||Wireless sensor networks (WSNs) have been deployed for many applications, such as battlefield monitoring and smart home systems. Since the sensor nodes in a WSN are usually deployed in open areas, we then face several security concerns, e.g., eavesdropping, forgery of sensor data, and denial-of-service attacks. As a result, how to deploy sensor nodes to achieve a better performance of random field reconstruction and, in the mean while, satisfy a certain security level is a critical problem. This thesis then considers the problem of designing a secure region where the eavesdroppers cannot listen the data sent from sensor nodes. Specifically, we design the optimal secure region in accordance with the criterion that the fusion center and eavesdropper have the largest difference in the mean square error of the field reconstruction. In|
the thesis, we also investigate the relation of the resulted optimal secure region and the number of sensors, the size of the secure region, and the various signal characteristics of the random field.