Segment LLL-Reduction with Floating Point Orthogonalization

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


We associate with an integer lattice basis a scaled basis that has orthogonal vectors of nearly equal length. The orthogonal vectors or the QR-factorization of a scaled basis can be accurately computed up to dimension 216 by Householder reflexions in floating point arithmetic (fpa) with 53 precision bits.

We develop a highly practical fpa-variant of the new segment LLL- reduction of Koy and Schnorr [KS01]. The LLL-steps are guided in this algorithm by the Gram-Schmidt coefficients of an associated scaled basis. The new reduction algorithm is much faster than previous codes for LLL-reduction and performs well beyond dimension 1000.


LLL-reduction Householder reflexion floating point arithmetic stability scaled basis segment LLL-reduction local LLL-reduction 


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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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