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Block-Anti-Circulant Unbalanced Oil and Vinegar

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Selected Areas in Cryptography – SAC 2019 (SAC 2019)

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Abstract

We introduce a new technique for compressing the public keys of the UOV signature scheme that makes use of block-anti-circulant matrices. These matrices admit a compact representation as for every block, the remaining elements can be inferred from the first row. This space saving translates to the public key, which as a result of this technique can be shrunk by a small integer factor. We propose parameters sets that take into account the most important attacks, and present performance statistics derived from a C implementation along with a comparison to LUOV.

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Notes

  1. 1.

    We restrict focus to odd-characteristic fields because the use of even-characteristic fields induces a security degradation, as shown in Sect. 4.2.

  2. 2.

    Or any one of the irreducible factors of largest degree, if there are more than one.

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Acknowledgements

This work was supported in part by the Research Council KU Leuven: C16/15/058. In addition, this work was supported by the European Commission through the Horizon 2020 research and innovation programme under grant agreement H2020-DS-LEIT-2017-780108 FENTEC, by the Flemish Government through FWO SBO project SNIPPET S007619N and by the IF/C1 on Cryptanalysis of post-quantum cryptography. Alan Szepieniec was supported by a doctoral grant from Flemish Agency for Innovation and Entrepreneurship (VLAIO, formerly IWT) and is supported by Nervos Foundation. Lastly, the authors would like to thank Ward Beullens for useful feedback.

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Authors and Affiliations

  1. imec-COSIC KU Leuven, Leuven, Belgium

    Alan Szepieniec & Bart Preneel

  2. Nervos Foundation, Panama City, Panama

    Alan Szepieniec

Authors
  1. Alan Szepieniec
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  2. Bart Preneel
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Correspondence to Alan Szepieniec .

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Editors and Affiliations

  1. ETH Zürich, Zurich, Switzerland

    Kenneth G. Paterson

  2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada

    Douglas Stebila

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Szepieniec, A., Preneel, B. (2020). Block-Anti-Circulant Unbalanced Oil and Vinegar. In: Paterson, K., Stebila, D. (eds) Selected Areas in Cryptography – SAC 2019. SAC 2019. Lecture Notes in Computer Science(), vol 11959. Springer, Cham. https://doi.org/10.1007/978-3-030-38471-5_23

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  • DOI: https://doi.org/10.1007/978-3-030-38471-5_23

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  • Print ISBN: 978-3-030-38470-8

  • Online ISBN: 978-3-030-38471-5

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