in random sampling were mainly proposed by Fukase and Kashiwabara in 2015 and Aono and Nguyen in 2017. Although they extended the sampling space compared to Schnorr’s work through the natural number representation, they did not show how to sample specifically in practice and what vectors should be sampled, in order to find short enough lattice vectors. In this paper, the authors firstly introduce a practical random sampling algorithm under some reasonable assumptions which can find short enough lattice vectors efficiently. Then, as an application of this new random sampling algorithm, the authors show that it can improve the performance of progressive BKZ algorithm in practice. Finally, the authors solve the Darmstadt’s Lattice Challenge and get a series of new records in the dimension from 500 to 825, using the improved progressive BKZ algorithm.

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Acknowledgements

We thank Professor Shi Bai for providing important discussions and suggestions in this paper.

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Authors and Affiliations

  1. College of Sciences, National University of Defense Technology, Changsha, 410073, China

    Minghao Sun & Longjiang Qu

  2. Academy of Military Sciences, Beijing, 100091, China

    Shixiong Wang

  3. College of Information Science and Technology/Cyber Security, Jinan University, Guangzhou, 510632, China

    Hao Chen

Authors
  1. Minghao Sun
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  2. Shixiong Wang
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  3. Hao Chen
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  4. Longjiang Qu
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Corresponding author

Correspondence to Longjiang Qu.

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The authors declare no conflict of interest.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 62032009 and 62102440.

This paper was recommended for publication by Editor PAN Yanbin.

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Sun, M., Wang, S., Chen, H. et al. A New Random Sampling Method and Its Application in Improving Progressive BKZ Algorithm. J Syst Sci Complex (2023). https://doi.org/10.1007/s11424-023-3107-7

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  • DOI: https://doi.org/10.1007/s11424-023-3107-7

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