{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T12:57:20Z","timestamp":1693227440358},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2014,8]]},"abstract":"<jats:p> Constructing 2m-variable Boolean functions with optimal algebraic immunity based on decomposition of additive group of the finite field [Formula: see text] seems to be a promising approach since Tu and Deng's work. In this paper, we consider the same problem in a new way. Based on polar decomposition of the multiplicative group of [Formula: see text], we propose a new construction of Boolean functions with optimal algebraic immunity. By a slight modification of it, we obtain a class of balanced Boolean functions achieving optimal algebraic immunity, which also have optimal algebraic degree and high nonlinearity. Computer investigations imply that this class of functions also behaves well against fast algebraic attacks. <\/jats:p>","DOI":"10.1142\/s0129054114500208","type":"journal-article","created":{"date-parts":[[2014,8,29]],"date-time":"2014-08-29T09:11:47Z","timestamp":1409303507000},"page":"537-551","source":"Crossref","is-referenced-by-count":4,"title":["CONSTRUCTING 2<i>m<\/i>-VARIABLE BOOLEAN FUNCTIONSWITH OPTIMAL ALGEBRAIC IMMUNITY BASED ON POLAR DECOMPOSITION OF $\\mathbb{F}^\\ast_{2^{2m}}$"],"prefix":"10.1142","volume":"25","author":[{"given":"JIA","family":"ZHENG","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R., China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"BAOFENG","family":"WU","sequence":"additional","affiliation":[{"name":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R., China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YUFU","family":"CHEN","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R., China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ZHUOJUN","family":"LIU","sequence":"additional","affiliation":[{"name":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R., China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,8,29]]},"reference":[{"key":"p_3","first-page":"606","volume":"200","author":"Carlet C.","year":"2009","journal-title":"Report"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.876253"},{"key":"p_6","first-page":"400","volume":"201","author":"Cohen G.","year":"2011","journal-title":"Report"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-005-6300-x"},{"key":"p_10","first-page":"515","volume":"201","author":"Jin Q.","year":"2011","journal-title":"Report"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.862121"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2007.915914"},{"key":"p_16","first-page":"498","volume":"201","author":"Liu M.","year":"2012","journal-title":"Report"},{"key":"p_17","first-page":"335","volume":"201","author":"Lou Y.","year":"2012","journal-title":"Report"},{"key":"p_20","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-010-9460-2"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2012.2217476"},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-010-9413-9"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054114500208","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:29:44Z","timestamp":1565123384000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054114500208"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8]]},"references-count":12,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2014,8,29]]},"published-print":{"date-parts":[[2014,8]]}},"alternative-id":["10.1142\/S0129054114500208"],"URL":"https:\/\/doi.org\/10.1142\/s0129054114500208","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,8]]}}}