Structural Control Operators for Composing Diagrams of Strand Spaces of Concurrent Cryptographic Protocols

The diagram of strand spaces is introduced. It is a formal model for a cryptographic protocol running in an infinite concurrent way, viz. a complex dynamic system, on the base of the theory for strand spaces. The open bundle, which is only one element for composing diagrams of strand spaces, was defined. And two operators such as prefixing, parallel composition over the set of open bundles were also defined. The open bundle set and its operators were written as the open bundle algebra. The bi-simulation of open bundles and the bi-simulation equivalent relation of diagrams of strand spaces were introduced. They are used to prove safety properties of cryptographic protocols in the open bundle algebra. The model of diagrams of strand spaces is a novel tool to prove safety properties of cryptographic protocols running in an infinite concurrent way, and is used to describe other normal concurrent systems