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- W2950318849 abstract "Carlitz rank and index are two important measures for the complexity of a permutation polynomial $f(x)$ over the finite field $F_q$. In particular, for cryptographic applications we need both, a high Carlitz rank and a high index. In this article we study the relationship between Carlitz rank $Crk(f)$ and index $Ind(f)$. More precisely, if the permutation polynomial is neither close to a polynomial of the form $ax$ nor a rational function of the form $ax^{-1}$, then we show that $Crk(f)>q- max{3 Ind(f),(3q)^{1/2}}$. Moreover we show that the permutation polynomial which represents the discrete logarithm guarantees both a large index and a large Carlitz rank." @default.
- W2950318849 created "2019-06-27" @default.
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- W2950318849 date "2016-11-19" @default.
- W2950318849 modified "2023-09-27" @default.
- W2950318849 title "Carlitz Rank and Index of Permutation Polynomials" @default.
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