{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:39:17Z","timestamp":1787027957521,"version":"build-2736575974"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T00:00:00Z","timestamp":1600387200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["814951-2"],"award-info":[{"award-number":["814951-2"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The evolution of modern automobiles to higher levels of connectivity and automatism has also increased the need to focus on the mitigation of potential cybersecurity risks. Researchers have proven in recent years that attacks on in-vehicle networks of automotive vehicles are possible and the research community has investigated various cybersecurity mitigation techniques and intrusion detection systems which can be adopted in the automotive sector. In comparison to conventional intrusion detection systems in large fixed networks and ICT infrastructures in general, in-vehicle systems have limited computing capabilities and other constraints related to data transfer and the management of cryptographic systems. In addition, it is important that attacks are detected in a short time-frame as cybersecurity attacks in vehicles can lead to safety hazards. This paper proposes an approach for intrusion detection of cybersecurity attacks in in-vehicle networks, which takes in consideration the constraints listed above. The approach is based on the application of an information entropy-based method based on a sliding window, which is quite efficient from time point of view, it does not require the implementation of complex cryptographic systems and it still provides a very high detection accuracy. Different entropy measures are used in the evaluation: Shannon Entropy, Renyi Entropy, Sample Entropy, Approximate Entropy, Permutation Entropy, Dispersion and Fuzzy Entropy. This paper evaluates the impact of the different hyperparameters present in the definition of entropy measures on a very large public data set of CAN-bus traffic with millions of CAN-bus messages with four different types of attacks: Denial of Service, Fuzzy Attack and two spoofing attacks related to RPM and Gear information. The sliding window approach in combination with entropy measures can detect attacks in a time-efficient way and with great accuracy for specific choices of the hyperparameters and entropy measures.<\/jats:p>","DOI":"10.3390\/e22091044","type":"journal-article","created":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T10:22:23Z","timestamp":1600424543000},"page":"1044","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["On the Application of Entropy Measures with Sliding Window for Intrusion Detection in Automotive In-Vehicle Networks"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4830-1227","authenticated-orcid":false,"given":"Gianmarco","family":"Baldini","sequence":"first","affiliation":[{"name":"European Commission, Joint Research Centre, 21027 Ispra, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,18]]},"reference":[{"key":"ref_1","unstructured":"Checkoway, S., McCoy, D., Kantor, B., Anderson, D., Shacham, H., Savage, S., Koscher, K., Czeskis, A., Roesner, F., and Kohno, T. (2011, January 8\u201312). Comprehensive experimental analyses of automotive attack surfaces. Proceedings of the USENIX Security Symposium, San Francisco, CA, USA."},{"key":"ref_2","first-page":"546","article-title":"Potential cyberattacks on automated vehicles","volume":"16","author":"Petit","year":"2014","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Marchetti, M., Stabili, D., Guido, A., and Colajanni, M. (2016, January 7\u20139). Evaluation of anomaly detection for in-vehicle networks through information-theoretic algorithms. Proceedings of the 2016 IEEE 2nd International Forum on Research and Technologies for Society and Industry Leveraging a better tomorrow (RTSI), Bologna, Italy.","DOI":"10.1109\/RTSI.2016.7740627"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"21266","DOI":"10.1109\/ACCESS.2019.2894183","article-title":"Intrusion detection systems for intra-vehicle networks: A review","volume":"7","author":"Maple","year":"2019","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.adhoc.2018.10.002","article-title":"A taxonomy and survey of cyber-physical intrusion detection approaches for vehicles","volume":"84","author":"Loukas","year":"2019","journal-title":"Ad Hoc Netw."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1109\/MDAT.2019.2899062","article-title":"Survey of automotive controller area network intrusion detection systems","volume":"36","author":"Young","year":"2019","journal-title":"IEEE Des. Test"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"127580","DOI":"10.1109\/ACCESS.2019.2937576","article-title":"An Intelligent Secured Framework for Cyberattack Detection in Electric Vehicles\u2019 CAN Bus Using Machine Learning","volume":"7","author":"Avatefipour","year":"2019","journal-title":"IEEE Access"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Kang, M.J., and Kang, J.W. (2016). Intrusion detection system using deep neural network for in-vehicle network security. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0155781"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"186","DOI":"10.3390\/e22020186","article-title":"A Multiple R\u00e9nyi Entropy Based Intrusion Detection System for Connected Vehicles","volume":"22","author":"Yu","year":"2020","journal-title":"Entropy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2114","DOI":"10.1109\/TIFS.2018.2812149","article-title":"VoltageIDS: Low-level communication characteristics for automotive intrusion detection system","volume":"13","author":"Choi","year":"2018","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1109\/TIFS.2018.2869351","article-title":"Efficient intrusion detection with bloom filtering in controller area networks","volume":"14","author":"Groza","year":"2018","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"M\u00fcter, M., and Asaj, N. (2011, January 5\u20139). Entropy-based anomaly detection for in-vehicle networks. Proceedings of the 2011 IEEE Intelligent Vehicles Symposium (IV), Baden, Germany.","DOI":"10.1109\/IVS.2011.5940552"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"45233","DOI":"10.1109\/ACCESS.2018.2865169","article-title":"Sliding window optimized information entropy analysis method for intrusion detection on in-vehicle