Skip to main content
SpringerLink
Log in

Improving the security of protocols of quantum key agreement solely using Bell states and Bell measurement

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In a recent study, Shukla et al. (Quantum Inf Process 13:2391–2405, 2014) proposed two quantum key agreement protocols based on Bell state and Bell measurement, and they claimed that their two protocols were secure. However, in this study, we will show that the three-party protocol they proposed is not secure. Any participant in the protocol can directly obtain other two participants’ secret keys. More seriously, two dishonest participants in the protocol can conclude to determine the shared key alone. Furthermore, we will show that there is another minor flaw in their two protocols; that is, eavesdroppers can flip any bit of the final key without introducing any error. In the end, some possible improvements are proposed to avoid these flaws.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Zhou, N., Zeng, G., Xiong, J.: Quantum key agreement protocol. Electron. Lett. 40, 1149 (2004)

    Article  Google Scholar 

  2. Diffie, W., Hellman, M.: New directions in cryptography. IEEE Trans. Inf. Theory 22, 644–654 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  3. Ingemarsson, I., Tang, D.T., Wong, C.K.: A conference key distribution system. IEEE Trans. Inf. Theory 28, 714–719 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  4. Burmester, M., Desmedt, Y.: A secure and efficient conference key distribution system. In: Advances in Cryptology-Eurocrypt’94, pp. 275–286. Springer, Berlin (1994)

  5. Steiner, M., Tsudik, G., Waidner, M.: Key agreement in dynamic peer groups. IEEE Trans. Parallel Distrib. Syst. 11, 769–780 (2000)

    Article  Google Scholar 

  6. Bellare, M., Canetti, R., Krawczyk, H.: A modular approach to the design and analysis of authentication and key exchange protocols. In: Proceedings of the 30th Annual Symposium on the Theory of Computing, pp. 419–428. ACM, New York (1998)

  7. Bellare, M., Pointcheval, D., Rogaway, P.: Authenticated key exchange secure against dictionary attacks. In: Advances in Cryptology-Eurocrypt’00, pp. 139–155. Springer, Berlin (2000)

  8. Bellare, M., Rogaway, P.: Entity authentication and key distribution. In: Advances in Cryptology-Crypto’93, pp. 232-249. Springer, Berlin (1993)

  9. Bellare, M., Rogaway, P.: Provably secure session key distribution-the three party case. In: Proceedings of the 27th Annual ACM Symposium on Theory of Computing, pp. 57–66. ACM, New York (1995)

  10. Blake-Wilson, S., Johnson, D., Menezes, A.: Key agreement protocols and their security analysis. In: Proceedings of 6th IMA International Conference on Cryptography and Coding, pp. 30–45. Springer, Berlin (1997)

  11. Kudla, C.: Paterson, K.G.: Modular security proofs for key agreement protocols. In: Advances in Cryptology-Asiacrypt’05, pp. 549–565. Springer, Berlin (2005)

  12. Chong, S.K., Hwang, T.: Quantum key agreement protocol based on BB84. Opt. Commun. 283, 1192 (2010)

    Article  ADS  Google Scholar 

  13. Shi, R.H., Zhong, H.: Multi-party quantum key agreement with bell states and bell measurements. Quantum Inf. Process. 12, 921 (2013)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. Liu, B., Gao, F., Huang, W., Wen, Q.Y.: Multiparty quantum key agreement with single particles. Quantum Inf. Process. 12, 1797 (2013)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. Yin, X.R., Ma, W.P., Liu, W.Y.: Three-party quantum key agreement with two-photon entanglement. Int. J. Theor. Phys. 52, 3915 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  16. Huang, W., Wen, Q.Y., Liu, B., Gao, F., Sun, Y.: Quantum key agreement with EPR pairs and single-particle measurements. Quantum Inf. Process. 13, 649 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  17. Huang, W., Su, Q., Wu, X., Li, Y.B., Sun, Y.: Quantum key agreement against collective decoherence. Int. J. Theor. Phys. 53, 2891 (2014)

    Article  MATH  Google Scholar 

  18. Xu, G.B., Wen, Q.Y., Gao, F., Qin, S.J.: Novel multiparty quantum key agreement protocol with GHZ states. Quantum Inf. Process. 13, 2587 (2014)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  19. Gao, F., Qin, S.J., Guo, F.Z., Wen, Q.Y.: Cryptanalysis of the arbitrated quantum signature protocols. Phys. Rev. A 84, 022344 (2011)

