广义部分Bent函数和广义Bent函数的关系

Bent函数是一类特殊的布尔函数，因其非线性性和稳定性在密码学和通信等领域有很重要的应用，但它们数量少，不平衡且无相关免疫性，为了弥补Bent函数的不足，Claud Carlet提出了部分Bent函数的概念，部分Bent函数是包含Bent函数的更大的函数类，后来，人们又将这两种函数概念先后都拓广到了环zm^n(m为正整数）上，分别被称为zm^n上的广义Bent函数和广义部分Bent函数，本文利用zp^n(p为素数）上广义部分Bent函数的Chrestenson循环谱特征讨论了zp^n上的广义部分Bent函数和广义Bent函数之间的关系，给出了这两种函数之间的函数关系式和谱值关系式。

THE RELATION BETWEEN GENERALIZED PARTIALLY BENT AND GENERALIZED BENT FUNCTIONS

Bent functions,a special class of Boolean functions,are of great use in the fields of cryptography and communication due to their nonlinear and stable properties.But their number is rare and they are neither balanced and nor correlation-immune.Partially Bent functions containing Bent functions are a larger class of Boolean functions presented by Claud Carlet to remedy the defects of Bent functions.Now concepts of Bent and partially Bent functions have been extended onto Ring znm(m is a positive integer) called generalized Bent and generalized partially Bent functions on znm.In this paper,the relation between generalized partially Bent and generalized Bent functions on znp(p is prime) is studied according to the Chrestenson cyclic spectral characteristic of generalized partially Bent functions on znp.The function and the spectral relation formulas between them are presented.