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Quantum meet-in-the-middle attack on Feistel construction

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Abstract

Inspired by Hosoyamada and Sasaki (in: International conference on security and cryptography for networks, pp 386–403. Springer, 2018), we propose a new quantum meet-in-the-middle (QMITM) attack on r-round (\(r \ge 7\)) Feistel construction to reduce the time complexity, which is based on Guo et al. (Des Codes Cryptogr 80(3):587–618, 2016) classical meet-in-the-middle (MITM) attack. In our attack, we adjust the size of truncated differentials to balance the complexities between constructing the tables and querying firstly and introduce a quantum claw finding algorithm to solve the collision search problem in classical MITM attack. The total time complexities of our attack are only \(O({2^{2n/3}} \cdot n)\), \(O({2^{19n/24}} \cdot n)\) and \(O({2^{(r - 5)n/4}} \cdot n)\), when \(r = 7\), \(r = 8\) and \(r > 8\), lower than classical and quantum attacks. Moreover, our attack belongs to Q1 model and is more practical than other quantum attacks.

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Acknowledgements

This work was supported by the Open Fund of Advanced Cryptography and System Security Key Laboratory of Sichuan Province (Grant No. SKLACSS-202103), BUPT Excellent Ph.D. Students Foundation (CX2022140) and the 13th Five-Year Plan National Cryptography Development Fund (MMJJ20180217).

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Authors and Affiliations

  1. State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Yinsong Xu & Zheng Yuan

  2. Advanced Cryptography and System Security Key Laboratory of Sichuan Province, Chengdu, 610103, China

    Yinsong Xu & Zheng Yuan

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

    Yinsong Xu & Zheng Yuan

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  1. Yinsong Xu
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Xu, Y., Yuan, Z. Quantum meet-in-the-middle attack on Feistel construction. Quantum Inf Process 22, 155 (2023). https://doi.org/10.1007/s11128-022-03715-2

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