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

Abstract

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.