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Sharing the LUOV: Threshold Post-quantum Signatures

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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 examine all of the signature submissions to Round-2 of the NIST PQC “competition” in the context of whether one can transform them into threshold signature schemes in a relatively straight forward manner. We conclude that all schemes, except the ones in the MQ family, have significant issues when one wishes to convert them using relatively generic MPC techniques. The lattice based schemes are hampered by requiring a mix of operations which are suited to both linear secret shared schemes (LSSS)-based and garbled circuits (GC)-based MPC techniques (thus requiring costly transfers between the two paradigms). The Picnic and SPHINCS+ algorithms are hampered by the need to compute a large number of hash function queries on secret data. Of the nine submissions the two which would appear to be most suitable for using in a threshold like manner are Rainbow and LUOV, with LUOV requiring less rounds and less data storage.

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Notes

  1. 1.

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

  2. 2.

    This is not strictly true as one often does not represent the function as a pure arithmetic circuit. But as a first order approximation this holds.

  3. 3.

    Arithmetic modulo a prime of size \(2^{20}\) is faster, but on the other hand one then has to perform more work to obtain the same level of active security.

  4. 4.

    Note the definition of \({\mathsf {len}}_1\) in the specification is wrong and need correcting which we do below.

  5. 5.

    To enable comparison with the NIST submissions we use the same notation in the sections which follow as used in the submissions. We hope this does not confuse the reader.

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Acknowledgments

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, United States Air Force, DARPA or FWO. The authors would like to thank Cyprien Delpech de Saint Guilhem and Dragos Rotaru for helpful discussions whilst this work was carried out.

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

    Daniele Cozzo & Nigel P. Smart

  2. University of Bristol, Bristol, UK

    Nigel P. Smart

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  1. Daniele Cozzo
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Correspondence to Nigel P. Smart .

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    Martin Albrecht

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Cozzo, D., Smart, N.P. (2019). Sharing the LUOV: Threshold Post-quantum Signatures. 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_7

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