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Controlled Quantum Secure Direct Communication with Authentication Based on Quantum Search Algorithm

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Abstract

A controlled quantum secure direct communication protocol with authentication based on quantum search algorithm is put forward, consisting of three participants: a sender, a receiver and one controller. Two unitary operators \(U_{w}\) and \(U_{S}\) in quantum search algorithm are used to encode classical bits and decode information, respectively, and the decoy photons based on identity sequences are adopted to detect the channel security and authenticate the identity of the communication parties. The secret message can be reconstructed successfully with the help of the controller. Moreover, the security analysis reveals that this protocol can not only effectively prevent the eavesdropper from stealing useful information but also discover the eavesdropping behavior. Compared with the existing QSDC protocols with quantum search algorithm, the proposed one has the advantages of identity authentication of the communicators, detecting man-in-the-middle attack and the attack from dishonest controller, and its qubit efficiency can reach as high as 25%.

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References

  1. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, 20–22 Nov. pp. 124–134 (1994)

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

  4. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67(6), 661 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Shor, P.W., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Phys Rev Lett 85(2), 441–444 (2000)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. Cui, Z.X., Zhong, W., Zhou, L., Sheng, Y.B.: Measurement-device-independent quantum key distribution with hyper-encoding. Sci. China: Phys. Mech. Astron. 62(11), 110311 (2019)

  9. Xu, F.H., Ma, X.F., Zhang, Q., Pan, J.W.: Secure quantum key distribution with realistic devices. Rev. Mod. Phys. 92(2), 025002 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  10. Yin, H.L., Chen, T.Y., Yu, Z.W., Liu, H., You, L.X., Zhou, Y.H., Chen, S.J., Mao, Y.Q., Huang, M.Q., Zhang, W.J., Chen, H., Li M.J., Nolan, D., Zhou, F., Jiang, X., Wang, Z., Zhang, Q., Wang, X.B., Pan, J.W.: Measurement-device-independent quantum key distribution over a 404 km optical fiber. Phys. Rev. Lett. 117(19), 190501 (2016)

  11. Tang, G.Z., Li, C.Y., Wang, M.: Polarization discriminated time-bin phase-encoding measurement-device-independent quantum key distribution. Quant. Eng. 3(4), e79 (2021)

    Google Scholar 

  12. Fanyuan, G.J., Wang, S., Yin, Z.Q., Chen, W., He, D.Y., Guo, G.C., Han, Z.F.: Afterpulse analysis for passive decoy quantum key distribution. Quant. Eng. 2(4), e56 (2020)

  13. Wang, X.F., Sun, X.J., Liu, Y.X., Wang, W., Kan, B.X., Dong, P., Zhao, L.L.: Transmission of photonic polarization states from geosynchronous Earth orbit satellite to the ground. Quant. Eng. 3(3), e73 (2021)

  14. Kwek, L., Cao, L., Luo, W., Wang, Y.X., Sun, S.H., Wang, X.B., Liu, A.Q.: Chip-based quantum key distribution. AAPPS Bull. 31(1), 15 (2021)

  15. Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65(3), 032302 (2002)

    Article  ADS  Google Scholar 

  16. 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(4), 042317 (2003)

    Article  ADS  Google Scholar 

  17. Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69(5), 052319 (2004)

    Article  ADS  Google Scholar 

  18. Wang, C., Deng, F.G., Li, Y.S., Liu, X.S., Long, G.L.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71(4), 44305 (2005)

  19. Shi, J., Gong, Y.X., Xu, P., Zhu, S.N., Zhan, Y.B.: Quantum secure direct communication by using three-dimensional hyperentanglement. Commun. Theor. Phys. 56(5), 831–836 (2011)

  20. Zheng, X.Y., Long, Y.X.: Controlled quantum secure direct communication with authentication protocol based on five-particle cluster state and classical XOR operation. Quantum Inf. Process. 18(5), 129 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  21. Meslouhi, A., Hassouni, Y.: A quantum secure direct communication protocol using entangled modified spin coherent states. Quantum Inf. Process. 12(7), 2603–2621 (2013)

    Article  ADS  MATH  Google Scholar 

  22. Cao, H.J., Song, H.S.: Quantum secure direct communication with W state. Chin. Phys. Lett. 23(2), 290–292 (2006)

    Article  ADS  Google Scholar 

  23. Cao, W.F., Yang, Y.G., Wen, Q.Y.: Quantum secure direct communication with cluster states. Sci. China: Phys. Mech. Astron. 53(7), 1271–1275 (2010)

