{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,18]],"date-time":"2024-07-18T23:17:00Z","timestamp":1721344620389},"reference-count":29,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,5,27]],"date-time":"2021-05-27T00:00:00Z","timestamp":1622073600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["CB 2017\u20132018 A1-S-45697"],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005324","name":"Universidad Aut\u00f3noma de San Luis Potos\u00ed","doi-asserted-by":"publisher","award":["C20-FAI-10-48.48"],"id":[{"id":"10.13039\/501100005324","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"Despite that many image encryption systems based on chaotic or hyperchaotic systems have been proposed to protect different kinds of information, it has been crucial to achieve as much security as possible in such systems. In this sense, we numerically implement a known image encryption system with some variants, making special emphasis when two operations are considered in the scrambling stage. The variants of such an encryption system are based on some hyperchaotic systems, which generated some substitution boxes and the keys of the system. With the aim to have a more complete evaluation, some internal stages of the image encryption scheme have been evaluated by using common statistical tests, and also the scaling behavior of the encrypted images has been calculated by means of a two-dimensional detrended fluctuation analysis (2D-DFA). Our results show that the image encryption systems that include two operations or transformations in the scrambling stage present a better performance than those encryption systems that consider just one operation. In fact, the 2D-DFA approach was more sensitive than some common statistical tests to determine more clearly the impact of multiple operations in the scrambling process, confirming that this scaling method can be used as a perceptual security metric, and it may contribute to having better image encryption systems.<\/jats:p>","DOI":"10.3390\/e23060672","type":"journal-article","created":{"date-parts":[[2021,5,27]],"date-time":"2021-05-27T15:07:02Z","timestamp":1622128022000},"page":"672","source":"Crossref","is-referenced-by-count":4,"title":["Scaling Analysis of an Image Encryption Scheme Based on Chaotic Dynamical Systems"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-0541-1215","authenticated-orcid":false,"given":"L. E.","family":"Reyes-L\u00f3pez","sequence":"first","affiliation":[{"name":"Insituto de Investigaci\u00f3n en Comunicaci\u00f3n \u00d3ptica, Universidad Aut\u00f3noma de San Luis Potos\u00ed, \u00c1lvaro Obreg\u00f3n 64, 78000 San Luis Potos\u00ed, Mexico"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-7239-8968","authenticated-orcid":false,"given":"J. S.","family":"Murgu\u00eda","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias, Universidad Aut\u00f3noma de San Luis Potos\u00ed, Av. Chapultepec 1570, Priv. del Pedregal, 78295 San Luis Potos\u00ed, Mexico"},{"name":"Laboratorio Nacional CI3M, Facultad de Ciencias, Universidad Aut\u00f3noma de San Luis Potos\u00ed, Av. Chapultepec 1570, Priv. del Pedregal, 78295 San Luis Potos\u00ed, Mexico"}]},{"given":"H.","family":"Gonz\u00e1lez-Aguilar","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias, Universidad Aut\u00f3noma de San Luis Potos\u00ed, Av. Chapultepec 1570, Priv. del Pedregal, 78295 San Luis Potos\u00ed, Mexico"},{"name":"Laboratorio Nacional CI3M, Facultad de Ciencias, Universidad Aut\u00f3noma de San Luis Potos\u00ed, Av. Chapultepec 1570, Priv. del Pedregal, 78295 San Luis Potos\u00ed, Mexico"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-7457-7318","authenticated-orcid":false,"given":"M. T.","family":"Ram\u00edrez-Torres","sequence":"additional","affiliation":[{"name":"Coordinaci\u00f3n Acad\u00e9mica Regi\u00f3n Altiplano Oeste, Universidad Aut\u00f3noma de San Luis Potos\u00ed, Carretera Salinas-Santo Domingo 200 Salinas, 78600 San Luis Potos\u00ed, Mexico"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-2872-9461","authenticated-orcid":false,"given":"M.","family":"Mej\u00eda-Carlos","sequence":"additional","affiliation":[{"name":"Insituto de Investigaci\u00f3n en Comunicaci\u00f3n \u00d3ptica, Universidad Aut\u00f3noma de San Luis Potos\u00ed, \u00c1lvaro Obreg\u00f3n 64, 78000 San Luis Potos\u00ed, Mexico"}]},{"given":"J. O.","family":"Armijo-Correa","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias, Universidad Aut\u00f3noma de San Luis Potos\u00ed, Av. Chapultepec 1570, Priv. del Pedregal, 78295 San Luis Potos\u00ed, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.cnsns.2013.06.031","article-title":"An image encryption scheme based on rotation matrix bit-level permutation and block diffusion","volume":"19","author":"Zhang","year":"2014","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.ins.2019.10.070","article-title":"Design and implementation of a simple dynamical 4-D chaotic circuit with applications in image encryption","volume":"515","author":"Tsafack","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"105581","DOI":"10.1016\/j.optlastec.2019.105581","article-title":"An image encryption algorithm based on ZigZag transform and LL compound chaotic system","volume":"119","author":"Wang","year":"2019","journal-title":"Opt. Laser Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"52364","DOI":"10.1109\/ACCESS.2021.3069977","article-title":"A New Fractional Chaotic System and Its Application in Image Encryption with DNA Mutation","volume":"9","author":"Hao","year":"2021","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhang, D., Chen, L., and Li, T. (2021). Hyper-Chaotic Color Image Encryption Based on Transformed Zigzag Diffusion and RNA Operation. Entropy, 23.","DOI":"10.3390\/e23030361"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","article-title":"Communication theory of secrecy systems","volume":"28","author":"Shannon","year":"1949","journal-title":"Bell Syst. Tech. J."