Lattice basis reduction : improved practical algorithms and solving subset sum problems

  • We report on improved practical algorithms for lattice basis reduction. We propose a practical floating point version of theL3-algorithm of Lenstra, Lenstra, Lovász (1982). We present a variant of theL3-algorithm with "deep insertions" and a practical algorithm for block Korkin—Zolotarev reduction, a concept introduced by Schnorr (1987). Empirical tests show that the strongest of these algorithms solves almost all subset sum problems with up to 66 random weights of arbitrary bit length within at most a few hours on a UNISYS 6000/70 or within a couple of minutes on a SPARC1 + computer.

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Author:Claus Peter SchnorrGND, Martin Euchner
Document Type:Preprint
Year of Completion:1993
Year of first Publication:1993
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/07/12
Tag:Block Korkin—Zolotarev reduction; Knapsack problem; Korkin—Zolotarev reduction; LLL-reduction; Lattice basis reduction; Low density subset sum algorithm; Shortest lattice vector problem; Stable reduction algorithm; Subset sum problem
Page Number:27
First Page:1
Last Page:27
Erschienen in: Mathematical programming, 66.1994, Nr. 1-3, S. 181-199, doi:10.1007/BF01581144
Institutes:Informatik und Mathematik / Mathematik
Informatik und Mathematik / Informatik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht