An efficient exponentiation algorithm in GF(2(m)) using Euclidean inversion

We introduce a new type of exponentiation algorithm in GF(2(m)) using Euclidean inversion. Our approach is based on the fact that Euclidean inversion cost much less logic gates than ordinary multiplication in GF(2(m)). By applying signed binary form of the exponent instead of classic binary form, the proposed algorithm can reduce the number of operations further compared with the classic algorithms.