State space reduction in the Maude-NRL Protocol Analyzer

The Maude-NRL Protocol Analyzer (Maude-NPA) is a tool and inference system for reasoning about the security of cryptographic protocols in which the cryptosystems satisfy different equational properties. It both extends and provides a formal framework for the original NRL Protocol Analyzer, which supported equational reasoning in a more limited way. Maude-NPA supports a wide variety of algebraic properties that includes many crypto-systems of interest such as, for example, one-time pads and Diffie–Hellman. Maude-NPA, like the original NPA, looks for attacks by searching backwards from an insecure attack state, and assumes an unbounded number of sessions. Because of the unbounded number of sessions and the support for different equational theories, it is necessary to develop ways of reducing the search space and avoiding infinite search paths. In order for the techniques to prove useful, they need not only to speed up the search, but should not violate completeness, so that failure to find attacks still guarantees security. In this paper we describe some state space reduction techniques that we have implemented in Maude-NPA. We also provide completeness proofs, and experimental evaluations of their effect on the performance of Maude-NPA.We would like to thank Antonio Gonzalez for his help in providing several protocol specifications in Maude-NPA. S. Escobar and S. Santiago have been partially supported by the EU (FEDER) and the Spanish MEC/MICINN under grant TIN 2010-21062-C02-02, and by Generalitat Valenciana PROMETEO2011/052. J. Meseguer and S. Escobar have been partially supported by NSF grants CNS 09-04749, and CCF 09-05584.Escobar Román, S.; Meadows, C.; Meseguer, J.; Santiago Pinazo, S. (2014). State space reduction in the Maude-NRL Protocol Analyzer. Information and Computation. 238:157-186. https://doi.org/10.1016/j.ic.2014.07.007S15718623

An Optimizing Protocol Transformation for Constructor Finite Variant Theories in Maude-NPA

