# Applied calculus

May 12th, 2015
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Applied pi calculusMark D. Ryan and Ben SmythSchool of Computer Science,University of Birmingham,United KingdomJuly 2010Revised: November 2010, March 2011,November 2012, March 2013.AbstractThe applied pi calculus is a language for modelling security protocols. It is an extension ofthe pi calculus, a language for studying concurrency and process interaction. This chapterpresents the applied pi calculus in a tutorial style. It describes reachability, correspondence,and observational equivalence properties, with examples showing how to model secrecy, authentication, and privacy aspects of protocols.Keywords: Cryptographic protocols, protocol verification, formal methods, reachability, correspondence properties, observational equivalence, tutorial.1IntroductionThe applied pi calculus [AF01] is a language for describing and analysing security protocols. Itprovides an intuitive process syntax for detailing the actions of the participants in a protocol, emphasising their communication. The syntax is coupled with a formal semantics to allow reasoningabout protocols. The language is based on the pi calculus with the addition of a rich term algebrato enable modelling of the cryptographic operations used by security protocols. A wide varietyof cryptographic primitives can be abstractly modelled by means of an equational theory. Thecalculus allows one to express several types of security goal, and to analyse whether the protocolmeets its goal or not. This ana

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