New Kloosterman sums identities over F2m for all m

Recently, Shin and Sung found new identities for Kloosterman sums over F2m with odd m. They posed the question whether similar results could be obtained for even m. In this paper, we will give a positive answer to this question. We will present new results that hold for any m and include as special cases the results of Shin and Sung in the case where m is odd