Abstract
Research in the formal analysis of cryptographic protocols has produced much good work in the solving of equality constraints, developing new methods for unification, matching, and deducibility. However, considerably less attention has been paid to disequality constraints. These also arise quite naturally in cryptographic protocol analysis, in particular for analysis of indistinguishability properties. Thus methods for deciding whether or not they are satisfiable could potentially be quite useful in reducing the size of the search space by protocol analysis tools. In this paper we develop a framework for reasoning about disequality constraints centered around the paradigm of the most discriminating Dolev-Yao attacker, who is able to detect a disequality if it is satisfied in some implementation of the crypto-algebra satisfying given equality properties. We develop several strategies for handling disequalities, prove their soundness and completeness, and demonstrate the result of experimental analyses using the various strategies. Finally, we discuss how disequality checking algorithms could be incorporated within symbolic reachability protocol analysis methods.
The rights of this work are transferred to the extent transferable according to title 17 §105 U.S.C
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
It is well-known that protocols proved secure modulo equational axioms E may sometimes be attacked at the computational level. That is why the qualification that an attack is possible “when only the theory E is assumed” is important here.
References
Baader, F., Schulz, K.U.: Combination techniques and decision problems for disunification. Theor. Comput. Sci. 142(2), 229–255 (1995)
Blanchet, B.: Using horn clauses for analyzing security protocols. In: Cortier, V., Kremer, S. (eds.) Formal Models and Techniques for Analyzing Security Protocols. Cryptology and Information Security Series, vol. 5, pp. 86–111. IOS Press, March 2011
Blanchet, B., Abadi, M., Fournet, C.: Automated verification of selected equivalences for security protocols. J. Log. Algebr. Program. 75(1), 3–51 (2008)
Comon, H., Lescanne, P.: Equational problems and disunification. J. Symb. Comput. 7, 371–425 (1989)
Comon, H.: Complete axiomatizations of some quotient term algebras. In: Albert, J.L., Monien, B., Artalejo, M.R. (eds.) Automata, Languages and Programming. LNCS, vol. 510, pp. 469–480. Springer, Heidelberg (1991)
Comon, H.: Disunification: a survey. In: Computational Logic - Essays in Honor of Alan Robinson, pp. 322–359 (1991)
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., Delaune, S., Lafourcade, P.: A survey of algebraic properties used in cryptographic protocols. J. Comput. Secur. 14(1), 1–43 (2006)
Dolev, D., Yao, A.: On the security of public key protocols. IEEE Trans. Inf. Theory 29(2), 198–208 (1983)
Erbatur, S., et al.: Effective symbolic protocol analysis via equational irreducibility conditions. In: Foresti, S., Yung, M., Martinelli, F. (eds.) ESORICS 2012. LNCS, vol. 7459, pp. 73–90. Springer, Heidelberg (2012)
Escobar, S., Hendrix, J., Meadows, C., Meseguer, J.: Diffie-Hellman cryptographic reasoning in the Maude-NRL protocol analyzer. In: Proceedings of the 2nd International Workshop on Security and Rewriting Techniques (SecReT 2007) (2007)
Escobar, S., Meadows, C., Meseguer, J.: A rewriting-based inference system for the NRL protocol analyzer and its meta-logical properties. Theor. Comput. Sci. 367(1–2), 162–202 (2006)
Escobar, S., Meadows, C., Meseguer, J.: Equational cryptographic reasoning in the Maude-NRL protocol analyzer. In: Proceedings of the 1st International Workshop on Security and Rewriting Techniques (SecReT 2006). ENTCS, vol. 171, no. 4, pp. 23–36. Elsevier (2007)
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. LNCS, vol. 5705, pp. 1–50. Springer, Heidelberg (2009)
Escobar, S., Sasse, R., Meseguer, J.: Folding variant narrowing and optimal variant termination. J. Log. Algebr. Program. 81(7–8), 898–928 (2012)
Thayer Fabrega, F.J., Herzog, J., Guttman, J.: Strand spaces: what makes a security protocol correct? J. Comput. Secur. 7, 191–230 (1999)
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)
Meseguer, J.: Conditional rewriting logic as a unified model of concurrency. Theor. Comput. Sci. 96(1), 73–155 (1992)
Meseguer, J.: Membership algebra as a logical framework for equational specification. In: Presicce, F.P. (ed.) Recent Trends in Algebraic Development Techniques. LNCS, vol. 1376, pp. 18–61. Springer, Heidelberg (1997)
Mödersheim, S., Viganò, L., Basin, D.A.: Constraint differentiation: Search-space reduction for the constraint-based analysis of security protocols. J. Comput. Secur. 18(4), 575–618 (2010)
Needham, R.M., Schroeder, M.D.: Using encryption for authentication in large networks of computers. Commun. ACM 21(12), 993–999 (1978)
Santiago, S., Escobar, S., Meadows, C., Meseguer, J.: A formal definition of protocol indistinguishability and its verification using Maude-NPA. In: Mauw, S., Jensen, C.D. (eds.) STM 2014. LNCS, vol. 8743, pp. 162–177. Springer, Heidelberg (2014)
Sasse, R., Escobar, S., Meadows, C., Meseguer, J.: Protocol analysis modulo combination of theories: a case study in Maude-NPA. In: Cuellar, J., Lopez, J., Barthe, G., Pretschner, A. (eds.) STM 2010. LNCS, vol. 6710, pp. 163–178. Springer, Heidelberg (2011)
TeReSe: Term Rewriting Systems. Cambridge University Press, Cambridge (2003)
Thati, P., Meseguer, J.: Symbolic reachability analysis using narrowing and its application verification of cryptographic protocols. J. Higher-Order Symb. Comput. 20(1–2), 123–160 (2007)
Acknowledgements
This work has been partially supported by NSF grant CNS 13-19109, by the EU (FEDER) and the Spanish MINECO under grant TIN 2013-45732-C4-1-P, and by Spanish Generalitat Valenciana under grant PROMETEOII/2015/013.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland (outside the US)
About this chapter
Cite this chapter
Escobar, S., Meadows, C., Meseguer, J., Santiago, S. (2015). Symbolic Protocol Analysis with Disequality Constraints Modulo Equational Theories. In: Bodei, C., Ferrari, G., Priami, C. (eds) Programming Languages with Applications to Biology and Security. Lecture Notes in Computer Science(), vol 9465. Springer, Cham. https://doi.org/10.1007/978-3-319-25527-9_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-25527-9_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-25526-2
Online ISBN: 978-3-319-25527-9
eBook Packages: Computer ScienceComputer Science (R0)