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

The authors report on improved practical algorithms for lattice basis reduction. They propose a practical floating point version of the L³-algorithm of Lenstra, Lenstra, Lovász. The authors present a variant of the L³-algorithm with ‘deep insertions’ and a practical algorithm for block Korkin-Zolotarev reduction, a concept introduced by Schnorr. Empirical tests show that the strongest of these algorithms solves almost all subset sum problems with up to 66 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 SPARC1+computer.