Skip to main content
Log in

Circular mediated semi-quantum key distribution

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Mediated semi-quantum key distribution (M-SQKD) allows two “semi-quantum” or “classical” users to establish a secret key with the help of a third party (TP), in which TP has full quantum power and possibly adversarial. It is the basis of the multi-party semi-quantum cryptography protocol for securing the private data of classical users. In this work, we propose a M-SQKD protocol based on circular transport structure and prove the protocol is unconditional security. Even in the worst case (i.e., TP is untrusted), the protocol’s noise tolerance is also close to the BB84 protocol. The results show that our protocol can reach the similar level of security as the full quantum protocol. Besides, due to the scalability of the circular transport structure, our protocol is easily extended to multi-party scenarios, which offers an approach to realizing multiple “classical” users’ key distribution. Therefore, it can be used to protect the private data of multiple classical users and may have potential application scenarios in the future.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data Availability

No datasets were generated or analyzed during this article.

References

  1. Bennet C. H.: Quantum cryptography: Public key distribution and coin tossing, in: IEEE International Conference on Computers, Systems and Signal Processing, Dec. (1984)

  2. Renner, R., Gisin, N., Kraus, B.: Information-theoretic security proof for quantum-key-distribution protocols. Phys. Rev. A 72(1), 012332 (2005)

    Article  ADS  Google Scholar 

  3. 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 

  4. She, L.G., Zhang, C.M.: Reference-frame-independent quantum key distribution with modified coherent states. Quantum Inf. Process. 21(5), 161 (2022)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Nie, Y.F., Zhang, C.M.: Afterpulse analysis for reference-frame-independent quantum key distribution. Quantum Inf. Process. 21(9), 340 (2022)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Cui, W., Song, Z., Huang, G., et al.: Satellite-based phase-matching quantum key distribution. Quantum Inf. Process. 21(9), 313 (2022)

    Article  ADS  MATH  Google Scholar 

  7. Ranu, S.K., Prabhakar, A., Mandayam, P.: Differential phase encoded measurement-device-independent quantum key distribution. Quantum Inf. Process. 20, 1–37 (2021)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Kwek, L.C., Cao, L., Luo, W., et al.: Chip-based quantum key distribution. AAPPS Bull. 31, 1–8 (2021)

    Article  Google Scholar 

  9. Cui, Z.X., Zhong, W., Zhou, L., et al.: Measurement-device-independent quantum key distribution with hyper-encoding. Sci. China Phys. Mech. Astron. 62(11), 110311 (2019)

    Article  ADS  Google Scholar 

  10. Park, J., Lee, J., Heo, J.: Improved statistical fluctuation analysis for twin-field quantum key distribution. Quantum Inf. Process. 20, 1–9 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu, B., Xia, S., Xiao, D., et al.: Decoy-state method for quantum-key-distribution-based quantum private query. Sci. China Phys. Mech. Astron. 65(4), 240312 (2022)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

  14. Zhang, W., Qiu, D.W., Mateus, P.: Security of a single-state semi-quantum key distribution protocol. Quantum Inf. Process. 17(6), 1–21 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zhou, N.R., Zhu, K.N., Zou, X.F.: Multi-party semi-quantum key distribution protocol with four-particle cluster states. Ann. Phys. 531(8), 1800520 (2019)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  17. Wang, M.M., Gong, L.M., Shao, L.H.: Efficient semiquantum key distribution without entanglement. Quantum Inf. Process. 18(9), 1–10 (2019)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Amer, O., Krawec, W.O.: Semiquantum key distribution with high quantum noise tolerance. Phys. Rev. A 100(2), 022319 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  19. Iqbal, H., Krawec, W.O.: High-dimensional semiquantum cryptography. IEEE Trans. Quantum Eng. 1, 1–17 (2020)

