Theoretical Framework and Application Exploration of Fully Homomorphic Encryption

Abstract

With the rapid development of big data and cloud computing, the issues of data privacy and security have gradually attracted widespread attention worldwide. Fully Homomorphic Encryption (FHE), as one of the key technologies for solving privacy computing problems, can perform addition and multiplication operations in the encrypted state, thereby enabling effective computation while ensuring data privacy. This paper reviews the theoretical framework and application exploration of FHE. Firstly, it comprehensively summarizes the theoretical basis, development history, and key mathematical tools of FHE, and focuses on analyzing the algorithm principles and latest progress of mainstream schemes such as Brakerski-Fan-Vercauteren (BFV), Cheon-Kim-Kim-Song (CKKS), and Torus FHE (TFHE). It explores the application potential of FHE in fields such as machine learning, medical health, and cloud computing, and analyzes the core challenges it faces, including performance bottlenecks, bootstrapping overhead, and multi-user management. Finally, it looks forward to future research directions such as the integration of FHE and AI, and the construction of cross-domain privacy computing platforms, emphasizing the significant importance of FHE in promoting the two-way advancement of data security and privacy protection.