Survey on Fully Homomorphic Encryption, Theory, and Applications

This paper comprehensively addresses homomorphic encryption from both theoretical and practical perspectives. The paper delves into the mathematical foundations required to understand fully homomorphic encryption FHE. It consequently covers design fundamentals and security properties of FHE, and describes the main FHE schemes based on various mathematical problems. On a more practical level, the paper presents a view on privacy-preserving Machine Learning using homomorphic encryption, then surveys FHE at length from an engineering angle, covering the potential application of FHE in fog computing, and cloud computing services. It also provides a comprehensive analysis of existing state-of-the-art FHE libraries and tools, implemented in software and hardware, and the performance thereof.