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Quantum Information Processing

, Volume 15, Issue 10, pp 4283–4301 | Cite as

Fault-tolerant quantum blind signature protocols against collective noise

  • Ming-Hui Zhang
  • Hui-Fang Li
Article

Abstract

This work proposes two fault-tolerant quantum blind signature protocols based on the entanglement swapping of logical Bell states, which are robust against two kinds of collective noises: the collective-dephasing noise and the collective-rotation noise, respectively. Both of the quantum blind signature protocols are constructed from four-qubit decoherence-free (DF) states, i.e., logical Bell qubits. The initial message is encoded on the logical Bell qubits with logical unitary operations, which will not destroy the anti-noise trait of the logical Bell qubits. Based on the fundamental property of quantum entanglement swapping, the receiver simply performs two Bell-state measurements (rather than four-qubit joint measurements) on the logical Bell qubits to verify the signature, which makes the protocols more convenient in a practical application. Different from the existing quantum signature protocols, our protocols can offer the high fidelity of quantum communication with the employment of logical qubits. Moreover, we hereinafter prove the security of the protocols against some individual eavesdropping attacks, and we show that our protocols have the characteristics of unforgeability, undeniability and blindness.

Keywords

Quantum cryptography Quantum blind signature Entanglement swapping Fault-tolerant Collective noise Decoherence-free states 

Notes

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 61273250) and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (Grant No. CX201618).

