Arbitrated quantum signature scheme with quantum walk-based teleportation

  • Yanyan Feng
  • Ronghua Shi
  • Jinjing ShiEmail author
  • Jian Zhou
  • Ying Guo


Quantum walks can be applied for some quantum information processing tasks such as quantum search, element distinctness, state transfer and teleportation. In this paper, we present an arbitrated quantum signature scheme with quantum walk-based teleportation. The teleportation is used for the transmission of message copy from the signer Alice to the verifier Bob. The necessary entangled states for teleportation do not need to be prepared in advance in the initial phase and can be produced naturally via quantum walk in the signature phase. Furthermore, to resist against Bob’s existential forgery for Alice’s signature under known message attack in the previous arbitrated quantum signature proposals, we employ a random number and a public board in the verification phase. Security analyses show the suggested scheme is with impossibility of disavowal of Alice and Bob, impossibility of forgery of anyone. Discussions indicate that the scheme may not prevent the disavowal of Alice and we advance the potential improvements on it. Note that the proposed arbitrated quantum signature scheme may be feasible because quantum walks prove to be implemented in different physical systems and experiments.


Quantum signature Arbitrated quantum signature Quantum teleportation Quantum walk Entanglement 



This work was supported by the National Natural Science Foundation of China (Grant Nos. 61871407, 61572529, 61872390), the Fundamental Research Funds for the Central Universities of Central South University (No. 2018zzts179), and the Natural Science Foundation of Hunan Province (2017JJ3415).


