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
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.
History
Primary Research Area
Algorithmic Foundations and Cryptography
BibTeX
@misc{Agathocleous:Anupindi:Bachmayr:Martindale:Nchiwo:Stanojkovski:2023,
title = "On homomorphic encryption using abelian groups: Classical security
analysis",
author = "Agathocleous, Eleni" AND "Anupindi, Vishnupriya" AND "Bachmayr, Annette" AND "Martindale, Chloe" AND "Nchiwo, Rahinatou Yuh Njah" AND "Stanojkovski, Mima",
year = 2023,
month = 2
}