Sun Chunyang, Wang Erfu, Zhao Bing
Electronic Engineering College, Heilongjiang University, Harbin 150080, China.
Entropy (Basel). 2021 Feb 27;23(3):291. doi: 10.3390/e23030291.
Digital images can be large in size and contain sensitive information that needs protection. Compression using compressed sensing performs well, but the measurement matrix directly affects the signal compression and reconstruction performance. The good cryptographic characteristics of chaotic systems mean that using one to construct the measurement matrix has obvious advantages. However, existing low-dimensional chaotic systems have low complexity and generate sequences with poor randomness. Hence, a new six-dimensional non-degenerate discrete hyperchaotic system with six positive Lyapunov exponents is proposed in this paper. Using this chaotic system to design the measurement matrix can improve the performance of image compression and reconstruction. Because image encryption using compressed sensing cannot resist known- and chosen-plaintext attacks, the chaotic system proposed in this paper is introduced into the compressed sensing encryption framework. A scrambling algorithm and two-way diffusion algorithm for the plaintext are used to encrypt the measured value matrix. The security of the encryption system is further improved by generating the SHA-256 value of the original image to calculate the initial conditions of the chaotic map. A simulation and performance analysis shows that the proposed image compression-encryption scheme has high compression and reconstruction performance and the ability to resist known- and chosen-plaintext attacks.
数字图像可能尺寸较大且包含需要保护的敏感信息。使用压缩感知进行压缩效果良好，但测量矩阵直接影响信号压缩和重建性能。混沌系统良好的加密特性意味着利用其构建测量矩阵具有明显优势。然而，现有的低维混沌系统复杂度较低，生成的序列随机性较差。因此，本文提出了一种具有六个正李雅普诺夫指数的新型六维非退化离散超混沌系统。利用该混沌系统设计测量矩阵可提高图像压缩和重建性能。由于基于压缩感知的图像加密无法抵抗已知明文和选择明文攻击，本文将所提出的混沌系统引入压缩感知加密框架。采用明文置乱算法和双向扩散算法对测量值矩阵进行加密。通过生成原始图像的SHA - 256值来计算混沌映射的初始条件，进一步提高了加密系统的安全性。仿真和性能分析表明，所提出的图像压缩加密方案具有高压缩和重建性能以及抵抗已知明文和选择明文攻击的能力。
