Abstract
Formal methods have been very successful in analyzing security protocols for reachability properties such as secrecy or authentication. In contrast, there are very few results for equivalence-based properties, crucial for studying e.g. privacy-like properties such as anonymity or vote secrecy.
We study the problem of checking equivalence of security protocols for an unbounded number of sessions. Since replication leads very quickly to undecidability (even in the simple case of secrecy), we focus on a limited fragment of protocols (standard primitives but pairs, one variable per protocol’s rules) for which the secrecy preservation problem is known to be decidable. Surprisingly, this fragment turns out to be undecidable for equivalence. Then, restricting our attention to deterministic protocols, we propose the first decidability result for checking equivalence of protocols for an unbounded number of sessions. This result is obtained through a characterization of equivalence of protocols in terms of equality of languages of (generalized, real-time) deterministic pushdown automata.
Full version available at http://hal.inria.fr/hal-00817230 . The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n° 258865, project ProSecure, and the ANR project JCJC VIP no 11 JS02 006 01.
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References
Arapinis, M., Chothia, T., Ritter, E., Ryan, M.: Analysing unlinkability and anonymity using the applied pi calculus. In: 23rd Computer Security Foundations Symposium (CSF 2010), pp. 107–121. IEEE Computer Society Press (2010)
Basin, D., Mödersheim, S., Viganò, L.: A symbolic model checker for security protocols. Journal of Information Security 4(3), 181–208 (2005)
Baudet, M.: Deciding security of protocols against off-line guessing attacks. In: 12th ACM Conference on Computer and Communications Security (CCS 2005). ACM Press (2005)
Blanchet, B.: An efficient cryptographic protocol verifier based on prolog rules. In: 14th Computer Security Foundations Workshop (CSFW 2001). IEEE Computer Society Press (2001)
Blanchet, B., Abadi, M., Fournet, C.: Automated Verification of Selected Equivalences for Security Protocols. In: 20th Symposium on Logic in Computer Science (2005)
Bruso, M., Chatzikokolakis, K., den Hartog, J.: Formal verification of privacy for RFID systems. In: 23rd Computer Security Foundations Symposium, CSF 2010 (2010)
Cheval, V., Comon-Lundh, H., Delaune, S.: Trace equivalence decision: Negative tests and non-determinism. In: 18th ACM Conference on Computer and Communications Security (CCS 2011). ACM Press (2011)
Chevalier, Y., Rusinowitch, M.: Decidability of equivalence of symbolic derivations. J. Autom. Reasoning 48(2), 263–292 (2012)
Comon-Lundh, H., Cortier, V.: New decidability results for fragments of first-order logic and application to cryptographic protocols. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 148–164. Springer, Heidelberg (2003)
Cortier, V., Delaune, S.: A method for proving observational equivalence. In: 22nd IEEE Computer Security Foundations Symposium (CSF 2009). IEEE Computer Society Press (2009)
Cremers, C.: Unbounded verification, falsification, and characterization of security protocols by pattern refinement. In: 15th ACM Conference on Computer and Communications Security (CCS 2008). ACM (2008)
Friedman, E.P.: The inclusion problem for simple languages. Theor. Comput. Sci. 1(4), 297–316 (1976)
Rusinowitch, M., Turuani, M.: Protocol Insecurity with Finite Number of Sessions and Composed Keys is NP-complete. Theoretical Computer Science 299, 451–475 (2003)
Sénizergues, G.: The equivalence problem for deterministic pushdown automata is decidable. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256, pp. 671–681. Springer, Heidelberg (1997)
Sénizergues, G.: L(A)=L(B)? Decidability results from complete formal systems. Theor. Comput. Sci. 251(1-2), 1–166 (2001)
Stirling, C.: Deciding DPDA equivalence is primitive recursive. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 821–832. Springer, Heidelberg (2002)
Tiu, A., Dawson, J.E.: Automating open bisimulation checking for the SPI calculus. In: 23rd IEEE Computer Security Foundations Symposium (CSF 2010), pp. 307–321 (2010)
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Chrétien, R., Cortier, V., Delaune, S. (2013). From Security Protocols to Pushdown Automata. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7966. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39212-2_15
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DOI: https://doi.org/10.1007/978-3-642-39212-2_15
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