Heuristics on lattice basis reduction in practice

In this paper we provide a survey on LLL lattice basis reduction in practice. We introduce several new heuristics as to speed up known lattice basis reduction methods and improve the quality of the computed reduced lattice basis in practice. We analyze substantial experimental data and to our knowledge, we are the first to present general heuristics for determining which variant of the reduction algorithm, for varied parameter choices, yields the most efficient reduction strategy for reducing a particular problem instance.