On Privacy of Dynamical Systems: An Optimal Probabilistic Mapping Approach (Extended Preprint)

We address the problem of maximizing privacy of stochastic dynamical systems whose state information is released through quantized sensor data. In particular, we consider the setting where information about the system state is obtained using noisy sensor measurements. This data is quantized and transmitted to a remote station through a public/unsecured communication network. We aim at keeping the state of the system private; however, because the network is not secure, adversaries might have access to sensor data, which can be used to estimate the system state. To prevent such adversaries from obtaining an accurate state estimate, before transmission, we randomize quantized sensor data using additive random vectors, and send the corrupted data to the remote station instead. We design the joint probability distribution of these additive vectors (over a time window) to minimize the mutual information (our privacy metric) between some linear function of the system state (a desired private output) and the randomized sensor data for a desired level of distortion--how different quantized sensor measurements and distorted data are allowed to be. We pose the problem of synthesizing the joint probability distribution of the additive vectors as a convex program subject to linear constraints. Simulation experiments are presented to illustrate our privacy scheme.