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In recent years, many schemes adopt mutual authentication and key agreement to ensure secure communication in SG. However, most existing methods have their own shortcomings in either security or efficiency which make them difficult to satisfy the security requirements of SG. In this paper, we propose a provable secure and lightweight authenticated key agreement scheme based on the Elliptic Curve Cryptosystem (ECC) for the cloud-edge-end collaboration SG communication network. The proposed scheme can guarantee the security of the communication and provide anonymity for both the edge server and the smart meters. The anonymity of the smart meters can be provided by a pseudonym mechanism. By rigorous security analysis, the proposed scheme can resist to the typical attacks including replay attacks and identity forgery attacks. The security properties are also evaluated by using the Canetti and Krawczyk (CK) adversary model. The performance simulation results denotes that the proposed scheme not only owns stronger security functions but also improves computation efficiency by 24.5% on average than other four schemes. By simulation results, the proposed scheme has been shown to hold high efficiency.<\/jats:p>","DOI":"10.1007\/s00607-023-01188-4","type":"journal-article","created":{"date-parts":[[2023,6,27]],"date-time":"2023-06-27T13:02:59Z","timestamp":1687870979000},"page":"2511-2537","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["A provable secure and lightweight ECC-based authenticated key agreement scheme for edge computing infrastructure in smart grid"],"prefix":"10.1007","volume":"105","author":[{"given":"Cong","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Huo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1438-7018","authenticated-orcid":false,"given":"Maode","family":"Ma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tong","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiying","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,6,27]]},"reference":[{"issue":"8","key":"1188_CR1","doi-asserted-by":"publisher","first-page":"3733","DOI":"10.1109\/TII.2018.2803782","volume":"14","author":"L Lingjuan","year":"2018","unstructured":"Lingjuan L, Karthik N et al (2018) PPEA: privacy preserving fog-enabled aggregation in smart grid. 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