    Article  Google Scholar 

  20. Ye, C.Q., Li, J., Chen, X.B., Tian, Y., Hou, Y.Y.: An efficient semi-quantum key distribution protocol and its security proof. IEEE Commun. Lett. 26(6), 1226–1230 (2022)

    Article  Google Scholar 

  21. Ye, T.Y., Geng, M.J., Xu, T.J., et al.: Efficient semiquantum key distribution based on single photons in both polarization and spatial-mode degrees of freedom. Quantum Inf. Process. 21(4), 123 (2022)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Ye, T.Y., Li, H.K., Hu, J.L.: Semi-quantum key distribution with single photons in both polarization and spatial-mode degrees of freedom. Int. J. Theor. Phys. 59(9), 2807–2815 (2020)

    Article  MATH  Google Scholar 

  23. Tian, Y., Li, J., Ye, C.Q., et al.: Multi-party semi-quantum key distribution protocol based on hyperentangled Bell states. Front. Phys. 10, 966 (2022)

    Article  Google Scholar 

  24. Zou, X.F., Qiu, D.W.: Three-step semiquantum secure direct communication protocol. Sci. China Phys. Mech. Astron. 57(9), 1696–1702 (2014)

    Article  ADS  Google Scholar 

  25. Luo, Y.P., Hwang, T.: Authenticated semi-quantum direct communication protocols using Bell states. Quantum Inf. Process. 15(2), 947–958 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Zhang, M.H., Li, H.F., Xia, Z.Q., et al.: Semiquantum secure direct communication using EPR pairs. Quantum Inf. Process. 16(5), 1–14 (2017)

    Article  ADS  MATH  Google Scholar 

  27. Li, Q., Chan, W.H., Long, D.Y.: Semiquantum secret sharing using entangled states. Phys. Rev. A 82(2), 022303 (2010)

    Article  ADS  Google Scholar 

  28. Li, L., Qiu, D.W., Mateus, P.: Quantum secret sharing with classical Bobs. J. Phys. A: Math. Theor. 46(4), 045304 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Yu, K.F., Gu, J., Hwang, T., Gope, P.: Multi-party semi-quantum key distribution-convertible multi-party semi-quantum secret sharing. Quantum Inf. Process. 16(8), 1–14 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  30. Chen, Y., Ye, T.Y.: Semiquantum secret sharing by using X-type states. Eur. Phys. J. Plus 137(12), 1331 (2022)

    Article  Google Scholar 

  31. Thapliyal, K., Sharma, R.D., Pathak, A.: Orthogonal-state-based and semi-quantum protocols for quantum private comparison in noisy environment. Int. J. Quantum Inform. 16(05), 1850047 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Lin, P.H., Hwang, T., Tsai, C.W.: Efficient semi-quantum private comparison using single photons. Quantum Inf. Process. 18(7), 1–14 (2019)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Ye, C.Q., Li, J., Chen, X.B., Tian, Y.: Efficient semi-quantum private comparison without using entanglement resource and pre-shared key. Quantum Inf. Process. 20(8), 1–19 (2021)

    MathSciNet  MATH  Google Scholar 

  34. Ye, T.Y., Ye, C.Q.: Measure-resend semi-quantum private comparison without entanglement. Int. J. Theor. Phys. 57, 3819–3834 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  35. Geng, M.J., Chen, Y., Xu, T.J., et al.: Single-state semiquantum private comparison based on Bell states. EPJ Quantum Technol. 9(1), 1–24 (2022)

    Article  Google Scholar 

  36. Ye, T.Y., Lian, J.Y.: A novel multi-party semiquantum private comparison protocol of size relationship with d-dimensional single-particle states. Phys. A 611, 128424 (2023)

    Article  MathSciNet  MATH  Google Scholar 

  37. Ye, T.Y., Hu, J.L.: Multi-party quantum private comparison based on entanglement swapping of Bell entangled states within d-level quantum system. Int. J. Theor. Phys. 60, 1471–1480 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  38. Iqbal, H., Krawec, W.O.: Semi-quantum cryptography. Quantum Inf. Process. 19(3), 1–52 (2020)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  40. Krawec, W.O.: An improved asymptotic key rate bound for a mediated semi-quantum key distribution protocol. Quantum Inform. Comput. 16(9–10), 813–834 (2016)

