{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T16:16:16Z","timestamp":1774455376295,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,15]],"date-time":"2025-03-15T00:00:00Z","timestamp":1741996800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62272199"],"award-info":[{"award-number":["62272199"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>Federated learning is a powerful tool for securing participants\u2019 private data due to its ability to make data \u201cavailable but not visible\u201d. In recent years, federated learning has been enhanced by the emergence of multi-weight aggregation protocols, which minimize the impact of erroneous parameters, and verifiable protocols, which prevent server misbehavior. However, it still faces significant security and performance challenges. Malicious participants may infer the private data of others or carry out poisoning attacks to compromise the model\u2019s correctness. Similarly, malicious servers may return incorrect aggregation results, undermining the model\u2019s convergence. Furthermore, substantial communication overhead caused by interactions between participants or between participants and servers hinders the development of federated learning. In response to this, this paper proposes GHEFL, a group-based, verifiable, federated learning method based on homomorphic encryption that aims to prevent servers from maliciously stealing participant privacy data or performing malicious aggregation. While ensuring the usability of the aggregated model, it strives to minimize the workload on the server as much as possible. Finally, we experimentally evaluate the performance of GHEFL.<\/jats:p>","DOI":"10.3390\/fi17030128","type":"journal-article","created":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T04:29:28Z","timestamp":1742185768000},"page":"128","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["GHEFL: Grouping Based on Homomorphic Encryption Validates Federated Learning"],"prefix":"10.3390","volume":"17","author":[{"given":"Yulin","family":"Kang","sequence":"first","affiliation":[{"name":"College of Cyber Security, Jinan University, Guangzhou 511436, China"}]},{"given":"Wuzheng","family":"Tan","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Jinan University, Guangzhou 511436, China"}]},{"given":"Linlin","family":"Fan","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Jinan University, Guangzhou 511436, China"}]},{"given":"Yinuo","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Jinan University, Guangzhou 511436, China"}]},{"given":"Xinbin","family":"Lai","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Jinan University, Guangzhou 511436, China"}]},{"given":"Jian","family":"Weng","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Jinan University, Guangzhou 511436, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4329","DOI":"10.1109\/TIFS.2023.3295949","article-title":"Privacy-preserving federated learning with malicious clients and honest-but-curious servers","volume":"18","author":"Le","year":"2023","journal-title":"IEEE Trans. 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