{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T11:21:26Z","timestamp":1764588086046,"version":"3.37.3"},"reference-count":22,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,6,12]],"date-time":"2020-06-12T00:00:00Z","timestamp":1591920000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61672030"],"award-info":[{"award-number":["61672030"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Security and Communication Networks"],"published-print":{"date-parts":[[2020,6,12]]},"abstract":"<jats:p>We present a secure backpropagation neural network training model (SecureBP), which allows a neural network to be trained while retaining the confidentiality of the training data, based on the homomorphic encryption scheme. We make two contributions. The first one is to introduce a method to find a more accurate and numerically stable polynomial approximation of functions in a certain interval. The second one is to find a strategy of refreshing ciphertext during training, which keeps the order of magnitude of noise at <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mover accent=\"true\"><mml:mi>O<\/mml:mi><mml:mo>\u02dc<\/mml:mo><\/mml:mover><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:msup><mml:mrow><mml:mi>e<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>33<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mfenced><\/mml:math>.<\/jats:p>","DOI":"10.1155\/2020\/5328059","type":"journal-article","created":{"date-parts":[[2020,6,12]],"date-time":"2020-06-12T23:33:15Z","timestamp":1592004795000},"page":"1-9","source":"Crossref","is-referenced-by-count":2,"title":["SecureBP from Homomorphic Encryption"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2105-6295","authenticated-orcid":true,"given":"Qinju","family":"Liu","sequence":"first","affiliation":[{"name":"State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China"},{"name":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Xianhui","family":"Lu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China"},{"name":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Fucai","family":"Luo","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China"},{"name":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Shuai","family":"Zhou","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and Information Technology Engineering, University of Technology Sydney, Ultimo, NSW 2007, Australia"}]},{"given":"Jingnan","family":"He","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China"},{"name":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Kunpeng","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China"},{"name":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1038\/nature21056"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1001\/jama.2016.17216"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2009.2026902"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1186\/1687-417x-2007-037343"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-09699-5_3"},{"first-page":"169","volume-title":"On data banks and privacy homomorphisms","year":"1978","key":"8"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1145\/2633600"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1137\/120868669"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-32009-5_49"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-40041-4_5"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-46800-5_24"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-53887-6_1"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-70694-8_14"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-78381-9_14"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-70694-8_15"},{"year":"1998","key":"25"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-96878-0_17"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1186\/s12920-018-0401-7"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbi.2014.04.003"},{"key":"34","doi-asserted-by":"publisher","DOI":"10.1109\/tpds.2013.18"},{"key":"35","doi-asserted-by":"publisher","DOI":"10.1515\/jmc-2015-0016"},{"key":"36","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-10970-7_16"}],"container-title":["Security and Communication Networks"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2020\/5328059.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2020\/5328059.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2020\/5328059.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,12]],"date-time":"2020-06-12T23:33:16Z","timestamp":1592004796000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/scn\/2020\/5328059\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,12]]},"references-count":22,"alternative-id":["5328059","5328059"],"URL":"https:\/\/doi.org\/10.1155\/2020\/5328059","relation":{},"ISSN":["1939-0114","1939-0122"],"issn-type":[{"type":"print","value":"1939-0114"},{"type":"electronic","value":"1939-0122"}],"subject":[],"published":{"date-parts":[[2020,6,12]]}}}