Survey on Fully Homomorphic Encryption, Theory, and Applications

Abstract

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 privacypreserving 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.

A Review of Homomorphic Encryption for Privacy-Preserving Biometrics

“…Moreover, the authors reviewed homomorphic cryptosystems in healthcare. Marcolla et al [ 13 ] provided a comprehensive review of HE from both the theoretical and practical points of view. This survey demonstrates the mathematical foundation required to understand fully homomorphic encryption (FHE).…”

“…For FHE, there is no limit to the number of operations that can be undertaken [ 32 ]. The inherent characteristic of HE is that, each time a homomorphic operation is performed, the errors increase [ 13 ]. As a result, after a certain number of multiplications or additions, ciphertexts cannot be decrypted correctly because of the growth in the error.…”

“…The helper data are generated by an irreversible cryptographic process so that it is difficult for adversaries to acquire the original biometric features from the helper data [ 12 ]. Homomorphic encryption (HE): HE tackles the data privacy issues by performing multiple operations on the encrypted data without any decryption [ 13 ]. Because the result of the HE computation remains encrypted and can only be decrypted by the data owners, confidentiality is kept and any third party can operate over the ciphertext without accessing the original plaintext [ 14 ].…”

Multi-party computation enables secure polynomial control based solely on secret-sharing

“…The main idea of this procedure is to evaluate the decryption process, which subsequently enables refreshing the ciphertext, in an encrypted fashion. For an overview of recent progress, we refer to [10], [11]. In more modern fully homomorphic cryptosystems, such as CKKS [12], which we build on in this paper, the core of bootstrapping corresponds to a so-called modular reduction, which entails a polynomial approximation of the modulo function.…”

Training of Classification Models via Federated Learning and Homomorphic Encryption

“…Two widely known privacy-enhancing technologies are federated learning [ 6 ], which is a distributed machine learning approach that uses decentralized data and seeks to generate a model from data stored on multiple remote devices or clients, and homomorphic encryption [ 7 , 8 ] that is a form of cryptography in which mathematical or logical operations can be performed on encrypted data. In this work, both technologies are used to introduce a protocol to train multilayer perceptrons for classification while preserving data privacy during training.…”