Burtsev, A. A.; Gashkov, I. B.; Gashkov, S. B. Complexity of Boolean schemes for arithmetic in some towers of finite fields. (Russian, English) Zbl 1150.06315 Vestn. Mosk. Univ., Ser. I 2006, No. 5, 10-16 (2006); translation in Mosc. Univ. Math. Bull. 61, No. 5, 9-14 (2006). In the paper it is proved that for any \(\epsilon>0\) and any \(m\), if \(n=m^s\) and \(s\geq s_\epsilon\), then in the field GF\((2^n)\) a basis can be taken for which scheme multiplication complexity is less than \(n^{1+\epsilon/2}\) and inversion complexity is less than \(n^{1+\epsilon}\). For some basis, when \(n=2\cdot 3^k\), complexity estimates \(n(\log_3 n)^{(\log_2\log_3n)/2+O(1)}\) for multiplication and estimates of the same order for inversion are obtained. Reviewer: V. G. Miladzhanov (Andizhan) Cited in 2 Documents MSC: 06E30 Boolean functions 94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010) Keywords:scheme complexity; multiplication; complexity inversion PDFBibTeX XMLCite \textit{A. A. Burtsev} et al., Vestn. Mosk. Univ., Ser. I 2006, No. 5, 10--16 (2006; Zbl 1150.06315); translation in Mosc. Univ. Math. Bull. 61, No. 5, 9--14 (2006)