基于四维超混沌系统的图像加密算法设计

Design of Image Encryption Algorithm Based on Four-dimensional Hyperchaotic System

目的 针对构造具有混沌特性的复杂四维超混沌系统以及提高图像数据保护的安全问题,提出在经典系统Lü基础之上,引入一个状态反馈控制器构建只有一个平衡点的四维超混沌系统,通过理论分析四维超混沌系统的动力学特性并设计超混沌加密算法以保护图像加密后的数据安全性。方法 利用Matlab软件对该超混沌系统进行数值仿真,如系统耗散性和平衡点稳定性、Lyapunov指数谱和分岔图、Poincare截面;同时设计了四维超混沌系统的模拟电路,通过基本的电路元件,以运算放大电路为基础搭建超混沌系统的模拟电路模型;最后将四维超混沌系统与置乱-扩散算法相结合,利用超混沌系统混沌序列的复杂性和伪随机性设计了一种高效且安全的四维超混沌图像加密算法,通过Matlab软件对明文和密文图像进行直方图、相邻像素相关性、信息熵和抗攻击性分析。结果仿真数据表明:该四维超混沌系统具有周期、混沌、超混沌吸引子的复杂混沌行为,同时利用Multisim软件验证电路实现的准确性和物理可实现性。图像加密实验数据表明:该超系统对混沌密钥和明文非常敏感,超混沌加密算法的安全性更高,同时在保证安全性的前提之下,可以有效抵御统计攻击和差分攻击,也加快了图像解密和加密的速度。结论 实验结论表明:该四维超混沌系统在不同参数下可以表现出复杂的动力学特性,利用超混沌系统产生的混沌序列设计的混沌加密算法安全性很高。

Objective To construct a complex four-dimensional hyperchaotic system with chaotic characteristics and to improve the security of image data protection,a four-dimensional hyperchaotic system with only one equilibrium point by introducing a state feedback controller based on the classical system Lüwas proposed and constructed.The dynamics of the four-dimensional hyperchaotic system was analyzed theoretically,and a hyperchaotic encryption algorithm to protect the data security after image encryption was designed.Methods Numerical simulations of this hyperchaotic system,such as system dissipation and equilibrium point stability,Lyapunov exponential spectrum and bifurcation diagram,and Poincare cross-section,were performed using Matlab software.Meanwhile,the simulation circuit of the four-dimensional hyperchaotic system was designed,and the simulation circuit model of the hyperchaotic system was built based on the operational amplifier circuit through the basic circuit components.Finally,the four-dimensional hyperchaotic system is combined with the dislocation-diffusion algorithm to design an efficient and secure four-dimensional hyperchaotic image encryption algorithm by using the complexity and pseudo-randomness of the chaotic sequence of the hyperchaotic system,and the histogram,adjacent pixel correlation,information entropy and attack resistance of plaintext and ciphertext images were analyzed by Matlab software.Results Simulation data showed that this four-dimensional hyperchaotic system has complex chaotic behavior with periodic,chaotic,and hyperchaotic attractors,while Multisim software was used to verify the accuracy and physical realizability of the circuit implementation.The experimental data of image encryption show that the super system is very sensitive to chaotic keys and plaintexts,and the hyperchaotic encryption algorithm is more secure.Meanwhile,it can effectively resist statistical and differential attacks under the premise of ensuring security,and it also speeds up image decryption and encryption.Conclusion The experimental conclusion shows that this four-dimensional hyperchaotic system can exhibit complex dynamics under different parameters,and the chaotic encryption algorithm designed by using the chaotic sequence generated by the hyperchaotic system has high security.