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Short Signatures from Regular Syndrome Decoding in the Head

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Advances in Cryptology – EUROCRYPT 2023 (EUROCRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14008))

Abstract

We introduce a new candidate post-quantum digital signature scheme from the regular syndrome decoding (RSD) assumption, an established variant of the syndrome decoding assumption which asserts that it is hard to find \(w \)-regular solutions to systems of linear equations over \(\mathbb {F}_2\) (a vector is regular if it is a concatenation of \(w \) unit vectors). Our signature is obtained by introducing and compiling a new 5-round zero-knowledge proof system constructed using the MPC-in-the-head paradigm. At the heart of our result is an efficient MPC protocol in the preprocessing model that checks correctness of a regular syndrome decoding instance by using a share ring-conversion mechanism.

The analysis of our construction is non-trivial and forms a core technical contribution of our work. It requires careful combinatorial analysis and combines several new ideas, such as analyzing soundness in a relaxed setting where a cheating prover is allowed to use any witness sufficiently close to a regular vector. We complement our analysis with an in-depth overview of existing attacks against RSD.

Our signatures are competitive with the best-known code-based signatures, ranging from 12.52 KB (fast setting, with signing time of the order of a few milliseconds on a single core of a standard laptop) to about 9 KB (short setting, with estimated signing time of the order of 15 ms).

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Notes

  1. 1.

    https://csrc.nist.gov/projects/post-quantum-cryptography.

  2. 2.

    https://bench.cr.yp.to/results-hash.html.

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Acknowledgement

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 945332.

The first and second author acknowledge the support of the French Agence Nationale de la Recherche (ANR), under grant ANR-20-CE39-0001 (project SCENE). This work was also supported by the France 2030 ANR Project ANR-22-PECY-003 SecureCompute.

The third Author of this work has been supported by the European Union’s H2020 Programme under grant agreement number ERC-669891.

Author information

Authors and Affiliations

  1. IRIF, Université Paris Cité, Paris, France

    Eliana Carozza

  2. CNRS, IRIF, Université Paris Cité, Paris, France

    Geoffroy Couteau

  3. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Antoine Joux

Authors
  1. Eliana Carozza
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  2. Geoffroy Couteau
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  3. Antoine Joux
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Correspondence to Geoffroy Couteau .

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Editors and Affiliations

  1. Bar-Ilan University, Ramat Gan, Israel

    Carmit Hazay

  2. Simula UiB, Bergen, Norway

    Martijn Stam

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Carozza, E., Couteau, G., Joux, A. (2023). Short Signatures from Regular Syndrome Decoding in the Head. In: Hazay, C., Stam, M. (eds) Advances in Cryptology – EUROCRYPT 2023. EUROCRYPT 2023. Lecture Notes in Computer Science, vol 14008. Springer, Cham. https://doi.org/10.1007/978-3-031-30589-4_19

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  • DOI: https://doi.org/10.1007/978-3-031-30589-4_19

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