基于混沌系统和RSA算法的图像加密算法

Image Encryption Algorithm Based on Chaotic System and RSA Algorithm

为了提高图像加密算法的复杂性和安全性,构造了一种新的四维四翼混沌系统,其相图呈现四翼形态,通过研究系统的平衡点性质、Poincaré映射、Lyapunov指数和分岔图等基本动力学特性,发现该系统对初值有高度的敏感性,并且动力学特性较为复杂。同时基于电路仿真软件设计了一个模拟振荡电路,仿真结果证明了该混沌电路可在硬件层面上实现。最后基于新混沌系统和RSA算法设计了一种图像加密方案,该方案利用RSA算法大整数模幂运算增强混沌系统的不确定性,借助混沌系统构建一个伪随机序列发生器,通过加取模算法混淆像素点,其次通过明文相关置乱算法隐藏图像数据,再次执行GF(17)有限域扩散算法进一步隐藏图像信息。结果表明,提出的图像加密方案是有效的,应用于图像加密具有较强的抗攻击性和密钥敏感性。

In order to improve the complexity and security of the image encryption algorithm,a new four-dimensional four-wing chaotic system is constructed,and its phase diagram presents a four-wing shape.By studying the basic dynamic properties of the system such as equilibrium point properties,Poincarémaps,Lyapunov exponents and bifurcation diagrams,it is found that the system has a high degree of sensitivity on the initial value,and the dynamic characteristics are more complex.At the same time,an analog oscillating circuit is designed based on the circuit simulation software.The simulation results prove that the chaotic circuit can be realized at the hardware level.Finally,an image encryption scheme is designed based on the new chaotic system and the RSA algorithm.This scheme uses the large integer modular exponentiation operation of the RSA algorithm to enhance the uncertainty of the chaotic system,builds a pseudo-random sequence generator with the help of the chaotic system,diffuses the pixels through the addition and modulo operation,and then scrambles the hidden image data through plaintext correlation,and executes GF(17)finite field diffusion algorithm again to further hide the image information.The results show that the proposed image encryption scheme is effective and has strong anti-attack and key sensitivity when applied to image encryption.