Concrete Constructions Of Some Classes Of Weightwise Perfectly Balanced Boolean Functions

With the deepening of information technology,information security has been paid more and more attention,and the correlation between the research and analysis of cryptographic algo-rithm theory and social information security has also been deepening.In the research and design of cryptographic algorithm theory,Boolean function as an important component has received a lot of attention and research.In 2016,the European Commission propose FLIP password,and FLIP password algorithm requires the input of filtering function to have a fixed Hamming weight,so the input of filtering function with a constant Hamming weight attract the attention of scholars.Since balancedness is an important property of cryptographic functions,Carlet et al.give the first construction of weightwise perfectly balanced Boolean function by recursion in2017.In recent years,the construction of weightwise perfectly balanced Boolean function with good cryptographic properties has been concerned by some cryptographers research direction.This paper mainly presents the concrete constructions of several classes of weightwise per-fectly balanced Boolean functions.The main research results are summarized as the following:1.In this chapter,we first introduce a class of 2~m-variable Boolean functions with alge-braic degree 8,where m is an integer no less than 4.Then a class of weighewise perfectly balanced Boolean functions with high algebraic degree is constructed by modifying the support of these Boolean functions.Finally,the algebraic degree,the weightwise nonlinearity and the algebraic immunity of the newly constructed weighewise perfectly balanced Boolean functions are studied from theoretically.2.Based on a class of linear Boolean functions and a class of quadratic Boolean functions proposed by Mesnager and Su,and a class of quadratic Boolean functions proposed by Li et al,the method of weighewise perfectly balanced Boolean functions with simple algebraic normal form is given by modifying the support of these three types of Boolean functions.At the same time,the related cryptographic properties of the newly constructed weighewise per-fectly balanced Boolean functions are studied,such as the algebraic degree,the weightwise nonlinearity and algebraic immunity.3.Firstly,a class of quadratic Boolean functions is proposed,and then a class of weighe-wise perfectly balanced Boolean functions with high nonlinearity is constructed by modifying the support of this class of quadratic Boolean functions.Finally,the algebraic degree,the weightwise nonlinearity and the algebraic immunity of the newly constructed weighewise per-fectly balanced Boolean functions with high nonlinearity are studied.