Skip to main content

Advertisement

Springer Nature Link
Log in

A dynamic multiparty quantum direct secret sharing based on generalized GHZ states

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

This paper proposes a new dynamic multiparty quantum direct secret sharing (DQDSS) using mutually unbiased measurements based on generalized GHZ states. Without any unitary operations, an agent can obtain a shadow of the secret by simply performing a measurement on single photons. In the proposed scheme, multiple agents can be added or deleted and the shared secret need not be changed. Our DQDSS scheme has several advantages. The dealer is not required to retain any photons and can further share a predetermined key instead of a random key to the agents. Agents can update their shadows periodically, and the dealer does not need to be online. Furthermore, the proposed scheme can resist not only the existing attacks, but also cheating attacks from dishonest agents. Hence, compared to some famous DQSS schemes, the proposed scheme is more efficient and more practical. Finally, we establish a mathematical model about the efficiency and security of the scheme and perform simulation analyses with different parameters using MATLAB.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Smith, A.: Multi-party quantum computation. Arxiv Cornell University Library (2001)

  2. Liu, B., Xiao, D., Huang, W., et al.: Quantum private comparison employing single-photon interference. Quantum Inf. Process. 16, 180 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Tseng, H.Y., Lin, J., Hwang, T.: New quantum private comparison protocol using EPR pairs. Quantum Inf. Process. 11, 373–384 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Sharma, R.D., Thapliyal, K., Pathak, A.: Quantum sealed-bid auction using a modified scheme for multiparty circular quantum key agreement. Quantum Inf. Process. 16, 169 (2017)

    Article  ADS  MATH  Google Scholar 

  5. Gao, F., Liu, B., Huang, W., et al.: Postprocessing of the oblivious key in quantum private query. IEEE J. Sel. Top. Quantum Electron. 21, 98–108 (2014)

    ADS  Google Scholar 

  6. Huang, W., Wen, Q.Y., Liu, B., et al.: Robust and efficient quantum private comparison of equality with collective detection over collective-noise channels. Sci. China-Phys. Mech. Astron. 56, 1670–1678 (2013)

    Article  ADS  Google Scholar 

  7. Zhang, L., Sun, H.W., Zhang, K.J., et al.: An improved arbitrated quantum signature protocol based on the key-controlled chained CNOT encryption. Quantum Inf. Process. 16, 70 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Zeng, G., Keitel, C.H.: Arbitrated quantum-signature scheme. Phys. Rev. A 65, 042312 (2001)

    Article  ADS  Google Scholar 

  9. Hillery, M., Buzek, V., Berthiaunie, A.: Quantum secret sharing. Phys. Rev. A 59, 1829–1840 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. 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 

  11. Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162–168 (1999)

    Article  ADS  Google Scholar 

  12. Lu, H., et al.: Secret sharing of a quantum state. Phys. Rev. Lett. 117, 030501 (2016)

    Article  ADS  Google Scholar 

  13. Gao, X., Zhang, S., Chang, Y.: Cryptanalysis and improvement of the semi-quantum secret sharing protocol. Int. J. Theor. Phys. 56, 2512–2520 (2017)

    Article  MATH  Google Scholar 

  14. Matsumoto, R.: Unitary reconstruction of secret for stabilizer-based quantum secret sharing. Quantum Inf. Process. 16, 202 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Qin, H.W., Zhu, X.H., Dai, Y.W.: A proactive quantum secret sharing scheme based on GHZ state. Mod. Phys. Lett. B 29, 550165 (2015)

    Article  MathSciNet  Google Scholar 

  17. Yu, K.F., et al.: Multi-party semi-quantum key distribution-convertible multi-party semi-quantum secret sharing. Quantum Inf. Process. 16, 194 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Fiedler, L., Naaijkens, P., Osborne, T.J.: Jones index, secret sharing and total quantum dimension. New J. Phys. 19, 023039 (2017)

    Article  ADS  Google Scholar 

  19. Kogias, I., Xiang, Y., He, Q., et al.: Unconditional security of entanglement-based continuous-variable quantum secret sharing. Phys. Rev. A 95, 012315 (2017)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. Chen, X.B., Dou, Z., Xu, G., et al.: A kind of universal quantum secret sharing protocol. Sci. Rep. 7, 39845 (2017)

    Article  ADS  Google Scholar 

  22. Xu, T.T., Li, Z.H., et al.: A new improving quantum secret sharing scheme. Int. J. Theor. Phys. 56, 1–10 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Ahmadi, M., Wu, Y.D., Sanders, B.C.: Relativistic (2, 3)-threshold quantum secret sharing. Phys. Rev. D Part. Fields 96, 065018 (2017)

