Abstract
Based on unitary phase shift operation on single qubit in association with Shamir’s (t, n) secret sharing, a (t, n) threshold quantum secret sharing scheme (or (t, n)-QSS) is proposed to share both classical information and quantum states. The scheme uses decoy photons to prevent eavesdropping and employs the secret in Shamir’s scheme as the private value to guarantee the correctness of secret reconstruction. Analyses show it is resistant to typical intercept-and-resend attack, entangle-and-measure attack and participant attacks such as entanglement swapping attack. Moreover, it is easier to realize in physic and more practical in applications when compared with related ones. By the method in our scheme, new (t, n)-QSS schemes can be easily constructed using other classical (t, n) secret sharing.
Similar content being viewed by others
References
Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)
Blakley, G.R.: Safeguarding cryptographic keys. In: AFIPS, p. 313. IEEE Computer Society (1979)
Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)
Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)
Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829–1834 (1999)
Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59(1), 162–168 (1999)
Cleve, R., Gottesman, D., Lo, H.K.: How to share a quantum secret. Phys. Rev. Lett 83(3), 648–651 (1999)
Tokunaga, Y., Okamoto, T., Imoto, N.: Threshold quantum cryptography. Phys. Rev. A 71(1), 012314 (2005)
Zhang, Z.J., Li, Y., Man, Z.X.: Multiparty quantum secret sharing. Phys. Rev. A 71(4), 044301 (2005)
Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61(4), 042311 (2000)
Wang, X.J., An, L.X., Yu, X.T., Zhang, Z.C.: Multilayer quantum secret sharing based on GHZ state and generalized Bell basis measurement in multiparty agents. Phys. Lett. A 381, 3282–3288 (2017)
Wang, J., Li, L., Peng, H., Yang, Y.: Quantum-secret-sharing scheme based on local distinguishability of orthogonal multiqudit entangled states. Phys. Rev. A 95, 022320 (2017)
Yan, F.L., Gao, T.: Quantum secret sharing between multiparty and multiparty without entanglement. Phys. Rev. A 72(1), 012304 (2005)
Schmid, C., Trojek, P., Bourennane, M., Kurtsiefer, C., Zukowski, M., Weinfurter, H.: Experimental single qubit quantum secret sharing. Phys. Rev. Lett. 95, 230505 (2005)
Li, B.K., Yang, Y.G., Wen, Q.Y.: Threshold quantum secret sharing of secure direct communication. Chin. Phys. Lett. 26(1), 010302 (2009)
Qin, H., Zhu, X., Dai, Y.: \((t, n)\) Threshold quantum secret sharing using the phase shift operation. Quantum Inf. Process 14(8), 2997 (2015)
Karimipour, V., Marvian, M.: Secure quantum carriers for quantum state sharing. Int. J. Quantum Inf. 10(2), 1250018 (2012)
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)
Yang, Y.H., Gao, F., Wu, X., Qin, S.J., Zuo, H.J., Wen, Q.Y.: Quantum secret sharing via local operations and classical communication. Sci. Rep. 5, 16967 (2015)
Song, X.L., Liu, Y.B., Deng, H.Y., Xiao, Y.G.: \((t, n)\) threshold d-level quantum secret sharing. Sci. Rep. 7, 6366 (2017)
Hsu, L.Y., Li, C.M.: Quantum secret sharing using product states. Phys. Rev. A 71(2), 022321 (2005)
Yang, Y.G., Wen, Q.Y.: Threshold quantum secret sharing between multi-party and multi-party. Sci. China Ser. G Phys. Mech. Astron. 51(9), 1308–1315 (2008)
Cai, Q.Y., Li, W.B.: Deterministic secure communication without using entanglement. Chin. Phys. Lett. 21, 601–603 (2004)
Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)
He, G.P.: Comment on “experimental single qubit quantum secret sharing”. Phys. Rev. Lett. 98(2), 028901 (2007)
McEliece, R.J., Sarwate, D.V.: On sharing secrets and Reed-Solomon codes. Commun. ACM 24, 583–584 (1981)
Massey, J.L.: Proceedings of the 6th Joint Swedish-Russian International Workshop on Information Theory, pp. 276–279. IEEE Press, Washington (1993)
Asmuth, C., Bloom, J.: A modular approach to key safeguarding. IEEE. Trans. Inform. Theory 30(2), 208–210 (1983)
Mignotte, M., Beth, T. (eds.): Cryptography. Lecture Notes in Computer Science, vol 149, pp. 371–375. Springer, Berlin (1983)
Acknowledgements
We would like to thank the anonymous reviewer for helpful suggestions. This work was supported by the National Natural Science Foundation of China under 61572454, 61572453, 61472382, 61520106007.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lu, C., Miao, F., Meng, K. et al. Threshold quantum secret sharing based on single qubit. Quantum Inf Process 17, 64 (2018). https://doi.org/10.1007/s11128-017-1793-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-017-1793-6