Cyber-security enhancement of networked control systems using homomorphic encryption

Kogiso, Kiminao; Fujita, Takeshi

doi:10.1109/cdc.2015.7403296

Cited by 193 publications

(146 citation statements)

References 11 publications

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“…Another issue is how to treat the sign of an integer for encryption. [19] solves this problem by mapping negative values to the end of the group Z n where n = pq is given by the public key. We offer an alternative solution by taking advantage of the fact that encryption algorithms blindly treat bit strings as an unsigned integer.…”

Section: B Subtraction and Negative Valuesmentioning

confidence: 99%

Secure and Privacy-Preserving Consensus

Ruan

Gao

Wang

2019

IEEE Trans. Automat. Contr.

200

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Consensus is fundamental for distributed systems since it underpins key functionalities of such systems ranging from distributed information fusion, decision-making, to decentralized control. In order to reach an agreement, existing consensus algorithms require each agent to exchange explicit state information with its neighbors. This leads to the disclosure of private state information, which is undesirable in cases where privacy is of concern. In this paper, we propose a novel approach for undirected networks which can enable secure and privacypreserving average consensus in a decentralized architecture in the absence of an aggregator or third-party. By leveraging partial homomorphic cryptography to embed secrecy in pairwise interaction dynamics, our approach can guarantee convergence to the consensus value (subject to a quantization error) in a deterministic manner without disclosing a node's state to its neighbors. We provide a new privacy definition for dynamical systems, and give a new framework to rigorously prove that a node's privacy can be protected as long as it has at least one legitimate neighbor which follows the consensus protocol faithfully without attempts to infer other nodes' states. In addition to enabling resilience to passive attackers aiming to steal state information, the approach also allows easy incorporation of defending mechanisms against active attackers who try to alter the content of exchanged messages. Furthermore, in contrast to existing noise-injection based privacy-preserving mechanisms which have to reconfigure the entire network when the topology or number of nodes varies, our approach is applicable to dynamic environments with time-varying coupling topologies. This secure and privacypreserving approach is also applicable to weighted average consensus as well as maximum/minimum consensus under a new update rule. Numerical simulations and comparison with existing approaches confirm the theoretical results. Experimental results on a Raspberry-Pi board based micro-controller network are also presented to verify the effectiveness and efficiency of the approach.

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Section: B Subtraction and Negative Valuesmentioning

confidence: 99%

Secure and Privacy-Preserving Consensus

Ruan

Gao

Wang

2019

IEEE Trans. Automat. Contr.

200

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“…Homomorphic encryption has been used previously for third-party cloud-computing services [1,17,20,32,35,60]. More recent studies [16,25,27,28,50] have considered challenges associated with the use of homomorphic encryption in closed-loop control of physical systems, such as maintaining stability and performance, albeit without considering timing concerns (by not getting into the computational time of encryption, computation, and decryption and assuming all underlying computations are instantaneous). None of these studies consider dynamic control laws; they are all restricted to static control laws without any form of memory.…”

Section: Related Studiesmentioning

confidence: 99%

Implementing homomorphic encryption based secure feedback control

Tran¹,

Farokhi

Cantoni

et al. 2020

Control Engineering Practice

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This paper is about an encryption based approach to the secure implementation of feedback controllers for physical systems. Specifically, Paillier's homomorphic encryption is used to digitally implement a class of linear dynamic controllers, which includes the commonplace static gain and PID type feedback control laws as special cases. The developed implementation is amenable to Field Programmable Gate Array (FPGA) realization. Experimental results, including timing analysis and resource usage characteristics for different encryption key lengths, are presented for the realization of an inverted pendulum controller; as this is an unstable plant, the control is necessarily fast.

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“…Without loss of generality, let m 1 be the multiplicand and m 2 be the multiplier for the product m 2 m 1 . For the multiplicand m 1 , we use the previous encryption function m 1…”

Section: Homomorphic Property Of Lwe-based Cryptosystemmentioning

confidence: 99%

“…Applications of homomorphic cryptography to the feedback controller are relatively new. To the authors' knowledge, the first contribution was made by Kogiso and Fujita [1] in 2015, followed by Farokhi et al [2] and Kim et al [3] both in 2016. Interestingly, each of them uses different homomorphic encryption schemes; El-Gamal [4], Paillier [5], and LWE [6] are employed, respectively.…”

Section: Introductionmentioning

confidence: 99%

Comprehensive Introduction to Fully Homomorphic Encryption for Dynamic Feedback Controller via LWE-Based Cryptosystem

Kim

Shim

Han

2019

Privacy in Dynamical Systems

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The cryptosystem based on the Learning-with-Errors (LWE) problem is considered as a post-quantum cryptosystem, because it is not based on the factoring problem with large primes which is easily solved by a quantum computer. Moreover, the LWE-based cryptosystem allows fully homomorphic arithmetics so that two encrypted variables can be added and multiplied without decrypting them. This chapter provides a comprehensive introduction to the LWE-based cryptosystem with examples. A key to the security of the LWE-based cryptosystem is the injection of random errors in the ciphertexts, which however hinders unlimited recursive operation of homomorphic arithmetics on ciphertexts due to the growth of the error. We show that this limitation can be overcome when the cryptosystem is used for a dynamic feedback controller that guarantees stability of the closed-loop system. Finally, we illustrate through MATLAB codes how the LWE-based cryptosystem arXiv:1904.08025v1 [cs.SY]

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Cyber-security enhancement of networked control systems using homomorphic encryption

Cited by 193 publications

References 11 publications

Secure and Privacy-Preserving Consensus

Secure and Privacy-Preserving Consensus

Implementing homomorphic encryption based secure feedback control

Comprehensive Introduction to Fully Homomorphic Encryption for Dynamic Feedback Controller via LWE-Based Cryptosystem

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