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Distributing Any Elliptic Curve Based Protocol

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Cryptography and Coding (IMACC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11929))

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Abstract

We show how to perform a full-threshold n-party actively secure MPC protocol over a subgroup of order p of an elliptic curve group E(K). This is done by utilizing a full-threshold n-party actively secure MPC protocol over \(\mathbb {F}_p\) in the pre-processing model (such as SPDZ), and then locally mapping the Beaver triples from this protocol into equivalent triples for the elliptic curve. This allows us to transform essentially any (algebraic) one-party protocol over an elliptic curve, into an n-party one. As an example we show how to transform a general \(\varSigma \)-protocol over elliptic curves and the shuffle protocol of Abe into an n-party protocol. This latter application requires us to also give an MPC protocol to derive the switches in a Waksman network from a generic permutation, which may be of independent interest.

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Notes

  1. 1.

    https://www.nist.gov/news-events/events/2019/03/nist-threshold-cryptography-workshop-2019.

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Acknowledgements

The authors would like to thank Tim Wood, for insightful discussions and suggestions. 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 contracts No. N66001-15-C-4070 and FA8750-19-C-0502, and by the FWO under an Odysseus project GOH9718N. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the ERC, DARPA or FWO.

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Authors and Affiliations

  1. University of Bristol, Bristol, UK

    Nigel P. Smart

  2. KU Leuven, Leuven, Belgium

    Nigel P. Smart & Younes Talibi Alaoui

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  1. Nigel P. Smart
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  2. Younes Talibi Alaoui
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Correspondence to Nigel P. Smart .

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  1. Royal Holloway, University of London, London, UK

    Martin Albrecht

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Smart, N.P., Talibi Alaoui, Y. (2019). Distributing Any Elliptic Curve Based Protocol. In: Albrecht, M. (eds) Cryptography and Coding. IMACC 2019. Lecture Notes in Computer Science(), vol 11929. Springer, Cham. https://doi.org/10.1007/978-3-030-35199-1_17

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  • DOI: https://doi.org/10.1007/978-3-030-35199-1_17

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