### 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 |

### Other

Other | 44th Annual ACM Symposium on Theory of Computing, STOC '12 |
---|---|

Country | United States |

City | New York, NY |

Period | 5/19/12 → 5/22/12 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Software

### Cite this

*STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing*(pp. 277-288) https://doi.org/10.1145/2213977.2214004

**2 log1-εn hardness for the closest vector problem with preprocessing.** / Khot, Subhash; Popat, Preyas; Vishnoi, Nisheeth K.

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

*STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing.*pp. 277-288, 44th Annual ACM Symposium on Theory of Computing, STOC '12, New York, NY, United States, 5/19/12. https://doi.org/10.1145/2213977.2214004

}

TY - GEN

T1 - 2 log1-εn hardness for the closest vector problem with preprocessing

AU - Khot, Subhash

AU - Popat, Preyas

AU - Vishnoi, Nisheeth K.

PY - 2012

Y1 - 2012

N2 - 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].

AB - 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].

KW - closest vector problem

KW - hardness of approximation

KW - lattices

KW - nearest codeword problem

KW - PCP

UR - http://www.scopus.com/inward/record.url?scp=84862632621&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862632621&partnerID=8YFLogxK

U2 - 10.1145/2213977.2214004

DO - 10.1145/2213977.2214004

M3 - Conference contribution

AN - SCOPUS:84862632621

SN - 9781450312455

SP - 277

EP - 288

BT - STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing

ER -