Abstract
General E-unification is an important tool in cryptographic protocol analysis, where the equational theory E represents properties of the cryptographic algorithm, and uninterpreted function symbols represent other functions. Some important properties are XOR, Abelian groups, and homomorphisms over them. Polynomial time algorithms exist for unification in those theories. However, the general E-unification problem in these theories is NP-complete, and existing algorithms are highly nondeterministic. We give a mostly deterministic set of inference rules for solving general E-unification modulo XOR with (or without) a homomorphism, and prove that it is sound, complete and terminating. These inference rules have been implemented in Maude, and are being incorporated into the Maude NPA. They are designed in such a way so that they can be extended to an Abelian group with a homomorphism.
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References
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)
Baader, F., Snyder, W.: Unification theory. In: Robinson, Voronkov (eds.) [9], pp. 445–532.
Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Bevilacqua, V., Talcott, C. L. (eds.): All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Heidelberg (2007)
Brady, B., Lankford, D., Butler, G.: Abelian group unification algorithms for elementary terms. Contemporary Mathematics 29, 193–199 (1984)
Dershowitz, N., Plaisted, D.A.: Rewriting. In: Robinson, Voronkov (eds.) [9], pp. 535–610.
Escobar, S., Meadows, C., Meseguer, J.: Maude-npa: Cryptographic protocol analysis modulo equational properties. In: Aldini, A., Barthe, G., Gorrieri, R. (eds.) FOSAD. LNCS, vol. 5705, pp. 1–50. Springer, Heidelberg (2007)
Guo, Q., Narendran, P., Wolfram, D.A.: Unification and matching modulo nilpotence. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. LNCS, vol. 1104, pp. 261–274. Springer, Heidelberg (1996)
Meadows, C.: Formal verification of cryptographic protocols: A survey. In: Pieprzyk, J., Safavi-Naini, R. (eds.) ASIACRYPT 1994. LNCS, vol. 917, pp. 135–150. Springer, Heidelberg (1995)
Robinson, J.A., Voronkov, A. (eds.): Handbook of Automated Reasoning (in 2 volumes). Elsevier, MIT Press, Amsterdam (2001)
Tuengerthal, M., Küsters, R., Turuani, M.: Implementing a unification algorithm for protocol analysis with xor. In: CoRR, abs/cs/0610014 (2006)
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Liu, Z., Lynch, C. (2011). Efficient General Unification for XOR with Homomorphism. In: Bjørner, N., Sofronie-Stokkermans, V. (eds) Automated Deduction – CADE-23. CADE 2011. Lecture Notes in Computer Science(), vol 6803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22438-6_31
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DOI: https://doi.org/10.1007/978-3-642-22438-6_31
Publisher Name: Springer, Berlin, Heidelberg
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