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Paper: Somewhat Non-Committing Encryption and Efficient Adaptively Secure Oblivious Transfer

Authors:
Juan Garay
Daniel Wichs
Hong-Sheng Zhou
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URL: http://eprint.iacr.org/2008/534
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Abstract: Designing efficient cryptographic protocols tolerating adaptive adversaries, who are able to corrupt parties on the fly as the computation proceeds, has been an elusive task. Indeed, thus far no \emph{efficient} protocols achieve adaptive security for general multi-party computation, or even for many specific two-party tasks such as oblivious transfer (OT). In fact, it is difficult and expensive to achieve adaptive security even for the task of \emph{secure communication}, which is arguably the most basic task in cryptography. In this paper we make progress in this area. First, we introduce a new notion called \emph{semi-adaptive} security which is slightly stronger than static security but \emph{significantly weaker than fully adaptive security}. The main difference between adaptive and semi-adaptive security is that, for semi-adaptive security, the simulator is not required to handle the case where \emph{both} parties start out honest and one becomes corrupted later on during the protocol execution. As such, semi-adaptive security is much easier to achieve than fully adaptive security. We then give a simple, generic protocol compiler which transforms any semi-adaptively secure protocol into a fully adaptively secure one. The compilation effectively decomposes the problem of adaptive security into two (simpler) problems which can be tackled separately: the problem of semi-adaptive security and the problem of realizing a weaker variant of secure channels. We solve the latter problem by means of a new primitive that we call {\em somewhat non-committing encryption} resulting in significant efficiency improvements over the standard method for realizing (fully) secure channels using (fully) non-committing encryption. Somewhat non-committing encryption has two parameters: an equivocality parameter $\ell$ (measuring the number of ways that a ciphertext can be ``opened'') and the message sizes $k$. Our implementation is very efficient for small values $\ell$, \emph{even} when $k$ is large. This translates into a very efficient compilation of many semi-adaptively secure protocols (in particular, for a task with small input/output domains such as bit-OT) into a fully adaptively secure protocol. Finally, we showcase our methodology by applying it to the recent Oblivious Transfer protocol by Peikert \etal\ [Crypto 2008], which is only secure against static corruptions, to obtain the first efficient (expected-constant round, expected-constant number of public-key operations), adaptively secure and composable bit-OT protocol.
BibTeX
@misc{eprint-2008-18076,
  title={Somewhat Non-Committing Encryption and Efficient Adaptively Secure Oblivious Transfer},
  booktitle={IACR Eprint archive},
  keywords={cryptographic protocols /},
  url={http://eprint.iacr.org/2008/534},
  note={ hszhou@cse.uconn.edu 14290 received 19 Dec 2008, last revised 14 Feb 2009},
  author={Juan Garay and Daniel Wichs and Hong-Sheng Zhou},
  year=2008
}