TY - JOUR
T1 - Observability Blocking for Functional Privacy of Dynamic Networks
AU - Zhang, Yuan
AU - Cheng, Ranbo
AU - Luo, Ziyuan
AU - Xia, Yuanqing
AU - Wang, Yupei
AU - Liu, Huabo
N1 - Publisher Copyright:
© 2013 IEEE.
PY - 2026
Y1 - 2026
N2 - This paper addresses the problem of identifying the minimum set of state variables in a network that must be protected from direct measurements by existing sensors to ensure functional privacy. Central to our work is the novel insight that functional observability is inherently linked to the ability of inferring a linear functional of states, which underpins the concept of functional privacy. Our goal is to prevent curious observers or eavesdroppers from deducing a linear functional of the states, either vector-wise or entry-wise. We prove that both problems are NP-hard. However, by assuming a reasonable diagonalizability condition and a constant bound on the geometric multiplicities of the system's eigenvalues, we present a polynomial-time complexity exact algorithm for the vector-wise functional privacy protection problem. Building on this algorithm, we propose a greedy algorithm for addressing the entry-wise privacy protection problem. Furthermore, we extend our results to structured systems where only the zero-nonzero patterns of system matrices, rather than their exact parameter values, are known. Our approach leverages a relationship between these problems and (structural) functional observability, utilizing a PBH-like criterion for assessing (structural) functional observability. Finally, two examples are provided to illustrate the effectiveness of our proposed approaches.
AB - This paper addresses the problem of identifying the minimum set of state variables in a network that must be protected from direct measurements by existing sensors to ensure functional privacy. Central to our work is the novel insight that functional observability is inherently linked to the ability of inferring a linear functional of states, which underpins the concept of functional privacy. Our goal is to prevent curious observers or eavesdroppers from deducing a linear functional of the states, either vector-wise or entry-wise. We prove that both problems are NP-hard. However, by assuming a reasonable diagonalizability condition and a constant bound on the geometric multiplicities of the system's eigenvalues, we present a polynomial-time complexity exact algorithm for the vector-wise functional privacy protection problem. Building on this algorithm, we propose a greedy algorithm for addressing the entry-wise privacy protection problem. Furthermore, we extend our results to structured systems where only the zero-nonzero patterns of system matrices, rather than their exact parameter values, are known. Our approach leverages a relationship between these problems and (structural) functional observability, utilizing a PBH-like criterion for assessing (structural) functional observability. Finally, two examples are provided to illustrate the effectiveness of our proposed approaches.
KW - Functional privacy
KW - curious eavesdroppers
KW - functional observability
KW - network structure
KW - sensor blocking
UR - https://www.scopus.com/pages/publications/105018832357
U2 - 10.1109/TNSE.2025.3618388
DO - 10.1109/TNSE.2025.3618388
M3 - Article
AN - SCOPUS:105018832357
SN - 2327-4697
VL - 13
SP - 2558
EP - 2571
JO - IEEE Transactions on Network Science and Engineering
JF - IEEE Transactions on Network Science and Engineering
ER -