摘要
It is already known that there are several nonlinearity criteria such as algebrajc degree,nonlinearity,distance to linear structures,correlation immune,propagation criterion,differential uniformity,which are used to check whether a cryptographic function is weak or not,in this paper we will discuss these criteria from a valuation point of view,and consider the largest transformation group which leave a criterion invariant,which is named its symmetry group.it can serve as a way of coparing the stability of nonlinearity criteria under the action of invertible transformations.
It is already known that there are several nonlinearity criteria such asalgebraic degree nonlinearity, distance to linear structures, correlation immune, propagationcriterion, differential uniformity, which are used to check whether a cryptographic function is weakor not. In this paper we will discuss these criteria from a valuation point of view, and considerthe largest transformation group which leave a criterion invariant, which is named its symmetrygroup. It can serve as a way of comparing the stability of nonlinearity criteria under the action ofinvertible transformations.
基金
This research is supported by the National Natural Science Foundation of China(19831070)
关键词
对称群
非线性准则
密码学函数
评价函数
cryptographic functions
nonlinearity criteria
symmetry group of a valuation
