Analyzing Boolean Functions via Solving Parametric Polynomial Systems

作     者：HUANG Zhenyu SUN Yao LIN Dongdai HUANG Zhenyu;SUN Yao;LIN Dongdai

作者机构：SKLOISInstitute of Information EngineeringChinese Academy of SciencesBeijing 100093China 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2021年第34卷第2期

页      面：792-808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 under Grant Nos.61977060 and 61877058 

主　　题：Boolean functions characteristic set method correlation nonlinearity parametric Boolean polynomial systems 

摘      要：In this paper,a new method to analyze Boolean functions is *** this method,one can analyze the balancedness,the nonlinearity,and the input-output correlation of vectorial Boolean *** basic idea of this method is to compute the refined covers of some parametric Boolean polynomial systems which are equivalent to these *** a refined cover,the parameter space is divided into several disjoint components,and on each component,the parametric Boolean polynomial system has a fixed number of *** efficient algorithm based on the characteristic set method to compute refined covers of parametric Boolean polynomial systems is *** experimental results about some instances generated from cryptanalysis show that this new method is efficient and can solve some instances which can not be solved in reasonable time by other methods.