Using Progressive Success Probabilities for Sound-pruned Enumerations in BKZ Algorithm

Abstract

We introduce a new technique for BKZ reduction, which incorporated four improvements of BKZ 2.0 (including: sound pruning, preprocessing of local blocks, shorter enumeration radius and early-abortion). This algorithm is designed based on five claims which be verified strongly in experimental results. The main idea is that, similar to progressive BKZ which using decrement of enumeration cost after each sequence incremental reduction to augment the block size, we use the decrement of enumeration cost after each round of our algorithm to augment the success probability of bounding function. Also we discussed parallelization considerations in our technique.