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J. Found. Comput. Sci."],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p> The notion of [Formula: see text]-differential uniformity was proposed by Ellingsen et al., which generalizes the classical differential uniformity measuring the resistance against differential cryptanalysis. Since then, the research of functions with low [Formula: see text]-differential uniformity over finite fields attracted many researchers\u2019 attention. However, it seems that there is no study of function with low [Formula: see text]-differential uniformity over integer rings modulo [Formula: see text]. In this paper, we give an extension of the [Formula: see text]-differential uniformity concept to rings of integers module some [Formula: see text], and we present several perfect [Formula: see text]-nonlinear polynomial functions on the integer ring [Formula: see text] for the different integer [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0129054124500096","type":"journal-article","created":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T07:58:34Z","timestamp":1719475114000},"page":"97-110","source":"Crossref","is-referenced-by-count":0,"title":["Some Special Perfect c-Nonlinear Functions on \u2124n"],"prefix":"10.1142","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-9680-6085","authenticated-orcid":false,"given":"Yan-Ping","family":"Wang","sequence":"first","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, P. R. China"},{"name":"Key Laboratory of Cryptography and Data Analytics, Northwest Normal University, Lanzhou 730070, P. R. China"},{"name":"Gansu Provincial Research Center for Basic, Disciplines of Mathematics and Statistics, Lanzhou 730070, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5161-8650","authenticated-orcid":false,"given":"Wei-Guo","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an, 710071, P. R. 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