CAJ | 학술논문

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。
밀마함수적상관계수재밀마함수연구중구유중요작용，위차，이용Fourier계수화상관계수적정의급이유결론，급출2개q-진제밀마함수호상관계수여기각자Fourier계수간적관계，병기우해관계식，분별득도1개밀마함수적Fourier계수여기자상관계수간적관계，이급2개밀마함수적호상관계수여기자상관계수간적관계。동시이용정칙Bent함수적정의화이유결론，대정칙Bent함수진행연구，토론정칙Bent함수적대우성，득도2개정칙Bent함수적도수여기대우함수도수Fourier계수간적관계。
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.