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Error Detection in Monotone Span Programs with Application to Communication-Efficient Multi-party Computation

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Topics in Cryptology – CT-RSA 2019 (CT-RSA 2019)

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Abstract

Recent improvements in the state-of-the-art of MPC for non-full-threshold access structures introduced the idea of using a collision-resistant hash functions and redundancy in the secret-sharing scheme to construct a communication-efficient MPC protocol which is computationally-secure against malicious adversaries, with abort. The prior work is based on replicated secret-sharing; in this work we extend this methodology to any LSSS implementing a \(\mathcal {Q}_{2}\) access structure. To do so we need to establish a folklore property of error detection for such LSSS and their associated Monotone Span Programs. In doing so we obtain communication-efficient online and offline protocols for MPC in the pre-processing model.

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Notes

  1. 1.

    In the full version we provide a formal description of MSPs in which all qualified sets of parties can reconstruct the entire share vector and explain how such MSPs are “good” for our protocol.

  2. 2.

    If using a small ring/finite field we simply need to modify the sacrificing stage in the triple production process; no changes are needed for the online phase at all.

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Acknowledgements

We thank for the anonymous reviewers for their helpful comments and remarks. This work has been supported in part by ERC Advanced Grant ERC-2015-AdG-IMPaCT, by the Defense Advanced Research Projects Agency (DARPA) and Space and Naval Warfare Systems Center, Pacific (SSC Pacific) under contract No. N66001-15-C-4070, and by EPSRC via grant EP/N021940/1.

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Authors and Affiliations

  1. University of Bristol, Bristol, UK

    Nigel P. Smart & Tim Wood

  2. KU Leuven, Leuven, Belgium

    Nigel P. Smart & Tim Wood

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  1. Nigel P. Smart
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Correspondence to Nigel P. Smart .

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  1. Mitsubishi Electric Corporation, Kamakura, Japan

    Mitsuru Matsui

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Smart, N.P., Wood, T. (2019). Error Detection in Monotone Span Programs with Application to Communication-Efficient Multi-party Computation. In: Matsui, M. (eds) Topics in Cryptology – CT-RSA 2019. CT-RSA 2019. Lecture Notes in Computer Science(), vol 11405. Springer, Cham. https://doi.org/10.1007/978-3-030-12612-4_11

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  • DOI: https://doi.org/10.1007/978-3-030-12612-4_11

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