{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T17:16:50Z","timestamp":1760203010338,"version":"3.37.3"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T00:00:00Z","timestamp":1648857600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T00:00:00Z","timestamp":1648857600000},"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":["Cryptogr. Commun."],"published-print":{"date-parts":[[2022,9]]},"DOI":"10.1007\/s12095-022-00574-7","type":"journal-article","created":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T14:21:42Z","timestamp":1648909302000},"page":"1055-1066","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On the higher-order nonlinearity of a Boolean bent function class (Constructed via Niho power functions)"],"prefix":"10.1007","volume":"14","author":[{"given":"Kezia","family":"Saini","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2066-5221","authenticated-orcid":false,"given":"Manish","family":"Garg","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,4,2]]},"reference":[{"key":"574_CR1","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.ffa.2007.02.004","volume":"14","author":"A Canteaut","year":"2008","unstructured":"Canteaut, A., Charpin, P., Kyureghyan, G.M.: A new class of monomial bent functions. Finit. Fields Appl. 14, 221\u2013241 (2008)","journal-title":"Finit. Fields Appl."},{"key":"574_CR2","doi-asserted-by":"crossref","unstructured":"Carlet, C.: Vectorial boolean functions for cryptography. In: Boolean Models and Methods in Mathematics, Computer Science, and Engineering, vol. 134, pp 398\u2013469 (2010)","DOI":"10.1017\/CBO9780511780448.012"},{"key":"574_CR3","doi-asserted-by":"publisher","first-page":"1262","DOI":"10.1109\/TIT.2007.915704","volume":"54","author":"C Carlet","year":"2008","unstructured":"Carlet, C.: Recursive lower bounds on the nonlinearity profile of Boolean functions and their applications. IEEE Trans. Inf. Theory 54, 1262\u20131272 (2008)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"574_CR4","doi-asserted-by":"crossref","unstructured":"Carlet, C.: Boolean functions for cryptography and error correcting codes. In: Boolean Models and Methods in Mathematics, Computer Science, and Engineering, vol. 2, pp 257\u2013397 (2010)","DOI":"10.1017\/CBO9780511780448.011"},{"key":"574_CR5","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1109\/TIT.2006.887494","volume":"53","author":"C Carlet","year":"2006","unstructured":"Carlet, C., Mesnager, S.: Improving the upper bounds on the covering radii of binary Reed\u2013Muller codes. IEEE Trans. Inf. Theory 53, 162\u2013173 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"574_CR6","doi-asserted-by":"crossref","unstructured":"Carlet, C.: Boolean functions for cryptography and coding theory, Monograph in Cambridge University Press, pp. 1\u2013562 (2021)","DOI":"10.1017\/9781108606806"},{"key":"574_CR7","first-page":"541","volume-title":"Covering Codes","author":"G Cohen","year":"1997","unstructured":"Cohen, G., Honkala, I., Litsyn, S., Lobstein, A.: Covering Codes, p 541. Elsevier, North Holland (1997)"},{"key":"574_CR8","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1016\/j.jcta.2005.07.009","volume":"113","author":"H Dobbertin","year":"2006","unstructured":"Dobbertin, H., Leander, G., Canteaut, A., Carlet, C., Felke, P., Gaborit, P.: Construction of bent functions via Niho power functions. J. Comb. Theory Ser. A 113, 779\u2013798 (2006)","journal-title":"J. Comb. Theory Ser. A"},{"key":"574_CR9","doi-asserted-by":"crossref","unstructured":"Dumer, I., Kabatiansky, G., Tavernier, C.: List decoding of Reed-Muller codes up to the Johnson bound with almost linear complexity. IEEE International Symposium on Information Theory\u2013Proceedings, pp. 138\u2013142 (2006)","DOI":"10.1109\/ISIT.2006.261690"},{"key":"574_CR10","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/s10623-008-9184-8","volume":"49","author":"R Fourquet","year":"2008","unstructured":"Fourquet, R., Tavernier, C.: An improved list decoding algorithm for the second order reed\u2013muller codes and its applications. Des Codes Crypt 49, 323\u2013340 (2008)","journal-title":"Des Codes Crypt"},{"key":"574_CR11","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1016\/j.ins.2009.09.006","volume":"180","author":"S Gangopadhyay","year":"2010","unstructured":"Gangopadhyay, S., Sarkar, S., Telang, R.: On the lower bounds of the second order nonlinearities of some Boolean functions. Inform. Sci. 180, 266\u2013273 (2010)","journal-title":"Inform. Sci."},{"key":"574_CR12","doi-asserted-by":"publisher","first-page":"2397","DOI":"10.1587\/transfun.E101.A.2397","volume":"101","author":"Q Gao","year":"2018","unstructured":"Gao, Q., Tang, D.: A lower bound on the second-order nonlinearity of the generalized maiorana-mcfarland boolean functions. IEICE Trans. Fundam. Electron. Commun. Comput Sci. 101, 2397\u20132401 (2018)","journal-title":"IEICE Trans. Fundam. Electron. Commun. Comput Sci."