### Abstract

In this paper, we report that we have solved the SVP Challenge over a 128-dimensional lattice in Ideal Lattice Challenge from TU Darmstadt, which is currently the highest dimension in the challenge that has ever been solved. The security of lattice-based cryptography is based on the hardness of solving the shortest vector problem (SVP) in lattices. In 2010, Micciancio and Voulgaris proposed a Gauss Sieve algorithm for heuristically solving the SVP using a list L of Gauss-reduced vectors. Milde and Schneider proposed a parallel implementation method for the Gauss Sieve algorithm. However, the efficiency of the more than 10 threads in their implementation decreased due to the large number of non-Gauss-reduced vectors appearing in the distributed list of each thread. In this paper, we propose a more practical parallelized Gauss Sieve algorithm. Our algorithm deploys an additional Gauss-reduced list V of sample vectors assigned to each thread, and all vectors in list L remain Gauss-reduced by mutually reducing them using all sample vectors in V. Therefore, our algorithm allows the Gauss Sieve algorithm to run for large dimensions with a small communication overhead. Finally, we succeeded in solving the SVP Challenge over a 128-dimensional ideal lattice generated by the cyclotomic polynomial x^{128}+1 using about 30,000 CPU hours.

Original language | English |
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Title of host publication | Public-Key Cryptography, PKC 2014 - 17th International Conference on Practice and Theory in Public-Key Cryptography, Proceedings |

Publisher | Springer Verlag |

Pages | 411-428 |

Number of pages | 18 |

ISBN (Print) | 9783642546303 |

DOIs | |

Publication status | Published - Jan 1 2014 |

Event | 17th IACR International Conference on Practice and Theory in Public-Key Cryptography, PKC 2014 - Buenos Aires, Argentina Duration: Mar 26 2014 → Mar 28 2014 |

### 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 | 8383 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 17th IACR International Conference on Practice and Theory in Public-Key Cryptography, PKC 2014 |
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Country | Argentina |

City | Buenos Aires |

Period | 3/26/14 → 3/28/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Public-Key Cryptography, PKC 2014 - 17th International Conference on Practice and Theory in Public-Key Cryptography, Proceedings*(pp. 411-428). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8383 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-54631-0_24