Privacy-Preserving Average Consensus Research Articles

Real-Time Privacy-Preserving Average Consensus and Its Application to Secondary Control for AC Microgrid

Real-Time Privacy-Preserving Average Consensus and Its Application to Secondary Control for AC Microgrid

Privacy-Preserving Average Consensus Algorithm Under Round-Robin Scheduling Protocol

Privacy-Preserving Average Consensus Algorithm Under Round-Robin Scheduling Protocol

Average consensus of whole-process privacy protection: A scale parameter method

Privacy-preserving average consensus is a distributed control/estimation framework where a group of agents cooperatively compute the average of initial state. Meanwhile, the initial state and real-time state (such as initial opinion, initial location, real-time location, real-time active power ratio) in the communication and computation process may contain some sensitive information, which do not want other nodes of the network to obtain. However, existing privacy protection results mainly focused on protecting the initial state, and rarely took into account the privacy effect from the beginning to the end. To deal with this problem, a novel and interesting scale parameter method is proposed. First, a group of privacy coefficients is designed and assigned in advance for each node, which ensures that only their own parameters can be known and has no knowledge of others. Correspondingly, the initial state and real-time state can be hidden in the false values after multiplying these scale parameters. Then, the correctness analysis and privacy analysis of this method are provided respectively. Later, the generalization on directed networks is discussed. Finally, numerical simulations are conducted to show the effectiveness of obtained theoretical results.

Fake information mechanism based privacy-preserving average consensus

ABSTRACT In order to reach an agreement, each agent in distributed systems needs to exchange its state information with neighbours. In this case, however, it is difficult to guarantee sensitive information will not be leaked. To tackle the problem, this paper proposes an encryption method, which does not need to compromise accuracy to privacy, nor does it need to encrypt and decrypt state information every time. Meanwhile, the method in this paper not only keeps the initial state secret, but also considers the real-time state privacy. Then, we further elaborate two aspects of the proposed method by simple proofs. Finally, simulations are presented to verify the effectiveness of our algorithm.

Privacy-Preserving Average Consensus in Multiagent Systems via Partial Information Transmission

This article investigates the privacy-preserving average consensus problem in multiagent systems. A new approach is proposed to achieve the accurate average consensus value while protecting the initial state information of agents. The key idea to achieve these goals is based on partial information transmission. Each agent decomposes its initial state information into several different subinformation. The values of these subinformation are chosen randomly but with their mean value fixed to the original initial value. Then, based on multiple communication channels, agents share all their subinformation, but ensure that each neighbor can only obtain partial subinformation. We prove that the privacy can be protected under our method if each agent has at least two neighbors, and one of the neighbors is neutral. The generalization on the directed graph about this method is also considered. Finally, two examples are provided to illustrate the design process and practical applications of the proposed approach.

Differentiated Output-Based Privacy-Preserving Average Consensus

This letter investigates the differentiated output-based privacy-preserving average consensus problem over digraphs. A new stochastic obfuscation algorithm is proposed to achieve better privacy-preserving effect. When the output messages for at least one out-neighbour are not leaked, the algorithm can be designed to achieve any pre-given consensus accuracy and privacy-preserving level simultaneously by properly selecting the private weights. Even if all the output messages are leaked, the algorithm can still ensure that each agent’s initial state is protected to a certain extent. The mean square convergence of the algorithm is proved. The efficiency of the algorithm is verified by a numerical example.

Privacy-Preserving Optimal Energy Management for Smart Grid With Cloud-Edge Computing

Optimal energy management of smart grids requires the information exchange between devices, which may disclose private information to the adversaries and further lead to great losses. To this end, this article considers the privacy-preserving optimal energy management problem for smart grids, which integrates both the power allocation of distributed energy resources on the supply side and the demand response of distributed load demands on the demand side. We first propose a cloud-edge computing structure of the smart grid and model the optimal energy management problem as the maximization problem of social welfare including the supply-side net benefit and the demand-side net utility, while maintaining the supply–demand balance and satisfying the operating constraints. A privacy-preserving average consensus algorithm is then developed, where each node sends the projected states to their neighbors to protect the privacy of the initial state. By applying the privacy-preserving average consensus algorithm, we propose a distributed privacy-preserving optimal energy management algorithm based on the generalized alternating direction method of multipliers. Finally, simulation examples are provided to validate the effectiveness of the proposed algorithms.

