Differential privacy for dynamical sensitive data

We introduce the problem of protecting the privacy of time-varying sensitive data using differential privacy. Contrary to prior work that considers fixed private data, we wish to design a privacy-preserving mechanism that, at each time and given the observations so far, keeps the current state of a dynamical system private. Our work protects dynamical systems from being tracked by an adversary by providing differentially private guarantees. Specifically, we propose a mechanism which adds artificial noise to (i) the input of the system and (ii) the measurements which are then published. In particular, two scenarios are considered: for a scalar dynamical system under ε-differential privacy, we derive a mechanism that, at each time, publishes the most accurate approximation of the current state while preserving privacy. Next, for a general linear system under (e, δ)-differential privacy, we propose a Gaussian-based privacy-preserving mechanism with a quadratic cost.