Survey on Fully Homomorphic Encryption, Theory, and Applications
Chiara Marcolla, Victor Sucasas, Marc Manzano, Riccardo Bassoli, Frank H. P. Fitzek, Najwa Aaraj
Abstract
Data privacy concerns are increasing significantly in the context of the Internet of Things, cloud services, edge computing, artificial intelligence applications, and other applications enabled by next-generation networks. Homomorphic encryption addresses privacy challenges by enabling multiple operations to be performed on encrypted messages without decryption. This article comprehensively addresses homomorphic encryption from both theoretical and practical perspectives. This article delves into the mathematical foundations required to understand fully homomorphic encryption ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textsf {FHE}$ </tex-math></inline-formula> ). It consequently covers design fundamentals and security properties of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textsf {FHE}$ </tex-math></inline-formula> and describes the main <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textsf {FHE}$ </tex-math></inline-formula> schemes based on various mathematical problems. On a more practical level, this article presents a view on privacy-preserving machine learning using homomorphic encryption and then surveys <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textsf {FHE}$ </tex-math></inline-formula> at length from an engineering angle, covering the potential application of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textsf {FHE}$ </tex-math></inline-formula> in fog computing and cloud computing services. It also provides a comprehensive analysis of existing state-of-the-art <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textsf {FHE}$ </tex-math></inline-formula> libraries and tools, implemented in software and hardware, and the performance thereof.