[Resource Topic] 2023/304: On homomorphic encryption using abelian groups: Classical security analysis

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Title:
On homomorphic encryption using abelian groups: Classical security analysis

Authors: Eleni Agathocleous, Vishnupriya Anupindi, Annette Bachmayr, Chloe Martindale, Rahinatou Yuh Njah Nchiwo, Mima Stanojkovski

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.

ePrint: https://eprint.iacr.org/2023/304

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