Paper 2023/304
On homomorphic encryption using abelian groups: Classical security analysis
Abstract
In [15], Leonardi and Ruiz-Lopez propose an additively homomorphic public key encryption scheme whose security is expected to depend on the hardness of the $\textit{learning homomorphism with noise problem}$ (LHN). Choosing parameters for their primitive requires choosing three groups $G$, $H$, and $K$. In their paper, Leonardi and Ruiz-Lopez claim that, when $G$, $H$, and $K$ are abelian, then their public-key cryptosystem is not quantum secure. In this paper, we study security for finite abelian groups $G$, $H$, and $K$ in the classical case. Moreover, we study quantum attacks on instantiations with solvable groups.
Metadata
- Available format(s)
-
PDF
- Category
- Attacks and cryptanalysis
- Publication info
- Preprint.
- Keywords
- homomorphic encryptioncryptanalysisabstract groupsabelian groupssolvable groupsLHN
- Contact author(s)
-
eleni agathocleous @ cispa de
vishnupriya anupindi @ oeaw ac at
bachmayr @ mathematik rwth-aachen de
chloe martindale @ bristol ac uk
rahinatou njah @ aalto fi
mima stanojkovski @ unitn it - History
- 2023-03-01: approved
- 2023-03-01: received
- See all versions
- Short URL
- https://ia.cr/2023/304
- License
-
CC0
BibTeX
@misc{cryptoeprint:2023/304,
author = {Eleni Agathocleous and Vishnupriya Anupindi and Annette Bachmayr and Chloe Martindale and Rahinatou Yuh Njah Nchiwo and Mima Stanojkovski},
title = {On homomorphic encryption using abelian groups: Classical security analysis},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/304},
year = {2023},
url = {https://eprint.iacr.org/2023/304}
}
