A secure rational quantum state sharing protocol


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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  1. 1

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

    MathSciNet  Article  MATH  Google Scholar 

  2. 2

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

    Google Scholar 

  3. 3

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

    Article  Google Scholar 

  4. 4

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

    MathSciNet  Article  MATH  Google Scholar 

  5. 5

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

    MathSciNet  Article  MATH  Google Scholar 

  6. 6

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

    Article  Google Scholar 

  7. 7

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

    Article  MATH  Google Scholar 

  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

    MathSciNet  Article  MATH  Google Scholar 

  9. 9

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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    MathSciNet  Article  MATH  Google Scholar 

  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

    Google Scholar 

  15. 15

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

    Article  Google Scholar 

  16. 16

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

    Google Scholar 

  17. 17

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

    Article  Google Scholar 

  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

    MathSciNet  Article  MATH  Google Scholar 

  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

    MathSciNet  Article  MATH  Google Scholar 

  20. 20

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

    MathSciNet  Article  MATH  Google Scholar 

  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

    MathSciNet  Article  MATH  Google Scholar 

  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

    Article  Google Scholar 

  23. 23

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

    Article  Google Scholar 

  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

    Google Scholar 

  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

    MathSciNet  MATH  Google Scholar 

  26. 26

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

    Article  Google Scholar 

  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

    Google Scholar 

  28. 28

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

    MathSciNet  Article  MATH  Google Scholar 

  29. 29

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

    Article  Google Scholar 

  30. 30

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

    Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Google Scholar 

  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

    MathSciNet  Article  MATH  Google Scholar 

  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

    Article  Google Scholar 

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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).

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Correspondence to Xiu-Bo Chen.

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

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Dou, Z., Xu, G., Chen, XB. 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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  • rational
  • quantum state sharing
  • Nash equilibrium
  • secure
  • correct