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Standard (k, n)-threshold hierarchical quantum secret sharing

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Abstract

Hierarchical quantum secret sharing has important theoretical value and realistic significance in quantum secret sharing schemes. In order to expand the access structure of participants and improve the performance of schemes, this paper presents a standard (k, n)-threshold hierarchical quantum secret sharing scheme. Firstly, we construct a specific pair of orthogonal entangled states and use their local distinguishable property to achieve the standard (k, n)-threshold structure at each level in the hierarchy, which not only enhances the practical value of hierarchical quantum secret sharing schemes, but also reduces the computational expenses. Secondly, our scheme does not require any quantum operations to recover the secret during the reconstruction phase, which greatly reduces the quantum computational complexity. Finally, performance analysis shows that our scheme owns higher information efficiency compared with the existing schemes. Security analysis shows that our scheme is resistant to not only a series of typical external attacks but also both personal attacks from dishonest internal participants and collusion attacks.

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Acknowledgements

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

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Authors and Affiliations

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

    Fulin Li, Qingao Wu & Shixin Zhu

  2. College of Mathematics and Physics, Xinjiang Agricultural University, Ürümqi, 830052, China

    Fulin Li

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

    Shixin Zhu

  4. School of Mathematics and Statistics, Key Laboratory of Analytical Mathematics and Applications (Ministry of Education), Fujian Normal University, Fuzhou, 350117, China

    Changlu Lin

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  1. Fulin Li
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  2. Qingao Wu
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Contributions

FL and QW provide initial research ideas and theoretical support and write and revise the first draft of this paper. CL is responsible for the overall design and direction of the entire research program, providing important guidance and advice during the research process, as well as comprehensive evaluation and interpretation of the research methodology and experimental results. In addition, they deeply scrutinize and evaluate the background literature and related work of the study, and comprehensively sort out and revise the overall structure and details of this paper. SZ provides a series of important information as well as financial support.

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Correspondence to Qingao Wu.

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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., Wu, Q., Lin, C. et al. Standard (k, n)-threshold hierarchical quantum secret sharing. Quantum Inf Process 23, 168 (2024). https://doi.org/10.1007/s11128-024-04378-x

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