Theory of Cryptography Conference

TCC 2010: Theory of Cryptography pp 109-127

On the Necessary and Sufficient Assumptions for UC Computation

  • Ivan Damgård
  • Jesper Buus Nielsen
  • Claudio Orlandi
Conference paper

DOI: 10.1007/978-3-642-11799-2_8

Volume 5978 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Damgård I., Nielsen J.B., Orlandi C. (2010) On the Necessary and Sufficient Assumptions for UC Computation. In: Micciancio D. (eds) Theory of Cryptography. TCC 2010. Lecture Notes in Computer Science, vol 5978. Springer, Berlin, Heidelberg

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 uniform random string model and the key-registration authority model (KRA), and provide new results 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.

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Copyright information

© IFIP International Federation for Information Processing 2010

Authors and Affiliations

  • Ivan Damgård
    • 1
  • Jesper Buus Nielsen
    • 1
  • Claudio Orlandi
    • 1
  1. 1.Department of Computer ScienceAarhus UniversityDenmark