Abstract: S-function, proposed by Nicky Mouha, is the function that can calculate the i-th output bit using only the inputs of the i-th bit position and a finite state S[i]. Using S-function can analyse the property of modulo addition and XOR effectively. To study the property of modulo addition of MIX function which is the core component of Skein, this paper transforms MIX function to the S-function, then gives a method of accurately calculating the modulo additive probability of MIX function, and explains why this result is more accurate than the result which is multiplication of differential probability of each component in theory.

Key words: MIX function, S-function, additive differential probability

摘要： S函数由Nicky Mouha提出，是只需输入字的第i个bit和第i个运算状态S[i]即可计算出输出字的第i个bit的一类函数，利用其可以有效研究模加、异或运算的性质。为研究Skein算法的核心部件MIX函数的模加差分性质，将MIX函数转化为S函数的形式，给出了一种精确计算MIX函数模加差分概率的方法，通过理论分析，说明相对于通过求各运算部件概率之积以获得整体函数的概率的一般方法，利用S函数的方法得到的结果更为精确。

关键词: MIX函数, S函数, 模加差分概率