Differential Privacy of Network Parameters from a System Identification Perspective

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 $(\epsilon,\delta)$-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.