Abstract
Multi-party quantum private comparison (MQPC) enables \(n (n\ge 2)\) parties to compare the equality of their private secrets without leaking them. In this paper, a class of MQPC protocols are proposed based on single-particle states and maximally entangled states. With the help of a semi-honest third party, our protocols can compare the equality of n parties’ private secrets. Our protocol uses single-particle states and a class of maximally entangled states as the information carriers, which means that our protocol has flexibility in the selection of quantum states compared with all previous protocols; after all, each of the previous protocols only uses a specific quantum state. In addition, our protocols adopt traveling mode, which can significantly reduce resource consumption. What is more, the qubit efficiency of each of our protocols can reach 100%, which is much higher than that of all previous MQPC protocols. We show that our protocols are secure against the outside and participant attacks.
Similar content being viewed by others
References
Yao, A.C.: Protocols for secure computations. In: Proceedings of 23rd IEEE Symposium on Foundations of Computer Science (FOCS’82), Washington, DC, p. 160 (1982)
Bennett, C.H., Brassard, G.: Quantum cryptography: public-key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, pp. 175–179. IEEE Press, Bangalore (1984)
Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without Bell’s theorem. Phys. Rev. Lett. 68, 557–559 (1992)
Cabello, A.: Quantum key distribution in the Holevo limit. Phys. Rev. Lett. 85, 5635 (2000)
Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)
Deng, F.G., Zhou, H.Y., Long, G.L.: Circular quantum secret sharing. J. Phys. A Math. Theor. 39(45), 14089–14099 (2006)
Chai, G., Cao, Z., Liu, W., et al.: Parameter estimation of atmospheric continuous-variable quantum key distribution. Phys. Rev. A 99(3), 032326 (2019)
Boyer, M., Kenigsberg, D., Mor, T.: Quantum key distribution with classical Bob. Phys. Rev. Lett. 99(14), 140501 (2007)
Yang, Y.G., Wen, Q.Y.: An efficient two-party quantum private comparison protocol with decoy photons and two-photon entanglement. J. Phys. A Math. Theor. 42(5), 055305 (2009)
Yang, Y.G., Gao, W.F., Wen, Q.Y.: Secure quantum private comparison. Phys. Scr. 80(6), 065002 (2009)
Chen, X.B., Su, Y., Niu, X.X., Yang, Y.X.: Efficient and feasible quantum private comparison of equality against the collective amplitude damping noise. Quantum Inf. Process. 13(1), 101–112 (2014)
Liu, B., Gao, F., Jia, H.Y., Huang, W., Zhang, W.W., Wen, Q.Y.: Efficient quantum private comparison employing single photons and collective detection. Quantum Inf. Process. 12(2), 887–897 (2013)
Yang, Y.G., Xia, J., Jia, X., Zhang, H.: Comment on quantum private comparison protocols with a semi-honest third party. Quantum Inf. Process. 12(2), 877–885 (2013)
Ye, T.Y.: Quantum private comparison via cavity QED. Commun. Theor. Phys. 67(2), 147–156 (2017)
Liu, W., Wang, Y.B., Cui, W.: Quantum private comparison protocol based on Bell entangled states. Commun. Theor. Phys. 57(4), 583–588 (2012)
Zi, W., Guo, F.Z., Luo, Y., Cao, S.H., Wen, Q.Y.: Quantum private comparison protocol with the random rotation. Int. J. Theor. Phys. 52(9), 3212–3219 (2013)
Tseng, H.Y., Lin, J., Hwang, T.: New quantum private comparison protocol using EPR pairs. Quantum Inf. Process. 11(2), 373–384 (2012)
Zhang, W.W., Zhang, K.J.: Cryptanalysis and improvement of the quantum private comparison protocol with semi-honest third party. Quantum Inf. Process. 12(5), 1981–1990 (2013)
Lin, J., Yang, C.W., Hwang, T.: Quantum private comparison of equality protocol without a third party. Quantum Inf. Process. 13(2), 239–247 (2014)
Chen, X.B., Xu, G., Niu, X.X., Wen, Q.Y., Yang, Y.X.: An efficient protocol for the private comparison of equal information based on the triplet entangled state and single-particle measurement. Opt. Commun. 283(7), 1561–1565 (2010)
