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.

翻译：近年来，尽管已有一些同态加密算法被提出以提供加性同态加密和乘性同态加密，但在同态加密密文下进行搜索和查询仍需相似度度量方法。因此，本研究考虑余弦相似度、角度相似度、Tanimoto相似度及软余弦相似度，并将其与同态加密算法相结合进行相似度计算。本研究提出数学模型以证明所提出的基于同态加密的相似度计算方法，并通过实际案例解释这些方法。在实验中，所提出的基于同态加密的相似度计算方法在不同安全强度下的性能得到了评估。