{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T21:43:41Z","timestamp":1774907021355,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2022,7,27]],"date-time":"2022-07-27T00:00:00Z","timestamp":1658880000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,7,27]],"date-time":"2022-07-27T00:00:00Z","timestamp":1658880000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1007\/s10623-022-01086-4","type":"journal-article","created":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T17:07:39Z","timestamp":1659114459000},"page":"2385-2405","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["On the c-differential spectrum of power functions over finite fields"],"prefix":"10.1007","volume":"90","author":[{"given":"Haode","family":"Yan","sequence":"first","affiliation":[]},{"given":"Kun","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,7,27]]},"reference":[{"key":"1086_CR1","doi-asserted-by":"publisher","first-page":"101835","DOI":"10.1016\/j.ffa.2021.101835","volume":"72","author":"D Bartoli","year":"2021","unstructured":"Bartoli D., Calderini M.: On construction and (non) existence of $$ c $$-(almost) perfect nonlinear functions. Finite Fields Appl. 72, 101835 (2021).","journal-title":"Finite Fields Appl."},{"key":"1086_CR2","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/s10801-019-00899-2","volume":"52","author":"D Bartoli","year":"2020","unstructured":"Bartoli D., Timpanella M.: On a generalization of planar functions. J. Algebr. Comb. 52, 187\u2013213 (2020).","journal-title":"J. Algebr. Comb."},{"issue":"1","key":"1086_CR3","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/BF00630563","volume":"4","author":"E Biham","year":"1991","unstructured":"Biham E., Shamir A.: Differential cryptanalysis of DES-like cryptosystems. J. Cryptol. 4(1), 3\u201372 (1991).","journal-title":"J. Cryptol."},{"key":"1086_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9314-6","volume-title":"Differential Cryptanalysis of the Data Encryption Standard","author":"E Biham","year":"1993","unstructured":"Biham E., Shamir A.: Differential Cryptanalysis of the Data Encryption Standard. Springer, Berlin (1993)."},{"issue":"2","key":"1086_CR5","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1007\/s10623-014-9948-2","volume":"73","author":"C Blondeau","year":"2014","unstructured":"Blondeau C., Perrin L.: More differentially $$6$$-uniform power functions. Des. Codes Cryptogr. 73(2), 487\u2013505 (2014).","journal-title":"Des. Codes Cryptogr."},{"issue":"2","key":"1086_CR6","first-page":"149","volume":"1","author":"C Blondeau","year":"2010","unstructured":"Blondeau C., Canteaut A., Charpin P.: Differential properties of power functions. Int. J. Inf. Coding Theory 1(2), 149\u2013170 (2010).","journal-title":"Int. J. Inf. Coding Theory"},{"issue":"12","key":"1086_CR7","doi-asserted-by":"publisher","first-page":"8127","DOI":"10.1109\/TIT.2011.2169129","volume":"57","author":"C Blondeau","year":"2011","unstructured":"Blondeau C., Canteaut A., Charpin P.: Differential properties of $$x \\mapsto x^{2^t-1}$$. IEEE Trans. Inf. Theory 57(12), 8127\u20138137 (2011).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1086_CR8","doi-asserted-by":"crossref","unstructured":"Borisov N., Chew M., Johnson R., Wagner D.: Multiplicative differentials. International Workshop on Fast Software Encryption 2365, 17\u201333 (2002).","DOI":"10.1007\/3-540-45661-9_2"},{"issue":"4","key":"1086_CR9","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/j.ffa.2010.03.001","volume":"16","author":"C Bracken","year":"2010","unstructured":"Bracken C., Leander G.: A highly nonlinear differentially $$ 4 $$ uniform power mapping that permutes fields of even degree. Finite Fields Appl. 16(4), 231\u2013242 (2010).","journal-title":"Finite Fields Appl."},{"key":"1086_CR10","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1016\/j.ffa.2014.02.003","volume":"28","author":"P Charpin","year":"2014","unstructured":"Charpin P., Kyureghyan G.M., Suder V.: Sparse permutations with low differential uniformity. Finite Fields Appl. 28, 214\u2013243 (2014).","journal-title":"Finite Fields Appl."},{"key":"1086_CR11","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.ffa.2013.01.002","volume":"21","author":"S-T Choi","year":"2013","unstructured":"Choi S.-T., Hong S., No J.-S., Chung H.: Differential spectrum of some power functions in odd prime characteristic. Finite Fields Appl. 21, 11\u201329 (2013).","journal-title":"Finite Fields Appl."},{"issue":"2","key":"1086_CR12","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1023\/A:1008292303803","volume":"10","author":"RS Coulter","year":"1997","unstructured":"Coulter R.S., Matthews R.: Planar functions and planes of Lenz-Barlotti class II. Des. Codes Cryptogr. 