{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T20:18:34Z","timestamp":1649103514226},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2014,4]]},"abstract":"<jats:p> The Global Avalanche Characteristics (including the sum-of-squares indicator and the absolute indicator) measure the overall avalanche characteristics of a cryptographic Boolean function. Son et al. (1998) gave the lower bound on the sum-of-squares indicator for a balanced Boolean function. In this paper, we give a sufficient and necessary condition on a balanced Boolean function reaching the lower bound on the sum-of-squares indicator. We also analyze whether these balanced Boolean functions exist, and if they reach the lower bounds on the sum-of-squares indicator or not. Our result implies that there does not exist a balanced Boolean function with n-variable for odd n(n \u2265 5). We conclude that there does not exist a m(m \u2265 1)-resilient function reaching the lower bound on the sum-of-squares indicator with n-variable for n \u2265 7. <\/jats:p>","DOI":"10.1142\/s0129054114500178","type":"journal-article","created":{"date-parts":[[2014,7,25]],"date-time":"2014-07-25T01:48:52Z","timestamp":1406252932000},"page":"343-353","source":"Crossref","is-referenced-by-count":3,"title":["ONE SUFFICIENT AND NECESSARY CONDITION ON BALANCED BOOLEAN FUNCTIONS WITH \u03c3<sub>f<\/sub> = 2<sup>2n<\/sup> + 2<sup>n+3<\/sup>(n \u2265 3)"],"prefix":"10.1142","volume":"25","author":[{"given":"YU","family":"ZHOU","sequence":"first","affiliation":[{"name":"Science and Technology on Communication Security Laboratory, Chengdu 610041, P. R. China"}]},{"given":"LIN","family":"WANG","sequence":"additional","affiliation":[{"name":"Science and Technology on Communication Security Laboratory, Chengdu 610041, P. R. China"}]},{"given":"WEIQIONG","family":"WANG","sequence":"additional","affiliation":[{"name":"School of Science, Chang'an University, Xi'an 710064, P. R. China"}]},{"given":"XINFENG","family":"DONG","sequence":"additional","affiliation":[{"name":"Science and Technology on Communication Security Laboratory, Chengdu 610041, P. R. China"}]},{"given":"XIAONI","family":"DU","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2014,7,24]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1109\/18.57222"},{"key":"p_2","first-page":"2551","volume":"2002","author":"Clark J.","year":"2002","journal-title":"Proc. Indcorypt"},{"key":"p_4","first-page":"3006","volume":"2003","author":"Gong G.","year":"2004","journal-title":"Proc. SAC"},{"key":"p_5","first-page":"2247","volume":"2001","author":"Maitra S.","year":"2001","journal-title":"Proc. INDOCRYPT"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(98)00009-X"},{"key":"p_8","first-page":"C172","volume":"79","author":"Stnic P.","year":"2001","journal-title":"Inform. Process. Lett."},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(98)00184-7"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2009.2032736"},{"issue":"5","key":"p_12","first-page":"316","volume":"1","author":"Zhang X. M.","year":"1995","journal-title":"Journal for Universal Computer Science"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.3934\/amc.2013.7.335"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2009.09.012"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054114500178","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:54:35Z","timestamp":1565186075000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054114500178"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4]]},"references-count":11,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2014,7,24]]},"published-print":{"date-parts":[[2014,4]]}},"alternative-id":["10.1142\/S0129054114500178"],"URL":"https:\/\/doi.org\/10.1142\/s0129054114500178","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,4]]}}}