[EN] Maude-NPA is an analysis tool for cryptographic security protocols that takes into account the algebraic properties of the cryptosystem. Maude-NPA can reason about a wide range of cryptographic properties. However, some algebraic properties, and protocols using them, have been beyond Maude-NPA capabilities, either because the cryptographic properties cannot be expressed using its equational unification features or because the state space is unmanageable. In this paper, we provide a protocol transformation that can safely get rid of cryptographic properties under some conditions. The time and space difference between verifying the protocol with all the crypto properties and verifying the protocol with a minimal set of the crypto properties is remarkable. We also provide, for the first time, an encoding of the theory of bilinear pairing into Maude-NPA that goes beyond the encoding of bilinear pairing available in the Tamarin toolPartially supported by the EU (FEDER) and the Spanish MCIU under grant RTI2018-094403-B-C32, by the Spanish Generalitat Valenciana under grant PROMETEO/2019/098, and by the US Air Force Office of Scientific Research under award number FA9550-17-1-0286. Julia Sapiña has been supported by the Generalitat Valenciana APOSTD/2019/127 grantAparicio-Sánchez, D.; Escobar Román, S.; Gutiérrez Gil, R.; Sapiña-Sanchis, J. (2020). An Optimizing Protocol Transformation for Constructor Finite Variant Theories in Maude-NPA. Springer Nature. 230-250. https://doi.org/10.1007/978-3-030-59013-0_12S230250Maude-NPA manual v3.1. http://maude.cs.illinois.edu/w/index.php/Maude_Tools:_Maude-NPAThe Tamarin-Prover Manual, 4 June 2019. https://tamarin-prover.github.io/manual/tex/tamarin-manual.pdfAl-Riyami, S.S., Paterson, K.G.: Tripartite authenticated key agreement protocols from pairings. In: Paterson, K.G. (ed.) Cryptography and Coding 2003. LNCS, vol. 2898, pp. 332–359. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-40974-8_27Baader, F., Snyder, W.: Unification theory. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. 1, pp. 447–533. Elsevier Science (2001)Baelde, D., Delaune, S., Gazeau, I., Kremer, S.: Symbolic verification of privacy-type properties for security protocols with XOR. In: 30th IEEE Computer Security Foundations Symposium, CSF 2017, pp. 234–248. IEEE Computer Society (2017)Blanchet, B.: Modeling and verifying security protocols with the applied pi calculus and ProVerif. Found. Trends Privacy Secur. 1(1–2), 1–135 (2016)Clavel, M., et al.: Maude manual (version 3.0). Technical report, SRI International, Computer Science Laboratory (2020). http://maude.cs.uiuc.eduComon-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). https://doi.org/10.1007/978-3-540-32033-3_22Cremers, 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). https://doi.org/10.1007/978-3-540-70545-1_38Dreier, J., Duménil, C., Kremer, S., Sasse, R.: Beyond subterm-convergent equational theories in automated verification of stateful protocols. In: Maffei, M., Ryan, M. (eds.) POST 2017. LNCS, vol. 10204, pp. 117–140. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54455-6_6Escobar, S., Hendrix, J., Meadows, C., Meseguer, J.: Diffie-Hellman cryptographic reasoning in the Maude-NRL protocol analyzer. In: Proceedings of 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.: Maude-NPA: cryptographic protocol analysis modulo equational properties. In: Aldini, A., Barthe, G., Gorrieri, R. (eds.) FOSAD 2007-2009. LNCS, vol. 5705, pp. 1–50. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03829-7_1Escobar, S., et al.: Protocol analysis in Maude-NPA using unification modulo homomorphic encryption. In: Proceedings of PPDP 2011, pp. 65–76. ACM (2011)Escobar, S., Meadows, C.A., Meseguer, J., Santiago, S.: State space reduction in the Maude-NRL protocol analyzer. Inf. Comput. 238, 157–186 (2014)Escobar, S., Sasse, R., Meseguer, J.: Folding variant narrowing and optimal variant termination. J. Log. Algebr. Program. 81(7–8), 898–928 (2012)Fabrega, F.J.T., Herzog, J.C., Guttman, J.D.: Strand spaces: why is a security protocol correct? In: Proceedings of IEEE Symposium on Security and Privacy, pp. 160–171 (1998)Guttman, J.D.: Security goals and protocol transformations. In: Mödersheim, S., Palamidessi, C. (eds.) TOSCA 2011. LNCS, vol. 6993, pp. 130–147. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-27375-9_8Joux, A.: A one round protocol for tripartite Diffie-Hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 385–393. Springer, Heidelberg (2000). https://doi.org/10.1007/10722028_23Kim, Y., Perrig, A., Tsudik, G.: Communication-efficient group key agreement. In: Dupuy, M., Paradinas, P. (eds.) SEC 2001. IIFIP, vol. 65, pp. 229–244. Springer, Boston, MA (2002). https://doi.org/10.1007/0-306-46998-7_16Küsters, R., Truderung, T.: Using ProVerif to analyze protocols with Diffie-Hellman exponentiation. In: IEEE Computer Security Foundations, pp. 157–171 (2009)Küsters, R., Truderung, T.: Reducing protocol analysis with XOR to the XOR-free case in the horn theory based approach. J. Autom. Reason. 46(3–4), 325–352 (2011)Meadows, C.: The NRL protocol analyzer: an overview. J. Logic Program. 26(2), 113–131 (1996)Meier, S., Cremers, C., Basin, D.: Strong invariants for the efficient construction of machine-checked protocol security proofs. In: 2010 23rd IEEE Computer Security Foundations Symposium, pp. 231–245 (2010)Meseguer, J.: Conditional rewriting logic as a united model of concurrency. Theoret. Comput. Sci. 96(1), 73–155 (1992)Meseguer, J.: Variant-based satisfiability in initial algebras. Sci. Comput. Program. 154, 3–41 (2018)Meseguer, J.: Generalized rewrite theories, coherence completion, and symbolic methods. J. Log. Algebr. Meth. Program. 110, 100483 (2020)Mödersheim, S., Viganò, L.: The open-source fixed-point model checker for symbolic analysis of security protocols. In: Aldini, A., Barthe, G., Gorrieri, R. (eds.) FOSAD 2007-2009. LNCS, vol. 5705, pp. 166–194. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03829-7_6Sasse, 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). https://doi.org/10.1007/978-3-642-22444-7_11Schmidt, B., Sasse, R., Cremers, C., Basin, D.A.: Automated verification of group key agreement protocols. In: 2014 IEEE Symposium on Security and Privacy, SP 2014, pp. 179–194. 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Debugging of Web Applications with Web-TLR

