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On subspaces of Kloosterman zeros and permutations of the form $L 1(x^{-1})+L 2(x)$ by Göloğlu, Faruk; Kölsch, Lukas; Kyureghyan, Gohar; Perrin, Léo is a scholarly article available to read on EtoBox.

What is On subspaces of Kloosterman zeros and permutations of the form $L 1(x^{-1})+L 2(x)$ about?

Permutations of the form $F=L_1(x^{-1})+L_2(x)$ with linear functions $L_1,L_2$ are closely related to several interesting questions regarding CCZ-equivalence and EA-equivalence of the inverse function. In this paper, we show that $F$ cannot be a permutation if the kernel of $L_1$ or $L_2$ is too large. A key step of the proof is a new result on the maximal size of a subspace of $\mathbb{F}_{2^n}$ that contains only Kloosterman zeros, i.e. a subspace $V$ such that $K_n(v)=0$ for all $v \in V$ where $K_n(v)$ denotes the Kloosterman sum of $v$.}

Author

Göloğlu, Faruk; Kölsch, Lukas; Kyureghyan, Gohar; Perrin, Léo

Published

2020

Language

EN