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A secure rational quantum state sharing protocol

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Abstract

A novel rational protocol to share two arbitrary qubits among multiple parties is investigated in this paper. First, the protocol is presented, which is learned from Li et al.’s protocol. Second, the utility, security, correctness, fairness, Nash equilibrium, and Pareto optimality of our scheme are discussed in detail, where the utility, correctness, and fairness of rational quantum state sharing protocols are creatively given because the agent who recovers the state plays a different and more important role. Another important point is that assumptions about our protocol are more practical and suitable than existing protocols.

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References

  1. 1

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

  2. 2

    Blakley G R. Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference 1979, New York, 1979. 313–317

  3. 3

    Lo H K, Chau H F. Unconditional security of quantum key distribution over arbitrarily long distances. Science, 1999, 283: 2050–2056

  4. 4

    Mayers D. Unconditional security in quantum cryptography. J ACM, 2001, 48: 351–406

  5. 5

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

  6. 6

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

  7. 7

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

  8. 8

    Li Y, Zhang K, Peng K. Multiparty secret sharing of quantum information based on entanglement swapping. Phys Lett A, 2004, 324: 420–424

  9. 9

    Lance A M, Symul T, Bowen W P, et al. Tripartite quantum state sharing. Phys Rev Lett, 2004, 92: 177903

  10. 10

    Deng F G, Li C Y, Li Y S, et al. Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement. Phys Rev A, 2005, 72: 022338

  11. 11

    Li X H, Zhou P, Li C Y, et al. Efficient symmetric multiparty quantum state sharing of an arbitrary m-qubit state. J Phys B-At Mol Opt, 2006, 39: 1975

  12. 12

    Muralidharan S, Panigrahi P K. Perfect teleportation, quantum-state sharing, and superdense coding through a genuinely entangled five-qubit state. Phys Rev A, 2008, 77: 032321

  13. 13

    Li D, Wang R, Zhang F, et al. Quantum information splitting of arbitrary two-qubit state by using four-qubit cluster state and Bell-state. Quantum Inf Proc, 2015, 14: 1103–1116

  14. 14

    Halpern J, Teague V. Rational secret sharing and multiparty computation. In: Proceedings of the 36th Annual ACM Symposium on Theory of Computing, New York, 2004. 623–632

  15. 15

    Maitra A, Joyee de S, Paul G, et al. Proposal for quantum rational secret sharing. Phys Rev A, 2015, 92: 022305

  16. 16

    Stefanov A, Gisin N, Guinnard O, et al. Optical quantum random number generator. J Mod Opt, 2000, 47: 595–598

  17. 17

    Rigolin G. Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement. Phys Rev A, 2005, 71: 032303

  18. 18

    Zha X W, Song H Y. Non-Bell-pair quantum channel for teleporting an arbitrary two-qubit state. Phys Lett A, 2007, 369: 377–379

  19. 19

    Li Y B, Wang T Y, Chen H Y, et al. Fault-tolerate quantum private comparison based on GHZ states and ECC. Int J Theor Phys, 2013, 52: 2818–2825

  20. 20

    Li Y B. Analysis of counterfactual quantum key distribution using error-correcting theory. Quantum Inf Proc, 2014, 13: 2325–2342

  21. 21

    Li Y B, Qin S J, Yuan Z, et al. Quantum private comparison against decoherence noise. Quantum Inf Proc, 2013, 12: 2191–2205

  22. 22

    Li Y B, Wen Q Y, Gao F, et al. Information leak in Liu et al.’s quantum private comparison and a new protocol. Eur Phys J D, 2012, 66: 1–6

  23. 23

    Makarov V, Anisimov A, Skaar J. Effects of detector efficiency mismatch on security of quantum cryptosystems. Phys Rev A, 2006, 74: 022313

  24. 24

    Jain N, Stiller B, Khan I, et al. Attacks on practical quantum key distribution systems (and how to prevent them). Contemp Phys, 2016, 5: 51–61

  25. 25

    Qi B, Fung C H F, Lo H K, et al. Time-shift attack in practical quantum cryptosystems. Quantum Inf Comput, 2007, 7: 73–82

  26. 26

    Shor P W, Preskill J. Simple proof of security of the BB84 quantum key distribution protocol. Phys Rev Lett, 2000, 85: 441

  27. 27

    Groce A, Katz J. Fair computation with rational players. In: Proceedings of Annual International Conference on the Theory and Applications of Cryptographic Techniques. Berlin: Springer, 2012. 81–98

  28. 28

    Rubinstein A. Perfect equilibrium in a bargaining model. Econometrica, 1982, 50: 97–109

  29. 29

    Thaler R H. Anomalies: the ultimatum game. J Econ Perspect, 1988, 2: 195–206

  30. 30

    Ståhl I. Bargaining Theory. Stockholm: Stockholm School of Economics, 1972

  31. 31

    Xia Z, Wang X, Sun X, et al. A secure and dynamic multi-keyword ranked search scheme over encrypted cloud data. IEEE Trans Parall Distr, 2016, 27: 340–352

  32. 32

    Fu Z, Ren K, Shu J, et al. Enabling personalized search over encrypted outsourced data with efficiency improvement. IEEE Trans Parall Distr, 2016, 27: 2546–2559

  33. 33

    Chen Y D, Hao C Y, Wu W, et al. Robust dense reconstruction by range merging based on confidence estimation. Sci China Inf Sci, 2016, 59: 092103

  34. 34

    Shen J, Shen J, Chen X F, et al. An efficient public auditing protocol with novel dynamic structure for cloud data. IEEE Trans Inf Forensics Secur, 2017, 12: 2402–2415

  35. 35

    Fu Z, Wu X, Guan C, et al. Toward efficient multi-keyword fuzzy search over encrypted outsourced data with accuracy improvement. IEEE Trans Inf Foren Sec, 2016, 11: 2706–2716

  36. 36

    Fu Z, Sun X, Ji S, et al. Towards efficient content-aware search over encrypted outsourced data in cloud. In: Proceedings of the 35th Annual IEEE International on Conference Computer Communications, San Francisco, 2016. 1–9

  37. 37

    Chen X B, Xu G, Yang Y X, et al. An efficient protocol for the secure multi-party quantum summation. Int J Theor Phys, 2010, 49: 2793–2804

  38. 38

    Chen X B, Xu G, Niu X X, et al. An efficient protocol for the private comparison of equal information based on the triplet entangled state and single-particle measurement. Opt Commun, 2010, 283: 1561–1565

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61671087, 61272514, 61170272), National Development Foundation for Cryptological Research (Grant No. MMJJ201401012), Fok Ying Tung Education Foundation (Grant No. 131067), Natural Science Foundation of Inner Mongolia (Grant No. 2017MS0602), University Scientific Research Project of Inner Mongolia (Grant No. NJZY17164), and Open Foundation of Guizhou Provincial Key Laboratory of Public Big Data (Grant No. 2017BDKFJJ007).

Author information

Correspondence to Xiu-Bo Chen.

Additional information

Conflict of interest The authors declare that they have no conflict of interest.

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Cite this article

Dou, Z., Xu, G., Chen, X. et al. A secure rational quantum state sharing protocol. Sci. China Inf. Sci. 61, 022501 (2018). https://doi.org/10.1007/s11432-016-9151-x

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Keywords

  • rational
  • quantum state sharing
  • Nash equilibrium
  • secure
  • correct