Web-TLR is a Web verification engine that is based on the well-established Rewriting Logic--Maude/LTLR tandem for Web system specification and model-checking. In Web-TLR, Web applications are expressed as rewrite theories that can be formally verified by using the Maude built-in LTLR model-checker. Whenever a property is refuted, a counterexample trace is delivered that reveals an undesired, erroneous navigation sequence. Unfortunately, the analysis (or even the simple inspection) of such counterexamples may be unfeasible because of the size and complexity of the traces under examination. In this paper, we endow Web-TLR with a new Web debugging facility that supports the efficient manipulation of counterexample traces. This facility is based on a backward trace-slicing technique for rewriting logic theories that allows the pieces of information that we are interested to be traced back through inverse rewrite sequences. The slicing process drastically simplifies the computation trace by dropping useless data that do not influence the final result. By using this facility, the Web engineer can focus on the relevant fragments of the failing application, which greatly reduces the manual debugging effort and also decreases the number of iterative verifications.Comment: In Proceedings WWV 2011, arXiv:1108.208

Effective symbolic protocol analysis via equational irreducibility conditions

We address a problem that arises in cryptographic protocol analysis when the equational properties of the cryptosystem are taken into account: in many situations it is necessary to guarantee that certain terms generated during a state exploration are in normal form with respect to the equational theory. We give a tool-independent methodology for state exploration, based on unification and narrowing, that generates states that obey these irreducibility constraints, called contextual symbolic reachability analysis, prove its soundness and completeness, and describe its implementation in the Maude-NPA protocol analysis tool. Contextual symbolic reachability analysis also introduces a new type of unification mechanism, which we call asymmetric unification, in which any solution must leave the right side of the solution irreducible. We also present experiments showing the effectiveness of our methodology.S. Escobar and S. Santiago have been partially supported by the EU (FEDER) and the Spanish MEC/MICINN under grant TIN 2010-21062-C02-02, and by Generalitat Valenciana PROMETEO2011/052. The following authors have been partially supported by NSF: S. Escobar, J. Meseguer and R. Sasse under grants CCF 09- 05584, CNS 09-04749, and CNS 09-05584; D. Kapur under grant CNS 09-05222; C. Lynch, Z. Liu, and C. Meadows under grant CNS 09-05378, and P. Narendran and S. Erbatur under grant CNS 09-05286.Erbatur, S.; Escobar Román, S.; Kapur, D.; Liu, Z.; Lynch, C.; Meadows, C.; Meseguer, J.... (2012). Effective symbolic protocol analysis via equational irreducibility conditions. En Computer Security - ESORICS 2012. Springer Verlag (Germany). 7459:73-90. doi:10.1007/978-3-642-33167-1_5S73907459IEEE 802.11 Local and Metropolitan Area Networks: Wireless LAN Medium Access Control (MAC) and Physical (PHY) Specifications (1999)Abadi, M., Cortier, V.: Deciding knowledge in security protocols under equational theories. Theor. Comput. Sci. 367(1-2), 2–32 (2006)Arapinis, M., Bursuc, S., Ryan, M.: Privacy Supporting Cloud Computing: ConfiChair, a Case Study. In: Degano, P., Guttman, J.D. (eds.) Principles of Security and Trust. LNCS, vol. 7215, pp. 89–108. Springer, Heidelberg (2012)Basin, D., 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 (2001)Blanchet, B.: Using horn clauses for analyzing security protocols. In: Cortier, V., Kremer, S. (eds.) Formal Models and Techniques for Analyzing Security Protocols. IOS Press (2011)Blanchet, B., Abadi, M., Fournet, C.: Automated verification of selected equivalences for security protocols. J. Log. Algebr. Program. 