  In this paper, we consider the problem of distributed detection in tree
topologies in the presence of Byzantines. The expression for minimum attacking
power required by the Byzantines to blind the fusion center (FC) is obtained.
More specifically, we show that when more than a certain fraction of individual
node decisions are falsified, the decision fusion scheme becomes completely
incapable. We obtain closed form expressions for the optimal attacking
strategies that minimize the detection error exponent at the FC. We also look
at the possible counter-measures from the FC's perspective to protect the
network from these Byzantines. We formulate the robust topology design problem
as a bi-level program and provide an efficient algorithm to solve it. We also
provide some numerical results to gain insights into the solution.
