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Fog devices can perform data processing, which can significantly reduce the delay for the application. Moreover, data aggregation can be carried out by fog devices which decrease the bandwidth needed being very important for the wireless part of the communication with the cloud servers. The edge-fog-cloud architecture is currently being rolled out for several applications in the field of connected cars, health care monitoring, etc. In this paper, we propose an identity-based, mutual authenticated key agreement protocol for this fog architecture, in which end device and fog are able to establish a secure communication without leakage of their identities. Only the cloud server is able to control the identities of device and fog. We formally prove that the session keys are also protected in the Canetti\u2013Krawczyk security model, in which adversaries are considered to have access to session state specific information, previous session keys, or long-term private keys. The scheme is very efficient as it only utilises elliptic curve operations and basic symmetric key operations.<\/jats:p>","DOI":"10.1007\/s11276-019-02084-6","type":"journal-article","created":{"date-parts":[[2019,7,11]],"date-time":"2019-07-11T13:49:41Z","timestamp":1562852981000},"page":"1017-1029","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["Identity-based and anonymous key agreement protocol for fog computing resistant in the Canetti\u2013Krawczyk security model"],"prefix":"10.1007","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2178-1462","authenticated-orcid":false,"given":"Simone","family":"Patonico","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"An","family":"Braeken","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kris","family":"Steenhaut","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,7,11]]},"reference":[{"key":"2084_CR1","doi-asserted-by":"publisher","unstructured":"Hong, H. 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