Chemical Engineering Department, University of California, Santa Barbara, Santa Barbara, CA, United States of America.
PLoS One. 2024 Aug 12;19(8):e0303589. doi: 10.1371/journal.pone.0303589. eCollection 2024.
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 permute, or rearrange, pixels. However, ACM is periodic, and its period is relatively short. This periodicity decreases the effective key-space and security of a cryptosystem using ACM. Further, ACM is typically only able to be performed on square images. To solve the low periodicity and typical limitation to square images, this paper proposes performing ACM on overlapping square partitions which cover the entirety of an image. The presence of overlap results in a greatly increased image period. The resulting system will be referred to as overlapping ACM or OACM. Several papers have already discussed systems involving overlapping ACM. However, they did not discuss the implementation or periodicity of such a system in detail. This paper does cover the implementation and periodicity analysis of OACM and proposes a simple symmetric encryption system which uses OACM. The proposed encryption system is not as sophisticated or secure as other modern encryption schemes, since it is mainly intended as an initial test of OACM's utility. Histogram and sensitivity analyses did however indicate a level of security against various cryptographic attacks, and OACM performed reasonably in both the permutation and diffusion stages of the cryptosystem.
阿诺德猫映射（ACM）是一种常用于图像加密的流行混沌映射。混沌映射以其对初始条件的敏感性和对像素的排列或重排能力而闻名。然而，ACM 是周期性的，其周期相对较短。这种周期性降低了使用 ACM 的密码系统的有效密钥空间和安全性。此外，ACM 通常只能在正方形图像上执行。为了解决低周期性和典型的正方形图像限制问题，本文提出在覆盖图像全部的重叠正方形分区上执行 ACM。重叠的存在导致图像周期大大增加。由此产生的系统将被称为重叠 ACM 或 OACM。已经有几篇论文讨论了涉及重叠 ACM 的系统。然而，它们没有详细讨论这样的系统的实现或周期性。本文确实涵盖了 OACM 的实现和周期性分析，并提出了一种使用 OACM 的简单对称加密系统。所提出的加密系统不如其他现代加密方案复杂或安全，因为它主要是作为 OACM 的效用的初步测试。然而，直方图和敏感性分析表明，该系统具有针对各种密码攻击的一定安全性，并且 OACM 在密码系统的排列和扩散阶段表现合理。