networks","volume":"6","author":"Wu","year":"2018","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.88.174102","article-title":"Permutation entropy: A natural complexity measure for time series","volume":"88","author":"Bandt","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1230","DOI":"10.1016\/j.future.2018.07.027","article-title":"Detecting stealthy attacks on industrial control systems using a permutation entropy-based method","volume":"108","author":"Hu","year":"2018","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Zanin, M., G\u00f3mez-Andr\u00e9s, D., Pulido-Valdeolivas, I., Mart\u00edn-Gonzalo, J.A., L\u00f3pez-L\u00f3pez, J., Pascual-Pascual, S.I., and Rausell, E. (2018). Characterizing normal and pathological gait through permutation entropy. Entropy, 20.","DOI":"10.3390\/e20010077"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"669","DOI":"10.3390\/e17020669","article-title":"Application of entropy measures on intrinsic mode functions for the automated identification of focal electroencephalogram signals","volume":"17","author":"Sharma","year":"2015","journal-title":"Entropy"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"6573","DOI":"10.3390\/e16126573","article-title":"Automatic sleep stages classification using EEG entropy features and unsupervised pattern analysis techniques","volume":"16","author":"Peluffo","year":"2014","journal-title":"Entropy"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1109\/LSP.2016.2542881","article-title":"Dispersion entropy: A measure for time-series analysis","volume":"23","author":"Rostaghi","year":"2016","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Baldini, G., Giuliani, R., Steri, G., and Neisse, R. (2017, January 6\u20139). Physical layer authentication of Internet of Things wireless devices through permutation and dispersion entropy. Proceedings of the 2017 IEEE Global Internet of Things Summit (GIoTS), Geneva, Switzerland.","DOI":"10.1109\/GIOTS.2017.8016272"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.jsv.2018.08.025","article-title":"Application of dispersion entropy to status characterization of rotary machines","volume":"438","author":"Rostaghi","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"35042","DOI":"10.1109\/ACCESS.2018.2834540","article-title":"A novel fault diagnosis method based on integrating empirical wavelet transform and fuzzy entropy for motor bearing","volume":"6","author":"Deng","year":"2018","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1016\/j.procs.2016.05.203","article-title":"Feature selection using relative fuzzy entropy and ant colony optimization applied to real-time intrusion detection system","volume":"85","author":"Varma","year":"2016","journal-title":"Procedia Comput. Sci."},{"key":"ref_24","unstructured":"Lima, C.F.L., Assis, F.M., and de Souza, C.P. (2011, January 10\u201311). A comparative study of use of Shannon, R\u00e9nyi and Tsallis entropy for attribute selecting in network intrusion detection. Proceedings of the 2011 IEEE International Workshop on Measurements and Networking Proceedings (M&N), Anacapri, Italy."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2367","DOI":"10.3390\/e17042367","article-title":"An entropy-based network anomaly detection method","volume":"17","author":"Jasiul","year":"2015","journal-title":"Entropy"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Seo, E., Song, H.M., and Kim, H.K. (2018, January 28\u201330). GIDS: GAN based intrusion detection system for in-vehicle network. Proceedings of the 2018 IEEE 16th Annual Conference on Privacy, Security and Trust (PST), Belfast, UK.","DOI":"10.1109\/PST.2018.8514157"},{"key":"ref_27","first-page":"100198","article-title":"In-vehicle network intrusion detection using deep convolutional neural network","volume":"21","author":"Song","year":"2020","journal-title":"Veh. Commun."},{"key":"ref_28","unstructured":"Wenye, G. (2020, September 04). Shannon and Non-Extensive Entropy. MATLAB Central File Exchange. Available online: https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/18133-shannon-and-non-extensive-entropy."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2872","DOI":"10.1109\/TBME.2017.2679136","article-title":"Refined composite multiscale dispersion entropy and its application to biomedical signals","volume":"64","author":"Azami","year":"2017","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2297","DOI":"10.1073\/pnas.88.6.2297","article-title":"Approximate entropy as a measure of system complexity","volume":"88","author":"Pincus","year":"1991","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1016\/j.cels.2017.10.001","article-title":"hctsa: A computational framework for automated time-series phenotyping using massive feature extraction","volume":"5","author":"Fulcher","year":"2017","journal-title":"Cell Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"20130048","DOI":"10.1098\/rsif.2013.0048","article-title":"Highly comparative time-series analysis: The empirical structure of time series and their methods","volume":"10","author":"Fulcher","year":"2013","journal-title":"J. R. Soc. Interface"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"H2039","DOI":"10.1152\/ajpheart.2000.278.6.H2039","article-title":"Physiological time-series analysis using approximate entropy and sample entropy","volume":"278","author":"Richman","year":"2000","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2037","DOI":"10.1007\/s11517-017-1647-5","article-title":"Refined multiscale fuzzy entropy based on standard deviation for biomedical signal analysis","volume":"55","author":"Azami","year":"2017","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.medengphy.2008.04.005","article-title":"Measuring complexity using fuzzyen, apen, and sampen","volume":"31","author":"Chen","year":"2009","journal-title":"Med. Eng. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Delgado-Bonal, A., and Marshak, A. (2019). Approximate entropy and sample entropy: A comprehensive tutorial. Entropy, 21.","DOI":"10.3390\/e21060541"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/9\/1044\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:11:27Z","timestamp":1760177487000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/9\/1044"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,18]]},"references-count":36,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["e22091044"],"URL":"https:\/\/doi.org\/10.3390\/e22091044","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,18]]}}}