Finite Horizon Privacy of Stochastic Dynamical Systems: A Synthesis Framework for Dependent Gaussian Mechanisms

TL;DR

This paper develops a convex optimization framework for designing dependent Gaussian privacy mechanisms in stochastic dynamical systems, balancing privacy and data distortion over finite horizons.

Contribution

It introduces a novel synthesis method for dependent Gaussian mechanisms that maximize privacy in dynamical systems under finite horizon constraints.

Findings

Convex program formulation for privacy mechanism synthesis.

Effective privacy-distortion trade-offs demonstrated.

Mechanisms protect private outputs against adversaries.

Abstract

We address the problem of synthesizing distorting mechanisms that maximize privacy of stochastic dynamical systems. Information about the system state is obtained through sensor measurements. This data is transmitted to a remote station through an unsecured/public communication network. We aim to keep part of the system state private (a private output); however, because the network is unsecured, adversaries might access sensor data and input signals, which can be used to estimate private outputs. To prevent an accurate estimation, we pass sensor data and input signals through a distorting (privacy-preserving) mechanism before transmission, and send the distorted data to the trusted user. These mechanisms consist of a coordinate transformation and additive dependent Gaussian vectors. We formulate the synthesis of the distorting mechanisms as a convex program, where we minimize the mutual information (our privacy metric) between an arbitrarily large sequence of private outputs and the disclosed distorted data for desired distortion levels -- how different actual and distorted data are allowed to be.