  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.
