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- W4387294590 abstract "In 1953, Carlitz~cite{Car53} showed that all permutation polynomials over $F_q$, where $q>2$ is a power of a prime, are generated by the special permutation polynomials $x^{q-2}$ (the inversion) and $ ax+b$ (affine functions, where $0neq a, bin F_q$). Recently, Nikova, Nikov and Rijmen~cite{NNR19} proposed an algorithm (NNR) to find a decomposition of the inverse function in quadratics, and computationally covered all dimensions $nleq 16$. Petrides~cite{P23} found a class of integers for which it is easy to decompose the inverse into quadratics, and improved the NNR algorithm, thereby extending the computation up to $nleq 32$. Here, we extend Petrides' result, as well as we propose a number theoretical approach, which allows us to cover easily all (surely, odd) exponents up to~$250$, at least." @default.
- W4387294590 created "2023-10-03" @default.
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- W4387294590 date "2023-09-29" @default.
- W4387294590 modified "2023-10-04" @default.
- W4387294590 title "Representing the inverse map as a composition of quadratics in a finite field of characteristic $2$" @default.
- W4387294590 doi "https://doi.org/10.48550/arxiv.2309.17424" @default.
- W4387294590 hasPublicationYear "2023" @default.
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