{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T08:40:48Z","timestamp":1766738448850,"version":"3.48.0"},"reference-count":51,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T00:00:00Z","timestamp":1766707200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002713","name":"Imam Mohammad ibn Saud Islamic University","doi-asserted-by":"publisher","award":["IMSIU-DDRSP2504"],"award-info":[{"award-number":["IMSIU-DDRSP2504"]}],"id":[{"id":"10.13039\/501100002713","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The rapid growth of Internet of Things (IoT) devices and the emergence of 5G\/6G networks have created major challenges in secure and reliable data transmission. Traditional cryptographic algorithms, while robust, often suffer from high computational complexity and latency, making them less suitable for large-scale, real-time applications. This paper proposes a chaos-based encryption framework that uses the Sprott chaotic oscillator to generate secure and unpredictable signals for encryption. To achieve accurate synchronization between the transmitter and the receiver, two bio-inspired metaheuristic algorithms\u2014the Pachycondyla Apicalis Algorithm (API) and the Penguin Search Optimization Algorithm (PeSOA)\u2014are employed to identify the optimal control parameters of the Sprott system. This optimization improves synchronization accuracy and reduces computational overhead. Simulation results show that PeSOA-based synchronization outperforms API in convergence speed and Root Mean Square Error (RMSE). The proposed framework provides robust, scalable, and low-latency encryption for IoT and 5G\/6G networks, where massive connectivity and real-time data protection are essential.<\/jats:p>","DOI":"10.3390\/e28010030","type":"journal-article","created":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T08:38:14Z","timestamp":1766738294000},"page":"30","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Secure Signal Encryption in IoT and 5G\/6G Networks via Bio-Inspired Optimization of Sprott Chaotic Oscillator Synchronization"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-8011-4172","authenticated-orcid":false,"given":"Fouzia","family":"Maamri","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Sciences and Technologies, Abbes Laghrour University, Khenchela 40000, Algeria"},{"name":"Laboratory of Systems and Applications of Information and Communication Technologies (SATIT), Faculty of Sciences and Technologies, Abbes Laghrour University, Khenchela 40000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanane","family":"Djellab","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Sciences and Technologies, Echahid Cheikh Larbi Tebessi University, Tebessa 12000, Algeria"},{"name":"Laboratory of Signals and Smart Systems (L3S), Faculty of Sciences and Technologies, Echahid Cheikh Larbi Tebessi University, Tebessa 12000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9395-4417","authenticated-orcid":false,"given":"Sofiane","family":"Bououden","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Sciences and Technologies, Abbes Laghrour University, Khenchela 40000, Algeria"},{"name":"Laboratory of Systems and Applications of Information and Communication Technologies (SATIT), Faculty of Sciences and Technologies, Abbes Laghrour University, Khenchela 40000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6186-2232","authenticated-orcid":false,"given":"Farouk","family":"Boumehrez","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Sciences and Technologies, Abbes Laghrour University, Khenchela 40000, Algeria"},{"name":"Laboratory of Telecommunications (LT), Telecommunications Institute, 8 May 1945 University, Guelma 24000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdelhakim","family":"Sahour","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Sciences and Technologies, Abbes Laghrour University, Khenchela 40000, Algeria"},{"name":"Laboratory of Systems and Applications of Information and Communication Technologies (SATIT), Faculty of Sciences and Technologies, Abbes Laghrour University, Khenchela 40000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2661-7108","authenticated-orcid":false,"given":"Mohamad A.","family":"Alawad","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Engineering, Imam Mohammad Ibn Saud Islamic University, Riyadh 11432, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ilyes","family":"Boulkaibet","sequence":"additional","affiliation":[{"name":"College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yazeed","family":"Alkhrijah","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Engineering, Imam Mohammad Ibn Saud Islamic University, Riyadh 11432, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"511","DOI":"10.6028\/jres.106.023","article-title":"Report on the Development of the Advanced Encryption Standard (AES)","volume":"106","author":"Nechvatal","year":"2001","journal-title":"J. Res. Natl. Inst. Stand. Technol."