In this paper, we consider the problem of achieving uniform and ergodic peer sampling in large scale dynamic systems under adversarial behaviors. The main challenge is to guarantee that any honest node is able to construct a uniform and non-fixed (ergodic) sample of the node identifiers in the system, and this, despite the presence of malicious nodes controlled by an adversary. This sample is built out of a stream of events received at each node. We consider and study two types of adversary: an omniscient adversary that has the capacity to eavesdrop all the messages that are exchanged within the system, and a blind adversary that can only observe messages that have been sent or received by the manipulated nodes. The former model allows us to derive lower bounds on the impact that the adversary has on the sampling functionality while the latter one corresponds to a realistic model. Given any sampling strategy, we quantify the minimum effort exerted by both types of adversary on any input stream to prevent this strategy from outputting a uniform and ergodic sample.
Anceaume et al. REF have proposed a characterization of the adversarial power to bias uniform and ergodic sampling in large scale system.
Characterizing the adversarial power in uniform and ergodic node sampling
AlMoDEP '11
Computer Science