Welcome to the resource topic for 2022/843
Title:
Predicting BKZ Z-Shapes on q-ary Lattices
Authors: Martin R. Albrecht and Jianwei Li
Abstract:Primal attacks against the Learning With Errors (LWE) problem rely on reducing (q)-ary lattices. These reduced bases have been observed to exhibit a so-called ``Z-shape’’ on their Gram–Schmidt vectors. We propose an efficient simulator to accurately predict this Z-shape behaviour, which we back up with extensive simulations and experiments. We also formalise (under standard heuristics) the intuition that the presence of a Z-shape makes enumeration-based primal lattice attacks faster. Furthermore, we upgrade the LWE or lattice estimator with our simulator to assess and then rule out the impact of the (q)-ary Z-shape on solving LWE instances derived from parameter sets for NIST PQC candidates. We consider this improved estimator to be of independent interest.
ePrint: https://eprint.iacr.org/2022/843
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