Skip to main content
SpringerLink
Log in

Verifiable Quantum Secret Sharing Scheme Based on LDPC Codes

  • Research
  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

In this paper, we propose a novel verifiable quantum secret sharing scheme tailored for a specific class of low-density parity-check (LDPC) codes. In the proposed protocol, Alice, the dealer, initially utilizes the generator matrix of the chosen LDPC code to calculate all secret shares and distributes individual shares to all participants in a quantum secure direct communication channel. In the distribution phase, each participant computes a hash value based on their respective share and a randomly generated sequence, which is then published. In the recover phase, each participant performs a unitary operation on these received particles and sends them to the next participant using the decoy-photon technique. Furthermore, the last participant performs Bell measurements on the final quantum states to obtain the original secret. At last, we demonstrate our protocol to be secure against intercept-and-resend attack, entangle-and-measure attack and dishonest participant attack. In addition, we present a comparison of our protocol with other existing schemes.

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
Fig. 3

Similar content being viewed by others

Data Availability

The data sets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

References

  1. Cabello, A.: Quantum key distribution in the Holevo limit. Phys. Rev. Lett. 85(26), 5635 (2000)

    Article  ADS  CAS  PubMed  Google Scholar 

  2. Zhou, N., Zeng, G., Xiong, J.: Quantum key agreement protocol. Electron. Lett. 40(18), 1 (2004)

    Article  CAS  Google Scholar 

  3. Yang, Y.G., Lv, X.L., Gao, S., et al.: Detector-device-independent quantum key agreement based on single-photon bell state measurement. Int. J. Theor. Phys. 61(2), 1–16 (2022)

    Article  MathSciNet  Google Scholar 

  4. Sheng, Y.B., Zhou, L., Long, G.L.: One-step quantum secure direct communication. Sci. Bull. 67(4), 367–374 (2022)

    Article  Google Scholar 

  5. Hillery, M., Buzek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  6. Cleve, R., Gottesman, D., Lo, H.-K.: How to share a quantum secret. Phys. Rev. Lett. 83, 648 (1999)

    Article  ADS  CAS  Google Scholar 

  7. Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61, 042311 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  8. Lipinska, V., Murta, G., Ribeiro, J., Wehner, S.: Verifiable hybrid secret sharing with few qubits. Phys. Rev. A 101, 032332 (2020)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  9. Li, F., Chen, T., Zhu, S.: Dynamic \((t, n)\) threshold quantum secret sharing based on d-dimensional Bell state. Physica A Stat. Mech. Appl. 606, 128122 (2022)

    Article  MathSciNet  Google Scholar 

  10. Yang, C.W., Tsai, C.W.: Improved dynamic multiparty quantum direct secret sharing protocol based on generalized GHZ states to prevent collusion attack. Mod. Phys. Lett. A 35(8), 2050040 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  11. Yang, C.W., Tsai, C.W.: Participant attack and improving dynamic quantum secret sharing using d-dimensional GHZ state. Mod. Phys. Lett. A 35(6), 2050024 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  12. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612 (1979)

    Article  MathSciNet  Google Scholar 

  13. Blakley, G.R.: in Proceedings of the National Computer Conference (AFIPS, 1979), pp. 313–317 (1979)

  14. Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299(5886), 802–803 (1982)

    Article  ADS  CAS  Google Scholar 

  15. Xiao, L., Long, G.L., Deng, F.G., Pan, J.W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69, 052307 (2004)

    Article  ADS  Google Scholar 

  16. Grice, W.P., Qi, B.: Quantum secret sharing using weak coherent states. Phys. Rev. A 100, 022339 (2019)

    Article  ADS  CAS  Google Scholar 

  17. Qin, H.W., Zhu, X.H., Dai, Y.W.: \((t, n)\) threshold quantum secret sharing using the phase shift operation. Quantum Inf Process 14, 2997–3004 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  18. Maitra, A., De, S.J., Paul, G., Pal, A.K.: Proposal for quantum rational secret sharing. Phys. Rev. A 92, 022305 (2015)

    Article  ADS  Google Scholar 

  19. Gu, J., Cao, X.Y., Yin, H.L., et al.: Differential phase shift quantum secret sharing using a twin field. Optics Express 29(6), 9165–9173 (2021)

    Article  ADS  PubMed  Google Scholar 

  20. Mashhadi, S.: Improvement of a \((t, n)\) threshold d-level quantum secret sharing scheme. Journal of Applied Security Research 17(1), 123–134 (2022)

    Article  Google Scholar 

  21. Bai, C.M., Li, Z.H., Wang, J.T., et al.: Restricted (k, n)-threshold quantum secret sharing scheme based on local distinguishability of orthogonal multiqudit entangled states. Quantum Inf Process 17(11), 312 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  22. Li, F., Luo, M., Zhu, H., et al.: A \((w, t, n)\)-weighted threshold dynamic quantum secret sharing scheme with cheating identification. Physica A Stat. Mech. Appl. 612, 128494 (2023)

    Article  MathSciNet  Google Scholar 

  23. Li, L., Li, Z.: An efficient quantum secret sharing scheme based on restricted threshold access structure. Entropy 25(2), 265 (2023)

