The framework of Universally Composable (UC) security [Canetti'01] defines
a notion of security which guarantees privacy and correctness for a
cryptographic protocol in an arbitrary network environment.
Unfortunately, this definitional framework has been shown to be impossible
to achieve in the "standard" model, where there is no Trusted Party
present at any time.

We put forward a new notion of security, which involves comparing the
protocol executions with an ideal execution involving ideal
functionalities (just as in UC-security), but allowing the environment and
adversary access to some limited super-polynomial computational power. We
argue the meaningfulness of the new notion, which in particular subsumes
many of the traditional notions of security.

We generalize the Universal Composition theorem of [Canetti] to the new
setting. Then under new computational assumptions, we realize secure
multiparty computation (for static adversaries), without a common
reference string or any other setup assumptions, in the new framework.
This is known to be impossible under the UC framework.

Joint work with Manoj Prabhakaran. (STOC 2004)