### Abstract

We prove that for an arbitrarily small constant ε > 0, assuming NP⊈DTIME (2 ^{log O(1-εn}), the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor better than 2 ^{log 1-ε n}. This improves upon the previous hardness factor of (log n) ^{δ} for some δ > 0 due to [AKKV05].

Original language | English (US) |
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Title of host publication | STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing |

Pages | 277-288 |

Number of pages | 12 |

DOIs | |

State | Published - 2012 |

Event | 44th Annual ACM Symposium on Theory of Computing, STOC '12 - New York, NY, United States Duration: May 19 2012 → May 22 2012 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0737-8017 |

### Other

Other | 44th Annual ACM Symposium on Theory of Computing, STOC '12 |
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Country | United States |

City | New York, NY |

Period | 5/19/12 → 5/22/12 |

### Keywords

- PCP
- closest vector problem
- hardness of approximation
- lattices
- nearest codeword problem

### ASJC Scopus subject areas

- Software

## Fingerprint Dive into the research topics of '2 <sup>log1-εn</sup> hardness for the closest vector problem with preprocessing'. Together they form a unique fingerprint.

## Cite this

Khot, S. A., Popat, P., & Vishnoi, N. K. (2012). 2

^{log1-εn}hardness for the closest vector problem with preprocessing. In*STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing*(pp. 277-288). (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/2213977.2214004