Boolean functions of an odd number of variables with maximum algebraic immunity

作     者：LI Na QI WenFeng 

作者机构：Department of Applied Mathematics Zhengzhou Information Engineering University Zhengzhou 450002China 

出 版 物：《Science in China(Series F)》 (中国科学（F辑英文版）)

年 卷 期：2007年第50卷第3期

页      面：307-317页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：the National Natural Science Foundation of China (Grant No. 60673081) the "863" project (Grant No. 2006AA01Z417) 

主　　题：algebraic attacks algebraic immunity nonlinearity correlation immunity 

摘      要：In this paper, we study Boolean functions of an odd number of variables with maximum algebraic immunity. We identify three classes of such functions, and give some necessary conditions of such functions, which help to examine whether a Boolean function of an odd number of variables has the maximum algebraic immunity. Further, some necessary conditions for such functions to have also higher nonlinearity are proposed, and a class of these functions are also obtained. Finally, we present a sufficient and necessary condition for Boolean functions of an odd number of variables to achieve maximum algebraic immunity and to be also 1-resilient.