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A Timing Attack on the HQC Encryption Scheme

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Selected Areas in Cryptography – SAC 2019 (SAC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11959))

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Abstract

The HQC public-key encryption scheme is a promising code-based submission to NIST’s post-quantum cryptography standardization process. The scheme is based on the decisional decoding problem for random quasi-cyclic codes. One problem of the HQC’s reference implementation submitted to NIST in the first round of the standardization process is that the decryption operation is not constant-time. In particular, the decryption time depends on the number of errors decoded by a BCH decoder. We use this to present the first timing attack against HQC. The attack is practical, requiring the attacker to record the decryption time of around 400 million ciphertexts for a set of HQC parameters corresponding to 128 bits of security. This makes the use of constant-time decoders mandatory for the scheme to be considered secure.

T. B. Paiva is supported by CAPES. R. Terada is supported by CNPq grant number 442014/2014-7.

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Notes

  1. 1.

    Here we present a slightly more general version of Guo’s et al. reconstruction algorithm that does not require the key’s spectrum to be completely determined, but the idea is the same.

  2. 2.

    This sentence remains valid if we substitute \(\mathbf {y} \) and \(\mathbf {r}_1\) by \(\mathbf {x} \) and \(\mathbf {r}_2\), respectively.

  3. 3.

    Recall that we use \((\gamma : m) \in \sigma (\mathbf {y})\) to denote that cyclic distance \(\gamma \) occurs m times between non-null entries of \(\mathbf {y}\).

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Acknowledgments

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. This research is part of the INCT of the Future Internet for Smart Cities funded by CNPq proc. 465446/2014-0, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001, FAPESP proc. 14/50937-1, and FAPESP proc. 15/24485-9.

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  1. Universidade de São Paulo, São Paulo, Brazil

    Thales Bandiera Paiva & Routo Terada

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  1. Thales Bandiera Paiva
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  2. Routo Terada
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Correspondence to Thales Bandiera Paiva .

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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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Paiva, T.B., Terada, R. (2020). A Timing Attack on the HQC Encryption Scheme. 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_22

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  • DOI: https://doi.org/10.1007/978-3-030-38471-5_22

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