Abstract
This paper proposes a pioneering quantum private comparison (QPC) protocol for n users. State-of-the-art QPC protocols have been designed for two users who wish to compare their private information. However, if n users want to perform the equality comparison, these two-user QPC protocols have to be executed repeatedly at least n − 1 times. The proposed protocol allows n users’ private information to be compared within one protocol execution. The proposed QPC protocol takes the Greenberger–Horne–Zeilinger (GHZ) class as a quantum resource and uses a special property in the GHZ-class state to perform the equality comparison. Moreover, due to the one-step quantum transmission, the protocol is free from Trojan horse attacks and it is also shown to be secure against other well-known attacks.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Bennett, C.H., Brassard, G.: Quantum cryptography: public-key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, New York, Bangalore, India, pp. 175–179 (1984)
Bennett CH., Brassard G., Crépeau C., Jozsa R., Peres A., Wootters WK.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70(13), 1895–1899 (1993)
Furusawa A., Sørensen J.L., Braunstein S.L., Fuchs C.A., Kimble H.J., Polzik E.S.: Unconditional quantum teleportation. Science 282(5389), 706–709 (1998)
Zhang Z.J., Man Z.X.: Many-agent controlled teleportation of multi-qubit quantum information. Phys. Lett. A 341(1–4), 55–59 (2005)
Zhang W., Liu Y.M., Liu J., Zhang Z.J.: Teleportation of arbitrary unknown two atom state with cluster state via thermal cavity. Chin. Phys. B 17(9), 3203–3208 (2008)
Zhang Z.Y., Liu Y.M., Zuo X.Q., Zhang W., Zhang Z.J.: Transformation operator and criterion for perfectly teleporting arbitrary three-qubit state with six-qubit channel and Bell-state measurement. Chin. Phys. Lett. 26(12), 120303 (2009)
Tsai C.W., Hwang T.: Teleportation of a pure EPR state via GHZ-like state. Int. J. Theor. Phys. 49(8), 1969–1975 (2010)
Hillery M., Buzek V., Berthiaume A.: Quantum secret sharing. Phys. Rev. A 59(3), 1829–1834 (1999)
Xiao L., Long G.L., Deng F.G., Pan J.W.: Efficient multiparty quantum secret sharing schemes. Phys. Rev. A 69(5), 052307 (2004)
Zhang Z.J., Man Z.X.: Multiparty quantum secret sharing of classical messages based on entanglement swapping. Phys. Rev. A 72(2), 022303 (2005)
Deng F.G., Long G.L., Zhou H.Y.: An efficient quantum secret sharing scheme with Einstein– Podolsky–Rosen pairs. Phys. Lett. A 340(1–4), 43–50 (2005)
Deng F.G., Zhou H.Y., Long G.L.: Circular quantum secret sharing. J. Phys. A Math. Gen. 39(45), 14089–14099 (2006)
Han L.F., Liu Y.M., Liu J., Zhang Z.J.: Multiparty quantum secret sharing of secure direct communication using single photons. Opt. Commun. 281(9), 2690–2694 (2008)
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)
Sun Y., Wen Q.Y., Gao F., Chen X.B., Zhu F.C.: Multiparty quantum secret sharing based on Bell measurement. Opt. Commun. 282(17), 3647–3651 (2009)
Shi R.H., Huang L.S., Yang W., Zhong H.: Multiparty quantum secret sharing with Bell states and Bell measurements. Opt. Commun. 283(11), 2476–2480 (2010)
Bostroem K., Felbinger T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89(18), 187902 (2002)
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)
Man Z.X., Zhang Z.J., Li Y.: Deterministic secure direct communication by using swapping quantum entanglement and local unitary operations. Chin. Phys. Lett. 22(1), 18–21 (2005)
Zhan Y.B., Zhang L.L., Zhang Q.Y.: Quantum secure direct communication by entangled qutrits and entanglement swapping. Opt. Commun. 282(23), 4633–4636 (2009)
Yang C.W., Tsai C.W., Hwang T.: Fault tolerant two-step quantum secure direct communication protocol against collective noises. Sci. China Ser. G: Phys. Mech. Astron. 54(3), 496–501 (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)
