On the trade-offs between accuracy, privacy, and resilience in average consensus algorithms

There can be none. In this paper, we address the problem of a set of discrete-time networked agents reaching average consensus privately and resiliently in the presence of a subset of attacked agents. Existing approaches to the problem rely on trade-offs between accuracy, privacy, and resilience, sacrificing one for the others. We show that a separation-like principle for privacy-preserving and resilient discrete-time average consensus is possible. Specifically, we propose a scheme that combines strategies from resilient average consensus and private average consensus, which yields both desired properties. The proposed scheme has polynomial time-complexity on the number of agents and the maximum number of attacked agents. In other words, each agent that is not under attack is able to detect and discard the values of the attacked agents, reaching the average consensus of non-attacked agents while keeping each agent's initial state private. Finally, we demonstrate the effectiveness of the proposed method with numerical results.