Privacy protection under the exposure of systems' prior information

TL;DR

This paper introduces a systematic approach using pointwise maximal leakage to protect the privacy of linear systems against adversaries with prior knowledge, providing new insights and design procedures.

Contribution

It develops necessary and sufficient conditions for PML privacy in linear systems and relates it to differential and mutual-information privacy, with practical design methods.

Findings

Derived a lower bound on estimation error covariance under PML privacy.

Established relationships between PML, differential, and mutual-information privacy.

Provided a case study on privacy in distributed sensing for smart buildings.

Abstract

For systems whose states implicate sensitive information, their privacy is of great concern. While notions like differential privacy have been successfully introduced to dynamical systems, it is still unclear how a system's privacy can be properly protected when facing the challenging yet frequently-encountered scenario where an adversary possesses prior knowledge, e.g., the steady state, of the system. This paper presents a new systematic approach to protect the privacy of a discrete-time linear time-invariant system against adversaries knowledgeable of the system's prior information. We employ a tailored \emph{pointwise maximal leakage (PML) privacy} criterion. PML characterizes the worst-case privacy performance, which is sharply different from that of the better-known mutual-information privacy. We derive necessary and sufficient conditions for PML privacy and construct tractable design procedures. Furthermore, our analysis leads to insight into how PML privacy, differential privacy, and mutual-information privacy are related. We then revisit Kalman filters from the perspective of PML privacy and derive a lower bound on the steady-state estimation-error covariance in terms of the PML parameters. Finally, the derived results are illustrated in a case study of privacy protection for distributed sensing in smart buildings.