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A rational hierarchical (t,n)-threshold quantum secret sharing scheme

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Abstract

Quantum secret sharing plays a crucial role in quantum cryptography. In this paper, we present a rational hierarchical (t,n)-threshold quantum secret sharing scheme based on Lagrange interpolation. In our scheme, participants possess rational and hierarchical properties, and the secret can be reconstructed when the number of rational participants satisfies the hierarchical (t,n)-threshold structure proposed in this paper. The reconstructed secret can encompass both classical information and quantum state information, enhancing the practicality and flexibility of our scheme compared to existing ones. Additionally, we redefine the utility of participants based on their roles in the secret recovery process. This newly defined utility allows for a more precise analysis of the correctness, fairness, and equilibrium of our scheme. Finally, our scheme not only resists a typical set of external attacks but also incorporates mechanisms to detect forgery and collusion among participants.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (No.U21A20428, No.61972126, No.12171134).

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Authors and Affiliations

  1. School of Mathematics, HeFei University of Technology, Hefei, 230009, China

    Fulin Li, Zhuo Liu, Li Liu & Shixin Zhu

  2. Intelligent Interconnected Systems Laboratory of Anhui Province, Hefei, China

    Fulin Li & Shixin Zhu

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  1. Fulin Li
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  2. Zhuo Liu
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  3. Li Liu
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  4. Shixin Zhu
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Contributions

FL, ZL and SZ have written this paper and have done the research which supports it. FL and ZL have collaborated in the conception, research and design of the paper. SZ and LL have collaborated in the language polishment and the typesetting. Above all authors have tried best to review the manuscript carefully.

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Correspondence to Fulin Li.

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This research was supported by the National Natural Science Foundation of China (Nos. U21A20428, 61972126, 12171134).

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Li, F., Liu, Z., Liu, L. et al. A rational hierarchical (t,n)-threshold quantum secret sharing scheme. Quantum Inf Process 23, 60 (2024). https://doi.org/10.1007/s11128-024-04269-1

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