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Rational quantum secret sharing scheme based on GHZ state

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Abstract

In this paper, a new rational quantum secret sharing scheme based on GHZ state is proposed. It realizes the secret sharing among n agents by encoding the secret with the link between measurement base and measurement result. Comprehensive security analysis shows that our presented scheme can defend eavesdropping attack, entanglement attack and collusion attack. Moreover, it is also proved that the new protocol can achieve correctness, fairness, strict Nash equilibrium and k-resilient equilibrium, which are required by rational secret sharing protocol. Compared with the existing rational quantum secret sharing schemes, our scheme is simple and can achieve stronger balance. Besides, it is feasible in practical application since a relevant protocol has been recently implemented on the IBM quantum computer.

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References

  1. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  2. Blakley, G.R.: Safeguarding cryptographic keys. In: managing requirements knowledge, International Workshop On, pp. 313–313 (1979). IEEE Computer Society

  3. Benaloh, J., Leichter, J.: Generalized secret sharing and monotone functions. In: Conference on the Theory and Application of Cryptography, pp. 27–35 (1988). Springer

  4. Brickell, E.F.: Some ideal secret sharing schemes. In: Workshop on the Theory and Application of of Cryptographic Techniques, pp. 468–475 (1989). Springer

  5. Stinson, D.R.: An explication of secret sharing schemes. Des., Codes Cryptogr. 2(4), 357–390 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  6. Stinson, D.R.: Decomposition constructions for secret-sharing schemes. IEEE Trans. Inf. Theor. 40(1), 118–125 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  7. Farràs, O., Martí-Farré, J., Padró, C.: Ideal multipartite secret sharing schemes. J. Cryptol. 25(3), 434–463 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Rauh, J.: Secret sharing and shared information. Entropy 19(11), 601 (2017)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Cleve, R., Gottesman, D., Lo, H.-K.: How to share a quantum secret. Phys. Rev. Lett. 83(3), 648 (1999)

    Article  ADS  Google Scholar 

  11. Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61(4), 042311 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  12. Tittel, W., Zbinden, H., Gisin, N.: Experimental demonstration of quantum secret sharing. Phys. Rev. A 63(4), 042301 (2001)

    Article  ADS  Google Scholar 

  13. Hsu, L.-Y., Li, C.-M.: Quantum secret sharing using product states. Phys. Rev. A 71(2), 022321 (2005)

    Article  ADS  Google Scholar 

  14. Li, X.-H., Zhou, P., Li, C.-Y., Zhou, H.-Y., Deng, F.-G.: Efficient symmetric multiparty quantum state sharing of an arbitrary m-qubit state. J. Phys. B: Atomic, Mol. Opt. Phys. 39(8), 1975 (2006)

    Article  ADS  Google Scholar 

  15. Xiao, L., Long, G.L., Deng, F.-G., Pan, J.-W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69(5), 052307 (2004)

    Article  ADS  Google Scholar 

  16. Tsai, C., Hwang, T.: Multi-party quantum secret sharing based on two special entangled states. Sci. China Phys., Mech. Astron. 55(3), 460–464 (2012)

    Article  ADS  Google Scholar 

  17. Lau, H.-K., Weedbrook, C.: Quantum secret sharing with continuous-variable cluster states. Phys. Rev. A 88(4), 042313 (2013)

    Article  ADS  Google Scholar 

  18. Gao, G.: Secure multiparty quantum secret sharing with the collective eavesdropping-check character. Q. Inf. Process. 12(1), 55–68 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  19. Liao, C.-H., Yang, C.-W., Hwang, T.: Dynamic quantum secret sharing protocol based on ghz state. Q. Inf. Process. 13(8), 1907–1916 (2014)

    Article  MATH  Google Scholar 

  20. Liu, F., Qin, S.-J., Wen, Q.-Y.: A quantum secret-sharing protocol with fairness. Phys. Scripta 89(7), 075104 (2014)

    Article  ADS  Google Scholar 

  21. Chen, R.-K., Zhang, Y.-Y., Shi, J.-H., Li, F.-G.: A multiparty error-correcting method for quantum secret sharing. Q. Inf. Process. 13(1), 21–31 (2014)