},{"key":"574_CR13","doi-asserted-by":"publisher","first-page":"413","DOI":"10.3233\/FI-2011-570","volume":"111","author":"M Garg","year":"2011","unstructured":"Garg, M., Gangopadhyay, S.: A lower bound of the second\u2013order nonlinearities of boolean bent functions. Fundam. Informaticae 111, 413\u2013422 (2011)","journal-title":"Fundam. Informaticae"},{"key":"574_CR14","doi-asserted-by":"publisher","first-page":"1311","DOI":"10.1080\/00207160.2012.687725","volume":"89","author":"M Garg","year":"2012","unstructured":"Garg, M., Khalyavin, A.: Higher-order nonlinearity of Kasami functions. Int. J. Comput. Math. 89, 1311\u20131318 (2012)","journal-title":"Int. J. Comput. Math."},{"key":"574_CR15","first-page":"502","volume":"2009","author":"R Gode","year":"2009","unstructured":"Gode, R., Gangopadhyay, S.: On second-order nonlinearities of cubic monomial Boolean functions. IACR Crypt. ePrint Archieve 2009, 502 (2009)","journal-title":"IACR Crypt. ePrint Archieve"},{"key":"574_CR16","first-page":"341","volume":"35","author":"R Gode","year":"2010","unstructured":"Gode, R., Gangopadhyay, S.: On higher-order nonlinearities of monomial partial spreads type boolean functions. J. Comb. Inf. Syst. Sci. 35, 341\u2013360 (2010)","journal-title":"J. Comb. Inf. Syst. Sci."},{"key":"574_CR17","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/s12095-009-0017-z","volume":"2","author":"R Gode","year":"2010","unstructured":"Gode, R., Gangopadhyay, S.: Third-order nonlinearities of a subclass of Kasami functions. Cryptogr. Commun. 2, 69\u201383 (2010)","journal-title":"Cryptogr. Commun."},{"key":"574_CR18","doi-asserted-by":"crossref","unstructured":"Iwata, T., Kurosawa, K.: Probabilistic higher order differential attack and higher order bent functions. In: International Conference on the Theory and Application of Cryptology and Information Security, Springer, pp 62\u201374 (1999)","DOI":"10.1007\/978-3-540-48000-6_7"},{"key":"574_CR19","unstructured":"Kabatiansky, G., Tavernier, C.: List decoding of second order reed-muller codes, Proc. 8Th Intern. Simp. Comm. Theory and Applications, Ambleside, UK (2005)"},{"key":"574_CR20","unstructured":"MacWilliams, F.J., Sloane, N.J.A.: The theory of Error-Correcting codes, vol. 16. Elsevier (1977)"},{"key":"574_CR21","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1016\/0097-3165(76)90024-8","volume":"20","author":"OS Rothaus","year":"1976","unstructured":"Rothaus, O.S.: On ben functions. J. Comb. Theory. Series A 20, 300\u2013305 (1976)","journal-title":"J. Comb. Theory. Series A"},{"key":"574_CR22","first-page":"1","volume":"2014","author":"BK Singh","year":"2014","unstructured":"Singh, B.K.: On third-order nonlinearity of biquadratic monomial boolean functions. Int. J. Eng. Math. 2014, 1\u20137 (2014)","journal-title":"Int. J. Eng. Math."},{"key":"574_CR23","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1016\/j.ins.2008.10.002","volume":"179","author":"G Sun","year":"2009","unstructured":"Sun, G., Wu, C.: The lower bounds on the second order nonlinearity of three classes of Boolean functions with high nonlinearity. Inform. Sci. 179, 267\u2013278 (2009)","journal-title":"Inform. Sci."},{"key":"574_CR24","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s00200-010-0136-y","volume":"22","author":"G Sun","year":"2011","unstructured":"Sun, G., Wu, C.: The lower bound on the second-order nonlinearity of a class of Boolean functions with high nonlinearity. Appl. Algebra Eng. Commun. Comput. 22, 37\u201345 (2011)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"key":"574_CR25","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s12095-019-00360-y","volume":"12","author":"D Tang","year":"2020","unstructured":"Tang, D., Yan, H., Zhou, Z., Zhang, X.: A new lower bound on the second-order nonlinearity of a class of monomial bent functions. Cryptogr. Commun. 12, 77\u201383 (2020)","journal-title":"Cryptogr. Commun."},{"key":"574_CR26","doi-asserted-by":"crossref","unstructured":"Wang, Q., Johansson, T.: A note on fast algebraic attacks and higher order nonlinearities. In: International Conference on Information Security and Cryptology, pp 404\u2013414. Springer (2010)","DOI":"10.1007\/978-3-642-21518-6_28"}],"container-title":["Cryptography and Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-022-00574-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12095-022-00574-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-022-00574-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,18]],"date-time":"2022-08-18T10:21:27Z","timestamp":1660818087000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12095-022-00574-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,2]]},"references-count":26,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["574"],"URL":"https:\/\/doi.org\/10.1007\/s12095-022-00574-7","relation":{},"ISSN":["1936-2447","1936-2455"],"issn-type":[{"type":"print","value":"1936-2447"},{"type":"electronic","value":"1936-2455"}],"subject":[],"published":{"date-parts":[[2022,4,2]]},"assertion":[{"value":"15 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 March 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 April 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}