The Arnold Cat Map (ACM) is a popular chaotic map used in image encryption. Chaotic maps are known for their sensitivity to initial conditions and their ability to mix, or rearrange, pixels. However, ACM is periodic, and the period is relatively short. This periodicity decreases the effective key space for a cryptosystem. Further, ACM can only be performed on square matrices. For non-square images, this issue can be solved by performing ACM on multiple square partitions of the image. If these partitions overlap, the periodicity will greatly increase. The resulting system will be referred to as overlapping ACM or OACM. This paper will cover the implementation and periodicity analysis for these overlapping systems, which previous papers involving similar overlapping block partitions did not. Viewing OACM as a scan as opposed to a map allows for faster implementation and period analysis.

翻译：阿诺德猫映射（ACM）是一种在图像加密中广泛应用的混沌映射。混沌映射因其对初始条件的敏感性以及混合（即重排）像素的能力而著称。然而，ACM具有周期性且周期相对较短，这降低了密码系统的有效密钥空间。此外，ACM仅适用于方阵图像。对于非方阵图像，可通过将图像划分为多个方形分块来解决该问题。若这些分块相互重叠，则周期性将显著增强。由此产生的系统称为重叠阿诺德猫映射（OACM）。本文旨在涵盖这些重叠系统的实现与周期性分析，而此前涉及类似重叠分块的研究均未涉及此内容。将OACM视为一种扫描模式而非映射，可加速实现并简化周期分析。