Abstract
AbstractThe BKZ algorithm has been one of the most important tools for analyzing and assessing lattice-based cryptosystems. The second order statistical behavior of BKZ algorithm on random lattices has been well measured in the work of Yu and Ducas. Several simulators have been proposed to efficiently and accurately predict the profile shape for random lattices. But for the case q-ary lattices, the situation is much less understood. Recently, Albrecht and Li proposed a simulator that predicts the Z-shape of q-ary lattices a good accuracy. However, we find that this simulator still has its limitations when Z-shape disappears. Our experiments reveal more features for the shape profile of q-ary lattices. Based on some results on the distribution of the length of short vectors and reasonable heuristics, we propose a new simulator for random q-ary lattices with some extensions. Furthermore, the second order statistical behavior of BKZ algorithm on q-ary lattices is characterized, their similarities and differences compared to that for random lattices have been briefly analyzed.KeywordsBKZ algorithmq-ary latticeCryptanalysisSimulator
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