{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T18:16:36Z","timestamp":1761156996763,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,21]],"date-time":"2020-09-21T00:00:00Z","timestamp":1600646400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Japan Society of the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (B)","award":["16KT0017"],"award-info":[{"award-number":["16KT0017"]}]},{"name":"the Japan Society of the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (A)","award":["17H01280"],"award-info":[{"award-number":["17H01280"]}]},{"name":"the Japan Society of the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (C)","award":["16K00014","17K05591"],"award-info":[{"award-number":["16K00014","17K05591"]}]},{"name":"the Kayamori Foundation of Informational Science Advancement","award":["K27-XX-467"],"award-info":[{"award-number":["K27-XX-467"]}]},{"name":"the Okawa Research Grant","award":["15-02"],"award-info":[{"award-number":["15-02"]}]},{"name":"Guangdong Provincial Key Laboratory","award":["2019B121203002"],"award-info":[{"award-number":["2019B121203002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We discuss the effect of sequential error injection on information leakage under a network code. We formulate a network code for the single transmission setting and the multiple transmission setting. Under this formulation, we show that the eavesdropper cannot increase the power of eavesdropping by sequential error injection when the operations in the network are linear operations. We demonstrated the usefulness of this reduction theorem by applying a concrete example of network.<\/jats:p>","DOI":"10.3390\/e22091053","type":"journal-article","created":{"date-parts":[[2020,9,21]],"date-time":"2020-09-21T08:18:01Z","timestamp":1600676281000},"page":"1053","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Reduction Theorem for Secrecy over Linear Network Code for Active Attacks"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3104-1000","authenticated-orcid":false,"given":"Masahito","family":"Hayashi","sequence":"first","affiliation":[{"name":"Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China"},{"name":"Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China"},{"name":"Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China"},{"name":"Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8247-4768","authenticated-orcid":false,"given":"Masaki","family":"Owari","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Faculty of Informatics, Shizuoka University, Shizuoka 422-8529, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5030-5230","authenticated-orcid":false,"given":"Go","family":"Kato","sequence":"additional","affiliation":[{"name":"NTT Communication Science Laboratories, NTT Corporation, Tokyo 100-8116, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2281-5924","authenticated-orcid":false,"given":"Ning","family":"Cai","sequence":"additional","affiliation":[{"name":"The School of Information Science and Technology, ShanghaiTech University, Middle Huaxia Road no. 393, Pudong, Shanghai 201210, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,21]]},"reference":[{"key":"ref_1","unstructured":"Cai, N., and Yeung, R. 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