Skip to main content
SpringerLink
Log in

Security of a single-state semi-quantum key distribution protocol

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Semi-quantum key distribution protocols are allowed to set up a secure secret key between two users. Compared with their full quantum counterparts, one of the two users is restricted to perform some “classical” or “semi-quantum” operations, which potentially makes them easily realizable by using less quantum resource. However, the semi-quantum key distribution protocols mainly rely on a two-way quantum channel. The eavesdropper has two opportunities to intercept the quantum states transmitted in the quantum communication stage. It may allow the eavesdropper to get more information and make the security analysis more complicated. In the past ten years, many semi-quantum key distribution protocols have been proposed and proved to be robust. However, there are few works concerning their unconditional security. It is doubted that how secure the semi-quantum ones are and how much noise they can tolerate to establish a secure secret key. In this paper, we prove the unconditional security of a single-state semi-quantum key distribution protocol proposed by Zou et al. (Phys Rev A 79:052312, 2009). We present a complete proof from information theory aspect by deriving a lower bound of the protocol’s key rate in the asymptotic scenario. Using this bound, we figure out an error threshold value such that for all error rates that are less than this threshold value, the secure secret key can be established between the legitimate users definitely. Otherwise, the users should abort the protocol. We make an illustration of the protocol under the circumstance that the reverse quantum channel is a depolarizing one with parameter q. Additionally, we compare the error threshold value with some full quantum protocols and several existing semi-quantum ones whose unconditional security proofs have been provided recently.

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. 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, IEEE, Bangalore, pp. 175C179 (1984)

  2. Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68, 3121–3124 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Acin, A., Gisin, N., Scarani, V.: Coherent-pulse implementations of quantum cryptography protocols resistant to photon-number-splitting attacks. Phys. Rev. A 69, 012309 (2004)

    Article  ADS  Google Scholar 

  4. Fung, C.H.F., Lo, H.K.: Security proof of a three-state quantum-key-distribution protocol without rotational symmetry. Phys. Rev. A 74, 042342 (2006)

    Article  ADS  Google Scholar 

  5. Lo, H.K., Chau, H.F.: Unconditional security of quantum key distribution over arbitrarily long distances. Science 283(5410), 2050 (1999)

    Article  ADS  Google Scholar 

  6. Shor, P.W., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85(2), 441–444 (2000)

    Article  ADS  Google Scholar 

  7. Mayers, D.: Unconditional security in quantum cryptography. J. ACM (JACM) 48(3), 351–406 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. Boyer, M., Kenigsberg, D., Mor, T.: Quantum key distribution with classical Bob. Phys. Rev. Lett. 99(14), 140501 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Hua, L., Cai, Q.Y.: Quantum key distribution with classical alice. Int. J. Quantum Inf. 6(06), 1195–1202 (2008)

    Article  MATH  Google Scholar 

  10. Boyer, M., Gelles, R., Kenigsberg, D., Mor, T.: Semiquantum key distribution. Phys. Rev. A 79, 032341 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Zou, X., Qiu, D., Li, L., Wu, L., Li, L.: Semiquantum-key distribution using less than four quantum states. Phys. Rev. A 79, 052312 (2009)

    Article  ADS  Google Scholar 

  12. Zhang, X.Z., Gong, W.G., Tan, Y.G.: Quantum key distribution series network protocol with m-classical bobs. Chin. Phys. B 18(6), 2143 (2009)

    Article  ADS  Google Scholar 

  13. Wang, J., Zhang, S., Zhang, Q., Tang, C.: Semiquantum key distribution using entangled states. Chin. Phys. Lett. 28(10), 100301 (2011)

    Article  ADS  Google Scholar 

  14. Sun, Z.W., Du, R.G., Long, D.Y.: Quantum key distributionwith limited classical bob. Int. J. Quantum Inf. 11(1), 1350005 (2013)

    Article  MathSciNet  Google Scholar 

  15. Yu, K.F., Yang, C.W., Liao, C.H., Hwang, T.: Authenticated semi-quantum key distribution protocol using bell states. Quantum Inf. Process. 13(6), 1457–1465 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Krawec, W.O.: Mediated semiquantum key distribution. Phys. Rev. A 91(3), 032323 (2015)

    Article  ADS  Google Scholar 

  17. Zou, X., Qiu, D., Zhang, S., Mateus, P.: Semiquantum key distribution without invoking the classical partys measurement capability. Quantum Inf. Process. 14(8), 2981–2996 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Li, Q., Chan, W.H., Zhang, S.: Real semiquantum key distribution with secure delegated quantum computation. ArXiv preprint arXiv:1508.07090 (2015)

  19. Krawec, W.O.: Security of a semi-quantum protocol where reflections contribute to the secret key. Quantum Inf. Process. 15(5), 2067–2090 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Miyadera, T.: Relation between information and disturbance in quantum key distribution protocol with classical alice. Int. J. Quantum Inf. 9(6), 1427–1435 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Krawec, W.O.: Restricted attacks on semi-quantum key distribution protocols. Quantum Inf. Process. 13(11), 2417–2436 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Krawec, W.O.: Security proof of a semi-quantum key distribution protocol. In: IEEE International Symposium on Information Theory (ISIT), IEEE, pp. 686–690 (2015)