    Article  ADS  Google Scholar 

  24. Abulkasim, H., Hamad, S., et al.: Quantum secret sharing with identity authentication based on Bell states. Int. J. Quantum Inf. 15, 1750023 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  25. Hsu, J.L., Chong, S.K., Hwang, T., Tsai, C.W.: Dynamic quantum secret sharing. Quantum Inf. Process. 12, 331–344 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Jia, H.Y., Wen, Q.Y., Gao, F., et al.: Dynamic quantum secret sharing. Phys. Lett. A 376, 1035–1041 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Chen, Q., Chen, J., Wang, K., Du, J.: Efficient construction of two-dimensional cluster states with probabilistic quantum gates. Phys. Rev. A 73, 012303 (2006)

    Article  ADS  Google Scholar 

  28. Wang, T.Y., Li, Y.P.: Cryptanalysis of dynamic quantum secret sharing. Quantum Inf. Process. 12, 1991–1997 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  29. Liao, C.H., Yang, C.W., Hwang, T.: Dynamic quantum secret sharing protocol based on GHZ state. Quantum Inf. Process. 13, 1907–1916 (2014)

    Article  ADS  MATH  Google Scholar 

  30. Qin, H., Dai, Y.: Dynamic quantum secret sharing by using \(d\)-dimensional GHZ state. Quantum Inf. Process. 16, 64 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Shi, R.H., Mu, Y., Zhong, H., et al.: Secure multiparty quantum computation for summation and multiplication. Sci. Rep. 6, 19655 (2016)

    Article  ADS  Google Scholar 

  32. Vaccaro, J.A., Spring, J., Chefles, A.: Quantum protocols for anonymous voting and surveying. Phys. Rev. A 75, 10064–10070 (2007)

    Article  Google Scholar 

  33. Huang, W., Wen, Q.Y., Liu, B., et al.: Quantum anonymous ranking. Phys. Rev. A 89, 87–90 (2014)

    Google Scholar 

  34. Dolev, S., Pitowsky, I., Tamir, B.A.: Quantum secret ballot. Computer Science (2006)

  35. Pittenge, A.O., Rubin, M.H.: Mutually unbiased bases, generalized spin matrices and separability. Linear Algebra Appl. 390, 255–278 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  36. Jennewein, T., Simon, C., Weihs, G., et al.: Quantum cryptography with entangled photons. Phys. Rev. Lett. 84, 4729 (2000)

    Article  ADS  Google Scholar 

  37. Beveratos, A., Brouri, R., Gacoin, T., et al.: Single photon quantum cryptography. Phys. Rev. Lett. 89, 187901 (2002)

    Article  ADS  Google Scholar 

  38. Hughes, R.J., Nordholt, J.E., Derkacs, D., et al.: Practical free-space quantum key distribution over 10 km in daylight, and at night. New J. Phys. 4, 3283–3286 (2002)

    Article  Google Scholar 

  39. Gobby, C., Yuan, Z.L., Shields, A.J.: Quantum key distribution over 122 km of standard telecom fiber. Appl. Phys. Lett. 84, 3762–3764 (2004)

    Article  ADS  Google Scholar 

  40. Shi, R.H., Huang, L.S., Yang, W., et al.: Multiparty quantum secret sharing with Bell states and Bell. Opt. Commun. 283, 2476–2480 (2010)

    Article  ADS  Google Scholar 

  41. Gao, F., Guo, F.Z., Wen, Q.Y., et al.: Quantum key distribution without alternative measurements and rotations. Phys. Rev. A 349, 53–58 (2006)

    MATH  Google Scholar 

  42. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  43. Cai, Q.Y., Li, B.W.: Improving the capacity of the Boström–Felbinger protocol. Phys. Rev. A 69, 521–524 (2004)

    Article  Google Scholar 

  44. Barnum, H., Caves, C.M., Fuchs, C.A., et al.: Noncommuting mixed states cannot be broadcast. Phys. Rev. Lett. 76, 2818–2821 (1996)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous referees for their very valuable comments that enhance the quality of this paper. This work was supported by the National Natural Science Foundation of China (61602291, 61671280, 11671244) and China Postdoctoral Science Foundation (2018M633456).

Author information

Authors and Affiliations

  1. School of Computer Science, Shaanxi Normal University, Xi’an, 710062, China

    Yun Song & Yongming Li

  2. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Zhihui Li

Authors
  1. Yun Song
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Zhihui Li
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Yongming Li
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Yun Song.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Song, Y., Li, Z. & Li, Y. A dynamic multiparty quantum direct secret sharing based on generalized GHZ states. Quantum Inf Process 17, 244 (2018). https://doi.org/10.1007/s11128-018-1970-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-1970-2

Keywords