【摘要】 研究一类重要的多输出布尔函数——弹性函数((n,m,1)-resilientfunctions)的构造与计数问题.弹性函数的一个重要作用是抵御密码体制中的信息泄露.为保证密码体制的安全性,要求弹性函数的数目必须足够多,因此,研究弹性函数的构造与计数问题是十分必要的.文中研究了弹性性t=1,n-m>t时,(n,m,1)-弹性函数的构造与计数问题.基于已有的n元平衡的1阶相关免疫函数的构造法,并利用弹性函数与0,1上多维空间的正交分划(一个正交矩阵组)之间的等价关系,构造了3类(n,m,1)-弹性函数,给出了(n,m,1)-弹性函数的一个计数下界.更多还原

【Abstract】 The resilient function is one of the multiple-output Boolean functions, An important work the resilient function has to do is to prevent the information eavesdropping. The more numbers of the resilient functions have the more safety the cryptographic system will be. On the other hand, construction, as well as enumeration in (n,m,1)-resilient functions, has to be paid more attention to. Construction and enumeration were studied when the order of resiliency was t=1,(n-m>)t, upon which, three classes of (n,m,1)-resilient functions, based on the construction of n-variables balanced correlation-immune functions of the first-order, and on the equivalence between resilient functions and large sets of orthogonal arrays(a group of orthogonal arrays), are implemented in the case of (n-)m>t=1. Also, an enumeration lower bound of a (n,m,1)-resilient function was presented.更多还原