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Codes Cryptogr."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this work we give several generalizations of the isotopic shift construction, introduced recently by Budaghyan et al. (IEEE Trans Inform Theory 66:5299\u20135309, 2020), when the initial function is a Gold function. In particular, we derive a general construction of APN functions which covers several unclassified APN functions for <jats:inline-formula><jats:alternatives><jats:tex-math>$$n=8$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>8<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and produces fifteen new APN functions for <jats:inline-formula><jats:alternatives><jats:tex-math>$$n=9$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>9<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s10623-020-00803-1","type":"journal-article","created":{"date-parts":[[2020,10,7]],"date-time":"2020-10-07T06:02:31Z","timestamp":1602050551000},"page":"19-32","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Generalized isotopic shift construction for APN functions"],"prefix":"10.1007","volume":"89","author":[{"given":"Lilya","family":"Budaghyan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6817-3421","authenticated-orcid":false,"given":"Marco","family":"Calderini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Claude","family":"Carlet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Coulter","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Irene","family":"Villa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,10,7]]},"reference":[{"key":"803_CR1","unstructured":"Albert, A.A.: Finite division algebras and finite planes, Combinatorial Analysis: Proceedings of the 10th Symposium in Applied Mathematics (Providence), Symposia in Applied Mathematics, vol.\u00a010, American Mathematical Society, pp.\u00a053\u201370 (1960)."},{"key":"803_CR2","unstructured":"Beth T., Ding C.: On almost perfect nonlinear permutations, Advances in Cryptology-EUROCRYPT\u201993, vol. 765. 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