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Two Quantum Secret Sharing Schemes with Adversary Structure

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Abstract

Quantum secret sharing is an important technology in quantum cryptography, and it is used in the fields of secure multiparty computation, quantum auction and fiber network configuration. In this paper, we construct two quantum secret sharing schemes with adversary structure by using three-qudit GHZ state and three qubits. In the proposed scheme, the dealer first generates the private keys based on the adversary structure, then the participants in authorized subset use their private keys to perform the unitary operations on the quantum state and recover the original secret. The security analysis shows the attacks of intercept-and-resend, entangle-and-measure and participant are impossible in our schemes. Compared with the existing quantum secret sharing schemes, we realize the sharing of classical information and quantum state, and need less computational cost. Moreover, our schemes are more efficient when the adversary structure can be obtained directly.

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All data generated or analysed during this study are included in the published article.

References

  1. Gutub, A., Al-Juaid, N., Khan, E.: Counting-based secret sharing technique for multimedia applications. Multimed. Tools Appl. 78(5), 5591–5619 (2019)

    Article  Google Scholar 

  2. AlKhodaidi, T., Gutub, A.: Trustworthy target key alteration helping counting-based secret sharing applicability. Arab. J. Sci. Eng. 45(4), 3403–3423 (2020)

    Article  Google Scholar 

  3. Alkhodaidi, T., Gutub, A.: Scalable shares generation to increase participants of counting-based secret sharing technique. Int. J. Inf. Secur. 17(1-2), 119–146 (2022)

    Google Scholar 

  4. Al-Ghamdi, M., Al-Ghamdi, M., Gutub, A.: Security enhancement of shares generation process for multimedia counting-based secret-sharing technique. Multimed. Tools Appl. 78(12), 16283–16310 (2019)

    Article  Google Scholar 

  5. Hureib, E., Gutub, A.: Enhancing medical data security via combining Elliptic Curve cryptography with 1-LSB and 2-LSB image steganography. Int. J. Comput. Sci. Net. Sec. 20(12), 232–241 (2020)

    Google Scholar 

  6. Gutub, A.: Boosting image watermarking authenticity spreading secrecy from counting-based secret-sharing. https://doi.org/10.1049/cit2.12093 (2022)

  7. Kheshaifaty, N., Gutub, A.: Engineering graphical captcha and AES crypto hash functions for secure online authentication. https://doi.org/10.36909/jer.13761 (2021)

  8. Al-Shaarani, F., Gutub, A.: Increasing participants using counting-based secret sharing via involving matrices and practical steganography. Arab. J. Sci. Eng. 47(2), 2455–2477 (2022)

    Article  Google Scholar 

  9. Gutub, A.: Secure shares generation via M-Blocks partitioning for counting-based secret sharing. J. Eng. Res. 8(3), 91–117 (2020)

    Article  Google Scholar 

  10. Al-Shaarani, F., Gutub, A.: Securing matrix counting-based secret-sharing involving crypto steganography. https://doi.org/10.1016/j.jksuci.2021.09.009 (2021)

  11. Gutub, A., AlKhodaidi, T.: Smart expansion of target key for more handlers to access multimedia counting-based secret sharing. Multimed. Tools Appl. 79(25-26), 17373–17401 (2020)

    Article  Google Scholar 

  12. Al-Juaid, N., Gutub, A.: Combining RSA and audio steganography on personal computers for enhancing security. SN Appl. Sci. 1, 830 (2019)

    Article  Google Scholar 

  13. Gutub, A.: Regulating watermarking semi-authentication of multimedia audio via counting-based secret sharing. Pamukkale U J. Eng. Sci. 28(2), 324–332 (2022)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. Blakley, G. R.: Safeguarding Cryptographic Keys. In: AFIPS, p. 313. IEEE Computer Society (1979)

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59(1), 162–168 (1999)

    Article  ADS  Google Scholar 

  18. Tokunaga, Y., Okamoto, T., Imoto, N.: Threshold quantum cryptography. Phys. Rev. A 71(1), 012314 (2005)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. 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(R), 030301 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  21. Cleve, R., Gottesman, D., Lo, H. K.: How to share a quantum secret. Phys. Rev. Lett. 83, 648–651 (1999)

    Article  ADS  Google Scholar 

  22. Tyc, T., Sanders, B. C.: How to share a continuous-variable quantum secret by optical interferometry. Phys. Rev. A 65, 042310 (2002)

    Article  ADS  Google Scholar 

  23. Li, B.K., Yang, Y.G., Wen, Q.Y.: Threshold quantum secret sharing of secure direct communication. Chin. Phys. Lett. 26(1), 010302 (2009)

