Observability Blocking for Functional Privacy of Linear Dynamic Networks

TL;DR

This paper investigates how to block certain state variables in linear dynamic networks to prevent privacy breaches, providing NP-hardness results and polynomial-time algorithms under specific conditions.

Contribution

It introduces the first polynomial-time algorithm for vector-wise functional privacy protection in linear networks under bounded eigenvalue multiplicities.

Findings

NP-hardness of the blocking problem established

Polynomial-time algorithm for vector-wise privacy protection

Greedy algorithm for entry-wise privacy protection

Abstract

This paper addresses the problem of determining the minimum set of state variables in a network that need to be blocked from direct measurements in order to protect functional privacy with respect to {\emph{any}} output matrices. The goal is to prevent adversarial observers or eavesdroppers from inferring a linear functional of states, either vector-wise or entry-wise. We prove that both problems are NP-hard. However, by assuming a reasonable constant bound on the geometric multiplicities of the system's eigenvalues, we present an exact algorithm with polynomial time complexity for the vector-wise functional privacy protection problem. Based on this algorithm, we then provide a greedy algorithm for the entry-wise privacy protection problem. Our approach is based on relating these problems to functional observability and leveraging a PBH-like criterion for functional observability. Finally, we provide an example to demonstrate the effectiveness of our proposed approach.