Science China Information Sciences

, Volume 57, Issue 3, pp 1–7 | Cite as

A polynomial time algorithm for GapCVPP in l 1 norm

Research Paper

Abstract

This paper concerns the hardness of approximating the closest vector in a lattice with preprocessing in l 1 norm, and gives a polynomial time algorithm for GapCVPPγ in l 1 norm with gap γ = O(n/logn). The gap is smaller than that obtained by simply generalizing the approach given by Aharonov and Regev. The main technical ingredient used in this paper is the discrete Laplace distribution on lattices which may be of independent interest.

Keywords

lattices algorithm Laplace measures closest vector problem with preprocessing computational complexity 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Key Laboratory of Cryptologic Technology and Information Security, Ministry of EducationShandong UniversityJinanChina
  2. 2.School of MathematicsShandong UniversityJinanChina
  3. 3.Institute for Advanced StudyTsinghua UniversityBeijingChina
  4. 4.Department of Electrical Engineering and Computer ScienceUniversity of Wisconsin-MilwaukeeMilwaukeeUSA

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