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Bisimulation through probabilistic testing
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Abstract interpretation and application to logic programs
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Reactive, generative, and stratified models of probabilistic processes
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Anonymity protocols as noisy channels
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In this paper we lay the semantic basis for a quantitative security analysis of probabilistic systems by introducing notions of approximate confinement based on various process equivalences. We recast the operational semantics classically expressed via probabilistic transition systems (PTS) in terms of linear operators and we present a technique for defining approximate semantics as probabilistic abstract interpretations of the PTS semantics. An operator norm is then used to quantify this approximation. This provides a quantitative measure ε of the indistinguishability of two processes and therefore of their confinement. In this security setting a statistical interpretation is then given of the quantity ε which relates it to the number of tests needed to breach the security of the system.