Skip to main content
Log in

Cryptanalysis and Improvement of a Multiparty Quantum Direct Secret Sharing of Classical Messages with Bell States and Bell Measurements

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Recently, a multiparty quantum direct secret sharing protocol with Bell states was presented (Song et al., Int. J Theor. Phys. 57, 1559, 2018). In this protocol, the secret message of the dealer is directly encoding into the transmitted particles. All agents obtain their pieces of secret by making Bell state measurement on their receiving particles, then cooperate to recover the dealer’s secret. However, as we show, this protocol is insecure, because an outside attacker or two special dishonest agents can eavesdrop the secret fully. Furthermore, an improved version of this protocol is proposed, which can stand against the presented attacks.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bennett, C.-H., Brassard, G.: Quantum cryptography: public-key distribution and coin tossing. In: Proc. IEEE Int. Conf. on Computers, Systems, and Signal Processing, Bangalore, India, pp 175–179 (1984)

  2. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Guo, G.P., Guo, G.C.: Quantum secret sharing without entanglement. Phys. Lett. A 310, 247 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. 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 

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

    Article  ADS  Google Scholar 

  9. Yan, F.-L., Gao, T.: Quantum secret sharing between multiparty and multiparty without entanglement. Phys. Rev. A 72, 012304 (2005)

    Article  ADS  Google Scholar 

  10. Yu, I.-C., Lin, F.-L., Huang, C.: Quantum secret sharing with multilevel mutually (un)biased bases. Phys. Rev. A 78, 012344 (2008)

    Article  ADS  Google Scholar 

  11. Lin, S., Wen, Q.-Y., Qin, S.-J., Zhu, F.-C.: Multiparty quantum secret sharing with collective eavesdropping-check. Opt. Commun. 282, 4455–4459 (2009)

    Article  ADS  Google Scholar 

  12. Li, Q., Chan, W.-H., Long, D.-Y.: Semiquantum secret sharing using entangled states. Phys. Rev. A 82, 022303 (2010)

    Article  ADS  Google Scholar 

  13. Yang, Y.-G., Teng, Y.-W., Chai, H.-P., Wen, Q.-Y.: Verifiable quantum (k,n)-threshold secret key sharing. Int. J Theor. Phys. 50, 792–798 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Shi, R.-H., Huang, L.-S., Yang, W., Zhong, H.: Multi-party quantum state sharing of an arbitrary two-qubit state with Bell states. Quantum Inf Process 10, 231–239 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  15. Gu, B., Xu, F., Ding, L.-G., Zhang, Y.-A.: High-capacity three-party quantum secret sharing with hyperentanglement. Int. J Theor. Phys. 51, 3559–3566 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. Chen, X.-B., Dou, Z., Xu, G., He, X.-Y., Yang, Y.-X.: A kind of universal quantum secret sharing protocol. Sci. Rep. 7, 39845 (2017)

    Article  ADS  Google Scholar 

  19. Yang, X.-Q., Wei, K.-J., Ma, H.-Q., Liu, H.-W., Yin, Z.-Q., Cao, Z., Wu, L.-A.: Detector-device-independent quantum secret sharing with source flaws. Sci. Rep. 8, 5728 (2018)

    Article  ADS  Google Scholar 

  20. Qin, H. -W., Tso, R.: Threshold quantum state sharing based on entanglement swapping. Quantum Inf Process. 17, 142 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Song, Y., Li, Y., Wang, W.: Multiparty quantum direct secret sharing of classical information with Bell states and Bell measurements. Int. J Theor. Phys. 57, 1559 (2018)

    Article  MATH  Google Scholar 

  22. Gao, F., Qin, S.-J., Wen, Q.-Y., Zhu, F.-C.: A simple participant attack on the Bradler-Dusek protocol. Quan. Infor. Comp. 7, 329 (2007)

    MathSciNet  MATH  Google Scholar 

  23. Qin, S.-J., Gao, F., Wen, Q.-Y., Zhu, F.-C.: Cryptanalysis of the Hillery-Buzek-Berthiaume quantum secret-sharing protocol. Phys. Rev. A 76, 062324 (2007)

    Article  ADS  Google Scholar 

  24. Guo, F.-Z., Qin, S.-J., Gao, F., Lin, S., Wen, Q.-Y., Zhu, F.: Participant attack on a kind of MQSS schemes based on entanglement swapping. Eur. Phys. J D 56, 445–448 (2010)

    Article  ADS  Google Scholar 

  25. Zhang, K.-J., Qin, S.-J.: The cryptanalysis of Yuan others.’s multiparty quantum secret sharing protocol. Int. J Theor. Phys. 52, 3953 (2013)

    Article  MATH  Google Scholar 

  26. Liu, F., Su, Q., Wen, Q.-Y.: Eavesdropping on multiparty quantum secret sharing scheme based on the phase shift operations. Int. J Theor. Phys. 53, 1730 (2014)

    Article  MATH  Google Scholar 

  27. Lin, S., Guo, G.-D., Xu, Y.-Z., Sun, Y., Liu, X.-F.: Cryptanalysis of quantum secret sharing with d-level single particles. Phys. Rev. A 93, 062343 (2016)

    Article  ADS  Google Scholar 

  28. Wang, T.-Y., Liu, Y.-Z., Wei, C.-Y., Cai, X.-Q., Ma, J.-F.: Security of a kind of quantum secret sharing with entangled states. Sci. Rep. 7, 2485 (2017)

    Article  ADS  Google Scholar 

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

    Article  MATH  Google Scholar 

  30. Chen, X.-B., Tang, X., Xu, G., Dou, Z., Chen, Y.-L., Yang, Y.-X.: Cryptanalysis of secret sharing with a single d-level quantum system. Quan. Inf Process 17, 225 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Lo, H.K., Ko, T.M.: Some attacks on quantum-based cryptographic protocols. Quan. Inf. Comput. 5, 40–47 (2005)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiao-Fen Liu.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 61772134), China Postdoctoral Science Foundation Funded Project (Grant No. 2016M600494), Fujian Province Natural Science Foundation (Grant Nos. 2016J01288, 2018J01776, and 2018J01775), and Foundation of Fujian Education Bureau (Grant No. JA15131).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, XF. Cryptanalysis and Improvement of a Multiparty Quantum Direct Secret Sharing of Classical Messages with Bell States and Bell Measurements. Int J Theor Phys 58, 713–718 (2019). https://doi.org/10.1007/s10773-018-3969-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-018-3969-y

Keywords

Navigation