10(2), 167\u2013184 (1997).","journal-title":"Des. Codes Cryptogr."},{"issue":"3","key":"1086_CR13","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/BF01111042","volume":"103","author":"P Dembowski","year":"1968","unstructured":"Dembowski P., Ostrom T.G.: Planes of order $$ n $$ with collineation groups of order $$ n^2 $$. Math. Z. 103(3), 239\u2013258 (1968).","journal-title":"Math. Z."},{"issue":"4","key":"1086_CR14","doi-asserted-by":"publisher","first-page":"1271","DOI":"10.1109\/18.761283","volume":"45","author":"H Dobbertin","year":"1999","unstructured":"Dobbertin H.: Almost perfect nonlinear power functions on $$ GF(2^{n}) $$: The Welch case. IEEE Trans. Inf. Theory 45(4), 1271\u20131275 (1999).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1\u20132","key":"1086_CR15","first-page":"57","volume":"151","author":"H Dobbertin","year":"1999","unstructured":"Dobbertin H.: Almost perfect nonlinear power functions on $$ GF(2^{n}) $$: the Niho case. IEEE Trans. Inf. Theory 151(1\u20132), 57\u201372 (1999).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"4","key":"1086_CR16","doi-asserted-by":"publisher","first-page":"1473","DOI":"10.1109\/18.923728","volume":"47","author":"H Dobbertin","year":"2001","unstructured":"Dobbertin H., Helleseth T., Kumar P.V., Martinsen H.: Ternary $$m$$-sequences with three-valued cross-correlation function: new decimations of Welch and Niho type. IEEE Trans. Inf. Theory 47(4), 1473\u20131481 (2001).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"9","key":"1086_CR17","doi-asserted-by":"publisher","first-page":"5781","DOI":"10.1109\/TIT.2020.2971988","volume":"66","author":"P Ellingsen","year":"2020","unstructured":"Ellingsen P., Felke P., Riera C., St\u0103nic\u0103 P., Tkachenko A.: C-differentials, multiplicative uniformity, and (almost) perfect c-nonlinearity. IEEE Trans. Inf. Theory 66(9), 5781\u20135789 (2020).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"1086_CR18","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/s10623-020-00812-0","volume":"89","author":"SU Hasan","year":"2021","unstructured":"Hasan S.U., Pal M., Riera C., St\u0103nic\u0103 P.: On the $$ c $$-differential uniformity of certain maps over finite fields. Des. Codes Cryptogr. 89(2), 221\u2013239 (2021).","journal-title":"Des. Codes Cryptogr."},{"key":"1086_CR19","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/s002000050073","volume":"8","author":"T Helleseth","year":"1997","unstructured":"Helleseth T., Sandberg D.: Some power mappings with low differential uniformity. Appl. Algeb. Eng. Commun. Comput. 8, 363\u2013370 (1997).","journal-title":"Appl. Algeb. Eng. Commun. Comput."},{"issue":"2","key":"1086_CR20","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1109\/18.748997","volume":"45","author":"T Helleseth","year":"1999","unstructured":"Helleseth T., Rong C., Sandberg D.: New families of almost perfect nonlinear power mappings. IEEE Trans. Inf. Theory 45(2), 475\u2013485 (1999).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1086_CR21","unstructured":"Lei L., Ren W., Fan C.L.: The differential spectrum of a class of power functions over finite fields. Adv. Math. Commun. (2019)."},{"key":"1086_CR22","unstructured":"Li N., Wu Y.N., Zeng X.Y., Tang X.H.: On the differential spectrum of a class of power functions over finite fields. arXiv:2012.04316."},{"key":"1086_CR23","volume-title":"Finite Fields, Encyclopedia of Mathematics and Its Applications","author":"R Lidl","year":"1997","unstructured":"Lidl R., Niederreite H.: Finite Fields, Encyclopedia of Mathematics and Its Applications, vol. 20. Cambridge University Press, Cambridge (1997)."},{"issue":"10","key":"1086_CR24","doi-asserted-by":"publisher","first-page":"6916","DOI":"10.1109\/TIT.2021.3081348","volume":"67","author":"S Mesnager","year":"2021","unstructured":"Mesnager S., Riera C., St\u0103nic\u0103 P., Yan H.D., Zhou Z.C.: Investigations on $$ c $$-(almost) perfect nonlinear functions. IEEE Trans. Inf. Theory 67(10), 6916\u20136925 (2021).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1086_CR25","first-page":"55","volume-title":"Advances in cryptology\u2014EUROCRYPT\u201993. Norway. 1993. LNCS","author":"K Nyberg","year":"1994","unstructured":"Nyberg K.: Differentially uniform mappings for cryptography. In: Helleseth T. (ed.) Advances in cryptology\u2014EUROCRYPT\u201993. Norway. 1993. LNCS, vol. 765, pp. 55\u201364. Springer, Berlin (1994)."},{"key":"1086_CR26","unstructured":"Tu Z.R., Zeng X.Y., Jiang Y.P., Tang X.H.: A class of AP$$c$$N power functions over finite fields of even characteristic. arXiv:2107.06464."