Paper 2023/304

On homomorphic encryption using abelian groups: Classical security analysis

Eleni Agathocleous, CISPA Helmholtz Center for Information Security
Vishnupriya Anupindi, RICAM Austrian Academy of Sciences
Annette Bachmayr, RWTH Aachen University
Chloe Martindale, University of Bristol
Rahinatou Yuh Njah Nchiwo, Aalto University
Mima Stanojkovski, Università di Trento

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.

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Attacks and cryptanalysis
Publication info
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
2023-03-01: approved
2023-03-01: received
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      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},
      note = {\url{}},
      url = {}
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