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arXiv · 2304.07928

Observability Blocking for Functional Privacy of Linear Dynamic Networks

Yuan Zhang·Ranbo Cheng·Yuanqing Xia
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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.

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Yuan Zhang, Ranbo Cheng, Yuanqing Xia. 2023-04-17. Observability Blocking for Functional Privacy of Linear Dynamic Networks. https://arxiv.org/abs/2304.07928

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