对有限域上复合变换的线性逼近

Linear Approximation to Composition Transformations over Finite Fields

中文关键词:  线性逼近  复合变换  相关系数  谱  有限域  有限交换群

英文关键词:linear approximation  composition function  correlation coefficient  spectrum  finite field  finite Abelian group

中文摘要:

      本文解决了有限交换群上复合函数的特征谱的计算问题,定义了有限交换群上函数的相关 系数的概念,并解决了有限域上复合函数与线性映射的相关系数的计算问题,从而建立了对密码算 法中的复合变换进行线性逼近的理论基础.

英文摘要:

      In this paper, the problem of how to compute the characteristic spectrum for composition transformations over finite Abelian groups is solved, the concept of correlation coefficient of functions over finite Abelian groups is defined, and the problem of how to compute the correlation coefficient between a composition function and a linear function over finite field is solved, so the theoretic foundation of linear approximation to composition transformations in cryptography algorithm is established.