Fuzzy Infinite-Step Opacity Measure of Discrete Event Systems and Its Applications

Opacity is an important security notion for discrete event systems (DESs) to measure the secret behaviors leaked to an intruder. The intruder is usually modeled as a malicious observer who always attempts to infer secret behaviors based on his dynamical observations of the system. In our earlier research, we proposed several opacity measures for DESs from the perspective of fuzzy logic, in which the intruder is assumed to only infer the current secret behaviors. Considering that modern computers usually have a powerful computation ability and rich memory resources, this article presents a new opacity measure of DESs, called as fuzzy infinite-step opacity (FIO) measure, where the intruder is assumed to have the ability of inferring all the secret behaviors that occurred in the past. In addition, the properties and the calculation of the FIO measure are also investigated. The FIO measure can be used to assess the secret-leakage situations of fuzzy DESs attacked by powerful intruders. For the purpose of illustration, we present a practical application of the FIO measure in evaluating the privacy protection mechanisms in location-based services.