This paper studies the privacy of transmitted data and the security of distributed state estimation against data integrity attacks in cyber-physical systems. Assume that each sensor is equipped with a pseudo-random number generator and a buffer to encode the transmitted data and store the currently encoded data, respectively. For honest-but-curious sensors that collude with each other, the sum of the innovations for neighboring sensors is calculated through multi-party computation to ensure that the state update does not share its own state to neighboring sensors. The privacy leakage risk of a sensor is measured as a privacy index, for which the minimum privacy protection measure is derived. Furthermore, a detection paradigm is developed for multi-party scenarios involving data privacy protection and attack detection issues. Consider a case that semi-honest sensors collude with external attackers, where the former leak all its information to the latter and direct them to launch attacks. Utilizing the buffer and multi-party computation, the communication channels subject to external attacks can be effectively detected by a secondary confirmation method. Under a specific attack model, this method can also remove the attack signals to ensure the estimation accuracy of the estimators. Finally, the effectiveness of the proposed method is verified through an unmanned aerial vehicle example.
Wang et al. (Mon,) studied this question.