Composing Strand Spaces

Abstract

The strand space model for the analysis of security protocols is known to have some limitations in the patterns of nondeterminism it allows and in the ways in which strand spaces can be composed. Its successful application to a broad range of security protocols may therefore seem surprising. This paper gives a formal explanation of the wide applicability of strand spaces. We start with an extension of strand spaces which permits several operations to be defined in a compositional way, forming a process language for building up strand spaces. We then show, under reasonable conditions how to reduce the extended strand spaces to ones of a traditional kind. For security protocols we are mainly interested in their safety properties. This suggests a strand-space equivalence: two strand spaces are equivalent if and only if they have essentially the same sets of bundles. However this equivalence is not a congruence with respect to the strand-space operations. By extending the notion of bundle we show how to define the strand-space operations directly on ``bundle spaces''. This leads to a characterisation of the largest congruence within the strand-space equivalence. Finally, we relate strand spaces to event structures, a well known model for concurrency.