The development of information technology has brought great convenience to our lives, but at the same time, the unfairness and privacy issues brought about by traditional centralized systems cannot be ignored. Blockchain is a peer-to-peer and decentralized ledger technology that has the characteristics of transparency, consistency, traceability and fairness, but it reveals private information in some scenarios. Secure multi-party computation (MPC) guarantees enhanced privacy and correctness, so many researchers have been trying to combine secure MPC with blockchain to deal with privacy and trust issues. In this paper, we used homomorphic encryption, secret sharing and zero-knowledge proofs to construct a publicly verifiable secure MPC protocol consisting of two parts—an on-chain computation phase and an off-chain preprocessing phase—and we integrated the protocol as part of the chaincode in Hyperledger Fabric to protect the privacy of transaction data. Experiments showed that our solution performed well on a permissioned blockchain. Most of the time taken to complete the protocol was spent on communication, so the performance has a great deal of room to grow.

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Using Secure Multi-Party Computation to Protect Privacy on a Permissioned Blockchain.

With the tremendous growth of technology, providing data security to critical applications such as smart grid, health care, and military is indispensable. On the other hand, due to the proliferation of external data threats in these applications, the loss incurred is incredibly high. Standard encryption algorithms such as RSA, ElGamal, and ECC facilitate in protecting sensitive data from outside attackers; however, they cannot perform computations on sensitive data while being encrypted. To perform computations and to process encrypted query on encrypted data, various homomorphic encryption (HE) schemes are proposed. Each of the schemes has its own shortcomings either related to performance or with storage that acts as the barrier for applying in real-time applications. With that conception, our objective is to design HE schemes that are simple by design, efficient in performance, and highly unimpeachable against attacks. Our first proposed scheme is based on Carmichael's Theorem, referred to as Carmichael's Theorem-based Homomorphic Encryption (CTHE), and the second is an improved version of Gorti's Enhanced Homomorphic Encryption Scheme, referred to as Modified Enhanced Homomorphic Encryption (MEHE). For brevity, the schemes are referred to as CTHE and MEHE. Both the schemes are provably secure under the hardness of integer factorization, discrete logarithm, and quadratic residuosity problems. To reduce the noise in these schemes, the modulus switching method is adopted and proved theoretically. The schemes' efficiency is proven by collecting the data from cardiovascular dataset (statically)/blood pressure monitor (dynamically) and is homomorphically encrypted in the edge server. Further analysis on encrypted data is carried out to identify whether a person has hypotension or hypertension with the aid of parameters, namely, mean arterial pressure. As the schemes are probabilistic in nature, breaking the schemes by a polynomial time adversary is impossible and is proven in the article.

Preserving Health Care Data Security and Privacy Using Carmichael's Theorem-Based Homomorphic Encryption and Modified Enhanced Homomorphic Encryption Schemes in Edge Computing Systems.

With the tremendous growth of technology, providing data security to critical applications such as smart grid, health care, and military is indispensable. On the other hand, due to the proliferation of external data threats in these applications, the loss incurred is incredibly high. Standard encryption algorithms such as RSA, ElGamal, and ECC facilitate in protecting sensitive data from outside attackers; however, they cannot perform computations on sensitive data while being encrypted. To perform computations and to process encrypted query on encrypted data, various homomorphic encryption (HE) schemes are proposed. Each of the schemes has its own shortcomings either related to performance or with storage that acts as the barrier for applying in real-time applications. With that conception, our objective is to design HE schemes that are simple by design, efficient in performance, and highly unimpeachable against attacks. Our first proposed scheme is based on Carmichael's Theorem, referred to as Carmichael's Theorem-based Homomorphic Encryption (CTHE), and the second is an improved version of Gorti's Enhanced Homomorphic Encryption Scheme, referred to as Modified Enhanced Homomorphic Encryption (MEHE). For brevity, the schemes are referred to as CTHE and MEHE. Both the schemes are provably secure under the hardness of integer factorization, discrete logarithm, and quadratic residuosity problems. To reduce the noise in these schemes, the modulus switching method is adopted and proved theoretically. The schemes' efficiency is proven by collecting the data from cardiovascular dataset (statically)/blood pressure monitor (dynamically) and is homomorphically encrypted in the edge server. Further analysis on encrypted data is carried out to identify whether a person has hypotension or hypertension with the aid of parameters, namely, mean arterial pressure. As the schemes are probabilistic in nature, breaking the schemes by a polynomial time adversary is impossible and is proven in the article. 

Preserving Health Care Data Security and Privacy Using Carmichael's Theorem-Based Homomorphic Encryption and Modified Enhanced Homomorphic Encryption Schemes in Edge Computing Systems

Privacy-preserving techniques allow private information to be used without compromising privacy. Most encryption algorithms, such as the Advanced Encryption Standard (AES) algorithm, cannot perform computational operations on encrypted data without first applying the decryption process. Homomorphic encryption algorithms provide innovative solutions to support computations on encrypted data while preserving the content of private information. However, these algorithms have some limitations, such as computational cost as well as the need for modifications for each case study. In this paper, we present a comprehensive overview of various homomorphic encryption tools for Big Data analysis and their applications. We also discuss a security framework for Big Data analysis while preserving privacy using homomorphic encryption algorithms. We highlight the fundamental features and tradeoffs that should be considered when choosing the right approach for Big Data applications in practice. We then present a comparison of popular current homomorphic encryption tools with respect to these identified characteristics. We examine the implementation results of various homomorphic encryption toolkits and compare their performances. Finally, we highlight some important issues and research opportunities. We aim to anticipate how homomorphic encryption technology will be useful for secure Big Data processing, especially to improve the utility and performance of privacy-preserving machine learning.

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Towards Secure Big Data Analysis via Fully Homomorphic Encryption Algorithms

Security and trust are seen as the most important issues in electronic voting systems. Therefore, it is necessary to use cryptographic procedures to ensure anonymity, security, privacy, and reliability in these systems. In recent years, blockchain has become one of the most commonly used methods for securing data storage and transmission through decentralized applications. E-voting is one of these application areas. However, data manipulation is still seen as a major potential problem in e-voting systems. In theproposed model, administrators or miners are prevented from previewing election results which are normally accessible data due to the blockchain structure. A double-layer encryption model is proposed and tested to prevent manipulations that may occur with the election results. It is ensured that the election results can be counted after the participation of all stakeholders at the end. In this way, potential manipulations may be prevented during the election period. As a result of the model, the privacy of voters is ensured, no central authority is needed, and the recorded votes are kept in a distributed structure.

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A Manipulation Prevention Model for Blockchain-Based E-Voting Systems

With its decentralization, reliable database, security, and quasi anonymity, blockchain provides a new solution for data storage and sharing as well as privacy protection This paper combines the advantages of blockchain and edge computing and constructs the key technology solutions of edge computing based on blockchain On one hand, it achieves the security protection and integrity check of cloud data; and on the other hand, it also realizes more extensive secure multiparty computation In order to assure the operating efficiency of blockchain and alleviate the computational burden of client, it also introduces the Paillier cryptosystem which supports additive homomorphism The task execution side encrypts all data, while the edge node can process the ciphertext of the data received, acquire and return the ciphertext of the final result to the client The simulation experiment proves that the proposed algorithm is effective and feasible

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Xiaoyan Yan

Papers

A Homomorphic Encryption and Privacy Protection Method Based on Blockchain and Edge Computing