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Secure Protocols for Complex Tasks in Complex Environments Amit Sahai University of California Los Angeles sahai cs ucla edu Over the last two decades there has been tremendous success in placing cryptography on a sound theoretical foundation and building an amazingly successful theory out of it The key elements in this Modern Cryptographic Theory are the de nitions capturing the intuitive yet elusive notions of security in various cryptographic settings The de nitions of the early 80 s proved to be extremely successful in this regard But with time as the theory started addressing more and more complex concerns further notions of security had to be introduced One of the most important concerns theory ventured into is of complex environments where di erent parties are communicating with each other concurrently in many di erent protocols A series of e orts in extending security de nitions led to the paradigm of Universally Composable UC Security 1 which along with modeling a general complex network of parties and providing de nitions of security in that framework provided powerful tools for building protocols satisfying such de nitions 1 The basic underlying notion of security in the UC framework and its many predecessors is based on simulation An ideal world is described where all requisite tasks get accomplished securely as if by magic The goal of the protocol designer is to nd a way to accomplish these tasks in the real world so that no malicious adversary can take advantage of this substitution of ideal magic by real protocols To formalize this we say that for every malicious adversary A that tries to take advantage of the real world there is an adversary S that can achieve essentially the same results in the ideal world The results are re ected in the behavior of an environment In this survey we shall refer to this notion of security as Environmental Security If a real life protocol Environmentally Securely realizes a task it ensures us that replacing the magic

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