},{"key":"ref_2","unstructured":"Biham, E., and Shamir, A. (1990). Differential Cryptanalysis of DES-like Cryptosystems. Advances in Cryptology\u2014Proceedings of CRYPTO \u201990; Lecture Notes in Computer Science, Springer."},{"key":"ref_3","first-page":"51","article-title":"Optimizing Advanced Encryption Standard (AES) for Enhanced File Security in University Networks Using Dynamic Key Expansion","volume":"3","author":"Astillero","year":"2024","journal-title":"Technol. A Glob. J. Technol. Dev. Sci. Innov."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1557","DOI":"10.22214\/ijraset.2024.64392","article-title":"Analysis of Image Encryption Using Triple DES","volume":"12","author":"George","year":"2024","journal-title":"Int. J. Res. Appl. Sci. Eng. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"125","DOI":"10.37676\/jki.v2i2.294","article-title":"Implementation of the International Data Encryption Algorithm (IDEA) in Web-Based Database Security","volume":"2","author":"Giovani","year":"2023","journal-title":"J. Komput. Indones."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4999","DOI":"10.1109\/TNNLS.2019.2955165","article-title":"Neural Cryptography Based on Complex-Valued Neural Network","volume":"31","author":"Dong","year":"2020","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zolfaghari, B., Bibak, K., and Koshiba, T. (2022). The Odyssey of Entropy: Cryptography. Entropy, 24.","DOI":"10.3390\/e24020266"},{"key":"ref_8","first-page":"15","article-title":"Genetic Algorithm Using Feistel and Genetic Operator Acting at the Bit Level for Images Encryption","volume":"14","author":"Abdellah","year":"2024","journal-title":"Int. J. Saf. Secur. Eng."},{"key":"ref_9","first-page":"25","article-title":"Biometric Encryption: Integrating Artificial Intelligence for Robust Authentication","volume":"35","author":"Zahoor","year":"2023","journal-title":"J. Ballist."},{"key":"ref_10","unstructured":"Rajavel, D., and Periyasamy, S. (2016, January 1\u20133). Scrambling Algorithm for Encryption of Text Using Cube Rotation Artificial Intelligence Technique. Proceedings of the 2016 International Conference, Istanbul, Turkey."},{"key":"ref_11","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_12","first-page":"1","article-title":"An Effective Framework for Chaotic Image Encryption Based on 3D Logistic Map","volume":"2018","author":"Ye","year":"2018","journal-title":"Secur. Commun. Netw."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"27873","DOI":"10.1364\/OE.21.027873","article-title":"An Improved Permutation-Diffusion Type Image Cipher with a Chaotic Orbit Perturbing Mechanism","volume":"21","author":"Chen","year":"2013","journal-title":"Opt. Express"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1109\/MC.2018.2381131","article-title":"Deep Learning for the Internet of Things","volume":"51","author":"Yao","year":"2018","journal-title":"IEEE Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1103\/PhysRevLett.64.821","article-title":"Synchronization in Chaotic Systems","volume":"64","author":"Pecora","year":"1990","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"11453","DOI":"10.1109\/JSEN.2023.3265777","article-title":"Application of Chaotic Encryption and Decryption in Wireless Transmission from Sensory Toolholders on Machine Tools","volume":"23","author":"Lin","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"155080","DOI":"10.1016\/j.aeue.2023.155080","article-title":"Parametric Fractional-Order Analysis of Arneodo Chaotic System and Microcontroller-Based Secure Communication Implementation","volume":"175","author":"Gokyildirim","year":"2024","journal-title":"AEU-Int. J. Electron. