An application of the method of additive chains to inversion in finite fieldsстатья
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Аннотация:We obtain estimates of complexity and depth of Boolean inverter circuits in normal and polynomial bases of finite fields. In particular, we show that it is possible to construct a Boolean inverter circuit in the normal basis of the field GF(2n) whose complexity is at most (λ(n − 1) + (1 + o(1))λ(n)/λ(λ(n)))M(n) and the depth is at most (λ(n − 1) + 2)D(n), where M(n), D(n) are the complexity and the depth, respectively, of the circuits for multiplication in this basis and λ(n) = ⌊log2 n⌋.