Abstract: The correlation coefficients of cryptographic functions are very important concepts in designing cryptographic functions. In this paper,by using some known conclusions and the definitions of Fourier coefficients and cross-correlation coefficients,the relationship between cross-correlation coefficients and Fourier coefficients of two q-ary cryptographic functions is given. Based on it,the relationships between Fourier coefficients and auto-correlation coefficients of one function,and cross-correlation coefficients of two functions and their auto-correlation coefficients are obtained. Also,the regular Bent functios are discussed. In particular,the duality of regular Bent functions is studied by using some known conculsions,and the relationship between the Fourier coefficients of derivate of two regular Bent functions and the Fourier coefficients of derivate of their dual functions is obtained.

Key words: q-ary cryptographic function, cross-correlation coefficient, auto-correlation coefficient, Fourier coefficient, regular Bent function, dual function

摘要： 密码函数的相关系数在密码函数研究中具有重要作用,为此,利用Fourier 系数和相关系数的定义及已有 结论,给出2 个q-进制密码函数互相关系数与其各自Fourier 系数间的关系,并基于该关系式,分别得到1 个密码函 数的Fourier 系数与其自相关系数间的关系,以及2 个密码函数的互相关系数与其自相关系数间的关系。同时利用 正则Bent 函数的定义和已有结论,对正则Bent 函数进行研究,讨论正则Bent 函数的对偶性,得到2 个正则Bent 函 数的导数与其对偶函数导数Fourier 系数间的关系。

关键词: q-进制密码函数, 互相关系数, 自相关系数, Fourier 系数, 正则Bent 函数, 对偶函数

CLC Number: 

• TP309