Consensus with preserved privacy against neighbor collusion
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RESEARCH ARTICLE
Consensus with preserved privacy against neighbor collusion Silun Zhang1 · Thomas Ohlson Timoudas2 · Munther A. Dahleh1 Received: 11 September 2020 / Revised: 28 September 2020 / Accepted: 28 September 2020 / Published online: 2 December 2020 © South China University of Technology, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper proposes a privacy-preserving algorithm to solve the average-consensus problem based on Shamir’s secret sharing scheme, in which a network of agents reach an agreement on their states without exposing their individual states until an agreement is reached. Unlike other methods, the proposed algorithm renders the network resistant to the collusion of any given number of neighbors (even with all neighbors’ colluding). Another virtue of this work is that such a method can protect the network consensus procedure from eavesdropping. Keywords Privacy-preserving consensus · Cyber security · Network control · Secret sharing scheme
1 Introduction As a successful conceptual abstraction of many emerging phenomena in nature, the multi-agent model (MAM) has been extensively studied in the last decades. These studies initiated from the fundamental but also inspiring problem, namely multi-agent consensus, which aims at driving the states of agents to a global agreement. The formal study of the consensus problem was first introduced by Degroot [1] in the 1970s, which sparked many further extensions and developments (see, e.g., [2–4] and the references therein). The methods and results, which were conceived in the study of the consensus problem, were later adapted to network coordination problems in control theory, such as formation control [5–9], distributed optimization [10–13], and also network games [14, 15]. In the control setting, the situation is further complicated, as the agents are governed by nonlinear dynamics [16, 17]. * Thomas Ohlson Timoudas [email protected] Silun Zhang [email protected] Munther A. Dahleh [email protected] 1
Laboratory for Information and Decision Systems (LIDS), MIT, Cambridge, MA 02139, USA
KTH Royal Institute of Technology, 100 44 Stockholm, Sweden
2
In distributed algorithms, each agent typically requires access to the states of its neighbors to compute a local update. This may leave the agents in the network vulnerable, as some of them may not wish to disclose this local information to their neighbors, especially if some of it is highly private or sensitive. For many applications, it is, therefore, essential to achieve network consensus, while preserving the privacy of each agent. For example, in opinion dynamics [18], opinions may relate to a sensitive topic, and the participating individuals expect these to remain secret, especially from their acquaintances, i.e., each of their neighbors. The fundamental idea of many existing approaches to privacy-preserving consensus algorithms is to conceal the individual state by adding a deterministic or stochastic disturbance to
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