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Quantum secret sharing for a class of special hypergraph access structures

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Abstract

In this paper, we study a class of special hypergraph access structures. According to this structure, we construct a group of orthogonal multipartite entangled states in n-dimensional system and investigate the distinguishability of these entangled states under restricted local operations and classical communication. Based on these properties, we propose a quantum secret sharing scheme. In the proposed protocol, the participants measure these orthogonal states by the computational basis and use all measurements by the adder modulo n to distinguish these states. Through the above process, participants in the authorized set can obtain the original information encoded in the quantum states. Furthermore, we also analyze the security of our scheme in four primary quantum attacks.

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Data Availability Statement

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

References

  1. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612 (1979)

    Article  MathSciNet  Google Scholar 

  2. Blakley, G.R.: In: Proceedings of the National Computer Conference (AFIPS, 1979), pp. 313–317 (1979)

  3. Hillery, M., Buzek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  4. Cleve, R., Gottesman, D., Lo, H.-K.: How to share a quantum secret. Phys. Rev. Lett. 83, 648 (1999)

    Article  ADS  Google Scholar 

  5. Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61, 042311 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  6. Deng, F.G., Zhou, H.Y., Long, G.L.: Circular quantum secret sharing. J. Phys. A Math. Gen. 39, 14089–14099 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  7. Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162 (1999)

    Article  ADS  Google Scholar 

  8. Xiao, L., Long, G.L., Deng, F.G., Pan, J.W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69, 052307 (2004)

    Article  ADS  Google Scholar 

  9. Qin, H.W., Zhu, X.H., Dai, Y.W.: \((t,n)\) Threshold quantum secret sharing using the phase shift operation. Quantum Inf. Process. 14, 2997–3004 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  10. Hsu, L.Y., Li, C.W.: Quantum secret sharing using product states. Phys. Rev. A 71, 022321 (2005)

    Article  ADS  Google Scholar 

  11. Maitra, A., De, S.J., Paul, G., Pal, A.K.: Proposal for quantum rational secret sharing. Phys. Rev. A 92, 022305 (2015)

    Article  ADS  Google Scholar 

  12. Sarvepalli, P., Raussendorf, R.: Matroids and quantum-secret-sharing schemes. Phys. Rev. A 81, 052333 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  13. Lin, S., Guo, G.D., Xu, Y.Z., et al.: Cryptanalysis of quantum secret sharing with d-level single particles. Phys. Rev. A 93(6), 062343 (2016)

    Article  ADS  Google Scholar 

  14. Qin, H., Tso, R., Dai, Y.: Quantum secret sharing by using Fourier transform on orbital angular momentum. IET Inf. Secur. 13(2), 104–108 (2018)

    Article  Google Scholar 

  15. Grice, W.P., Qi, B.: Quantum secret sharing using weak coherent states. Phys. Rev. A 100, 022339 (2019)

    Article  ADS  Google Scholar 

  16. Wu, X., Wang, Y., Huang, D.: Passive continuous-variable quantum secret sharing using a thermal source. Phys. Rev. A 101(2), 022301 (2020)

    Article  ADS  Google Scholar 

  17. Liao, Q., Liu, H., Zhu, L., et al.: Quantum secret sharing using discretely modulated coherent states. Phys. Rev. A 103(3), 032410 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  18. Roy, S., Mukhopadhyay, S.: Device-independent quantum secret sharing in arbitrary even dimensions. Phys. Rev. A 100, 012319 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  19. Moreno, M.G.M., Brito, S., Nery, R.V., Chaves, R.: Device-independent secret sharing and a stronger form of Bell nonlocality. Phys. Rev. A 101, 052339 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  20. Gao, Z.K., Li, T., Li, Z.H.: Deterministic measurement-device-independent quantum secret sharing. Sci. China Phys. Mech. Astron. 63(12), 1–8 (2020)

