Construction of Balanced Rotation Symmetric Boolean Functions with Optimal Algebraic Immunity  

作　　者：ZHANG Wenying 

机构地区：[1]School of Information Science and Engineering,Shandong Normal University [2]Science and Technology on Information Assume Laboratory

出　　处：《Wuhan University Journal of Natural Sciences》2014年第4期301-306,共6页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China(61272434);the Natural Science Foundation of Shandong Province(ZR 2012FM004,ZR2013FQ021);the Foundation of Science and Technology on Information Assume Laboratory(KJ-13-004)

摘　　要：Algebraic immunity is a new cryptographic criterion proposed against algebraic attacks. In order to resist algebraic attacks, Boolean functions used in many stream ciphers should possess high algebraic immunity. This paper presents one main result to find balanced rotation symmetric Boolean functions with maximum algebraic immunity. Through swapping the values of two orbits of rotation class of the majority function, a class of 4k＋l variable Boolean functions with maximum algebraic immu- nity is constructed. The function f（x） we construct always has terms of degree n-2 independence of what ever n is. And the nonlinearity off（x） is relatively good for large n.Algebraic immunity is a new cryptographic criterion proposed against algebraic attacks. In order to resist algebraic attacks, Boolean functions used in many stream ciphers should possess high algebraic immunity. This paper presents one main result to find balanced rotation symmetric Boolean functions with maximum algebraic immunity. Through swapping the values of two orbits of rotation class of the majority function, a class of 4k＋l variable Boolean functions with maximum algebraic immu- nity is constructed. The function f（x） we construct always has terms of degree n-2 independence of what ever n is. And the nonlinearity off（x） is relatively good for large n.

关 键 词：Boolean function algebraic attack Walsh spectrum algebraic degree algebraic immunity （AI） 

分 类 号：TN918.1[电子电信—通信与信息系统]