Invited Lectures

Fundamentals of Computation Theory

Volume 529 of the series Lecture Notes in Computer Science pp 68-85

Date:

Lattice basis reduction: Improved practical algorithms and solving subset sum problems

  • C. P. SchnorrAffiliated withFachbereich Mathematik/Informatik, Universität Frankfurt
  • , M. EuchnerAffiliated withFachbereich Mathematik/Informatik, Universität Frankfurt

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Abstract

We report on improved practical algorithms for lattice basis reduction. We present a variant of the L 3-algorithm with “deep insertions” and a practical algorithm for blockwise Korkine-Zolotarev reduction, a concept extending L 3-reduction, that has been introduced by Schnorr (1987). Empirical tests show that the strongest of these algorithms solves almost all subset sum problems with up to 58 random weights of arbitrary bit length within at most a few hours on a UNISYS 6000/70 or within a couple of minutes on a SPARC 2 computer.