{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T04:22:01Z","timestamp":1780719721574,"version":"3.54.1"},"reference-count":77,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T00:00:00Z","timestamp":1694476800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002383","name":"King Saud University","doi-asserted-by":"publisher","award":["RSP2023R260"],"award-info":[{"award-number":["RSP2023R260"]}],"id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, a new physical layer authenticated encryption (PLAE) scheme based on the multi-parameter fractional Fourier transform\u2013Orthogonal frequency division multiplexing (MP-FrFT-OFDM) is suggested for secure image transmission over the IoT network. In addition, a new robust multi-cascaded chaotic modular fractional sine map (MCC-MF sine map) is designed and analyzed. Also, a new dynamic chaotic biometric signature (DCBS) generator based on combining the biometric signature and the proposed MCC-MF sine map random chaotic sequence output is also designed. The final output of the proposed DCBS generator is used as a dynamic secret key for the MPFrFT OFDM system in which the encryption process is applied in the frequency domain. The proposed DCBS secret key generator generates a very large key space of 22200. The proposed DCBS secret keys generator can achieve the confidentiality and authentication properties. Statistical analysis, differential analysis and a key sensitivity test are performed to estimate the security strengths of the proposed DCBS-MP-FrFT-OFDM cryptosystem over the IoT network. The experimental results show that the proposed DCBS-MP-FrFT-OFDM cryptosystem is robust against common signal processing attacks and provides a high security level for image encryption application.<\/jats:p>","DOI":"10.3390\/s23187843","type":"journal-article","created":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T21:41:12Z","timestamp":1694554872000},"page":"7843","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Physical Layer Authenticated Image Encryption for IoT Network Based on Biometric Chaotic Signature for MPFrFT OFDM System"],"prefix":"10.3390","volume":"23","author":[{"given":"Esam A. A.","family":"Hagras","sequence":"first","affiliation":[{"name":"Faculty of Engineering, Delta University for Science and Technology, Gamasa 35712, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Saad","family":"Aldosary","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Community College, King Saud University, Riyadh 11437, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5865-3686","authenticated-orcid":false,"given":"Haitham","family":"Khaled","sequence":"additional","affiliation":[{"name":"Department of Electronics and Communications, School of Engineering, Edith Cowan University, Perth, WA 6027, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tarek M.","family":"Hassan","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Delta University for Science and Technology, Gamasa 35712, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,12]]},"reference":[{"key":"ref_1","unstructured":"Gloukhovtsev, M. (2018). IOT Security: Challenges, Solutions & Future Prospects, Dell Inc.. Knowledge Sharing Article."},{"key":"ref_2","first-page":"65","article-title":"Security in the IoT: State-of-the-Art, Issues, Solutions, and Challenges","volume":"14","author":"Srhir","year":"2023","journal-title":"Int. J. Adv. Comput. Sci. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Hou, Y., Li, G., Dang, S., Hu, L., and Hu, A. (2022, January 26\u201329). Physical Layer Encryption Scheme Based on Dynamic Constellation Rotation. Proceedings of the 2022 IEEE 96th Vehicular Technology Conference (VTC2022-Fall), London, UK.","DOI":"10.1109\/VTC2022-Fall57202.2022.10012740"},{"key":"ref_4","first-page":"1","article-title":"PLS-IoT Enhancement against Eavesdropping via Spatially Distributed Constellation Obfuscation","volume":"25","author":"Salman","year":"2023","journal-title":"IEEE Wireless Commun. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ashraf, A.M., Elmedany, W.M., and Sharif, M.S. (2022, January 22\u201324). Secure IoT Data Transmission at Physical Layer using RC6 Encryption Technique. Proceedings of the 2022 9th International Conference on Future Internet of Things and Cloud (FiCloud), Online.","DOI":"10.1109\/FiCloud57274.2022.00051"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Liu, J., Ren, A., Sun, R., Du, X., and Guiza, M. (2019, January 9\u201313). A Novel Chaos-Based Physical Layer Security Transmission Scheme for Internet of Things. Proceedings of the 2019 IEEE Global Communications Conference (GLOBECOM), Waikoloa, HI, USA.","DOI":"10.1109\/GLOBECOM38437.2019.9013489"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Liu, J., Hu, Q., Sun, R., Du, X., and