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However, the security issues of open channel transmission in IoT still persist. Researchers have proposed a lot of solutions, but the forward secrecy, session key security, and other aspects have not been effectively solved. This paper proposes a provably secure authenticated key agreement scheme, which constructs a secure channel between endpoint, gateway, and cloud server (CS). Compared with other schemes, this scheme has three characteristics: (1) According to the different computing resources of devices, gateways and CSs, a segmented differential authentication and secret key negotiation protocol is designed by using cryptographic primitives with different computing overheads; (2) after verification with the ProVerif tool, rigorous proof with the real\u2010or\u2010random (ROR) model, and informal analysis, the protocol has been proven to be secure, effectively guarding against typical threats; and (3) compared with the five most recent schemes, it can be seen that the protocol is at least 35% superior to other schemes in endpoint computational overhead, and it meets 10 security objectives, making it very suitable for application scenarios where endpoint resources are limited.<\/jats:p>","DOI":"10.1049\/ise2\/5277286","type":"journal-article","created":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T15:56:50Z","timestamp":1761753410000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Provably Secure Authentication Protocol Based on PUF and ECC for IoT Cloud\u2010Edge Environments"],"prefix":"10.1049","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1222-6950","authenticated-orcid":false,"given":"Xiong","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3310-926X","authenticated-orcid":false,"given":"Guosheng","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6527-2897","authenticated-orcid":false,"given":"Chenyu","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7504-3457","authenticated-orcid":false,"given":"Jinwen","family":"Xi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9582-0698","authenticated-orcid":false,"given":"Guoai","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"265","published-online":{"date-parts":[[2025,10,29]]},"reference":[{"key":"e_1_2_12_1_2","doi-asserted-by":"publisher","DOI":"10.23919\/JCC.2020.10.004"},{"key":"e_1_2_12_2_2","doi-asserted-by":"publisher","DOI":"10.1145\/3362031"},{"key":"e_1_2_12_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/SURV.2012.013012.00028"},{"key":"e_1_2_12_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/JIOT.2017.2780232"},{"key":"e_1_2_12_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11277-020-07527-4"},{"key":"e_1_2_12_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12652-018-1015-9"},{"key":"e_1_2_12_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.future.2019.05.058"},{"key":"e_1_2_12_8_2","first-page":"1095","article-title":"PrivHome: Privacy-Preserving Authenticated Communication in Smart Home Environment","volume":"18","author":"Poh G. 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