Differential Privacy of Network Parameters from a System Identification Perspective

2025-09-24

AI Summary

To address the vulnerability of graph-structured privacy in cyber-physical system (CPS) simulations to system identification (SI) attacks, this paper proposes a differential privacy mechanism targeting graph filter outputs. By injecting Gaussian noise into node excitations, graph shift operator (GSO) identification is formulated as a noisy inverse problem. We derive an explicit theoretical relationship between the $(varepsilon,delta)$-differential privacy guarantee and both the spectral response of the graph filter and the condition number of the noise covariance matrix. Theoretically, we prove that smoother filters and lower-condition-number covariance matrices significantly enhance privacy protection. Experiments demonstrate that the method effectively prevents GSO inference while preserving the utility of filtered outputs for downstream tasks, enabling a quantifiable privacy–utility trade-off.

Technology Category

• Machine Learning: Privacy
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

This paper addresses the problem of protecting network information from privacy system identification (SI) attacks when sharing cyber-physical system simulations. We model analyst observations of networked states as time-series outputs of a graph filter driven by differentially private (DP) nodal excitations, with the analyst aiming to infer the underlying graph shift operator (GSO). Unlike traditional SI, which estimates system parameters, we study the inverse problem: what assumptions prevent adversaries from identifying the GSO while preserving utility for legitimate analysis. We show that applying DP mechanisms to inputs provides formal privacy guarantees for the GSO, linking the $(ε,δ)$-DP bound to the spectral properties of the graph filter and noise covariance. More precisely, for DP Gaussian signals, the spectral characteristics of both the filter and noise covariance determine the privacy bound, with smooth filters and low-condition-number covariance yielding greater privacy.

Problem

• Protecting network parameters from identification attacks when sharing cyber-physical system simulations
• Preventing adversaries from inferring the graph shift operator while maintaining analytical utility
• Establishing differential privacy guarantees for network structure through input perturbation mechanisms

Innovation

• DP mechanisms on inputs protect GSO
• Privacy bounds linked to filter spectral properties
• Smooth filters and low-condition noise enhance privacy