Hierarchical combination of intruder theories

International audienceRecently automated deduction tools have proved to be very effective for detecting attacks on cryptographic protocols. These analysis can be improved, for finding more subtle weaknesses, by a more accurate modelling of operators employed by protocols. Several works have shown how to handle a single algebraic operator (associated with a fixed intruder theory) or how to combine several operators satisfying disjoint theories. However several interesting equational theories, such as exponentiation with an abelian group law for exponents remain out of the scope of these techniques. This has motivated us to introduce a new notion of hierarchical combination for non-disjoint intruder theories and to show decidability results for the deduction problem in these theories. We have also shown that under natural hypotheses hierarchical intruder constraints can be decided. This result applies to an exponentiation theory that appears to be more general than the one considered before

Hierarchical Combination of Intruder Theories

Abstract. Recently automated deduction tools have proved to be very effective for detecting attacks on cryptographic protocols. These analysis can be improved, for finding more subtle weaknesses, by a more accurate modelling of operators employed by protocols. Several works have shown how to handle a single algebraic operator (associated with a fixed intruder theory) or how to combine several operators satisfying disjoint theories. However several interesting equational theories, such as exponentiation with an abelian group law for exponents remain out of the scope of these techniques. This has motivated us to introduce a new notion of hierarchical combination for intruder theories and to show decidability results for the deduction problem in these theories. Under a simple hypothesis, we were able to simplify this deduction problem. This simplification is then applied to prove the decidability of constraint systems w.r.t. an intruder relying on exponentiation theory.

A Symbolic Intruder Model for Hash-Collision Attacks

In the recent years, several practical methods have been published to compute collisions on some commonly used hash functions. In this paper we present a method to take into account, at the symbolic level, that an intruder actively attacking a protocol execution may use these collision algorithms in reasonable time during the attack. Our decision procedure relies on the reduction of constraint solving for an intruder exploiting the collision properties of hush functions to constraint solving for an intruder operating on words

Modeling Adversaries in a Logic for Security Protocol Analysis

Logics for security protocol analysis require the formalization of an adversary model that specifies the capabilities of adversaries. A common model is the Dolev-Yao model, which considers only adversaries that can compose and replay messages, and decipher them with known keys. The Dolev-Yao model is a useful abstraction, but it suffers from some drawbacks: it cannot handle the adversary knowing protocol-specific information, and it cannot handle probabilistic notions, such as the adversary attempting to guess the keys. We show how we can analyze security protocols under different adversary models by using a logic with a notion of algorithmic knowledge. Roughly speaking, adversaries are assumed to use algorithms to compute their knowledge; adversary capabilities are captured by suitable restrictions on the algorithms used. We show how we can model the standard Dolev-Yao adversary in this setting, and how we can capture more general capabilities including protocol-specific knowledge and guesses.Comment: 23 pages. A preliminary version appeared in the proceedings of FaSec'0

Deciding equivalence-based properties using constraint solving

Formal methods have proved their usefulness for analyzing the security of protocols. Most existing results focus on trace properties like secrecy or authentication. There are however several security properties, which cannot be defined (or cannot be naturally defined) as trace properties and require a notion of behavioural equivalence. Typical examples are anonymity, privacy related properties or statements closer to security properties used in cryptography. In this paper, we consider three notions of equivalence defined in the applied pi calculus: observational equivalence, may-testing equivalence, and trace equivalence. First, we study the relationship between these three notions. We show that for determinate processes, observational equivalence actually coincides with trace equivalence, a notion simpler to reason with. We exhibit a large class of determinate processes, called simple processes, that capture most existing protocols and cryptographic primitives. While trace equivalence and may-testing equivalence seem very similar, we show that may-testing equivalence is actually strictly stronger than trace equivalence. We prove that the two notions coincide for image-finite processes, such as processes without replication. Second, we reduce the decidability of trace equivalence (for finite processes) to deciding symbolic equivalence between sets of constraint systems. For simple processes without replication and with trivial else branches, it turns out that it is actually sufficient to decide symbolic equivalence between pairs of positive constraint systems. Thanks to this reduction and relying on a result first proved by M. Baudet, this yields the first decidability result of observational equivalence for a general class of equational theories (for processes without else branch nor replication). Moreover, based on another decidability result for deciding equivalence between sets of constraint systems, we get decidability of trace equivalence for processes with else branch for standard primitives

Reducing Equational Theories for the Decision of Static Equivalence

International audienceStatic equivalence is a well established notion of indistinguishability of sequences of terms which is useful in the symbolic analysis of cryptographic protocols. Static equivalence modulo equational theories allows for a more accurate representation of cryptographic primitives by modelling properties of operators by equational axioms. We develop a method that allows us in some cases to simplify the task of deciding static equivalence in a multi-sorted setting, by removing a symbol from the term signature and reducing the problem to several simpler equational theories. We illustrate our technique at hand of bilinear pairings

Computing Knowledge in Equational Extensions of Subterm Convergent Theories

International audienceWe study decision procedures for two knowledge problems critical to the verification of security protocols, namely the intruder deduction and the static equivalence problems. These problems can be related to particular forms of context matching and context unification. Both problems are defined with respect to an equational theory and are known to be decidable when the equational theory is given by a subterm convergent term rewrite system. In this work we extend this to consider a subterm convergent term rewrite system defined modulo an equational theory, like Commutativity. We present two pairs of solutions for these important problems. The first solves the deduction and static equivalence problems in systems modulo shallow theories such as Commutativity. The second provides a general procedure that solves the deduction and static equivalence problems in subterm convergent systems modulo syntactic permutative theories, provided a finite measure is ensured. Several examples of such theories are also given

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