Skip to main content
SpringerLink
Log in

Security analysis of the semi-quantum secret-sharing protocol of specific bits and its improvement

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Recently, Tian et al. (Quantum Inf. Process., 20(6), 217(2021)) proposed an efficient semi-quantum secret-sharing protocol of specific bits. In their protocol, the dealer can split a specific secret such that two classical agents can efficiently and corporately reconstruct the secret by applying the simple operations such as Z-base measurement and reflecting operation. The qubit efficiency of their protocol can be up to 50%. Unfortunately, according to our security analysis, their protocol is vulnerable to the eavesdropping attacks. We prove that the eavesdropper can steal the dealer’s secret without being detected by applying the double-controlled NOT attack (DCNA) to the quantum channels. Then, some improvements are proposed, which can overcome the security flaw of the old protocol. We prove the improved protocol has enhanced security against DCNA, intercept–resend attack, entangle–measure attack and Trojan horse attack. In particular, the security proof shows that inserting decoy photons into the quantum message and reordering the quantum sequence is very helpful in detecting the adversary’s entangle–measure attack, even the adversary uses two auxiliary probes to eavesdrop the quantum channel. Furthermore, the improved eavesdropping check strategy can effectively increase the length of the shared secret.

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

Similar content being viewed by others

Data availability

The manuscript has no associated data.

References

  1. Shamir, A.: How to share a secret. Commun. ACM 22, 612–613 (1979)

    Article  MathSciNet  Google Scholar 

  2. Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59(3), 1829–1834 (1999)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  3. Williams, B.P., Lukens, J.M., Peters, N.A., et al.: Quantum secret sharing with polarization-entangled photon pairs. Phys. Rev. A 99, 062311 (2019)

    Article  CAS  ADS  Google Scholar 

  4. Sutradhar, K., Om, H.: Efficient quantum secret sharing without a trusted player. Quantum Inf. Process. 19, 73 (2020)

    Article  MathSciNet  ADS  Google Scholar 

  5. Liao, Q., Liu, H., Zhu, L., et al.: Quantum secret sharing using discretely modulated coherent states. Phys. Rev. A 103, 032410 (2021)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  6. Chen, M.B., Zhang, S., Liu, Lu.: Fair quantum secret sharing based on symmetric bivariate polynomial. Physica A 589, 126673 (2022)

    Article  MathSciNet  Google Scholar 

  7. Xu, J., Li, X., Han, Y., et al.: Quantitative security analysis of three-level unitary operations in quantum secret sharing without entanglement. Front. Phys. 11, 1213153 (2023)

    Article  Google Scholar 

  8. 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 

  9. Lin, J., Yang, C.W., Tsai, C.W., et al.: Intercept-resend attacks on semi-quantum secret sharing and the improvements. Int. J. Theor. Phys. 52, 156–162 (2013)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  11. Yu, K.F., Gu, J., Hwang, T., et al.: Multi-party semi-quantum key distribution-convertible multi-party semi-quantum secret sharing. Quantum Inf Process. 16(8), 194 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  12. Ye, C.Q., Ye, T.Y., He, D., et al.: Multiparty semi-quantum secret sharing with d-Level single-particle states. Int. J. Theor. Phys. 58, 3797–3814 (2019)

    Article  MathSciNet  Google Scholar 

  13. Yang, C.W., Hwang, T.: Efficient key construction on semi-quantum secret sharing protocols. Int. J. Quantum Inf. 11(5), 1350052 (2013)

    Article  MathSciNet  Google Scholar 

  14. Gao, G., Wang, Y., Wang, D.: Multiparty semiquantum secret sharing based on rearranging orders of qubits. Mod. Phys. Lett. B 30(10), 1650130 (2016)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  15. Xie, C., Li, L.Z., Qiu, D.W.: A novel semi-quantum secret sharing scheme of specific bits. Int. J. Theor. Phys. 54, 3819–3824 (2015)

    Article  MathSciNet  Google Scholar 

  16. Yin, A., Fu, F.: Eavesdropping on semi-quantum secret sharing scheme of specific bits. Int. J. Theor. Phys. 55(9), 4027–4035 (2016)

    Article  MathSciNet  Google Scholar 

  17. Gao, X., Zhang, S., Chang, Y.: Cryptanalysis and improvement of the semi-quantum secret sharing protocol. Int. J. Theor. Phys. 56, 2512–2520 (2017)

    Article  CAS  Google Scholar 

  18. Zhou, M.K.: Improvement of the semi-quantum secret sharing protocol of specific bits. Int. J. Theor. Phys. 59, 1772–1776 (2020)

    Article  Google Scholar 

  19. Zhi-Gang, G.: Improvement of Gao et al’.s semi-quantum secret sharing protocol. Int. J. Theor. Phys. 59, 930–935 (2020)

    Article  MathSciNet  Google Scholar 

  20. Hu, W.W., Zhou, R.G., Jia, L.: Semi-quantum secret sharing in high-dimensional quantum system using product states. Chin. J. Phys. 77, 1701–1712 (2022)

    Article  MathSciNet  Google Scholar 

  21. Tian, Y., Bian, G., Chang, J., et al.: A semi-quantum secret-sharing protocol with a high channel capacity. Entropy 25, 742 (2023)

    Article  MathSciNet  PubMed  PubMed Central  ADS  Google Scholar 

  22. Yin, A., Wang, Z., Fu, F.: A novel semi-quantum secret sharing scheme based on Bell states. Mod. Phys. Lett. B 31, 1750150 (2017)

    Article  CAS  ADS  Google Scholar 

  23. Gao, G., Wang, Y., Wang, D.: Cryptanalysis of a semi-quantum secret sharing scheme based on Bell states. Mod. Phys. Lett. B 32(9), 1850117 (2018)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  24. Ye, C.Q., Ye, T.Y.: Circular semi-quantum secret sharing using single particles. Commun. Theor. Phys. 70, 661–671 (2018)

