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We identify the least squares (LS) approach as the best suited for privately training. We then optimize fixed-point precision, ensuring accuracy while keeping low running time and communication. The technical details of the optimization involve bounds on the step size of a gradient method to solve a linear system, which might be of independent interest. We further propose and analyse different alternatives to improve the LS approach on an MPC implementation, and we compare their performance. The best improvement yields up to 2\u00d7 reduction of the running time and communication complexity, without affecting the accuracy of the trained model. In order to illustrate the feasibility of our solution, we securely train SVMs for two realistic tasks.<\/jats:p>","DOI":"10.1145\/3749373","type":"journal-article","created":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T11:13:48Z","timestamp":1753182828000},"page":"1-27","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Privacy-Preserving Training of Support Vector Machines via Secure Multiparty Computation"],"prefix":"10.1145","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7849-407X","authenticated-orcid":false,"given":"Daniel","family":"Cabarcas Jaramillo","sequence":"first","affiliation":[{"name":"Universidad Nacional de Colombia Sede Medell\u00edn","place":["Medell\u00edn, Colombia"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5662-9663","authenticated-orcid":false,"given":"Hernan Dario","family":"Vanegas Madrigal","sequence":"additional","affiliation":[{"name":"School of Mathematics, Universidad Nacional de Colombia Sede Medell\u00edn","place":["Medell\u00edn, Colombia"]},{"name":"HashCloak Inc.","place":["Medell\u00edn, Colombia"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2375-0034","authenticated-orcid":false,"given":"Daniel","family":"Escudero","sequence":"additional","affiliation":[{"name":"JPMorgan AI Research & JPMorgan AlgoCRYPT CoE","place":["New York, United States"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5691-1247","authenticated-orcid":false,"given":"Fernando Alberto","family":"Morales Jauregui","sequence":"additional","affiliation":[{"name":"School of Mathematics, Universidad Nacional de Colombia Sede Medell\u00edn","place":["Medell\u00edn, Colombia"]}]}],"member":"320","published-online":{"date-parts":[[2025,9,12]]},"reference":[{"issue":"1","key":"e_1_3_3_2_2","doi-asserted-by":"crossref","first-page":"167","DOI":"10.2478\/popets-2021-0010","article-title":"Secure training of decision trees with continuous attributes","volume":"2021","author":"Abspoel Mark","year":"2021","unstructured":"Mark Abspoel, Daniel Escudero, and Nikolaj Volgushev. 2021. 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