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, 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