    Article  MathSciNet  ADS  Google Scholar 

  25. Li, Z., Li, Q., Liu, C., et al.: Limited resource semiquantum secret sharing. Quantum Inf. Process. 17, 285 (2018)

    Article  ADS  Google Scholar 

  26. Xiang, Y., Liu, J., Bai, M.Q., et al.: Limited resource semi-quantum secret sharing based on multi-level systems. Int. J. Theor. Phys. 58, 2883–2892 (2019)

    Article  MathSciNet  Google Scholar 

  27. Tsai, C.W., Chang, Y.C., Lai, Y.H., et al.: Cryptanalysis of limited resource semi-quantum secret Sharing. Quantum Inf. Process. 19, 224 (2020)

    Article  ADS  Google Scholar 

  28. Yin, A., Chen, T.: Authenticated semi-quantum secret sharing based on GHZ-type states. Int. J. Theor. Phys. 60, 265–273 (2021)

    Article  MathSciNet  Google Scholar 

  29. Tian, Y., Li, J., Chen, X.B., et al.: An efficient semi-quantum secret sharing protocol of specific bits. Quantum Inf. Process. 20, 217 (2021)

    Article  MathSciNet  ADS  Google Scholar 

  30. Tian, Y., Li, J., Chen, X.B., Ye, C.Q., Li, H.J.: An efficient semi-quantum secret sharing protocol of specific bits. Quantum Inf. Process. 20(6), 217 (2021)

    Article  MathSciNet  ADS  Google Scholar 

  31. Lin, P.-H., Hwang, T., Tsai, C.-W.: Double CNOT attack on “Quantum key distribution with limited classical Bob.” Int. J. Quant. Infor. 17(02), 1975001 (2019)

    Article  MathSciNet  Google Scholar 

  32. Gu, J., Hwang, T.: Double C-NOT attack on a single-state semi-quantum key distribution protocol and its improvement. Electronics 11(16), 2522 (2022)

    Article  Google Scholar 

  33. Gu, J., Lin, P.H., Hwang, T.: Double C-NOT attack and counterattack on ‘Three-step semi-quantum secure direct communication protocol.’ Quantum Inf. Process. 17, 1–8 (2018)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  34. Yang, C.W.: Efficient and secure semi-quantum secure direct communication protocol against double CNOT attack. Quantum Inf. Process. 19(2), 50 (2020)

    Article  MathSciNet  ADS  Google Scholar 

  35. Tsai, C.-W., Chang, Y.-C., Lai, Y.-H., Yang, C.-W.: Cryptanalysis of limited resource semi-quantum secret sharing. Quantum Inf. Process. 19(8), 224 (2020)

    Article  ADS  Google Scholar 

  36. Tsai, C.-W., Lin, J., Yang, C.-W.: Cryptanalysis and improvement in semi-quantum private comparison based on Bell states. Quantum Inf. Process. 20(3), 120 (2021)

    Article  MathSciNet  ADS  Google Scholar 

  37. Li, Q., Li, P., Xie, L., Chen, L., Quan, J.: Security analysis and improvement of a semi-quantum private comparison protocol with three-particle G-like states. Quantum Inf. Process. 21(4), 127 (2022)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  38. Bennett, C.H., Brassard, G., Crepeau, C., et al.: Generalized privacy amplification. IEEE Trans. Inf. Theory 41, 1915–1923 (1995)

    Article  MathSciNet  Google Scholar 

  39. Deutsch, D., Ekert, A., Jozsa, R., et al.: Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 77, 2818 (1996)

    Article  CAS  PubMed  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  41. Gisin, N., Ribordy, G.G., Tittel, W., et al.: Quantum cryptography. Rev. Mod. Phys. 74(1), 145–195 (2002)

    Article  ADS  Google Scholar 

  42. 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 

  43. 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 

  44. Yang, C.W., Hwang, T., Luo, Y.P.: Enhancement on “Quantum blind signature based on two-state vector formalism.” Quantum Inf. Process. 12(1), 109–117 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  45. Goldreich, O.: Foudations of cryptography: basic applications. Publishing House of Electronics Industry, Beijing (2004)

    Google Scholar 

  46. Yang, L., Xiang, C., Li, B.: Quantum probabilistic encryption scheme based on conjugate coding. China Commun. 10(2), 19–26 (2013)

    Article  Google Scholar 

  47. Hwang, T., Lee, K.C.: EPR quantum key distribution protocols with 100% qubit efficiency. IET Inf. Secur. 1(1), 43–45 (2007)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No.62272090) and the Key Scientific Research Project of Colleges and Universities in Henan Province (Grant No.22A413010).

Funding

The funding was provided by National Natural Science Foundation of China, 62272090, fagen Li, Key Scientific Research Project of Colleges and Universities in Henan Province, 22A413010, Xiangjun Xin

Author information

Authors and Affiliations

  1. College of Software Engineering, Zhengzhou University of Light Industry, Zhengzhou, 450002, China

    Fan He, Xiangjun Xin & Chaoyang Li

  2. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Fagen Li

Authors
  1. Fan He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiangjun Xin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chaoyang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fagen Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The improved protocol was proposed by XX and FH. The security of the protocol was analyzed by XX and FH. The efficiency analysis was presented by CL and FL. The draft of the manuscript was written by XX and FH. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Xiangjun Xin.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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

He, F., Xin, X., Li, C. et al. Security analysis of the semi-quantum secret-sharing protocol of specific bits and its improvement. Quantum Inf Process 23, 51 (2024). https://doi.org/10.1007/s11128-023-04255-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-04255-z

Keywords

Search

Navigation