    Article  Google Scholar 

  21. Lipinska, V., Murta, G., Ribeiro, J., Wehner, S.: Verifiable hybrid secret sharing with few qubits. Phys. Rev. A 101, 032332 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  22. Gheorghiu, V., Sanders, B.C.: Accessing quantum secrets via local operations and classical communication. Phys. Rev. A 88(2), 022340 (2013)

    Article  ADS  Google Scholar 

  23. Rahaman, R., Parker, M.G.: Quantum scheme for secret sharing based on local distinguishability. Phys. Rev. A 91, 022330 (2015)

    Article  ADS  Google Scholar 

  24. Yang, Y.H., Gao, F., Wu, X., et al.: Quantum secret sharing via local operations and classical communication. Sci. Rep. 5, 16967 (2015)

    Article  ADS  Google Scholar 

  25. Bai, C.M., Li, Z.H., Xu, T.T., et al.: Quantum secret sharing using the d-dimensional GHZ state. Quantum Inf. Process. 16, 59 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  26. Wang, J., Li, L., Peng, H., Yang, Y.: Quantum-secret-sharing scheme based on local distinguishability of orthogonal multiqudit entangled states. Phys. Rev. A 95(2), 022320 (2017)

    Article  ADS  Google Scholar 

  27. Bai, C.M., Li, Z.H., Liu, C.J., et al.: Quantum secret sharing using orthogonal multiqudit entangled states. Quantum Inf. Process. 16, 304 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  28. Bai, C.M., Li, Z.H., Wang, J.T., et al.: Restricted (k, n)-threshold quantum secret sharing scheme based on local distinguishability of orthogonal multiqudit entangled states. Quantum Inf. Process. 17(11), 312 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  29. Bai, C.M., Zhang, S.J., Liu, L.: \((t,n)\)-threshold quantum secret sharing based on one-way local distinguishability. IEEE Access 7, 147256–147265 (2019)

    Article  Google Scholar 

  30. Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)

    Article  ADS  Google Scholar 

  31. Li, C.Y., Zhou, H.Y., Wang, Y., Deng, F.G.: Secure quantum key distribution network with Bell states and local unitary operations. Chin. Phys. Lett. 22, 1049 (2005)

    Article  ADS  Google Scholar 

  32. Li, C.Y., Li, X.H., Deng, F.G., et al.: Efficient quantum cryptography network without entanglement and quantum memory. Chin. Phys. Lett. 23, 2896 (2006)

    Article  ADS  Google Scholar 

  33. Deng, F.G., Long, G.L., Wang, Y., Xiao, L.: Increasing the efficiencies of random-choice-based quantum communication protocols with delayed measurement. Chin. Phys. Lett. 21, 2097 (2004)

    Article  ADS  Google Scholar 

  34. Giovanni, D.C., Clemente, G.: Hypergraph decomposition and secret sharing. Discrete Appl. Math. 157(5), 928–946 (2009)

    Article  MathSciNet  Google Scholar 

  35. Deng, F., Li, X., Zhou, H., Zhang, Z.: Improving the security of multiparty quantum secret sharing against Trojan horse attack. Phys. Rev. A 72(4), 044302 (2005)

    Article  ADS  Google Scholar 

  36. Li, X.H., Deng, F.G., Zhou, H.Y.: Improving the security of secure direct communication based on the secret transmitting order of particles. Phys. Rev. A 74, 054302 (2006)

    Article  ADS  Google Scholar 

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Acknowledgements

We want to express our gratitude to anonymous referees for their valuable and constructive comments. This work was sponsored by Hebei Natural Science Foundation of China under Grant No. A2019210057, and the National Natural Science Foundation of China under Grant No. 12001480.

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Authors and Affiliations

  1. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Chen-Ming Bai, Sujuan Zhang & Lu Liu

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  1. Chen-Ming Bai
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  2. Sujuan Zhang
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  3. Lu Liu
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Correspondence to Chen-Ming Bai.

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Bai, CM., Zhang, S. & Liu, L. Quantum secret sharing for a class of special hypergraph access structures. Quantum Inf Process 21, 119 (2022). https://doi.org/10.1007/s11128-022-03425-9

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