    Article  ADS  Google Scholar 

  20. Zhang, Y.S., Li, C.F., Guo, G.C.: Comment on “quantum key distribution without alternative measurements” [Phys. Rev. A 61, 052312 (2000)]. Phys. Rev. A 63, 036301 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  21. Wójcik, A.: Eavesdropping on the “ping-pong” quantum communication protocol. Phys. Rev. Lett. 90, 157901 (2003)

    Article  ADS  Google Scholar 

  22. Cai, Q.Y.: The “ping-pong” protocol can be attacked without eavesdropping. Phys. Rev. Lett. 91, 109801 (2003)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  24. Gao, F., Qin, S.J., Wen, Q.Y., Zhu, F.C.: A simple participant attack on the brádler-dušek protocol. Quantum Inf. Comput. 7, 329 (2007)

    MATH  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. Gao, F., Wen, Q.Y., Zhu, F.C.: Comment on: “quantum exam” [Phys. Lett. A 350 (2006) 174]. Phys. Lett. A 360, 748 (2007)

    Article  ADS  Google Scholar 

  27. Gao, F., Guo, F.Z., Wen, Q.Y., Zhu, F.C.: Comment on “experimental demonstration of a quantum protocol for Byzantine agreement and Liar detection”. Phys. Rev. Lett. 101, 208901 (2008)

    Article  ADS  Google Scholar 

  28. Song, T.T., Zhang, J., Gao, F., Wen, Q.Y., Zhu, F.C.: Participant attack on quantum secret sharing based on entanglement swapping. Chin. Phys. B 18, 1333 (2009)

    Article  ADS  Google Scholar 

  29. Gao, F., Qin, S.J., Wen, Q.Y., Zhu, F.C.: Cryptanalysis of multiparty controlled quantum secure direct communication using Greenberger–Horne–Zeilinger state. Opt. Commun. 283, 192 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Shukla, C., Alam, N., Pathak, A.: Protocols of quantum key agreement solely using Bell states and Bell measurement. Quantum Inf. Process. 13, 2391 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  32. Sun, Z.W., Zhang, C., Wang, B.H., Li, Q., Long, D.Y.: Improvements on “multiparty quantum key agreement with single particles”. Quantum Inf. Process. 12, 3411 (2013)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  33. Bennett, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, pp. 175-179. IEEE, New York (1984) [Bennett, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. Theor. Comput. Sci. 560, 7 (2014)]

  34. Gottesman, D., Lo, H.K.: Proof of security of quantum key distribution with two-way classical communications. IEEE Trans. Inf. Theory 49, 457–475 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  35. Shukla, C., Pathak, A., Srikanth, R.: Beyond the Goldenberg–Vaidman protocol: secure and efficient quantum communication using arbitrary, orthogonal, multi-particle quantum states. Int. J. Quantum Inf. 10, 1241009 (2012)

    Article  MathSciNet  Google Scholar 

  36. Yadav, P., Srikanth, R., Pathak, A.: Two-step orthogonal-state-based protocol of quantum secure direct communication with the help of order-rearrangement technique. Quantum Inf. Process. 13, 2731 (2014)

    Article  MATH  MathSciNet  ADS  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous reviewers and editor for their comments that improved the quality of this paper. This work is supported by the National Science Foundation of China (Grant Nos. 61202448 and 61202352) and the National High-Tech Research and Development Program of China (Grant No. 2013AA014001).

Author information

Authors and Affiliations

  1. Information Security Research Center, Southeast University, Nanjing, 210096, China

    Zhen-Chao Zhu & Ai-Qun Hu

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Zhen-Chao Zhu

  3. School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing, 210094, China

    An-Min Fu

Authors
  1. Zhen-Chao Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ai-Qun Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. An-Min Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhen-Chao Zhu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhu, ZC., Hu, AQ. & Fu, AM. Improving the security of protocols of quantum key agreement solely using Bell states and Bell measurement. Quantum Inf Process 14, 4245–4254 (2015). https://doi.org/10.1007/s11128-015-1110-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-015-1110-1

Keywords

Search

Navigation