基于Moore扫描曲线和DNA编码的混沌图像加密算法

Chaotic Image Encryption Algorithm Based on Moore Scanning Curve and DNA Encoding

摘要: 本文结合混沌系统，Moore扫描曲线与DNA编码的技术，提出一种新型灰度图像加密算法。该算法以二维Arnold混沌映射为核心，利用明文图像SHA-256哈希值动态修正映射参数与初始值，实现密钥与明文的高度关联；基于混沌序列驱动Moore扫描曲线生成自适应置乱索引，对图像像素完成空间位置置乱，有效打破像素间的空间邻域相关性；引入动态DNA编码运算规则，利用混沌序列随机确定DNA加法、减法、异或及同或运算的组合模式，对置乱图像实施扩散操作，实现像素灰度值的深度混淆。通过卡方检验、相关系数、信息熵、差分攻击等指标对算法性能进行详细分析验证，实验结果表明，该算法的密文图像灰度分布均匀，相邻像素相关系数、信息熵以及密钥与明文敏感性指标均很接近理论值，算法能有效抵御统计分析攻击、暴力攻击与差分攻击等。

Abstract: This paper integrates techniques of chaotic system, Moore scanning curve, and DNA encoding to propose a novel grayscale image encryption algorithm. The algorithm takes the two-dimensional Arnold chaotic map as its core, utilizing the SHA-256 hash value of the plain image to dynamically adjust the map’s parameters and initial values, thereby achieving a high degree of association between the key and the plain image. Based on chaotic sequences driving the Moore scanning curve, adaptive scrambling indices are generated to permute the spatial positions of image pixels, effectively disrupting the spatial neighborhood correlations among pixels. Dynamic DNA encoding and operation rules are introduced, where chaotic sequences randomly determine the combination modes of DNA addition, subtraction, XOR, and XNOR operations to perform diffusion operation on the scrambled image, achieving deep confusion of pixel gray values. The algorithm’s performance is thoroughly analyzed and validated through metrics such as chi-square test, correlation coefficient, information entropy, and differential attack and so on. Experimental results show that the cipher image produced by the encryption algorithm exhibits uniform grayscale distribution, with adjacent pixel correlation coefficients, information entropy, and key/plaintext sensitivity indices all closely approximating theoretical values. The algorithm effectively resists statistical analysis attacks, brute-force attacks, and differential attacks, etc.