  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.