75(1), 3–51 (2008)Ciobâcă, Ş., Delaune, S., Kremer, S.: Computing Knowledge in Security Protocols under Convergent Equational Theories. In: Schmidt, R.A. (ed.) CADE-22. LNCS (LNAI), 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)Comon-Lundh, H., Delaune, S., Millen, J.: Constraint solving techniques and enriching the model with equational theories. In: Cortier, V., Kremer, S. (eds.) Formal Models and Techniques for Analyzing Security Protocols. Cryptology and Information Security Series, vol. 5, pp. 35–61. IOS Press (2011)Comon-Lundh, H., Shmatikov, V.: Intruder deductions, constraint solving and insecurity decision in presence of exclusive or. In: LICS, pp. 271–280. IEEE Computer Society (2003)Ciobâcă, Ş.: Knowledge in security protocolsDolev, D., Yao, A.C.-C.: On the security of public key protocols (extended abstract). In: FOCS, pp. 350–357 (1981)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.: State Space Reduction in the Maude-NRL Protocol Analyzer. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 548–562. Springer, Heidelberg (2008)Escobar, S., Meadows, C., Meseguer, J.: Maude-NPA: Cryptographic Protocol Analysis Modulo Equational Properties. In: Aldini, A., Barthe, G., Gorrieri, R. (eds.) FOSAD 2007. LNCS, vol. 5705, pp. 1–50. Springer, Heidelberg (2009)Escobar, S., Meadows, C., Meseguer, J., Santiago, S.: State space reduction in the maude-nrl protocol analyzer. 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Twenty years of rewriting logic

AbstractRewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality. This paper provides a gentle, intuitive introduction to its main ideas, as well as a survey of the work that many researchers have carried out over the last twenty years in advancing: (i) its foundations; (ii) its semantic framework and logical framework uses; (iii) its language implementations and its formal tools; and (iv) its many applications to automated deduction, software and hardware specification and verification, security, real-time and cyber-physical systems, probabilistic systems, bioinformatics and chemical systems

Relating state-based and process-based concurrency through linear logic (full-version)

AbstractThis paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones.Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, much effort has been invested in tracing the foundations of concurrency in logic. The starting points of such investigations have been various idealized languages of concurrent and distributed programming, in particular the well established state-transformation model inspired by Petri nets and multiset rewriting, and the prolific process-based models such as the π-calculus and other process algebras. In nearly all cases, the target of these investigations has been linear logic, a formal language that supports a view of formulas as consumable resources. In the first part of this paper, we review some of these interpretations of concurrent languages into linear logic and observe that, possibly modulo duality, they invariably target a small semantic fragment of linear logic that we call LVobs.In the second part of the paper, we propose a new approach to understanding concurrent and distributed programming as a manifestation of logic, which yields a language that merges those two main paradigms of concurrency. Specifically, we present a new semantics for multiset rewriting founded on an alternative view of linear logic and specifically LVobs. The resulting interpretation is extended with a majority of linear connectives into the language of ω-multisets. This interpretation drops the distinction between multiset elements and rewrite rules, and considerably enriches the expressive power of standard multiset rewriting with embedded rules, choice, replication, and more. Derivations are now primarily viewed as open objects, and are closed only to examine intermediate rewriting states. The resulting language can also be interpreted as a process algebra. For example, a simple translation maps process constructors of the asynchronous π-calculus to rewrite operators. The language of ω-multisets forms the basis for the security protocol specification language MSR 3. With relations to both multiset rewriting and process algebra, it supports specifications that are process-based, state-based, or of a mixed nature, with the potential of combining verification techniques from both worlds. Additionally, its logical underpinning makes it an ideal common ground for systematically comparing protocol specification languages

