Similarity Calculation Based on Homomorphic Encryption

TL;DR

This paper develops methods for calculating various similarity measures directly on homomorphically encrypted data, enabling privacy-preserving searches and queries.

Contribution

It introduces mathematical models and practical algorithms for similarity calculations using homomorphic encryption, addressing a key challenge in privacy-preserving data analysis.

Findings

The methods support cosine, angular, Tanimoto, and soft cosine similarity calculations.

Performance varies with different security strengths, demonstrating practical viability.

The approach enables secure similarity searches on encrypted data.

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.