| The S-box is the only non-linear component in the block cipher algorithm,and its cryptographic properties determine the security of the block cipher algorithm to a large extent.Therefore,the design of S-boxes with excellent cryptographic properties is an important link in the design of block cipher algorithms.The construction based on vector Boolean function and the construction based on cryptographic structure are two important ways to construct S-boxes.This paper is dedicated to using these two construction methods to design new S-boxes,and proposes a class of S-box constructions based on vector Boolean functions and a class of S-box constructions based on cryptographic structures.The specific research contents are described as follows.Firstly,based on the design criterion of MAI function,BCH bound in coding theory and Gaussian sum in finite field are introduced simultaneously,and a class of balanced Boolean functions with high nonlinearity is proposed.Based on the analysis of the existing three types of vector Boolean functions for constructing the highest algebraic immunity,it is found that there are disadvantages such as difficult to guarantee balance and low nonlinearity.In this paper,when constructing a new class of Boolean functions with the optimal algebraic immunity,the highest algebraic degree and better nonlinearity,two different Boolean functions are constructed respectively,and the parameter u is set to find the larger non-linearity.In the case of linearity,the two different Boolean functions constructed are XORed to obtain a new Boolean function,and the BCH bound and Gaussian sum are introduced,which can be obtained through theoretical analysis.The Boolean function satisfies the optimal algebraic Immunity,the highest algebraic number,and higher nonlinearity.Then,the specific nonlinearity of the Boolean function under different parameters is calculated through simulation experiments,and the results are analyzed.Secondly,based on the design idea of cryptography structure,a new construction method of S-box is proposed.First of all,this paper expands the algebraic immunity of S-boxes,introduces the definition of graph-algebraic immunity,and then analyzes the construction method of small-scale S-boxes to construct large-scale S-boxes,referring to the design ideas of MISTY structure and Feistel structure,proposed an S-box construction method with the highest graph algebraic immunity,the highest algebraic number,and higher nonlinearity,and designed an algorithm for searching this type of Sbox,and verified the performance superiority of the algorithm in this chapter through computer simulation experiments,and listed the expected 8-bit S-box,analyzed and concluded that the improved S-box has better properties.Finally,the S-boxes constructed in this paper have the highest algebraic immunity,the highest algebraic number,and better nonlinearity and differential uniformity.If these S-boxes are applied to the design of block ciphers,it will be more helpful for block ciphers to resist Algebra attack. |
