Stateful Applied Pi Calculus

We extend the applied pi calculus with state cells, which are used toreason about protocols that store persistent information. Examples are protocolsinvolving databases or hardware modules with internal state. We distinguish be-tween private state cells, which are not available to the attacker, and public statecells, which arise when a private state cell is compromised by the attacker. Forprocesses involving only private state cells we define observational equivalenceand labelled bisimilarity in the same way as in the original applied pi calculus, andshow that they coincide. Our result implies Abadi-Fournet’s theorem – the coinci-dence of observational equivalence and labelled bisimilarity – in a revised versionof the applied pi calculus. For processes involving public state cells, we can es-sentially keep the definition of observational equivalence, but need to strengthenthe definition of labelled bisimulation in order to show that observational equiva-lence and labelled bisimilarity coincide in this case as well.