{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T19:43:21Z","timestamp":1774554201555,"version":"3.50.1"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T00:00:00Z","timestamp":1771632000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T00:00:00Z","timestamp":1771632000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Science and Technology Development Plan Project of Jilin Province, China","award":["20230101181JC"],"award-info":[{"award-number":["20230101181JC"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-026-05106-3","type":"journal-article","created":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T10:53:25Z","timestamp":1771671205000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An entropy-increasing circuit for quantum walking and its application in quantum encryption"],"prefix":"10.1007","volume":"25","author":[{"given":"QingJi","family":"Zeng","sequence":"first","affiliation":[]},{"given":"JinQing","family":"Li","sequence":"additional","affiliation":[]},{"given":"XiaoQiang","family":"Di","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,2,21]]},"reference":[{"key":"5106_CR1","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1007\/s10773-018-3932-y","volume":"58","author":"J Wang","year":"2019","unstructured":"Wang, J., Geng, Y.-C., Han, L., Liu, J.-Q.: Quantum image encryption algorithm based on quantum key image. Int. J. Theor. Phys. 58, 308\u2013322 (2019)","journal-title":"Int. J. Theor. Phys."},{"issue":"8","key":"5106_CR2","doi-asserted-by":"publisher","first-page":"2833","DOI":"10.1007\/s11128-013-0567-z","volume":"12","author":"Y Zhang","year":"2013","unstructured":"Zhang, Y., Kai, L., Gao, Y., Wang, M.: Neqr: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12(8), 2833\u20132860 (2013)","journal-title":"Quantum Inf. Process."},{"issue":"3","key":"5106_CR3","doi-asserted-by":"publisher","first-page":"2815","DOI":"10.1007\/s11071-022-07942-1","volume":"111","author":"M Hu","year":"2023","unstructured":"Hu, M., Li, J., Di, X.: Quantum image encryption scheme based on 2d s ine 2-l ogistic chaotic map. Nonlinear Dyn. 111(3), 2815\u20132839 (2023)","journal-title":"Nonlinear Dyn."},{"issue":"2","key":"5106_CR4","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1007\/s10773-023-05277-0","volume":"62","author":"Z Jiang","year":"2023","unstructured":"Jiang, Z., Liu, X.: Image encryption algorithm based on discrete quantum baker map and chen hyperchaotic system. Int. J. Theor. Phys. 62(2), 22 (2023)","journal-title":"Int. J. Theor. Phys."},{"key":"5106_CR5","doi-asserted-by":"publisher","first-page":"1230294","DOI":"10.3389\/fphy.2024.1230294","volume":"12","author":"X-D Liu","year":"2024","unstructured":"Liu, X.-D., Chen, Q.-H., Zhao, R.-S., Liu, G.-Z., Guan, S., Wu, L.-L., Fan, X.-K.: Quantum image encryption algorithm based on four-dimensional chaos. Frontiers in Physics 12, 1230294 (2024)","journal-title":"Frontiers in Physics"},{"issue":"4","key":"5106_CR6","doi-asserted-by":"publisher","first-page":"3829","DOI":"10.1007\/s11071-024-10403-6","volume":"113","author":"V Verma","year":"2025","unstructured":"Verma, V., Kumar, S.: Quantum image encryption algorithm based on 3d-bnm chaotic map. Nonlinear Dyn. 113(4), 3829\u20133855 (2025)","journal-title":"Nonlinear Dyn."},{"issue":"2","key":"5106_CR7","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/s10773-022-05262-z","volume":"62","author":"F-F Yu","year":"2023","unstructured":"Yu, F.-F., Dai, J.-Y., Liu, S.-H., Gong, L.-H.: Visually meaningful quantum color image encryption scheme based on measured alternate quantum walks and quantum logistic mixed linear-nonlinear coupled mapping lattices. Int. J. Theor. Phys. 62(2), 33 (2023)","journal-title":"Int. J. Theor. Phys."},{"issue":"27","key":"5106_CR8","doi-asserted-by":"publisher","first-page":"42679","DOI":"10.1007\/s11042-023-15189-0","volume":"82","author":"Y Su","year":"2023","unstructured":"Su, Y., Wang, X.: Quantum color image encryption based on controlled two-particle quantum walks. Multimedia Tools and Applications 82(27), 42679\u201342697 (2023)","journal-title":"Multimedia Tools and Applications"},{"key":"5106_CR9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jisa.2024.103698","volume":"81","author":"J He","year":"2024","unstructured":"He, J., Zhu, H., Zhou, X.: Quantum image encryption algorithm via optimized quantum circuit and parity bit-plane permutation. Journal of Information Security and Applications 81, 103698 (2024)","journal-title":"Journal of Information Security and Applications"},{"issue":"10","key":"5106_CR10","doi-asserted-by":"publisher","first-page":"2092","DOI":"10.3390\/electronics14102092","volume":"14","author":"P Wang","year":"2025","unstructured":"Wang, P., Xiang, Y., Huang, L.: A novel image encryption scheme based on a quantum logistic map, hyper-chaotic lorenz map, and dna dynamic encoding. Electronics 14(10), 2092 (2025)","journal-title":"Electronics"},{"key":"5106_CR11","doi-asserted-by":"crossref","unstructured":"Song, F.-Y., Xu, G.-B., Wang, H.-K., Jiang, D.-H.: A quantum image encryption algorithm based on chaotic system and rubik\u2019s cube principle. Quantum Information Processing 23(8) (2024)","DOI":"10.1007\/s11128-024-04492-w"},{"issue":"1","key":"5106_CR12","doi-asserted-by":"publisher","first-page":"1930","DOI":"10.1038\/s41598-020-58636-w","volume":"10","author":"AA Abd El-Latif","year":"2020","unstructured":"Abd El-Latif, A.A., Abd-El-Atty, B., Amin, M., Iliyasu, A.M.: Quantum-inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications. Sci. Rep. 10(1), 1930 (2020)","journal-title":"Sci. Rep."