A logical approach to multilevel security of probabilistic systems

Summary.

We set out a modal logic for reasoning about multilevel security of probabilistic systems. This logic contains expressions for time, probability, and knowledge. Making use of the Halpern-Tuttle framework for reasoning about knowledge and probability, we give a semantics for our logic and prove it is sound. We give two syntactic definitions of perfect multilevel security and show that their semantic interpretations are equivalent to earlier, independently motivated characterizations. We also discuss the relation between these characterizations of security and between their usefulness in security analysis.