{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T12:01:48Z","timestamp":1777982508897,"version":"3.51.4"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T00:00:00Z","timestamp":1771804800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T00:00:00Z","timestamp":1771804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2022M3H3A106307411"],"award-info":[{"award-number":["2022M3H3A106307411"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-026-05081-9","type":"journal-article","created":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T06:43:06Z","timestamp":1771828986000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["QryptGen+: a quantum GAN-based high-security image encryption key generator with enhanced chaotic modeling"],"prefix":"10.1007","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-7296-8500","authenticated-orcid":false,"given":"Gilsang","family":"Ahn","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7506-4023","authenticated-orcid":false,"given":"Seokhie","family":"Hong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,2,23]]},"reference":[{"key":"5081_CR1","doi-asserted-by":"crossref","unstructured":"Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 130\u2013141 (1963) doi: 10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2"},{"key":"5081_CR2","doi-asserted-by":"crossref","unstructured":"Henon, M.: A two-dimensional mapping with a strange attractor. Commun. Math. Phys. 69\u201377 (1976) doi: 10.1007\/BF01608556","DOI":"10.1007\/BF01608556"},{"key":"5081_CR3","doi-asserted-by":"crossref","unstructured":"May, R.M.: Simple mathematical models with very complicated dynamics. Nature, 459\u2013467 (1976) doi: 10.1038\/261459a0","DOI":"10.1038\/261459a0"},{"key":"5081_CR4","doi-asserted-by":"crossref","unstructured":"Chai, X.: Tpe-gan: Thumbnail preserving encryption based on gan with key. IEEE Signal Processing Letters, 972\u2013976 (2022) doi: 10.1109\/LSP.2022.3163685","DOI":"10.1109\/LSP.2022.3163685"},{"key":"5081_CR5","doi-asserted-by":"publisher","DOI":"10.3390\/systems11010036","author":"K Panwar","year":"2023","unstructured":"Panwar, K.: Encipher gan: an end-to-end color image encryption system using a deep generative model. MDPI (2023). https:\/\/doi.org\/10.3390\/systems11010036","journal-title":"MDPI"},{"key":"5081_CR6","doi-asserted-by":"publisher","DOI":"10.1109\/TCE.2023.3285626","author":"M Singh","year":"2023","unstructured":"Singh, M.: Using gan-based encryption to secure digital images with reconstruction through customized super resolution network. IEEE ToCE (2023). https:\/\/doi.org\/10.1109\/TCE.2023.3285626","journal-title":"IEEE ToCE"},{"key":"5081_CR7","doi-asserted-by":"crossref","unstructured":"P. Rebentrost, M.M., Lloyd, S.: Quantum support vector machine for big data classification. Phys. Rev. Lett. 113(130503) (2014) doi: 10.1103\/PhysRevLett.113.130503","DOI":"10.1103\/PhysRevLett.113.130503"},{"key":"5081_CR8","doi-asserted-by":"crossref","unstructured":"Amin, M.H., Andriyash, E., J. Rolfe, B.K., Melko, R.: Quantum boltzmann machine. Phys. Rev. X 8(021050) (2018) doi: 10.1103\/PhysRevX.8.021050","DOI":"10.1103\/PhysRevX.8.021050"},{"key":"5081_CR9","doi-asserted-by":"crossref","unstructured":"M. T. West, S.-L.T., S.Low, J.: Towards quantum enhanced adversarial robustness in machine learning. Nature Mach. Intell. 