On the bijectivity of the map $\chi$

Anna-Maurin Graner; Björn Kriepke; Lucas Krompholz; Gohar M. Kyureghyan

Paper 2024/187

On the bijectivity of the map $\chi$

Anna-Maurin Graner

, University of Rostock

Björn Kriepke

, University of Rostock

Lucas Krompholz

, University of Rostock

Gohar M. Kyureghyan

, University of Rostock

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.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: chi-map bijectivity differential map rank
Contact author(s): anna-maurin graner @ uni-rostock de
bjoern kriepke @ uni-rostock de
lucas krompholz @ uni-rostock de
gohar kyureghyan @ uni-rostock de
History: 2024-02-09: approved; 2024-02-07: received; See all versions
Short URL: https://ia.cr/2024/187
License: CC BY

BibTeX

@misc{cryptoeprint:2024/187,
      author = {Anna-Maurin Graner and Björn Kriepke and Lucas Krompholz and Gohar M. Kyureghyan},
      title = {On the bijectivity of the map $\chi$},
      howpublished = {Cryptology ePrint Archive, Paper 2024/187},
      year = {2024},
      note = {\url{https://eprint.iacr.org/2024/187}},
      url = {https://eprint.iacr.org/2024/187}
}