Fixed Complexity LLL Algorithm

A common technique to perform lattice basis reduction is the Lenstra, Lenstra, Lovasz (LLL) algorithm. An implementation of this algorithm in real-time systems suffers from the problem of variable run-time and complexity. This correspondence proposes a modification of the LLL algorithm. The signal flow is altered to follow a deterministic structure, which promises to obtain an easier implementation as well as a fixed execution time known in advance. In the case of a maximum number of iterations as it is likely in real-time systems, our modification clearly outperforms the original LLL algorithm as far as the quality of the reduced lattice basis is concerned.