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In this paper, we develop and analyze a gossip-based average consensusalgorithm that enables all of the components of a distributed system, each withsome initial value, to reach (approximate) average consensus on their initialvalues after executing a finite number of iterations, and without having toreveal the specific value they contribute to the average calculation. Weconsider a fully-connected (undirected) network in which each pair ofcomponents (nodes) can be randomly selected to perform pairwise standard gossipaveraging of their values, and propose an enhancement that can be followed byeach node that does not want to reveal its initial value to other (curious)nodes. We assume that curious nodes try to identify the initial values of othernodes but do not interfere in the computation in any other way; however, as aworst-case assumption, curious nodes are allowed to collaborate arbitrarily andare assumed to know the privacy-preserving strategy (but not the actualparameters chosen by the nodes that want to preserve their privacy). Wecharacterize precisely conditions on the information exchange that guaranteeprivacy-preservation for a specific node. The protocol also provides acriterion that allows the nodes to determine, in a distributed manner (whilerunning the enhanced gossip protocol), when to terminate their operationbecause approximate average consensus has been reached, i.e., all nodes haveobtained values that are within a small distance from the exact average oftheir initial values.

Privacy-Preserving Distributed Average Consensus in Finite Time using Random Gossip