A fast variant of the Gaussian reduction algorithm

  • We propose a fast variant of the Gaussian algorithm for the reduction of two dimensional lattices for the l1-, l2- and l-infinite- norm. The algorithm runs in at most O(nM(B) logB) bit operations for the l-infinite- norm and in O(n log n M(B) logB) bit operations for the l1 and l2 norm on input vectors a, b 2 ZZn with norm at most 2B where M(B) is a time bound for B-bit integer multiplication. This generalizes Schönhages monotone Algorithm [Sch91] to the centered case and to various norms.

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Author:Michael Kaib
Document Type:Preprint
Date of Publication (online):2005/07/18
Year of first Publication:1994
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/07/18
Preprint, später in: International Symposium on Algorithmic Number Theory, 1994
Source:International Symposium on Algorithmic Number Theory, 1994 , http://www.mi.informatik.uni-frankfurt.de/research/papers.html
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht