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Sashimi: Cutting up CSI-FiSh Secret Keys to Produce an Actively Secure Distributed Signing Protocol

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Post-Quantum Cryptography (PQCrypto 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12100))

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Abstract

We present the first actively secure variant of a distributed signature scheme based on isogenies. The protocol produces signatures from the recent CSI-FiSh signature scheme. Our scheme works for any access structure, as we use a replicated secret sharing scheme to define the underlying secret sharing; as such it is only practical when the number of maximally unqualified sets is relatively small. This, however, includes the important case of full threshold, and (n, t)-threshold schemes when n is small.

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Notes

  1. 1.

    For highest computational efficiency [1] selects, for \(\mathsf {sec}=128\), the values \(S=2^{15}\) and \(t_\mathsf {S}=7\), using a hash function which is \(2^{16}\) times slower than SHA-3.

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Acknowledgments

We would like to thank Frederik Vercauteren for the numerous and useful discussions on the arithmetic of isogenies. This work has been supported in part by ERC Advanced Grant ERC-2015-AdG-IMPaCT, 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 or FWO.

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Authors and Affiliations

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

    Daniele Cozzo & Nigel P. Smart

  2. University of Bristol, Bristol, UK

    Nigel P. Smart

Authors
  1. Daniele Cozzo
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  2. Nigel P. Smart
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Correspondence to Nigel P. Smart .

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Editors and Affiliations

  1. University of Cincinnati, Cincinnati, OH, USA

    Jintai Ding

  2. Inria, Paris, France

    Jean-Pierre Tillich

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Cozzo, D., Smart, N.P. (2020). Sashimi: Cutting up CSI-FiSh Secret Keys to Produce an Actively Secure Distributed Signing Protocol. In: Ding, J., Tillich, JP. (eds) Post-Quantum Cryptography. PQCrypto 2020. Lecture Notes in Computer Science(), vol 12100. Springer, Cham. https://doi.org/10.1007/978-3-030-44223-1_10

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  • DOI: https://doi.org/10.1007/978-3-030-44223-1_10

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