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A polynomial time algorithm for GapCVPP in l 1 norm

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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.

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Authors and Affiliations

  1. Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan, 250100, China

    ChengLiang Tian

  2. School of Mathematics, Shandong University, Jinan, 250100, China

    ChengLiang Tian

  3. Institute for Advanced Study, Tsinghua University, Beijing, 100084, China

    LiDong Han

  4. Department of Electrical Engineering and Computer Science, University of Wisconsin-Milwaukee, Milwaukee, WI, 53201, USA

    GuangWu Xu

Authors
  1. ChengLiang Tian
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  2. LiDong Han
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  3. GuangWu Xu
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Correspondence to ChengLiang Tian.

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Tian, C., Han, L. & Xu, G. A polynomial time algorithm for GapCVPP in l 1 norm. Sci. China Inf. Sci. 57, 1–7 (2014). https://doi.org/10.1007/s11432-013-4795-8

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  • DOI: https://doi.org/10.1007/s11432-013-4795-8

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