Secure gossip against intermittently malicious agents

Security of distributed consensus algorithms is rapidly becoming a matter of paramount importance. Existing approaches address it by identifying corrupted nodes and deleting them from the network, but this results in the permanent loss of the contribution of these agents even if they return to their proper functionality. In this paper, we consider the case when legitimate nodes might exhibit malicious behavior that occurs intermittently and only for certain time instants. In particular, we provide a strategy to ensure that corrupted values never get incorporated in consensus computations, but without having to permanently exclude any nodes from the network and allowing them to participate to the consensus calculations once they have regained proper behavior. This approach allows the network to use all available information to achieve consensus and preserves the graph connectivity. Moreover, the proposed protocol relaxes several of the assumptions traditionally required by alternative state of the art methodologies. Our approach is based on reiterated exchange and comparison among each node and its one- and two-hop neighbors, and amounts to a variation of the standard gossip algorithm in which three nodes are involved at each round. After analyzing the convergence of the proposed algorithm, simulations are carried out to illustrate its effectiveness.