{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:31:02Z","timestamp":1764981062927,"version":"3.46.0"},"reference-count":14,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,11,21]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    The notion of confusion coefficient (CC) is a property that attempts to characterize the confusion property of cryptographic algorithms against differential power analysis. In this article, we establish a relationship between CC and the transparency order (TO) for any Boolean function and deduce some relationships between the sum-of-squares of CC, signal-to-noise ratio, and TO. We also give a tight upper bound and a tight lower bound on the sum-of-squares of CC for balanced s-plateaued functions. Finally, the results generalized a lower bound on the sum-of-squares of CC of Boolean functions with the Hamming weight\n                    <jats:italic>k<\/jats:italic>\n                    .\n                  <\/jats:p>","DOI":"10.1515\/jmc-2021-0039","type":"journal-article","created":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T08:50:02Z","timestamp":1700556602000},"source":"Crossref","is-referenced-by-count":0,"title":["Further research results on confusion coefficient of Boolean functions"],"prefix":"10.1515","volume":"17","author":[{"given":"Zhenyu","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematical Science, Huaibei Normal University , Huaibei , Anhui 235000 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zepeng","family":"Zhuo","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Huaibei Normal University , Huaibei , Anhui 235000 , China"},{"name":"School of Cyber Science, University of Science and Technology of China , Hefei 230027 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,11,21]]},"reference":[{"key":"2025120600280478762_j_jmc-2021-0039_ref_001","doi-asserted-by":"crossref","unstructured":"Kocher P, Jaffe J, Jun B. Differential power analysis. Advances in Cryptology-CRYPTOa99. LNCS 1666. Berlin: Springer; 1999. p. 388\u2013397.","DOI":"10.1007\/3-540-48405-1_25"},{"key":"2025120600280478762_j_jmc-2021-0039_ref_002","doi-asserted-by":"crossref","unstructured":"Guilley S, Hoogvorst P, Pacalet R. Differential power analysis model and some results. In Smart Card Research and Advanced Applications VI, IFIP 18th World Computer Congress, TC8\/WG8.8 and TC11\/WG11.2 Sixth International Conference on Smart Card Research and Advanced Applications(CARDIS), Toulouse, France, 2004. p. 127\u2013142.","DOI":"10.1007\/1-4020-8147-2_9"},{"key":"2025120600280478762_j_jmc-2021-0039_ref_003","doi-asserted-by":"crossref","unstructured":"Prouff E. DPA attacks and s-boxes. Fast Software Encryption-FSE 2005. LNCS 3557. 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