5(581) (2023) doi: 10.1038\/s42256-023-00661-1","DOI":"10.1038\/s42256-023-00661-1"},{"key":"5081_CR10","doi-asserted-by":"crossref","unstructured":"Maxwell T. West, S.M.E., Usman, M.: Benchmarking adversarially robust quantum machine learning at scale. Phys. Rev. Res. 5(023186) (2023) doi: 10.1103\/PhysRevResearch.5.023186","DOI":"10.1103\/PhysRevResearch.5.023186"},{"key":"5081_CR11","doi-asserted-by":"crossref","unstructured":"Dallaire-Demers, P.-L., Killoran, N.: Quantum generative adversarial networks. Phys. Rev. A. 98(012324) (2018) doi: 10.1103\/PhysRevA.98.012324","DOI":"10.1103\/PhysRevA.98.012324"},{"key":"5081_CR12","doi-asserted-by":"crossref","unstructured":"Lloyd, S., Weedbrook, C.: Quantum generative adversarial learning. Phys. Rev. Lett. 121(040502) (2018) doi: 10.1103\/PhysRevLett.121.040502","DOI":"10.1103\/PhysRevLett.121.040502"},{"key":"5081_CR13","doi-asserted-by":"crossref","unstructured":"Samuel A. Stein, B.B., Chen, D.: Qugan: A quantum state fidelity based generative adversarial network. in Proc. IEEE Int. Conf. Quantum Comput. Eng., 71\u201381 (2021) doi: 10.1109\/QCE52317.2021.00023","DOI":"10.1109\/QCE52317.2021.00023"},{"key":"5081_CR14","doi-asserted-by":"crossref","unstructured":"C. Chu, M.S. G. Skipper, Chen, F.: Iqgan: Robust quantum generative adversarial network for image synthesis on nisq devices (2022) arXiv:2210.16857","DOI":"10.1109\/ICASSP49357.2023.10096772"},{"key":"5081_CR15","doi-asserted-by":"crossref","unstructured":"Tsang, S.L., West, M.T.: Hybrid quantum-classical generative adversarial network for high-resolution image generation. IEEE TQE (3102419) (2023) doi: 10.1109\/TQE.2023.3319319","DOI":"10.1109\/TQE.2023.3319319"},{"key":"5081_CR16","doi-asserted-by":"crossref","unstructured":"A. Khatun, Y.s.W. K.y. Aydeiz, Usman, M.: Quantum generative learning for high-resolution medical image generation. Mach. Learn. Sci. Technol. 6(025032) (2025) doi: 10.1088\/2632-2153\/add1a9","DOI":"10.1088\/2632-2153\/add1a9"},{"key":"5081_CR17","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1038\/nature23655","volume":"549","author":"S-K Liao","year":"2017","unstructured":"Liao, S.-K., Pan, J.-W.: Satellite-to-ground quantum key distribution. Nature 549, 43\u201347 (2017). https:\/\/doi.org\/10.1038\/nature23655","journal-title":"Nature"},{"key":"5081_CR18","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1038\/nphoton.2013.46","volume":"7","author":"S Nauerth","year":"2013","unstructured":"Nauerth, S., Weinfurter, H.: Air-to-ground quantum communication. Nat. Photonics 7, 382\u2013386 (2013). https:\/\/doi.org\/10.1038\/nphoton.2013.46","journal-title":"Nat. Photonics"},{"key":"5081_CR19","doi-asserted-by":"crossref","unstructured":"A., G., H., S.: Qryptgen: a quantum gan-based image encryption key generator using chaotic data distributions. Quantum Information Processing 24(136) (2025) doi: 10.1007\/s11128-025-04750-5","DOI":"10.1007\/s11128-025-04750-5"},{"key":"5081_CR20","unstructured":"Technologies, X.Q.: Strongly entangling layers. pennylane (2013). available at https:\/\/docs.pennylane.ai\/en\/stable\/code\/api\/pennylane.StronglyEntanglingLayers.html"},{"key":"5081_CR21","unstructured":"Goodfellow, I.: Generative adversarial networks. In: Proc. Adv. Neural Inf. Process. Syst., 2672\u20132680 (2014) https:\/\/doi.org\/10.48550\/arXiv.1406.2661"},{"key":"5081_CR22","unstructured":"Gulrajani, I., Ahmed, F., Arjovsky, M., Dumoulin, V., Courville, A.: Improved training of wasserstein gans (2017) arXiv:1704.00028v3"},{"key":"5081_CR23","doi-asserted-by":"crossref","unstructured":"Ryan Sweke, F.W., Eisert, J.: Stochastic gradient descent for hybrid quantum classical optimization. Quantum 4(314) (2020) https:\/\/doi.org\/10.22331\/q-2020-08-31-314","DOI":"10.22331\/q-2020-08-31-314"},{"key":"5081_CR24","doi-asserted-by":"crossref","unstructured":"M. Benedetti, S.S. E. Lloyd, Fiorentini, M.: Parameterized quantum circuits as machine learning models. Quantum Sci. Technol. 