arXiv:2609.19548 · v3

A generalization of the map $χ$

首次提交 2026-09-17 09:17

版本更新 2026-11-10 10:51

雷达观测 2026-11-11 11:04

摘要

The mapping $ χ_n:\mathbb{F}_2^n \to \mathbb{F}_2^n$ defined by $y=χ_n(x)$ with $y_i = x_i + x_{i+1}x_{i+2} + x_{i+2}$, where the indices are computed modulo $n$, has been widely studied for its application in lightweight cryptography. In this paper, we generalize this mapping and completely characterize all these shift-invariant permutations of the form $y_i=x_{i+u}+x_{i+v}(x_{i+w}+a_i)$, where $0\le u, v, w<n$ and $a_i\in \mathbb{F}_2$, $1\le i\le n$. We also determine their compositional inverses explicitly.

作者备注：added a few remarks