[Resource Topic] 2023/826: Ring/Module Learning with Errors under Linear Leakage -- Hardness and Applications

Welcome to the resource topic for 2023/826

Title:
Ring/Module Learning with Errors under Linear Leakage – Hardness and Applications

Authors: Zhedong Wang, Qiqi Lai, Feng-Hao Liu

Abstract:

This paper studies the hardness of decision Module Learning with Errors (\MLWE) under linear leakage, which has been used as a foundation to derive more efficient lattice-based zero-knowledge proofs in a recent paradigm of Lyubashevsky, Nguyen, and Seiler (PKC 21). Unlike in the plain \LWE~setting, it was unknown whether this problem remains provably hard in the module/ring setting.

This work shows a reduction from the search \MLWE~to decision \MLWE~with linear leakage. Thus, the main problem remains hard asymptotically as long as the non-leakage version of \MLWE~is hard. Additionally, we also refine the paradigm of Lyubashevsky, Nguyen, and Seiler (PKC 21) by showing a more fine-grained tradeoff between efficiency and leakage. This can lead to further optimizations of lattice proofs under the paradigm.

ePrint: https://eprint.iacr.org/2023/826

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