{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T16:09:47Z","timestamp":1781626187683,"version":"3.54.5"},"reference-count":57,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,21]],"date-time":"2024-03-21T00:00:00Z","timestamp":1710979200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>In the past few decades, the transmission of data over an unsecure channel has resulted in an increased rate of hacking. The requirement to make multimedia data more secure is increasing day by day. Numerous algorithms have been developed to improve efficiency and robustness in the encryption process. In this article, a novel and secure image encryption algorithm is presented. It is based on a modified chaotic logistic map (CLM) that provides the advantage of taking less computational time to encrypt an input image. The encryption algorithm is based on Shannon\u2019s idea of using a substitution\u2013permutation and one-time pad network to achieve ideal secrecy. The CLM is used for substitution and permutation to improve randomness and increase dependency on the encryption key. Various statistical tests are conducted, such as keyspace analysis, complexity analysis, sensitivity analysis, strict avalanche criteria (SAC), histogram analysis, entropy analysis, mean of absolute deviation (MAD) analysis, correlation analysis, contrast analysis and homogeneity, to give a comparative analysis of the proposed algorithm and verify its security. As a result of various statistical tests, it is evident that the proposed algorithm is more efficient and robust as compared to previous ones.<\/jats:p>","DOI":"10.3390\/info15030172","type":"journal-article","created":{"date-parts":[[2024,3,21]],"date-time":"2024-03-21T06:35:30Z","timestamp":1711002930000},"page":"172","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Secure and Fast Image Encryption Algorithm Based on Modified Logistic Map"],"prefix":"10.3390","volume":"15","author":[{"given":"Mamoon","family":"Riaz","sequence":"first","affiliation":[{"name":"Department of Electronics, Quaid-i-Azam University, Islamabad 45320, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hammad","family":"Dilpazir","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, National University of Modern Languages, Islamabad 44000, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sundus","family":"Naseer","sequence":"additional","affiliation":[{"name":"Department of Electronics, Quaid-i-Azam University, Islamabad 45320, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hasan","family":"Mahmood","sequence":"additional","affiliation":[{"name":"Department of Electronics, Quaid-i-Azam University, Islamabad 45320, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Asim","family":"Anwar","sequence":"additional","affiliation":[{"name":"Department of Technology, The University of Lahore, Lahore 54000, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2393-3132","authenticated-orcid":false,"given":"Junaid","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Environmental & IT Engineering, Chungnam National University, Daejeon 34134, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0114-2217","authenticated-orcid":false,"given":"Ian B.","family":"Benitez","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, College of Engineering, FEU Institute of Technology, Manila 1015, Philippines"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0594-652X","authenticated-orcid":false,"given":"Tanveer","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Cyprus & CYENS Centre of Excellence, Nicosia 20537, Cyprus"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,21]]},"reference":[{"key":"ref_1","unstructured":"Su, Z., Zhang, G., and Jiang, J. (2012). Multimedia\u2014A Multidisciplinary Approach to Complex Issues, InTech."},{"key":"ref_2","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_3","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1007\/s10773-022-04979-1","article-title":"Quantum image encryption based on Baker map and 2D logistic map","volume":"61","author":"Wu","year":"2022","journal-title":"Int. J. Theor. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11128-020-02952-7","article-title":"Three-level quantum image encryption based on Arnold transform and logistic map","volume":"20","author":"Liu","year":"2021","journal-title":"Quantum Inf. Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1007\/s42514-020-00043-8","article-title":"Quantum image encryption algorithm based on generalized Arnold transform and Logistic map","volume":"2","author":"Hu","year":"2020","journal-title":"CCF Trans. High Perform. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"167904","DOI":"10.1109\/ACCESS.2019.2952140","article-title":"High intensity image encryption scheme based on quantum logistic chaotic map and complex hyperchaotic system","volume":"7","author":"Xu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2986","DOI":"10.1016\/j.sigpro.2013.03.031","article-title":"A new approach to chaotic image encryption based on quantum chaotic system, exploiting color spaces","volume":"93","author":"Li","year":"2013","journal-title":"Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"van Tilborg, H.C.A., and Jajodia, S. (2011). Encyclopedia of Cryptography and Security, Springer US.","DOI":"10.1007\/978-1-4419-5906-5"},{"key":"ref_9","first-page":"127","article-title":"Development and analysis of symmetric encryption algorithm Qamal based on a substitution-permutation network","volume":"67","author":"Biyashev","year":"2021","journal-title":"Int. J. Electron. Telecommun."