{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T09:26:41Z","timestamp":1777368401922,"version":"3.51.4"},"reference-count":17,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2015,1,8]],"date-time":"2015-01-08T00:00:00Z","timestamp":1420675200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["60973162"],"award-info":[{"award-number":["60973162"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012558","name":"Foundation of Science and Technology on Information Assurance Laboratory","doi-asserted-by":"publisher","award":["KJ-14-005"],"award-info":[{"award-number":["KJ-14-005"]}],"id":[{"id":"10.13039\/501100012558","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Cryptology Development Foundation of China","award":["MMJJ201301006"],"award-info":[{"award-number":["MMJJ201301006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper proposes a new four-dimensional hyperchaotic map based on the Rabinovich system to realize chaotic encryption in higher dimension and improve the security. The chaotic sequences generated by Runge-Kutta method are combined with the chaotic sequences generated by an exponential chaos map to generate key sequences. The key sequences are used for image encryption. The security test results indicate that the new hyperchaotic system has high security and complexity. The comparison between the new hyperchaotic system and the several low-dimensional chaotic systems shows that the proposed system performs more efficiently.<\/jats:p>","DOI":"10.3390\/e17010181","type":"journal-article","created":{"date-parts":[[2015,1,8]],"date-time":"2015-01-08T11:29:32Z","timestamp":1420716572000},"page":"181-196","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":54,"title":["An Image Encryption Scheme Based on Hyperchaotic Rabinovich and Exponential Chaos Maps"],"prefix":"10.3390","volume":"17","author":[{"given":"Xiaojun","family":"Tong","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Harbin Institute of Technology, Weihai, 264209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Harbin Institute of Technology, Weihai, 264209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Harbin Institute of Technology, Weihai, 264209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Harbin Institute of Technology, Weihai, 264209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhu","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information and Electrical Engineering, Harbin Institute of Technology, Weihai, 264209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,1,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1007\/s11071-013-1086-2","article-title":"A novel image encryption algorithm based on dynamic S-boxes constructed by chaos","volume":"75","author":"Wang","year":"2014","journal-title":"Nonlinear Dyn"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1016\/j.cpc.2012.11.017","article-title":"Pseudorandom sequence generator based on the Chen chaotic system","volume":"184","author":"Hu","year":"2013","journal-title":"Computer Phys. Commun"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/j.ins.2012.09.037","article-title":"Secure chaotic system with application to chaotic ciphers","volume":"221","author":"Wang","year":"2013","journal-title":"Inf. Sci"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1671","DOI":"10.1016\/S0960-0779(04)00431-X","article-title":"On a four-dimensional chaotic system","volume":"23","author":"Qi","year":"2005","journal-title":"Chaos Solitons Fractals"},{"key":"ref_5","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_6","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1088\/1674-1056\/20\/1\/010509","article-title":"A new four-dimensional hyperchaotic Lorenz system and its adaptive control","volume":"20","author":"Si","year":"2011","journal-title":"Chin. Phys. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.optcom.2011.08.079","article-title":"A novel image encryption scheme based on improved hyperchaotic sequences","volume":"285","author":"Zhu","year":"2012","journal-title":"Optics Commun"},{"key":"ref_8","first-page":"125","article-title":"A new four-dimensional hyperchaotic Chen system and its generalized synchronization","volume":"19","author":"Jia","year":"2010","journal-title":"Chin. Phys. B"},{"key":"ref_9","first-page":"9","article-title":"A new image encryption algorithm based on improved Rossler chaotic sequence","volume":"31","author":"Deng","year":"2011","journal-title":"J. Hangzhou Dianzi Uni"},{"key":"ref_10","first-page":"71","article-title":"A new hyperchaotic system and its circuit simulation by electronic workbench","volume":"22","author":"Shen","year":"2010","journal-title":"J. Chongqing Uni. Posts Telecommun"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2775","DOI":"10.1016\/j.cam.2010.11.029","article-title":"A new hyperchaotic system from the L\u00fc system and its control","volume":"235","author":"Pang","year":"2011","journal-title":"J. Comput. Appl. Math"},{"key":"ref_12","first-page":"74","article-title":"Dynamical analysis and anti-synchronization for a new four dimensional hyperchaotic system","volume":"16","author":"Huang","year":"2011","journal-title":"J. Circuits Syst"},{"key":"ref_13","first-page":"1","article-title":"Analysis of Properties of Qi Unified Hyperchaotic System and Its Realization","volume":"9","author":"Zhang","year":"2011","journal-title":"J. Nanjing Inst. Technol"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Jian, J.G., Deng, X.L., and Wang, J.F. (2009, January 26\u201329). Globally Exponentially Attractive Set and Synchronization of a Class of Chaotic Finance System. Wuhan, China. Lecture Notes in Computer Science; Volume 5551; Springer: Berlin\/Heidelberg, Germany, 2009; pp. 253\u2013261.","DOI":"10.1007\/978-3-642-01507-6_30"},{"key":"ref_15","first-page":"715","article-title":"Onset of stochasticity in decay confinement of parametric instability","volume":"47","author":"Pikovski","year":"1978","journal-title":"Soviet Phys. JEPT"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1216","DOI":"10.1088\/1009-1963\/15\/6\/015","article-title":"The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system","volume":"15","author":"Wang","year":"2006","journal-title":"Chin. Phys"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"16","DOI":"10.54254\/2755-2721\/38\/20230524","article-title":"A sequence based on the gray Exponential Chaotic Image Encryption Algorithm","volume":"38","author":"Li","year":"2002","journal-title":"Comput. Eng. Appl"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/1\/181\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:41:26Z","timestamp":1760215286000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/1\/181"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,8]]},"references-count":17,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1]]}},"alternative-id":["e17010181"],"URL":"https:\/\/doi.org\/10.3390\/e17010181","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1,8]]}}}