LATTICE BASIS REDUCTION - IMPROVED PRACTICAL ALGORITHMS AND SOLVING SUBSET SUM PROBLEMS

We report on improved practical algorithms for lattice basis reduction. We present a variant of the L3-algorithm with "deep insertions" and a practical algorithm for blockwise Korkine-Zolotarev reduction, a concept extending L3-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.