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This paper presents a Bulk-Synchronous Parallel (BSP) algorithm to compute on-the-fly whether a structured model of a security protocol satisfies a LTL formula. Using the structured nature of the security protocols allows us to design a simple and efficient parallelisation of an algorithm which constructs the state-space under consideration in a need-driven fashion. A prototype implementation has been developed, allowing to run benchmarks.doi:10.1109/ispdc.2012.10 dblp:conf/ispdc/GavaGP12 fatcat:zx65px4cc5a3zods2hccg76vxy