Abstract
Quantum private comparison (QPC) protocol can guarantee the two participants to compare the equality of their private information without leaking them. Based on the entanglement swapping between the four-qubit cluster state and extended Bell state, an efficient QPC protocol has been proposed. Three bits of the secret inputs have been compared in each comparison time, which improves the efficiency compared with the previous QPC protocols’ one or two bits. Then, based on a random sequence pre-shared between the two participants, the semi-honest third party can only execute the protocol’s process without obtaining the information of the participants’ secrets and comparison results. Last, various kinds of attacks have been analyzed, which show that the proposed protocol is secure against the outside and participants attacks.
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Bennett, C.H., Brassard, G.: Quantum cryptography: public-key distribution and coin tossing. In: IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, pp. 175–179. IEEE, New York (1984)
Li, J., Li, N., Zhang, Y., Wen, S., et al.: Special issue on quantum communication: a survey on quantum cryptography. Chin. J. Electron. 27(2), 223–228 (2018)
Bennett, C.H., Wiesner, S.J.: Communication via one and two particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992)
Bostrom, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902 (2002)
Li, J., Li, N., Li, L.L., Wang, T.: One step quantum key distribution based on EPR entanglement. Sci. Rep. 6(28767), 1–6 (2016)
Li, L.L., Li, J., Li, H.J., Tian, Y., Zheng, Y., Yang, Y.G.: Deterministic quantum secure direct communication protocol based on Omega state. IEEE Access 7, 6915–6921 (2019)
Hillery, M., Buzek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829–1834 (1999)
Kogias, I., Xiang, Y., He, Q., et al.: Unconditional security of entanglement-based continuous-variable quantum secret sharing. Phys. Rev. A 95, 012315 (2017)
Chen, X.B., Tang, X., Xu, G., Dou, Z., Chen, Y.L., et al.: Cryptanalysis of secret sharing with a single \(d\)-level quantum system. Quantum Inf. Process. 17(9), 225 (2018)
Wang, T.Y., Ma, J.F., Cai, X.Q.: The postprocessing of quantum digital signatures. Quantum Inf. Process. 16(1), 19 (2017)
Wang, T.Y., Wei, Z.L.: One-time proxy signature based on quantum cryptography. Quantum Inf. Process. 11(2), 455–463 (2012)
Yang, Y.G., Lei, A.H., Liu, A.Z., Zhou, Y.H., Shi, W.M.: Arbitrated quantum signature scheme based on cluster states. Quantum Inf. Process. 15(6), 2487–2497 (2016)
Wang, T.Y., Cai, X.Q., Zhang, R.L.: Security of a sessional blind signature based on quantum cryptograph. Quantum Inf. Process. 13(8), 1677–1685 (2014)
Wang, T.Y., Cai, X.Q., Ren, Y.L., Zhang, R.L.: Security of quantum digital signatures for classical messages. Sci. Rep. 5, 9231 (2015)
Yao, A.C.: Protocols for secure computations. In: Proceedings of the 23rd Annual Symposium on Foundations of Computer Science, pp. 160–164 (1982)
Du, W., Atallah, M.J.: Secure multi-party computation problems and their applications: a review and open problems. In: Proceedings of the 2001 Workshop on New Security Paradigms, Cloudcroft, America, pp. 13–22. ACM, New York (2001)
Shor, Peter W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)
Bonanome, M., Bužek, V., Hillery, M., et al.: Toward protocols for quantum-ensured privacy and secure voting. Phys. Rev. A 84(2), 022331 (2011)
Vaccaro, J.A., Spring, J., Chefles, A.: Quantum protocols for anonymous voting and surveying. Phys. Rev. A 75(1), 012333 (2007)
Huang, W., Wen, Q.Y., Liu, B., et al.: Quantum anonymous ranking. Phys. Rev. A 89(3), 032325 (2014)