Guizani, M. (2020, January 7\u201311). A Physical Layer Security Scheme with Compressed Sensing in OFDM-based IoT Systems. Proceedings of the ICC 2020\u20142020 IEEE International Conference on Communications (ICC), Dublin, Ireland.","DOI":"10.1109\/ICC40277.2020.9149096"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Quan, M., Jin, Q., Ba, B., Zhang, J., and Jian, C. (2022). Constellation Encryption Design Based on Chaotic Sequence and the RSA Algorithm. Electronics, 11.","DOI":"10.3390\/electronics11203346"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Sun, L., and Du, Q. (2018). A Review of Physical Layer Security Techniques for Internet of Things: Challenges and Solutions. Entropy, 20.","DOI":"10.3390\/e20100730"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5345","DOI":"10.1007\/s11042-015-2936-3","article-title":"Security enhancement for video transmission via noise aggregation in immersive systems","volume":"75","author":"Hussain","year":"2016","journal-title":"Multimed. Tools Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"9681","DOI":"10.1109\/TVT.2018.2861836","article-title":"Unequal secrecy protection for untrusted two-way relaying systems: Constellation overlapping and noise aggregation","volume":"67","author":"Sun","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_12","unstructured":"Luby, M. (2002, January 16\u201319). LT codes. Proceedings of the 43rd IEEE Annual Symposium on Foundations of Computer Science, Vancouver, BC, Canada."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1528","DOI":"10.1109\/JSAC.2002.803996","article-title":"A digital fountain approach to asynchronous reliable multicast","volume":"20","author":"Byers","year":"2002","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1633","DOI":"10.1109\/TVT.2006.874547","article-title":"Adaptive low-complexity erasure-correcting code-based protocols for QoS-driven mobile multicast services over wireless networks","volume":"55","author":"Zhang","year":"2006","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2551","DOI":"10.1109\/TIT.2006.874390","article-title":"Rapter codes","volume":"52","author":"Shokrollahi","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1109\/90.720869","article-title":"Partity-based loss recovery for reliable multicast transmission","volume":"6","author":"Nonenmacher","year":"1998","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1062","DOI":"10.1049\/ip-com:20050237","article-title":"Fountain codes","volume":"152","author":"MacKay","year":"2005","journal-title":"IEE Proc. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1109\/LCOMM.2014.030914.140030","article-title":"Exploiting fountain codes for secure wireless delivery","volume":"18","author":"Niu","year":"2014","journal-title":"IEEE Commun. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1453","DOI":"10.1109\/18.681321","article-title":"Signal space diversity: A power- and bandwidth-efficient diversity technique for the Rayleigh fading channel","volume":"44","author":"Boutros","year":"1998","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2468","DOI":"10.1109\/TWC.2011.062111.110321","article-title":"Inter-relay interference in two-path digital relaying systems: Detrimental or beneficial?","volume":"10","author":"Sun","year":"2011","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5758","DOI":"10.1109\/TVT.2015.2455497","article-title":"Analysis on decode-and-forward two-path relay networks: When and how to cooperate","volume":"65","author":"Lu","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"8767","DOI":"10.1109\/TVT.2015.2505715","article-title":"Two birds with one stone: Towards secure and interference-free D2D transmissions via constellation rotation","volume":"65","author":"Sun","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"7947","DOI":"10.1109\/TVT.2017.2691314","article-title":"Spectrum sharing with device-to-device successive relaying and hybrid complex field network coding","volume":"66","author":"Ren","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2270","DOI":"10.1109\/LCOMM.2015.2479231","article-title":"Securing two-way cooperative systems with an untrusted relay: A constellation-rotation aided approach","volume":"19","author":"Xu","year":"2015","journal-title":"IEEE Commun. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Khan, M.A., Asim, M., Jeoti, V., and Manzoor, R.S. (2007, January 25\u201328). On secure OFDM system: Chaos based constellation scrambling. Proceedings of the 2007 International Conference on Intelligent and Advanced Systems (ICIAS), Kuala Lumpur, Malaysia.","DOI":"10.1109\/ICIAS.2007.4658435"},{"key":"ref_26","unstructured":"Tseng, D., and Chiu, J. (November, January 30). An OFDM speech scrambler without residual intelligibility. Proceedings of the IEEE Region 10 Conference (TENCON), Taipei, Taiwan."