Paper 2022/1602

Survey on Fully Homomorphic Encryption, Theory, and Applications

Chiara Marcolla, Technology Innovation Institute
Victor Sucasas, Technology Innovation Institute
Marc Manzano, Sandbox Quantum
Riccardo Bassoli, Institute of Communication Technology, Faculty of Electrical and Computer Engineering, Technische Universität Dresden
Frank H.P. Fitzek, Institute of Communication Technology, Faculty of Electrical and Computer Engineering, Technische Universität Dresden
Najwa Aaraj, Technology Innovation Institute

Data privacy concerns are increasing significantly in the context of 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 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.

Available format(s)
Publication info
Published elsewhere. Proceedings of the IEEE
Fully Homomorphic Encryption Homomorphic Encryption Lattices Neural Networks Fog Computing Cloud Computing IoT
Contact author(s)
chiara marcolla @ tii ae
victor sucasas @ tii ae
marc @ sandboxquantum com
riccardo bassoli @ tu-dresden de
frank fitzek @ tu-dresden de
najwa aaraj @ tii ae
2022-12-08: revised
2022-11-17: received
See all versions
Short URL
Creative Commons Attribution


      author = {Chiara Marcolla and Victor Sucasas and Marc Manzano and Riccardo Bassoli and Frank H.P. Fitzek and Najwa Aaraj},
      title = {Survey on Fully Homomorphic Encryption, Theory, and Applications},
      howpublished = {Cryptology ePrint Archive, Paper 2022/1602},
      year = {2022},
      doi = {10.1109/JPROC.2022.3205665},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.