<p><b>Abstract</b>—A fast algorithm for multiplicative inversion in <tmath>$GF(2^m)$</tmath> using normal basis is proposed. It is an improvement on those proposed by Itoh and Tsujii and by Chang et al., which are based on Fermat's Theorem and require <tmath>$O(\log m)$</tmath> multiplications. The number of multiplications is reduced by decomposing <tmath>$m-1$</tmath> into several factors and a small remainder.</p>