Privacy-preserving anomaly detection in stochastic dynamical systems: Synthesis of optimal Gaussian mechanisms

We present a framework for designing distorting mechanisms that allow the remote operation of anomaly detectors while preserving privacy. We consider a problem setting in which a remote station seeks to identify anomalies in dynamical systems using system input–output signals transmitted over communication networks. However, disclosing the true input–output signals of the system is not desired, as it can be used to infer private information. To maintain privacy, we propose a privacy-preserving mechanism that distorts input and measurement data before transmission using additive dependent Gaussian random processes and sends the distorted data to the remote station (which inevitably leads to degraded detection performance). We formulate constructive design conditions for the probability distributions of these additive processes while taking into account the trade-off between privacy, quantified using information-theoretic metrics (mutual information and differential entropy), and anomaly detection performance, characterized by the detector false alarm rate. The design of the privacy mechanisms is formulated as the solution of a convex optimization problem where we maximize privacy over a finite window of realizations while guaranteeing a bound on performance degradation of the anomaly detector.