Research On Zero-determinant Strategy Based On Multi-player Threshold Gam

Permutation polynomials over finite fields have a wide range of applications in areas such as cryptography,coding theory,sequences,and combinatorial mathematics.For instance,they play a pivotal role in constructing the S-box of the Advanced Encryption Standard(AES)algorithm.Moreover,the construction of some cryptographic functions such as Bent functions and functions with low differential uniformity are closely related to permutation polynomials over finite fields.Consequently,the construction of permutation polynomials over finite fields holds paramount theoretical significance and practical utility.This paper builds upon previous research to conduct a further exploration of the construction of permutation polynomials over finite fields.In the course of our investigation,we have obtained several permutation polynomials characterized by simple algebraic structures and introduced innovative approaches and perspectives for their construction.Specifically,this paper presents findings in the following five aspects:(1)In the finite field of odd characteristics,two new permutation quadrinomials with Niho exponents are constructed and proved to be mutually multiplicative inequivalent inequivalent.In addition,based on the existing literature on Niho exponents in even characteristics,corresponding Niho exponents type permutation polynomials were constructed in the finite field of odd characteristics,covering eleven types of results proposed by Gupta in Des.Codes Cryptogr.in 2020;(2)Four classes of new permutation quadrinomials have been constructed over the finite field Fp3n,with two classes constructed over finite fields with even characteristic and two classes over finite fields with odd characteristic;(3)Several types of permutation polynomials based on linearized polynomial structures,i.e.,with the form of(xpm-x+δ)s+L(x)are presented,and through the utilization of cyclic sets,new piecewise permutation polynomials and complete permutation polynomials are constructed using known permutation polynomials;(4)Necessary and sufficient conditions for Dickson polynomials and various other types of polynomials as n-cycle permutation polynomials have been characterized,and we give some specific constructions of low cycle permutation polynomials;(5)Several classes of bivariate permutation polynomials are constructed.