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Secure quantum network coding based on quantum homomorphic message authentication

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Abstract

As the principal security threat, pollution attacks also seriously affect the security of quantum network coding, just like they do for the classical network coding. Based on this, we first propose two secure quantum homomorphic message authentication schemes based on quantum circuit, which well resist the pollution attacks launched by outside attackers and the attackers including inside untrusted nodes over the general quantum network. Then, we apply this authentication method into our extended quantum network coding scheme over the multi-unicast network \(\mathcal {N}\), solving the quantum k-pair problem securely and perfectly. Analysis results show that our proposed quantum network coding scheme has higher security and higher quantum communication rate, compared with the existing secure scheme.

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References

  1. Ahlswede, R., Cai, N., Li, S.-Y.R.: Network information flow. IEEE Trans. Inf. Theory 46(4), 1204–1216 (2000)

    MathSciNet  MATH  Google Scholar 

  2. Li, S.-Y.R., Yeung, R.W., Cai, N.: Linear network coding. IEEE Trans. Inf. Theory 49(2), 371–381 (2003)

    MathSciNet  MATH  Google Scholar 

  3. Sung, C.W., Shum, K.W., Huang, L., Kwan, H.Y.: Linear network coding for erasure broadcast channel with feedback: complexity and algorithms. IEEE Trans. Inf. Theory 62(5), 2493–2503 (2016)

    MathSciNet  MATH  Google Scholar 

  4. Guo, R., Zhang, Z., Liu, X., Lin, C.: Existence, uniqueness, and exponential stability analysis for complex-valued memristor-based BAM neural networks with time delays. Appl. Math. Comput. 311, 100–117 (2017)

    MathSciNet  MATH  Google Scholar 

  5. Pang, Z., Liu, G., Zhou, D., Sun, D.: Data-based predictive control for networked nonlinear systems with packet dropout and measurement noise. J. Syst. Sci. Complex 30(5), 1072–1083 (2017)

    MathSciNet  MATH  Google Scholar 

  6. Li, L., Wang, Z., Li, Y., Shen, H., Lu, J.: Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays. Appl. Math. Comput. 330, 152–169 (2018)

    MathSciNet  MATH  Google Scholar 

  7. Shen, H., Song, X., Li, F., Wang, Z., Chen, B.: Finite-time \(L^{2}-L^{\infty }\) filter design for networked Markov switched singular systems: a unified method. Appl. Math. Comput. 321, 450–462 (2018)

    MathSciNet  Google Scholar 

  8. Shin, W.Y., Chung, S.Y., Lee, Y.H.: Parallel opportunistic routing in wireless networks. IEEE Trans. Inf. Theory 59(10), 6290–6300 (2013)

    MathSciNet  MATH  Google Scholar 

  9. Dong, H., Zhang, Y., Zhang, Y., Yin, B.: Generalized bilinear differential operators, binary bell polynomials, and exact periodic wave solution of boiti-leon-manna-pempinelli equation. In: Xia, T. (ed.) Abstract and Applied Analysis. Hindawi (2014)

  10. Jiang, T., Jiang, Z., Ling, S.: An algebraic method for quaternion and complex least squares coneigen-problem in quantum mechanics. Appl. Math. Comput. 249, 222–228 (2014)

    MathSciNet  MATH  Google Scholar 

  11. Hayashi, M., Iwama, K., Nishimura, H.: Quantum network coding. In: Proceedings of 2007 Symposium Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, vol. 4393, pp. 610–621 (2007)

  12. Hayashi, M.: Prior entanglement between senders enables perfect quantum network coding with modification. Phys. Rev. A 76(4), 040301(R) (2007)

    ADS  MathSciNet  Google Scholar 

  13. Ma, S.Y., Chen, X.B.: Probabilistic quantum network coding of Mqudit states over the butterfly network. Opt. Commun. 283(3), 497–501 (2010)

    ADS  Google Scholar 

  14. Kobayashi, H., Le Gall, F., Nishimura, H., Rotteler, M.: General scheme for perfect quantum network coding with free classical communication. In: Proceedings of 36th International Colloquium on Automata, Languages and Programming (ICALP), Lecture Note in Computer Science, vol. 5555, pp. 622–633 (2009)

