Plausible deniability as a notion of privacy

This work is motivated by privacy concerns as a result of the growing rate of information exchange among components of complex cyber-physical systems, agents in a network, or actuators/sensors of a process. We propose a deterministic notion of privacy for a dynamical system, and completely characterize it for linear time-invariant dynamics. The proposed notion relies on a "plausible deniability" principle, which implies that a curious party will always be in doubt about the actual value of private variables of the system. In case privacy is guaranteed, we propose analytical metrics to assess the degree of privacy or privacy margin of the system. The size of the latter depends on the amount and structure of the information on the system which can be accessed by a curious party. We study the proposed notions and metrics for a class of distributed averaging algorithms.