Applying a chaotic system to digital image communication is an effective way to resist the attack of intelligent system with strong computing power. However, the traditional chaotic systems lack more complex dynamic behavior that is very valuable for a series of applications. Based on Lorenz system, this study proposes a hyper-chaotic system with multi-scroll coexistence attractors by using a piecework function. Through bifurcation diagram and Lyapunov exponents, we analyzed the dynamic behavior of the system, and observed multi-scroll coexistence attractors in the numerical simulation. The results show that compared with the traditional chaotic attractor, multi-scroll coexistence attractor has more complex structure and dynamic behavior. Furthermore, we design a cryptosystem based on this system for the digital image. Scrambling and diffusing images with the sequence of multi-scroll coexistence attractors can destroy the correlation of adjacent pixels and hide the information of all pixels. Theoretical analysis and simulation on key space, histogram, information entropy, key sensitivity and pixel correlation show that the encryption scheme is feasible and secure.

将混沌系统应用于数字图像通信是抵抗具有强大计算能力的智能系统的有效方法。然而，传统的混沌系统缺乏更复杂的动态行为，这对于一系列应用非常有价值。基于洛伦兹系统，本研究提出了一种基于计件函数的具有多卷共存吸引子的超混沌系统。通过分叉图和李雅普诺夫指数，我们分析了系统的动态行为，并在数值模拟中观察了多卷共存吸引子。结果表明，与传统的混沌吸引子相比，多卷共存吸引子具有更复杂的结构和动态行为。此外，我们基于该系统为数字图像设计了一个密码系统。以多滚动共存吸引子的顺序对图像进行加扰和扩散会破坏相邻像素的相关性，并隐藏所有像素的信息。对密钥空间，直方图，信息熵，密钥敏感度和像素相关性进行理论分析和仿真表明，该加密方案是可行且安全的。