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It proposes a novel neural cryptographic system supporting homomorphic addition on fixed-point encrypted data, and consisting of three networks, namely (1) an encryption network (Alice), (2) a homomorphic network (HO), and (3) a decryption network (Bob), along with an adversarial Eve network. Using the MNIST dataset, the proposed Neural Homomorphic Operation System (NHOS) is evaluated against a plaintext baseline and the CKKS scheme, a widely used public-key homomorphic encryption method. The results show that the proposed NHOS approach offers a satisfying performance, i.e., 88.10% accuracy, using quantized weights, highlighting its potential as a lightweight alternative to traditional homomorphic encryption in FL.<\/jats:p>","DOI":"10.1007\/s44163-025-00630-0","type":"journal-article","created":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T13:52:02Z","timestamp":1766411522000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Secure federated learning via neural cryptography with homomorphic operations"],"prefix":"10.1007","volume":"5","author":[{"given":"Espen","family":"Sele","sequence":"first","affiliation":[]},{"given":"Ferhat Ozgur","family":"Catak","sequence":"additional","affiliation":[]},{"given":"Jungwon","family":"Seo","sequence":"additional","affiliation":[]},{"given":"Murat","family":"Kuzlu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,12,22]]},"reference":[{"key":"630_CR1","unstructured":"McMahan HB, Moore E, Ramage D, Hampson S, y\u00a0Arcas BA. 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Available: https:\/\/proceedings.mlr.press\/v48\/gilad-bachrach16.html"},{"key":"630_CR10","unstructured":"W\u00f8ien M.\u00a0C. Asymmetric neural cryptography with homomorphic and probabilistic properties, Master\u2019s thesis, University of Stavanger, Stavanger, Norway, June 2024, faculty of Science and Technology."},{"issue":"5","key":"630_CR11","doi-asserted-by":"publisher","first-page":"1306","DOI":"10.3390\/s18051306","volume":"18","author":"M Coutinho","year":"2018","unstructured":"Coutinho M, De\u00a0Oliveira\u00a0Albuquerque R, Borges F, Garc\u00eda\u00a0Villalba LJ, Kim T-H. Learning perfectly secure cryptography to protect communications with adversarial neural cryptography,. Sensors. 2018;18(5):1306.","journal-title":"Sensors"},{"key":"630_CR12","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1016\/j.neucom.2020.08.041","volume":"415","author":"Z Li","year":"2020","unstructured":"Li Z, Yang X, Shen K, Zhu R, Jiang J. 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This article does not involve studies with human participants or animals.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for Publication"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}},{"value":"Not applicable. This article does not report the results of a clinical trial.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Clinical trial registration"}},{"value":"The authors have no Conflict of interest to declare. All co-authors have seen and agreed with the contents of the manuscript. We certify that the submission is original work and is not under review at any other publication.","order":6,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"392"}}