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**2024/187**

**Title:**

On the bijectivity of the map \chi

**Authors:**
Anna-Maurin Graner, Björn Kriepke, Lucas Krompholz, Gohar M. Kyureghyan

**Abstract:**

We prove that for n>1 the map \chi:\mathbb{F}_q^n \to \mathbb{F}_q^n, defined by y=\chi(x) with y_i = x_i + x_{i+2}\cdot(1+x_{i+1}) for 1\leq i \leq n, is bijective if and only if

q=2 and n is odd, as it was conjectured by Schoone and Daemen in 2023.

**ePrint:**
https://eprint.iacr.org/2024/187

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