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Ni, Z., Kang, X., and Wang, L. (2016, January 13\u201315). A novel image encryption algorithm based on bit-level improved Arnold transform and hyper chaotic map. Proceedings of the 2016 IEEE International Conference on Signal and Image Processing (ICSIP), Beijing, China.","DOI":"10.1109\/SIPROCESS.2016.7888243"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.optlaseng.2016.11.022","article-title":"Phase image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition","volume":"91","author":"Singh","year":"2017","journal-title":"Opt. Lasers Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2363","DOI":"10.1364\/OE.20.002363","article-title":"A chaos-based digital image encryption scheme with an improved diffusion strategy","volume":"20","author":"Fu","year":"2012","journal-title":"Opt. Express"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.physa.2014.01.051","article-title":"Spatiotemporal chaos in mixed linear\u2013nonlinear coupled logistic map lattice","volume":"402","author":"Zhang","year":"2014","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_14","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_15","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_16","doi-asserted-by":"crossref","first-page":"16511","DOI":"10.1007\/s11042-016-3925-x","article-title":"An image encryption algorithm based on Baker map with varying parameter","volume":"76","author":"Liu","year":"2017","journal-title":"Multimed. Tools Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.optlaseng.2016.03.019","article-title":"A fast image encryption algorithm based on chaotic map","volume":"84","author":"Liu","year":"2016","journal-title":"Opt. Lasers Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.optlaseng.2016.08.009","article-title":"A novel chaos-based image encryption algorithm using DNA sequence operations","volume":"88","author":"Chai","year":"2017","journal-title":"Opt. Lasers Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/s11071-015-2330-8","article-title":"A novel image encryption algorithm based on genetic recombination and hyper-chaotic systems","volume":"83","author":"Wang","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.optlaseng.2015.03.022","article-title":"A novel chaotic image encryption scheme using DNA sequence operations","volume":"73","author":"Wang","year":"2015","journal-title":"Opt. Lasers Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11128-017-1612-0","article-title":"Quantum image encryption scheme with iterative generalized Arnold transforms and quantum image cycle shift operations","volume":"16","author":"Zhou","year":"2017","journal-title":"Quantum Inf. Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1016\/j.optlaseng.2017.06.015","article-title":"Image encryption algorithm based on multiple mixed hash functions and cyclic shift","volume":"107","author":"Wang","year":"2018","journal-title":"Opt. Lasers Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11042-014-2221-x","article-title":"An efficient and noise resistive selective image encryption scheme for gray images based on chaotic maps and DNA complementary rules","volume":"75","author":"Kulsoom","year":"2016","journal-title":"Multimed. Tools Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.optlaseng.2015.07.015","article-title":"A novel hybrid color image encryption algorithm using two complex chaotic systems","volume":"77","author":"Wang","year":"2016","journal-title":"Opt. Lasers Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1417","DOI":"10.1007\/s11071-015-2579-y","article-title":"Image encryption scheme using chaos and simulated annealing algorithm","volume":"84","author":"Wang","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1595","DOI":"10.1007\/s11071-015-2590-3","article-title":"An effective and fast image encryption algorithm based on Chaos and interweaving of ranks","volume":"84","author":"Wang","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"23733","DOI":"10.1109\/ACCESS.2018.2805847","article-title":"An image encryption algorithm based on Josephus traversing and mixed chaotic map","volume":"6","author":"Wang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.ins.2019.02.049","article-title":"Fast image encryption algorithm based on parallel computing system","volume":"486","author":"Wang","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Jain, R., and Sharma, J. (2016, January 20\u201321). Symmetric color image encryption algorithm using fractional DRPM and chaotic baker map. Proceedings of the 2016 IEEE International Conference on Recent Trends in Electronics, Information & Communication Technology (RTEICT), Bangalore, India.","DOI":"10.1109\/RTEICT.2016.7808152"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.optcom.2014.12.043","article-title":"A color image encryption with heterogeneous bit-permutation and correlated chaos","volume":"342","author":"Wang","year":"2015","journal-title":"Opt. Commun."