SPEAKER: Claudio Orlandi TITLE: On the Necessary and Sufficient Assumptions for UC Computation AUTHORS: Ivan Damgård and Jesper Buus Nielsen and Claudio Orlandi ABSTRACT: We study the necessary and sufficient assumptions for universally composable (UC) computation, both in terms of setup and computational assumptions. We look at the common reference string model, the common random string model and the public-key infrastructure (PKI) model, and provide new result for all of them. Perhaps most interestingly we show that: - For even the minimal meaningful PKI, where we only assume that the secret key is a value which is hard to compute from the public key, one can UC securely compute any poly-time functionality if there exists a passive secure oblivious-transfer protocol for the stand-alone model. Since a PKI where the secret keys can be computed from the public keys is useless, and some setup assumption is needed for UC secure computation, this establishes the best we could hope for the PKI model: any non-trivial PKI is sufficient for UC computation. - We show that in the PKI model one-way functions are sufficient for UC commitment and UC zero-knowledge. These are the first examples of UC secure protocols for non-trivial tasks which do not assume the existence of public-key primitives. In particular, the protocols show that non-trivial UC computation is possible in Minicrypt. ONLINE VERSION: http://eprint.iacr.org/2009/247.pdf