Geodesic
Complexity of computation in finite fields
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 4, pp. 95-131

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We give a review of some works about the complexity of implementation of arithmetic operations in finite fields by Boolean circuits. 
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S. B. Gashkov; I. S. Sergeev. Complexity of computation in finite fields. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 4, pp. 95-131. http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a5/