},{"key":"1086_CR27","unstructured":"Wang X.Q., Zheng D.B.: Several classes of P$$c$$N power functions over finite fields. arXiv:2104.12942."},{"issue":"11","key":"1086_CR28","doi-asserted-by":"publisher","first-page":"2637","DOI":"10.1007\/s10623-021-00946-9","volume":"89","author":"YN Wu","year":"2021","unstructured":"Wu Y.N., Li N., Zeng X.Y.: New P$$c$$N and AP$$c$$N functions over finite fields. Des. Codes Cryptogr. 89(11), 2637\u20132651 (2021).","journal-title":"Des. Codes Cryptogr."},{"key":"1086_CR29","doi-asserted-by":"publisher","first-page":"101660","DOI":"10.1016\/j.ffa.2020.101660","volume":"64","author":"YX Xia","year":"2020","unstructured":"Xia Y.X., Zhang X.L., Li C.L., Helleseth T.: The differential spectrum of a ternary power mapping. Finite Fields Appl. 64, 101660 (2020).","journal-title":"Finite Fields Appl."},{"key":"1086_CR30","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/j.ffa.2017.07.008","volume":"48","author":"MS Xiong","year":"2017","unstructured":"Xiong M.S., Yan H.D.: A note on the differential spectrum of a differentially $$ 4 $$-uniform power function. Finite Fields Appl. 48, 117\u2013125 (2017).","journal-title":"Finite Fields Appl."},{"issue":"8","key":"1086_CR31","doi-asserted-by":"publisher","first-page":"1601","DOI":"10.1007\/s10623-017-0416-7","volume":"86","author":"MS Xiong","year":"2018","unstructured":"Xiong M.S., Yan H.D., Yuan P.Z.: On a conjecture of differentially $$8$$-uniform power functions. Des. Codes Cryptogr. 86(8), 1601\u20131621 (2018).","journal-title":"Des. Codes Cryptogr."},{"issue":"2","key":"1086_CR32","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1007\/s12095-021-00526-7","volume":"14","author":"HD Yan","year":"2022","unstructured":"Yan H.D.: On $$(-1)$$-differential uniformity of ternary APN power functions. Cryptogr. Comput. 14(2), 357\u2013369 (2022).","journal-title":"Cryptogr. Comput."},{"key":"1086_CR33","doi-asserted-by":"publisher","first-page":"1181","DOI":"10.1007\/s10623-021-00865-9","volume":"89","author":"HD Yan","year":"2021","unstructured":"Yan H.D., Li C.J.: Differential spectra of a class of power permutations with characteristic $$ 5 $$. Des. Codes Cryptogr. 89, 1181\u20131191 (2021).","journal-title":"Des. Codes Cryptogr."},{"issue":"10","key":"1086_CR34","doi-asserted-by":"publisher","first-page":"6819","DOI":"10.1109\/TIT.2019.2910070","volume":"65","author":"HD Yan","year":"2019","unstructured":"Yan H.D., Zhou Z.C., Wen J., Weng J.M., Helleseth T., Wang Q.: Differential spectrum of Kasami power permutations over odd characteristic finite fields. IEEE Trans. Inf. Theory 65(10), 6819\u20136826 (2019).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1086_CR35","unstructured":"Yan H.D., Xia Y.B., Li C.L., Helleseth T., Luo J.Q.: The differential spectrum of the power mapping $$ x^{p^ n-3} $$. IEEE Trans. Inf. Theory (2022)."},{"issue":"1","key":"1086_CR36","doi-asserted-by":"publisher","first-page":"1193","DOI":"10.1007\/s10623-021-00866-8","volume":"89","author":"ZB Zha","year":"2021","unstructured":"Zha Z.B., Hu L.: Some classes of power functions with low $$ c $$-differential uniformity over finite fields. Des. Codes Cryptogr. 89(1), 1193\u20131210 (2021).","journal-title":"Des. Codes Cryptogr."},{"issue":"2","key":"1086_CR37","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/j.ffa.2008.09.002","volume":"15","author":"ZB Zha","year":"2009","unstructured":"Zha Z.B., Kyureghyan G.M., Wang X.Q.: Perfect nonlinear binomials and their semifields. Finite Fields Appl. 15(2), 125\u2013133 (2009).","journal-title":"Finite Fields Appl."},{"key":"1086_CR38","doi-asserted-by":"publisher","first-page":"3912","DOI":"10.1016\/j.jalgebra.2009.04.042","volume":"332","author":"ZB Zha","year":"2009","unstructured":"Zha Z.B., Wang X.Q.: New families of perfect nonlinear polynomial functions. J. Algebra 332, 3912\u20133918 (2009).","journal-title":"J. Algebra"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-022-01086-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-022-01086-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-022-01086-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T17:15:45Z","timestamp":1663607745000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-022-01086-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,27]]},"references-count":38,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["1086"],"URL":"https:\/\/doi.org\/10.1007\/s10623-022-01086-4","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,27]]},"assertion":[{"value":"23 December 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 June 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 June 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 July 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}