Confidentiality-Preserving Refinement is Compositional — Sometimes

Confidentiality-preserving refinement describes a relation between a specification and an implementation that ensures that all confidentiality properties required in the specification are preserved by the implementation in a probabilistic setting. The present paper investigates the condition under which that notion of refinement is compositional, i.e. the condition under which refining a subsystem of a larger system yields a confidentiality-preserving refinement of the larger system. It turns out that the refinement relation is not composition in general, but the condition for compositionality can be stated in a way that builds on the analysis of subsystems thus aiding system designers in analyzing a composition.