Algebraic immunities of vector-valued functions over finite fields

作     者：Liu Zhenhua Zhang Jie Wen Qiaoyan 

作者机构：Computer science department China Women's University School of Science Beijing University of Posts and Telecommunications State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications 

出 版 物：《The Journal of China Universities of Posts and Telecommunications》 (中国邮电高校学报（英文版）)

年 卷 期：2015年第22卷第5期

页      面：16-21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：supported by National Natural Science Foundation of China(60873191 60903152 61003286 60821001) 

主　　题：cryptography Boolean functions algebraic immunity 

摘      要：Algebraic immunity is an important cryptographic property of Boolean functions. The notion of algebraic immunity of Boolean functions has been generalized in several ways to vector-valued functions over arbitrary finite fields. In this paper, the results of Ref. [25] are generalized to arbitrary finite fields. We obtain vector-valued functions over arbitrary finite fields such that their algebraic immunities can reach the upper bounds. Furthermore, all the component functions, together with their some nonzero linear combinations, of vector-valued Boolean functions achieved by this construction have optimal algebraic immunities simultaneously.