  In this paper, we investigate the design of distributed detection networks in
the presence of an eavesdropper (Eve). We consider the problem of designing
binary quantizers at the sensors that maximize the Kullback-Leibler (KL)
Divergence at the fusion center (FC), subject to a tolerable constraint on the
KL Divergence at Eve. In the case of i.i.d. received symbols at both the FC and
Eve, we prove that the structure of the optimal binary quantizers is a
likelihood ratio test (LRT). We also present an algorithm to find the threshold
of the optimal LRT, and illustrate it for the case of Additive White Gaussian
Noise (AWGN) observation models at the sensors. In the case of non-i.i.d.
received symbols at both FC and Eve, we propose a dynamic-programming based
algorithm to find efficient quantizers at the sensors. Numerical results are
presented to illustrate the performance of the proposed network design.
