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Quantum homomorphic signature based on Bell-state measurement

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Abstract

In this paper, a novel quantum homomorphic signature scheme based solely on Bell-state measurement is proposed. It allows an aggregator to merge two signature nodes’ signatures of their classical messages into one signature, which is an effective approach to identity authentication for multiple streams to enhance the security of quantum networks. And it is easy to generalize this scheme to multiple nodes. Bell-state measurement has been realized by using only linear optical elements in many experimental measurement-device-independent quantum key distribution schemes, which makes us believe that our scheme can be realized in the near future. It is shown that our scheme is a quantum group homomorphic signature scheme and is secure by the scheme analysis.

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References

  1. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring:Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on. IEEE, 1994: 124-134

  2. Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325 (1997)

    Article  ADS  Google Scholar 

  3. Gottesman, D., Chuang, I.: Quantum digital signatures. arXiv preprint arXiv:quant-ph/0105032, (2001)

  4. Zeng, G., Keitel, C.H.: Arbitrated quantum-signature scheme. Phys. Rev. A 65(4), 042312 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  5. Curty, M., Ltkenhaus, N.: Comment on arbitrated quantum-signature scheme. Phys. Rev. A 77(4), 1–4 (2008)

    Article  MathSciNet  Google Scholar 

  6. Zeng, G.H.: Reply to Comment on Arbitrated quantum-signature scheme. Phys. Rev. A 77(1), 1–5 (2008)

    MathSciNet  Google Scholar 

  7. Li, Q., Chan, W.H., Long, D.Y.: Arbitrated quantum signature scheme using Bell states. Phys. Rev. A 79, 054307 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  8. Zou, X.F., Qiu, D.W.: Security analysis and improvements of arbitrated quantum signature schemes. Phys. Rev. A 82, 042325 (2010)

    Article  ADS  Google Scholar 

  9. Yang, Y.G., Wen, Q.Y.: Arbitrated quantum signature of classical messages against collective amplitude damping noise. Opt. Commun. 283(16), 3198–3201 (2010)

    Article  ADS  Google Scholar 

  10. Yang, Y.G., Wen, Q.Y.: Erratum: arbitrated quantum signature of classical messages against collective amplitude damping noise. Opt. Commun. 283(19), 3830 (2010)

    Article  ADS  Google Scholar 

  11. Gao, F., Qin, S.J., Guo, F.Z., et al.: Cryptanalysis of the arbitrated quantum signature protocols. Phys. Rev. A 84(2), 17864–17875 (2011)

    Google Scholar 

  12. Zhang, K.J., Zhang, W.W., Li, D.: Improving the security of arbitrated quantum signature against the forgery attack. Quantum Inf. Process. 12(8), 2655–2669 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Dunjko, V., Wallden, P., Andersson, E.: Quantum digital signatures without quantum memory. Phys. Rev. Lett. 112(4), 672–672 (2014)

    Article  MATH  Google Scholar 

  14. 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(4), 1–14 (2014)

    Article  Google Scholar 

  15. Wallden, P., Dunjko, V., Kent, A.: Quantum digital signatures with quantum-key-distribution components. Phys. Rev. A 91(4), 042304 (2015)

    Article  ADS  Google Scholar 

  16. Yang, Y.G.: Multi-proxy quantum group signature scheme with threshold shared verification. Chin. Phys. B 17, 415 (2008)

    Article  ADS  Google Scholar 

  17. Yang, Y.G., Wen, Q.Y.: Threshold proxy quantum signature scheme with threshold shared verification. Sci. China, Ser. G Phys. Mech. Astron. 51, 1079–1088 (2008)

    Article  ADS  MATH  Google Scholar 

  18. Yang, Y.G., Wang, Y., Teng, Y.W., Chai, H.P., Wen, Q.Y.: Scalable arbitrated quantum signature of classical messages with multi-signers. Commun. Theor. Phys. 54, 84 (2010)

    Article  ADS  MATH  Google Scholar 

  19. Wen, X., Tian, Y., Ji, L., et al.: A group signature scheme based on quantum teleportation. Phys. Scr. 81(5), 561–578 (2010)

    Article  MATH  Google Scholar 

  20. Chaum, D.: Group Signature Advances in Cryptology Eurocrypt91 LNCS 547, pp. 257–265. Springer, Berlin (1992)

    Google Scholar 

  21. Zhang, K.J., Song, T.T., Zuo, H.J., et al.: A secure quantum signature scheme based on Bell states. Phys. Scr. 87, 045012 (2013)

