A secure rational quantum state sharing protocol

  • Zhao Dou
  • Gang Xu
  • Xiu-Bo Chen
  • Xin Liu
  • Yi-Xian Yang
Research Paper


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.


rational quantum state sharing Nash equilibrium secure correct 



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).


  1. 1.
    Shamir A. How to share a secret. Commun ACM, 1979, 22: 612–613MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Blakley G R. Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference 1979, New York, 1979. 313–317Google Scholar
  3. 3.
    Lo H K, Chau H F. Unconditional security of quantum key distribution over arbitrarily long distances. Science, 1999, 283: 2050–2056CrossRefGoogle Scholar
  4. 4.
    Mayers D. Unconditional security in quantum cryptography. J ACM, 2001, 48: 351–406MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Hillery M, Bužek V, Berthiaume A. Quantum secret sharing. Phys Rev A, 1999, 59: 1829MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Cleve R, Gottesman D, Lo H K. How to share a quantum secret. Phys Rev Lett, 1999, 83: 648CrossRefGoogle Scholar
  7. 7.
    Wootters W K, Zurek W H. A single quantum cannot be cloned. Nature, 1982, 299: 802–803CrossRefzbMATHGoogle Scholar
  8. 8.
    Li Y, Zhang K, Peng K. Multiparty secret sharing of quantum information based on entanglement swapping. Phys Lett A, 2004, 324: 420–424MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Lance A M, Symul T, Bowen W P, et al. Tripartite quantum state sharing. Phys Rev Lett, 2004, 92: 177903CrossRefGoogle 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: 022338CrossRefGoogle 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: 1975CrossRefGoogle 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: 032321CrossRefGoogle 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: 1103–1116MathSciNetCrossRefzbMATHGoogle 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. 623–632zbMATHGoogle Scholar
  15. 15.
    Maitra A, Joyee de S, Paul G, et al. Proposal for quantum rational secret sharing. Phys Rev A, 2015, 92: 022305CrossRefGoogle Scholar
  16. 16.
    Stefanov A, Gisin N, Guinnard O, et al. Optical quantum random number generator. J Mod Opt, 2000, 47: 595–598Google Scholar
  17. 17.
    Rigolin G. Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement. Phys Rev A, 2005, 71: 032303CrossRefGoogle 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: 377–379MathSciNetCrossRefzbMATHGoogle 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: 2818–2825MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Li Y B. Analysis of counterfactual quantum key distribution using error-correcting theory. Quantum Inf Proc, 2014, 13: 2325–2342MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Li Y B, Qin S J, Yuan Z, et al. Quantum private comparison against decoherence noise. Quantum Inf Proc, 2013, 12: 2191–2205MathSciNetCrossRefzbMATHGoogle 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: 1–6CrossRefGoogle Scholar
  23. 23.
    Makarov V, Anisimov A, Skaar J. Effects of detector efficiency mismatch on security of quantum cryptosystems. Phys Rev A, 2006, 74: 022313CrossRefGoogle 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: 51–61Google 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: 73–82MathSciNetzbMATHGoogle Scholar
  26. 26.
    Shor P W, Preskill J. Simple proof of security of the BB84 quantum key distribution protocol. Phys Rev Lett, 2000, 85: 441CrossRefGoogle 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. 81–98Google Scholar
  28. 28.
    Rubinstein A. Perfect equilibrium in a bargaining model. Econometrica, 1982, 50: 97–109MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Thaler R H. Anomalies: the ultimatum game. J Econ Perspect, 1988, 2: 195–206CrossRefGoogle Scholar
  30. 30.
    Ståhl I. Bargaining Theory. Stockholm: Stockholm School of Economics, 1972Google 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: 340–352CrossRefGoogle 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: 2546–2559CrossRefGoogle 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: 092103CrossRefGoogle 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: 2402–2415CrossRefGoogle 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: 2706–2716CrossRefGoogle 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. 1–9Google 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: 2793–2804MathSciNetCrossRefzbMATHGoogle 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: 1561–1565CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Zhao Dou
    • 1
  • Gang Xu
    • 1
    • 2
  • Xiu-Bo Chen
    • 1
    • 5
  • Xin Liu
    • 3
    • 4
  • Yi-Xian Yang
    • 1
    • 5
  1. 1.Information Security Center, State Key Laboratory of Networking and Switching TechnologyBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.School of Software EngineeringBeijing University of Posts and TelecommunicationsBeijingChina
  3. 3.School of Computer ScienceShaanxi Normal UniversityXi’anChina
  4. 4.School of Information EngineeringInner Mongolia University of Science and TechnologyBaotouChina
  5. 5.GuiZhou University, Guizhou Provincial Key Laboratory of Public Big DataGuiyangChina

Personalised recommendations