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However, there are still many security problems in social vehicle networking environments. Once the vehicle is networked, the biggest problem is data security according to the three levels of data collection, intelligent analysis, and decision control of the Internet of vehicles. Recently, Wu et al. proposed a lightweight vehicle social network security authentication protocol based on fog nodes. They claimed that their security authentication protocol could resist various attacks. However, we found that their authentication protocols are vulnerable to internal attacks, smart card theft attacks, and lack perfect forward security. In this study, we propose a new protocol to overcome these limitations. Finally, security and performance analyses show that our protocol perfectly overcomes these limitations and exhibits excellent performance and efficiency. <\/jats:p>","DOI":"10.1177\/15501329221104332","type":"journal-article","created":{"date-parts":[[2022,6,24]],"date-time":"2022-06-24T06:37:40Z","timestamp":1656052660000},"page":"155013292211043","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":38,"title":["A provably secure and lightweight mutual authentication protocol in fog-enabled social Internet of vehicles"],"prefix":"10.1177","volume":"18","author":[{"given":"Zhen","family":"Li","sequence":"first","affiliation":[{"name":"College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao, China"}]},{"given":"Qingkai","family":"Miao","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao, China"}]},{"given":"Shehzad Ashraf","family":"Chaudhry","sequence":"additional","affiliation":[{"name":"Istanbul Gelisim University, Istanbul, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6502-472X","authenticated-orcid":false,"given":"Chien-Ming","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao, China"}]}],"member":"179","published-online":{"date-parts":[[2022,6,23]]},"reference":[{"key":"bibr1-15501329221104332","doi-asserted-by":"publisher","DOI":"10.1109\/CC.2014.6969789"},{"key":"bibr2-15501329221104332","first-page":"116","volume-title":"2015 international conference on identification, information, and knowledge in the Internet of Things (IIKI)","author":"Sun Y"},{"key":"bibr3-15501329221104332","doi-asserted-by":"publisher","DOI":"10.1109\/JIOT.2017.2690902"},{"key":"bibr4-15501329221104332","first-page":"1","volume-title":"2017 international 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