Event-Triggered privacy-preserving average consensus for continuous-time multi-agent network systems

This paper deals with the privacy-preserving average consensus problem for continuous-time multi-agent network systems (MANSs) based on the event-triggered strategy. A novel event-triggered privacy-preserving consensus algorithm is designed to achieve the average consensus of MANSs while avoiding the disclosure of the agents’ initial states. Different from the approaches incorporating stochastic noises, an output mask function in the proposed algorithm is developed to make initial state of each agent indiscernible by the others. Particularly, under the output mask function, all agents can exactly tend to the average value of initial states rather than the mean square value. Under the proposed algorithm, detailed theoretical proof about average consensus and privacy of the MANSs are conducted. Moreover, the proposed algorithm is extended to nonlinear continuous-time MANSs, and the corresponding results are also derived. A numerical simulation eventually is performed to demonstrate the validity of our results.

Privacy-Preserving Average Consensus via Finite Time-Varying Transformation

The privacy-preserving average consensus problem in multi-agent systems means that all agents in the system can reach an agreement on the average of their initial values, but guarantees that their initial states are private. In this paper, a new approach is proposed to solve this problem, furthermore, it can solve both asymptotic time consensus problem and prescribed-time consensus problem. The core idea of this approach is to construct functions which can mask the real states of agents in finite time. That is, within a certain period of time, what agents transmit is no longer their real state values, but the values acting on the designed functions. These designed functions are time-varying, local (i.e., determined independently by each agent), and converging to the true states in finite time. It is proved that the correctness (accurate calculation of global average value) and privacy (the initial values of agents are not speculated by other agents) can be guaranteed under our method. Finally, some numerical simulations are given to verify the effectiveness of our approach.

Multi-Dimensional Privacy-Preserving Average Consensus in Wireless Sensor Networks

This brief studies the privacy preserving average consensus (PPAC) of wireless sensor networks (WSNs). Note that most of the PPAC schemes only focus on the consensus of one-dimensional state, which is not suitable for the actual scenarios. In view of this, the multi-dimensional privacy-preserving average consensus (MPPAC) problem is considered in this brief, where the nodes are divided into two types, the sink nodes and the ordinary ones. A novel MPPAC algorithm is proposed by introducing the super-increasing sequence as well as the RSA algorithm, where the super-increasing sequence plays a key role in tackling the multi-dimensional measurement of the sensors, and the RSA algorithm realizes the privacy preserving average consensus among sink nodes. Simulation results illustrate the effectiveness of this proposed scheme.

Concentrated differentially private average consensus algorithm for a discrete-time network with heterogeneous dynamics

This paper presents a privacy-preserving average consensus algorithm for a discrete-time network with heterogeneous dynamic nodes in the presence of Gaussian privacy noises. Rényi divergence is used to measure the privacy, and a distributed algorithm is proposed for each node in the network to protect the initial output state and ensure consensus almost surely. The convergence rate of the proposed algorithm relates to the communication topology, dynamics of systems, and decaying rates of privacy noises. Moreover, by increasing neighbors of nodes in the network, the proposed algorithm can strengthen preservation. To demonstrate the theoretical results, a numerical example is carried out on a network of one hundred nodes.

Event-Triggered Privacy-Preserving Average Consensus for Multiagent Networks With Time Delay: An Output Mask Approach

This article investigates the privacy-preserving average consensus problem for the general continuous-time multiagent network systems (MANSs) with time delay via the event-triggered communication scheme. In order to avoid disclosing the initial states of the network agents and at the same time achieve the agents' consensus for MANSs with time delay, a novel consensus control algorithm based on a new privacy-preserving approach is proposed. The new privacy-preserving approach is that we construct an output mask to make agents' internal states indiscernible by others, which is different from the existing privacy-preserving methods adding random noises to the update law of agents' states. Compared with the existing privacy-preserving methods, our approach makes all agents in MANSs exactly converge to the average value of initial states instead of its mean square value. Based on the proposed algorithm, we carry out the detailed theoretical consensus analysis of the network agents, from which, it is shown that the upper bound of the communication time delay between neighbors' agents can be estimated approximately. Moreover, the Zeno-behavior of event-triggered time sequences for each agent is excluded. Finally, two simulation examples are performed to demonstrate the effectiveness of our theoretical results.

