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

This paper introduces a new cryptographic notion for diffusion matrices, termed the Differential Pattern Transition (DPT). Building on this notion, we develop a systematic framework for describing the differential behavior of diffusion layers over multiple rounds in AES-like block ciphers. Specifically, the 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 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 DPT framework to the diffusion matrices used in MIDORI, PRINCE, QARMA, and AES, as well as a lightweight MDS matrix proposed in [SS16]. The results show that 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.