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A d-level quantum secret sharing scheme with cheat-detection (t, m) threshold

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Abstract

This paper proposes a cheating identifiable (t, m) threshold quantum secret sharing scheme based on the d-dimensional Bell state and single-qudit unitary operations. In the proposed protocol, the dealer generates a Bell state and transmits the first particle to the participants; then, t out of m participants perform the unitary operations on the Bell states’ particle. The dealer shares both classical and quantum information. The Bell states are used to reconstruct the secret and identify the malicious behavior of a dishonest participant. After verifying any eavesdropping and dishonest participant, the dealer transforms a unitary operation on the second particle of the Bell state and sends it to the participant to regenerate the secret. The protocol is reliable in identifying dishonest participants and negating any eavesdropping. The proposed protocol is more adaptable, effective, and practical than the relevant quantum secret sharing schemes.

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Data Availability Statement

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

References

  1. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  2. Blakley, G.R.: Safeguarding cryptographic keys. In: Managing Requirements Knowledge, International Workshop on, pp. 313–313. IEEE Computer Society (1979)

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Cleve, R., Gottesman, D., Lo, H.K.: How to share a quantum secret. Phys. Rev. Lett. 83(3), 648 (1999)

    Article  ADS  Google Scholar 

  5. Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59(1), 162 (1999)

    Article  ADS  Google Scholar 

  6. Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61(4), 042311 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  7. Xiao, L., Long, G.L., Deng, F.G., Pan, J.W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69(5), 052307 (2004)

    Article  ADS  Google Scholar 

  8. Deng, F.G., Li, X.H., Li, C.Y., Zhou, P., Zhou, H.Y.: Multiparty quantum-state sharing of an arbitrary two-particle state with Einstein-Podolsk-Rosen pairs. Phys. Rev. A 72(4), 044301 (2005)

    Article  ADS  Google Scholar 

  9. Qin, H., Zhu, X., Dai, Y.: (t, n) threshold quantum secret sharing using the phase shift operation. Q. Inf. Process. 14(8), 2997–3004 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lu, C., Miao, F., Meng, K., Yu, Y.: Threshold quantum secret sharing based on single qubit. Q. Inf. Process. 17(3), 1–13 (2018)

    MathSciNet  MATH  Google Scholar 

  11. Cao, H., Ma, W.: Verifiable threshold quantum state sharing scheme. IEEE Access 6, 10453–10457 (2018)

    Article  Google Scholar 

  12. Hsu, L.Y.: Quantum secret-sharing protocol based on Grover’s algorithm. Phys. Rev. A 68(2), 022306 (2003)

    Article  ADS  Google Scholar 

  13. Markham, D., Sanders, B.C.: Graph states for quantum secret sharing. Phys. Rev. A 78(4), 042309 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Yang, W., Huang, L., Shi, R., He, L.: Secret sharing based on quantum Fourier transform. Q. Inf. Process. 12(7), 2465–2474 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Maitra, A., De, S.J., Paul, G., Pal, A.K.: Proposal for quantum rational secret sharing. Phys. Rev. A 92(2), 022305 (2015)

    Article  ADS  Google Scholar 

  16. Fu, Y., Yin, H.L., Chen, T.Y., Chen, Z.B.: Long-distance measurement-device-independent multiparty quantum communication. Phys. Rev. Lett. 114(9), 090501 (2015)

    Article  ADS  Google Scholar 

  17. Musanna, F., Kumar, S.: A novel three-party quantum secret sharing scheme based on bell state sequential measurements with application in quantum image sharing. Q. Inf. Process. 19(10), 1–21 (2020)

    MathSciNet  MATH  Google Scholar 

  18. Gao, Z., Li, T., Li, Z.: Deterministic measurement-device-independent quantum secret sharing. Sci. China Phys. Mech. Astron. 63(12), 120311 (2020)

    Article  ADS  Google Scholar 

  19. Ju, X.X., Zhong, W., Sheng, Y.B., Zhou, L.: Measurement-device-independent quantum secret sharing with hyper-encoding. Chin. Phys. B 31(10), 100302 (2022)

    Article  ADS  Google Scholar 

  20. Zhang, T., Zhou, L., Zhong, W., Sheng, Y.B.: Multiple-participant measurement-device-independent quantum secret sharing protocol based on entanglement swapping. Laser Phys. Lett. 20(2), 025203 (2023)

    Article  ADS  Google Scholar 

  21. Shen, A., Cao, X.Y., Wang, Y., Fu, Y., Gu, J., Liu, W.B., Weng, C.X., Yin, H.L., Chen, Z.B.: Experimental quantum secret sharing based on phase encoding of coherent states. Sci. China-Phys. Mech, Astron (2023)