Chen X.B., Xu G., Niu X.X., Wen QY., 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)
Yao, A.C.: Protocols for secure computations. In: Proceedings of 23rd IEEE Symposium on Foundations of Computer Science (FOCS’ 82), Washington, DC, USA, p. 160 (1982)
Lo H.K.: Insecurity of quantum secure computations. Phys. Rev. A 56(2), 1154–1162 (1997)
Boudot F., Schoenmakers B., Traor’e J.: A fair and efficient solution to the socialist millionaires’ problem. Discret. Appl. Math. (Special issue on Coding and Cryptology) 111(1–2), 23–36 (2001)
Hillery M., Ziman M., Bužek V., Bieliková M.: Towards quantum-based privacy and voting. Phys. Lett. A 349(1–4), 5–81 (2006)
Vaccaro J.A., Spring J., Chefles A.: Quantum protocols for anonymous voting and surveying. Phys. Rev. A 75(1), 012333 (2007)
Hogg T., Harsha P., Chen K.Y.: Quantum auctions. Int. J. Quantum Inf. 5, 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)
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)
Cai Q.Y.: Eavesdropping on the two-way quantum communication protocols with invisible photons. Phys. Lett. A 351(1–2), 23–25 (2006)
Li X.H., Deng F.G., Zhou H.Y.: Improving the security of secure direct communication based on the secret transmitting order of particles. Phys. Rev. A 74(5), 054302 (2006)
Greenberger, D.M., Horne, M.A., Zeilinger, A.: Going beyond Bell’s theorem. Arxiv preprint arXiv:0712.0921 (2007)
Nielsen M.A.: Quantum computation by measurement and quantum memory. Phys. Lett. A 308(2–3), 96–100 (2003)
Jeffrey E., Brenner M., Kwiat P.: Delayed-choice quantum cryptography. Proc. SPIE 5161, 269–279 (2004)
Jeffrey, E., Altepeter, J., Kwiat, P.: Relativistic quantum cryptography. In: Frontiers in Optics, OSA Technical Digest (CD), Optical Society of America, paper FWB1 (2006)
Jeffrey, E., Altepeter, J., Kwiat, P.: Relativistic quantum cryptography with optical storage. In: International Conference on Quantum Information, OSA Technical Digest (CD), Optical Society of America, paper IFE1 (2007)
Jennewein T., Simon C., Weihs G., Weinfurter H., Zeilinger A.: Quantum cryptography with entangled photons. Phys. Rev. Lett. 84(20), 4729–4732 (2000)
Hughes R.J., Nordholt J.E., Derkacs D., Peterson C.G.: Practical free-space quantum key distribution over 10 km in daylight and at night. New. J. Phys. 4, 43.1–43.14 (2002)
Gobby C., Yuan Z.L., Shields A.J.: Quantum key distribution over 122 km of standard telecom fiber. Appl. Phys. Lett. 84(19), 3762–3764 (2004)
Chong S.K., Hwang T.: The enhancement of three-party simultaneous quantum secure direct communication scheme with EPR pairs. Opt. Commun. 284(1), 515–518 (2011)
Lin J., Hwang T.: An enhancement on Shi et al.’s multiparty quantum secret sharing protocol. Opt. Commun. 284(5), 1468–1471 (2011)
Tsai C.-W., Hwang T.: New deterministic quantum communication via symmetric W state. Opt. Commun. 283(21), 4397–4400 (2010)
Hsieh C.R., Tsai C.W., Hwang T.: Quantum secret sharing using GHZ-like state. Commun. Theor. Phys. 54(6), 1019–1022 (2010)
Tsai C.W., Hsieh C.R., Hwang T.: Dense coding using cluster states and it’s application on deterministic secure quantum communication. Eur. Phys. J. D 61(3), 779–783 (2011)
Hwang C.C., Hwang T., Tsai C.W.: Quantum key distribution protocol using dense coding of three-qubit W state. Eur. Phys. J. D 61(3), 785–790 (2011)
Tsai C.W., Hwang T.: Multiparty quantum secret sharing based on two special entangled states. Sci. China Phys. Mech. Astron. 55(3), 460–464 (2012)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chang, YJ., Tsai, CW. & Hwang, T. Multi-user private comparison protocol using GHZ class states. Quantum Inf Process 12, 1077–1088 (2013). https://doi.org/10.1007/s11128-012-0454-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11128-012-0454-z