Issue No.05 - May (2001 vol.50)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.926155
<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>
Finite field, finite field inversion, Fermat's theorem, normal basis.
Naofumi Takagi, Jun-ichi Yoshiki, Kazuyoshi Takagi, "A Fast Algorithm for Multiplicative Inversion in GF(2m) Using Normal Basis", IEEE Transactions on Computers, vol.50, no. 5, pp. 394-398, May 2001, doi:10.1109/12.926155