Paper 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 $n\geq 5$.

Metadata
Available format(s)
PDF
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
2010-11-10: received
Short URL
https://ia.cr/2010/573
License
Creative Commons Attribution
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},
      url = {https://eprint.iacr.org/2010/573}
}
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