Quantum Information Processing

, Volume 10, Issue 1, pp 97–106 | Cite as

Sharing a quantum secret without a trusted party

  • Qin Li
  • Dong Yang Long
  • W. H. Chan
  • Dao Wen Qiu
Article

Abstract

In a conventional quantum (k, n) threshold scheme, a trusted party shares a secret quantum state with n participants such that any k of those participants can cooperate to recover the original secret, while fewer than k participants obtain no information about the secret. In this paper we show how to construct a quantum (k, n) threshold scheme without the assistance of a trusted party, who generates and distributes shares among the participants. Instead, each participant chooses his private state and contributes the same to the determination of the final secret quantum state.

Keywords

Quantum secret sharing Quantum cryptography Quantum information processing Quantum communication 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Blakley, G.R.: Safeguarding cryptographic keys. In: Proceedings of National Computer Conference, pp. 313–317. AFIPS, New York (1979)Google Scholar
  2. 2.
    Shamir A.: How to share a secret. Commun. ACM 22, 612–613 (1979)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Ingemarsson, I., Simmons, G.J.: A protocol to set up shared secret schemes without the assistance of a mutually trusted party. In: Advances in Cryptology—Proceedings of Eurocrypt’90, pp. 266–282. Springer, Berlin (1991)Google Scholar
  4. 4.
    Pedersen, T.P.: A threshold cryptosystem without a trusted party. In: Advances in Cryptology— Proceedings of Eurocrypt’91, pp. 522–526. Springer, Berlin (1991)Google Scholar
  5. 5.
    Jackson, W.-A., Martin, K.M., O’Keefe, C.M.: Efficient secret sharing without a mutually trusted authority. In: Advances in Cryptology—Proceedings of Eurocrypt’95, pp. 183-193. Springer, Berlin (1995)Google Scholar
  6. 6.
    Hillery M., Bǔzek V., Berthiaume A.: Quantum secret sharing. Phys. Rev. A 59, 1829–1834 (1999)CrossRefMathSciNetADSGoogle Scholar
  7. 7.
    Karlsson A., Koashi M., Imoto N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162–168 (1999)CrossRefADSGoogle Scholar
  8. 8.
    Cleve R., Gottesman D., Lo H.-K.: How to share a quantum secret. Phys. Rev. Lett. 83, 648–651 (1999)CrossRefADSGoogle Scholar
  9. 9.
    Gottesman D.: Theory of quantum secret sharing. Phys. Rev. A 61, 042311 (2000)CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    Bandyopadhyay S.: Teleportation and secret sharing with pure entangled states. Phys. Rev. A 62, 012308 (2000)CrossRefMathSciNetADSGoogle Scholar
  11. 11.
    Nascimento A.C.A., Mueller-Quade J., Imai H.: Improving quantum secret-sharing schemes. Phys. Rev. A 64, 042311 (2001)CrossRefADSGoogle Scholar
  12. 12.
    Guo G.P., Guo G.C.: Quantum secret sharing without entanglement. Phys. Lett. A 310, 247–251 (2003)MATHCrossRefMathSciNetADSGoogle Scholar
  13. 13.
    Lance A.M., Symul T., Bowen W.P., Sanders B.C., Lam P.K.: Tripartite quantum state sharing. Phys. Rev. Lett. 92, 177903 (2004)CrossRefADSPubMedGoogle Scholar
  14. 14.
    Xiao L., Long G.L., Deng F.G., Pan J.W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69, 052307 (2004)CrossRefADSGoogle Scholar
  15. 15.
    Tokunaga Y., Okamoto T., Imoto N.: Threshold quantum cryptography. Phys. Rev. A 71, 012314 (2005)CrossRefADSGoogle Scholar
  16. 16.
    Zhang Z.J., Li Y., Man Z.X.: Multiparty quantum secret sharing. Phys. Rev. A 71, 044301 (2005)CrossRefMathSciNetADSGoogle Scholar
  17. 17.
    Deng F.G., Zhou H.Y., Long G.L.: Bidirectional quantum secret sharing and secret splitting with polarized single photons. Phys. Lett. A 337, 329–334 (2005)MATHCrossRefADSGoogle Scholar
  18. 18.
    Takesue H., Inoue K.: Quantum secret sharing based on modulated high-dimensional time-bin entanglement. Phys. Rev. A 74, 012315 (2006)CrossRefADSGoogle Scholar
  19. 19.
    Zhang Z.J.: Multiparty secret sharing of quantum information via cavity QED. Opt. Comm. 261, 199–202 (2006)CrossRefADSGoogle Scholar
  20. 20.
    Yu I.C., Lin F.L., Huang C.Y.: Quantum secret sharing with multilevel mutually (un)biased bases. Phys. Rev. A 78, 012344 (2008)CrossRefADSGoogle Scholar
  21. 21.
    Wootters W.K., Zurek W.H.: A single quantum cannot be cloned. Nature 299, 802–803 (1982)CrossRefADSGoogle Scholar
  22. 22.
    Aigner M., Ziegler G.M.: Proofs from the book, pp. 7–10. Springer, Berlin (2006)MATHGoogle Scholar
  23. 23.
    Crépeau, C., Gottesman, D., Smith, A.: Secure multi-party quantum computation. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing. pp. 643–652. ACM, New York (2002)Google Scholar
  24. 24.
    Ben-Or, M., Crépeau, C., Gottesman, D., Hassidim, A., Smith, A.: Secure multiparty quantum computation with (only) a strict honest majority. In: Proceedings of 47th Annual IEEE Symposium on the Foundations of Computer Science, pp. 249–260. IEEE, Los Alamitos (2006)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Qin Li
    • 1
    • 2
  • Dong Yang Long
    • 1
  • W. H. Chan
    • 2
  • Dao Wen Qiu
    • 1
  1. 1.Department of Computer ScienceSun Yat-sen UniversityGuangzhouChina
  2. 2.Department of MathematicsHong Kong Baptist UniversityKowloon, Hong KongChina

Personalised recommendations