A Lattice Reduction Algorithm Based on Sublattice BKZ

We present m-SubBKZ reduction algorithm that outputs a reduced lattice basis, containing a vector shorter than the original BKZ. The work is based on the properties of sublattices and the Gaussian Heuristic of the full lattice and sublattices. By theoretical analysis and simulation, we suggest a BKZ call on the sublattice is possible to produce a short vector close to the shortest vector in the full lattice. The key idea of our algorithm is to extract multiple sublattices from the preprocessed lattice, restricting the context in which a lattice reduction solver is called. The full basis is then updated with vectors from the reduced basis of each sublattice. The new algorithm improves on the efficiency of the original BKZ algorithm and the BKZ 2.0 variant. We show the experimental results on random lattices to compare the length of vectors produced by our algorithm and original BKZ and BKZ 2.0. On the 180-dimension basis, the m-SubBKZ reaches 47% of the output of BKZ and 46% of BKZ 2.0. The ratio drops with the dimension increasing. The effect is more oblivious with smaller blocks. The results show that the new algorithm is able to produce a shorter vector at a relatively low cost compared with previous algorithms, and the improvements are especially explicit for lattices of high dimensions.