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- W16976951 abstract "Based on a criterion of permutation polynomials of the form $x^rf(x^{frac{q-1}{m}})$ by Wan and Lidl (1991) and some very elementary techniques we show existence of permutation binomials of the following forms1 $x(x^{frac{2^n-1}{3}}+a) in mathbb{F}_{2^n}[x]$, for n>42 $x^{frac{2^{2n}-1}{2^{n}-1} + 1}+ax = x^{2^n+2} + ax in mathbb{F}_{2^{2n}}[x]$, for n≥3.In (i), we extend a result of Carlitz (1962) for even characteristic. Moreover we present the count of such permutation binomials when a is in a certain subfield of $mathbb{F}_{2^n}$. In (ii), we reprove, using much simpler technique, a recent result of Charpin and Kyureghyan (2008) and give the number of permutation binomials of this form. Finally, we discuss some cryptographic relevance of these results." @default.
- W16976951 created "2016-06-24" @default.
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- W16976951 date "2012-01-01" @default.
- W16976951 modified "2023-10-17" @default.
- W16976951 title "On Some Permutation Binomials of the Form $x^{frac{2^n-1}{k}+1} +ax$ over $mathbb{F}_{2^n}$ : Existence and Count" @default.
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- W16976951 doi "https://doi.org/10.1007/978-3-642-31662-3_17" @default.
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