### 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 language | English |
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Title of host publication | Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings |

Editors | Marc Fischlin, Jean-Sebastien Coron |

Publisher | Springer Verlag |

Pages | 789-819 |

Number of pages | 31 |

ISBN (Print) | 9783662498897 |

DOIs | |

Publication status | Published - Jan 1 2016 |

Event | 35th Annual International Conference on Theory and Applications of Cryptographic Techniques, EUROCRYPT 2016 - Vienna, Austria Duration: May 8 2016 → May 12 2016 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9665 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 35th Annual International Conference on Theory and Applications of Cryptographic Techniques, EUROCRYPT 2016 |
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Country | Austria |

City | Vienna |

Period | 5/8/16 → 5/12/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Improved progressive BKZ algorithms and their precise cost estimation by sharp simulator

AU - Aono, Yoshinori

AU - Wang, Yuntao

AU - Hayashi, Takuya

AU - Takagi, Tsuyoshi

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84979052734&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84979052734&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-49890-3_30

DO - 10.1007/978-3-662-49890-3_30

M3 - Conference contribution

AN - SCOPUS:84979052734

SN - 9783662498897

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 789

EP - 819

BT - Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings

A2 - Fischlin, Marc

A2 - Coron, Jean-Sebastien

PB - Springer Verlag

ER -