[Resource Topic] 2024/1791: Discrete gaussian sampling for BKZ-reduced basis

Welcome to the resource topic for 2024/1791

Title:
Discrete gaussian sampling for BKZ-reduced basis

Authors: Amaury Pouly, Yixin Shen

Abstract:

Discrete Gaussian sampling on lattices is a fundamental problem in lattice-based cryptography. In this paper, we revisit the Markov chain Monte Carlo (MCMC)-based Metropolis-Hastings-Klein (MHK) algorithm proposed by Wang and Ling
and study its complexity under the Geometric Series Assuption (GSA) when the given basis is BKZ-reduced. We give experimental evidence that the GSA is accurate in this context, and we give a very simple approximate formula for the complexity of the sampler that is accurate over a large range of parameters and easily computable. We apply our results to the dual attack on LWE of [Pouly and Shen 2024] and significantly improve the complexity estimates of the attack. Finally, we provide some results of independent interest on the Gaussian mass of a random q-ary lattices.

ePrint: https://eprint.iacr.org/2024/1791

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