m阶相关免疫函数的构造和计数

若布尔函数的输出不泄漏其输入值的有关信息,则称该函数是相关免疫的.这类函数在计算机保密应用中用途广泛.本文研究了m阶相关免疫函数的构造和计数问题,给出了两种新的构造方法.进一步,将这两种新构造方法与Seigenthaler,杨义先,Camion,Seberry以及温巧燕等人的构造方法进行了比较,证明了本文中的构造方法实际上推广了这些文献中的结论.利用本文中的构造方法,既可直接构造任意阶的相关免疫函数,又可根据已知的相关免疫函数来构造新的相关免疫函数.另外,基于新的构造方法,改进了m阶相关免疫的平衡函数的计数下界.

Construction and Enumeration of mth-Order Correlation Immune Functions

A Boolean function is said to be correlation immune if its output leaks no information about its input values.Such functions have extensive applications in computer security practices.This paper studies the construction and enumeration problem for mth-order correlation immune functions and presents two new construction methods.Furthermore,we compare new methods with Seigenthaler,Yang,Camion,Seberry,Wen et al's and show that new methods actually generalize relational conclusions in these references.Using new...