The Full Abstraction of the UC Framework

Two different approaches for general protocol security are proved equivalent. Concretely, we prove that security in the Universal Composability framework (UC) is equivalent to security in the probabilistic polynomial time calculus ppc. Security is defined under active and adaptive adversaries with synchronous and authenticated communication. In detail, we define an encoding from machines in UC to processes in ppc and show UC is fully abstract in ppc, i.e., we show the soundness and completeness of security in ppc with respect to UC. However, we restrict security in ppc to be quantified not over all possible contexts, but over those induced by UC-environments under encoding. This result is not overly-restricting security in ppc, since the threat and communication models we assume are meaningful in both practice and theory

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