## Abstract

We show that the problems of approximating the shortest and closest vector in a lattice to within a factor of √n lie in NP intersect coNP. The result (almost) subsumes the three mutually-incomparable previous results regarding these lattice problems: Banaszczyk, Goldreich and Goldwasser, and Aharonov and Regev. Our technique is based on a simple fact regarding succinct approximation of functions using their Fourier transform over the lattice. This technique might be useful elsewhere - we demonstrate this by giving a simple and efficient algorithm for one other lattice problem (CVPP) improving on a previous result of Regev. An interesting fact is that our result emerged from a "dequantization" of our previous quantum result in. This route to proving purely classical results might be beneficial elsewhere.

Original language | American English |
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Pages (from-to) | 362-371 |

Number of pages | 10 |

Journal | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |

State | Published - 2004 |

Event | Proceedings - 45th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2004 - Rome, Italy Duration: 17 Oct 2004 → 19 Oct 2004 |