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A Reaction Attack Against Cryptosystems Based on LRPC Codes

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Progress in Cryptology – LATINCRYPT 2019 (LATINCRYPT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11774))

Abstract

Rank metric is a very promising research direction for code-based cryptography. In fact, thanks to the high complexity of generic decoding attacks against codes in this metric, it is possible to easily select parameters that yield very small data sizes. In this paper we analyze cryptosystems based on Low-Rank Parity-Check (LRPC) codes, one of the classes of codes that are efficiently decodable in the rank metric. We show how to exploit the decoding failure rate, which is an inherent feature of these codes, to devise a reaction attack aimed at recovering the private key. As a case study, we cryptanalyze the recent McNie submission to NIST’s Post-Quantum Standardization process. Additionally, we provide details of a simple implementation to validate our approach.

This work has been supported by the European Commission through the ERC Starting Grant 805031 (EPOQUE); through the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 643161; and by Sweden through the WASP expedition project Massive, Secure, and Low-Latency Connectivity for IoT Applications.

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Notes

  1. 1.

    A circulant matrix can be defined as a special case of Toeplitz matrix; for more details about Toeplitz matrices see [19].

  2. 2.

    Recall that in Hamming metric, weight is preserved under multiplication by permutation matrices.

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Author information

Authors and Affiliations

  1. Radboud University, Nijmegen, The Netherlands

    Simona Samardjiska

  2. Universitá Politecnica delle Marche, Ancona, Italy

    Paolo Santini

  3. Florida Atlantic University, Boca Raton, USA

    Edoardo Persichetti

  4. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Gustavo Banegas

  5. Chalmers University of Technology, Gothenburg, Sweden

    Gustavo Banegas

Authors
  1. Simona Samardjiska
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  2. Paolo Santini
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  3. Edoardo Persichetti
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  4. Gustavo Banegas
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Corresponding author

Correspondence to Simona Samardjiska .

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Editors and Affiliations

  1. Radboud University Nijmegen, Nijmegen, The Netherlands

    Peter Schwabe

  2. Universidad de Santiago de Chile, Santiago, Chile

    Nicolas Thériault

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Samardjiska, S., Santini, P., Persichetti, E., Banegas, G. (2019). A Reaction Attack Against Cryptosystems Based on LRPC Codes. In: Schwabe, P., Thériault, N. (eds) Progress in Cryptology – LATINCRYPT 2019. LATINCRYPT 2019. Lecture Notes in Computer Science(), vol 11774. Springer, Cham. https://doi.org/10.1007/978-3-030-30530-7_10

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  • DOI: https://doi.org/10.1007/978-3-030-30530-7_10

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