Cryptology ePrint Archive: Report 2020/1238
Hardness of Module-LWE and Ring-LWE on General Entropic Distributions
Hao Lin and Yang Wang and Mingqiang Wang
Abstract: The hardness of Entropic LWE has been studied in a number of works. However, there is not work study the hardness of algebraically structured LWE with entropic secrets. In this work, we conduct a comprehensive study on establishing hardness reductions for Entropic Module-LWE and Entropic Ring-LWE. We show an entropy bound that guarantees the security of arbitrary Entropic Module-LWE and Entropic Ring-LWE, these are the first results on the hardness of algebraically structured LWE with entropic secrets. One of our central techniques is a new generalized leftover hash lemma over ring and a new decomposition theorem for continuous Gaussian distribution on KR, which might be of independent interests.
Category / Keywords: foundations / Lattice-based cryptography, Module learning with errors, Ring learning with errors, Entropic Module-LWE, Entropic Ring-LWE.
Date: received 7 Oct 2020
Contact author: lhao17 at mail sdu edu cn
Available format(s): PDF | BibTeX Citation
Version: 20201009:113322 (All versions of this report)
Short URL: ia.cr/2020/1238
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