On the construction of multi-output Boolean functions with optimal algebraic immunity  

作　　者：ZHANG Jie SONG ShouChao DU Jiao WEN QiaoYan 

机构地区：[1]School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China [2]State Key Laboratory of Networking and Switching Technology,Beijing University of Posts and Telecommunications Beijing 100876,China [3]Department of Mathematics,Xinxiang University,Xinxiang 453003,China

出　　处：《Science China(Information Sciences)》2012年第7期1617-1623,共7页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 611702070, 61121061,61102093);Fundamental Research for the Central Universities (Grant No. BUPT 2012RC0710)

摘　　要：In this paper, we show a construction of multi-output Boolean functions with optimal algebraic immunity. And, the relationship between the algebraic immunity of a multi-output Boolean function and those of its component functions is studied. We show that all the component functions, together with their nonzero linear combination, of the multi-output Boolean functions achieved by this construction have optimal algebraic immunity simultaneously.In this paper, we show a construction of multi-output Boolean functions with optimal algebraic immunity. And, the relationship between the algebraic immunity of a multi-output Boolean function and those of its component functions is studied. We show that all the component functions, together with their nonzero linear combination, of the multi-output Boolean functions achieved by this construction have optimal algebraic immunity simultaneously.

关 键 词：algebraic immunity Boolean functions algebraic attacks ANNIHILATORS 

分 类 号：TN918.4[电子电信—通信与信息系统] S858.315.3[电子电信—信息与通信工程]