Scalable PHY-Layer Security for Distributed Detection in Wireless Sensor Networks

The problem of binary hypothesis testing is considered in a bandwidth-constrained densely populated low-power wireless sensor network operating over insecure links. Observations of the sensors are quantized and encrypted before transmission. The encryption method maps the output of the quantizer to one of the possible quantizer output levels randomly according to a probability matrix. The intended (ally) fusion center (AFC) is aware of the encryption keys (probabilities) while the unauthorized (third party) fusion center (TPFC) is not. A constrained optimization problem is formulated from the point of view of AFC in order to design its decision rule along with the encryption probabilities. The objective function to be minimized is the error probability of AFC and the constraint is a lower bound on the error probability of TPFC. In the binary case the optimal solution is found and in the nonbinary case a good suboptimal solution is analytically obtained. Numerical results are presented to show that it is possible to degrade the error probability of TPFC significantly and still achieve very low probability of error for AFC. The proposed method which may be considered a PHY-layer security scheme is highly scalable since it does not increase the packet overhead or transmit power of the sensors and has very low computational complexity. A scheme is described to randomize the keys so as to defeat any key space exploration attack.