对称布尔函数的算术相关函数

Arithmetic correlations of symmetric Boolean function

算术相关函数是最近提出的一种研究布尔函数密码学性质的方法,该方法通过定义多元2-adic数上的加法和乘法运算,构建一种新的环结构,实现对经典相关函数的带进位计算的模拟。首先介绍了算术相关函数的定义,并针对具有良好密码学性质的对称布尔函数讨论了其算术相关函数的性质和取值,最后利用对称布尔函数的实值对称性证明了对称布尔函数的算术自相关函数也是一个与向量的重量有关的实值对称函数,至多是n+1值的。

The arithmetic correlation function is a new method for studying the cryptographic properties of Boolean functions. Based on the basic definitions of addition and multiplication of muhi-2-adic integer, the study constructed a new algebraic ring and realized the arithmetic or ＂with-carry＂ analogs of classic correlation functions. In this paper the definition of arithmetic autocorrelation function was introduced. The arithmetic correlation value of symmetric Boolean functions was studied. The results show that the arithmetic autocorrelation function of symmetric Boolean functions is a real symmetric function with at most n ＋ 1 values.