{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T12:49:09Z","timestamp":1765370949694,"version":"3.46.0"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","funder":[{"name":"University Grants Commission (UGC), Government of India"},{"name":"Science and Engineering Research Board, Government of India","award":["CRG\/2022\/005418"],"award-info":[{"award-number":["CRG\/2022\/005418"]}]},{"name":"NPS Foundation"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:p>Finding functions, particularly permutations, with good differential properties has received a lot of attention due to their varied applications. For instance, in combinatorial design theory, a correspondence of perfect c-nonlinear functions and difference sets in some quasigroups was recently shown by Anbar et\u00a0al. (J.\u00a0Comb. Des.\u00a031(12):1\u201324, 2023). Additionally, in a recent manuscript by Pal et\u00a0al. (Adv. Math. Communications, to appear), a very interesting connection between the c-differential uniformity and boomerang uniformity, when [Formula: see text], was pointed out, showing that they are the same for an odd APN permutation, sparking yet more interest in the construction of functions with low c-differential uniformity. We investigate the c-differential uniformity of some classes of permutation polynomials. As a result, we add four more classes of permutation polynomials to the family of functions that only contains a few (non-trivial) perfect c-nonlinear functions over finite fields of even characteristic. Moreover, we include a class of permutation polynomials with low c-differential uniformity over the field of characteristic\u00a0[Formula: see text]. To solve the involved equations over finite fields, we use various number theoretical techniques, in particular, we find explicitly many Walsh transform coefficients and Weil sums that may be of an independent interest.<\/jats:p>","DOI":"10.1142\/s012905412550008x","type":"journal-article","created":{"date-parts":[[2025,3,16]],"date-time":"2025-03-16T22:27:01Z","timestamp":1742164021000},"page":"1243-1275","source":"Crossref","is-referenced-by-count":1,"title":["The Differential Properties of Certain Permutation Polynomials over Finite Fields"],"prefix":"10.1142","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-8680-0235","authenticated-orcid":false,"given":"Kirpa","family":"Garg","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Jammu, Jammu 181221, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7962-3221","authenticated-orcid":false,"given":"Sartaj Ul","family":"Hasan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Jammu, Jammu 181221, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8622-7120","authenticated-orcid":false,"given":"Pantelimon","family":"St\u0103nic\u0103","sequence":"additional","affiliation":[{"name":"Applied Mathematics Department, Naval Postgraduate School, Monterey, CA 93943, USA"}]}],"member":"219","published-online":{"date-parts":[[2025,3,13]]},"reference":[{"key":"S012905412550008XBIB001","doi-asserted-by":"publisher","DOI":"10.1002\/jcd.21916"},{"key":"S012905412550008XBIB002","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45661-9_2"},{"key":"S012905412550008XBIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2017.11.005"},{"key":"S012905412550008XBIB004","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2013.2260795"},{"key":"S012905412550008XBIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2005.10.006"},{"key":"S012905412550008XBIB006","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2020.2971988"},{"key":"S012905412550008XBIB007","unstructured":"K. Garg, S. U. Hasan and P. St\u0103nic\u0103, Differential uniformity properties of some classes of permutation polynomials, https:\/\/arxiv.org\/abs\/2212.01931 (2022)."},{"key":"S012905412550008XBIB008","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-020-00812-0"},{"key":"S012905412550008XBIB009","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2021.3123104"},{"key":"S012905412550008XBIB010","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.872854"},{"key":"S012905412550008XBIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2023.102196"},{"key":"S012905412550008XBIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2022.102145"},{"key":"S012905412550008XBIB013","doi-asserted-by":"publisher","DOI":"10.1007\/s10998-023-00561-2"},{"key":"S012905412550008XBIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2005.08.003"},{"key":"S012905412550008XBIB015","unstructured":"C. Li, C. Riera and P. St\u0103nic\u0103, Low\n                      c\n                      -differentially uniform functions via an extension of Dillon\u2019s switching method, https:\/\/arxiv.org\/abs\/2204.08760 (2022), Boolean Functions & Applic. (BFA), 2022, Paper #1."},{"key":"S012905412550008XBIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2018.01.003"},{"key":"S012905412550008XBIB017","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-4730-9_23"},{"key":"S012905412550008XBIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2023.102212"},{"key":"S012905412550008XBIB019","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2021.3081348"},{"key":"S012905412550008XBIB020","doi-asserted-by":"publisher","DOI":"10.3934\/amc.2024059"},{"key":"S012905412550008XBIB021","doi-asserted-by":"publisher","DOI":"10.1049\/el:19980569"},{"key":"S012905412550008XBIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2021.112543"},{"key":"S012905412550008XBIB023","doi-asserted-by":"publisher","DOI":"10.1007\/s00200-021-00520-9"},{"key":"S012905412550008XBIB024","doi-asserted-by":"publisher","DOI":"10.1007\/s12095-021-00485-z"},{"key":"S012905412550008XBIB025","series-title":"LNCS","first-page":"25","volume-title":"Sequences and Their Applications","volume":"7280","author":"Tan Y."},{"key":"S012905412550008XBIB026","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2022.3198133"},{"key":"S012905412550008XBIB027","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2016.11.007"},{"key":"S012905412550008XBIB028","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2022.08.022"},{"key":"S012905412550008XBIB029","doi-asserted-by":"publisher","DOI":"10.1016\/0022-314X(75)90038-4"},{"key":"S012905412550008XBIB030","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-021-00946-9"},{"key":"S012905412550008XBIB031","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2016.04.003"},{"key":"S012905412550008XBIB032","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-021-00866-8"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S012905412550008X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T09:07:35Z","timestamp":1765357655000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S012905412550008X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,13]]},"references-count":32,"journal-issue":{"issue":"08","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["10.1142\/S012905412550008X"],"URL":"https:\/\/doi.org\/10.1142\/s012905412550008x","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"type":"print","value":"0129-0541"},{"type":"electronic","value":"1793-6373"}],"subject":[],"published":{"date-parts":[[2025,3,13]]}}}