},{"key":"5106_CR13","doi-asserted-by":"crossref","unstructured":"Vakulchyk, I., Fistul, M.V., Zolotaryuk, Y., Flach, S.: Almost compact moving breathers with fine-tuned discrete time quantum walks. Chaos: An Interdisciplinary Journal of Nonlinear Science 28(12) (2018)","DOI":"10.1063\/1.5060654"},{"key":"5106_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2022.127334","volume":"598","author":"Y-J Gao","year":"2022","unstructured":"Gao, Y.-J., Xie, H.-W., Zhang, J., Zhang, H.: A novel quantum image encryption technique based on improved controlled alternated quantum walks and hyperchaotic system. Physica A 598, 127334 (2022)","journal-title":"Physica A"},{"key":"5106_CR15","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.111926","volume":"157","author":"S Sahoo","year":"2022","unstructured":"Sahoo, S., Roy, B.K.: Design of multi-wing chaotic systems with higher largest lyapunov exponent. Chaos, Solitons Fractals 157, 111926 (2022)","journal-title":"Chaos, Solitons Fractals"},{"issue":"3","key":"5106_CR16","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/ad22c2","volume":"99","author":"D Mou","year":"2024","unstructured":"Mou, D., Dong, Y.: Color image encryption algorithm based on quantum random walk and multiple reset scrambling. Phys. Scr. 99(3), 035106 (2024)","journal-title":"Phys. Scr."},{"key":"5106_CR17","doi-asserted-by":"crossref","unstructured":"Hu, W., Dong, Y.: Quantum color image encryption based on a novel 3d chaotic system. Journal of Applied Physics 131(11) (2022)","DOI":"10.1063\/5.0084611"},{"issue":"2","key":"5106_CR18","doi-asserted-by":"publisher","first-page":"56","DOI":"10.3390\/computation13020056","volume":"13","author":"S Basiri","year":"2025","unstructured":"Basiri, S., Farhang Matin, L., Naseri, M.: Innovative quantum encryption method for rgb images based on bit-planes and logistic maps. Computation 13(2), 56 (2025)","journal-title":"Computation"},{"key":"5106_CR19","doi-asserted-by":"crossref","unstructured":"Abd EL Latif, A.A., Abd El Atty, B., Venegas Andraca, S.E.: Controlled Alter nate quantum walk-based pseudo-random number generator and its application to quantum color image encryption. Physica A: Statistical Mechanics and its Applications 547, 123869 (2020)","DOI":"10.1016\/j.physa.2019.123869"},{"issue":"2","key":"5106_CR20","doi-asserted-by":"publisher","first-page":"1859","DOI":"10.1007\/s11071-021-06663-1","volume":"105","author":"L Teng","year":"2021","unstructured":"Teng, L., Wang, X., Yang, F., Xian, Y.: Color image encryption based on cross 2d hyperchaotic map using combined cycle shift scrambling and selecting diffusion. Nonlinear Dyn. 105(2), 1859\u20131876 (2021)","journal-title":"Nonlinear Dyn."},{"key":"5106_CR21","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/j.ins.2012.07.049","volume":"222","author":"Y Wu","year":"2013","unstructured":"Wu, Y., Zhou, Y., Saveriades, G., Agaian, S., Noonan, J.P., Natarajan, P.: Local shannon entropy measure with statistical tests for image randomness. Inf. Sci. 222, 323\u2013342 (2013)","journal-title":"Inf. Sci."},{"key":"5106_CR22","doi-asserted-by":"publisher","first-page":"122210","DOI":"10.1109\/ACCESS.2020.3007550","volume":"8","author":"J Zhou","year":"2020","unstructured":"Zhou, J., Li, J., Di, X.: A novel lossless medical image encryption scheme based on game theory with optimized roi parameters and hidden roi position. Ieee Access 8, 122210\u2013122228 (2020)","journal-title":"Ieee Access"},{"issue":"8","key":"5106_CR23","doi-asserted-by":"publisher","first-page":"852","DOI":"10.3390\/e27080852","volume":"27","author":"X Zhang","year":"2025","unstructured":"Zhang, X., Wen, H., Feng, W., Kang, S., Xie, Z., Zhang, X., Lin, Y.: Weighted color image encryption algorithm based on rna extended dynamic coding and quantum chaotic system. Entropy 27(8), 852 (2025)","journal-title":"Entropy"},{"issue":"6","key":"5106_CR24","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/ac6d85","volume":"97","author":"Y Chen","year":"2022","unstructured":"Chen, Y., Xie, S., Zhang, J.: A novel double image encryption algorithm based on coupled chaotic system. Phys. Scr. 97(6), 065207 (2022)","journal-title":"Phys. Scr."},{"key":"5106_CR25","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2020.106162","volume":"90","author":"K Shahna","year":"2020","unstructured":"Shahna, K., Mohamed, A.: A novel image encryption scheme using both pixel level and bit level permutation with chaotic map. Appl. Soft Comput. 90, 106162 (2020)","journal-title":"Appl. Soft Comput."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-026-05106-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-026-05106-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-026-05106-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T09:55:12Z","timestamp":1774346112000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-026-05106-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,21]]},"references-count":25,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["5106"],"URL":"https:\/\/doi.org\/10.1007\/s11128-026-05106-3","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-6392028\/v1","asserted-by":"object"}]},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,21]]},"assertion":[{"value":"7 April 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 February 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 February 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 March 2026","order":5,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Update","order":6,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The Ref. [25] has been removed from the article.","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"82"}}