4(043001) (2019) doi: 10.1088\/2058-9565\/ab4eb5","DOI":"10.1088\/2058-9565\/ab4eb5"},{"key":"5081_CR25","doi-asserted-by":"crossref","unstructured":"Zoufal, C., Lucchi, A., Woerner, S.: Quantum generative adversarial networks for learning and loading random distributions. npj Quantum Information. 5(103) (2019) doi: 10.1038\/s41534-019-0223-2","DOI":"10.1038\/s41534-019-0223-2"},{"key":"5081_CR26","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/j.ins.2020.05.127","volume":"538","author":"H Situ","year":"2020","unstructured":"Situ, H., He, Z., Wang, Y., Li, L., Zheng, S.: Quantum generative adversarial network for generating discrete distribution. Inf. Sci. 538, 193\u2013208 (2020). https:\/\/doi.org\/10.1016\/j.ins.2020.05.127","journal-title":"Inf. Sci."},{"key":"5081_CR27","doi-asserted-by":"crossref","unstructured":"Niu, M.Y., Zlokapa, A., Broughton, M., Boixo, S., Mohseni, M., Smelyanskyi, V., Neven, H.: Entangling quantum generative adversarial networks. Phys. Rev. Lett. 128(220505) (2022) doi: 10.1103\/PhysRevLett.128.220505","DOI":"10.1103\/PhysRevLett.128.220505"},{"key":"5081_CR28","doi-asserted-by":"crossref","unstructured":"Huang, H.-L., Du, Y., Pan, J.-W.: Experimental quantum generative adversarial networks for image generation. Phys. Rev. Appl. 16(024051) (2021) doi: 10.1103\/PhysRevApplied.16.024051","DOI":"10.1103\/PhysRevApplied.16.024051"},{"key":"5081_CR29","doi-asserted-by":"crossref","unstructured":"Preskill, J.: Quantum computing in the nisq era and beyond. Quantum 2(79) (2018) https:\/\/doi.org\/10.22331\/q-2018-08-06-79","DOI":"10.22331\/q-2018-08-06-79"},{"key":"5081_CR30","unstructured":"Chakrabarti, S., Huang, Y., Li, T., Feizi, S., Wu, X.: Quantum wasserstein generative adversarial networks (2019) arXiv:1911.00111v1"},{"key":"5081_CR31","doi-asserted-by":"crossref","unstructured":"Kiani, B.T., Palma, G.D., Marvian, M., Liu, Z., Lloyd, S.: Learning quantum data with the quantum earth mover\u2019s distance. Quantum Sci. Technol. 7(045002) (2022) doi: 10.1088\/2058-9565\/ac79c9","DOI":"10.1088\/2058-9565\/ac79c9"},{"key":"5081_CR32","unstructured":"Choi., M.-S.: Q3: Symbolic quantum simulation. Github (2023). available at https:\/\/github.com\/quantum-mob\/Q3"},{"key":"5081_CR33","unstructured":"Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization (2014) arXiv:1412.6980v9"},{"key":"5081_CR34","doi-asserted-by":"crossref","unstructured":"Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 379\u2013426 (1948) doi: 10.1002\/j.1538-7305.1948.tb01338.x","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-026-05081-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-026-05081-9","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-026-05081-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T09:55:35Z","timestamp":1774346135000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-026-05081-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,23]]},"references-count":34,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["5081"],"URL":"https:\/\/doi.org\/10.1007\/s11128-026-05081-9","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-6927959\/v1","asserted-by":"object"}]},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,23]]},"assertion":[{"value":"19 June 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 January 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"84"}}