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Quantum Security Computation on Shared Secrets

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Abstract

Ouyang et al. proposed an (n, n) threshold quantum secret sharing scheme, where the number of participants was limited to n = 4k + 1, k ∈ Z+, and the security evaluation of the scheme was carried out accordingly. In this paper, we introduce an (n, n) threshold quantum secret sharing scheme for the number of participants n in any case (n ∈ Z+ ). The scheme is based on a quantum circuit, which consists of Clifford group gates and Toffoli gates. We study the properties of the quantum circuit in this paper and use the quantum circuit to analyze the security of the scheme for dishonest participant attack.

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References

  1. Bennett, C.H., Brassard, G.: Systems and Signal Processing, vol. 175. IEEE Press, New York (1984)

    Google Scholar 

  2. Ekert, A.K.: Quantum Cryptography Based on bells Theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Crpeau, C., Gottesman, D., Smith, A.: Secure Multi-party Quantum Computing, The Thiry-Fourth ACM Symposium. ACM, pp. 643–652 (2002)

  4. Broadbent, A., Fitzsimons, J., Kashefi, E.: Universal Blind Quantum Computation, Foundations of Computer Science, pp. 517–526 (2009)

  5. Morimae, T., Fujii, K.: Blind topological measurement-based quantum computation. Nat. Commun. 3, 1036 (2012)

    Article  ADS  Google Scholar 

  6. Barz, S., Kashefi, E., Broadbent, A., Fitzsimons, J.F., Zeilinger, A., Walther, P.: Experimental demonstration of blind quantum computing. Science 335, 303 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Broadbent, A., Fitzsimons, J., Kashefi, E.: Universal blind quantum computation. Found. Comput. Sci. 19, 517–526 (2009)

    MathSciNet  MATH  Google Scholar 

  8. Aharonov, D., Ben-Or, M., Eban, E.: Interactive proofs for quantum computations. In: Proceedings of Innovations in Computer Science, pp. 453–469 (2017)

  9. Reichardt, B., Unger, F., Vazirani, U.: Classical command of quantum systems. Nat. (Lond.) 496(7446), 456–460 (2013)

    Article  ADS  Google Scholar 

  10. Fitzsimons, J.F., Kashefi, E.: Unconditionally verifiable blind quantum computation. Phys. Rev. A 96, 012303 (2017)

    Article  ADS  Google Scholar 

  11. Morimae, T.: Verification for measurement-only blind quantum computing. Phys. Rev. A 89, 060302 (2014)

    Article  ADS  Google Scholar 

  12. Hayashi, M., Morimae, T.: Verifiable Measurement-Only blind quantum computing with stabilizer testing. Phys. Rev. Lett. 115, 220502 (2015)

    Article  ADS  Google Scholar 

  13. Zhou, Z.W., Tu, T., Gong, M., et al.: Progress and Prospect of quantum computing. Prog. Phys. 29, 127–165 (2009)

    Google Scholar 

  14. Ouyang, Y., Tan, S.H., Zhao, L., et al.: Computing on quantum shared secrets. Phys. Rev. A 96, 052333 (2017)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Bai, C.M., Li, Z. H., Xu, T.T., et al.: A generalized information theoretical model for quantum secret sharing. Int. J. Theor. Phys. 55, 4972–4986 (2016)

    Article  MATH  Google Scholar 

  17. Deng, F.G., Gui, L.L., Zhou, H.Y.: An efficient quantum secret sharing scheme with Einstein−Podolsky−Rosen pairs. Phys. Lett. A 340, 43–50 (2006)

    Article  ADS  MATH  Google Scholar 

  18. Bai, C.M., Li, Z.H., Liu, C.J., et al.: Quantum secret sharing using orthogonal multi-qudit entangled states. Quantum Inf. Process. 16, 304 (2017)

    Article  ADS  MATH  Google Scholar 

  19. Xiao, L., Long, G.L., Deng, F.G., et al.: Efficient multiparty quantum-secret-sharing schemes. Physics 69, 521–524 (2004)

    Google Scholar 

  20. Xu, T.T., Li, Z.H., Bai, C.M., et al.: A new improving quantum secret sharing scheme. Int. J. Theor. Phys. 56, 1–10 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Tittel, W, Zbinden, H, Gisin, N.: Experimental demonstration of quantum secret sharing. Phys. Rev. A 63, 42301 (2001)

    Article  ADS  Google Scholar 

  22. Bai, C.M., Li, Z.H., Xu, T.T., et al.: Quantum secret sharing using the d-dimensional GHZ state. Quantum Inf Process 16, 59 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  24. Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61(4), 192–193 (2000)

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Deutsch, D., Barenco, A., Ekert, A.: Universality in quantum computation. Proc. Math. Phys. Sci. 449(1937), 669–677 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  27. Zhou, X., Leung, D.W., Chuang, I.L.: Methodology for quantum logic gate constructions. Phys. Rev. A 62, 052316 (2000)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, China

    Hai-Yan Bai, Zhi-Hui Li & Na Hao

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  1. Hai-Yan Bai
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  2. Zhi-Hui Li
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  3. Na Hao
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Correspondence to Zhi-Hui Li.

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Bai, HY., Li, ZH. & Hao, N. Quantum Security Computation on Shared Secrets. Int J Theor Phys 58, 10–21 (2019). https://doi.org/10.1007/s10773-018-3905-1

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  • DOI: https://doi.org/10.1007/s10773-018-3905-1

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