Constructions Of New Permutation Polynomials Over Finite Fields

Permutation polynomials have important applications in distinct domains including cryptography,coding theory and sequence design.Constructing new permutation polynomials over finite fields is of great significance to current cryptography and information security.In this thesis,we discuss the constructions of new permutation polynomials over the finite fields with odd prime characteristic and construct some new permutation polynomials in the form of((xp~m-x)k+ δ)s+ axp~m+ bx and((xp~m-ax)k+ δ)s+ xp~m+ bx based on the AGW criterion.We propose some new permutation polynomials over Fpdmby trying different types of exponents s and distinct parameters a,b,k.We get a suitable commutative graph and find a polynomial g(u)over the small sets according to the AGW criterion,then using the equivalence relationship between f(x)is permutation polynomial and g(u)is bijective,to verify the proposed new permutation polynomial by both the piecewise method and the unique solution method.This thesis obtains more new permutation polynomials over finite fields by adding parameters a,b,k.The permutation polynomials with parameters a,b are better than the permutation polynomials without parameters.New constructing method in this thesis can generalize the existing results,and can easily explain some existed permutation polynomials.Furthermore,the verifying process of new method is more concise.