Optimal probabilistic encryption for distributed detection in wireless sensor networks based on immune differential evolution algorithm

The problem of binary hypothesis testing is considered in a bandwidth-constrained low-power wireless sensor network operating over insecure links. To prevent passive eavesdropping from enemy fusion center (EFC), the sensor observations are randomly flipped according to pre-deployed flipping rates before transmission. Accordingly, a constrained optimization problem is formulated to minimize the fusion error of ally fusion center (AFC) while maintain EFC’s error at high level. We demonstrated that the fusion error is a non-convex function of the flipping rates, thus an immune based differential evolution algorithm is designed to search the optimal flipping rates, such that the EFC always gets high error probability at the cost of a small degeneration of the AFC’s fusion performance. Furthermore, the optimal thresholds of the fusion rules are calculated based on the statistics of the sensor data, which further degenerates the detection performance of the EFC, since it is not aware of the statistics of the sensor observations after data flipping, resulting in its threshold does not match the observations. Simulation results demonstrated that the AFC can appropriately acquire the original nature state, while the EFC is prevent to detect the target regardless of the signal-to-noise and sensor numbers.