ARX函数的两轮迭代线性化条件研究

Research on Two-iteration Linearization Conditions of ARX Function

含模加运算、循环移位运算和异或加运算的密码算法称为ARX型算法,3种运算的混合使用可以达到更好的扩散和混乱效果。为此,给出二元ARX函数的定义,研究其两轮迭代同时线性化的条件,利用统计分析方法得到线性化条件成立的元素个数的计算公式。分析两轮独立条件下得到的线性化条件成立的概率,发现利用统计分析的方法能够更准确地刻画线性化条件成立概率的影响因素,并且增加一个左右块变换不会对两轮ARX函数的线性化条件产生影响。

The cryptographic algorithm including modular addition operation （Addition）, rotation shift operation （Rotation） and XOR operation （XOR） is called ARX type algorithm. The mixed use of the 3 operations can achieve better diffusion and confusion effects. This paper defines the ARX function of two variables, researches on the simultaneous linearization condition of two iterations of the function. Using the method of statistic analysis, the computational formula of the element number for guaranteeing the linearization conditions is given. Analyzing the probability of the linearized condition establishment under the condition that the two iterations are independent,it is found that the method of statistic analysis more accurately describes the factors that affect the probability of the linearized condition. Moreover, the addition of a left and right block transform does not affect the linearization condition of the ARX function