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The Universal Composability framework was introduced by Canetti to study the security of protocols which are concurrently executed with other protocols in a network environment. Unfortunately it was shown that in the so called plain model, a large class of functionalities cannot be securely realized. These severe impossibility results motivated the study of other models involving some sort of setup assumptions, where general positive results can be obtained. Until recently, all the setup assumptions which were proposed required some trusted third party (or parties).
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