    ADS  Google Scholar 

  24. Sun, Z.W., Du, R.G., Long, D.Y.: Quantum secure direct communication with two-photon four-qubit cluster states. Int. J. Theor. Phys. 51(6), 1946–1952 (2012)

    Article  MATH  Google Scholar 

  25. Liu, Z.H., Chen, H.W., Liu, W.J., Xu, J., Wang, D., Li, Z.Q.: Quantum secure direct communication with optimal quantum superdense coding by using general four-qubit states. Quantum Inf. Process. 12(1), 587–599 (2013)

  26. Wang, T.J., Li, T., Du, F.F., Deng, F.G.: High-capacity quantum secure direct communication based on quantum hyperdense coding with hyperentanglement. Chin. Phys. Lett. 28(4), 040305 (2011)

    Article  ADS  Google Scholar 

  27. Gao, T., Yan, F.L., Wang, Z.X.: Controlled quantum teleportation and secure direct communication. Chin. Phys. 14(5), 892–897 (2005)

    Google Scholar 

  28. Chen, X.B., Wang, T.Y., Du, J.Z., Wen, Q.Y., Zhu, F.C.: Controlled quantum secure direct communication with quantum encryption. Int. J. Quantum Inf. 6(3), 543–551 (2008)

  29. Li, Y.H., Li, X.L., Sang, M.H., Nie, Y.Y., Wang, Z.S.: Bidirectional controlled quantum teleportation and secure direct communication using five-qubit entangled state. Quantum Inf. Process. 12(12), 3835–3844 (2013)

  30. Patwardhan, S., Moulick, S.R., Panigrahi, P.K.: Efficient controlled quantum secure direct communication protocols. Int. J. Theor. Phys. 55(7), 3280–3288 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  31. Wang, J., Zhang, Q., Tang, C.J.: Multiparty controlled quantum secret direct communication using Greenberger-Horne-Zeilinger state. Opt. Commun. 266(2), 732–737 (2006)

    Article  ADS  Google Scholar 

  32. Kao, S.H., Tsai, C.W., Hwang, T.L.: Enhanced multiparty controlled QSDC using GHZ state. Commun. Theor. Phys. 55(6), 1007–1011 (2011)

    Article  ADS  MATH  Google Scholar 

  33. Gao, F., Qin, S.J., Guo, F.Z., Wen, Q.Y.: Cryptanalysis of quantum secure direct communication and authentication scheme via Bell states. Chin. Phys. Lett. 28(2), 020303 (2011)

  34. Lee, H., Lim, J., Yang, H.J.: Quantum authentication and quantum key distribution protocol. arXiv: quant-ph/ 0510144 (2005)

  35. Lee, H., Lim, J., Yang, H.J.: Quantum direct communication with authentication. Phys. Rev. A 73(4), 042305 (2006)

    Article  ADS  Google Scholar 

  36. Yang, J., Wang, C., Zhang, R.: Quantum secure direct communication with authentication expansion using single photons. Commun. Theor. Phys. 54(5), 829–834 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Chang, Y., Xu, C.X., Zhang, S.B., Yan, L.L.: Controlled quantum secure direct communication and authentication protocol based on five-particle cluster state and quantum one time pad. Chin. Sci. Bull. 59(21), 2541–2546 (2014)

    Article  Google Scholar 

  38. Khorasani, F.M., Houshmand, M., Anzabi-Nezhad, N.S.: Authenticated controlled quantum secure direct communication protocol based on five-particle Brown states. Int. J. Theor. Phys. 59(5), 1612–1622 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  39. Niu, P.H., Zhou, Z.R., Lin, Z.S., Sheng, Y.B., Yin, L.G.: Measurement-device-independent quantum communication without encryption. Sci. Bull. 63(20), 1345–1350 (2018)

  40. Zou, Z.K., Zhou, L., Zhong, W., Sheng, Y.B.: Measurement-device-independent quantum secure direct communication of multiple degrees of freedom of a single photon. Europhys. Lett. 131(4), 40005 (2020)

  41. Zhou, Z.R., Sheng, Y.B., Niu P.H., Yin, L.G., Long, G.L., Hanzo, L.: Measurement-device-independent quantum secure direct communication. Sci. China: Phys. Mech. Astron. 63(3), 230362 (2020)

