Distributed Detection in the Presence of

Distributed detection in the presence of cooperative (Byzantine)attackisconsidered.Itisassumedthatafractionofthe monitoring sensors are compromised by an adversary, and these compromised (Byzantine) sensors are reprogrammed to transmit fictitiousobservationsaimedat confusing thedecisionmakeratthe fusion center. For detection under binary hypotheses with quan- tized sensor observations, the optimal attacking distributions for Byzantine sensors that minimize the detection error exponent are obtained using a "water-filling" procedure. The smallest error ex- ponent, as a function of the Byzantine sensor population, charac- terizes the power of attack. Also obtained is the minimum fraction of Byzantine sensors that destroys the consistency of detection at the fusion center. The case when multiple measurements are made at the remote nodes is also considered, and it is shown that the de- tection performance scales with the number of sensors differently from the number of observations at each sensor. Index Terms—Byzantine attack, distributed detection, network defense.