Geodesic
The complexity and depth of Boolean circuits for multiplication and inversion in some fields $GF(2^n)$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2009), pp. 3-7 
S. B. Gashkov; I. S. Sergeev. The complexity and depth of Boolean circuits for multiplication and inversion in some fields $GF(2^n)$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2009), pp. 3-7. http://geodesic.mathdoc.fr/item/VMUMM_2009_4_a0/
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     author = {S. B. Gashkov and I. S. Sergeev},
     title = {The complexity and depth of {Boolean} circuits for multiplication and inversion in some fields $GF(2^n)$},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
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     year = {2009},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2009_4_a0/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $n=(p-1)\cdot p^k,$ where $p$ is a prime number such that $2$ is a primitive root modulo $p$, $2^{p-1}-1$ is not divided by $p^2$. For a standard basis of the field $GF(2^n)$, a multiplier of complexity $ O(\log \log p)n\log n\log\log_p n$ and an invertor of complexity $ O(\log p\log\log p)n\log n\log\log_p n$ are constructed. In particular, in the case $p=3$ the upper bound $$ 5\frac{5}{8}n\log_3 n\log_2\log_3 n+O(n\log n) $$ for the multiplication complexity and the asymptotically $2,5$ times greater bound for the inversion complexity are obtained.