Abstract
We thoroughly study the behavioural theory of epi, a π-calculus extended with polyadic synchronisation. We show that the natural contextual equivalence, barbed congruence, coincides with early bisimilarity, which is thus its co-inductive characterisation. Moreover, we relate early bisimilarity with the other usual notions, ground, late and open, obtaining a lattice of equivalence relations that clarifies the relationship among the “standard” bisimilarities. Furthermore, we apply the theory developed to obtain an expressiveness result: epi extended with key encryption primitives may be fully abstractly encoded in the original epi calculus. The proposed encoding is sound and complete with respect to barbed congruence; hence, cryptographic epi (crypto-epi) gets behavioural theory for free, which contrasts with other process languages with cryptographic constructs that usually require a big effort to develop such theory. Therefore, it is possible to use crypto-epi to analyse and to verify properties of security protocols using equational reasoning. To illustrate this claim, we prove compliance with symmetric and asymmetric cryptographic system laws, and the correctness of a protocol of secure message exchange.
Similar content being viewed by others
References
Abadi, M., Fournet, C.: Mobile values, new names, and secure communication. In: Proceedings of the 28th ACM Symposium on Principles of Programming Languages (POPL’01), pp. 104–115. ACM, New York (2001)
Abadi, M., Gordon, A.D.: A calculus for cryptographic protocols: The spi calculus. In: Proceedings of the 4th ACM Conference on Computer and Communications Security, pp. 36–47. ACM, New York (1997)
Baldamus, M., Parrow, J., Victor, B.: Spi calculus translated to π-calculus preserving may-testing. In: Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS ’04), pp. 21–31. IEEE Computer Society Press (2004)
Blanchet, B., Abadi, M., Fournet, C.: Automated verification of selected equivalences for security protocols. J. Logic Algebr. Program. 75, 3–51 (2007)
Boreale, M., De Nicola, R., Pugliese, R.: Proof techniques for cryptographic processes. SIAM J. Comput. 31(3), 947–986 (2002)
Borgström, J., Nestmann, U.: On bisimulations for the spi calculus. Math. Struct. Comput. Sci. 15(3), 487–552 (2005)
Carbone, M., Maffeis, S.: On the expressive power of polyadic synchronization in π-calculus. Nord. J. Comput. 10(2), 70–98 (2003)
Hansen, M., Hüttel, H., Kleist, J.: Bisimulations for asynchronous mobile processes. In: Proceedings of the Tiblisi Symposium on Language, Logic, and Computation. Research paper HCRC/RP-72, Human Communication Research Centre, University of Edinburgh (1995)
Martinho, J., Ravara, A.: Encoding cryptographic primitives in a calculus with polyadic synchronization. In: Proceedings of the International Conference on Theoretical and Mathematical Foundations of Computer Science (TMFCS ’08), pp. 102–109. ISRST 2008, ISBN 978-1-60651-006-3 (2008)
Milner, R.: Communication and Concurrency. Prentice Hall, Upper Saddle River (1989)
Milner, R.: The polyadic π-calculus: A tutorial. In: Bauer F.L., Brauer W., Schwichtenberg H. (eds.) Logic and Algebra of Specification, Proceedings of the International NATO Summer School (Marktoberdorf, Germany, 1991), vol. 94 of Series F: Computer and System Sciences. NATO Advanced Study Institute, Springer-Verlag, 1993. Available as Technical Report ECS-LFCS-91-180, University of Edinburgh, UK (1991)
Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes, part I/II. In: Journal of Information and Computation, vol. 100, pp. 1–77, 1992. Available as Technical Reports ECS-LFCS-89-85 and ECS-LFCS-89-86, University of Edinburgh, U. K. (1989)
Milner, R., Sangiorgi, D.: Barbed bisimulation. In: Proceedings of the 19th International Colloquium on Automata, Languages and Programming (ICALP ’92). Lecture Notes in Computer Science, vol. 623, pp. 685–695. Springer, Heidelberg (1992)
Quaglia, P.: The pi-calculus: notes on labelled semantics. Bull. Eur. Assoc. Theor. Comput. Sci. (EATCS) 68, 104–114 (1999)
Sangiorgi, D.: Expressing mobility in process algebras: first-order and higher-order paradigms. PhD thesis CST–99–93, Department of Computer Science, University of Edinburgh, UK (1992)
Sangiorgi, D.: A theory of bisimulation for the π-calculus. Acta Inform. 33, 69–97 (1996)
Sangiorgi, D.: Lazy functions and mobile processes. In: Plotkin, G., Stirling, C., Tofte, M. (eds.) Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT, Cambridge (2000)
Sangiorgi, D., Walker, D.: The π-calculus: a Theory of Mobile Processes. Cambridge University Press, Cambridge (2001)
Victor, B.: A verification tool for the polyadic π-calculus. Licentiate thesis, Department of Computer Systems, Uppsala University, Sweden. Available as Report DoCS 94/50 (1994)
Victor, B., Moller, F.: The mobility workbench—a tool for the π-calculus. In: Proceedings of the 6th International Conference on Computer Aided Verification (CAV ’94). Lecture Notes in Computer Science, vol. 818, pp. 428–440. Springer, Heidelberg (1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Martinho, J., Ravara, A. Encoding Cryptographic Primitives in a Calculus with Polyadic Synchronisation. J Autom Reasoning 46, 293–323 (2011). https://doi.org/10.1007/s10817-010-9189-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10817-010-9189-7