    Article  MathSciNet  Google Scholar 

  41. Liu, Z.R., Hwang, T.: Mediated semi-quantum key distribution without invoking quantum measurement. Ann. Phys. 530(4), 1700206 (2018)

    Article  MathSciNet  Google Scholar 

  42. Lin, P.H., Tsai, C.W., Hwang, T.: Mediated semi-quantum key distribution using single photons. Ann. Phys. 531(8), 1800347 (2019)

    Article  MathSciNet  Google Scholar 

  43. Chen, L., Li, Q., Liu, C., Peng, Y., Yu, F.: Efficient mediated semi-quantum key distribution. Phys. A 582, 126265 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  44. Guskind, J., Krawec, W.O.: Mediated semi-quantum key distribution with improved efficiency. Quantum Sci. Technol. 7(3), 035019 (2022)

    Article  ADS  Google Scholar 

  45. Mutreja, S., Krawec, W.O.: Improved semi-quantum key distribution with two almost-classical users. Quantum Inf. Process. 21(9), 319 (2022)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  46. Chen, C.Y., Hwang, T.: Mediated authenticated differential phase shift quantum key distribution. Optik 272, 170239 (2023)

    Article  ADS  Google Scholar 

  47. Tsai, C.W., Yang, C.W., Lee, N.Y.: Lightweight mediated semi-quantum key distribution protocol. Mod. Phys. Lett. A 34(34), 1950281 (2019)

    Article  ADS  Google Scholar 

  48. Tsai, C.W., Yang, C.W.: Lightweight mediated semi-quantum key distribution protocol with a dishonest third party based on Bell states. Sci. Rep. 11(1), 23222 (2021)

    Article  ADS  Google Scholar 

  49. Christandl, M., Koning, R., Renner, R.: Postselection technique for quantum channels with applications to quantum cryptography. Phys. Rev. Lett 102(2), 020504 (2009)

    Article  ADS  Google Scholar 

  50. Renner, R.: Symmetry of large physical systems implies independence of subsystems. Nat. Phys. 3(9), 645–649 (2007)

    Article  Google Scholar 

  51. Deng, F.G., Zhou, H.Y., Long, G.L.: Circular quantum secret sharing. J. Phys. A: Math. Gen. 39(45), 14089 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  52. 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(4), 044302 (2005)

    Article  ADS  Google Scholar 

  53. 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(5), 054302 (2006)

    Article  ADS  Google Scholar 

  54. Cai, Q.Y.: Eavesdropping on the two-way quantum communication protocols with invisible photons. Phys. Lett. A 351(1–2), 23–25 (2006)

    Article  ADS  MATH  Google Scholar 

  55. Boyer, M., Katz, M., Liss, R., et al.: Experimentally feasible protocol for semiquantum key distribution. Phys. Rev. A 96(6), 062335 (2017)

    Article  ADS  Google Scholar 

  56. Han, S., Huang, Y., Mi, S., et al.: Proof-of-principle demonstration of semi-quantum key distribution based on the Mirror protocol. EPJ Quantum Technol. 8(1), 28 (2021)

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the anonymous reviewers for their significant comments and suggestions to enhance the quality of this paper. This work was supported by the National Natural Science Foundation of China No. 62271070, and the BUPT Excellent Ph.D. Students Foundation No. CX2021117. The Open Research Fund of Key Laboratory of Cryptography of Zhejiang Province No. ZCL21006.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jian Li.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ye, CQ., Li, J., Chen, XB. et al. Circular mediated semi-quantum key distribution. Quantum Inf Process 22, 170 (2023). https://doi.org/10.1007/s11128-023-03915-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-03915-4

Keywords

Navigation