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"14050","DOI":"10.1038\/s41598-025-97822-6","article-title":"A Lightweight Encryption Algorithm for Resource-Constrained IoT Devices Using Quantum and Chaotic Techniques with Metaheuristic Optimization","volume":"15","author":"Aljaedi","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"R647","DOI":"10.1103\/PhysRevE.50.R647","article-title":"Some Chaotic Flows","volume":"50","author":"Sprott","year":"1994","journal-title":"Phys. Rev. E"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Gularte, K.H.M., Alves, L.M., Vargas, J.A.R., Maranh\u00e3o, J.P.A., Carvalho, G.C., Alfaro, S.C.A., and Romero, J.F.A. (2019, January 16\u201318). A Chaotic Synchronization Scheme for Information Security. Proceedings of the 13th International Conference on Signal Processing and Communication Systems (ICSPCS), Gold Coast, Australia.","DOI":"10.1109\/ICSPCS47537.2019.9008760"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Djibrilla, A., Kountche, N., Monmarch\u00e9, N., and Slimane, M. (May, January 29). The Pachycondyla Apicalis Ants Search Strategy for Data Clustering Problems. Proceedings of the International Symposium SIDE 2012, Zakopane, Poland.","DOI":"10.1007\/978-3-642-29353-5_1"},{"key":"ref_22","first-page":"371","article-title":"PeSOA: Penguins Search Optimisation Algorithm for Global Optimisation Problems","volume":"16","author":"Gheraibia","year":"2019","journal-title":"Int. Arab J. Inf. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1387","DOI":"10.1016\/S0960-0779(99)00051-X","article-title":"Adaptive Chaotic Synchronization and Performance Analysis","volume":"11","author":"Liao","year":"2000","journal-title":"Chaos Solitons Fractals"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Kuo, H.-H., Yen, H.-H., and Lin, J.-C. (2015, January 2\u20135). Synchronization of Discrete Sprott Chaotic Systems and Its Application in Secure Communication. Proceedings of the 3rd IIAE International Conference on Intelligent Systems and Image Processing (ICISIP 2015), Fukuoka, Japan.","DOI":"10.12792\/icisip2015.045"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Zeng, J., Yan, W., and Ding, Q. (2024). RBFNN\u2013PSO Intelligent Synchronisation Method for Sprott B Chaotic Systems with External Noise and Its Application in an Image Encryption System. Entropy, 26.","DOI":"10.3390\/e26100855"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"7468","DOI":"10.3390\/s120607468","article-title":"Bluetooth-Based Chaos Synchronization Using Particle Swarm Optimization and Its Applications to Image Encryption","volume":"12","author":"Yau","year":"2012","journal-title":"Sensors"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"38671","DOI":"10.1109\/ACCESS.2025.3545441","article-title":"Deep Adaptive Chaos Synchronization Based on Optimization Algorithm","volume":"13","author":"Liu","year":"2025","journal-title":"IEEE Access"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Laouar, M.R., Balas, V.E., Lejdel, B., Eom, S., and Boudia, M.A. (2022, January 22\u201323). Using Chua\u2019s Chaotic Oscillator in Encryption Communication by ACO Identifications. Proceedings of the 12th International Conference on Information Systems and Advanced Technologies (ICISAT 2022), Istanbul, Turkey. Lecture Notes in Networks and Systems.","DOI":"10.1007\/978-3-031-25344-7"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"153424","DOI":"10.1016\/j.aeue.2020.153424","article-title":"Secure Communication Based on Chaos Synchronization Using Brain Emotional Learning","volume":"127","author":"Samimi","year":"2020","journal-title":"AEU-Int. J. Electron. Commun."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zourmba, K., Wamba, J., and Fortuna, L. (2025). Multi-Level Synchronization of Chaotic Systems for Highly-Secured Communication. Electronics, 14.","DOI":"10.3390\/electronics14132592"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Dinu, A. (2025). From Chaos to Security: A Comparative Study of Lorenz and R\u00f6ssler Systems in Cryptography. Cryptography, 9.","DOI":"10.3390\/cryptography9030058"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"656","DOI":"10.31127\/tuje.1471445","article-title":"Interpretable AI Analysis of Chaos Systems Distribution in Time Series Data from Industrial Robotics","volume":"8","year":"2024","journal-title":"Turk. J. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.ifacol.2024.10.146","article-title":"Chaotic Masking Protocol for Secure Communication and Attack Detection in Remote Estimation of Cyber-Physical Systems","volume":"58","author":"Chen","year":"2024","journal-title":"IFAC-PapersOnLine"},{"key":"ref_34","first-page":"52","article-title":"The Security Trade-Offs in Resource-Constrained Nodes for IoT Applications","volume":"12","author":"Alharby","year":"2018","journal-title":"Int. J. Electr. Comput. Energ. Electron. Commun. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1080\/17445760.2017.1401622","article-title":"The Pachycondyla Apicalis Metaheuristic Algorithm for Parameter Identification of Chaotic Electrical Systems","volume":"33","author":"Maamri","year":"2018","journal-title":"Int. J. Parallel Emerg. Distrib. Syst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1080\/23335777.2021.1921038","article-title":"Identification of Chua\u2019s Chaotic Circuit Parameters Using Penguins Search Optimisation Algorithm","volume":"8","author":"Maamri","year":"2022","journal-title":"Cyber-Phys. