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Paper: MPC vs. SFE: Perfect Security in a Unified Corruption Model

Authors:
Zuzana Beerliová-Trubíniová
Matthias Fitzi
Martin Hirt
Ueli Maurer
Vassilis Zikas
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URL: http://eprint.iacr.org/2007/078
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Abstract: Secure function evaluation (SFE) allows a set of players to compute an arbitrary agreed function of their private inputs, even if an adversary may corrupt some of the players. Secure multi-party computation (MPC) is a generalization allowing to perform an arbitrary on-going (also called reactive or stateful) computation during which players can receive outputs and provide new inputs at intermediate stages. At Crypto~2006, Ishai \emph{et al.} considered mixed threshold adversaries that either passively corrupt some fixed number of players, or, alternatively, actively corrupt some (smaller) fixed number of players, and showed that for certain thresholds, cryptographic SFE is possible, whereas cryptographic MPC is not. However, this separation does not occur when one considers \emph{perfect} security. Actually, past work suggests that no such separation exists, as all known general protocols for perfectly secure SFE can also be used for MPC. Also, such a separation does not show up with \emph{general adversaries}, characterized by a collection of corruptible subsets of the players, when considering passive and active corruption. In this paper, we study the most general corruption model where the adversary is characterized by a collection of adversary classes, each specifying the subset of players that can be actively, passively, or fail-corrupted, respectively, and show that in this model, perfectly secure MPC separates from perfectly secure SFE. Furthermore, we derive the exact conditions on the adversary structure for the existence of perfectly secure SFE resp.~MPC, and provide efficient protocols for both cases.
BibTeX
@misc{eprint-2007-13360,
  title={MPC vs. SFE: Perfect Security in a Unified Corruption Model},
  booktitle={IACR Eprint archive},
  keywords={Secure Multi-Party Computation, Secure Function Evaluation, General Adversaries, Fail-Corruption, Perfect Security, Separation},
  url={http://eprint.iacr.org/2007/078},
  note={ vzikas@inf.ethz.ch 13761 received 1 Mar 2007, last revised 5 Sep 2007},
  author={Zuzana Beerliová-Trubíniová and Matthias Fitzi and Martin Hirt and Ueli Maurer and Vassilis Zikas},
  year=2007
}