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An application of the method of additive chains to inversion in finite fields
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S. B. Gashkov
Published/Copyright:
December 1, 2006
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) = ⌊log2n⌋.
Published Online: 2006-12-01
Published in Print: 2006-12-01
Copyright 2006, Walter de Gruyter
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Articles in the same Issue
- On transition of distributions of sums of independent identically distributed random variables from one lattice to another in the generalised allocation scheme
- A Poisson limit theorem for a two-stage equiprobable scheme of allocating particles into cells
- Some relations between discrete statistical problems and properties of probability measures on topological spaces
- Large deviations for the number of trees of a given size and for the maximum size of a tree in a random forest
- On the structure of equationally closed classes
- On circuits of functional elements of finite depth of branching
- Examples of α-complete systems of k-valued logic for k = 3, 4
- An application of the method of additive chains to inversion in finite fields
- Schemes of public distribution of a key based on a noncommutative operation
