基于忆阻隐藏超混沌系统的图像加密算法研究

Research on Image Encryption Algorithm Based on Memristor Hidden Hyperchaotic System

摘要: 针对传统超混沌Lorenz系统应用于图像加密时，存在密钥空间小、安全性不高等问题，本文在lv混沌系统的基础上，通过添加磁控忆阻器，提出一种具有稳定平衡点的四维忆阻超混沌系统，并应用于图像加密。通过相图、Lyapunov指数、分岔图等仿真分析，发现所构建的混沌系统具有稳定平衡点，并且随参数的变化，系统表现出周期–混沌–拟周期–超混沌的丰富动力学行为。通过模块化电路仿真设计，验证了混沌系统的物理可实现性。利用该混沌系统生成六个伪随机矩阵，先对明文图像进行扩散，然后通过置乱降低相邻像素点的相关性，再对置乱图像从最后一个像素点向前扩散，通过两次扩散和一次置乱，最终实现对明文图像加密。由直方图、密钥空间等仿真结果表明，使用新忆阻超混沌系统的图像加密算法比传统超混沌Lorenz算法密钥空间提高了2³⁴，密文的信息熵为7.9993，接近理论值，相邻像素点的相关性与超混沌Lorenz算法相比有数量级的降低，能抵御穷举攻击和差分攻击等常见的攻击方式，具有更高的安全性。

Abstract: Traditional hyperchaotic Lorenz system is applied to image encryption, but the disadvantages of traditional algorithm are small key space and low security, to solve this problem, in this paper, based on the lv chaotic system, a four-dimensional memristor hyperchaotic system with stable equilibrium point is proposed by adding a magnetron memristor, and it is applied to image encryp-tion. Through the analysis of phase diagram, Lyapunov exponent and bifurcation diagram, it is found that the new chaotic system has a stable equilibrium point, and with the change of parame-ters, the system shows a rich dynamic behavior, such as periodic, chaotic, quasi-periodic and hy-perchaotic. The physical realizability of the chaotic system is verified by a modular circuit simula-tion design. Firstly, the plaintext image was diffused, and then the correlation of adjacent pixels was reduced by scrambling. Secondly, the scrambled image was diffused again forward from the last pixel. Finally, the plaintext image was encrypted by twice diffusion and once scrambling. The simu-lation results of histogram and key space show that the key space of the image encryption algorithm using the new memristor hyperchaotic system is 2³⁴ higher than that of the traditional hyperchaotic Lorenz algorithm, the information entropy of the ciphertext is 7.9993, which is close to the theoret-ical value, and the correlation between adjacent pixels is orders of magnitude lower than that of the hyperchaotic Lorenz algorithm. It can resist the common attack methods such as exhaustive attack and differential attack, and has higher security.