New practical algorithms for the approximate shortest lattice vector

  • We present a practical algorithm that given an LLL-reduced lattice basis of dimension n, runs in time O(n3(k=6)k=4+n4) and approximates the length of the shortest, non-zero lattice vector to within a factor (k=6)n=(2k). This result is based on reasonable heuristics. Compared to previous practical algorithms the new method reduces the proven approximation factor achievable in a given time to less than its fourthth root. We also present a sieve algorithm inspired by Ajtai, Kumar, Sivakumar [AKS01].

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Author:Claus Peter SchnorrGND
Place of publication:Frankfurt am Main
Document Type:Report
Date of Publication (online):2005/07/01
Year of first Publication:2001
Publishing Institution:Universit├Ątsbibliothek Johann Christian Senckenberg
Release Date:2005/07/01
Issue:Preliminary Report
Page Number:16
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