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Algebraic Structure of the Iterates of $\chi$

Authors:
Björn Kriepke , University of Rostock
Gohar Kyureghyan , University of Rostock
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DOI: 10.1007/978-3-031-68385-5_13 (login may be required)
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Presentation: Slides
Conference: CRYPTO 2024
Abstract: We consider the map $\chi:\F_2^n\to\F_2^n$ for $n$ odd given by $y=\chi(x)$ with $y_i=x_i+x_{i+2}(1+x_{i+1})$, where the indices are computed modulo $n$. We suggest a generalization of the map $\chi$ which we call generalized $\chi$-maps. We show that these maps form an abelian group which is isomorphic to the group of units in $\F_2[X]/(X^{(n+1)/2})$. Using this isomorphism we easily obtain closed-form expressions for iterates of $\chi$ and explain their properties.
BibTeX
@inproceedings{crypto-2024-34145,
  title={Algebraic Structure of the Iterates of $\chi$},
  publisher={Springer-Verlag},
  doi={10.1007/978-3-031-68385-5_13},
  author={Björn Kriepke and Gohar Kyureghyan},
  year=2024
}