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On Actively Secure Fine-Grained Access Structures from Isogeny Assumptions

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Post-Quantum Cryptography (PQCrypto 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13512))

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Abstract

We present an actively secure threshold scheme in the setting of Hard Homogeneous Spaces (HHS) which allows fine-grained access structures. More precisely, we elevate a passively secure isogeny-based threshold scheme to an actively secure setting. We prove the active security and simulatability of our advanced schemes. By characterising the necessary properties, we open our schemes to a significantly wider field of applicable secret sharing schemes. Furthermore, we show that Shamir’s scheme has our generalised properties, and thereby our approach truly represents a less restrictive generalisation.

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Notes

  1. 1.

    https://csrc.nist.gov/Projects/post-quantum-cryptography/Post-Quantum-Cryptography-Standardization.

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Acknowledgements

We thank Lena Ries, Luca De Feo, and Michael Meyer for inspiring discussions. Philipp Muth was funded by the Deutsche Forschungsgemeinschaft (DFG) – SFB 1119 – 236615297.

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Authors and Affiliations

  1. RheinMain University of Applied Sciences, Wiesbaden, Germany

    Fabio Campos

  2. Radboud University, Nijmegen, The Netherlands

    Fabio Campos

  3. Technische Universität Darmstadt, Darmstadt, Germany

    Philipp Muth

Authors
  1. Fabio Campos
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  2. Philipp Muth
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Corresponding author

Correspondence to Fabio Campos .

Editor information

Editors and Affiliations

  1. Seoul National University, Seoul, Korea (Republic of)

    Jung Hee Cheon

  2. Lund University, Lund, Sweden

    Thomas Johansson

Appendix A Algorithms

Appendix A Algorithms

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Campos, F., Muth, P. (2022). On Actively Secure Fine-Grained Access Structures from Isogeny Assumptions. In: Cheon, J.H., Johansson, T. (eds) Post-Quantum Cryptography. PQCrypto 2022. Lecture Notes in Computer Science, vol 13512. Springer, Cham. https://doi.org/10.1007/978-3-031-17234-2_18

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  • DOI: https://doi.org/10.1007/978-3-031-17234-2_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-17233-5

  • Online ISBN: 978-3-031-17234-2

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