  1. 1.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325 (1997)ADSCrossRefGoogle Scholar
  3. 3.
    Nielsen, M.A., Chuang, I., Grover, L.K.: Quantum computation and quantum information. Am. J. Phys. 70, 558–559 (2002)ADSCrossRefGoogle Scholar
  4. 4.
    Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299(5886), 802–803 (1982)ADSCrossRefGoogle Scholar
  5. 5.
    Busch, P., Heinonen, T., Lahti, P.: Heisenberg’s uncertainty principle. Phys. Rep. 452(6), 155–176 (2007)ADSCrossRefGoogle Scholar
  6. 6.
    Gottesman, D., Chuang, I.: Quantum digital signatures. arXiv preprint arXiv:quant-ph/0105032 (2001)
  7. 7.
    Zeng, G., Lee, M., Guo, Y., He, G.: Continuous variable quantum signature algorithm. Int. J. Quantum Inf. 05(04), 553–573 (2008)CrossRefGoogle Scholar
  8. 8.
    Diffie, W., Hellman, M.: New directions in cryptography. IEEE Trans. Inf. Theory 22, 644–654 (1976)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Amiri, R., Andersson, E.: Unconditionally secure quantum signatures. Entropy 17, 5635–5659 (2015)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Chaum, D., Roijakkers, S.: Unconditionally-secure digital signatures. In: Menezes, A.J., Vanstone, S.A. (eds.) Conference on the Theory and Application of Cryptography, pp. 206–214. Springer, Berlin (1990)Google Scholar
  11. 11.
    Hanaoka, G., Shikata, J., Zheng, Y., Imai, H.: Unconditionally secure digital signature schemes admitting transferability. In: Okamoto, T. (ed.) Advances in Cryptology—ASIACRYPT 2000. ASIACRYPT 2000. Lecture Notes in Computer Science, vol. 1976, pp. 130–142. Springer, Berlin, Heidelberg (2000)Google Scholar
  12. 12.
    Meijer, H., Akl, S.: Digital signature schemes for computer communication networks. ACM SIGCOMM Comput. Commun. 11(4), 37–41 (1981)CrossRefGoogle Scholar
  13. 13.
    Zeng, G., Keitel, C.H.: Arbitrated quantum-signature scheme. Phys. Rev. A 65(4), 042312 (2002)ADSCrossRefGoogle Scholar
  14. 14.
    Lee, H., Hong, C., Kim, H., Lim, J., Yang, H.J.: Arbitrated quantum signature scheme with message recovery. Phys. Lett. A 321(5–6), 295–300 (2004)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Curty, M., Lütkenhaus, N.: Comment on Arbitrated quantum-signature scheme. Phys. Rev. A 77(4), 046301 (2008)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Zeng, G.: Reply to Comment on arbitrated quantum-signature scheme. Phys. Rev. A 78(1), 016301 (2008)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Li, Q., Chan, W.H., Long, D.Y.: Arbitrated quantum signature scheme using Bell states. Phys. Rev. A 79(5), 054307 (2009)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Zou, X., Qiu, D.: Security analysis and improvements of arbitrated quantum signature schemes. Phys. Rev. A 82(4), 042325 (2010)ADSCrossRefGoogle Scholar
  19. 19.
    Gao, F., Qin, S.J., Guo, F.Z., Wen, Q.Y.: Cryptanalysis of the arbitrated quantum signature protocols. Phys. Rev. A 84(2), 022344 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    Choi, J.W., Chang, K.Y., Hong, D.: Security problem on arbitrated quantum signature schemes. Phys. Rev. A 84(6), 062330 (2011)ADSCrossRefGoogle Scholar
  21. 21.
    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)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Li, F.G., Shi, J.H.: An arbitrated quantum signature protocol based on the chained CNOT operations encryption. Quantum Inf. Process. 14(6), 2171–2181 (2015)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Yang, Y.G., Lei, H., Liu, Z.C., Zhou, Y.H., Shi, W.M.: Arbitrated quantum signature scheme based on cluster states. Quantum Inf. Process. 15(6), 2487–2497 (2016)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Zhang, L., Sun, H.W., Zhang, K.J., Jia, H.Y.: An improved arbitrated quantum signature protocol based on the key-controlled chained CNOT encryption. Quantum Inf. Process. 16(3), 70 (2017)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    Cerf, N.J., Levy, M., Van Assche, G.: Quantum distribution of Gaussian keys using squeezed states. Phys. Rev. A 63(5), 052311 (2001)ADSCrossRefGoogle Scholar
  26. 26.
    Grosshans, F., Grangier, P.: Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88(5), 057902 (2002)ADSCrossRefGoogle Scholar
  27. 27.
    Guo, Y., Feng, Y., Huang, D., Shi, J.: Arbitrated quantum signature scheme with continuous-variable coherent states. Int. J. Theor. Phys. 55(4), 2290–2302 (2016)CrossRefGoogle Scholar
  28. 28.
    Feng, Y., Shi, R., Guo, Y.: Arbitrated quantum signature scheme with continuous-variable squeezed vacuum states. Chin. Phys. B 27(2), 020302 (2018)ADSCrossRefGoogle Scholar
  29. 29.
    Wang, Y., Shang, Y., Xue, P.: Generalized teleportation by quantum walks. Quantum Inf. Process. 16(9), 221 (2017)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Shang, Y., Wang, Y., Li, M., Lu, R.: Quantum communication protocols by quantum walks with two coins. arXiv preprint arXiv:1802.02400 (2018)
  31. 31.
    Braunstein, S.L., Kimble, H.J.: Teleportation of continuous quantum variables. Phys. Rev. Lett. 80(4), 869 (1998)ADSCrossRefGoogle Scholar
  32. 32.
    Takei, N., Aoki, T., Koike, S., Yoshino, K., Wakui, K., Yonezawa, H., Hiraoka, T., Mizuno, J., Takeoka, M., Ban, M., Furusawa, A.: Experimental demonstration of quantum teleportation of a squeezed state. Phys. Rev. A 72(4), 042304 (2005)ADSCrossRefGoogle Scholar
  33. 33.
