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Commun."],"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Various systematic modifications of vectorial Boolean functions have been used for finding new previously unknown classes of S-boxes with good or even optimal differential uniformity and nonlinearity. In this paper, a new general modification method is given that preserves the bijectivity property of the function in case the inverse of the function admits a linear structure. A previously known construction of such a modification based on bijective Gold functions in odd dimension is a special case of the new method.<\/jats:p>","DOI":"10.1007\/s12095-023-00631-9","type":"journal-article","created":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T19:25:13Z","timestamp":1675884313000},"page":"617-625","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Modifications of bijective S-Boxes with linear structures"],"prefix":"10.1007","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2885-6364","authenticated-orcid":false,"given":"Kaisa","family":"Nyberg","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,2,8]]},"reference":[{"issue":"6","key":"631_CR1","doi-asserted-by":"publisher","first-page":"1133","DOI":"10.1007\/s12095-020-00434-2","volume":"12","author":"C Beierle","year":"2020","unstructured":"Beierle, C., Leander, G.: 4-uniform permutations with null nonlinearity. 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