Identification of Malicious Activity in Distributed Average Consensus via Non-Concurrent Checking

We consider the problem of average consensus in a network system under a fixed, undirected communication topology, when there are malicious nodes present that may try to influence the average calculation. In the setting considered, the average consensus is performed by the nodes in a distributed fashion using a linear iterative algorithm. We assume malicious nodes can manipulate, in an arbitrary manner, the value of their state in the aforementioned algorithm; the problem is then to check whether or not each node is correctly performing the updates of its state. To address this problem, we propose a distributed algorithm whereby each node is in charge of checking the updates performed by its neighboring nodes based on information that it receives from them and also from the neighbors of its neighbors. The algorithm leverages ideas from non-concurrent error detection schemes and its main advantage is that information from two-hop neighbors is only needed infrequently—a relaxation that significantly reduces the communication overhead associated with the requirement to make such information available.