Fast LLL-type lattice reduction

We modify the concept of LLL-reduction of lattice bases in the sense of Lenstra, Lenstra, Lovasz [LLL82] towards a faster reduction algorithm. We organize LLL-reduction in segments of the basis. Our SLLL-bases approximat
We modify the concept of LLL-reduction of lattice bases in the sense of Lenstra, Lenstra, Lovasz [LLL82] towards a faster reduction algorithm. We organize LLL-reduction in segments of the basis. Our SLLL-bases approximate the successive minima of the lattice in nearly the same way as LLL-bases. For integer lattices of dimension n given by a basis of length 2exp(O(n)), SLLL-reduction runs in O(n.exp(5+epsilon)) bit operations for every epsilon > 0, compared to O(exp(n7+epsilon)) for the original LLL and to O(exp(n6+epsilon)) for the LLL-algorithms of Schnorr (1988) and Storjohann (1996). We present an even faster algorithm for SLLL-reduction via iterated subsegments running in O(n*exp(3)*log n) arithmetic steps.
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Metadaten
Author:Claus Peter Schnorr
URN:urn:nbn:de:hebis:30-12071
URL:http://www.mi.informatik.uni-frankfurt.de/research/papers.html
Document Type:Report
Language:English
Year of Completion:2004
Year of first Publication:2004
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/07/04
Tag:Householder reflection ; LLL-reduction ; SLLL-reduction ; error bounds; floating point errors ; length defect ; local LLLreduction ; segments
HeBIS PPN:191533750
Institutes:Mathematik
Informatik
Dewey Decimal Classification:510 Mathematik
Sammlungen:Universitätspublikationen
Licence (German):License Logo Veröffentlichungsvertrag für Publikationen

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