Some New Permutation Polynomials Having the Form 2 ( ) m x  x ï€«ï¤ t  x

Abstract

Permutation polynomials over finite field with character 2 have many applications on the block cipher. In this paper, we give some new permutation polynomials having the form x x x t m (   )  2 ï¤ over the finite field m F 2 2 , which firstly studied by Ziran Tu in 2015 by solving the equations directly. But the process is too complex. The key break through is the proper commutative diagrams are found for the new permutation polynomial, which make the process of proving the permutation property more simple. Our work also include some results found in the work of Ziran Tu.