    Article  MATH  Google Scholar 

  22. Karimipour, V., Asoudeh, M.: Quantum secret sharing and random hopping: using single states instead of entanglement. Phys. Rev. A 92(3), 030301 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  23. Rahaman, R., Parker, M.G.: Quantum scheme for secret sharing based on local distinguishability. Phys. Rev. A 91(2), 022330 (2015)

    Article  ADS  Google Scholar 

  24. Tavakoli, A., Herbauts, I., Żukowski, M., Bourennane, M.: Secret sharing with a single d-level quantum system. Phys. Rev. A 92(3), 030302 (2015)

    Article  ADS  Google Scholar 

  25. Lu, H., Zhang, Z., Chen, L.-K., Li, Z.-D., Liu, C., Li, L., Liu, N.-L., Ma, X., Chen, Y.-A., Pan, J.-W.: Secret sharing of a quantum state. Phys. Rev. Lett. 117(3), 030501 (2016)

    Article  ADS  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. Dou, Z., Xu, G., Chen, X.-B., Niu, X.-X., Yang, Y.-X., Yang, Y.: Searching for optimal quantum secret sharing scheme based on local distinguishability. Q. Inf. Process. 19(10), 1–19 (2020)

    MathSciNet  MATH  Google Scholar 

  28. Joy, D., Sabir, M., Behera, B.K., Panigrahi, P.K.: Implementation of quantum secret sharing and quantum binary voting protocol in the ibm quantum computer. Q. Inf. Process. 19(1), 1–20 (2020)

    MathSciNet  MATH  Google Scholar 

  29. Halpern, J., Teague, V.: Rational secret sharing and multiparty computation. In: Proceedings of the Thirty-sixth Annual ACM Symposium on Theory of Computing, pp. 623–632 (2004)

  30. Maitra, A., De, S.J., Paul, G., Pal, A.K.: Proposal for quantum rational secret sharing. Phys. Rev. A 92(2), 022305 (2015)

    Article  ADS  Google Scholar 

  31. Dou, Z., Xu, G., Chen, X.-B., Liu, X., Yang, Y.-X.: A secure rational quantum state sharing protocol. Sci. China Inf. Sci. 61(2), 1–12 (2018)

    Article  MathSciNet  Google Scholar 

  32. Qin, H., Tang, W.K., Tso, R.: Rational quantum secret sharing. Scientif. Rep. 8(1), 1–7 (2018)

    Google Scholar 

  33. Fu, Y., Yin, H.-L., Chen, T.-Y., Chen, Z.-B.: Long-distance measurement-device-independent multiparty quantum communication. Phys. Rev. Lett. 114(9), 090501 (2015)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  35. Wei, Y., Wang, S., Zhu, Y., Li, T.: Sender-controlled measurement-device-independent multiparty quantum communication. Front. Phys. 17(2), 1–9 (2022)

    Article  Google Scholar 

  36. Abraham, I., Dolev, D., Gonen, R., Halpern, J.: Distributed computing meets game theory: robust mechanisms for rational secret sharing and multiparty computation. In: Proceedings of the Twenty-fifth Annual ACM Symposium on Principles of Distributed Computing, pp. 53–62 (2006)

  37. Asharov, G., Lindell, Y.: Utility dependence in correct and fair rational secret sharing. J. Cryptol. 24(1), 157–202 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work is supported by the Youth project of Fujian Provincial Department of Education under Grant No. JAT170142, National Natural Science Foundation of China under Grant No. 61972095,62072104, 62171131,82072043, General projects of Fujian provincial fund under Grant No. 2020J01159, Guiding project of science and Technology Department of Fujian Province under Grander No. 2019H0010.

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Authors and Affiliations

  1. College of Computer and Cyber Security, Fujian Normal University, Fuzhou, 350108, China

    Xiaodong Zhang, Lili Wang, Song Lin, Ning Wang & Linjian Hong

  2. School of Information Science and Technology, Zhengzhou Normal University, Zhengzhou City, 450044, China

    Ning Wang

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  1. Xiaodong Zhang
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  2. Lili Wang
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  3. Song Lin
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Correspondence to Lili Wang.

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Zhang, X., Wang, L., Lin, S. et al. Rational quantum secret sharing scheme based on GHZ state. Quantum Inf Process 22, 91 (2023). https://doi.org/10.1007/s11128-022-03739-8

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