Advertisement

General secret sharing based on quantum Fourier transform

  • Samaneh MashhadiEmail author
Article
  • 67 Downloads

Abstract

In this paper, we based on the quantum Fourier transform and monotone span program design a hybrid secret sharing. This hybrid scheme has the advantages of both classical and quantum secret sharing. For example, it has general access structure, and is secure against quantum computation and eavesdropper attacks. Moreover, any one of the participants does not know the other participants’ shares.

Keywords

Quantum secret sharing d-dimensional space General access structure Verifiable Quantum Fourier transform Entanglement state 

Notes

References

  1. 1.
    Cai, Q.Y., Li, W.B.: Deterministic secure communication without using entanglement. Chin. Phys. Lett. 21, 601–603 (2004)ADSCrossRefGoogle Scholar
  2. 2.
    Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)ADSCrossRefGoogle Scholar
  3. 3.
    Guo, C., Chang, C.-C., Qin, C.: A multi-threshold secret image sharing scheme based on MSP. Pattern Recognit. Lett. 33, 1594–1600 (2012)CrossRefGoogle Scholar
  4. 4.
    Hillery, M., Buzek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 18291834 (1999)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hsu, C.-F., Cheng, Q., Tang, X., Zeng, B.: An ideal multi-secret sharing scheme based on MSP. Inf. Sci. 181, 1403–1409 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hsu, C.-F., Cui, G.-H., Cheng, Q., Chen, J.: A novel linear multi-secret sharing scheme for group communication in wireless mesh networks. J. Netw. Comput. Appl. 34, 464–468 (2011)CrossRefGoogle Scholar
  7. 7.
    Hsu, C.-F., Harn, L., Cui, G.: An ideal multi-secret sharing scheme based on connectivity of graphs. Wirel. Pers. Commun. 77, 383–394 (2014)CrossRefGoogle Scholar
  8. 8.
    Kao, S.-H., Hwang, T.: Comment on \((t,n)\) threshold \(d\)-level quantum secret sharing, arXiv:1803.00216v1 (2018)
  9. 9.
    Karchmer, M., Wigderson, A.: On span programs. In: Proceedings of the Eighth Annual Conference on Structure in Complexity, San Diego, CA, pp. 102–111 (1993)Google Scholar
  10. 10.
    Karimifard, Z., Mashhadi, S., Ebrahimi, D.: Semiquantum secret sharing using three particles without entanglement. J. Electron. Cyber Def. 4, 83–92 (2016)Google Scholar
  11. 11.
    Liu, M., Xiao, L., Zhang, Z.: Linear multi-secret sharing schemes based on multi-party computation. Finite Fields Their Appl. 12, 704–713 (2006)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Ma, C., Ding, X.: Proactive verifiable linear integer secret sharing scheme. Inf. Commun. Secur. LNCS 5927, 439–448 (2009)CrossRefGoogle Scholar
  13. 13.
    Mashhadi, S.: Secure publicly verifiable and proactive secret sharing schemes with general access structure. Inf. Sci. 378, 99–108 (2017)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Mashhadi, S., Hadian Dehkordi, M., Kiamari, N.: Provably secure verifiable multi-stage secret sharing scheme based on monotone span program. IET Inf. Secur. 11, 326331 (2017)CrossRefGoogle Scholar
  15. 15.
    Qin, H.: \(d\)-Dimensional quantum secret sharing without entanglement. J. Chin. Inst. Eng. 39, 623–626 (2016)CrossRefGoogle Scholar
  16. 16.
    Qin, H., Dai, Y.: \(d\)-Dimensional quantum state secret sharing with adversary structure. Quntum Inf. Process. 15, 1689–1701 (2016)ADSCrossRefGoogle Scholar
  17. 17.
    Qin, H., Dai, Y.: Verifiable \((t, n)\) threshold quantum secret sharing using \(d\)-dimensional Bell state. Inf. Process. Lett. 116, 351–355 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Qin, H., Tso, R., Dai, Y.: Multi-dimensional quantum state sharing based on quantum Fourier transform. Quntum Inf. Process. 17, 48 (2018).  https://doi.org/10.1007/s11128-018-1827-8 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Qin, H., Zhu, X., Dai, Y.: A quantum secret sharing scheme on access structure. J. Chin. Inst. Eng. 39, 186–191 (2016)CrossRefGoogle Scholar
  20. 20.
    Qin, H., Zhu, X., Dai, Y.: \((t, n)\) threshold quantum secret sharing using the phase shift operation. Quntum Inf. Process. 14, 2997–3004 (2015).  https://doi.org/10.1007/s11128-015-1037-6 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Shamir, A.: How to share a secret. Commun. ACM. 22, 612–613 (1979)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Song, X.-L., Liu, Y.-B., Deng, H.-Y., Xiao, Y.-G.: \((t, n)\) threshold \(d-\)level quantum secret sharing. Sci. Rep. 7, 6366 (2017).  https://doi.org/10.1038/s41598-017-06486-4 ADSCrossRefGoogle Scholar
  23. 23.
    Yang, W., Huang, L., Shi, R.: Secret sharing based on quantum Fourier transform. Quntum Inf. Process. 12, 2465–2474 (2013)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Zhang, J., Zhang, F.: Information-theoretical secure verifiable secret sharing with vector space access structures over bilinear groups and its application. Fut. Gener. Comput. Syst. 52, 109–115 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Cryptography and Data Security Laboratory, School of MathematicsIran University of Science and TechnologyNarmakIran

Personalised recommendations