Improved progressive BKZ algorithms and their precise cost estimation by sharp simulator

Yoshinori Aono, Yuntao Wang, Takuya Hayashi, Tsuyoshi Takagi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

28 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationAdvances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
EditorsMarc Fischlin, Jean-Sebastien Coron
PublisherSpringer Verlag
Pages789-819
Number of pages31
ISBN (Print)9783662498897
DOIs
Publication statusPublished - Jan 1 2016
Event35th Annual International Conference on Theory and Applications of Cryptographic Techniques, EUROCRYPT 2016 - Vienna, Austria
Duration: May 8 2016May 12 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9665
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other35th Annual International Conference on Theory and Applications of Cryptographic Techniques, EUROCRYPT 2016
CountryAustria
CityVienna
Period5/8/165/12/16

Fingerprint

Cost Estimation
Simulator
Simulators
Costs
Enumeration
LLL Algorithm
Geometric series
Pruning
Efficient Implementation
Accelerate
Computational Cost
Continue
Radius

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Aono, Y., Wang, Y., Hayashi, T., & Takagi, T. (2016). Improved progressive BKZ algorithms and their precise cost estimation by sharp simulator. In M. Fischlin, & J-S. Coron (Eds.), Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings (pp. 789-819). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9665). Springer Verlag. https://doi.org/10.1007/978-3-662-49890-3_30

Improved progressive BKZ algorithms and their precise cost estimation by sharp simulator. / Aono, Yoshinori; Wang, Yuntao; Hayashi, Takuya; Takagi, Tsuyoshi.

Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. ed. / Marc Fischlin; Jean-Sebastien Coron. Springer Verlag, 2016. p. 789-819 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9665).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Aono, Y, Wang, Y, Hayashi, T & Takagi, T 2016, Improved progressive BKZ algorithms and their precise cost estimation by sharp simulator. in M Fischlin & J-S Coron (eds), Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9665, Springer Verlag, pp. 789-819, 35th Annual International Conference on Theory and Applications of Cryptographic Techniques, EUROCRYPT 2016, Vienna, Austria, 5/8/16. https://doi.org/10.1007/978-3-662-49890-3_30
Aono Y, Wang Y, Hayashi T, Takagi T. Improved progressive BKZ algorithms and their precise cost estimation by sharp simulator. In Fischlin M, Coron J-S, editors, Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. Springer Verlag. 2016. p. 789-819. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-662-49890-3_30
Aono, Yoshinori ; Wang, Yuntao ; Hayashi, Takuya ; Takagi, Tsuyoshi. / Improved progressive BKZ algorithms and their precise cost estimation by sharp simulator. Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. editor / Marc Fischlin ; Jean-Sebastien Coron. Springer Verlag, 2016. pp. 789-819 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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