Lin, J., Tseng, H.Y., Hwang, T.: Intercept-resend attacks on Chen et al.’s quantum private comparison protocol and the improvements. Opt. Commun. 284(9), 2412–2414 (2011)
Guo, F.Z., Gao, F., Qin, S.J., Zhang, J., Wen, Q.Y.: Quantum private comparison protocol based on entanglement swapping of d-level Bell states. Quantum Inf. Process. 12, 2793–2802 (2013)
Li, J., Zhou, H.F., Jia, L., Zhang, T.T.: An efficient protocol for the private comparison of equal information based on four-particle entangled W state and Bell entangled states swapping. Int. J. Theor. Phys. 53(7), 2167–2176 (2014)
Ji, Z.X., Ye, T.Y.: Quantum private comparison of equal information based on highly entangled six qubit genuine state. Commun. Theor. Phys. 65, 711–715 (2016)
Ji, Z.X., Fan, P.R., Zhang, H.G., et al.: Several two-party protocols for quantum private comparison using entanglement and dense coding. Opt. Commun. 459, 124911 (2020)
Li, C., Chen, X., Li, H., et al.: Efficient quantum private comparison protocol based on the entanglement swapping between four-qubit cluster state and extended Bell state. Quantum Inf. Process. 18(5), 158 (2019)
Chen, X.B., Dou, Z., Xu, G., et al.: A class of protocols for quantum private comparison based on the symmetry of states. Quantum Inf. Process. 13(1), 85–100 (2014)
Chang, Y.J., Tsai, C.W., Hwang, T.: Multi-user private comparison protocol using GHZ class states. Quantum Inf. Process. 12(2), 1077–1088 (2013)
Liu, W., Wang, Y.B., Wang, X.M.: Multi-party quantum private comparison protocol using d-dimensional basis states without entanglement swapping. Int. J. Theor. Phys. 53(4), 1085–1091 (2014)
Hung, S.M., Hwang, S.L., Hwang, T., Kao, S.H.: Multiparty quantum private comparison with almost dishonest third parties for strangers. Quantum Inf. Process. 16(2), 36 (2017)
Wang, Q.L., Sun, H.X., Huang, W.: Multi-party quantum private comparison protocol with-level entangled states. Quantum Inf. Process. 13(11), 2375–2389 (2014)
Ye, C.Q., Ye, T.Y.: Circular Multi-party quantum private comparison with n-level single-particle states. Int. J. Theor. Phys. 58(4), 1282–1294 (2019)
Ji, Z.X., Ye, T.Y.: Multi-party quantum private comparison based on the entanglement swapping of d-level cat states and d-level Bell states. Quantum Inf. Process. 16(7), 177 (2017)
Luo, Q.B., Yang, G.W., She, K., Niu, W.N., Wang, Y.Q.: Multi-party quantum private comparison protocol based on d-dimensional entangled states. Quantum Inf. Process. 13, 2343–2352 (2014)
Huang, S.L., Hwang, T., Gope, P.: Multi-party quantum private comparison with an almost-dishonest third party. Quantum Inf. Process. 14(11), 4225–4235 (2015)
Ye, C.Q., Ye, T.Y.: Multi-party quantum private comparison of size relation with d-level single-particle states. Quantum Inf. Process. 17(10), 252 (2018)
Li, C.Y., Zhou, H.Y., Wang, Y., Deng, F.G.: Secure quantum key distribution network with Bell states and local unitary operations. Chin. Phys. Lett. 22(5), 1049 (2005)
Li, C.Y., Li, X.H., Deng, F.G., Zhou, P., Liang, Y.J., Zhou, H.Y.: Efficient quantum cryptography network without entanglement and quantum memory. Chin. Phys. Lett. 23(11), 2896 (2006)
Shor, P.W., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85(2), 441 (2000)
Song, X.L., Liu, Y.B., Deng, H.Y., Xiao, Y.G.: (t, n) threshold d-level quantum secret sharing. Sci. Rep. 7(1), 6366 (2017)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. U1636106, 61671087 and 61962009), the Natural Science Foundation of Beijing Municipality(Grant No. 4182006), and the Fund of the Fundamental Research Funds for the Central Universities (Grant No. 2019XD-A02).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Chongqiang, Y., Jian, L. & Zheng-wen, C. A class of protocols for multi-party quantum private comparison based on traveling mode. Quantum Inf Process 20, 56 (2021). https://doi.org/10.1007/s11128-020-02986-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-020-02986-x