基于广义Gray码变换和广义Arnold映射的彩色图像加密算法

Color Image Encryption Algorithm Based on Generalized Gray Code Transformation and Generalized Arnold Map

摘要: 本文通过结合混沌系统与数据编码，提出了一种新型彩色图像加密算法。该算法通过离散型广义Arnold映射对明文像素位置进行非线性置乱，破坏相邻像素相关性；引入广义Gray码变换对置乱后图像颜色分量值实施编码，初步隐藏视觉信息；利用连续型广义Arnold映射生成伪随机密钥流，对编码图像完成扩散运算，进一步破坏明文统计特征。加密算法融合了广义Gray码变换的局部混淆能力和广义Arnold映射的全局扩散特性，构建双重安全机制。一方面，离散型广义Arnold映射和广义Gray编码协同增强像素位置与灰度值的动态扰乱效果；另一方面，连续型广义Arnold映射扩展了加密算法的密钥空间。数值实验表明，该图像加密算法具有优良的加密性能，可以抵御蛮力攻击、统计分析攻击以及差分攻击等。

Abstract: The paper proposes a novel image encryption algorithm by integrating chaotic system with data coding. The algorithm employs a discrete generalized Arnold map to nonlinearly scramble plain image’s pixel positions, effectively disrupting adjacent pixel correlations. A generalized gray code transformation is introduced to perform encoding on color component values of the scrambled image, achieving preliminary visual information concealment. Subsequently, a continuous generalized Arnold map generates pseudo-random keystreams to execute diffusion operations on the encoded image, further eliminating statistical features of the plain image. Combining the local confusion capability of generalized gray code transformation with the global diffusion nature of generalized Arnold map, the encryption algorithm establishes a dual security mechanism. On the one hand, the collaborative effect of discrete generalized Arnold map and generalized gray coding enhances dynamic disruption of pixel positions and grayscale values; on the other hand, the continuous generalized Arnold map significantly expands the key space of the proposed encryption. Numerical experiments demonstrate that the proposed image encryption algorithm exhibits excellent performance and security, showing strong resistance against differential analysis attack, statistical attacks and brute-force attack, etc.