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SCIENCE CHINA Information Sciences, Volume 61, Issue 3: 032115(2018) https://doi.org/10.1007/s11432-017-9307-0

Orthogonalized lattice enumeration for solving SVP

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  • ReceivedSep 6, 2017
  • AcceptedNov 30, 2017
  • PublishedJan 17, 2018

Abstract

The orthogonalized integer representation wasindependently proposed by Ding et al. using genetic algorithm and Fukase et al. using sampling technique to solve shortest vector problem (SVP).Their results are promising.In this paper, we consider sparse orthogonalized integer representations for shortest vectors and propose a new enumeration method,called orthognalized enumeration, by integratingsuch a representation. Furthermore, we present a mixed BKZ method, called MBKZ, by alternately applying orthognalized enumeration andother existing enumeration methods. Compared to the existing ones,our methods have greater efficiency and achieve exponential speedups both in theory and in practice for solving SVP.Implementations of our algorithms have been tested to be effective in solving challenging lattice problems.


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