International Association
for Cryptologic Research

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.