References

  1. 1.
    Diffie, W., Hellman, M.: New directions in cryptography. IEEE. Trans. Inf. Theory 22, 644–654 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Chaum, D.: Blind signature for untraceable payments. In: Proceedings of CRYPTO’82, pp. 199–203 (1982)Google Scholar
  3. 3.
    Harn, L.: Cryptanalysis of the blind signature based on the discrete logarithm problem. Electron. Lett. 31, 1136–1137 (1995)CrossRefGoogle Scholar
  4. 4.
    Fan, C.I., Lei, C.L.: Efficient blind signature scheme based on quadratic residues. Electron. Lett. 32, 811–813 (1996)CrossRefGoogle Scholar
  5. 5.
    Mohammed, E., Emarah, A.E., El-Shennawy, K.: Elliptic curve cryptosystems on smart cards. In: Proceedings of 35th Annual International Carnahan Conference on Security Technology, pp. 213–222 (2001)Google Scholar
  6. 6.
    Chien, H., Jan, J., Tseng, Y.: RSA-based partially blind signature with low computation. In: Proceedings of 8th International Conference on Parallel and Distributed Systems (ICPADS), pp. 385–389 (2001)Google Scholar
  7. 7.
    Clarke, P.J., Collins, R.J., Dunjko, V., et al.: Experimental demonstration of quantum digital signatures using phase-encoded coherent states of light. Nat. Commun. 3, 1174 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    Gottesman, D., Chuang, I.: Quantum digital signatures. arXiv:quant-ph/0105032 (2001)
  9. 9.
    Zeng, G.H., Keitel, C.H.: Arbitrated quantum-signature scheme. Phys. Rev. A 65, 042312 (2002)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Li, Q., Chan, W.H., Long, D.Y.: Arbitrated quantum signature scheme using Bell states. Phys. Rev. A 79, 054307 (2009)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Andersson, E., Curty, M., Jex, I.: Experimentally realizable quantum comparison of coherent states and its applications. Phys. Rev. A 74, 022304 (2006)ADSCrossRefGoogle Scholar
  12. 12.
    Dunjko, V., Wallden, P., Andersson, E.: Quantum digital signatures without quantum memory. Phys. Rev. Lett. 112, 040502 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    Collins, R.J., Donaldson, R.J., Dunjko, V., et al.: Realization of quantum digital signatures without the requirement of quantum memory. Phys. Rev. Lett. 113, 040502 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    Wallden, P., Dunjko, V., Kent, A., et al.: Quantum digital signatures with quantum-key-distribution components. Phys. Rev. A 91, 042304 (2015)ADSCrossRefGoogle Scholar
  15. 15.
    Lee, H., Hong, C., Kim, H., et al.: Arbitrated quantum signature scheme with message recovery. Phys. Lett. A 321, 295–300 (2004)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Wen, X.J., Liu, Y., Sun, Y.: Quantum multi-signature protocol based on teleportation. Z. Naturforsch. A 62, 147–151 (2007)ADSCrossRefzbMATHGoogle Scholar
  17. 17.
    Zeng, G.H., Lee, M.H., Guo, Y., et al.: Continuous variable quantum signature algorithm. Int. J. Quantum Inf. 5, 553–573 (2007)CrossRefzbMATHGoogle Scholar
  18. 18.
    Wen, X.J., Niu, X.M., Ji, L.P., et al.: A weak blind signature scheme based on quantum cryptography. Opt. Commun. 282, 666–669 (2008)ADSCrossRefGoogle Scholar
  19. 19.
    Su, Q., Huang, Z., Wen, Q.Y., et al.: Quantum blind signature based on two-state vector formalism. Opt. Commun. 283, 4408–4410 (2010)CrossRefGoogle Scholar
  20. 20.
    Wang, T.Y., Wen, Q.Y.: Fair quantum blind signatures. Chin. Phys. B 19, 060307 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    Yin, X.R., Ma, W.P., Liu, W.Y.: A blind quantum signature scheme with \(\chi \)-type entangled states. Int. J. Theor. Phys. 51, 455–461 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Wang, M.M., Chen, X.B., Niu, X.X., et al.: Re-examining the security of blind quantum signature protocols. Phys. Scr. 86, 055006 (2012)CrossRefzbMATHGoogle Scholar
  23. 23.
    Khodambashi, S., Zakerolhosseini, A.: A sessional blind signature based on quantum cryptography. Quantum Inf. Process. 13, 121–130 (2014)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Zhang, M.H., Li, H.F.: Weak blind quantum signature protocol based on entanglement swapping. Photon. Res. 3, 324–328 (2015)CrossRefGoogle Scholar
  25. 25.
    Tian, Y., Chen, H., Ji, S.F., et al.: A broadcasting multiple blind signature scheme based on quantum teleportation. Opt. Quant. Electron. 46, 769–777 (2014)CrossRefGoogle Scholar
  26. 26.
    Ribeiro, J.: Quantum blind signature with an offline repository. Int. J. Quantum Inf. 13, 1550016 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Kurtsiefer, C., Zarda, P., Halder, M., et al.: A step towards global key distribution. Nature 419, 450–450 (2002)ADSCrossRefGoogle Scholar
  28. 28.
    Stucki, D., Ginsin, N., Guinnard, O., et al.: Quantum key distribution over 67 km with a plug & play system. New J. Phys. 4, 41 (2002)ADSCrossRefGoogle Scholar
  29. 29.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  30. 30.
    Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995)ADSCrossRefGoogle Scholar
  31. 31.
    Li, X.H., Deng, F.G., Zhou, H.Y.: Faithful qubit transmission against collective noise without ancillary qubits. Appl. Phys. Lett. 91, 144101 (2007)ADSCrossRefGoogle Scholar
  32. 32.
    Yamamoto, T., Shimamura, J., Ozdemir, S.K., et al.: Faithful qubit distribution assisted by one additional qubit against collective noise. Phys. Rev. Lett. 95, 040503 (2005)ADSCrossRefGoogle Scholar
  33. 33.
    Bennett, C.H., Brassard, G., Popescu, S., et al.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996)ADSCrossRefGoogle Scholar
  34. 34.
    Pan, J.W., Simon, C., Brukner, C., et al.: Entanglement purification for quantum communication. Nature 410, 1067–1070 (2001)ADSCrossRefGoogle Scholar