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1109\/LPT.2011.2149512","article-title":"Secure OFDM-PON based on chaos scrambling","volume":"23","author":"Zhang","year":"2011","journal-title":"IEEE Photon. Technol. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Li, H., Wang, X., and Hou, W. (2013, January 2\u20135). Secure transmission in OFDM systems by using time domain scrambling. Proceedings of the 77th IEEE Vehicular Technology Conference (VTC Spring), Dresden, Germany.","DOI":"10.1109\/VTCSpring.2013.6692745"},{"key":"ref_29","unstructured":"Dzung, D. (2010). Data Encryption on the Physical Layer of a Data Transmission System. (7752430B2), U.S. Patent."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1328","DOI":"10.1109\/TCE.2010.5606266","article-title":"Secure communication in TDS-OFDM system using constellation rotation and noise insertion","volume":"56","author":"Ma","year":"2010","journal-title":"IEEE Trans. Consum. Electron."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Reilly, D., and Kanter, G. (2009, January 18\u201322). Noise-enhanced encryption for physical layer security in an OFDM radio. Proceedings of the IEEE Radio and Wireless Symposium (RWS), San Diego, CA, USA.","DOI":"10.1109\/RWS.2009.4957350"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.adhoc.2018.03.004","article-title":"3GPP C-V2X and IEEE 802.11 p for vehicle-to-vehicle communications in highway platooning scenarios","volume":"74","author":"Vukadinovic","year":"2018","journal-title":"Ad Hoc Netw."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1504\/IJSNET.2018.090480","article-title":"System-level analysis of IEEE 802.11 ah technology for unsaturated MTC traffic","volume":"26","author":"Ometov","year":"2018","journal-title":"Int. J. Sens. Netw."},{"key":"ref_34","unstructured":"Park, M., Kenney, T., Perahia, E., Stacey, R., and Azizi, S. (2018). Method of Packet Classification for 802.11 ax. (9,882,687), U.S. Patent."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Wang, W., He, S., Yang, L., Zhang, Q., and Jiang, T. (2018). Wi-Fi teetertotter: Overclocking OFDM for internet of things. arXiv.","DOI":"10.1109\/INFOCOM.2018.8486233"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Mavromoustakis, C., Mastorakis, G., and Batalla, J. (2016). Internet of Things (IoT) in 5G Mobile Technologies, Springer.","DOI":"10.1007\/978-3-319-30913-2"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Al-Sarawi, S., Anbar, M., Alieyan, K., and Alzubaidi, M. (2017, January 17\u201318). Internet of things (IoT) communication protocols. Proceedings of the IEEE International Conference on Information Technology (ICIT), Amman, Jordan.","DOI":"10.1109\/ICITECH.2017.8079928"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1109\/LCOMM.2017.2651801","article-title":"Secure orthogonal transform division multiplexing (OTDM) waveform for 5G and beyond","volume":"21","author":"Hamamreh","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_39","unstructured":"Huo, F., and Gong, G. (May, January 27). A new efficient physical layer OFDM encryption scheme. Proceedings of the IEEE International Conference on Computer Communications (INFOCOM), Toronto, ON, Canada."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"e4369","DOI":"10.1002\/dac.4369","article-title":"Secure image transmission through crypto-OFDM system using Rubik\u2019s cube algorithm over an AWGN channel","volume":"33","author":"Dharavathu","year":"2020","journal-title":"Int. J. Commun. Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1109\/JLT.2012.2228630","article-title":"Theory and performance analyses in secure CO-OFDM transmission system based on two-dimensional permutation","volume":"31","author":"Zhang","year":"2013","journal-title":"J. Lightw. Technol."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Cheng, D., Gao, Z., Liu, F., and Liao, X. (2015, January 2\u20134). A general time-domain artificial noise design for OFDM AF relay systems. Proceedings of the IEEE\/CIC International Conference on Communications in China (ICCC), Shenzhen, China.","DOI":"10.1109\/ICCChina.2015.7448625"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Akitaya, T., and Saba, T. (2015, January 6\u201310). Energy efficient artificial fast fading for MISOOFDM systems. Proceedings of the IEEE Global Communications Conference (GLOBECOM), San Diego, CA, USA.","DOI":"10.1109\/GLOCOM.2015.7417411"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"3775","DOI":"10.1109\/TWC.2017.2688405","article-title":"Exploiting frame preamble waveforms to support new physical-layer functions in OFDM-based 802.11 systems","volume":"16","author":"Rahbari","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1109\/TIFS.2014.2384392","article-title":"Security-aware max-min resource allocation in multiuser OFDMA downlink","volume":"10","author":"Karachontzitis","year":"2015","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1109\/JIOT.2014.2297998","article-title":"Priwhisper: Enabling keyless secure acoustic communication for smartphones","volume":"1","author":"Zhang","year":"2014","journal-title":"IEEE Internet Things J."