Privacy-Preserving Average Consensus: Fundamental Analysis and a Generic Framework Design

Average consensus is a key component of multi-agent systems coordination, while data privacy becomes a serious concern. Through the information exchange process, the initial state of an agent may be disclosed to its neighbors. The existing privacy-preserving research mainly addressed the situation of single-neighbor eavesdropping and infinite-time consensus, and they cannot deal with the cases of multi-neighbors eavesdropping and collusion inference attack or ensuring finite-time consensus. In this paper, we prove that it is impossible to preserve a node's data privacy if all of its neighbors collusively infer the data. Otherwise, we propose a privacy-preserving framework to support conventional average consensus, push-sum consensus, and finite-time average consensus, which integrates multiplying random variables, finite-time error compensation, and updating rule jump. In this paper, each agent exchanges data with its neighbors by multiplying a random variable to its real-time state at each iteration. To eliminate errors caused by the random multiplier, a finite-time error compensation term and updating rule jump are designed, which ensure the accuracy of consensus. We prove that the proposed framework can converge and preserve privacy facing collusion inference attacks in both finite-time and infinite-time consensus, while traditional adding-noise-based methods cannot solve the finite-time case. We also derive the analytical expressions of the maximum privacy disclosure probability for the initial state of each agent, and present the impact of multiplying random variables. Extensive case studies demonstrate the effectiveness of the proposed framework.