{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T17:52:16Z","timestamp":1783705936144,"version":"3.55.0"},"reference-count":45,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,29]],"date-time":"2023-05-29T00:00:00Z","timestamp":1685318400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Shandong Province, China","award":["Nos. ZR2021MF049"],"award-info":[{"award-number":["Nos. ZR2021MF049"]}]},{"name":"Natural Science Foundation of Shandong Province, China","award":["Nos. ZR2022JQ04"],"award-info":[{"award-number":["Nos. ZR2022JQ04"]}]},{"name":"Natural Science Foundation of Shandong Province, China","award":["Nos. ZR2022LLZ012"],"award-info":[{"award-number":["Nos. ZR2022LLZ012"]}]},{"name":"Natural Science Foundation of Shandong Province, China","award":["Nos. ZR2021LLZ001"],"award-info":[{"award-number":["Nos. ZR2021LLZ001"]}]},{"name":"Natural Science Foundation of Shandong Province, China","award":["Nos. 11975132"],"award-info":[{"award-number":["Nos. 11975132"]}]},{"name":"Natural Science Foundation of Shandong Province, China","award":["Nos. 12005110"],"award-info":[{"award-number":["Nos. 12005110"]}]},{"name":"Joint Fund of Natural Science Foundation of Shandong Province","award":["Nos. ZR2021MF049"],"award-info":[{"award-number":["Nos. ZR2021MF049"]}]},{"name":"Joint Fund of Natural Science Foundation of Shandong Province","award":["Nos. ZR2022JQ04"],"award-info":[{"award-number":["Nos. ZR2022JQ04"]}]},{"name":"Joint Fund of Natural Science Foundation of Shandong Province","award":["Nos. ZR2022LLZ012"],"award-info":[{"award-number":["Nos. ZR2022LLZ012"]}]},{"name":"Joint Fund of Natural Science Foundation of Shandong Province","award":["Nos. ZR2021LLZ001"],"award-info":[{"award-number":["Nos. ZR2021LLZ001"]}]},{"name":"Joint Fund of Natural Science Foundation of Shandong Province","award":["Nos. 11975132"],"award-info":[{"award-number":["Nos. 11975132"]}]},{"name":"Joint Fund of Natural Science Foundation of Shandong Province","award":["Nos. 12005110"],"award-info":[{"award-number":["Nos. 12005110"]}]},{"name":"National Natural Science Foundation of China","award":["Nos. ZR2021MF049"],"award-info":[{"award-number":["Nos. ZR2021MF049"]}]},{"name":"National Natural Science Foundation of China","award":["Nos. ZR2022JQ04"],"award-info":[{"award-number":["Nos. ZR2022JQ04"]}]},{"name":"National Natural Science Foundation of China","award":["Nos. ZR2022LLZ012"],"award-info":[{"award-number":["Nos. ZR2022LLZ012"]}]},{"name":"National Natural Science Foundation of China","award":["Nos. ZR2021LLZ001"],"award-info":[{"award-number":["Nos. ZR2021LLZ001"]}]},{"name":"National Natural Science Foundation of China","award":["Nos. 11975132"],"award-info":[{"award-number":["Nos. 11975132"]}]},{"name":"National Natural Science Foundation of China","award":["Nos. 12005110"],"award-info":[{"award-number":["Nos. 12005110"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In order to increase the security and robustness of quantum images, this study combined the quantum DNA codec with quantum Hilbert scrambling to offer an enhanced quantum image encryption technique. Initially, to accomplish pixel-level diffusion and create enough key space for the picture, a quantum DNA codec was created to encode and decode the pixel color information of the quantum image using its special biological properties. Second, we used quantum Hilbert scrambling to muddle the image position data in order to double the encryption effect. In order to enhance the encryption effect, the altered picture was then employed as a key matrix in a quantum XOR operation with the original image. The inverse transformation of the encryption procedure may be used to decrypt the picture since all the quantum operations employed in this research are reversible. The two-dimensional optical image encryption technique presented in this study may significantly strengthen the anti-attack of quantum picture, according to experimental simulation and result analysis. The correlation chart demonstrates that the average information entropy of the RGB three channels is more than 7.999, the average NPCR and UACI are respectively 99.61% and 33.42%, and the peak value of the ciphertext picture histogram is uniform. It offers more security and robustness than earlier algorithms and can withstand statistical analysis and differential assaults.<\/jats:p>","DOI":"10.3390\/e25060865","type":"journal-article","created":{"date-parts":[[2023,5,29]],"date-time":"2023-05-29T07:54:16Z","timestamp":1685346856000},"page":"865","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Quantum Image Encryption Based on Quantum DNA Codec and Pixel-Level Scrambling"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-0668-822X","authenticated-orcid":false,"given":"Jie","family":"Gao","sequence":"first","affiliation":[{"name":"School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yinuo","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5616-2277","authenticated-orcid":false,"given":"Zhaoyang","family":"Song","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1899-5945","authenticated-orcid":false,"given":"Shumei","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1007\/s11831-021-09599-2","article-title":"Review of Quantum Image Processing","volume":"29","author":"Wang","year":"2022","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1119\/1.1463744","article-title":"Quantum computation and quantum information","volume":"70","author":"Nielsen","year":"2002","journal-title":"Am. J. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2981","DOI":"10.1103\/PhysRevLett.68.2981","article-title":"Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories","volume":"68","author":"Hardy","year":"1992","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1665","DOI":"10.1103\/PhysRevLett.71.1665","article-title":"Nonlocality for two particles without inequalities for almost all entangled states","volume":"71","author":"Hardy","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","unstructured":"Shor, P.W. (1994, January 20\u201322). Algorithms for quantum computatio: Discrete logarithms and factoring. Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, USA."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Grover, L.K. (1996, January 22\u201324). A fast quantum mechanical algorithm for database search. Proceedings of the Twenty Eighth Annual ACM Symposium on Theory of Computing, Philadelphia, PA, USA.","DOI":"10.1145\/237814.237866"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"032311","DOI":"10.1103\/PhysRevA.63.032311","article-title":"Asymptotically good quantum codes","volume":"63","author":"Ashikhmin","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3065","DOI":"10.1109\/18.959288","article-title":"Nonbinary quantum stabilizer codes","volume":"47","author":"Ashikhmin","year":"2001","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"067901","DOI":"10.1103\/PhysRevLett.87.067901","article-title":"Probabilistic quantum memories","volume":"87","author":"Trugenberger","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"277903","DOI":"10.1103\/PhysRevLett.89.277903","article-title":"Phase transitions in quantum pattern recognition","volume":"89","author":"Trugenberger","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","first-page":"137","article-title":"Storing, processing, and retrieving an image using quantum mechanics","volume":"5105","author":"Bose","year":"2003","journal-title":"Quantum Inf. Comput."},{"key":"ref_12","unstructured":"Klappenecker, A., and Rotteler, M. (2001, January 19\u201321). Discrete cosine transforms on quantum computers. Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis, Pula, Croatia."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Fijany, A., and Williams, C.P. (1999). Quantum Computing and Quantum Communications, Springer.","DOI":"10.1007\/978-1-4471-0839-9_16"},{"key":"ref_14","unstructured":"Beach, G., Lomont, C., and Cohen, C. (2003, January 15\u201317). Quantum image processing (quip). Proceedings of the 32nd Applied Imagery Pattern Recognition Workshop, Washington, DC, USA."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Caraiman, S., and Manta, V.I. (2009, January 18\u201320). New applications of quantum algorithms to computer graphic: The quantum random sample consensus algorithm. Proceedings of the 6th ACM Conference on Computing Frontiers, Ischia, Italy.","DOI":"10.1145\/1531743.1531757"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1693","DOI":"10.1007\/s11128-015-0932-1","article-title":"Image segmentation on a quantum computer","volume":"14","author":"Caraiman","year":"2015","journal-title":"Quantum Inf. Process."},{"key":"ref_17","unstructured":"Castleman, K.R. (1996). Digital Image Processing, Prentice Hall Press."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3745","DOI":"10.1007\/s10773-018-3887-z","article-title":"Quantum Image Encryption Algorithm Based on NASS","volume":"57","author":"Li","year":"2018","journal-title":"Int. J. Theor. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1950214","DOI":"10.1142\/S0217732319502146","article-title":"Quantum image encryption based on phase-shift transform and quantum Haar wavelet packet transform","volume":"34","author":"Li","year":"2019","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3477","DOI":"10.1007\/s11128-013-0612-y","article-title":"Novel image encryption\/decryption based on quantum Fourier transform and double phase encoding","volume":"12","author":"Yang","year":"2013","journal-title":"Quantum Inf. Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11128-015-1195-6","article-title":"A survey of quantum image representations","volume":"15","author":"Yan","year":"2016","journal-title":"Quantum Inf. Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s11128-010-0177-y","article-title":"A flexible representation of quantum images for polynomial preparation, image compression, and processing operations","volume":"10","author":"Le","year":"2011","journal-title":"Quantum Inf. Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2833","DOI":"10.1007\/s11128-013-0567-z","article-title":"NEQ: A novel enhanced quantum representation of digital images","volume":"12","author":"Zhang","year":"2013","journal-title":"Quantum Inf. Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"404","DOI":"10.20965\/jaciii.2013.p0404","article-title":"An RGB multi-channel representation for images on quantum computers","volume":"17","author":"Sun","year":"2013","journal-title":"J. Adv. Comput. Intell. Intell. Inform."