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.yofte.2014.08.014","article-title":"PAPR reduction based on chaos combined with SLM technique in optical OFDM IM\/DD system","volume":"21","author":"Xiao","year":"2015","journal-title":"Opt. Fiber Technol."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"42491","DOI":"10.1109\/ACCESS.2020.2974226","article-title":"Investigation of Chaotic Image Encryption in Spatial and FrFT Domains for Cybersecurity Applications","volume":"8","author":"Allah","year":"2020","journal-title":"IEEE Access"},{"key":"ref_49","unstructured":"Dasgupta, T., Paral, P., and Bhattacharya, S. (February, January 31). Color image encryption based on multiple fractional order chaotic systems. Proceedings of the International Conference on Control, Instrumentation, Energy and Communication (CIEC), Calcutta, India."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Ozaktas, H.M., Zalevsky, Z., and Kutay, M.A. (2000). The Fractional Fourier Transform with Applications in Optics and Signal Processing, Prentice Hall.","DOI":"10.23919\/ECC.2001.7076127"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1109\/LSP.2006.871721","article-title":"The multiple-parameter discrete fractional Fourier transform","volume":"13","author":"Pei","year":"2006","journal-title":"IEEE Signal Proc. Lett."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.optcom.2016.05.016","article-title":"Security of image encryption scheme based on multi-parameter fractional Fourier transform","volume":"376","author":"Zhao","year":"2016","journal-title":"Opt. Commun."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"3037","DOI":"10.1016\/j.optcom.2010.03.064","article-title":"Novel image encryption algorithm based on multiple-parameter discrete fractional random transform","volume":"283","author":"Zhou","year":"2010","journal-title":"Opt. Commun."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"734","DOI":"10.1109\/TIFS.2010.2068289","article-title":"Image encryption with multiorders of fractional Fourier transforms","volume":"5","author":"Tao","year":"2010","journal-title":"IEEE Trans. Inf. Forensic. Secur."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"2092","DOI":"10.1016\/j.optcom.2010.01.060","article-title":"Image encryption based on the multiple-parameter discrete fractional Fourier transform and chaos function","volume":"283","author":"Lang","year":"2010","journal-title":"Opt. Commun."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"74459","DOI":"10.1109\/ACCESS.2019.2921109","article-title":"MP-WFRFT and Chaotic Scrambling Aided Directional Modulation Technique for Physical Layer Security Enhancement","volume":"7","author":"Liu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_57","first-page":"100899","article-title":"A hybrid approach for latency and battery lifetime optimization in IoT devices through offloading and CNN learning","volume":"39","author":"Heidari","year":"2023","journal-title":"Sustain. Comput. Inform. Syst."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"107745","DOI":"10.1016\/j.cmpb.2023.107745","article-title":"The Applications of Machine Learning Techniques in Medical Data Processing based on Distributed Computing and the Internet of Things","volume":"241","author":"Aminizadeh","year":"2023","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Alhoraibi, L., Alghazzawi, D., Alhebshi, R., and Rabie, O.B.J. (2023). Physical Layer Authentication in Wireless Networks-Based Machine Learning Approaches. Sensors, 23.","DOI":"10.3390\/s23041814"},{"key":"ref_60","unstructured":"Hsue, W.L., and Pei, S.C. (2006, January 14\u201319). The Multiple-Parameter Discrete Fractional Fourier Transform and Its Application. Proceedings of the 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings, Toulouse, France."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"105777","DOI":"10.1016\/j.optlastec.2019.105777","article-title":"A novel chaos based optical image encryption using fractional Fourier transform and DNA sequence operation","volume":"121","author":"Farah","year":"2020","journal-title":"Opt. Laser Technol."