Fast Multiplication on Elliptic Curves over Small Fields of Characteristic Two

The paper shows how Frobenius expansions can be used to speed up mul­tiplication of points on elliptic curves that are defined over very small fields of charac­teristic two. The Frobenius expansion algorithm is analyzed in theory and in practice. It can gain significant improvements in practical applica­tions. These curves are there­fore especially interesting for implementations of elliptic curve cryptosystems.