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Lossiness and Entropic Hardness for Ring-LWE

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conference contribution
posted on 2023-11-29, 18:14 authored by Zvika Brakerski, Nico DöttlingNico Döttling
The hardness of the Ring Learning with Errors problem (RLWE) is a central building block for efficiency-oriented lattice-based cryptography. Many applications use an “entropic” variant of the problem where the so-called “secret” is not distributed uniformly as prescribed but instead comes from some distribution with sufficient min-entropy. However, the hardness of the entropic variant has not been substantiated thus far. For standard LWE (not over rings) entropic results are known, using a “lossiness approach” but it was not known how to adapt this approach to the ring setting. In this work we present the first such results, where entropic security is established either under RLWE or under the Decisional Small Polynomial Ratio (DSPR) assumption which is a mild variant of the NTRU assumption. In the context of general entropic distributions, our results in the ring setting essentially match the known lower bounds (Bolboceanu et al., Asiacrypt 2019; Brakerski and Döttling, Eurocrypt 2020).

History

Preferred Citation

Zvika Brakerski and Nico Döttling. Lossiness and Entropic Hardness for Ring-LWE. In: Theory of Cryptography Conference (TCC). 2020.

Primary Research Area

  • Algorithmic Foundations and Cryptography

Name of Conference

Theory of Cryptography Conference (TCC)

Legacy Posted Date

2021-02-04

Open Access Type

  • Unknown

BibTeX

@inproceedings{cispa_all_3354, title = "Lossiness and Entropic Hardness for Ring-LWE", author = "Brakerski, Zvika and Döttling, Nico", booktitle="{Theory of Cryptography Conference (TCC)}", year="2020", }

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