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/j.compeleceng.2018.01.028","article-title":"A Novel Approach to Fingerprint Biometric-Based Cryptographic Key Generation and its Applications to Storage Security","volume":"69","author":"Panchal","year":"2018","journal-title":"Comput. Electr. Eng."},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"El-Mahallawy, M.S., Hagras, E.A., Eldin, A.Z., and Fakhr, M.W. (2011, January 7\u201310). Robust Blind and Secure Biometric Watermarking Based on Partial Multi-Map Chaotic Encryption. Proceedings of the 4th IFIP International Conference on New Technologies, Mobility and Security, Paris, France.","DOI":"10.1109\/NTMS.2011.5721049"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"8198","DOI":"10.1016\/j.eswa.2015.06.035","article-title":"A robust embedded biometric authentication system based on fingerprint and chaotic encryption","volume":"42","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Zebbiche, K., Ghouti, L., Khelifi, F., and Bouridane, A. (2006, January 15\u201318). Protecting Fingerprint Data Using Watermarking. Proceedings of the First NASA\/ESA Conference on Adaptive Hardware and Systems (AHS\u201906), Istanbul, Turkey.","DOI":"10.1109\/AHS.2006.61"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"2001","DOI":"10.1109\/TCYB.2014.2363168","article-title":"Cascade Chaotic System with Applications","volume":"45","author":"Zhou","year":"2015","journal-title":"IEEE Trans. Cybern."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"21445","DOI":"10.1007\/s11042-017-5594-9","article-title":"A New Simple One-Dimensional Chaotic Map and Its Application for Image Encryption","volume":"77","author":"Liu","year":"2018","journal-title":"Multimed. Tools Appl."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"713201","DOI":"10.1155\/2011\/713201","article-title":"Existence Results for Nonlinear Fractional Difference Equation","volume":"2011","author":"Chen","year":"2011","journal-title":"Adv. Differ. Equ."},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Moore, R.E., Kearfott, R.B., and Cloud, M.J. (2009). Introduction to Interval Analysis, Society for Industrial and Applied Mathematics 3600, University City Science Center.","DOI":"10.1137\/1.9780898717716"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1080\/21642583.2016.1163296","article-title":"A lower bound error for free run simulation of the polynomial NARMAX","volume":"4","author":"Nepomuceno","year":"2016","journal-title":"Syst. Sci. Control. Eng. Open Access J."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1080\/21642583.2017.1387874","article-title":"On the lower bound error for discrete maps using associative property","volume":"5","author":"Nepomuceno","year":"2017","journal-title":"Syst. Sci. Control. Eng. Open Access J."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1016\/j.physleta.2013.12.010","article-title":"Discrete chaos in fractional sine and standard maps","volume":"378","author":"Wu","year":"2014","journal-title":"Phys. Lett. A"},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E., Leigh, S., Levenson, M., Vangel, M., Banks, D., and Heckert, A. (2001). A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, National Institute of Standards and Technology. NIST Special Publication 800-22.","DOI":"10.6028\/NIST.SP.800-22"},{"key":"ref_74","doi-asserted-by":"crossref","unstructured":"Hagras, E.A.A., Aldosary, S., Khaled, H., and Hassan, T.M. (2023). Authenticated Public Key Elliptic Curve Based on Deep Convolutional Neural Network for Cybersecurity Image Encryption Application. Sensors, 23.","DOI":"10.3390\/s23146589"},{"key":"ref_75","first-page":"1535","article-title":"An effective multiple-image encryption algorithm based on 3D cube and hyperchaotic map","volume":"34","author":"Gao","year":"2022","journal-title":"J. King Saud. Univ. Comput. Inf. Sci."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s11071-021-07192-7","article-title":"A fast and efficient multiple images encryption based on single-channel encryption and chaotic system","volume":"108","author":"Gao","year":"2022","journal-title":"Nonlinear Dyn."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"5091","DOI":"10.1007\/s11042-022-12169-8","article-title":"An efficient image encryption technique based on two-level security for internet of things","volume":"82","author":"Gupta","year":"2022","journal-title":"Multimed. Tools Appl."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/18\/7843\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:49:45Z","timestamp":1760129385000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/18\/7843"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,12]]},"references-count":77,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["s23187843"],"URL":"https:\/\/doi.org\/10.3390\/s23187843","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,12]]}}}