  23. Krawec, W.O.: Semi-Quantum Key Distribution. Ph.D. thesis, Stevens Institute of Technology (2015)

  24. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)

    Book  MATH  Google Scholar 

  25. Wilde, M.M.: From classical to quantum Shannon theory. arXiv:1106.1445 (2011)

  26. Renner, R., Gisin, N., Kraus, B.: Information-theoretic security proof for quantum-key-distribution protocols. Phys. Rev. A 72, 012332 (2005)

    Article  ADS  Google Scholar 

  27. Devetak, I., Winter, A.: Distillation of secret key and entanglement from quantum states. Proc. R. Soc. A Math. Phys. Eng. Sci. 461(2053), 207–235 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. Kraus, B., Gisin, N., Renner, R.: Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication. Phys. Rev. Lett. 95, 080501 (2005)

    Article  ADS  Google Scholar 

  29. Lo, H.K., Fung, C.H.F., Ardehali, M.: Efficient quantum key distribution scheme and a proof of its unconditional security. J. Cryptol. 18(2), 133–165 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  30. Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., et al.: The security of practical quantum key distribution. Rev. Mod. Phys. 81(3), 1301 (2009)

    Article  ADS  Google Scholar 

  31. König, R., Renner, R.: A de Finetti representation for finite symmetric quantum states. J. Math. Phys. 46(12), 122108 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Barnett, S.M., Huttner, B., Phoenix, S.J.D.: Eavesdropping strategies and rejected-data protocols in quantum cryptography. J. Mod. Opt. 40(12), 2501–2513 (1993)

    Article  ADS  Google Scholar 

  33. Watanabe, S., Matsumoto, R., Uyematsu, T.: Tomography increases key rates of quantum-key-distribution protocols. Phys. Rev. A 78(4), 042316 (2008)

    Article  ADS  Google Scholar 

  34. Matsumoto, R., Watanabe, S.: Key rate available from mismatched measurements in the BB84 protocol and the uncertainty principle. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 91(10), 2870–2873 (2008)

    Article  ADS  Google Scholar 

  35. Matsumoto, R., Watanabe, S.: Narrow basis angle doubles secret key in the BB84 protocol. J. Phys. A Math. Theor. 43(14), 145302 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Krawec, W.O.: Quantum key distribution with mismatched measurements over arbitrary channels. Quantum Inf. Comput. 17(3–4), 209–241 (2017)

    MathSciNet  Google Scholar 

  37. Christandl, M., Renner, R., Ekert, A.: A Generic Security Proof for Quantum Key Distribution. ArXiv preprint quant-ph/0402131 (2004)

  38. Matsumoto, R.: Improved asymptotic key rate of the B92 protocol. In: IEEE International Symposium on Information Theory Proceedings (ISIT), IEEE 2013, pp. 351–353 (2013)

  39. Cabello, A.: Quantum key distribution in the Holevo limit. Phys. Rev. Lett. 85, 5635 (2000)

    Article  ADS  Google Scholar 

  40. Krawec, W.O.: A genetic algorithm to analyze the security of quantum cryptographic protocols. In Proceedings of 2016 IEEE Congress on Evolutionary Computation (CEC), IEEE, 2016, pp. 2098–2105 (2016)

  41. Shukla, C., Thapliyal, K., Pathak, A.: Semi-quantum communication: protocols for key agreement, controlled secure direct communication and dialogue. Quantum Inf. Process. 16(12), 295 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

We are grateful to the anonymous referees and editor for important suggestions that help us improve the quality of the manuscript. This work is supported in part by the National Natural Science Foundation of China (Nos. 61572532, 61272058), the Natural Science Foundation of Guangdong Province of China (No. 2017B030311011), the Fundamental Research Funds for the Central Universities of China (No. 17lgjc24), Qiu and Mateus are Funded by FCT project UID/EEA/50008/2013. Zhang is supported in part by the Natural Science Foundation of Qiannan Normal University for Nationalities joint Guizhou Province of China (No. Qian-Ke-He LH Zi [2015]7719), the Natural Science Foundation of Central Government Special Fund for Universities of West China (No. 2014ZCSX17), the Industrial Technology Foundation of Qiannan State of China (No. Qiannan Ke He Gong Zi (2017) 9 Hao) and the Scientific Research Foundation for High-level Talents of Qiannan Normal University for Nationalities (No. qnsyrc201716).

Author information

Authors and Affiliations

  1. Institute of Computer Science Theory, School of Data and Computer Science, Sun Yat-sen University, Guangzhou, 510006, China

    Wei Zhang & Daowen Qiu

  2. School of Mathematics and Statistics, Qiannan Normal University for Nationalities, Duyun, 558000, China

    Wei Zhang

  3. Instituto de Telecomunicações, Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, Lisbon, 1049-001, Portugal

    Daowen Qiu & Paulo Mateus

Authors
  1. Wei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daowen Qiu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paulo Mateus
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daowen Qiu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, W., Qiu, D. & Mateus, P. Security of a single-state semi-quantum key distribution protocol. Quantum Inf Process 17, 135 (2018). https://doi.org/10.1007/s11128-018-1904-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-1904-z

Keywords

Search

Navigation