**On the Necessary and Sufficient Assumptions for UC Computation**

*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 key-registration authority (KRA) model, and provide new result for all of them. Perhaps most interestingly we show that:

- For even the minimal meaningful KRA, 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 KRA 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 KRA model: any non-trivial KRA is sufficient for UC computation.

- We show that in the KRA 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.

**Category / Keywords: **foundations / UC security, setup assumptions, public-key infrastructure, common reference string

**Publication Info: **Full version of a TCC 2010 paper

**Date: **received 29 May 2009, last revised 6 Dec 2009

**Contact author: **claudio at cs au dk

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

**Version: **20091206:194455 (All versions of this report)

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