{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:23:24Z","timestamp":1772252604407,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,14]],"date-time":"2023-02-14T00:00:00Z","timestamp":1676332800000},"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":["ZR2021MF049"],"award-info":[{"award-number":["ZR2021MF049"]}]},{"name":"Natural Science Foundation of Shandong Province, China","award":["ZR2022JQ04"],"award-info":[{"award-number":["ZR2022JQ04"]}]},{"name":"Natural Science Foundation of Shandong Province, China","award":["ZR2022LLZ012"],"award-info":[{"award-number":["ZR2022LLZ012"]}]},{"name":"Natural Science Foundation of Shandong Province, China","award":["ZR2021LLZ001"],"award-info":[{"award-number":["ZR2021LLZ001"]}]},{"name":"Natural Science Foundation of Shandong Province, China","award":["11975132"],"award-info":[{"award-number":["11975132"]}]},{"name":"Natural Science Foundation of Shandong Province, China","award":["12005110"],"award-info":[{"award-number":["12005110"]}]},{"name":"Joint Fund of the Natural Science Foundation of Shandong Province","award":["ZR2021MF049"],"award-info":[{"award-number":["ZR2021MF049"]}]},{"name":"Joint Fund of the Natural Science Foundation of Shandong Province","award":["ZR2022JQ04"],"award-info":[{"award-number":["ZR2022JQ04"]}]},{"name":"Joint Fund of the Natural Science Foundation of Shandong Province","award":["ZR2022LLZ012"],"award-info":[{"award-number":["ZR2022LLZ012"]}]},{"name":"Joint Fund of the Natural Science Foundation of Shandong Province","award":["ZR2021LLZ001"],"award-info":[{"award-number":["ZR2021LLZ001"]}]},{"name":"Joint Fund of the Natural Science Foundation of Shandong Province","award":["11975132"],"award-info":[{"award-number":["11975132"]}]},{"name":"Joint Fund of the Natural Science Foundation of Shandong Province","award":["12005110"],"award-info":[{"award-number":["12005110"]}]},{"name":"National Natural Science Foundation of China","award":["ZR2021MF049"],"award-info":[{"award-number":["ZR2021MF049"]}]},{"name":"National Natural Science Foundation of China","award":["ZR2022JQ04"],"award-info":[{"award-number":["ZR2022JQ04"]}]},{"name":"National Natural Science Foundation of China","award":["ZR2022LLZ012"],"award-info":[{"award-number":["ZR2022LLZ012"]}]},{"name":"National Natural Science Foundation of China","award":["ZR2021LLZ001"],"award-info":[{"award-number":["ZR2021LLZ001"]}]},{"name":"National Natural Science Foundation of China","award":["11975132"],"award-info":[{"award-number":["11975132"]}]},{"name":"National Natural Science Foundation of China","award":["12005110"],"award-info":[{"award-number":["12005110"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper proposes an encryption scheme for high pixel density images. Based on the application of the quantum random walk algorithm, the long short-term memory (LSTM) can effectively solve the problem of low efficiency of the quantum random walk algorithm in generating large-scale pseudorandom matrices, and further improve the statistical properties of the pseudorandom matrices required for encryption. The LSTM is then divided into columns and fed into the LSTM in order for training. Due to the randomness of the input matrix, the LSTM cannot be trained effectively, so the output matrix is predicted to be highly random. The LSTM prediction matrix of the same size as the key matrix is generated based on the pixel density of the image to be encrypted, which can effectively complete the encryption of the image. In the statistical performance test, the proposed encryption scheme achieves an average information entropy of 7.9992, an average number of pixels changed rate (NPCR) of 99.6231%, an average uniform average change intensity (UACI) of 33.6029%, and an average correlation of 0.0032. Finally, various noise simulation tests are also conducted to verify its robustness in real-world applications where common noise and attack interference are encountered.<\/jats:p>","DOI":"10.3390\/e25020353","type":"journal-article","created":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T02:31:23Z","timestamp":1676428283000},"page":"353","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Coupling Quantum Random Walks with Long- and Short-Term Memory for High Pixel Image Encryption Schemes"],"prefix":"10.3390","volume":"25","author":[{"given":"Junqing","family":"Liang","sequence":"first","affiliation":[{"name":"School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266033, China"}]},{"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 266033, China"}]},{"given":"Zhongwei","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266033, China"}]},{"given":"Mou","family":"Lv","sequence":"additional","affiliation":[{"name":"School of Environmental and Municipal Engineerin, Qingdao University of Technology, Qingdao 266033, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2680-5099","authenticated-orcid":false,"given":"Hongyang","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Science, Qingdao University of Technology, Qingdao 266033, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1147\/rd.383.0243","article-title":"The Data Encryption Standard (DES) and its strength against attacks","volume":"38","author":"Coppersmith","year":"1994","journal-title":"IBM J. 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