基于新型二维超混沌映射与动态DNA编码的卫星图像加密算法

Satellite Image Encryption Algorithm Based on Novel Two-Dimensional Hyperchaotic Mapping and Dynamic DNA Coding

摘要: 针对卫星遥感图像数据量大、空间相关性强且实时传输安全性要求高的特点，提出一种基于新型二维超混沌映射与动态DNA编码的加密算法。首先，构造一种具有双正李雅普诺夫指数和全区域混沌特性的新型二维超混沌指数耦合迭代映射(2D-HEICM)，并利用SHA-256生成与明文深度关联的初始密钥；其次，通过混沌序列驱动行列循环移位实现空间置乱；最后，设计一种极速动态DNA扩散策略，利用位运算和矩阵寻址实现DNA规则的动态切换与并行扩散，克服了传统DNA加密逐像素处理的效率瓶颈。实验分析表明，该算法密文信息熵逼近理论极限8，相邻像素相关系数降至10⁻²量级。在保持极高安全强度的同时，算法处理512 × 512图像耗时仅需约0.08秒，能够满足卫星图像实时安全传输的需求。

Abstract: Aiming at the characteristics of large data volume, strong spatial correlation, and high real-time security requirements for satellite remote sensing images, a satellite image encryption algorithm based on a novel 2nd-order hyperchaotic map and dynamic DNA coding is proposed. Firstly, a novel 2-Dimensional Hyperchaotic Exponentially-Coupled Iterative Map (2D-HEICM) with double positive Lyapunov exponents and full-mapping chaotic properties is constructed, and an initial secret key deeply associated with the plaintext is generated using the SHA-256 algorithm. Secondly, row-column circular shifting driven by chaotic sequences is utilized to achieve spatial confusion. Finally, a high-speed dynamic DNA diffusion strategy is designed. By leveraging bit-wise operations and matrix indexing, dynamic switching of DNA rules and parallel diffusion are achieved, effectively overcoming the efficiency bottleneck of pixel-by-pixel string conversion in traditional DNA encryption schemes. Experimental analysis shows that the information entropy of the ciphertext generated by the proposed algorithm approaches the theoretical limit of 8, and the correlation coefficients between adjacent pixels are reduced to the magnitude of 10⁻². While maintaining extremely high security strength, the algorithm requires only approximately 0.08 seconds to encrypt a 512 × 512 image, which can well meet the real-time secure transmission requirements of satellite observation data.