{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T06:50:47Z","timestamp":1757314247638,"version":"3.37.3"},"reference-count":42,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"5","license":[{"start":{"date-parts":[[2022,5,1]],"date-time":"2022-05-01T00:00:00Z","timestamp":1651363200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2022,5,1]],"date-time":"2022-05-01T00:00:00Z","timestamp":1651363200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2022,5,1]],"date-time":"2022-05-01T00:00:00Z","timestamp":1651363200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/100016190","name":"Trond Mohn stiftelse","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100016190","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005416","name":"Norwegian Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100005416","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2022,5]]},"DOI":"10.1109\/tit.2022.3147060","type":"journal-article","created":{"date-parts":[[2022,2,7]],"date-time":"2022-02-07T21:08:05Z","timestamp":1644268085000},"page":"3389-3403","source":"Crossref","is-referenced-by-count":9,"title":["On Two Fundamental Problems on APN Power Functions"],"prefix":"10.1109","volume":"68","author":[{"given":"Lilya","family":"Budaghyan","sequence":"first","affiliation":[{"name":"Department of Informatics, University of Bergen, Bergen, Norway"}]},{"given":"Marco","family":"Calderini","sequence":"additional","affiliation":[{"name":"Department of Informatics, University of Bergen, Bergen, Norway"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6118-7927","authenticated-orcid":false,"given":"Claude","family":"Carlet","sequence":"additional","affiliation":[{"name":"Department of Informatics, University of Bergen, Bergen, Norway"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7746-2823","authenticated-orcid":false,"given":"Diana","family":"Davidova","sequence":"additional","affiliation":[{"name":"Department of Informatics, University of Bergen, Bergen, Norway"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9695-1454","authenticated-orcid":false,"given":"Nikolay S.","family":"Kaleyski","sequence":"additional","affiliation":[{"name":"Department of Informatics, University of Bergen, Bergen, Norway"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-48285-7_7"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00630563"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2169129"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-008-9194-6"},{"article-title":"The equivalence of almost bent and almost perfect nonlinear functions and their generalization","year":"2005","author":"Budaghyan","key":"ref5"},{"volume-title":"A note on the Walsh spectrum of Dobbertin APN functions","year":"2020","author":"Budaghyan","key":"ref6"},{"volume-title":"On a relationship between gold and Kasami functions and other power APN functions","year":"2020","author":"Budaghyan","key":"ref7"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2022.3147060"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.864481"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/18.817504"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480198350057"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-46035-7_34"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1017\/9781108606806"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-020-00830-y"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2017.2761392"},{"issue":"2","key":"ref16","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1023\/A:1008344232130","article-title":"Codes, bent functions and permutations suitable for DES-like cryptosystems","volume":"15","author":"Carlet","year":"1998","journal-title":"Des., Codes, Cryptogr."},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-11793"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/bfb0053450"},{"key":"ref19","first-page":"171","article-title":"On the evaluation of a class of Weil sums in characteristic 2","volume":"28","author":"Coulter","year":"1999","journal-title":"New Zealand J. Math."},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04722-4"},{"key":"ref21","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1023\/A:1026435428030","article-title":"Multiplicative difference sets via additive characters","volume":"17","author":"Dillon","year":"1999","journal-title":"Des., Codes Cryptogr."},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2003.09.003"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1109\/18.761283"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1998.2764"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-56755-1_11"},{"key":"ref26","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1023\/A:1026475109375","article-title":"Another proof of Kasami\u2019s theorem","volume":"17","author":"Dobbertin","year":"1999","journal-title":"Des., Codes Cryptogr."},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.3934\/amc.2009.3.59"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1968.1054106"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-85912-3_9"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-007-9124-z"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1006\/ffta.2000.0281"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-56686-4_43"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1109\/18.54892"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.3934\/amc.2007.1.243"},{"issue":"1","key":"ref35","first-page":"55","article-title":"Analysis of Kasami-Welch functions in odd dimension using Stickelberger\u2019s theorem","volume":"2","author":"Langevin","year":"2010","journal-title":"J. Combinatorics Number Theory"},{"key":"ref36","article-title":"On the differential spectrum of a class of power functions over finite fields","author":"Li","year":"2020","journal-title":"arXiv:2012.04316"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-48285-7_33"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-48285-7_6"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(71)90473-6"},{"key":"ref40","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.ffa.2013.10.002","article-title":"On inversion in $Z^2n$\n- 1","volume":"25","author":"Kyureghyan","year":"2014","journal-title":"Finite Fields Their Appl."},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-020-00804-0"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1007\/s10801-016-0680-z"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/9760494\/09705538.pdf?arnumber=9705538","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,17]],"date-time":"2024-01-17T22:47:26Z","timestamp":1705531646000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9705538\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5]]},"references-count":42,"journal-issue":{"issue":"5"},"URL":"https:\/\/doi.org\/10.1109\/tit.2022.3147060","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"type":"print","value":"0018-9448"},{"type":"electronic","value":"1557-9654"}],"subject":[],"published":{"date-parts":[[2022,5]]}}}