Some Classes Of Permutation Polynomials With The Form(x^pm-x+δ)^s₁+(x^pm-x-δ)^s₂+ L（x）

In recent decades,with the advent of computer era,people’s awareness of infor-mation security has been gradually strengthened,so data security has become a hot topic.Permutation polynomial on the finite field is always studied,since it plays an important role in the encryption algorithm.Let Fq be a finite field of q elements,a polynomial f ∈ Fg[χ]is called a permutation polynomial(PP)if its associated map-ping f:c→ f(c)from lFq to itself is a bijection.In this paper,we study permutation polynomials of the form(χpm-χ + δ)S1 +(χpm-χ + δ)s2 + L(x)over Fpn with odd characteristic.In the past,researchers investigated permutation polynomials of the form(χpi-χ + δ)s + χ.In 2017,[1]constructed permutation polynomials of the form(χpi-χ + δ)s3 +(χpi-χ + δ)S2 + χ,where pis even.Inspired by this,we obtain some new classes permutation polynomials of the form(χpm-χ + δ)s1 +(χpm-χ + δ)S2 + χ with odd p.This article introduces the background and significance of permutation polynomi-als in the first part.In the second part,some preliminaries are proposed.In the third part,we construst two classes of permutation polynomials over F2m and F3m.Using some special properties of s1 and s2,the problem of investigating permutation polynomial of f(χ)=(χpm-χ+δ)s1 +(χpm-χ+δ)s2+L(χ)is transformed to that of investigating permutation polynomial of the form(χpm-χ +δ + L(χ).At the end of the article,we give four classes of new permutation polynomials.In the proof,the properties of the linearized polynomial and trace functions are used.We also use the method which is similar to polar coordinate decomposition in the finite field.