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<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.
Jun-ichi Yoshiki, Naofumi Takagi, Kazuyoshi Takagi, "A Fast Algorithm for Multiplicative Inversion in GF(2m) Using Normal Basis", IEEE Transactions on Computers, vol. 50, no. , pp. 394-398, May 2001, doi:10.1109/12.926155
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