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Segment LLL-Reduction of Lattice Bases

  • Henrik Koy
  • Claus Peter Schnorr
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2146)

Abstract

We present an efficient variant of LLL-reduction of lattice bases in the sense of Lenstra, Lenstra, Lovász. We organize LLL-reduction in segments of size k. Local LLL-reduction of segments is done using local coordinates of dimension k.

We introduce segment LLL-reduced bases, a variant of LLL-reduced bases achieving a slightly weaker notion of reducedness, but speeding up the reduction time of lattices of dimension n by a factor n. We also introduce a variant of LLL-reduction using iterated segments. The resulting reduction algorithm runs in O(n 3 log2 n) arithmetic steps for integer lattices of dimension n with basis vectors of length 22.

Keywords

LLL-reduction shortest lattice vector segments iterated segments local coordinates local LLL-reduction divide and conquer 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Henrik Koy
    • 1
  • Claus Peter Schnorr
    • 2
  1. 1.Deutsche Bank AG, Frankfurt am MainGermany
  2. 2.Fachbereiche Mathematik und InformatikUniversität FrankfurtFrankfurt am MainGermany

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