Wang, T.Y., Wen, Q.Y., Zhu, F.C.: Economical quantum anonymous transmissions. J. Phys. B At. Mol. Opt. Phys. 43(24), 245501 (2010)
Hogg, T., Harsha, P., Chen, K.Y.: Quantum auctions. Int. J. Quantum Inf. 5(05), 751–780 (2007)
Yang, Y.G., Naseri, M., Wen, Q.Y.: Improved secure quantum sealed-bid auction. Opt. Commun. 282(20), 4167–4170 (2009)
Zhao, Z., Naseri, M., Zheng, Y.: Secure quantum sealed-bid auction with post-confirmation. Opt. Commun. 283(16), 3194–3197 (2010)
Jia, H.Y., Wen, Q.Y., Song, T.T., et al.: Quantum protocol for millionaire problem. Opt. Commun. 284(1), 545–549 (2011)
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)
Wen, L., Wang, Y.B., Cui, W.: Quantum private comparison protocol based on Bell entangled states. Commun. Theor. Phys. 57(4), 583 (2012)
Chen, X.B., Xu, G., Niu, X.X., et al.: 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)
Liu, W., Wang, Y.B., Jiang, Z.T.: An efficient protocol for the quantum private comparison of equality with \(W\) state. Opt. Commun. 284(12), 3160–3163 (2011)
Tseng, H.Y., Lin, J., Hwang, T.: New quantum private comparison protocol using EPR pairs. Quantum Inf. Process. 11(2), 373–384 (2012)
Li, J., Zhou, H.F., Jia, L., et al.: 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)
Wei, H., Wen, Q.Y., Liu, B., et al.: Robust and efficient quantum private comparison of equality with collective detection over collective-noise channels. Sci. China Phys. Mech. Astron. 56(9), 1670–1678 (2013)
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)
Liu, X., Zhang, B., Wang, J., et al.: Differential phase shift quantum private comparison. Quantum Inf. Process. 13(1), 71–84 (2014)
Li, J., Jia, L., Zhou, H.F., et al.: Secure quantum private comparison protocol based on the entanglement swapping between three-particle \(W\)-class state and bell state. Int. J. Theor. Phys. 55(3), 1710–1718 (2016)
Xu, L., Zhao, Z.: Quantum private comparison protocol based on the entanglement swapping between \(\chi ^+\) state and \(W\)-class state. Quantum Inf. Process. 16(12), 302 (2017)
Xu, L., Wang, J., Ahmed, H., et al.: A new quantum private comparison protocol. In: AOPC 2017: Fiber Optic Sensing and Optical Communications. International Society for Optics and Photonics, vol. 10464, p. 104640M (2017)
Liu, B., Xiao, D., Huang, W., et al.: Quantum private comparison employing single-photon interference. Quantum Inf. Process. 16(7), 180 (2017)
Gao, X., Zhang, S.B., Chang, Y., et al.: Cryptanalysis of the quantum private comparison protocol based on the entanglement swapping between three-particle \(W\)-class state and Bell state. Int. J. Theor. Phys. 57(6), 1–7 (2018)
Briegel, H.J., Raussendorf, R.: Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86(5), 910 (2001)
Hein, M., Dür, W., Briegel, H.J.: Entanglement properties of multipartite entangled states under the influence of decoherence. Phys. Rev. A 71(3), 032350 (2005)
Walther, P., Resch, K.J., Rudolph, T., et al.: Experimental one-way quantum computing. Nature 434(7030), 169 (2005)
Acknowledgements
Project supported by the National Natural Science Foundation of China (Grant Nos. U1636106 and 61671087), Natural Science Foundation of Beijing Municipality under Grant 4182006, The Major Science and Technology Support Program of Guizhou Province under Grant 20183001, The Open Foundation of Guizhou Provincial Key Laboratory of Public Big Data under Grant 2018BDKFJJ016 and BUPT Excellent Ph.D. Students Foundation (Grant No. CX2019227).
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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, 158 (2019). https://doi.org/10.1007/s11128-019-2266-x
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DOI: https://doi.org/10.1007/s11128-019-2266-x