Skip to main content
SpringerLink
Log in

Quantum key agreement protocols with single photon in both polarization and spatial-mode degrees of freedom

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper, we propose a three-party and a multi-party quantum key agreement protocols with single photons in both polarization and spatial-mode degrees of freedom. Based on the defined collective unitary operations, the participants can agree on a secure shared key through encoding their sub-secret keys on the particles. Moreover, the security of our protocols is discussed comprehensively. It is showed that the presented protocols can defend both the outside attacks and participant attacks. The efficiency analysis also shows that our two protocols can achieve high qubit efficiency. Besides, our protocols are feasible since the preparation and the measurement of single-photon state in both polarization and spatial-mode degrees of freedom are available with current quantum techniques.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. Burmester, M., Desmedt, Y.: A secure and efficient conference key distribution system. In: Advances in CryptologyEUROCRYPT 1994. Lecture Notes in Computer Science, vol. 950, pp. 275–286 (1994)

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

    Article  Google Scholar 

  5. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  6. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of 35th Annual Symposium on Foundations of Computer Science, Los Alamitos, pp. 124–134 (1994)

  7. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of 28th Annual ACM Symposium on the Theory of Computing, Philadelphia, pp. 212–219 (1996)

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

    Article  Google Scholar 

  9. Hsueh, C.C., Chen, C.Y.: Quantum key agreement protocol with maximally entangled states. In: Proceedings of the 14th Information Security Conference (ISC 2004), pp. 236–242, National Taiwan University of Science and Technology, Taipei (2004)

  10. Tsai, C., Hwang, T.: On Quantum Key Agreement Protocol. Technical Report, C-S-I-E, NCKU, Taiwan, ROC (2009)

  11. Chong, S.K., Tsai, C.W., Hwang, T.: Improvement on quantum key agreement protocol with maximally entangled states. Int. J. Theor. Phys. 50, 1793–1802 (2011)

    Article  MATH  Google Scholar 

  12. Tsai, C.W., Chong S.K., Hwang, T.: Comment on quantum key agreement protocol with maximally entangled states. In: Proceedings of the 20th Cryptology and Information Security Conference (CISC 2010), pp. 210–213 (2010)

  13. Chong, S.K., Hwang, T.: Quantum key agreement protocol based on BB84. Opt. Commun. 283, 1192–1195 (2010)

    Article  ADS  Google Scholar 

  14. Shi, R.H., Zhong, H.: Multi-party quantum key agreement with bell states and bell measurements. Quantum Inf. Process. 12, 921–932 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Liu, B., Gao, F., Huang, W., Wen, Q.Y.: Multiparty quantum key agreement with single particles. Quantum Inf. Process. 12, 1797–1805 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. 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, 3411–3420 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Huang, W., Wen, Q.Y., Liu, B., Su, Q., Gao, F.: Cryptanalysis of a multi-party quantum key agreement protocol with single particles. Quantum Inf. Process. 13, 1651–1657 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  18. Shukla, C., Alam, N., Pathak, A.: Protocols of quantum key agreement solely using Bell states and Bell measurement. Quantum Inf. Process. 13, 2391–2405 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhu, Z.C., Hu, A.Q., Fu, A.M.: Improving the security of protocols of quantum key agreement solely using Bell states and Bell measurement. Quantum Inf. Process. 14, 4245–4254 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Xu, G.B., Wen, Q.Y., Gao, F., Qin, S.J.: Novel multiparty quantum key agreement protocol with GHZ states. Quantum Inf. Process. 13, 2587–2594 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Sun, Z.W., Yu, J., Wang, P.: Efficient multi-party quantum key agreement by cluster states. Quantum Inf. Process. 15, 373–384 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. 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, vol. 290, pp. 175–179, IEEE, Bangalore (1984)

  23. Liu, D., Chen, J.L., Jiang, W.: High-capacity quantum secure direct communication with single photons in both polarization and spatial-mode degrees of freedom. Int. J. Theor. Phys. 51, 2923–2929 (2012)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  25. 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 

  26. Li, C.Y., Li, X.H., Deng, F.G., Zhou, P., Liang, Y.J., Zhou, H.Y.: Efficient quantum cryptography network without entanglement and quantum memory. Chin. Phys. Lett. 23, 2896 (2006)

    Article  ADS  Google Scholar 

  27. 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  MathSciNet  MATH  Google Scholar 

  28. Deng, F.G., Li, X.H., Zhou, H.Y., Zhang, Z.J.: Erratum: Improving the security of multiparty quantum secret sharing against Trojan horse attack [Physical Review A (2005) 72 (044302)]. Phys. Rev. A 73, 049901 (2006)

    Article  ADS  Google Scholar 

  29. Cai, Q.Y.: Eavesdropping on the two-way quantum communication protocols with invisible photons. Phys. Lett. A 351, 23–25 (2006)

    Article  ADS  MATH  Google Scholar 

  30. 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 

  31. 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 

  32. Hughes, R.J., Nordholt, J.E., Derkacs, D., Peterson, C.G.: Practical free-space quantum key distribution over 10 km in daylight and at night. New. J. Phys. 4, 43 (2002)

    Article  ADS  Google Scholar 

  33. Beveratos, A., Brouri, R., Gacoin, T., Villing, A., Poizat, J.P., Grangier, P.: Single photon quantum cryptography. Phys. Rev. Lett. 89, 187901 (2002)

    Article  ADS  Google Scholar 

  34. 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 

  35. Lin J., Hwang T.: New circular quantum secret sharing for remote agents. Quantum Inf. Process. 12, 685–697 (2013)

  36. Chen, K.H., Chang, Z.H., Zeng, G.J., et al.: Multiparty quantum key agreement with GHZ state. In: IEEE International Conference on Systems, Man, and Cybernetics (SMC), IEEE, pp. 1589–1594 (2015)

  37. Sun, Z.W., Yu, J.P., Wang, P.: Efficient multi-party quantum key agreement by cluster states. Quantum Inf. Process. 15, 373–384 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 61373171, the 111 project under Grant No. B08038.

Author information

Authors and Affiliations

  1. Faculty of Software, Fujian Normal University, Fuzhou, 350108, China

    Lili Wang

  2. State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, 710071, China

    Wenping Ma

Authors
  1. Lili Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenping Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lili Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, L., Ma, W. Quantum key agreement protocols with single photon in both polarization and spatial-mode degrees of freedom. Quantum Inf Process 16, 130 (2017). https://doi.org/10.1007/s11128-017-1576-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-017-1576-0

Keywords

Search

Navigation