{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T19:37:38Z","timestamp":1771961858811,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T00:00:00Z","timestamp":1558051200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China,the Fundamental Research Funds for the Central Universities","award":["N171704004, 61402092, 61374178, 61603182"],"award-info":[{"award-number":["N171704004, 61402092, 61374178, 61603182"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, the properties of the classical confusion\u2013substitution structure and some recently proposed pseudorandom number generators using one-dimensional chaotic maps are investigated. To solve the low security problem of the original structure, a new bit-level cellular automata strategy is used to improve the sensitivity to the cryptosystem. We find that the new evolution effects among different generations of cells in cellular automata can significantly improve the diffusion effect. After this, a new one-dimensional chaotic map is proposed, which is constructed by coupling the logistic map and the Bernoulli map (LBM). The new map exhibits a much better random behavior and is more efficient than comparable ones. Due to the favorable properties of the new map and cellular automata algorithm, we propose a new image-encryption algorithm in which three-dimensional bit-level permutation with LBM is employed in the confusion phase. Simulations are carried out, and the results demonstrate the superior security and high efficiency of the proposed scheme.<\/jats:p>","DOI":"10.3390\/e21050504","type":"journal-article","created":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T11:06:46Z","timestamp":1558091206000},"page":"504","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["A Symmetric Image Encryption Algorithm Based on a Coupled Logistic\u2013Bernoulli Map and Cellular Automata Diffusion Strategy"],"prefix":"10.3390","volume":"21","author":[{"given":"Wei","family":"Zhang","sequence":"first","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110819, China"}]},{"given":"Zhiliang","family":"Zhu","sequence":"additional","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110819, China"}]},{"given":"Hai","family":"Yu","sequence":"additional","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110819, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6303","DOI":"10.1007\/s11042-015-2573-x","article-title":"Chaos-based image encryption scheme combining DNA coding and entropy","volume":"75","author":"Zhen","year":"2015","journal-title":"Multimed. Tools Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.ins.2014.08.005","article-title":"On the security of symmetric ciphers based on DNA coding","volume":"289","author":"Zhang","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_3","first-page":"1","article-title":"Efficient cryptosystem approaches: S-boxes and permutation\u2013substitution-based encryption","volume":"87","author":"Belazi","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_4","first-page":"1","article-title":"Image Encryption Based on Compressive Sensing and Scrambled Index for Secure Multimedia Transmission","volume":"12","author":"Li","year":"2016","journal-title":"Acm Trans. Multimed. Comput. Commun. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"11857","DOI":"10.1007\/s11042-018-6745-3","article-title":"Encryption of image data using compressive sensing and chaotic system","volume":"78","author":"Ponuma","year":"2019","journal-title":"Multimed. Tools Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2611","DOI":"10.1007\/s11042-017-4455-x","article-title":"An image encryption algorithm based on irregular wave representation","volume":"77","author":"Huang","year":"2018","journal-title":"Multimed. Tools Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.ins.2015.08.013","article-title":"2D Sudoku associated bijections for image scrambling","volume":"327","author":"Wu","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1663","DOI":"10.1140\/epjst\/e2014-02119-9","article-title":"Image encryption based on permutation-substitution using chaotic map and Latin Square Image Cipher","volume":"223","author":"Panduranga","year":"2014","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1142\/S021812749800098X","article-title":"Symmetric ciphers based on two-dimensional chaotic maps","volume":"8","author":"Fridrich","year":"1998","journal-title":"Int. J. Bifurcat. Chaos."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.sigpro.2013.10.034","article-title":"A new 1D chaotic system for image encryption","volume":"97","author":"Zhou","year":"2014","journal-title":"Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.ins.2014.11.018","article-title":"2D sine logistic modulation map for image encryption","volume":"297","author":"Hua","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.ins.2016.01.017","article-title":"Image encryption using 2D Logistic-adjusted-Sine map","volume":"339","author":"Hua","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3249","DOI":"10.1109\/TIT.2012.2235907","article-title":"Period distribution of the generalized discrete arnold cat map for N = 2e","volume":"59","author":"Chen","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1109\/TIT.2011.2171534","article-title":"Period distribution of generalized discrete arnold cat map for N = pe","volume":"58","author":"Chen","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/s11071-017-3874-6","article-title":"A novel scheme for image encryption using substitution box and chaotic system","volume":"91","author":"Ullah","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1016\/j.sigpro.2011.10.023","article-title":"A novel color image encryption algorithm based on chaos","volume":"92","author":"Wang","year":"2012","journal-title":"Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2066","DOI":"10.1016\/j.cnsns.2012.12.012","article-title":"An image encryption scheme using reverse 2-dimensional chaotic map and dependent diffusion reverse cat map","volume":"18","author":"Zhang","year":"2013","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2067","DOI":"10.1007\/s11071-015-2465-7","article-title":"Chaotic image encryption algorithm using wave-line permutation and block diffusion","volume":"83","author":"Ye","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1016\/j.ins.2010.11.009","article-title":"A chaos-based symmetric image encryption scheme using a bit-level permutation","volume":"181","author":"Zhu","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"584","DOI":"10.1016\/j.cnsns.2012.08.010","article-title":"A symmetric color image encryption algorithm using the intrinsic features of bit distributions","volume":"18","author":"Zhang","year":"2013","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2018.11.010","article-title":"A novel image cipher based on 3D bit matrix and latin cubes","volume":"478","author":"Xu","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.sigpro.2015.11.017","article-title":"Chaotic image encryption using pseudo-random masks and pixel mapping","volume":"125","author":"Li","year":"2016","journal-title":"Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.optcom.2013.11.003","article-title":"Combined use of BP neural network and computational integral imaging reconstruction for optical multiple-image security","volume":"315","author":"Li","year":"2014","journal-title":"Optics Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.ins.2016.02.041","article-title":"A novel lossless color image encryption scheme using 2D DWT and 6D hyperchaotic system","volume":"8","author":"Wu","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.sigpro.2015.06.008","article-title":"Image encryption based on three-dimensional bit matrix permutation","volume":"118","author":"Zhang","year":"2016","journal-title":"Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Driebe, D.J. (1999). The Bernoulli Map. Fully Chaotic Maps and Broken Time Symmetry, Springer Science & Business Media.","DOI":"10.1007\/978-94-017-1628-4"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1038\/311419a0","article-title":"Cellular automata as models of complexity","volume":"311","author":"Wolfram","year":"1984","journal-title":"Nature"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/0196-8858(86)90028-X","article-title":"Random sequence generation by cellular automata","volume":"7","author":"Wolfram","year":"1986","journal-title":"Adv. Appl. Math."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2343","DOI":"10.1016\/j.optcom.2012.01.029","article-title":"An image encryption scheme using lightweight bit level confusion and cascade cross circular diffusion","volume":"285","author":"Zhang","year":"2012","journal-title":"Optics Commun."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","article-title":"Communication theory of secrecy system","volume":"28","author":"Shannon","year":"1949","journal-title":"Bell Syst. Tech. J."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/5\/504\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:52:59Z","timestamp":1760187179000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/5\/504"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,17]]},"references-count":30,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2019,5]]}},"alternative-id":["e21050504"],"URL":"https:\/\/doi.org\/10.3390\/e21050504","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,17]]}}}