Privacy-Preserving Resilience of Cyber-Physical Systems to Adversaries

TL;DR

This paper develops a framework for ensuring the resilience of cyber-physical systems against multiple adversaries by combining stochastic game-based control synthesis with differential privacy to protect against eavesdroppers, validated on a UAV simulation.

Contribution

It introduces a novel approach that integrates control synthesis for adversarial environments with differential privacy to safeguard trajectory information without compromising system objectives.

Findings

Maximized satisfaction probability of LTL objectives under adversarial control.

Achieved differential privacy of system trajectories against eavesdroppers.

Validated approach on UAV simulation demonstrating practical effectiveness.

Abstract

A cyber-physical system (CPS) is expected to be resilient to more than one type of adversary. In this paper, we consider a CPS that has to satisfy a linear temporal logic (LTL) objective in the presence of two kinds of adversaries. The first adversary has the ability to tamper with inputs to the CPS to influence satisfaction of the LTL objective. The interaction of the CPS with this adversary is modeled as a stochastic game. We synthesize a controller for the CPS to maximize the probability of satisfying the LTL objective under any policy of this adversary. The second adversary is an eavesdropper who can observe labeled trajectories of the CPS generated from the previous step. It could then use this information to launch other kinds of attacks. A labeled trajectory is a sequence of labels, where a label is associated to a state and is linked to the satisfaction of the LTL objective at that state. We use differential privacy to quantify the indistinguishability between states that are related to each other when the eavesdropper sees a labeled trajectory. Two trajectories of equal length will be differentially private if they are differentially private at each state along the respective trajectories. We use a skewed Kantorovich metric to compute distances between probability distributions over states resulting from actions chosen according to policies from related states in order to quantify differential privacy. Moreover, we do this in a manner that does not affect the satisfaction probability of the LTL objective. We validate our approach on a simulation of a UAV that has to satisfy an LTL objective in an adversarial environment.