Privary Preserving Distributed Average Consensus via Homomorphic Encryption

We develop and analyze a distributed nonlinear iterative algorithm that enables the components of a multicomponent system, each with some integer initial value, to asymptotically reach average consensus on their initial values, without having to reveal to other components the specific value they contribute to the average calculation. In particular, we assume an arbitrary communication topology captured by a strongly connected digraph, in which certain nodes (components) might be curious but not malicious (i.e., they execute the proposed protocol correctly, but try to identify the initial values of other nodes). We first discuss how a distributed algorithm that operates exclusively on integer values can be used to obtain the average of the node values. We then describe how this algorithm can be adjusted using homomorphic encryption to allow the nodes to obtain the average of their initial values while ensuring their privacy, at least assuming the presence of a trusted node.