TY - GEN
T1 - Lattice problems in N P ∩ coNP
AU - Aharonov, Dorit
AU - Regev, Oded
PY - 2004
Y1 - 2004
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/17744382015
U2 - 10.1109/FOCS.2004.35
DO - 10.1109/FOCS.2004.35
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AN - SCOPUS:17744382015
SN - 0769522289
T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
SP - 362
EP - 371
BT - Proceedings - 45th Annual IEEE Symposium on Foundations of Computer Sciences, FOCS 2004
PB - IEEE Computer Society
T2 - 45th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2004
Y2 - 17 October 2004 through 19 October 2004
ER -