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ramasamy, P., Ranganathan, V., Kadry, S., Dama\u0161evi\u010dius, R., and Bla\u017eauskas, T. (2019). An image encryption scheme based on block scrambling, modified zigzag transformation and key generation using enhanced logistic\u2014Tent map. Entropy, 21.","DOI":"10.3390\/e21070656"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1007\/s11277-015-2667-9","article-title":"An experimental comparison of chaotic and non-chaotic image encryption schemes","volume":"84","author":"Ahmad","year":"2015","journal-title":"Wirel. Pers. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1450024","DOI":"10.1142\/S0217979214500246","article-title":"A New Color Image Encryption Based On High-Dimensional Chaotic Systems","volume":"28","author":"Li","year":"2014","journal-title":"Int. J. Mod. Phys. B"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Mansouri, A., and Wang, X. (2021). A novel block-based image encryption scheme using a new Sine powered chaotic map generator. Multimed. Tools Appl., 1\u201324.","DOI":"10.1007\/s11042-021-10757-8"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Li, Y., Li, X., Jin, X., Zhao, G., Ge, S., Tian, Y., and Wang, Z. (2015). An Image Encryption Algorithm Based on Zigzag Transformation and 3-Dimension Chaotic Logistic Map. Applications and Techniques in Information Security, Springer.","DOI":"10.1007\/978-3-662-48683-2_1"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"13951","DOI":"10.1007\/s11042-015-2973-y","article-title":"A secure image encryption scheme based on chaotic maps and affine transformation","volume":"75","author":"Ahmad","year":"2016","journal-title":"Multimed. Tools Appl."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Karawia, A.A. (2018). Encryption algorithm of multiple-image using mixed image elements and two dimensional chaotic economic map. Entropy, 20.","DOI":"10.3390\/e20100801"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2003","DOI":"10.1007\/s11071-018-4471-z","article-title":"Design of a strong S-box based on a matrix approach","volume":"94","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1550093","DOI":"10.1142\/S012918311550093X","article-title":"Two-dimensional DFA scaling analysis applied to encrypted images","volume":"26","author":"Rosu","year":"2015","journal-title":"Int. J. Mod. Phys. C"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"106165","DOI":"10.1016\/j.optlastec.2020.106165","article-title":"An improved visually meaningful encrypted image scheme","volume":"127","year":"2020","journal-title":"Opt. Laser Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3751","DOI":"10.1016\/j.physa.2008.02.020","article-title":"A hyperchaos generated from Lorenz system","volume":"387","author":"Wang","year":"2008","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/0375-9601(79)90150-6","article-title":"An equation for hyperchaos","volume":"71","author":"Rossler","year":"1979","journal-title":"Phys. Lett. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"030501","DOI":"10.1088\/1674-1056\/21\/3\/030501","article-title":"Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system","volume":"21","author":"Dong","year":"2012","journal-title":"Chin. Phys. B"},{"key":"ref_20","unstructured":"Kaplan, J.L., and Yorke, J.A. (1979). Functional Differential Equations and Approximations of Fixed Points, Springer. Lecture Notes in Mathematics."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1750094","DOI":"10.1142\/S0129183117500942","article-title":"Scaling analysis of hyperchaotic time series","volume":"28","year":"2017","journal-title":"Int. J. Mod. Phys. C"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"283","DOI":"10.31349\/RevMexFis.64.283","article-title":"Wavelet characterization of hyper-chaotic time series","volume":"64","author":"Rosu","year":"2018","journal-title":"Rev. Mex. F\u00eds."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.optlastec.2018.01.007","article-title":"Image compression-encryption algorithms by combining hyper-chaotic system with discrete fractional random transform","volume":"103","author":"Gong","year":"2018","journal-title":"Opt. Laser Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"061104","DOI":"10.1103\/PhysRevE.74.061104","article-title":"Detrended fluctuation analysis for fractals and multifractals in higher dimensions","volume":"74","author":"Gu","year":"2006","journal-title":"Phys. Rev. E"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Askar, S.S., Karawia, A.A., Al-Khedhairi, A., and Al-Ammar, F.S. (2019). An Algorithm of Image Encryption Using Logistic and Two-Dimensional Chaotic Economic Maps. Entropy, 21.","DOI":"10.3390\/e21010044"},{"key":"ref_26","first-page":"31","article-title":"NPCR and UACI randomness tests for image encryption","volume":"1","author":"Wu","year":"2011","journal-title":"Cyber J. Multidiscip. J. Sci. Technol. J. Sel. Areas Telecommun. (JSAT)"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"774","DOI":"10.4218\/etrij.10.1510.0063","article-title":"Efficient image chaotic encryption algorithm with no propagation error","volume":"32","author":"Awad","year":"2010","journal-title":"ETRI J."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.optlaseng.2015.12.004","article-title":"Multiple-image encryption with bit-plane decomposition and chaotic maps","volume":"80","author":"Tang","year":"2016","journal-title":"Opt. Lasers Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/j.compeleceng.2016.12.025","article-title":"Multiple-image encryption algorithm based on mixed image element and chaos","volume":"62","author":"Zhang","year":"2017","journal-title":"Comput. Electr. 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