Protocol analysis modulo combination of theories: A case study in Maude-NPA

There is a growing interest in formal methods and tools to analyze cryptographic protocols modulo algebraic properties of their underlying cryptographic functions. It is well-known that an intruder who uses algebraic equivalences of such functions can mount attacks that would be impossible if the cryptographic functions did not satisfy such equivalences. In practice, however, protocols use a collection of well-known functions, whose algebraic properties can naturally be grouped together as a union of theories E 1... ¿ n. Reasoning symbolically modulo the algebraic properties E 1... ¿ n requires performing (E 1... ¿ n)-unification. However, even if a unification algorithm for each individual E i is available, this requires combining the existing algorithms by methods that are highly non-deterministic and have high computational cost. In this work we present an alternative method to obtain unification algorithms for combined theories based on variant narrowing. Although variant narrowing is less efficient at the level of a single theory E i, it does not use any costly combination method. Furthermore, it does not require that each E i has a dedicated unification algorithm in a tool implementation. We illustrate the use of this method in the Maude-NPA tool by means of a well-known protocol requiring the combination of three distinct equational theories. © 2011 Springer-Verlag.R. Sasse and J. Meseguer have been partially supported by NSF Grants CNS0716638, CNS-0831064 and CNS-0904749. S. Escobar has been partially supported by the EU (FEDER) and the Spanish MEC/MICINN under grant TIN 2007-68093- C02-02. C. Meadows has been partially supported by NSF Grant CNS-0904749National Science Foundation, EEUUSasse, R.; Escobar Román, S.; Meadows, C.; Meseguer, J. (2011). Protocol analysis modulo combination of theories: A case study in Maude-NPA. En Security and Trust Management. Springer Verlag (Germany). 6710:163-178. doi:10.1007/978-3-642-22444-7_11S1631786710Abadi, M., Cortier, V.: Deciding knowledge in security protocols under equational theories. Theoretical Computer Science 367(1-2), 2–32 (2006)Armando, A., Basin, D.A., Boichut, Y., Chevalier, Y., Compagna, L., Cuéllar, J., Drielsma, P.H., Héam, P.-C., Kouchnarenko, O., Mantovani, J., Mödersheim, S., von Oheimb, D., Rusinowitch, M., Santiago, J., Turuani, M., Viganò, L., Vigneron, L.: The avispa tool for the automated validation of internet security protocols and applications. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 281–285. Springer, Heidelberg (2005)Baader, F., Schulz, K.U.: Unification in the union of disjoint equational theories: Combining decision procedures. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 50–65. Springer, Heidelberg (1992)Basin, D.A., Mödersheim, S., Viganò, L.: An on-the-fly model-checker for security protocol analysis. In: Snekkenes, E., Gollmann, D. (eds.) ESORICS 2003. LNCS, vol. 2808, pp. 253–270. Springer, Heidelberg (2003)Baudet, M., Cortier, V., Delaune, S.: YAPA: A generic tool for computing intruder knowledge. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 148–163. Springer, Heidelberg (2009)Blanchet, B.: An efficient cryptographic protocol verifier based on prolog rules. In: CSFW, pp. 82–96. IEEE Computer Society, Los Alamitos (2001)Bursuc, S., Comon-Lundh, H.: Protocol security and algebraic properties: Decision results for a bounded number of sessions. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 133–147. Springer, Heidelberg (2009)Chevalier, Y., Küsters, R., Rusinowitch, M., Turuani, M.: An NP decision procedure for protocol insecurity with XOR. In: LICS, pp. 261–270. IEEE Computer Society, Los Alamitos (2003)Chevalier, Y., Rusinowitch, M.: Hierarchical combination of intruder theories. Inf. Comput. 206(2-4), 352–377 (2008)Chevalier, Y., Rusinowitch, M.: Symbolic protocol analysis in the union of disjoint intruder theories: Combining decision procedures. Theor. Comput. Sci. 411(10), 1261–1282 (2010)Ciobâcă, Ş., Delaune, S., Kremer, S.: Computing knowledge in security protocols under convergent equational theories. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 355–370. Springer, Heidelberg (2009)Comon-Lundh, H., Delaune, S.: The finite variant property: How to get rid of some algebraic properties. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 294–307. Springer, Heidelberg (2005)Cortier, V., Delaitre, J., Delaune, S.: Safely composing security protocols. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 352–363. Springer, Heidelberg (2007)Cremers, C.J.F.: The scyther tool: Verification, falsification, and analysis of security protocols. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 414–418. Springer, Heidelberg (2008)Escobar, S., Meadows, C., Meseguer, J.: A rewriting-based inference system for the NRL protocol analyzer and its meta-logical properties. Theoretical Computer Science 367(1-2), 162–202 (2006)Escobar, S., Meadows, C., Meseguer, J.: Maude-NPA: Cryptographic protocol analysis modulo equational properties. In: Aldini, A., Barthe, G., Gorrieri, R. (eds.) FOSAD 2007/2008/2009 Tutorial Lectures. LNCS, vol. 5705, pp. 1–50. Springer, Heidelberg (2009)Escobar, S., Meseguer, J., Sasse, R.: Effectively checking or disproving the finite variant property. Technical Report UIUCDCS-R-2008-2960, Department of Computer Science - University of Illinois at Urbana-Champaign (April 2008)Escobar, S., Meseguer, J., Sasse, R.: Effectively checking the finite variant property. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 79–93. Springer, Heidelberg (2008)Escobar, S., Meseguer, J., Sasse, R.: Variant narrowing and equational unification. Electr. Notes Theor. Comput. Sci. 238(3), 103–119 (2009)Escobar, S., Sasse, R., Meseguer, J.: Folding variant narrowing and optimal variant termination. In: Ölveczky, P.C. (ed.) WRLA 2010. LNCS, vol. 6381, pp. 52–68. Springer, Heidelberg (2010)Fabrega, F.J.T., Herzog, J., Guttman, J.: Strand Spaces: What Makes a Security Protocol Correct? Journal of Computer Security 7, 191–230 (1999)Guo, Q., Narendran, P.: Unification and matching modulo nilpotence. In: CADE-13. LNCS, vol. 1104, pp. 261–274. Springer, Heidelberg (1996)Harkins, D., Carrel, D.: The Internet Key Exchange (IKE), IETF RFC 2409, (November 1998)Jouannaud, J.-P., Kirchner, C., Kirchner, H.: Incremental construction of unification algorithms in equational theories. In: Díaz, J. (ed.) ICALP 1983. LNCS, vol. 154, pp. 361–373. Springer, Heidelberg (1983)Küsters, R., Truderung, T.: Reducing protocol analysis with xor to the xor-free case in the Horn theory based approach. In: ACM Conference on Computer and Communications Security, pp. 129–138 (2008)Küsters, R., Truderung, T.: Using ProVerif to analyze protocols with Diffie-Hellman exponentiation. In: CSF, pp. 157–171. IEEE Computer Society, Los Alamitos (2009)Lafourcade, P., Terrade, V., Vigier, S.: Comparison of cryptographic verification tools dealing with algebraic properties. In: Degano, P., Guttman, J.D. (eds.) FAST 2009. LNCS, vol. 5983, pp. 173–185. Springer, Heidelberg (2010)Lowe, G.: Breaking and fixing the Needham-Schroeder public-key protocol using FDR. In: Margaria, T., Steffen, B. (eds.) TACAS 1996. LNCS, vol. 1055, pp. 147–166. Springer, Heidelberg (1996)Meadows, C.: The NRL protocol analyzer: An overview. J. Log. Program. 26(2), 113–131 (1996)Meseguer, J.: Conditional rewriting logic as a united model of concurrency. Theor. Comput. Sci. 96(1), 73–155 (1992)Meseguer, J.: Membership algebra as a logical framework for equational specification. In: Parisi-Presicce, F. (ed.) WADT 1997. LNCS, vol. 1376, pp. 18–61. Springer, Heidelberg (1998)Meseguer, J., Thati, P.: Symbolic reachability analysis using narrowing and its application to verification of cryptographic protocols. Higher-Order and Symbolic Computation 20(1–2), 123–160 (2007)Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, Heidelberg (2002)Santiago, S., Talcott, C.L., Escobar, S., Meadows, C., Meseguer, J.: A graphical user interface for Maude-NPA. Electr. Notes Theor. Comput. Sci. 258(1), 3–20 (2009)Schmidt-Schauß, M.: Unification in a combination of arbitrary disjoint equational theories. J. Symb. Comput. 8(1/2), 51–99 (1989)Terese (ed.): Term Rewriting Systems. Cambridge University Press, Cambridge (2003)Turuani, M.: The CL-atse protocol analyser. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 277–286. Springer, Heidelberg (2006

