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A Volumetric Privacy Measure for Dynamical Systems With Bounded Disturbance

Chuanghong Weng, Ehsan Nekouei

TL;DR

The paper addresses privacy in dynamical systems subject to bounded disturbances by introducing a volumetric privacy measure based on the volume of the private-state uncertainty set Vol(Y_{k|k}). It develops interval-analysis and (optionally) constrained convex generator approaches to bound privacy leakage and links leakage to information gain from observations. An optimization-based privacy filter is proposed that randomizes and refines observations via a linear program to maximize Vol(Y_{k|k}) under a utility constraint Vol(M^x_{k|k}) ≤ ε^x. The method is demonstrated on a production-inventory case study, showing improved robustness against inference attacks and outperformance of additive-noise and quantization baselines.

Abstract

In this paper, we first present a volumetric privacy measure for dynamical systems with bounded disturbances, wherein the states of the system contain private information and an adversary with access to sensor measurements attempts to infer the set of potential values of the private information. Under the proposed privacy measure, the volume of the uncertainty set of the adversary given the sensor measurements is considered as the privacy level of the system. We next characteristic the time evolution of the proposed privacy measure and study its properties for a particular system with both public and private states, where a set containing the public state is shared as the observation. Approximate set-membership estimation techniques are developed to compute the private-state uncertainty set, and the properties of the privacy measure are analyzed, demonstrating that the uncertainty reduction of the adversary is bounded by the information gain from the observation set. Furthermore, an optimization-based privacy filter design problem is formulated, employing randomization and linear programming to enhance the privacy level. The effectiveness of the proposed approach is validated through a production-inventory case study. Results show that the optimal privacy filter significantly improves robustness against inference attacks and outperforms two baseline mechanisms based on additive noise and quantization.

A Volumetric Privacy Measure for Dynamical Systems With Bounded Disturbance

TL;DR

The paper addresses privacy in dynamical systems subject to bounded disturbances by introducing a volumetric privacy measure based on the volume of the private-state uncertainty set Vol(Y_{k|k}). It develops interval-analysis and (optionally) constrained convex generator approaches to bound privacy leakage and links leakage to information gain from observations. An optimization-based privacy filter is proposed that randomizes and refines observations via a linear program to maximize Vol(Y_{k|k}) under a utility constraint Vol(M^x_{k|k}) ≤ ε^x. The method is demonstrated on a production-inventory case study, showing improved robustness against inference attacks and outperformance of additive-noise and quantization baselines.

Abstract

In this paper, we first present a volumetric privacy measure for dynamical systems with bounded disturbances, wherein the states of the system contain private information and an adversary with access to sensor measurements attempts to infer the set of potential values of the private information. Under the proposed privacy measure, the volume of the uncertainty set of the adversary given the sensor measurements is considered as the privacy level of the system. We next characteristic the time evolution of the proposed privacy measure and study its properties for a particular system with both public and private states, where a set containing the public state is shared as the observation. Approximate set-membership estimation techniques are developed to compute the private-state uncertainty set, and the properties of the privacy measure are analyzed, demonstrating that the uncertainty reduction of the adversary is bounded by the information gain from the observation set. Furthermore, an optimization-based privacy filter design problem is formulated, employing randomization and linear programming to enhance the privacy level. The effectiveness of the proposed approach is validated through a production-inventory case study. Results show that the optimal privacy filter significantly improves robustness against inference attacks and outperforms two baseline mechanisms based on additive noise and quantization.
Paper Structure (25 sections, 49 equations, 6 figures)

This paper contains 25 sections, 49 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related Work
  4. Contributions
  5. Outline
  6. Notation
  7. System Model and Privacy Measure
  8. System model
  9. Motivating Examples
  10. Privacy and Utility Measures
  11. Inference Attack for Linear Systems
  12. Inference Attack via Set Operations
  13. Inference Attack Approximation via CCGs
  14. Inference Attack Approximation via Interval Analysis
  15. Properties of the Interval Inference Attack
  16. ...and 10 more sections

Figures (6)

  • Figure 1: The system setup.
  • Figure 2: Structure of the proposed privacy filter.
  • Figure 3: Inference attack results after applying the optimal privacy filter: (a), (b) Estimated $X_k$ and (e), (f) Estimated $Y_k$ for $\mathrm{Vol}\!\left(\mathcal{M}_{k|k}^{x}\right) \leq 0.01$; (c), (d) Estimated $X_k$ and (g), (h) Estimated $Y_k$ for $\mathrm{Vol}\!\left(\mathcal{M}_{k|k}^{x}\right) \leq 0.5$.
  • Figure 4: The truncated Gaussian mechanism.
  • Figure 5: Interval-based inference given the interval privacy filter: the privacy level of the private state and utility of the public state.
  • ...and 1 more figures