We carry forward the work described in our previous papers [3, 14, 12] on the application of data independence to the model checking of cryptographic protocols using CSP [13] and FDR [5]. In particular, we showed how techniques based on data independence [7, 13] could be used to justify, by means of a finite FDR check, systems where agents can perform an unbounded number of protocol runs. Whilst this allows for a more complete analysis, there was one significant incompleteness in the results we

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... obtained: While each individual identity could perform an unlimited number of protocol runs sequentially, the degree of parallelism remained bounded (and small to avoid state space explosion). In this paper, we report significant progress towards the solution of this problem, by means anticipated in [3] , namely by "internalising" all or part of each agent identity within the "intruder" process. The internalisation of agents (initially only server roles) was introduced in [14] as a state-space reduction technique (for which it is usually spectacularly successful). It was quickly noticed that this had the beneficial side-effect of making the internalised server arbitrarily parallel, at least in cases where it did not generate any new values of data independent type. We now consider the case where internal agents do introduce fresh values and address the issue of capturing the state of mind of internal agents (for the purposes of analysis).