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1007\/s11128-013-0705-7","article-title":"Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state","volume":"13","author":"Li","year":"2014","journal-title":"Quantum Inf. Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2269","DOI":"10.1007\/s11128-012-0521-5","article-title":"Image storage, retrieval, compression and segmentation in a quantum system","volume":"12","author":"Li","year":"2013","journal-title":"Quantum Inf. Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3103","DOI":"10.1007\/s11128-013-0587-8","article-title":"A novel quantum representation for log-polar images","volume":"12","author":"Zhang","year":"2013","journal-title":"Quantum Inf. Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2930","DOI":"10.1007\/s10773-021-04862-5","article-title":"Quantum Image Encryption Based on Quantum Image Decomposition","volume":"60","author":"Zhang","year":"2021","journal-title":"Int. J. Theor. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1007\/s11128-017-1612-0","article-title":"Quantum image encryption scheme with iterative generalized Arnold transforms and quantum image cycle shift operations","volume":"16","author":"Zhou","year":"2017","journal-title":"Quantum Inf. Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1126\/science.7973651","article-title":"Molecular computation of solutions to combinatorial problems","volume":"266","author":"Adleman","year":"1994","journal-title":"Science"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/S0303-2647(00)00083-6","article-title":"Cryptography with DNA binary strands","volume":"57","author":"Leier","year":"2000","journal-title":"Biosystems"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1109\/TNB.2005.850474","article-title":"Fast parallel molecular algorithms for DNA-based computatio. factoring integers","volume":"4","author":"Chang","year":"2005","journal-title":"IEEE Trans. Nanobiosci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.sysarc.2019.02.005","article-title":"Bio-inspired cryptosystem with DNA cryptography and neural networks","volume":"94","author":"Basu","year":"2019","journal-title":"J. Syst. Archit."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/j.matcom.2020.05.016","article-title":"An efficient image encryption scheme based on chaotic and Deoxyribonucleic acid sequencing","volume":"177","author":"Alghafis","year":"2020","journal-title":"Math. Comput. Simul."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"21579","DOI":"10.1007\/s11042-020-08880-z","article-title":"A Multidimensional Chaotic Image Encryption Algorithm based on DNA Coding","volume":"79","author":"Liu","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.optlaseng.2015.03.022","article-title":"A novel chaotic image encryption scheme using DNA sequence operations","volume":"73","author":"Wang","year":"2015","journal-title":"Opt. Lasers Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"7841","DOI":"10.1007\/s11042-018-6496-1","article-title":"Multiple-image encryption algorithm based on DNA encoding and chaotic system","volume":"78","author":"Zhang","year":"2019","journal-title":"Multimed. Tools Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"230302","DOI":"10.7498\/aps.70.20211255","article-title":"Color image encryption algorithm based on DNA code and alternating quantum random walk","volume":"I","author":"Wang","year":"2021","journal-title":"Acta Phys. Sin."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1007\/s11128-016-1463-0","article-title":"A novel quantum representation of color digital images","volume":"16","author":"Sang","year":"2017","journal-title":"Quantum Inf. Process."},{"key":"ref_40","unstructured":"Arnold, V.I., and Avez, A. (1968). Ergodic Problems of Classical Mechanics, Benjamin."},{"key":"ref_41","first-page":"119","article-title":"A new algorithm of Hilbert scanning matrix and its MATLAB program","volume":"11","author":"Wang","year":"2006","journal-title":"J. Image Graph."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2463","DOI":"10.1007\/s10773-014-2046-4","article-title":"Quantum Hilbert Image Scrambling","volume":"53","author":"Jiang","year":"2014","journal-title":"Int. J. Theor. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"3234","DOI":"10.1007\/s10773-016-2954-6","article-title":"Quantum Image Encryption Algorithm Based on Quantum Image XOR Operations","volume":"55","author":"Gong","year":"2016","journal-title":"Int. J. Theor. Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"23849","DOI":"10.1007\/s11042-020-09043-w","article-title":"Chaos based encryption of quantum images","volume":"79","author":"Vagish","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"169042","DOI":"10.1016\/j.ijleo.2022.169042","article-title":"An image encryption algorithm based on discrete fractional wavelet transform and quantum chaos","volume":"260","author":"Li","year":"2022","journal-title":"Optik"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/6\/865\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:44:10Z","timestamp":1760125450000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/6\/865"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,29]]},"references-count":45,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["e25060865"],"URL":"https:\/\/doi.org\/10.3390\/e25060865","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,29]]}}}