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However, We found that the Kang et al.\u2019s protocol still has a fatal vulnerability, that is, it is attacked by offline password guessing, and malicious users can easily obtain the master key of the control server. In this article, we extend their work to design a lightweight pseudonym identity based authentication and key agreement protocol using smart card. For illustrating the security of our protocol, we used the security protocol analysis tools of AVISPA and Scyther to prove that the protocol can defend against various existing attacks. We will further analyze the interaction between participants authentication path to ensure security protection from simulated attacks detailedly. In addition, based on the comparison of security functions and computing performance, our protocol is superior to the other two related protocols. As a result, the enhanced protocol will be efficient and secure in distributed cloud computing architecture for smart city.<\/jats:p>","DOI":"10.1186\/s13638-021-02022-1","type":"journal-article","created":{"date-parts":[[2021,7,10]],"date-time":"2021-07-10T08:03:27Z","timestamp":1625904207000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["An efficient authentication and key agreement protocol for IoT-enabled devices in distributed cloud computing architecture"],"prefix":"10.1186","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2663-8240","authenticated-orcid":false,"given":"Huihui","family":"Huang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siqi","family":"Lu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zehui","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Wei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,7,10]]},"reference":[{"key":"2022_CR1","unstructured":"A.B. 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