Geodesic
On hardware and software implementation of arithmetic in finite fields of characteristic~7 for calculation of pairings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 3, pp. 75-111

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We study scheme (hardware) and program (software) methods of multiplication of polynomials over fields of characteristic 7 in order to apply them to parings based cryptographic protocols on hyperelliptic curves of genus three. We consider hardware and software implementations of arithmetic in $GF(7)$, $GF(7^2)$, $GF(7^n)$, $GF(7^{7n})$, and $GF(7^{14n})$ and estimate the complexity of corresponding schemes and programs. 
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     author = {S. B. Gashkov and A. A. Bolotov and A. A. Burtsev and S. Yu. Zhebet and A. B. Frolov},
     title = {On hardware and software implementation of arithmetic in finite fields of characteristic~7 for calculation of pairings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {75--111},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2009_15_3_a6/}
}
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S. B. Gashkov; A. A. Bolotov; A. A. Burtsev; S. Yu. Zhebet; A. B. Frolov. On hardware and software implementation of arithmetic in finite fields of characteristic~7 for calculation of pairings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 3, pp. 75-111. http://geodesic.mathdoc.fr/item/FPM_2009_15_3_a6/