q-进制密码函数的相关系数研究  

Research on Correlation Coefficients of q- ary Crytptographic Functions

作　　者：卓泽朋[1] 崇金凤[1] 余磊[2] 魏仕民[1] 

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000 [2]淮北师范大学计算机科学与技术学院,安徽淮北235000

出　　处：《计算机工程》2015年第5期130-132,共3页Computer Engineering

基　　金：安徽高校省级自然科学研究基金资助项目(KJ2014A220;KJ2014A231);安徽省自然科学基金资助项目(1208085QF119)

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。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.

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 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]