{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T16:23:47Z","timestamp":1778343827458,"version":"3.51.4"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,4,1]],"date-time":"2021-04-01T00:00:00Z","timestamp":1617235200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,1]],"date-time":"2021-04-01T00:00:00Z","timestamp":1617235200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["F2017201199"],"award-info":[{"award-number":["F2017201199"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2021,4]]},"DOI":"10.1007\/s11128-021-03059-3","type":"journal-article","created":{"date-parts":[[2021,4,25]],"date-time":"2021-04-25T06:16:22Z","timestamp":1619331382000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Quantum private comparison of size using d-level Bell states with a semi-honest third party"],"prefix":"10.1007","volume":"20","author":[{"given":"WanQing","family":"Wu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YongXin","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,4,24]]},"reference":[{"issue":"5","key":"3059_CR1","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1007\/s11128-020-02664-y","volume":"19","author":"Q Wang","year":"2020","unstructured":"Wang, Q., Li, Y., Yu, C., et al.: Quantum anonymous ranking and selection with verifiability. Quantum Inf. Process. 19(5), 166 (2020)","journal-title":"Quantum Inf. Process."},{"issue":"1","key":"3059_CR2","doi-asserted-by":"publisher","first-page":"012318","DOI":"10.1103\/PhysRevA.93.012318","volume":"93","author":"S Lin","year":"2016","unstructured":"Lin, S., Guo, G.D., Huang, F., et al.: Quantum anonymous ranking based on the Chinese remainder theorem. Phys. Rev. A 93(1), 012318 (2016)","journal-title":"Phys. Rev. A"},{"issue":"11","key":"3059_CR3","doi-asserted-by":"publisher","first-page":"3431","DOI":"10.1007\/s10773-017-3506-4","volume":"56","author":"WQ Wu","year":"2017","unstructured":"Wu, W.Q., Cai, Q.Y., Zhang, H.G., et al.: Quantum public key cryptosystem based on Bell states. Int. J. Theor. Phys. 56(11), 3431\u20133440 (2017)","journal-title":"Int. J. Theor. Phys."},{"issue":"12","key":"3059_CR4","first-page":"1","volume":"57","author":"WQ Wu","year":"2018","unstructured":"Wu, W.Q., Cai, Q.Y., Zhang, H.G., et al.: Bit-oriented quantum public-key cryptosystem based on Bell states. Int. J. Theor. Phys. 57(12), 1\u201311 (2018)","journal-title":"Int. J. Theor. Phys."},{"issue":"6","key":"3059_CR5","doi-asserted-by":"publisher","first-page":"1866","DOI":"10.1007\/s10773-020-04454-9","volume":"59","author":"WQ Wu","year":"2020","unstructured":"Wu, W.Q., Zhou, G.L., Zhao, Y.X., et al.: New quantum private comparison protocol without a third party. Int. J. Theor. Phys. 59(6), 1866\u20131875 (2020)","journal-title":"Int. J. Theor. Phys."},{"issue":"48","key":"3059_CR6","doi-asserted-by":"publisher","first-page":"4033","DOI":"10.1016\/j.physleta.2016.10.017","volume":"380","author":"YG Yang","year":"2016","unstructured":"Yang, Y.G., Liu, Z.C., Li, J., et al.: Quantum private query with perfect user privacy against a joint-measurement attack. Phys. Lett. A 380(48), 4033\u20134038 (2016)","journal-title":"Phys. Lett. A"},{"issue":"6","key":"3059_CR7","doi-asserted-by":"publisher","first-page":"065002","DOI":"10.1088\/0031-8949\/80\/06\/065002","volume":"80","author":"YG Yang","year":"2009","unstructured":"Yang, Y.G., Cao, W.F., Wen, Q.Y.: Secure quantum private comparison. Phys. Scr. 80(6), 065002 (2009)","journal-title":"Phys. Scr."},{"issue":"5","key":"3059_CR8","doi-asserted-by":"publisher","first-page":"1517","DOI":"10.1007\/s10773-017-3291-0","volume":"56","author":"TY Ye","year":"2017","unstructured":"Ye, T.Y., Ji, Z.X.: Two-party quantum private comparison with five-qubit entangled states. Int. J. Theor. Phys. 56(5), 1517\u20131529 (2017)","journal-title":"Int. J. Theor. Phys."},{"issue":"10","key":"3059_CR9","doi-asserted-by":"crossref","first-page":"3340","DOI":"10.1007\/s10773-017-3499-z","volume":"56","author":"HM Pan","year":"2017","unstructured":"Pan, H.M.: Quantum private comparison based on $$\\chi $$-type entangled states. Int. J. Theor. Phys. 56(10), 3340\u20133347 (2017)","journal-title":"Int. J. Theor. Phys."