    Google Scholar 

  15. Kobayashi, H., Le Gall, F., Nishimura, H., Rotteler, M.: Constructing quantum network coding schemes from classical nonlinear protocols. In: Proceedings of IEEE International Symposium Information Theory (ISIT), pp. 109–113 (2011)

  16. Xu, G., Chen, X.B., Li, J., Wang, C., Yang, Y.X., Li, Z.P.: Network coding for quantum cooperative multicast. Quantum Inf. Process. 14(11), 4297–4322 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  17. Li, J., Xu, G., Chen, X.B., Qu, Z., Niu, X.X., Yang, Y.X.: The solvability of quantum k-pair network in a measurement-based way. Sci. Rep. 7(1), 16775 (2017)

    ADS  Google Scholar 

  18. Satoh, T., Le Gall, F., Imai, H.: Quantum network coding for quantum repeaters. Phys. Rev. A 86(3), 032331(8) (2012)

    ADS  Google Scholar 

  19. Satoh, T., Ishizaki, K., Nagayamaand, S., Meter, R.V.: Analysis of quantum network coding for realistic repeater networks. Phys. Rev. A 93(3), 032331(10) (2012)

    Google Scholar 

  20. Epping, M., Kampermann, H., Bruß, D.: Robust entanglement distribution via quantum network coding. New J. Phys. 18(10), 103052 (2016)

    ADS  MathSciNet  Google Scholar 

  21. Akibue, S., Murao, M.: Network coding for distributed quantum computation over cluster and butterfly networks. IEEE Trans. Inf. Theory 62(11), 6620–6637 (2016)

    MathSciNet  MATH  Google Scholar 

  22. Oggier, F., Fathi, H.: An authentication code against pollution attacks in network coding. IEEE/Acm Trans. Netw. 19(6), 1587–1596 (2011)

    Google Scholar 

  23. Wu, X., Xu, Y., Yuen, C., Xiang, L.: A tag encoding scheme against pollution attack to linear network coding. IEEE Trans. Parallel Distrib. Syst. 25(1), 33–42 (2014)

    Google Scholar 

  24. Agrawal, S., Boneh, D.: Homomorphic MACs: MAC-based integrity for network coding. In: International Conference on Applied Cryptography and Network Security, pp. 292–305 (2009)

    Google Scholar 

  25. Cheng, C., Jiang, T.: A novel homomorphic MAC scheme for authentication in network coding. IEEE Commun. Lett. 15(11), 1228–1230 (2011)

    ADS  Google Scholar 

  26. Cheng, C., Jiang, T.: An efficient homomorphic MAC with small key size for authentication in network coding. IEEE Trans. Comput. 62(10), 2096–2100 (2013)

    MathSciNet  MATH  Google Scholar 

  27. Shang, T., Pei, Z., Zhao, X.J., Liu, J.W.: Quantum network coding against pollution attacks. IEEE Commun. Lett. 20(7), 1369–1372 (2016)

    Google Scholar 

  28. Owari, M., Kato, G., Hayashi, M.: Single-shot secure quantum network coding on butterfly network with free public communication. Quantum Sci. Technol. 3(1), 014001 (2018)

    ADS  Google Scholar 

  29. Curty, M., Santos, D.J.: Quantum authentication of classical messages. Phy. Rev. A 64(6), 062309 (2001)

    ADS  Google Scholar 

  30. Barnum, H., Crépeau, C., Gottesman, D., Smith, A., Tapp, A.: Authentication of quantum messages. In: The 43rd Annual IEEE Symposium on Foundations of Computer Science, pp. 449–458 (2002)

  31. Boneh, D., Zhandry, M.: Quantum-secure message authentication codes. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques, pp. 592–608 (2013)

    Google Scholar 

  32. Bartkiewicz, K., Černoch, A., Lemr, K.: Using quantum routers to implement quantum message authentication and Bell-state manipulation. Phys. Rev. A 90(2), 022335 (2014)