Advanced Features in Protocol Verification: Theory, Properties, and Efficiency in Maude-NPA

The area of formal analysis of cryptographic protocols has been an active one since the mid 80’s. The idea is to verify communication protocols that use encryption to guarantee secrecy and that use authentication of data to ensure security. Formal methods are used in protocol analysis to provide formal proofs of security, and to uncover bugs and security flaws that in some cases had remained unknown long after the original protocol publication, such as the case of the well known Needham-Schroeder Public Key (NSPK) protocol. In this thesis we tackle problems regarding the three main pillars of protocol verification: modelling capabilities, verifiable properties, and efficiency. This thesis is devoted to investigate advanced features in the analysis of cryptographic protocols tailored to the Maude-NPA tool. This tool is a model-checker for cryptographic protocol analysis that allows for the incorporation of different equational theories and operates in the unbounded session model without the use of data or control abstraction. An important contribution of this thesis is relative to theoretical aspects of protocol verification in Maude-NPA. First, we define a forwards operational semantics, using rewriting logic as the theoretical framework and the Maude programming language as tool support. This is the first time that a forwards rewriting-based semantics is given for Maude-NPA. Second, we also study the problem that arises in cryptographic protocol analysis when it is necessary to guarantee that certain terms generated during a state exploration are in normal form with respect to the protocol equational theory. We also study techniques to extend Maude-NPA capabilities to support the verification of a wider class of protocols and security properties. First, we present a framework to specify and verify sequential protocol compositions in which one or more child protocols make use of information obtained from running a parent protocol. Second, we present a theoretical framework to specify and verify protocol indistinguishability in Maude-NPA. This kind of properties aim to verify that an attacker cannot distinguish between two versions of a protocol: for example, one using one secret and one using another, as it happens in electronic voting protocols. Finally, this thesis contributes to improve the efficiency of protocol verification in Maude-NPA. We define several techniques which drastically reduce the state space, and can often yield a finite state space, so that whether the desired security property holds or not can in fact be decided automatically, in spite of the general undecidability of such problems.Santiago Pinazo, S. (2015). Advanced Features in Protocol Verification: Theory, Properties, and Efficiency in Maude-NPA [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/4852

Slicing-based debugging of web applications in rewriting logic

The pervasiveness of computing on the Internet has led to an explosive growth of Web applications that, together with their ever-increasing complexity, have turned their design and development in a major challenge. Unfortunately, the huge expansion of development and utilization of Web computation has not been paired by the development of methods, models and debugging tools to help the developer diagnose, quickly and easily, potential problems in a Web application. There is an urgent demand of analysis and verification facilities capable to prevent insecure software that could cause unavailability of systems or services, or provide access to private data or internal resources of a given organization. The main goal of this MSc thesis is to improve the debugging of Web applications by embedding novel analysis and verification techniques that rely on the program semantics. As a practical realization of the ideas, we use Web-TLR that is a verification engine for dynamic Web applications based on Rewrite Logic. We extend Web-TLR with a novel functionality that supports effective Web debugging for realistic Web applications involving complex execution traces. This functionality is based on a backward trace slicing technique that is based on dynamic labeling. In order to extend the class of programs covered by the debugging methodology we formalize a generalization of the slicer to Conditional Rewriting Logic theories, greatly simplifying the debugging task by providing a novel and sophisticated form of pattern matching.Frechina Navarro, F. (2011). Slicing-based debugging of web applications in rewriting logic. http://hdl.handle.net/10251/15637Archivo delegad