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We give a sequential model for noninterference security including probability(but not demonic choice), thus supporting reasoning about the likelihood thathigh-security values might be revealed by observations of low-securityactivity. Our novel methodological contribution is the definition of arefinement order and its use to compare security measures betweenspecifications and (their supposed) implementations. This contrasts with themore common practice of evaluating the security of individual programs inisolation.  The appropriateness of our model and order is supported by our showing thatour refinement order is the greatest compositional relation --the compositionalclosure-- with respect to our semantics and an "elementary" order based onBayes Risk --- a security measure already in widespread use. We also relaterefinement to other measures such as Shannon Entropy.  By applying the approach to a non-trivial example, the anonymous-majorityThree-Judges protocol, we demonstrate by example that correctness arguments canbe simplified by the sort of layered developments --through levels ofincreasing detail-- that are allowed and encouraged by compositional semantics.

Compositional closure for Bayes Risk in probabilistic noninterference