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Permutation polynomials EA-equivalent to the inverse function over $$\mathrm{GF}(2^n)$$. (English) Zbl 1251.94032
Summary: In this paper, a proof is given 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 $$n \geq 5$$, which was posed as a conjecture in [the authors, Des. Codes Cryptography 58, No. 3, 259–269 (2011; Zbl 1216.94049)]. As a consequence of this result, if a permutation is EA-equivalent to the inverse function over $$\mathbb F_{2^{n}}$$, then it is affine equivalent to the inverse mapping when $$n\geq 5$$.

##### MSC:
 94A60 Cryptography 06E30 Boolean functions 11T06 Polynomials over finite fields
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##### References:
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