Entropic Hardness of Module-LWE from Module-NTRU

Katharina Boudgoust; Corentin Jeudy; Adeline Roux-Langlois; Weiqiang Wen

Paper 2022/245 Original: eprint.iacr.org/2022/245 ↗

Entropic Hardness of Module-LWE from Module-NTRU

Katharina Boudgoust

Corentin Jeudy

Adeline Roux-Langlois

Weiqiang Wen

Abstract

The Module Learning With Errors problem (M-LWE) has gained popularity in recent years for its security-efficiency balance, and its hardness has been established for a number of variants. In this paper, we focus on proving the hardness of (search) M-LWE for general secret distributions, provided they carry sufficient min-entropy. This is called entropic hardness of M-LWE. First, we adapt the line of proof of Brakerski and Döttling on R-LWE (TCC’20) to prove that the existence of certain distributions implies the entropic hardness of M-LWE. Then, we provide one such distribution whose required properties rely on the hardness of the decisional Module-NTRU problem.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
History: 2023-02-20: last updated; 2022-03-02: published
Short URL: https://ia.cr/2022/245
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2022/245,
      author = {Katharina Boudgoust and Corentin Jeudy and Adeline Roux-Langlois and Weiqiang Wen},
      title = {Entropic Hardness of Module-LWE from Module-NTRU},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/245},
      year = {2022},
      url = {https://eprint.iacr.org/2022/245}
}