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On homomorphic encryption using abelian groups.pdf (520.2 kB)

On homomorphic encryption using abelian groups: Classical security analysis

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posted on 2024-02-09, 09:22 authored by Eleni Agathocleous, Vishnupriya Anupindi, Annette Bachmayr, Chloe Martindale, Rahinatou Yuh Njah Nchiwo, Mima Stanojkovski
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.

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  • Algorithmic Foundations and Cryptography

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@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 }

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