},{"issue":"7","key":"3059_CR10","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/s11128-017-1628-5","volume":"16","author":"ZX Ji","year":"2017","unstructured":"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)","journal-title":"Quantum Inf. Process."},{"issue":"8","key":"3059_CR11","doi-asserted-by":"crossref","first-page":"2671","DOI":"10.1007\/s10773-017-3425-4","volume":"56","author":"L Xu","year":"2017","unstructured":"Xu, L., Zhao, Z.: A robust and efficient quantum private comparison of equality based on the entangled swapping of GHZ-like state and $$\\chi ^{+}$$ state. Int. J. Theor. Phys. 56(8), 2671\u20132685 (2017)","journal-title":"Int. J. Theor. Phys."},{"issue":"12","key":"3059_CR12","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1007\/s11128-017-1755-z","volume":"16","author":"L Xu","year":"2017","unstructured":"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)","journal-title":"Quantum Inf. Process."},{"key":"3059_CR13","first-page":"1","volume":"2","author":"MK Zhou","year":"2017","unstructured":"Zhou, M.K.: Improvements of quantum private comparison protocol based on cluster states. Int. J. Theor. Phys. 2, 1\u20136 (2017)","journal-title":"Int. J. Theor. Phys."},{"key":"3059_CR14","doi-asserted-by":"publisher","first-page":"1854","DOI":"10.1007\/s10773-019-04080-0","volume":"58","author":"WQ Wu","year":"2019","unstructured":"Wu, W.Q., Cai, Q.Y., Wu, S.M., et al.: Cryptanalysis and improvement of Ye et al\u2019s quantum private comparison protocol. Int. J. Theor. Phys. 58, 1854\u20131860 (2019)","journal-title":"Int. J. Theor. Phys."},{"issue":"2","key":"3059_CR15","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1007\/s11128-016-1498-2","volume":"16","author":"SM Hung","year":"2017","unstructured":"Hung, S.M., Hwang, S.L., Hwang, T., et al.: Multiparty quantum private comparison with almost dishonest third parties for strangers. Quantum Inf. Process. 16(2), 36 (2017)","journal-title":"Quantum Inf. Process."},{"issue":"3","key":"3059_CR16","doi-asserted-by":"publisher","first-page":"1950026","DOI":"10.1142\/S0219749919500266","volume":"17","author":"WQ Wu","year":"2019","unstructured":"Wu, W.Q., Cai, Q.Y., Wu, S.M., et al.: Cryptanalysis of He\u2019s quantum private comparison protocol and a new protocol. Int. J. Quantum Inf. 17(3), 1950026 (2019)","journal-title":"Int. J. Quantum Inf."},{"issue":"1","key":"3059_CR17","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1016\/j.optcom.2010.09.005","volume":"284","author":"HY Jia","year":"2011","unstructured":"Jia, H.Y., Wen, Q.Y., Song, T.T., et al.: Quantum protocol for millionaire problem. Opt. Commun. 284(1), 545\u2013549 (2011)","journal-title":"Opt. Commun."},{"issue":"3","key":"3059_CR18","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1007\/s11128-019-2175-z","volume":"18","author":"WQ Wu","year":"2019","unstructured":"Wu, W.Q., Zhang, H.G.: A quantum query algorithm for computing the degree of a perfect nonlinear Boolean function. Quantum Inf. Process. 18(3), 62 (2019)","journal-title":"Quantum Inf. Process."},{"issue":"6","key":"3059_CR19","doi-asserted-by":"publisher","first-page":"1854","DOI":"10.1007\/s10773-020-04453-w","volume":"59","author":"WQ Wu","year":"2020","unstructured":"Wu, W.Q., Ma, X.X.: Quantum private comparison protocol without a third party. Int. J. Theor. Phys. 59(6), 1854\u20131865 (2020)","journal-title":"Int. J. Theor. Phys."},{"key":"3059_CR20","unstructured":"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\u2013179 (1984)"},{"issue":"6","key":"3059_CR21","doi-asserted-by":"publisher","first-page":"1711","DOI":"10.1016\/j.optcom.2010.11.038","volume":"284","author":"TY Wang","year":"2011","unstructured":"Wang, T.Y., Wen, Q.Y., Zhu, F.C.: Cryptanalysis of multiparty quantum secret sharing with Bell states and Bell measurements. Opt. Commun. 