(非)弱正则p值bent函数的间接构造

Secondary constructions of p-ary(non-)weakly regular bent functions

Bent函数在对称密码、序列设计、组合理论和编码理论等领域都有着重要的应用.基于已有的非直和与半直和构造研究方法,本文给出一类bent函数的间接构造.利用所得构造,通过选取合适的初始(向量)bent函数及其组合构造出高代数次数的(非)弱正则bent函数.更准确地,本文借助向量M-M(Maiorana-McFarland)类和PS(partial spread)类bent函数,给出了一些(弱)正则bent函数.特别地,给出了这些bent函数的对偶函数的显式表达式.进一步地,应用向量完美非线性(perfect nonlinear,PN)函数,生成了无限类非弱正则bent函数.

Bent functions can be used in many areas,such as symmetric cryptography,sequence design,and association schemes.In this paper,a generic secondary construction of bent functions from indirect sum and semidirect sum methods is presented.Our method can be used to construct high algebraic degree(non-)weakly regular bent functions by employing suitable initial(vectorial)bent functions or their combinations.More precisely,we present some classes of(weakly)regular bent functions by using vectorial M-M(Maiorana-Mc Farland)and PS(partial spread)bent functions,respectively.In particular,the explicit expressions for the dual of these(weakly)regular bent functions are obtained.Based on the vectorial perfect nonlinear(PN)functions,infinite families of non-weakly regular bent functions can also be produced.