    Ren, J.G., Xu, P., Yong, H.L., Zhang, L., Liao, S.K., Yin, J., Liu, W.Y., Cai, W.Q., Yang, M., Li, L., Yang, K.X., Han, X., Yao, Y.Q., Li, J., Wu, H.Y., Wan, S., Liu, L., Liu, D.Q., Kuang, Y.W., He, Z.P., Shang, P., Guo, C., Zheng, R.H., Tian, K., Zhu, Z.C., Liu, N.L., Lu, C.Y., Shu, R., Chen, Y.A., Peng, C.Z., Wang, J.Y., Pan, J.W.: Ground-to-satellite quantum teleportation. Nature 549(7670), 70 (2017)ADSCrossRefGoogle Scholar
  34. 34.
    Aharonov, Y., Davidovich, L., Zagury, N.: Quantum random walks. Phys. Rev. A 48(2), 1687 (1993)ADSCrossRefGoogle Scholar
  35. 35.
    Ambainis, A., Bachy, E., Nayakz, A., Vishwanathx, A., Watrous, J.: One-dimensional quantum walks. In: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing (STOC01), pp. 37–49 (2001)Google Scholar
  36. 36.
    Aharonov, D., Ambainis, A., Kempe, J., Vazirani, U.: Quantum walks on graphs. In: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing (STOC01), pp. 50–59 (2001)Google Scholar
  37. 37.
    Meyer, D.A.: From quantum cellular automata to quantum lattice gases. J. Stat. Phys. 85(5–6), 551–574 (1996)ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    Farhi, E., Gutmann, S.: Quantum computation and decision trees. Phys. Rev. A 58(2), 915 (1998)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    Childs, A.M.: On the relationship between continuous-and discrete-time quantum walk. Commun. Math. Phys. 294(2), 581–603 (2010)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    Shikano, Y.: From discrete time quantum walk to continuous time quantum walk in limit distribution. J. Comput. Theor. Nanosci. 10(7), 1558–1570 (2013)CrossRefGoogle Scholar
  41. 41.
    Shenvi, N., Kempe, J., Whaley, K.B.: Quantum random-walk search algorithm. Phys. Rev. A 67(5), 052307 (2003)ADSCrossRefGoogle Scholar
  42. 42.
    Ambainis, A.: Quantum walks and their algorithmic applications. Int. J. Quantum Inf. 1(04), 507–518 (2003)CrossRefGoogle Scholar
  43. 43.
    Childs, A.M., Goldstone, J.: Spatial search by quantum walk. Phys. Rev. A 70(2), 022314 (2004)ADSCrossRefGoogle Scholar
  44. 44.
    Potoček, V., Gbris, A., Kiss, T., Jex, I.: Optimized quantum random-walk search algorithms on the hypercube. Phys. Rev. A 79(1), 012325 (2009)ADSCrossRefGoogle Scholar
  45. 45.
    Ambainis, A.: Quantum walk algorithm for element distinctness. SIAM J. Comput. 37(1), 210–239 (2007)MathSciNetCrossRefGoogle Scholar
  46. 46.
    Lovett, N.B., Cooper, S., Everitt, M., Trevers, M., Kendon, V.: Universal quantum computation using the discrete-time quantum walk. Phys. Rev. A 81(4), 042330 (2010)ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    Childs, A.M., Gosset, D., Webb, Z.: Universal computation by multiparticle quantum walk. Science 339(6121), 791–794 (2013)ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    Du, J., Li, H., Xu, X., Shi, M., Wu, J., Zhou, X., Han, R.: Experimental implementation of the quantum random-walk algorithm. Phys. Rev. A 67(4), 042316 (2003)ADSCrossRefGoogle Scholar
  49. 49.
    Di, T., Hillery, M., Zubairy, M.S.: Cavity QED-based quantum walk. Phys. Rev. A 70(3), 032304 (2004)ADSCrossRefGoogle Scholar
  50. 50.
    Eckert, K., Mompart, J., Birkl, G., Lewenstein, M.: One-and two-dimensional quantum walks in arrays of optical traps. Phys. Rev. A 72(1), 012327 (2005)ADSCrossRefGoogle Scholar
  51. 51.
    Zou, X., Dong, Y., Guo, G.: Optical implementation of one-dimensional quantum random walks using orbital angular momentum of a single photon. New J. Phys. 8(5), 81 (2006)ADSCrossRefGoogle Scholar
  52. 52.
    Perets, H.B., Lahini, Y., Pozzi, F., Sorel, M., Morandotti, R., Silberberg, Y.: Realization of quantum walks with negligible decoherence in waveguide lattices. Phys. Rev. Lett. 100(17), 170506 (2008)ADSCrossRefGoogle Scholar
  53. 53.
    Bian, Z.H., Li, J., Zhan, X., Twamley, J., Xue, P.: Experimental implementation of a quantum walk on a circle with single photons. Phys. Rev. A 95(5), 052338 (2017)ADSCrossRefGoogle Scholar
  54. 54.
    Tang, H., Lin, X.F., Feng, Z., Chen, J.Y., Gao, J., Sun, K., Wang, C.Y., Lai, P.C., Xu, X.Y., Wang, Y., Qiao, L.F., Yang, A.L., Jin, X.M.: Experimental two-dimensional quantum walk on a photonic chip. Sci. Adv. 4(5), eaat3174 (2018)ADSCrossRefGoogle Scholar
  55. 55.
    Brun, T.A., Carteret, H.A., Ambainis, A.: Quantum walks driven by many coins. Phys. Rev. A. 67(5), 052317 (2003)ADSMathSciNetCrossRefGoogle Scholar
  56. 56.
    Jouguet, P., Kunz-Jacques, S., Leverrier, A.: Long-distance continuous-variable quantum key distribution with a Gaussian modulation. Phys. Rev. A 84(6), 062317 (2011)ADSCrossRefGoogle Scholar
  57. 57.
    Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67(6), 661 (1991)ADSMathSciNetCrossRefGoogle Scholar
  58. 58.
    Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68(21), 3121 (1992)ADSMathSciNetCrossRefGoogle Scholar
  59. 59.
    Cai, H., Long, C.M., DeRose, C.T., Boynton, N., Urayama, J., Camacho, R., Pomerene, A., Starbuck, A.L., Trotter, D.C., Davids, P.S., Lentine, A.L.: Silicon photonic transceiver circuit for high-speed polarization-based discrete variable quantum key distribution. Opt. Express 25(11), 12282–12294 (2017)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.School of Computer Science and EngineeringCentral South UniversityChangshaChina

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