Noninterference Analysis of Irreversible or Reversible Systems with Nondeterminism and Probabilities

Abstract: Noninterference theory supports the analysis of secure computations in multi-level security systems. Classical equivalence-based approaches to noninterference mainly rely on bisimilarity. In a nondeterministic setting, assessing noninterference through weak bisimilarity is adequate for irreversible systems, whereas for reversible ones branching bisimilarity has been recently proven to be more appropriate. In this paper we address the same two families of systems, with the difference that probabilities come into play in addition to nondeterminism. For irreversible systems we extend the results of Aldini, Bravetti, and Gorrieri developed in a generative-reactive probabilistic setting, while for reversible systems we extend the results of Esposito, Aldini, Bernardo, and Rossi developed in a purely nondeterministic setting. We recast noninterference properties by adopting probabilistic variants of weak and branching bisimilarities for irreversible and reversible systems respectively. Then we investigate a taxonomy of those properties as well as their preservation and compositionality aspects, along with a comparison with the nondeterministic taxonomy. The adequacy of the extended noninterference theory is illustrated via a probabilistic smart contract example.