  35. 35.
    Kwiat, P.G., Berglund, A.J., Altepeter, J.B., et al.: Experimental verification of decoherence-free subspaces. Science 290, 498–501 (2000)ADSCrossRefGoogle Scholar
  36. 36.
    Kempe, J., Bacon, D., Lidar, D.A., et al.: Theory of decoherence-free fault tolerant universal quantum computation. Phys. Rev. A 63, 042307 (2001)ADSCrossRefGoogle Scholar
  37. 37.
    Walton, Z.D., Abouraddy, A.F., Sergienko, A.V., et al.: Decoherence-free subspaces in quantum key distribution. Phys. Rev. Lett. 91, 087901 (2003)ADSCrossRefGoogle Scholar
  38. 38.
    Boileau, J.C., Gottesman, D., Laflamme, R., et al.: Robust polarization-based quantum key distribution over a collective-noise channel. Phys. Rev. Lett. 92, 017901 (2004)ADSCrossRefGoogle Scholar
  39. 39.
    Wang, X.B.: Fault tolerant quantum key distribution protocol with collective random unitary noise. Phys. Rev. A 72, 050304 (2005)ADSCrossRefGoogle Scholar
  40. 40.
    Li, X.H., Deng, F.G., Zhou, H.Y.: Efficient quantum key distribution over a collective noise channel. Phys. Rev. A 78, 022321 (2008)ADSCrossRefGoogle Scholar
  41. 41.
    Li, X.H., Zhao, B.K., Sheng, Y.B., et al.: Fault tolerant quantum key distribution based on quantum dense coding with collective noise. Int. J. Quantum Inf. 8, 1479–1489 (2009)CrossRefzbMATHGoogle Scholar
  42. 42.
    Xiu, X.M., Dong, L., Gao, Y.J., et al.: Quantum key distribution protocols with six-photon states against collective noise. Opt. Commun. 282, 4171–4174 (2009)ADSCrossRefGoogle Scholar
  43. 43.
    Sun, Y., Wen, Q.Y., Gao, F., et al.: Robust variations of the Bennett-Brassard 1984 protocol against collective noise. Phys. Rev. A 80, 032321 (2009)ADSCrossRefGoogle Scholar
  44. 44.
    Lidar, D.A., Bacon, D., Kempe, J., et al.: Protecting quantum information encoded in decoherence-free states against exchange errors. Phys. Rev. A 61, 052307 (2000)ADSCrossRefGoogle Scholar
  45. 45.
    Bourennane, M., Eibl, M., Gaertner, S., et al.: Decoherence-free quantum information processing with four-photon entangled states. Phys. Rev. Lett. 92, 107901 (2004)ADSCrossRefGoogle Scholar
  46. 46.
    Ge, H., Liu, W.Y.: A new quantum secure direct communication protocol using decoherence-free subspace. Chin. Phys. Lett. 24, 2727–2729 (2007)ADSCrossRefGoogle Scholar
  47. 47.
    Qin, S.J., Wen, Q.Y., Meng, L.M., et al.: Quantum secure direct communication over the collective amplitude damping channel. Sci. China-Phys. Mech. Astron. 52, 1208–1212 (2009)ADSCrossRefGoogle Scholar
  48. 48.
    Gu, B., Zhang, C.Y., Cheng, G.S., et al.: Robust quantum secure direct communication with a quantum one-time pad over a collective-noise channel. Sci. China-Phys. Mech. Astron. 54, 942–947 (2011)ADSCrossRefGoogle Scholar
  49. 49.
    Yang, C.W., Tsai, C.W., Hwang, T.: Fault tolerant two-step quantum secure direct communication protocol against collective noises. Sci. China-Phys. Mech. Astron. 54, 496–501 (2011)ADSCrossRefGoogle Scholar
  50. 50.
    Chang, Y., Zhang, S.B., Li, J., et al.: Robust EPR-pairs-based quantum secure communication with authentication resisting collective noise. Sci. China-Phys. Mech. Astron. 57, 1907–1912 (2014)ADSCrossRefGoogle Scholar
  51. 51.
    Zhang, Z.J.: Robust multiparty quantum secret key sharing over two collective-noise channels. Phys. A 361, 233–238 (2006)ADSCrossRefGoogle Scholar
  52. 52.
    Gu, B., Mu, L., Ding, L., et al.: Fault tolerant three-party quantum secret sharing against collective noise. Opt. Commun. 283, 3099–3103 (2010)ADSCrossRefGoogle Scholar
  53. 53.
    Lin, J., Hwang, T.: Bell state entanglement swappings over collective noises and their applications on quantum cryptography. Quantum Inf. Process. 12, 1089–1107 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  54. 54.
    Yang, C.W., Hwang, T.: Quantum dialogue protocols immune to collective noise. Quantum Inf. Process. 12, 2131–2142 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  55. 55.
    Ye, T.Y.: Information leakage resistant quantum dialogue against collective noise. Sci. China-Phys. Mech. Astron. 57, 2266–2275 (2014)ADSCrossRefGoogle Scholar
  56. 56.
    Ye, T.Y.: Robust quantum dialogue based on the entanglement swapping between any two logical Bell states and the shared auxiliary logical Bell state. Quantum Inf. Process. 14, 1469–1486 (2015)ADSCrossRefzbMATHGoogle Scholar
  57. 57.
    Gu, B., Pei, S.X., Song, B., et al.: Deterministic secure quantum communication over a collective-noise channel. Sci. China-Phys. Mech. Astron. 52, 1913–1918 (2009)ADSCrossRefGoogle Scholar
  58. 58.
    Shor, P., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85, 441–444 (2000)ADSCrossRefGoogle Scholar
  59. 59.
    Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, pp. 175–179 (1984)Google Scholar
  60. 60.
    Deng, F.G., Long, G.L., Liu, X.S.: Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A 68, 042317 (2003)ADSCrossRefGoogle Scholar
  61. 61.
    Bostrom, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902 (2002)ADSCrossRefGoogle Scholar
  62. 62.
    Deng, F.G., Long, G.L.: Bidirectional quantum key distribution protocol with practical faint laser pulses. Phys. Rev. A 70, 012311 (2004)ADSCrossRefGoogle Scholar
  63. 63.
    Deng, F.G., Zhou, H.Y., Long, G.L.: Circular quantum secret sharing. J. Phys. A-Math. Gen. 39, 14089–14099 (2006)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  64. 64.
    Hoeffding, W.: Probability-inequalities for sums of bounded random-variables. J. Am. Stat. Assoc. 58, 13–30 (1963)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of Electronic and InformationNorthwestern Polytechnical UniversityXi’anChina

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