Rule-Based Unification in Combined Theories and the Finite Variant Property

International audienceWe investigate the unification problemin theories defined by rewrite systems which are both convergent andforward-closed. These theories are also known in the context ofprotocol analysis as theories with the finite variant property andadmit a variant-based unification algorithm. In this paper, wepresent a new rule-based unification algorithm which can be seen as analternative to the variant-based approach. In addition, we defineforward-closed combination to capture the union of a forward-closedconvergent rewrite system with another theory, such as theAssociativity-Commutativity, whose function symbols may occur inright-hand sides of the rewrite system. Finally, we present acombination algorithm for this particular class of non-disjoint unionsof theories

The hitchhiker's guide to decidability and complexity of equivalence properties in security protocols

International audiencePrivacy-preserving security properties in cryptographic protocols are typically modelled by observational equivalences in process calculi such as the applied pi-calulus. We survey decidability and complexity results for the automated verification of such equivalences, casting existing results in a common framework which allows for a precise comparison. This unified view, beyond providing a clearer insight on the current state of the art, allowed us to identify some variations in the statements of the decision problems-sometimes resulting in different complexity results. Additionally, we prove a couple of novel or strengthened results

Maude-NPA: Cryptographic protocol analysis modulo equational properties

Abstract. In this tutorial, we give an overview of the Maude-NRL Protocol Analyzer (Maude-NPA), a tool for the analysis of cryptographic protocols using functions that obey di erent equational theories. We show the reader how to use Maude-NPA, and how it works, and also give some of the theoretical background behind the tool.