Paper 2016/1169
LWE from Non-commutative Group Rings
Qi Cheng, Jun Zhang, and Jincheng Zhuang
Abstract
The Ring Learning-With-Errors (LWE) problem, whose security is based on hard ideal lattice problems, has proven to be a promising primitive with diverse applications in cryptography. There are however recent discoveries of faster algorithms for the principal ideal SVP problem, and attempts to generalize the attack to non-principal ideals. In this work, we study the LWE problem on group rings, and build cryptographic schemes based on this new primitive. One can regard the LWE on cyclotomic integers as a special case when the underlying group is cyclic, while our proposal utilizes non-commutative groups, which eliminates the weakness associated with the principal ideal lattices. In particular, we show how to build public key encryption schemes from dihedral group rings, which maintains the efficiency of the ring-LWE and improves its security.
Note: A refined security analysis is provided.
Metadata
- Available format(s)
-
PDF
- Publication info
- Preprint. MINOR revision.
- Keywords
- ring-LWENon-commutative group ringDihedral group ring
- Contact author(s)
- zhuangjincheng @ iie ac cn
- History
- 2017-06-21: last of 2 revisions
- 2016-12-28: received
- See all versions
- Short URL
- https://ia.cr/2016/1169
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2016/1169,
author = {Qi Cheng and Jun Zhang and Jincheng Zhuang},
title = {{LWE} from Non-commutative Group Rings},
howpublished = {Cryptology {ePrint} Archive, Paper 2016/1169},
year = {2016},
url = {https://eprint.iacr.org/2016/1169}
}
