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Thresholdizing HashEdDSA: MPC to the Rescue

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Abstract

Following recent comments in a NIST document related to threshold cryptographic standards, we examine the case of thresholdizing the HashEdDSA signature scheme. This is a deterministic signature scheme based on Edwards elliptic curves. Unlike DSA, it has a Schnorr-like signature equation, which is an advantage for threshold implementations, but it has the disadvantage of having the ephemeral secret obtained by hashing the secret key and the message. We show that one can obtain relatively efficient implementations of threshold HashEdDSA with no modifications to the behaviour of the signing algorithm; we achieve this using a doubly authenticated bit (daBit) generation protocol tailored for \(\mathcal {Q}_2\) access structures that is more efficient than prior work. However, if one was to modify the standard algorithm to use an MPC-friendly hash function, such as Rescue, the performance becomes very fast indeed.

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Notes

  1. Standard TLS satisfies the properties we need for our secure channels.

  2. Note other methodologies can reduce the total number of rounds or the total number of multiplications, i.e. when considering online and offline phases as one.

  3. We note this is a conservative choice since taking \(c=1\) is possible due to us having \(q \approx 2^{2 \cdot \kappa }\).

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Acknowledgements

The authors would like to thank Tomer Ashur, Siemen Dhooghe, Marcel Keller, Emmanuela Orsini and Dragos Rotaru for various conversations whilst the work was carried out.

Funding

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. FA8750-19-C-0502, by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA) via Contract No. 2019-1902070006, by the FWO under an Odysseus project GOH9718N, and by CyberSecurity Research Flanders with reference number VR20192203. 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, ODNI, United States Air Force, IARPA, DARPA, the US Government or FWO. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.

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  1. imec-COSIC, KU Leuven, Leuven, Belgium

    Charlotte Bonte, Nigel P. Smart & Titouan Tanguy

  2. University of Bristol, Bristol, UK

    Nigel P. Smart

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  1. Charlotte Bonte
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Correspondence to Nigel P. Smart.

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Author Bonte declares no conflict of interest. Author Smart owns stock in UnboundTech a company working in this space. Author Tanguy did a summer internship at SRI within the last 2 years

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Bonte, C., Smart, N.P. & Tanguy, T. Thresholdizing HashEdDSA: MPC to the Rescue. Int. J. Inf. Secur. 20, 879–894 (2021). https://doi.org/10.1007/s10207-021-00539-6

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