Ensuring utility while enforcing current-state opacity

In this paper, we deal with current-state opacity and we address one of the main criticisms of opacity enforcement through obfuscation techniques raised in the literature: in order to conceal the secret behavior of the system from the intruder, additional information is obfuscated to the legitimate receiver. We then propose an Opacity-Enforcer that misleads the intruder to never infer that the secret behavior has been executed (opacity enforcement) while the legitimate receiver must always acknowledge when the utility behavior has occurred (ensuring utility). We also provide necessary and sufficient conditions to model the behavior of the Opacity-Enforcer, together with an algorithm for its realization, when possible.