Permutation Properties of Chebyshev Polynomials of the Second Kind over a Finite Field

A class of permutation polynomials amongst the Chebyshev polynomials of the second kind has been described by the second author. Cohen has shown that in prime fields of odd order or their degree 2 extensions these are the only examples of such polynomials. In this paper, the authors present new classes of such permutation polynomials in fields of characteristic ≤ 5. The results are extended to fields of characceristic 2, a case not considered previously.