On homomorphic encryption using abelian groups: Classical security analysis

2023/02/24 by Eleni Agathocleous, Agathocleous, Eleni, Vishnupriya Anupindi +9
Computer Science · Engineering · #Coding theory and cryptography #Cryptography and Data Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2302.12867

openalex publication_date 2023/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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 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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