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Nowadays it is widely accepted to formulate the security of a protocol carrying out a given task via the "Trusted-party paradigm," where the protocol execution is compared with an ideal process where the outputs are computed by a trusted party that sees all the inputs. A protocol is said to securely carry out a given task if running the protocol with a realistic adversary amounts to "Emulating" the ideal process with the appropriate trusted party. In the Universal Composability (UC) framework the program run by the trusted party is called an ideal functionality.
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