Abstract
We consider a mild extension of universal algebra in which terms are built both from deterministic and probabilistic variables, and are interpreted as distributions. We formulate an equational proof system to establish equality between probabilistic terms, show its soundness, and provide heuristics for proving the validity of equations. Moreover, we provide decision procedures for deciding the validity of a system of equations under specific theories that are commonly used in cryptographic proofs, and use concatenation, truncation, and xor. We illustrate the applicability of our formalism in cryptographic proofs, showing how it can be used to prove standard equalities such as optimistic sampling and one-time padding as well as non-trivial equalities for standard schemes such as OAEP.
This work was partially supported by French ANR SESUR-012, SCALP, Spanish project TIN2009-14599 DESAFIOS 10, and Madrid Regional project S2009TIC-1465 PROMETIDOS.
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Barthe, G., Daubignard, M., Kapron, B., Lakhnech, Y., Laporte, V. (2010). On the Equality of Probabilistic Terms. In: Clarke, E.M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2010. Lecture Notes in Computer Science(), vol 6355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17511-4_4
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DOI: https://doi.org/10.1007/978-3-642-17511-4_4
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