### Abstract

We prove that for an arbitrarily small constant < 0, the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor 2^{log1-e}n, under the assumption that NP ⊈ SIZE(2^{logO(1/e)}n).

Original language | English (US) |
---|---|

Pages (from-to) | 1184-1205 |

Number of pages | 22 |

Journal | SIAM Journal on Computing |

Volume | 43 |

Issue number | 3 |

DOIs | |

State | Published - 2014 |

### Fingerprint

### Keywords

- Closest vector problem
- Hardness of approximation
- Smooth label cover
- Sum check protocol

### ASJC Scopus subject areas

- Mathematics(all)
- Computer Science(all)

### Cite this

*SIAM Journal on Computing*,

*43*(3), 1184-1205. https://doi.org/10.1137/130919623

**Almost polynomial factor hardness for closest vector problem with preprocessing.** / Khot, Subhash; Popat, Preyas; Vishnoi, Nisheeth K.

Research output: Contribution to journal › Article

*SIAM Journal on Computing*, vol. 43, no. 3, pp. 1184-1205. https://doi.org/10.1137/130919623

}

TY - JOUR

T1 - Almost polynomial factor hardness for closest vector problem with preprocessing

AU - Khot, Subhash

AU - Popat, Preyas

AU - Vishnoi, Nisheeth K.

PY - 2014

Y1 - 2014

N2 - We prove that for an arbitrarily small constant < 0, the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor 2log1-en, under the assumption that NP ⊈ SIZE(2logO(1/e)n).

AB - We prove that for an arbitrarily small constant < 0, the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor 2log1-en, under the assumption that NP ⊈ SIZE(2logO(1/e)n).

KW - Closest vector problem

KW - Hardness of approximation

KW - Smooth label cover

KW - Sum check protocol

UR - http://www.scopus.com/inward/record.url?scp=84904796466&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904796466&partnerID=8YFLogxK

U2 - 10.1137/130919623

DO - 10.1137/130919623

M3 - Article

AN - SCOPUS:84904796466

VL - 43

SP - 1184

EP - 1205

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 3

ER -