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Maamri, F., Bououden, S., and Boulkaibet, I. (2015, January 21\u201323). An Ant Colony Optimization Approach for Parameter Identification of Piezoelectric Resonator Chaotic System. Proceedings of the 16th IEEE International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA), Monastir, Tunisia.","DOI":"10.1109\/STA.2015.7505182"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"18292","DOI":"10.1364\/OE.18.018292","article-title":"Synchronization of Random Bit Generators Based on Coupled Chaotic Lasers and Application to Cryptography","volume":"18","author":"Kanter","year":"2010","journal-title":"Opt. Express"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Gokyildirim, A. (2023). Circuit Realization of the Fractional-Order Sprott K Chaotic System with Standard Components. Fractal Fract., 7.","DOI":"10.3390\/fractalfract7060470"},{"key":"ref_40","first-page":"21","article-title":"Global Chaos Synchronization of Sprott-L and Sprott-M Systems by Active Control","volume":"2","author":"Vaidyanathan","year":"2012","journal-title":"Int. J. Control Theory Comput. Model."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1016\/S0167-739X(00)00047-9","article-title":"On How Pachycondyla Apicalis Ants Suggest a New Search Algorithm","volume":"16","author":"Venturini","year":"2000","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_42","first-page":"222","article-title":"Penguins Search Optimization Algorithm (PeSOA)","volume":"Volume 7906","author":"Gheraibia","year":"2013","journal-title":"Proceedings of the 26th International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems (IEA\/AIE 2013)"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"95995","DOI":"10.1038\/s41598-025-95995-8","article-title":"A Compressed Image Encryption Algorithm Leveraging Optimized 3D Chaotic Maps for Secure Image Communication","volume":"15","author":"Tiwari","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Lin, Z., and Pattanayak, A.K. (2024). A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC). Entropy, 26.","DOI":"10.20944\/preprints202410.2283.v1"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Iqbal, A., Khurshaid, T., Nauman, A., and Rhee, S.-B. (2025). Energy-Aware Ultra-Reliable Low-Latency Communication for Healthcare IoT in Beyond 5G and 6G Networks. Sensors, 25.","DOI":"10.3390\/s25113474"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"5094","DOI":"10.1109\/TVT.2022.3224614","article-title":"End-to-End V2X Latency Modeling and Analysis in 5G Networks","volume":"72","author":"Shimizu","year":"2023","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.icte.2023.11.008","article-title":"Bandwidth Allocation of URLLC for Real-Time Packet Traffic in B5G: A Deep-RL Framework","volume":"10","author":"Salh","year":"2024","journal-title":"ICT Express"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2266","DOI":"10.1016\/j.cnsns.2008.06.028","article-title":"Chaotic Synchronization with Experimental Application to Secure Communications","volume":"14","author":"Nana","year":"2009","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"125244","DOI":"10.1088\/1402-4896\/ad8e9a","article-title":"Comparative Analysis of Two Novel Chaotic Systems, and Validation of Hybrid Function Projective and Complete Synchronization Using Active-Adaptive Control","volume":"99","author":"Khattar","year":"2024","journal-title":"Phys. Scr."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1080\/00207721.2017.1410251","article-title":"Analysis, Synchronization and Circuit Design of a New Highly Nonlinear Chaotic System","volume":"49","author":"Mobayen","year":"2018","journal-title":"Int. J. Syst. Sci."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"154647","DOI":"10.1016\/j.aeue.2023.154647","article-title":"Nonlinear Model and Characteristic Analysis of High Frequency Oscillator","volume":"165","author":"Li","year":"2023","journal-title":"AEU-Int. J. Electron. Commun."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/1\/30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T08:39:30Z","timestamp":1766738370000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/1\/30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,26]]},"references-count":51,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["e28010030"],"URL":"https:\/\/doi.org\/10.3390\/e28010030","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,26]]}}}