Abstract
The main contribution of the paper is a PTIME decision procedure for the satisfiability problem in a class of first-order Horn clauses. Our result is an extension of the tractable classes of Horn clauses of Basin & Ganzinger in several respects. For instance, our clauses may contain atomic formulas S ⊢ t where ⊢ is a predicate symbol and S is a finite set of terms instead of a term. ⊢ is used to represent any possible computation of an attacker, given a set of messages S. The class of clauses that we consider encompasses the clauses designed by Bana & Comon-Lundh for security proofs of protocols in a computational model.
Because of the (variadic) ⊢ predicate symbol, we cannot use ordered resolution strategies only, as in Basin & Ganzinger: given S ⊢ t, we must avoid computing S′ ⊢ t for all subsets S′ of S. Instead, we design PTIME entailment procedures for increasingly expressive fragments, such procedures being used as oracles for the next fragment.
Finally, we obtain a PTIME procedure for arbitrary ground clauses and saturated Horn clauses (as in Basin & Ganzinger), together with a particular class of (non saturated) Horn clauses with the ⊢ predicate and constraints (which are necessary to cover the application).
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References
Abadi, M., Rogaway, P.: Reconciling two views of cryptography (the computational soundness of formal encryption). J. Cryptology 15(2), 103–127 (2002)
Backes, M., Pfitzmann, B.: Symmetric encryption in a simulatable Dolev-Yao style cryptographic library. In: 17th IEEE Computer Science Foundations Workshop (CSFW 2004), pp. 204–218 (2004)
Bana, G., Adao, P., Sakurada, H.: Computationally complete symbolic attacker in action. In: 32nd Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012), pp. 546–560 (2012)
Bana, G., Comon-Lundh, H.: Towards unconditional soundness: Computationally complete symbolic attacker. In: Degano, P., Guttman, J.D. (eds.) POST 2012. LNCS, vol. 7215, pp. 189–208. Springer, Heidelberg (2012)
Barthe, G., Grégoire, B., Heraud, S., Béguelin, S.Z.: Computer-aided security proofs for the working cryptographer. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 71–90. Springer, Heidelberg (2011)
Basin, D., Ganzinger, H.: Automated complexity analysis based on ordered resolution. J. of the Association of Computing Machinery 48(1), 70–109 (2001)
Blanchet, B.: A computationally sound mechanized prover for security protocols. In: IEEE Symposium on Security and Privacy (S&P 2006), pp. 140–154 (2006)
Comon, H., Treinen, R.: The first-order theory of lexicographic path orderings is undecidable. Theoretical Computer Science 176(1-2), 67–87 (1997)
Datta, A., Derek, A., Mitchell, J.C., Warinschi, B.: Computationally sound compositional logic for key exchange protocols. In: 19th IEEE Computer Security Foundations Workshop (CSF 2006), pp. 321–334 (2006)
McAllester, D.: Automatic recognition of tractability in inference relations. Journal of the ACM 40(2) (1993)
Micciancio, D., Warinschi, B.: Soundness of formal encryption in the presence of active adversaries. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 133–151. Springer, Heidelberg (2004)
Nieuwenhuis, R., Rubio, A.: Handbook of Automated Reasoning, chapter Paramodulation-Based Theorem Proving. Elsevier Science and MIT Press (2001)
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Comon-Lundh, H., Cortier, V., Scerri, G. (2013). Tractable Inference Systems: An Extension with a Deducibility Predicate. In: Bonacina, M.P. (eds) Automated Deduction – CADE-24. CADE 2013. Lecture Notes in Computer Science(), vol 7898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38574-2_6
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DOI: https://doi.org/10.1007/978-3-642-38574-2_6
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