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Quantum claw-finding attacks on 5-round Feistel structure and generalized Feistel schemes

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Abstract

Feistel structure is a fundamental symmetric cryptographic primitive. In this paper, we investigate the security of 5-round Feistel structure and generalized Feistel scheme (GFS) in a quantum environment and propose a family of quantum claw-finding attacks in both Q1 and Q2 models. The quantum attack uses claw-finding algorithm with the period function’s approximate promise. By employing the constructed functions g and h as inputs for claw-finding algorithm, secret information can be extracted. The attack on 5-round Feistel structure in Q1 model, which is easier to implement than Q2 model, enriched the diversity of the attack scenarios. The attacks on 5-round Feistel structure, Type-I, Type-II, and Type-III GFS in Q2 model, exhibit an exponentially lower product indicator for quantum and classical query complexity. The strongest reduction occurs in attacks on Type-I and Type-II GFS, decreasing from \(2^{4n}\) to \(2^{2n}\).

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Notes

  1. This paper follows the assumption of [13].

  2. The quantum truncation technology is used to partition the ciphertext state [11, 32].

  3. The classical truncation technology is used to partition the ciphertext state.

  4. The error probability of claw-finding algorithm is \( 1/3 \) [33], but the error probability for gold claw-finding problem is not explicitly determined [22].

  5. This requires the assumption that internal function exhibits strong randomness, as referenced in the original text [18] under Case I.

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Acknowledgements

Our deepest gratitude goes to the anonymous reviewers for their careful work and suggestions that have helped improve this paper substantially.

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Authors and Affiliations

  1. College of Computer Science and Technology, Harbin Engineering University, Harbin, 150001, China

    Xiaoning Feng & Hongyu Wu

  2. School of Mathematical Science, Heilongjiang University, Harbin, 150080, China

    Kejia Zhang

  3. State Key Laboratory of Public Big Data, GuiZhou University, Guiyang, 550025, China

    Kejia Zhang

  4. School of Computer and Big Data, Heilongjiang University, Harbin, 150080, China

    Hongwei Sun

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  1. Xiaoning Feng
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Feng. and Wu. wrote the main manuscript text. Zhang. and Sun. prepared figures 1-7. All authors reviewed the manuscript.

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Correspondence to Hongyu Wu.

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Feng, X., Wu, H., Zhang, K. et al. Quantum claw-finding attacks on 5-round Feistel structure and generalized Feistel schemes. Quantum Inf Process 24, 52 (2025). https://doi.org/10.1007/s11128-025-04671-3

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