Privacy-Preserving Average Consensus via State Decomposition

Average consensus underpins key functionalities of distributed systems ranging from distributed information fusion, decision-making, distributed optimization, to load balancing and decentralized control. Existing distributed average consensus algorithms require each node to exchange and disclose state information to its neighbors, which is undesirable in cases where the state is private or contains sensitive information. In this paper, we propose a novel approach that avoids disclosing individual state information in average consensus by letting each node decompose its state into 2 substates. For each node, one of the two substates involves in computation and internode interactions as if it were the original state, while the other substate interacts only with the first substate of the same node, being completely invisible to other nodes. The initial values of the two substates are chosen randomly but with their mean fixed to the initial value of the original state, which is key to guarantee convergence to the desired consensus value. In direct contrast to differential-privacy based privacy-preserving average-consensus approaches, which enable privacy by compromising accuracy in the consensus value, the proposed approach can guarantee convergence to the exact desired value without any error. Not only is the proposed approach able to prevent the disclosure of a node's initial state to honest-but-curious neighbors, it can also provide protection against inference by external eavesdroppers able to wiretap communication links. Numerical simulations demonstrate the effectiveness of the approach and its advantages over state-of-the-art counterparts.

Secure and Privacy-Preserving Consensus

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 privacy-preserving 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 that 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 privacy-preserving 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 microcontroller network are also presented to verify the effectiveness and efficiency of the approach.

Privacy-Preserving Average Consensus: Privacy Analysis and Algorithm Design

Privacy-preserving average consensus aims to guarantee the privacy of initial states and asymptotic consensus on the exact average of the initial values. In this paper, it is achieved by adding variance-decaying and zero-sum random noises to the consensus process. However, there is lack of theoretical analysis to quantify the degree of the data privacy protection. In this paper, we introduce the maximum disclosure probability that other nodes can infer one node's initial state within a given small interval to quantify the data privacy. We utilize a novel privacy definition, named $(\alpha, \beta)$ -data-privacy, to depict the relationship between the maximum disclosure probability and the estimation accuracy. Then, we prove that the general privacy-preserving average consensus provides $(\alpha, \beta)$ -data-privacy, and obtain the closed-form expression of the relationship between $\alpha$ and $\beta$ given the noise distribution. We reveal that the added noise with a uniform distribution is optimal in terms of achieving the highest $(\alpha, \beta)$ -data-privacy. We also prove that under what condition, the data-privacy will be compromised. Finally, an optimal privacy-preserving average consensus algorithm is proposed to achieve the highest $(\alpha, \beta)$ -data-privacy. Simulations verify the analytical results.

Preserving Data-Privacy With Added Noises: Optimal Estimation and Privacy Analysis

Networked system often relies on distributed algorithms to achieve a global computation goal with iterative local information exchanges between neighbor nodes. To preserve data privacy, a node may add a random noise to its original data for information exchange at each iteration. Nevertheless, a neighbor node can estimate other's original data based on the information it received. The estimation accuracy and data privacy can be measured in terms of $(\epsilon, \delta)$-data-privacy, defined as the probability of $\epsilon$-accurate estimation (the difference of an estimation and the original data is within $\epsilon$) is no larger than $\delta$ (the disclosure probability). How to optimize the estimation and analyze data privacy is a critical and open issue. In this paper, a theoretical framework is developed to investigate how to optimize the estimation of neighbor's original data using the local information received, named optimal distributed estimation. Then, we study the disclosure probability under the optimal estimation for data privacy analysis. We further apply the developed framework to analyze the data privacy of the privacy-preserving average consensus algorithm and identify the optimal noises for the algorithm.

Privacy Preserving Average Consensus

Average consensus is a widely used algorithm for distributed computing and control, where all the agents in the network constantly communicate and update their states in order to achieve an agreement. This approach could result in an undesirable disclosure of information on the initial state of agent i to the other agents. In this paper, we propose a privacy preserving average consensus algorithm to guarantee the privacy of the initial state and the convergence of the algorithm to the exact average of the initial values, by adding and subtracting random noises to the consensus process. We characterize the mean square convergence rate of our consensus algorithm and derive upper and lower bounds for the covariance matrix of the maximum likelihood estimate on the initial state. A numerical example is provided to illustrate the effectiveness of the proposed design.

Differentially Private Average Consensus with Optimal Noise Selection

This paper studies the problem of privacy-preserving average consensus in multi-agent systems. The network objective is to compute the average of the initial agent states while keeping these values differentially private against an adversary that has access to all interagent messages. We establish an impossibility result that shows that exact average consensus cannot be achieved by any algorithm that preserves differential privacy. This result motives our design of a differentially private discrete-time distributed algorithm that corrupts messages with Laplacian noise and is guaranteed to achieve average consensus in expectation. We examine how to optimally select the noise parameters in order to minimize the variance of the network convergence point for a desired level of privacy.