284(6), 1711\u20131713 (2011)","journal-title":"Opt. Commun."},{"issue":"2","key":"3059_CR22","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1007\/s11128-011-0251-0","volume":"11","author":"HY Tseng","year":"2012","unstructured":"Tseng, H.Y., Lin, J., Hwang, T.: New quantum private comparison protocol using EPR pairs. Quantum Inf. Process. 11(2), 373\u2013384 (2012)","journal-title":"Quantum Inf. Process."},{"issue":"1","key":"3059_CR23","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1007\/s11128-012-0395-6","volume":"12","author":"S Lin","year":"2013","unstructured":"Lin, S., Sun, Y., Liu, X.F., et al.: Quantum private comparison protocol with d-dimensional Bell states. Quantum Inf. Process. 12(1), 559\u2013568 (2013)","journal-title":"Quantum Inf. Process."},{"issue":"8","key":"3059_CR24","doi-asserted-by":"publisher","first-page":"2793","DOI":"10.1007\/s11128-013-0536-6","volume":"12","author":"FZ Guo","year":"2013","unstructured":"Guo, F.Z., Gao, F., Qin, S.J., et al.: Quantum private comparison protocol based on entanglement swapping of (d)-level Bell states. Quantum Inf. Process. 12(8), 2793\u20132802 (2013)","journal-title":"Quantum Inf. Process."},{"issue":"6","key":"3059_CR25","doi-asserted-by":"publisher","first-page":"065013","DOI":"10.1088\/0031-8949\/88\/06\/065013","volume":"88","author":"CH Yu","year":"2013","unstructured":"Yu, C.H., Guo, G.D., Lin, S.: Quantum private comparison with d-level single-particle states. Phys. Scr. 88(6), 065013 (2013)","journal-title":"Phys. Scr."},{"issue":"10","key":"3059_CR26","doi-asserted-by":"publisher","first-page":"2343","DOI":"10.1007\/s11128-014-0805-z","volume":"13","author":"QB Luo","year":"2014","unstructured":"Luo, Q.B., Yang, G.W., She, K., et al.: Multi-party quantum private comparison protocol based on d-dimensional entangled states. Quantum Inf. Process. 13(10), 2343\u20132352 (2014)","journal-title":"Quantum Inf. Process."},{"key":"3059_CR27","doi-asserted-by":"publisher","first-page":"4225","DOI":"10.1007\/s11128-015-1104-z","volume":"14","author":"S Huang","year":"2015","unstructured":"Huang, S., Hwang, T., Gope, P.: Multi-party quantum private comparison with an almost-dishonest third party. Quantum Inf. Process. 14, 4225\u20134235 (2015)","journal-title":"Quantum Inf. Process."},{"issue":"10","key":"3059_CR28","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1007\/s11128-018-2021-8","volume":"17","author":"CQ Ye","year":"2018","unstructured":"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)","journal-title":"Quantum Inf. Process."},{"key":"3059_CR29","doi-asserted-by":"publisher","first-page":"142507","DOI":"10.1109\/ACCESS.2019.2944785","volume":"7","author":"XL Song","year":"2019","unstructured":"Song, X.L., Wen, A.J., Gou, R.: Multiparty quantum private comparison of size relation based on single-particle states. IEEE Access 7, 142507\u2013142514 (2019)","journal-title":"IEEE Access"},{"key":"3059_CR30","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1007\/s11128-019-2401-8","volume":"18","author":"H Cao","year":"2019","unstructured":"Cao, H., Ma, W.P., Lv, L.D., et al.: Multi-party quantum privacy comparison of size based on d-level GHZ states. Quantum Inf. Process. 18, 287 (2019)","journal-title":"Quantum Inf. Process."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03059-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-021-03059-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03059-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,6]],"date-time":"2021-05-06T01:15:51Z","timestamp":1620263751000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-021-03059-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["3059"],"URL":"https:\/\/doi.org\/10.1007\/s11128-021-03059-3","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4]]},"assertion":[{"value":"22 April 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 March 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 April 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"155"}}