Quasi-Open Bisimilarity with Mismatch is Intuitionistic

Abstract

Quasi-open bisimilarity is the coarsest notion of bisimilarity for the π-calculus that is also a congruence. This work extends quasi-open bisimilarity to handle mismatch (guards with inequalities). This minimal extension of quasi-open bisimilarity allows fresh names to be manufactured to provide constructive evidence that an inequality holds. The extension of quasi-open bisimilarity is canonical and robust-coinciding with open barbed bisimilarity (an objective notion of bisimilarity congruence) and characterised by an intuitionistic variant of an established modal logic. The more famous open bisimilarity is also considered, for which the coarsest extension for handling mismatch is identified. Applications to checking privacy properties are highlighted. Examples and soundness results are mechanised using the proof assistant Abella.

Breaking Unlinkability of the ICAO 9303 Standard for e-Passports Using Bisimilarity

“…2. When a distinguishing strategy is discovered using open bisimilarity, we determine whether it is an attack by constructing a distinguishing formula in an intermediate modal logic called intuitionistic FM [21,22]. 3.…”

Compositional Analysis of Protocol Equivalence in the Applied $$\pi $$-Calculus Using Quasi-open Bisimilarity

“…Fortunately, we will see in this paper that quasi-open bisimilarity addresses the above limitation of open bisimilarity. Quasi-open bisimilarity is also intuitionistic [29]. It handles open terms (with free variables) intuitionistically; but handles private messages that an attacker cannot interfere with more subtly.…”

“…Considering all contexts at every execution step reflects that new knowledge about the environment may be discovered during execution. Such testing equivalences have been used to inform the design of labelled transition systems and their corresponding notions of labelled equivalence for a range of process calculi including the π-calculus, which led to the emergence of quasi-open bisimilarity [29,41] -the notion of labelled bisimilarity that coincides with open barbed bisimilarity for the π-calculus.…”

A Characterisation of Open Bisimilarity using an Intuitionistic Modal Logic

“…Results in subsequent sections do not depend on intuitionistic negation. However, related work [HALT18] highlights that intuitionistic negation has a role when logically characterising open bisimilarity for processes with mismatch (inequality guards, which can model the else branch of an if-then-else statement). Thus this formulation of OM is robust for some useful extensions of the π-calculus.…”

“…Secondly, results obtained using such a more abstract approach should be treated with caution, since it does not immediately cover many richer process calculi, for which the definition of open bisimilarity must be modified. For example, when extending our results to the π-calculus with mismatch [HALT18], we require that the definition of open bisimilarity is extended to allow for the retrospective creation of fresh private names in the past, when our supply of private names runs out, otherwise open bisimilarity is not a congruence. Going further, for the applied π-calculus [ABF18] or ψcalculi [BJPV11], to define open bisimilarity the labels employed are of a more general form, so both the labels and the definition of open bisimilarity change in order to conservatively extend open bisimilarity to these settings while retaining the property that open bisimilarity is a congruence [HM21].…”