This paper proposes an improved Lorenz chaotic system and a secure and efficient image encryption method to enhance encryption effectiveness in encrypted images. The proposed improved Lorenz chaotic system addresses the problem of applying the Lorenz chaotic system to image encryption, resulting in weak chaotic characteristics and susceptibility to reconstruction. Dynamic analysis, sensitivity analysis, and randomness testing demonstrate that the improved Lorenz chaotic system exhibits hyperchaotic characteristics, with a maximum Lyapunov exponent of 2.9897. Based on the improved Lorenz chaotic system, this paper proposes an image encryption method that combines image pyramid structure permutation and Galois field diffusion. Unlike most of the current permutation methods limited to a single image layer, this paper proposes a multilayer permutation method based on the image pyramid structure to enhance the permutation effect of image encryption. Although diffusion based on Galois field multiplication operation is efficient and secure, it is less effective in encrypting pixel points with a pixel value of '0′. To address this issue, this paper incorporates DNA computing into diffusion based on Galois field operations, enabling even pure black images to achieve better encryption effectiveness. Experimental results demonstrate that the encryption method proposed in this paper effectively conceals information contained in the plain image. The global Shannon entropy of the encrypted Lena image can reach 7.9975, indicating a high level of randomness and complexity. Notably, even a slight alteration, such as changing a single pixel, results in a significant divergence, with 99.6307 % of the cipher image's pixels being distinct. Moreover, it effectively withstands analysis from various attacks. Therefore, the encryption method proposed in this paper can be effectively applied to grayscale image encryption scenarios requiring relatively high security and encryption efficiency, such as remote sensing image encryption and personal privacy image encryption.

中文翻译：

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一种基于改进洛伦兹混沌系统和伽罗瓦域的图像加密方法

本文提出了一种改进的洛伦兹混沌系统和一种安全高效的图像加密方法，以增强加密图像的加密效果。所提出的改进洛伦兹混沌系统解决了将洛伦兹混沌系统应用于图像加密时导致的混沌特性较弱且易重构的问题。动力学分析、敏感性分析和随机性检验表明，改进后的Lorenz混沌系统表现出超混沌特性，最大Lyapunov指数为2.9897。基于改进的洛伦兹混沌系统，提出一种结合图像金字塔结构排列和伽罗瓦场扩散的图像加密方法。与目前大多数排列方法仅限于单个图像层不同，本文提出一种基于图像金字塔结构的多层排列方法，以增强图像加密的排列效果。虽然基于伽罗瓦域乘运算的扩散是高效且安全的，但它在加密像素值为“0”的像素点时效果较差。针对这一问题，本文将DNA计算融入基于伽罗瓦域运算的扩散中，即使是纯黑色图像也能获得更好的加密效果。实验结果表明，本文提出的加密方法有效地隐藏了明文图像中包含的信息。加密Lena图像的全局香农熵可以达到7.9975，表明具有很高的随机性和复杂性。值得注意的是，即使是轻微的改变，例如改变单个像素，也会导致显着的差异，密码图像的 99.6307 % 的像素是不同的。此外，它还能有效抵御各种攻击的分析。因此，本文提出的加密方法可以有效应用于对安全性和加密效率要求较高的灰度图像加密场景，例如遥感图像加密、个人隐私图像加密等。