Similarity Calculation Based on Homomorphic Encryption

Abstract: In recent years, although some homomorphic encryption algorithms have been proposed to provide additive homomorphic encryption and multiplicative homomorphic encryption. However, similarity measures are required for searches and queries under homomorphic encrypted ciphertexts. Therefore, this study considers the cosine similarity, angular similarity, Tanimoto similarity, and soft cosine similarity and combines homomorphic encryption algorithms for similarity calculation. This study proposes mathematical models to prove the proposed homomorphic encryption-based similarity calculation methods and gives practical cases to explain the proposed methods. In experiments, the performance of the proposed homomorphic encryption-based similarity calculation methods has been evaluated under different security strengths.