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Quantum zero correlation linear cryptanalysis

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Abstract

The advent of large-scale quantum computers would greatly threaten the security of current cryptosystems. It is urgent to investigate how quantum computing will affect the security of symmetric cryptosystems. Since the security of symmetric schemes heavily depends on the development of cryptanalytic tools, studying the applications of quantum algorithms to classical cryptanalytic tools is critical. To this end, we study quantum zero correlation linear cryptanalysis and propose two quantum algorithms for finding zero correlation linear hulls of Feistel ciphers and SPN ciphers, respectively. We prove that, as long as the attacked block ciphers satisfy certain algebraic conditions, the linear approximations output by the proposed algorithms have zero correlation with a probability close to one. The proposed algorithms have polynomial-time quantum complexity and do not require any quantum or classical query to the attacked block ciphers. Compared to the classical zero correlation linear cryptanalysis, the quantum version has the advantage for extending the number of rounds of zero correlation linear approximations.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request

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Acknowledgements

This work was funded by National Defense Basic Research Program of China (Grant No. JCKY2019102C001), the Open Research Fund of Key Laboratory of Cryptography of Zhejiang Province (Grant No. ZCL21012) and the Fundamental Research Funds for the Central Universities (Grant No. 328201915).

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Authors and Affiliations

  1. School of Cyberspace Security, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Rui Shi

  2. Key Laboratory of Cryptography of Zhejiang Province, Hangzhou Normal University, Hangzhou, 311121, China

    Rui Shi & Huiqin Xie

  3. Beijing Electronic Science and Technology Institute, Beijing, 100070, China

    Rui Shi, Huiqin Xie, Huamin Feng & Biao Liu

  4. Institute 706, Second Academy of China Aerospace Science and Industry Corporation Limited, Beijing, 100854, China

    Feng Yuan

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  1. Rui Shi
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  2. Huiqin Xie
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  4. Feng Yuan
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  5. Biao Liu
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Correspondence to Huiqin Xie.

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Shi, R., Xie, H., Feng, H. et al. Quantum zero correlation linear cryptanalysis. Quantum Inf Process 21, 293 (2022). https://doi.org/10.1007/s11128-022-03642-2

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  • DOI: https://doi.org/10.1007/s11128-022-03642-2

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