### 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 $n\geq 5$.

Available format(s)
Category
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Inverse functionEA-equivalencePermutation polynomialS-boxKloosterman sums
Contact author(s)
liyongqiang @ is iscas ac cn
History
Short URL
https://ia.cr/2010/573

CC BY

BibTeX

@misc{cryptoeprint:2010/573,
author = {Yongqiang Li and Mingsheng Wang},
title = {On permutation polynomials EA-equivalent to the inverse function over $GF(2^n)$},
howpublished = {Cryptology ePrint Archive, Paper 2010/573},
year = {2010},
note = {\url{https://eprint.iacr.org/2010/573}},
url = {https://eprint.iacr.org/2010/573}
}

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