},{"key":"ref_31","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":"349","author":"Wu","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.optlaseng.2015.09.007","article-title":"A novel bit-level image encryption algorithm based on chaotic maps","volume":"78","author":"Xu","year":"2016","journal-title":"Opt. Lasers Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1016\/j.asoc.2012.01.016","article-title":"Image encryption using DNA complementary rule and chaotic maps","volume":"12","author":"Liu","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.optlaseng.2016.02.002","article-title":"An image encryption scheme based on the MLNCML system using DNA sequences","volume":"82","author":"Zhang","year":"2016","journal-title":"Opt. Lasers Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3106","DOI":"10.1016\/j.cnsns.2014.02.011","article-title":"Chaotic substitution for highly autocorrelated data in encryption algorithm","volume":"19","author":"Anees","year":"2014","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"12966","DOI":"10.1109\/ACCESS.2022.3146792","article-title":"A novel chaotic permutation-substitution image encryption scheme based on logistic map and random substitution","volume":"10","author":"Arif","year":"2022","journal-title":"IEEE Access"},{"key":"ref_37","first-page":"101595","article-title":"A novel chaos-based permutation for image encryption","volume":"35","author":"Alawida","year":"2023","journal-title":"J. King Saud Univ. Comput. Inf. Sci."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1007\/s40314-023-02208-x","article-title":"A novel encryption algorithm using multiple semifield S-boxes based on permutation of symmetric group","volume":"42","author":"Hussain","year":"2023","journal-title":"Comput. Appl. Math."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3402\/tellusa.v16i1.8893","article-title":"The problem of deducing the climate from the governing equations","volume":"16","author":"Lorenz","year":"1964","journal-title":"Tellus"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s11277-017-5039-9","article-title":"Novel secure pseudorandom number generator based on duffing map","volume":"99","author":"Riaz","year":"2018","journal-title":"Wirel. Pers. Commun."},{"key":"ref_41","first-page":"2347","article-title":"Analysis and review of encryption and decryption for secure communication","volume":"2","author":"Agrawal","year":"2014","journal-title":"Int. J. Sci. Eng. Res."},{"key":"ref_42","unstructured":"(2023, September 19). SIPI Image Database\u2014Sipi.usc.edu. Available online: http:\/\/sipi.usc.edu\/database\/database.php."},{"key":"ref_43","unstructured":"Mishra, M., and Mankar, V. (2012). Advances in Computer Science, Engineering & Applications, Springer."},{"key":"ref_44","first-page":"2145","article-title":"Symmetric Image Encryption Algorithm Using 3D Rossler System","volume":"14","author":"Kamat","year":"2014","journal-title":"Int. J. Comput. Sci. Bus. Inform."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.jare.2015.07.002","article-title":"Symmetric encryption algorithms using chaotic and non-chaotic generators: A review","volume":"7","author":"Radwan","year":"2016","journal-title":"J. Adv. Res."},{"key":"ref_46","unstructured":"Motara, Y.M., and Irwin, B. (2016, January 17\u201318). Sha-1 and the strict avalanche criterion. Proceedings of the 2016 Information security for South Africa (ISSA), Johannesburg, South Africa."},{"key":"ref_47","first-page":"25","article-title":"New analysis methods on strict avalanche criterion of S-boxes","volume":"48","author":"Mar","year":"2008","journal-title":"World Acad. Sci. Eng. Technol."},{"key":"ref_48","first-page":"2385","article-title":"Analyses of SKIPJACK S-box","volume":"13","author":"Hussain","year":"2011","journal-title":"World Appl. Sci. J."},{"key":"ref_49","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":"2016","journal-title":"Multimed. Tools Appl."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Wu, Y., Noonan, J.P., and Agaian, S. (2011, January 9\u201312). A novel information entropy based randomness test for image encryption. Proceedings of the 2011 IEEE International Conference on Systems, Man, and Cybernetics, Anchorage, AK, USA.","DOI":"10.1109\/ICSMC.2011.6084076"},{"key":"ref_51","first-page":"745","article-title":"A modified AES based algorithm for image encryption","volume":"1","author":"Zeghid","year":"2007","journal-title":"Int. J. Comput. Inf. Eng."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1002\/bimj.4710360403","article-title":"Robustness of the standard deviation and other measures of dispersion","volume":"36","author":"Schmid","year":"1994","journal-title":"Biom. J."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1774","DOI":"10.1016\/j.spl.2009.05.006","article-title":"Bahadur representations for the median absolute deviation and its modifications","volume":"79","author":"Mazumder","year":"2009","journal-title":"Stat. Probab. Lett."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"098201","DOI":"10.1117\/1.3223629","article-title":"Phase-only optical encryption based on the zeroth-order phase-contrast technique","volume":"48","author":"Pizolato","year":"2009","journal-title":"Opt. Eng."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Bibi, N., Farwa, S., Muhammad, N., Jahngir, A., and Usman, M. (2018). A novel encryption scheme for high-contrast image data in the Fresnelet domain. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0208305"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.sigpro.2018.03.010","article-title":"2D Logistic-Sine-coupling map for image encryption","volume":"149","author":"Hua","year":"2018","journal-title":"Signal Process."},{"key":"ref_57","unstructured":"Gao, S., Wu, R., Wang, X., Liu, J., Li, Q., Wang, C., and Tang, X. (2023). IEEE Transactions on Circuits and Systems for Video Technology, IEEE."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/15\/3\/172\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:17:17Z","timestamp":1760105837000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/15\/3\/172"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,21]]},"references-count":57,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["info15030172"],"URL":"https:\/\/doi.org\/10.3390\/info15030172","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,21]]}}}