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 he compromised. Finally, an optimal privacy-preserving average consensus algorithm is proposed to achieve the highest (alpha, beta)-data-privacy. Simulations verify the analytical results.