ermutation polynomial which has attractive aspects and applications in both mathematics and engineering has been studied in this thesis . Applications of these special classes of polynomials in cryptography are the main motivation of this study . Hermit was the first who figure out the significance of permutation polynomials over the finite fields . After that , Dickson investigated the properties of permutation polynomials over finite fields seriously and released his fundamental results . More precisely , he found all the permutation polynomials up to the degree 6 in 1897 . But , there is some drawbacks with his classification and some researchers believed that the Dickson’s list is incomplete.
