A generalization of the map $χ$

2026-09-16

AI Summary

本文研究了映射χ_n的推广，通过完全刻画所有代数次数为2的移位不变置换，解决了轻量级密码学中的应用问题。

Abstract

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 algebraic degree $2$.

Problem

• generalization
• mapping
• shift-invariant permutations
• algebraic degree

Innovation

• generalization
• shift-invariant permutations
• algebraic degree 2