  22. Yu, I.C., Lin, F.L., Huang, C.Y.: Quantum secret sharing with multilevel mutually (un) biased bases. Phys. Rev. A 78(1), 012344 (2008)

    Article  ADS  Google Scholar 

  23. Tavakoli, A., Herbauts, I., Żukowski, M., Bourennane, M.: Secret sharing with a single d-level quantum system. Phys. Rev. A 92(3), 030302 (2015)

    Article  ADS  Google Scholar 

  24. Chen, X.B., Tang, X., Xu, G., Dou, Z., Chen, Y.L., Yang, Y.X.: Cryptanalysis of secret sharing with a single d-level quantum system. Q. Inf. Process. 17(9), 1–11 (2018)

    MathSciNet  MATH  Google Scholar 

  25. 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  MATH  Google Scholar 

  26. Li, F., Yan, J., Zhu, S.: General quantum secret sharing scheme based on two qudit. Q. Inf. Process. 20(10), 1–19 (2021)

    MathSciNet  MATH  Google Scholar 

  27. Bai, C.M., Li, Z.H., Liu, C.J., Li, Y.M.: Quantum secret sharing using orthogonal multiqudit entangled states. Q. Inf. Process. 16(12), 1–18 (2017)

    MathSciNet  MATH  Google Scholar 

  28. Song, X.L., Liu, Y.B., Deng, H.Y., Xiao, Y.G.: (t, n) threshold d-level quantum secret sharing. Sci. Rep. 7(1), 1–9 (2017)

    ADS  Google Scholar 

  29. Lu, C., Miao, F., Hou, J., Meng, K.: Verifiable threshold quantum secret sharing with sequential communication. Q. Inf. Process. 17(11), 1–13 (2018)

    MathSciNet  MATH  Google Scholar 

  30. Sutradhar, K., Om, H.: Enhanced (t, n) threshold d-level quantum secret sharing. Sci. Rep. 11(1), 1–7 (2021)

    Article  ADS  Google Scholar 

  31. Bai, C.M., Zhang, S., Liu, L.: Verifiable quantum secret sharing scheme using d-dimensional GHZ state. Int. J. Theoret. Phys. 60(10), 3993–4005 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  32. Qin, H., Tso, R.: Threshold quantum state sharing based on entanglement swapping. Q. Inf. Process. 17(6), 1–11 (2018)

    MathSciNet  MATH  Google Scholar 

  33. Qin, H., Tso, R., Dai, Y.: Multi-dimensional quantum state sharing based on quantum Fourier transform. Q. Inf. Process. 17(3), 1–12 (2018)

    MathSciNet  MATH  Google Scholar 

  34. Song, X., Liu, Y., Xiao, M., Deng, H.: A verifiable \((t, n) \) threshold quantum state sharing against denial attack. IEEE Access 7, 98908–98920 (2019)

    Article  Google Scholar 

  35. Yan, C., Li, Z., Liu, L., Lu, D.: Cheating identifiable (k, n) threshold quantum secret sharing scheme. Q. Inf. Process. 21(1), 1–24 (2022)

    MathSciNet  MATH  Google Scholar 

  36. Beige, A., Englert, B.G., Kurtsiefer, C., Weinfurter, H.: Secure communication with single-photon two-qubit states. J. Phys. A Math. Gen. 35(28), L407 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  37. Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69(5), 052319 (2004)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  39. Ying, J.W., Zhou, L., Zhong, W., Sheng, Y.B.: Measurement-device-independent one-step quantum secure direct communication. Chin. Phys. B 31(12), 120303 (2022)

    Article  ADS  Google Scholar 

  40. Zhou, L., Sheng, Y.B.: One-step device-independent quantum secure direct communication. Sci. China-Phys. Mech. Astron. 65, 250311 (2022)

    Article  ADS  Google Scholar 

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Acknowledgements

The first author with grant number 09/143(0951)/2019-EMR-I is grateful to Council of Scientific and Industrial Research (CSIR), India, for providing financial support to carry out this work. The work is also supported by SERB core grant number CRG/2020/002040.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India

    Deepa Rathi

  2. Department of Mathematics, Mehta Family School of Data Science and Artificial Intelligence, Indian Institute of Technology Roorkee, Roorkee, India

    Sanjeev Kumar

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  1. Deepa Rathi
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  2. Sanjeev Kumar
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Correspondence to Sanjeev Kumar.

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Rathi, D., Kumar, S. A d-level quantum secret sharing scheme with cheat-detection (t, m) threshold. Quantum Inf Process 22, 183 (2023). https://doi.org/10.1007/s11128-023-03928-z

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