In this paper, a new four-dimensional memristive hyperchaotic system is constructed based on Liu chaotic system by introducing a flux-controlled memristor model. Then the dynamic characteristics of the new system such as phase portraits, dissipation, Lyapunov exponent and power spectrum are investigated. Subsequently, a novel image encryption algorithm is designed based on the chaotic sequence generated by the proposed hyperchaotic system combining the hash algorithm and DNA sequence operations. In this image encryption algorithm, the coupling relationship between plaintext and ciphertext is established by using the hash value of plaintext image obtained by hash algorithm, and then the plaintext is decomposed into eight bit-plane, to improve the efficiency of the algorithm, only the higher four bit-plane are selected for scrambling. After scrambling, the data stream is further processed by the DNA encoding/decoding rules and DNA sequence operations to obtain the intermediate ciphertext. Finally, the ultimate encrypted image is obtained by performing order and reverse-order diffusion operations at the pixel level on the intermediate ciphertext. Experimental results and security analysis show that the proposed algorithm has excellent image encryption performance and can resist a variety of common attacks against the image encryption system.

本文通过引入磁通量控制忆阻器模型，在Liu混沌系统的基础上构造了一种新型的四维忆阻超混沌系统。然后研究了新系统的动态特性，如相图，耗散，李雅普诺夫指数和功率谱。随后，结合哈希算法和DNA序列运算，设计了一种新的图像加密算法，该算法基于所提出的超混沌系统产生的混沌序列。在该图像加密算法中，利用哈希算法获得的明文图像的哈希值建立明文与密文之间的耦合关系，然后将明文分解为八个位平面，以提高算法的效率。选择较高的四个位平面进行加扰。加扰后，数据流通过DNA编码/解码规则和DNA序列操作进一步处理，以获得中间密文。最后，通过在中间密文上的像素级别执行有序和逆序扩散操作，可以获得最终的加密图像。实验结果和安全性分析表明，该算法具有良好的图像加密性能，可以抵抗针对图像加密系统的各种常见攻击。