  42. Zhou, L., Sheng, Y.B., Long, G.L.: Device-independent quantum secure direct communication against collective attacks. Sci. Bull. 65(1), 12–20 (2020)

    Article  Google Scholar 

  43. Zhou, L., Sheng, Y.B.: One-step device-independent quantum secure direct communication. Sci. China: Phys. Mech. Astron. 65(5), 250311 (2022)

    ADS  MathSciNet  Google Scholar 

  44. Li, T., Long, G.L.: Quantum secure direct communication based on single-photon Bell-state measurement. New J. Phys. 22(6), 063017 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  45. Liu, X., Li, Z.J., Luo, D., Huang, C.F., Ma, D., Geng, M.M., Wang, J.W., Zhang, Z.R., Wei, K.J.: Practical decoy-state quantum secure direct communication. Sci. China: Phys. Mech. Astron. 64(12), 120311 (2021)

  46. Sun, S.H., Long, G.L.: Deterministic secure quantum communication with practical devices. Quant. Eng. 3(4), e86 (2021)

    Google Scholar 

  47. Gao, C.Y., Guo, P.L., Ren, B.C.: Efficient quantum secure direct communication with complete Bell-state measurement. Quant. Eng. 3(4), e83 (2021)

    Google Scholar 

  48. Sheng, Y.B., Zhou, L., GL, Long: One-step quantum secure direct communication. Sci. Bull. 67(4), 367–374 (2022)

    Article  Google Scholar 

  49. Yang, L., Wu, J.W., Lin, Z.S., Yin, L.G., Long, G.L.: Quantum secure direct communication with entanglement source and single-photon measurement. Sci. China: Phys. Mech. Astron. 63(11), 110311 (2020)

  50. Long, G.L., Zhang, H.R.: Drastic increase of channel capacity in quantum secure direct communication using masking. Sci. Bull. 66(13), 1267–1269 (2021)

    Article  Google Scholar 

  51. Hu, J.Y., Yu, B., Jing, M.Y., Xiao, L.T., Jia, S.T., Qin, G.Q., Long, G.L.: Experimental quantum secure direct communication with single photons. Light: Sci. Appl. 5(9), e16144 (2016)

  52. Zhang, W., Ding, D.S., Sheng, Y.B., Zhou, L., Shi, B.S., Guo, G.C.: Quantum secure direct communication with quantum memory. Phys. Rev. Lett. 118(22), 220501 (2017)

  53. Zhu, F., Zhang, W., Sheng, Y.B., Huang, Y.D.: Experimental long-distance quantum secure direct communication. Sci. Bull. 62(22), 1519–1524 (2017)

  54. Sun, Z., Song, L.Y., Huang, Q., Yin, L.G., Long, G.L., Lu, J.H., Hanzo, L.: Toward practical quantum secure direct communication: a quantum-memory-free Protocol and code design. IEEE Trans. Commun. 68(9), 5778–5792 (2020)

  55. Qi, R.Y., Sun, Z., Lin, Z.S., Niu, P.H., Hao, W.T., Song, L.Y., Huang, Q., Gao, J.C., Yin, L.G., Long, G.L.: Implementation and security analysis of practical quantum secure direct communication. Light: Sci. Appl. 8(1), 22 (2019)

  56. Wang, C.: Quantum secure direct communication: intersection of communication and cryptography. Fundamental Res. 1(1), 91–92 (2021)

    Article  Google Scholar 

  57. Pan, D., Lin, Z.S., Wu, J.W., Yin, L.G., Long, G.L.: Experimental free-space quantum secure direct communication and its security analysis. Photonics Res. 8(9), 1522–1531 (2020)

  58. You, X.H., Wang, C.X., Huang, J., et al.: Towards 6G wireless communication networks: vision, enabling technologies, and new paradigm shifts. Sci. China Inf. Sci. 64(1), 110301 (2021)

    Article  Google Scholar 

  59. Qi, Z.T., Li, Y.H., Huang, Y.W., Feng, J., Zheng, Y.L., Chen, X.F.: A 15-user quantum secure direct communication network. Light: Sci. Appl. 10, 183 (2021)

  60. Grover, L.K.: A fast quantum mechanical algorithm for database search. Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, New York, pp. 212–219 (1996)

  61. Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997)