    Article  ADS  Google Scholar 

  22. Su, Q., Li, W.M.: Improved Group Signature Scheme Based on Quantum Teleportation. Int. J. Theor. Phys. 53(4), 1208–1216 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  23. Xu, G.B., Zhang, K.J.: A novel quantum group signature scheme without using entangled states. Quantum Inf. Process. 14, 2577–2587 (2015). doi:10.1007/s11128-015-0995-z

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Shang, T., Zhao, X.J., Wang, C., et al.: Quantum homomorphic signature. Quantum Inf. Process. 14(1), 393–410 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Johnson, R., Molnar, D., Song, D., et al.: Homomorphic Signature Schemes[M]//Topics in Cryptology CT-RSA 2002. Springer, Berlin Heidelberg (2002)

    Google Scholar 

  26. Grice, W.P.: Arbitrarily complete Bell-state measurement using only linear optical elements. Phys. Rev. A 84(4), 042331 (2011)

    Article  ADS  Google Scholar 

  27. Kok, P., Munro, W.J., Nemoto, K., et al.: Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79(1), 135 (2007)

    Article  ADS  Google Scholar 

  28. Bennett, C.H., Brassard, G.: Quantum cryptography: public-key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, New York, Bangalore, India, 175-179 (1984)

  29. Lo, H.K., Curty, M., Qi, B.: Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 108(13), 130503 (2012)

    Article  ADS  Google Scholar 

  30. Liu, Y., Chen, T.Y., Wang, L.J., et al.: Experimental measurement-device-independent quantum key distribution. Phys. Rev. Lett. 111(13), 130502 (2013)

    Article  ADS  Google Scholar 

  31. Tang, Z., Liao, Z., Xu, F., et al.: Experimental demonstration of polarization encoding measurement-device-independent quantum key distribution. Phys. Rev. Lett. 112(19), 190503 (2014)

    Article  ADS  Google Scholar 

  32. Tang, Z., Wei, K., Bedroya, O., et al.: Experimental Measurement-Device-Independent Quantum Key Distribution with Imperfect Sources[J]. arXiv preprint arXiv:1508.03562, (2015)

  33. Hong, C.K., Ou, Z.Y., Mandel, L.: Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59(18), 2044 (1987)

    Article  ADS  Google Scholar 

  34. Kim, Y.H., Kulik, S.P., Shih, Y.: Quantum teleportation of a polarization state with a complete Bell state measurement. Phys. Rev. Lett. 86(7), 1370 (2001)

    Article  ADS  Google Scholar 

  35. Lo, H.K., Chau, H.F.: Efficient quantum key distribution scheme and a proof of its unconditional security. J. Cryptol. 18, 133–165 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  36. Luo, Q.B., Yang, G.W., She, K., et al.: Multi-party quantum private comparison protocol based on d-dimensional entangled states. Quantum. Inf. Process. 13(10), 2343–2352 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Chang, Y., Tsai, C., Hwang, T.: Multi-user private comparison protocol using GHZ class states. Quantum Inf. Process. 12(2), 1077–1088 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. Hwang, W.Y.: Quantum key distribution with high loss: toward global secure communication. Phys. Rev. Lett. 91(5), 057901 (2003)

    Article  ADS  Google Scholar 

  39. Lo, H.K., Ma, X., Chen, K.: Decoy state quantum key distribution. Phys. Rev. Lett. 94(23), 230504 (2005)

    Article  ADS  Google Scholar 

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Acknowledgments

The authors thank the anonymous reviewers for their constructive comments and useful suggestions. This work is supported by China State Scholarship Fund, National Natural Science Foundation of China (Nos. 61272175, 61401176, 61572109, 61502082), the Fundamental Research Funds for the Central Universities (No. ZYGX2014J065) and Natural Science Foundation of Guangdong Province, China (No. 2014A030310205).

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Correspondence to Qing-bin Luo.

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Luo, Qb., Yang, Gw., She, K. et al. Quantum homomorphic signature based on Bell-state measurement. Quantum Inf Process 15, 5051–5061 (2016). https://doi.org/10.1007/s11128-016-1440-7

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  • DOI: https://doi.org/10.1007/s11128-016-1440-7

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