## Cryptology ePrint Archive: Report 2010/573

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