Optimal Probabilistic Encryption for Secure Detection in Wireless Sensor Networks

We consider the problem of secure detection in wireless sensor networks operating over insecure links. It is assumed that an eavesdropping fusion center (EFC) attempts to intercept the transmissions of the sensors and to detect the state of nature. The sensor nodes quantize their observations using a multilevel quantizer. Before transmission to the ally fusion center (AFC), the senor nodes encrypt their data using a probabilistic encryption scheme, which randomly maps the sensor´s data to another quantizer output level using a stochastic cipher matrix (key). The communication between the sensors and each fusion center is assumed to be over a parallel access channel with identical and independent branches, and with each branch being a discrete memoryless channel. We employ J-divergence as the performance criterion for both the AFC and EFC. The optimal solution for the cipher matrices is obtained in order to maximize J-divergence for AFC, whereas ensuring that it is zero for the EFC. With the proposed method, as long as the EFC is not aware of the specific cipher matrix employed by each sensor, its detection performance will be very poor. The cost of this method is a small degradation in the detection performance of the AFC. The proposed scheme has no communication overhead and minimal processing requirements making it suitable for sensors with limited resources. Numerical results showing the detection performance of the AFC and EFC verify the efficacy of the proposed method.