The notion of Universal Composability for cryptographic protocols was introduced by Ran Canetti in 2000. It has since been accepted as the "ultimate" security goal when designing a protocol for some specific cryptographic task.
In this new paradigm for defining security, the salient property is that protocols proven secure according to this definition are guaranteed to remain secure even when composed with an arbitrary set of protocols, or more generally when the protocol is used as a component of an arbitrary system. This is an essential property for maintaining security of cryptographic protocols in complex and unpredictable environments such as the Internet. In particular, universally composable definitions guarantee security even when an unbounded number of protocol instances are executed concurrently in an adversarially controlled manner, they guarantee non-malleability with respect to arbitrary protocols, and more.
We have shown how to formulate universally composable definitions of security for practically any cryptographic task. Furthermore, we have demonstrated that practically any such definition can be realized using known general techniques, as long as only a minority of the participants are corrupted. We also formulated universally composable definitions for a wide array of cryptographic tasks, including authenticated and secure communication, key-exchange, public-key encryption, signature, commitment, oblivious transfer, zero-knowledge, and more. We also considered the realizability of the proposed definitions in other natural settings.
B.Barak, R.Canetti, Y.Lindell, R.Pass and T.Rabin. Secure Computation Without Authentication. CRYPTO 2005, Springer LNCS 3621, pp.361-377.
R.Canetti, S.Halevi, J.Katz, Y.Lindell and P.D.MacKenzie. Universally Composable Password-Based Key Exchange. Extended version of the paper that appeared at EUROCRYPT 2005, Springer LNCS 3494, pp.404-421.
R.Canetti. Universally Composable Signatures, Certification and Authentication.Extended version of the paper that appeared at CSFW 2004.
R.Canetti and T.Rabin. Universal Composition with Joint State.Extended version of the paper that appeared at CRYPTO 2003.
R.Canetti, E.Kushilevitz and Y.Lindell. On the Limitations of Universally Composable Two-Party Computation without Set-up Assumptions. Extended version of the paper that appeared at EUROCRYPT 2003: 68-86.
R.Canetti, Y.Lindell, R.Ostrovsky, A.Sahai. Universally Composable Two-Party and Multi-Party Secure Computation. Extended version of the paper that appeared at the 34th Symposium on Theory of Computing (STOC 2002), pp.494-503.
R.Canetti and H.Krawczyk. Universally Composable Notions of Key Exchange and Secure Channelts. Extended version of the paper that appeared at EUROCRYPT 2002: 337-351.
R.Canetti and M.Fischlin. Universally Composable Commitments.. Extended version of the paper that appeared at CRYPTO 2001.
R. Canetti. Universally composable security: A new paradigm for cryptographic protocols. Extended version of the paper that appeared at the 42nd Foundations of Computer Science Symposium (FOCS'01).