Randomized gossip algorithms under attack

Abstract

Recently, gossip-based algorithms have received significant attention for data aggregation in distributed environments. The main advantage of gossip-based algorithms is their robustness in dynamic and fault-prone environments with unintentional faults such as link failure and channel noise. However, the robustness of such algorithms in hostile environments with intentional faults has remained unexplored. In this paper, we call attention to the risks which may be caused by the use of gossip algorithms in hostile environments, i.e., when some malicious nodes collude to skew aggregation results by violating the normal execution of the protocol. We first introduce a model of hostile environment and then examine the behavior of randomized gossip algorithms in this model using probabilistic analysis. Our model of hostile environment is general enough to cover a wide range of attacks. However, to achieve stronger results, we focus our analysis on fully connected networks and some powerful attacks. Our analysis shows that in the presence of malicious nodes, after some initial steps, randomized gossip algorithms reach a point at which the lengthening of gossiping is harmful, i.e., the average accuracy of the estimates of the aggregate value begins to decrease strictly. © 2013 Springer-Verlag Berlin Heidelberg.