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Four approximation coefficients of the four images are extracted by performing the two-dimensional lifting wavelet transform. Then, the four approximation coefficients are synthesized to generate a real-valued output with the reality-preserving discrete fractional angular transform. Finally, based on the deoxyribonucleic acid operation and the Logistic-sine system, the real-valued intermedium output will be encrypted to yield the final ciphertext image. To enhance the security of the image encryption algorithm, the initial value of the chaotic system is calculated by the 256-bit binary sequence, which is obtained by taking the statistics information of the plaintext images as the input of SHA-256. Deoxyribonucleic acid sequence operations, as nonlinear processes, could help to improve the robustness of the cryptosystem. Simulation results and security analysis demonstrate the effectiveness of the image encryption algorithm and the capability of withstanding various common attacks.<\/jats:p>","DOI":"10.1155\/2021\/6650515","type":"journal-article","created":{"date-parts":[[2021,6,15]],"date-time":"2021-06-15T01:35:06Z","timestamp":1623720906000},"page":"1-18","source":"Crossref","is-referenced-by-count":5,"title":["Nonlinear Multi-Image Encryption Scheme with the Reality-Preserving Discrete Fractional Angular Transform and DNA Sequences"],"prefix":"10.1155","volume":"2021","author":[{"given":"Liang-Jia","family":"Tong","sequence":"first","affiliation":[{"name":"Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5080-2189","authenticated-orcid":true,"given":"Nan-Run","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi-Jing","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5870-6565","authenticated-orcid":true,"given":"Xin-Wen","family":"Xie","sequence":"additional","affiliation":[{"name":"Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China"},{"name":"School of Electronic Engineering, Jiujiang University, Jiujiang 332005, China"},{"name":"Xiexun Postdoctoral Practice Base, Xiexun Electronics Co., Ltd., Ji\u2019an 343100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ya-Ru","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Engineering, Jiangxi Agricultural University, Nanchang 330045, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2018.09.029"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1364\/aop.6.000120"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-015-2392-7"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.11.018"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2014.10.033"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1364\/ol.20.000767"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2011.11.004"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.optcom.2011.02.065"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.optcom.2011.02.066"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.optlaseng.2016.07.010"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/9721675"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.optcom.2012.08.051"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.3807\/josk.2014.18.2.129"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.optlaseng.2014.10.011"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1364\/oe.18.013772"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1364\/oe.23.018955"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1364\/oe.25.008690"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1364\/ol.35.000118"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1088\/2040-8978\/16\/2\/025402"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.optlaseng.2015.09.008"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1007\/s11042-016-4279-0"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2016.01.017"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/8402578"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.optlaseng.2018.08.020"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2019.107340"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2019.02.049"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2020.09.055"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1016\/j.optlaseng.2012.08.004"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1007\/s11042-017-4637-6"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1016\/j.optlaseng.2019.105816"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1016\/j.optlaseng.2011.08.006"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1016\/j.optlaseng.2015.12.016"},{"volume-title":"The Fractional Fourier Transform: with Applications in Optics and Signal Processing","year":"1995","author":"H. 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