Privacy-Preserving Average Consensus over Digraphs in the Presence of Time Delays

Abstract

In this paper, we propose a privacy-preserving discrete-time asymptotic average consensus mechanism that allows components of a multi-component system to calculate the exact average of their initial values without revealing to other components their specific value. We assume that components (nodes) interact with other components via possibly directed communication links (edges), forming a generally directed communication topology (digraph). The proposed distributed protocol can be followed by any component that wants to maintain its privacy (i.e., not reveal the initial value it contributes to the average) to possibly multiple curious but not malicious nodes (curious nodes try to identify the initial values of other nodes, and can exchange information with other curious nodes, but do not interfere in the computation in any other way). We devise a distributed mechanism, based on ratio consensus, where each node updates its information state by combining the available information received by its in-neighbors using constant positive weights and by adding an offset (only at one of the two states communicated during the execution of the algorithm). We establish that this privacy-preserving version of ratio consensus, henceforth called the privacy-preserving ratio consensus algorithm, converges to the exact average of the nodes' initial values, even in the presence of bounded time-varying delays. Illustrative examples demonstrate the validity and performance of our proposed algorithm.