一种(n+s,m,t+s)-Resilient函数的构造(英文)  

A Construction of (n+s,m,t+s)-Resilient Functions

作　　者：岳廷海[1] 陈鲁生[2] 符方伟[2] 

机构地区：[1]天津理工大学计算机科学与技术学院,天津300191 [2]南开大学数学科学学院,天津300071

出　　处：《南开大学学报（自然科学版）》2007年第6期21-27,共7页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported in part by the Natonal Natural Science Foundation of China (60172060)

摘　　要：首次给出一个从2^s个已知的（n，m，t）-resilient函数构造（n＋s，m，t＋s）-resilient函数的充分必要条件．它不仅提供了一种构造二元向量输出Resilient函数的方法，而且Resiliency的阶数和Vn的维数是同步增加的，以及Resiliency的阶数的增加速度比已知的构造方法更快．进一步讨论了利用此方法构造的（n＋s）个输入，m个输出函数的非线性度和传播特征以及在特殊情况下计算它们的代数次数，得了一些有应用价值的结果．最后给出一个例子来说明此种构造方法．For constructing （n＋s,m,t＋s）-resilient functions from 2^s known （n,m,t）-resilient functions, a necessary and sufficient condition is given firstly in this paper. Not only does it provide a construction technique for multiple output binary resilient functions, but also the order of resiliency and the dimension of Vn are increased synchronously, and the order of resiliency is increased more quickly than some previously known construction methods. Next the nonlinearity and propagation characteristics for （n＋s）-input, m-output functions constructed by this method are discussed and the algebraic degree for a special case is calculated. Some useful and important results are obtained. Finally, an example is given to illustrate this construction method.

关 键 词：代数次数 非线性度 传播准则 resilient函数 

分 类 号：TN918.1[电子电信—通信与信息系统]