{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,6]],"date-time":"2026-07-06T15:20:16Z","timestamp":1783351216743,"version":"3.54.6"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T00:00:00Z","timestamp":1740614400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Development Foundation of Shanghai University of Finance and Economics Zhejiang College","award":["2024FZJJ08"],"award-info":[{"award-number":["2024FZJJ08"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>As an important branch of machine learning, federated learning still suffers from statistical heterogeneity. Therefore, personalized federated learning (PFL) is proposed to deal with this obstacle. However, the privacy of local and global gradients is still under threat in the scope of PFL. Additionally, the correctness of the aggregated result is unable to be identified. Therefore, we propose a secure and verifiable personalized federated learning protocol that could protect privacy using homomorphic encryption and verify the aggregated result using Lagrange interpolation and commitment. Furthermore, it could resist the collusion attacks performed by servers and clients who try to pass verification. Comprehensive theoretical analysis is provided to verify our protocol\u2019s security. Extensive experiments on MNIST, Fashion-MNIST and CIFAR-10 are carried out to demonstrate the effectiveness of our protocol. Our model achieved accuracies of 88.25% in CIFAR-10, 99.01% in MNIST and 96.29% in Fashion-MNIST. The results show that our protocol could improve security while maintaining the classification accuracy of the training model.<\/jats:p>","DOI":"10.3390\/sym17030361","type":"journal-article","created":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T05:13:58Z","timestamp":1740633238000},"page":"361","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Privacy-Preserving and Verifiable Personalized Federated Learning"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-0219-9887","authenticated-orcid":false,"given":"Dailin","family":"Xie","sequence":"first","affiliation":[{"name":"School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dan","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Economics and Information Management, Shanghai University of Finance and Economics Zhejiang College, Jinhua 321000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1145\/3575637.3575644","article-title":"Federated Graph Machine Learning: A Survey of Concepts, Techniques, and Applications","volume":"24","author":"Fu","year":"2022","journal-title":"SIGKDD Explor."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3775","DOI":"10.1109\/TII.2018.2808966","article-title":"Intelligent Impulsive Synchronization of Nonlinear Interconnected Neural Networks for Image Protection","volume":"14","author":"Hu","year":"2018","journal-title":"IEEE Trans. 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