    Article  ADS  Google Scholar 

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

    Google Scholar 

  25. Yang, Y. H., Gao, F., Wu, X., Qin, S. J., Zuo, H. J., Wen, Q. Y.: Quantum secret sharing via local operations and classical communication. Sci. Rep. 5, 16967 (2015)

    Article  ADS  Google Scholar 

  26. Sarvepalli, P. K., Klappenecker, A.: Sharing classical secrets with Calderbank-Shor-Steane codes. Phys. Rev. A 80, 022321 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Sarvepalli, P.: Nonthreshold quantum secret-sharing schemes in the graph-state formalism. Phys. Rev. A 86, 042303 (2012)

    Article  ADS  Google Scholar 

  28. Wang, M. M., Chen, X. B., Yang, Y. X.: Quantum secret sharing for general access structures based on multiparticle entanglements. Quantum Inf. Process. 13, 429–443 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Bai, C. M., Li, Z. H., Li, Y. M.: Sequential quantum secret sharing using a single qudit. Commun. Theor. Phys. 69(5), 513–518 (2018)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  32. Song, X., Liu, Y., Deng, H., Xiao, Y.: (t, n) Threshold d-level quantum secret sharing. Sci. Rep. 7, 6366 (2017)

    Article  ADS  Google Scholar 

  33. Lu, C., Miao, F., Hou, J., et al.: Verifiable threshold quantum secret sharing with sequential communication. Quantum Inf Processing. 17(11), 310 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. Mashhadi, S.: General secret sharing based on quantum Fourier transform. Quantum Inf. Process. 18, 114 (2019)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

  36. Liu, L., Li, Z., Han, Z., et al.: A quantum secret sharing scheme with verifiable function. Eur. Phys. J.D 74 (2020)

  37. Zhi, D. L., Li, Z. H., Han, Z. W., Liu, L. J.: Verifiable quantum secret sharing based on a single qudit. Int. J. Theor. Phys. 59(12), 3672–3684 (2020)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  39. Kao, S. H., Hwang, T.: Comment on (t,n) threshold d-level quantum secret sharing. arXiv:1803.00216v1 (2018)

  40. Cleve, R., Gottesman, D., Lo, H.K.: How to share a quantum secret. Phys. Rev. Lett 83(3), 648–651 (1999)

    Article  ADS  Google Scholar 

  41. Qin, H., Zhu, X., Dai, Y.: (t, n) Threshold quantum secret sharing using the phase shift operation. Quantum Inf. Process. 14(8), 2997 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. Qin, H., Dai, Y.: d-Dimensional quantum state sharing with adversary structure. Quantum Inf. Process. 15, 1689–1701 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. Lu, C., Miao, F., Meng, K., et al.: Threshold quantum secret sharing based on single qubit. Quantum Inf. Process. 17 (2018)

  44. Qin, H., Tso, R., Dai, Y.: Multi-dimensional quantum state sharing based on quantum Fourier transform. Quntum Inf. Process. 17, 48 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  46. Malkhi, D., Reiter, M.K.: Byzantine quorum systems. Distributed Comput 11(4), 203–213 (1998)

    Article  MATH  Google Scholar 

  47. Hirt, M., Maurer, U.: Player simulation and general adversary structures in perfect multiparty computation. Journal of Cryptology. 13(1), 31–60 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  48. Cai, Q. Y., Li, W. B.: Deterministic secure communication without using entanglement. Chin. Phys. Lett. 21, 601–603 (2004)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant No. U21A20428 and No. 12171134.

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Authors and Affiliations

  1. School of Mathematics, HeFei University of Technology, Hefei, 230009, China

    Tingting Wu, Shixin Zhu, Fulin Li & Li Liu

  2. Intelligent Interconnected Systems Laboratory of Anhui Province, Hefei, China

    Tingting Wu, Shixin Zhu, Fulin Li & Li Liu

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  1. Tingting Wu
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  2. Shixin Zhu
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  3. Fulin Li
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  4. Li Liu
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Contributions

Tingting Wu and Shixin Zhu wrote the main manuscript text; Fulin Li and Li Liu collected a lot of information related to our paper; Tingting Wu prepared Table 1-3; All authors reviewed the manuscript.

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Correspondence to Shixin Zhu.

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Wu, T., Zhu, S., Li, F. et al. Two Quantum Secret Sharing Schemes with Adversary Structure. Int J Theor Phys 61, 206 (2022). https://doi.org/10.1007/s10773-022-05176-w

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