基于HLSE混沌映射和改进Zigzag变换的图像加密算法

Image Encryption Algorithm Based on HLSE Chaotic Map and Improved Zigzag Transform

摘要: 针对现有图像加密算法中一维混沌映射存在的混沌范围有限、易出现周期窗口以及标准Zigzag变换置乱效果不佳等问题，本文提出了一种基于HLSE (Hybrid Logistic-Sine-Exponential)混沌映射和改进Zigzag变换的图像加密算法。首先，设计了一种新的一维HLSE混沌映射，该映射通过结合Logistic映射、Sine映射和指数函数，相比于传统的Logistic映射和Sine映射，展现出更大的混沌范围、更复杂的动态行为和对初始值的强敏感性。其次，对标准Zigzag变换进行了改进，通过引入分两次扫描并将结果交叉排列的方式，有效克服了原变换置乱不充分、部分像素位置可能不变的缺陷，增强了置乱的均匀性和彻底性。加密算法利用SHA-256算法根据明文图像生成HLSE混沌映射的初始值和控制参数，确保了密钥的敏感性和与明文的关联性。加密过程包括改进Zigzag置乱、基于混沌序列的索引置乱以及异或扩散操作。实验结果和安全性分析表明，该算法具有足够大的密钥空间、高度的密钥敏感性，能够有效抵抗统计攻击和差分攻击，同时对数据裁剪和噪声污染也表现出较好的鲁棒性，且具有较高的加密效率。

Abstract: To address the issues that existing one-dimensional (1D) chaotic maps in image encryption algorithms suffer from limited chaotic range, proneness to periodic windows, and the unsatisfactory scrambling effect of the standard Zigzag transform, this paper proposes an image encryption algorithm based on an HLSE (Hybrid Logistic-Sine-Exponential) chaotic map and an improved Zigzag transform. Firstly, a novel 1D HLSE chaotic map is designed. By combining the Logistic map, Sine map, and exponential function, this map exhibits a larger chaotic range, more complex dynamical behavior, and strong sensitivity to initial values compared to traditional Logistic and Sine maps. Secondly, the standard Zigzag transform is improved. By introducing a two-pass scanning method and cross-arranging the results, it effectively overcomes the deficiencies of the original transform, such as insufficient scrambling and the possibility of some pixel positions remaining unchanged, thereby enhancing the uniformity and thoroughness of the scrambling. The encryption algorithm utilizes the SHA-256 algorithm to generate the initial values and control parameters for the HLSE chaotic map based on the plaintext image, ensuring the sensitivity of the key and its correlation with the plaintext. The encryption process includes improved Zigzag scrambling, chaotic sequence-based index scrambling, and XOR diffusion operations. Experimental results and security analysis demonstrate that the proposed algorithm possesses a sufficiently large key space and high key sensitivity, can effectively resist statistical attacks and differential attacks, and also exhibits good robustness against data cropping and noise pollution, while maintaining high encryption efficiency.