{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T21:03:15Z","timestamp":1785790995892,"version":"3.56.0"},"reference-count":51,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T00:00:00Z","timestamp":1617840000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2018YFB0704400"],"award-info":[{"award-number":["2018YFB0704400"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>Privacy protection has been an important concern with the great success of machine learning. In this paper, it proposes a multi-party privacy preserving machine learning framework, named PFMLP, based on partially homomorphic encryption and federated learning. The core idea is all learning parties just transmitting the encrypted gradients by homomorphic encryption. From experiments, the model trained by PFMLP has almost the same accuracy, and the deviation is less than 1%. Considering the computational overhead of homomorphic encryption, we use an improved Paillier algorithm which can speed up the training by 25\u201328%. Moreover, comparisons on encryption key length, the learning network structure, number of learning clients, etc. are also discussed in detail in the paper.<\/jats:p>","DOI":"10.3390\/fi13040094","type":"journal-article","created":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T11:58:45Z","timestamp":1617883125000},"page":"94","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":390,"title":["Privacy Preserving Machine Learning with Homomorphic Encryption and Federated Learning"],"prefix":"10.3390","volume":"13","author":[{"given":"Haokun","family":"Fang","sequence":"first","affiliation":[{"name":"School of Computer Engineering &amp; Science, Shanghai University, Shanghai 200444, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Quan","family":"Qian","sequence":"additional","affiliation":[{"name":"School of Computer Engineering &amp; Science, Shanghai University, Shanghai 200444, China"},{"name":"Materials Genome Institute, Shanghai University, Shanghai 200444, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bonawitz, K., Ivanov, V., Kreuter, B., Marcedone, A., McMahan, H.B., Patel, S., Ramage, D., Segal, A., and Seth, K. 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