基于压缩感知和动态DNA编码的图像加密算法

An Image Encryption Algorithm Based on Compressed Sensing and Dynamic DNA Coding

摘要: 针对图像在传输过程中面临的安全性问题，提出了一种基于混沌系统、压缩感知与动态DNA编码相结合的图像加密方案。首先，对原始图像进行二维离散余弦变换(DCT)实现稀疏表示，利用Logistic混沌映射生成的测量矩阵完成二维压缩感知测量，在实现数据压缩的同时引入初步加密。随后，采用Zigzag进行全局索引置乱，有效破坏像素间相关性；再经非线性映射完成量化，并结合高维混沌系统生成的混沌序列对其进行扩散。进一步地，引入基于Logistic混沌映射与四维超混沌系统的动态DNA编码机制，对加密图像进行DNA编码、DNA运算及跨块级联扩散，有效增强密钥空间和扩散性能。最后，通过加密的逆过程以及重构算法得到重构图像。实验结果表明，该方案在保证较高压缩效率和良好解密质量的同时，复杂度较高，加密效果好，具有较强的安全性。

Abstract: To address the issues of security and limited bandwidth during image transmission, an image encryption scheme integrating a chaotic system, compressive sensing, and dynamic DNA coding is proposed. First, the original image is sparsely represented using a two-dimensional discrete cosine transform (DCT). A measurement matrix generated by the Logistic chaotic map is then employed to perform two-dimensional compressive sensing measurements, achieving data compression while introducing preliminary encryption. Subsequently, a zigzag-based global index scrambling strategy is applied to effectively disrupt inter-pixel correlations. The measured data are then quantized through a nonlinear mapping, followed by diffusion using chaotic sequences generated by a high-dimensional chaotic system. Furthermore, a dynamic DNA coding mechanism based on the Logistic chaotic map and a four-dimensional hyperchaotic system is introduced. The encrypted image undergoes DNA encoding, DNA operations, and inter-block cascading diffusion, significantly enhancing the key space and diffusion performance. Finally, the reconstructed image is obtained through the inverse encryption process combined with a reconstruction algorithm. Experimental results demonstrate that the proposed scheme achieves high compression efficiency and satisfactory decryption quality, while exhibiting strong encryption performance, high computational complexity, and robust security.