**On permutation polynomials EA-equivalent to the inverse function over $GF(2^n)$**

*Yongqiang Li and Mingsheng Wang*

**Abstract: **It is proved that there does not exist a linearized polynomial
$L(x)\in\mathbb{F}_{2^n}[x]$ such that $x^{-1}+L(x)$ is a
permutation on $\mathbb{F}_{2^n}$ when $n\geq5$, which is proposed
as a conjecture in \cite{li}. As a consequence, a permutation is
EA-equivalent to the inverse function over $\mathbb{F}_{2^n}$ if and
only if it is affine equivalent to it when $n\geq 5$.

**Category / Keywords: **secret-key cryptography / Inverse function, EA-equivalence, Permutation polynomial, S-box, Kloosterman sums

**Date: **received 10 Nov 2010

**Contact author: **liyongqiang at is iscas ac cn

**Available format(s): **PDF | BibTeX Citation

**Version: **20101110:234248 (All versions of this report)

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