    ADS  Google Scholar 

  33. Alagic, G., Majenz, C., Russell, A., Song, F.: Quantum-secure message authentication via blind-unforgeability. arXiv:1803.03761 (2018)

  34. Lo, H.K., Chau, H.F., Ardehali, M.: Efficient quantum key distribution scheme and a proof of its unconditional security. J. Cryptol. 18(2), 133–165 (2005)

    MathSciNet  MATH  Google Scholar 

  35. Tan, X., Zhang, X.: Controlled quantum secure direct communication by entanglement distillation or generalized measurement. Quantum Inf. Process. 15(5), 2137–2154 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  36. Deng, F.G., Li, X.H., Zhou, H.Y.: Efficient high-capacity quantum secret sharing with two-photon entanglement. Phys. Lett. A 372(12), 1957–1962 (2008)

    ADS  MathSciNet  MATH  Google Scholar 

  37. Tseng, H.Y., Lin, J., Hwang, T.: New quantum private comparison protocol using EPR pairs. Quantum Inf. Process. 11(2), 373–384 (2012)

    MathSciNet  MATH  Google Scholar 

  38. Giovannetti, V., Lloyd, S., Maccone, L.: Quantum private queries. Phys. Rev. Lett. 100(23), 230502 (2008)

    ADS  MathSciNet  MATH  Google Scholar 

  39. Chen, X.B., Su, Y., Xu, G., Sun, Y., Yang, Y.X.: Quantum state secure transmission in network communications. Inf. Sci. 276, 363–376 (2014)

    MathSciNet  MATH  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  42. Lim, C.C.W., Curty, M., Walenta, N., Xu, F., Zbinden, H.: Concise security bounds for practical decoy-state quantum key distribution. Phys. Rev. A 89(2), 022307 (2014)

    ADS  Google Scholar 

  43. Dougherty, R., Zeger, K.: Nonreversibility and equivalent constructions of multiple-unicast networks. IEEE Trans. Inf. Theory 52(11), 5067–5077 (2006)

    MathSciNet  MATH  Google Scholar 

  44. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70(13), 1895–1899 (1993)

    ADS  MathSciNet  MATH  Google Scholar 

  45. Bennett, C.H., Brassard, G.: Quantum cryptography: public-key distribution and coin tossing. In Proceedings of IEEE International Conference on Computers System and Signal Processing, pp. 175–179 (1984)

  46. Lo, H.K., Chau, H.F.: Unconditional security of quantum key distribution over arbitrarily long distances. Science 283(5410), 2050–2056 (1999)

    ADS  Google Scholar 

  47. Shor, P.W., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85(2), 441 (2000)

    ADS  Google Scholar 

  48. Leung, D., Oppenheim, J., Winter, A.: Quantum network communication—the butterfly and beyond. IEEE Trans. Inf. Theory 56(7), 3478–3490 (2010)

    MathSciNet  MATH  Google Scholar 

  49. Nishimura, H.: Quantum network coding—how can network coding be applied to quantum information? In Proceedings of 2013 IEEE International Symposium on Network Coding, pp. 1–5 (2013)

  50. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61671087, 61272514, 61170272, 61003287, 61373131), the Fok Ying Tong Education Foundation (Grant No. 131067), the Major Science and Technology Support Program of Guizhou Province (Grant No. 20183001), and Open Foundation of Guizhou Provincial Key Laboratory of Public Big Data (2018BDKFJJ016). CCF-Tencent Open Fund WeBank Special Funding(CCF-WebankRAGR20180104).

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Authors and Affiliations

  1. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Zhen-zhen Li, Gang Xu, Xiu-Bo Chen & Yi-Xian Yang

  2. Guizhou University, Guizhou Provincial Key Laboratory of Public Big Data, Guiyang, 550025, Guizhou, China

    Xiu-Bo Chen & Yi-Xian Yang

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  1. Zhen-zhen Li
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  2. Gang Xu
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Correspondence to Xiu-Bo Chen.

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Li, Zz., Xu, G., Chen, XB. et al. Secure quantum network coding based on quantum homomorphic message authentication. Quantum Inf Process 18, 14 (2019). https://doi.org/10.1007/s11128-018-2127-z

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