{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T16:29:51Z","timestamp":1781713791199,"version":"3.54.5"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,7,13]],"date-time":"2025-07-13T00:00:00Z","timestamp":1752364800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,7,13]],"date-time":"2025-07-13T00:00:00Z","timestamp":1752364800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cybersecurity"],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Privacy-preserving deep learning based on secure multi-party computation (MPC) has emerged as a critical research focus in recent years. While existing approaches predominantly employ additive secret sharing with a fixed number of parties, they have yet to fully leverage the more efficient Shamir-based schemes. However, the adoption of Shamir secret sharing faces two key challenges: limitations of decimal computation and signed number representation. Furthermore, current solutions often lack optimization for specific computational modules and rely on conventional methods ill-suited for MPC environments. To address these issues, this paper proposes a fixed-point decimal-supported Shamir secret sharing scheme. A key innovation is our truncation algorithm, which effectively manages the expanded decimal digits resulting from multiplication operations, enabling comprehensive fixed-point arithmetic within the Shamir-based MPC framework. Extensive large-scale simulations validate the accuracy of our truncation method. Moreover, we introduce optimized protocols for two crucial deep learning operations: convolution and Softmax function computation. Our convolution protocol leverages the Winograd algorithm to significantly reduce multiplication gate count, yielding over 50% performance improvement. For Softmax computation, we extend existing two-party protocols to a multi-party Shamir setting, developing the nQSMax algorithm. This algorithm achieves exceptional accuracy exceeding 99% within seconds, requiring only a few iterations.<\/jats:p>","DOI":"10.1186\/s42400-024-00343-4","type":"journal-article","created":{"date-parts":[[2025,7,13]],"date-time":"2025-07-13T02:02:17Z","timestamp":1752372137000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Efficient and secure multi-party computation protocol supporting deep learning"],"prefix":"10.1186","volume":"8","author":[{"given":"Shancheng","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gang","family":"Qu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1358-4933","authenticated-orcid":false,"given":"Zongyang","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minzhe","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haochun","family":"Jin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liqun","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,7,13]]},"reference":[{"key":"343_CR1","unstructured":"Agarap AF (2018) Deep learning using rectified linear units (relu). 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