    Article  ADS  Google Scholar 

  62. Hsu, L.Y.: Quantum secret-sharing protocol based on Grover’s algorithm. Phys. Rev. A 68(2), 022306 (2003)

    Article  ADS  Google Scholar 

  63. Zhang, W.W., Li, D., Song, T.T., Li, Y.B.: Quantum private comparison based on quantum search algorithm. Int. J. Theor. Phys. 52(5), 1466–1473 (2013)

    Article  MathSciNet  Google Scholar 

  64. Huang, X., Zhang, S.B., Chang, Y., Qiu, C., Liu, D.M., Hou, M.: Quantum Key Agreement Protocol Based on Quantum Search Algorithm. Int. J. Theor. Phys. 60(3), 838–847 (2021)

  65. Wang, C., Hao, L., Song, S.Y., Long, G.L.: Quantum direct communication based on quantum search algorithm. Int. J. Quantum Inf. 8(3), 443–450 (2010)

  66. Tseng, H.Y., Tsai, C.W., Hwang, T.L.: Controlled deterministic secure quantum communication based on quantum search algorithm. Int. J. Theor. Phys. 51(8), 2447–2454 (2012)

    Article  MATH  Google Scholar 

  67. Kao, S.H., Hwang, T.L.: Multiparty controlled quantum secure direct communication based on quantum search algorithm. Quantum Inf. Process. 12(12), 3791–3805 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  68. Yin, A.H., Lin, W.B., He, K.M., Han, Z.F, Fan, P.: Controlled bidirectional quantum secure direct communication protocol based on Grover’s algorithm. Mod. Phys. Lett. A 35(28), 2050228 (2020)

  69. Chuang, I., Gershenfeld, N., Kubinec, M.: Experimental implementation of fast quantum searching. Phys. Rev. Lett. 80(15), 3408–3411 (1998)

    Article  ADS  Google Scholar 

  70. Long, G.L., Yan, H.Y., Li, Y.S., Tu, C.C., Tao, J.X., Chen, H.M., Liu, M.L., Zhang, X., Luo, J., Xiao, L., Zeng, X.Z.: Experimental NMR realization of a generalized quantum search algorithm. Phys. Lett. A 286(2–3), 121–126 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  71. Chang, Y., Xu, C.X., Zhang, S.B., Yan, L.L.: Quantum secure direct communication and authentication protocol with single photons. Chin. Sci. Bull. 56(36), 4571–4576 (2013)

    Article  Google Scholar 

  72. Man, Z.X., Zhang, Z.J., Li, Y.: Quantum dialogue revisited. Chin. Phys. Lett. 22(1), 22–24 (2005)

    Article  ADS  Google Scholar 

  73. Gisin, N., Ribordy, G., Tittel W., Zbinden, H.: Quantum Cryptography. Rev. Mod. Phys. 74(1), 145–195 (2002)

  74. Cai, Q.Y.: Eavesdropping on the two-way quantum communication protocols with invisible photons. Phys. Lett. A 351(1–2), 23–25 (2006)

    Article  ADS  MATH  Google Scholar 

  75. Deng, F.G., Li, X.H., Zhou, H.Y., Zhang, Z.J.: Improving the security of multiparty quantum secret sharing against Trojan horse attack. Phys. Rev. A 72(4), 044302 (2005)

  76. Cabello, A.: Quantum key distribution in the Holevo limit. Phys. Rev. Lett. 85(26), 5635–5638 (2000)

    Article  ADS  Google Scholar 

  77. Wen, K., Deng, F.G., Long, G.L.: Secure reusable base-string in quantum key distribution. arXiv: 0706.3791 (2007)

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 61871205).

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  1. School of Mathematics and Computer Sciences, Nanchang University, Nanchang, 330031, China

    You-Feng Yang, Long-Zhen Duan, Tao-Rong Qiu & Xu-Ming Xie

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  1. You-Feng Yang
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Contributions

Y.F. Yang: Conceptualization, Methodology, Writing-Original Draft, Writing-Review & Editing; L.Z. Duan: Data Curation, Writing-Review & Editing, Supervision; T.R. Qiu: Conceptualization, Methodology, Writing-Review & Editing; X.M. Xie: Conceptualization, Writing-Original Draft, Writing-Review & Editing.

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Correspondence to Long-Zhen Duan.

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Yang, YF., Duan, LZ., Qiu, TR. et al. Controlled Quantum Secure Direct Communication with Authentication Based on Quantum Search Algorithm. Int J Theor Phys 61, 184 (2022). https://doi.org/10.1007/s10773-022-05138-2

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