    Article  ADS  MathSciNet  PubMed  PubMed Central  Google Scholar 

  24. Jia, H.Y., Wen, Q.Y., Gao, F., Qin, S.J., Guo, F.Z.: Dynamic quantum secret sharing. Phys. Lett. A 376(10?C11), 1035–1041 (2012)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  25. Hsu, J.L., Chong, S.K., Hwang, T., Tsai, C.W.: Dynamic quantum secret sharing. Quantum Inf Process 12(1), 331–344 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  26. Liao, C.H., Yang, C.W., Hwang, T.: Dynamic quantum secret sharing protocol based on GHZ state. Quantum Inf Process 13(8), 1907–1916 (2014)

    Article  ADS  Google Scholar 

  27. Ito, M., Saito, A., Nishizeki, T.: Secret sharing scheme realizing general access structure. Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 72(9), 56–64 (1989)

    MathSciNet  Google Scholar 

  28. Roy, S., Mukhopadhyay, S.: Device-independent quantum secret sharing in arbitrary even dimensions. Phys. Rev. A 100, 012319 (2019)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  29. Liao, Q., Liu, H., Zhu, L., et al.: Quantum secret sharing using discretely modulated coherent states. Phys. Rev. A 103(3), 032410 (2021)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  30. Yang, C.W., Tsai, C.W.: Efficient and secure dynamic quantum secret sharing protocol based on bell states. Quantum Inf Process 19(5), 162 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  31. Wang, N., Zhang, X., Zhang, X., et al.: \((t, n)\) threshold quantum secret sharing using rotation operation. Int. J. Theor. Phys. 61(6), 1–19 (2022)

    Article  MathSciNet  Google Scholar 

  32. Wang, J., Li, L., Peng, H., Yang, Y.: Quantum-secret-sharing scheme based on local distinguishability of orthogonal multiqudit entangled states. Phys. Rev. A 95(2), 022320 (2017)

    Article  ADS  Google Scholar 

  33. Bai, C.M., Zhang, S., Liu, L.: Quantum secret sharing for a class of special hypergraph access structures. Quantum Inf Process 21(3), 1–17 (2022)

    Article  MathSciNet  Google Scholar 

  34. Senthoor, K., Sarvepalli, P.K.: Theory of communication efficient quantum secret sharing. IEEE Trans. Inf. Theory. 68(5), 3164–3186 (2022)

    Article  MathSciNet  Google Scholar 

  35. Gallager, R.: Low-density parity-check codes. IRE Trans. Inf. Theory. 8(1), 21–28 (1962)

    Article  MathSciNet  Google Scholar 

  36. Ryan, W., Lin, S.: Channel codes: classical and modern. Cambridge university press, (2009)

  37. Massey, J.L.: Minimal codewords and secret sharing //Proceedings of the 6th joint Swedish-Russian international workshop on information theory, pp. 276-279 (1993)

  38. Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)

    Article  ADS  Google Scholar 

  39. 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 

  40. Feng, Y., Deng, S., Wang, L., et al.: Minimum distances of three families of low-density parity-check codes based on finite geometries. Front. Math. China 11, 279–289 (2016)

    Article  MathSciNet  Google Scholar 

  41. Tavakoli, A., Herbauts, I., Zukowski, M., Bourennane, M.: Secret sharing with a single d-level quantum system. Phys. Rev. A 92, 030302(R) (2015)

    Article  ADS  Google Scholar 

  42. Karimipour, V., Asoudeh, M., Gheorghiu, V., Looi, S.Y., Griffiths, R.B.: Quantum secret sharing and random hopping: using single states instead of entanglement. Phys. Rev. A 92, 030301(R) (2015)

    Article  ADS  MathSciNet  Google Scholar 

  43. Cao, H., Ma, W.: \((t, n)\) threshold quantum state sharing scheme based on linear equations and unitary operation. IEEE Photon. J. 9(1), 1–7 (2017)

    Article  MathSciNet  Google Scholar 

  44. Bai, C.M., Zhang, S., Liu, L.: Verifiable quantum secret sharing scheme using d-dimensional GHZ state. Int. J. Theor. Phys. 60, 3993–4005 (2021)

    Article  MathSciNet  Google Scholar 

  45. Qin, H., Dai, Y.: Verifiable \((t, n)\) threshold quantum secret sharing using d-dimensional Bell state. Inf. Process. Lett. 116(5), 351–355 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We want to express our gratitude to anonymous referees for their valuable and constructive comments. This work supported by the National Natural Science Foundation of China under Grant No.12301590, the Natural Science Foundation of Hebei Province under Grant No.A2022210002 and No.A2021210027 and the Department of Education of Hebei Province under Grant No.QN2020196.

Author information

Authors and Affiliations

  1. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Chen-Ming Bai, Yanan Feng, Sujuan Zhang & Lu Liu

Authors
  1. Chen-Ming Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yanan Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sujuan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lu Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Chen-Ming Bai: Conceptualization, Methodology, Investigation, Supervision, Writing original draft. Yanan Feng and Sujuan Zhang: Discussing, Validation, Writing- review. Lu Liu: Discussing, Writing review.

Corresponding author

Correspondence to Chen-Ming Bai.

Ethics declarations

Competing of interest

The authors declare no competing interests.

Declaration of Interest Statement

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

Bai, CM., Feng, Y., Zhang, S. et al. Verifiable Quantum Secret Sharing Scheme Based on LDPC Codes. Int J Theor Phys 63, 6 (2024). https://doi.org/10.1007/s10773-023-05533-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-023-05533-3

Keywords

Search

Navigation