Paper 2026/176

Differential Pattern Transition: Characterizing the Differential Behavior of AES-like Linear Layers

Abstract

This paper introduces a new cryptographic notion for diffusion matrices, termed the Differential Pattern Transition($\textsf{DPT}$). Building on this notion, we develop a systematic framework for describing the differential behavior of diffusion layers over multiple rounds in $\texttt{AES}$-like block ciphers. Specifically, the $\textsf{DPT}$ framework enables a finer-grained evaluation of diffusion strength against differential attacks, allowing distinctions even among matrices sharing the same branch number. Furthermore, the $\textsf{DPT}$ framework facilitates the classification of shuffle layers and assists in identifying permutation layers that maximize differential resistance. As a case study, we apply the $\textsf{DPT}$ framework to the diffusion matrices used in $\texttt{MIDORI}$, $\texttt{PRINCE}$, $\texttt{QARMA}$, and $\texttt{AES}$, as well as a lightweight MDS matrix proposed in [SS16]. The results show that $\textsf{DPT}$ provides both theoretical insights and practical guidance for the selection and design of diffusion and shuffle layers in secure and efficient block cipher constructions.