Advances and Applications in Fully Homomorphic Encryption Research

With the rapid advancement of information technology and the widespread adoption of cloud computing, data security and privacy protection have increasingly become global priorities. In this context, Fully Homomorphic Encryption (FHE) has emerged as a sophisticated encryption technology capable of performing arbitrary computations on encrypted data without the need for decryption, thereby attracting significant interest from both academia and industry. Initially proposed by Rivest et al. in 1978 and practically realized by Gentry in 2009, FHE has evolved through four generations of schemes, each introducing novel construction methods and optimization techniques to enhance security and computational efficiency. Central to modern FHE schemes are lattice-based hard problems such as Learning with Errors (LWE) and Ring-Learning with Errors (RLWE), which provide robust resistance against quantum computing attacks. Additionally, advancements in optimizing the bootstrapping process and exploring hierarchical structures have further improved the practicality and performance of FHE. FHE applications span diverse fields, including cloud computing, artificial intelligence, and blockchain technology, demonstrating its immense potential in ensuring data privacy and facilitating secure computations. However, FHE still faces significant challenges related to computational efficiency, implementation complexity, and application scalability. Future research directions aim to enhance computational performance, broaden application scenarios, strengthen security measures, simplify implementation processes, and develop multi-modal and hybrid encryption schemes. Through a comprehensive review of FHE's development, current progress, applications, and challenges, this paper seeks to provide researchers and engineers with a thorough understanding of the FHE landscape, thereby promoting its continued advancement and practical utilization.