Enumetate Plateaued Functions From Dillon Exponents

The construction of cryptographic function needs to meet the requirements of many aspects,such as high nonlinearity,avalanche criterion,balance,high correlation immunity order,etc.Bent function is a cryptographic function with the highest degree of nonlinearity.On the basis of Bent function,scholars have further studied partial Bent function,semi-Bent function and even Plateaued function which is to be studied in this paper.This paper mainly studies the Dillon type Plateaued function and determines the number of such type functions.In this paper,we first study the Walsh transformation of monomial Dillon type function Tr(ax2m-1)and binomial Dillon type function Tr(ax2m-1)+Tr(?x22m-1/3),and completely determine the number of Plateaued functions.The relation between the Bent property and the exponential sum of the binomial functions of Mesnager and the binomial Dillon type functions Tr1m(axq-1+bwx3(q-1)of coefficients in the extended domain is further studied.Finally,we study the semi-Bent property of the function yTr1n((a+b)xq-1)+Tr1n(axq-1)and give the number of the semi-Bent function.