Paper 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.
Metadata
- Available format(s)
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- Lattice-based cryptographyModule learning with errorsRing learning with errorsEntropic Module-LWEEntropic Ring-LWE.
- Contact author(s)
- lhao17 @ mail sdu edu cn
- History
- 2022-05-13: revised
- 2020-10-09: received
- See all versions
- Short URL
- https://ia.cr/2020/1238
- License
-
CC BY