{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T22:07:37Z","timestamp":1767650857812,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2022,10,12]],"date-time":"2022-10-12T00:00:00Z","timestamp":1665532800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"SMARTiLab\/EMSI"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Wireless Sensors Networks are integrating human daily life at a fast rate. Applications cover a wide range of fields, including home security, agriculture, climate change, fire prevention, and so on and so forth. If WSN were initially flat networks, hierarchical, or cluster-based networks have been introduced in order to achieve a better performance in terms of energy efficiency, topology management, delay minimization, load balancing, routing techniques, etc. As cluster-based algorithms proved to be efficient in terms of energy balancing, security has been of less importance in the field. Data shared by nodes in a WSN can be very sensitive depending on the field of application. Therefore, it is important to ensure security at various levels of WSN. This paper proposes a formal modeling of the energy consumed to secure communications in a cluster-based WSN in general. The concept is implemented using the Proof of Authentication (POAh) paradigm of blockchain and applied to a Multi-hop Clustering Algorithm based on spectral classification. The studied metrics are residual energy in the network, the number of alive nodes, first and last dead node.<\/jats:p>","DOI":"10.3390\/s22207730","type":"journal-article","created":{"date-parts":[[2022,10,12]],"date-time":"2022-10-12T05:31:18Z","timestamp":1665552678000},"page":"7730","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Formal Energy Consumption Analysis to Secure Cluster-Based WSN: A Case Study of Multi-Hop Clustering Algorithm Based on Spectral Classification Using Lightweight Blockchain"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4929-7362","authenticated-orcid":false,"given":"Yves Fr\u00e9d\u00e9ric","family":"Ebobiss\u00e9 Dj\u00e9n\u00e9","sequence":"first","affiliation":[{"name":"LRI, Faculty of Sciences, Ibn Tofail University, Kenitra 14000, Morocco"},{"name":"SMARTiLab\/EMSI, 49 Patrice Lumumba, Hassan, Rabat 10000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9892-0600","authenticated-orcid":false,"given":"Mohammed Sbai","family":"El Idrissi","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Faculty of Sciences, Sherbrooke University, 2500 Bd de l\u2019Universit\u00e9, Sherbrooke, QC J1K 2R1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7413-6897","authenticated-orcid":false,"given":"Pierre-Martin","family":"Tardif","sequence":"additional","affiliation":[{"name":"GRIC, Management School, Sherbrooke University, 2500 Bd de l\u2019Universit\u00e9, Sherbrooke, QC J1K 2R1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ali","family":"Jorio","sequence":"additional","affiliation":[{"name":"SMARTiLab\/EMSI, 49 Patrice Lumumba, Hassan, Rabat 10000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8119-3243","authenticated-orcid":false,"given":"Brahim","family":"El Bhiri","sequence":"additional","affiliation":[{"name":"SMARTiLab\/EMSI, 49 Patrice Lumumba, Hassan, Rabat 10000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5647-303X","authenticated-orcid":false,"given":"Youssef","family":"Fakhri","sequence":"additional","affiliation":[{"name":"LRI, Faculty of Sciences, Ibn Tofail University, Kenitra 14000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4979142","DOI":"10.1177\/155014774979142","article-title":"Clustering Analysis in Wireless Sensor Networks: The Ambit of Performance Metrics and Schemes Taxonomy","volume":"12","author":"Zeb","year":"2016","journal-title":"Int. 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