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On the Correlation Complexity of MPC with Cheater Identification

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Financial Cryptography and Data Security (FC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13950))

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Abstract

Composable protocols for Multi-Party Computation that provide security with Identifiable Abort against a dishonest majority require some form of setup, e.g. correlated randomness among the parties. While this is a very useful model, it has the downside that the setup’s randomness must be programmable, otherwise security becomes provably impossible. Since programmability is more realistic for smaller setups (in terms of number of parties), it is crucial to minimize the correlation complexity (degree of correlation) of the setup’s randomness.

We give a tight tradeoff between the correlation complexity \(\beta \) and the corruption threshold \(t\). Our bounds are strong in that \(\beta \)-wise correlation is sufficient for statistical security while \(\beta -1\)-wise correlation is insufficient even for computational security. In particular, for strong security, i.e., \(t< n\), full \(n\)-wise correlation is necessary. However, for any constant fraction of honest parties, we provide a protocol with constant correlation complexity which tightens the gap between the theoretical model and the setup’s implementation in the real world. In contrast, previous state-of-the-art protocols require full \(n\)-wise correlation regardless of \(t\).

Work done while the first author was supported by ERC Project PREP-CRYPTO 724307, the second author was at the Karlsruhe Institute of Technology, Germany, and the third author was at the FZI Research Center for Information Technology, Germany.

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Notes

  1. 1.

    Throughout the paper, we require a setup among each subset of parties of size \(\beta \).

  2. 2.

    To our knowledge this is the first full characterization of Identifiable Abort in the dishonest majority setting.

  3. 3.

    As a side note we generalize the notion of the minimal complete cardinality (MCC) from [16] to the setting where the number of parties varies in the security parameter \(\lambda \). This was not captured by the original definition of MCC in [16] and—to the best of our knowledge—not formally addressed in previous literature.

  4. 4.

    Throughout the paper we assume that each subset of parties of the appropriate cardinality has access to a setup.

  5. 5.

    In particular, Claim 3.1 in [29] and our Lemma 3 share the same core idea but are stated in different terms with different applications in mind.

  6. 6.

    Recall that we only assume setups to have security with Identifiable Abort.

  7. 7.

    Note that is vertex is their own neighbor because the graph is reflexive.

  8. 8.

    We note that [28] state their results in the stand-alone model.

  9. 9.

    The postprocessing \(\phi \) corresponds to removing edges from parties with strictly more than \(t\) conflicts.

  10. 10.

    The sender inputs the same shares into each setup that it participates in.

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Authors and Affiliations

  1. ETH Zurich, Zurich, Switzerland

    Nicholas Brandt

  2. CNRS, IRIF, Université de Paris, Paris, France

    Sven Maier

  3. Karlsruhe, Germany

    Tobias Müller

  4. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Jörn Müller-Quade

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Correspondence to Nicholas Brandt .

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  1. George Mason University, Fairfax, VA, USA

    Foteini Baldimtsi

  2. University of Bern, Bern, Switzerland

    Christian Cachin

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Brandt, N., Maier, S., Müller, T., Müller-Quade, J. (2024). On the Correlation Complexity of MPC with Cheater Identification. In: Baldimtsi, F., Cachin, C. (eds) Financial Cryptography and Data Security. FC 2023. Lecture Notes in Computer Science, vol 13950. Springer, Cham. https://doi.org/10.1007/978-3-031-47754-6_8

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  • DOI: https://doi.org/10.1007/978-3-031-47754-6_8

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