{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T04:25:49Z","timestamp":1741753549838,"version":"3.38.0"},"reference-count":0,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2011,8,1]],"date-time":"2011-08-01T00:00:00Z","timestamp":1312156800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2011,8]]},"abstract":" In this paper we find a lower bound of the second-order nonlinearities of Boolean bent functions of the form ${\\rm f}({\\rm x}) = {\\rm Tr}_{1}^{{\\rm n}}(\\rmalpha_{1}{\\rm x}^{{\\rm d}_{1}} + \\rmalpha_{2}{\\rm x}^{{\\rm d}_{2}})$, where d1<\/jats:sub> and d2<\/jats:sub> are Niho exponents. A lower bound of the second-order nonlinearities of these Boolean functions can also be obtained by using a recent result of Li, Hu and Gao (eprint.iacr.org\/2010 \/009.pdf). It is shown in Section 3, by a direct computation, that for large values of n, the lower bound obtained in this paper are better than the lower bound obtained by Li, Hu and Gao. <\/jats:p>","DOI":"10.3233\/fi-2011-570","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T04:49:12Z","timestamp":1575348552000},"page":"413-422","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["A Lower Bound of the Second\u2013order Nonlinearities of Boolean Bent Functions"],"prefix":"10.1177","volume":"111","author":[{"given":"Manish","family":"Garg","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee\u2013247667, Uttarakhand, INDIA. manishiitr8@gmail.com"}]},{"given":"Sugata","family":"Gangopadhyay","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee\u2013247667, Uttarakhand, INDIA. gsugata@gmail.com"}]}],"member":"179","published-online":{"date-parts":[[2011,8,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2011-570","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2011-570","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T07:47:26Z","timestamp":1741679246000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2011-570"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,8]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2011,8]]}},"alternative-id":["10.3233\/FI-2011-570"],"URL":"https:\/\/doi.org\/10.3233\/fi-2011-570","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"type":"print","value":"0169-2968"},{"type":"electronic","value":"1875-8681"}],"subject":[],"published":{"date-parts":[[2011,8]]}}}