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Opacity is a security property capturing a system's ability to keep a subset of its behavior hidden from passive, but knowledgeable, observers. In this paper we use the formal definitions of opacity in three of its forms (simple opacity, -step weak opacity and -step strong opacity), basing on finite Labeled Transition Systems as a model. Then we present efficient algorithms for verifying opacity in all these forms within the context of a hybrid, on-the-fly approach. This approach is based on the construction of a Symbolic Observation Graph (SOG) that allows not only the abstraction of the systems behavior but also the preservation of the structure necessary for conducting opacity checking. Our preliminary experimental results are promising and demonstrate effectiveness facing the state-explosion problem which represents the main drawback of existing model checking techniques.

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