摘要： 基于低维混沌系统的数字图像加密算法存在密钥空间小、安全性不高等问题。为此，在三维Lorenz系统的基础上，通过增加变量w使其成为四维微分方程组，并引入一个非线性项来增强系统运动的复杂性，由此构造一个四维超混沌系统。基于该系统提出一种新的数字图像加密算法。Lyapunov指数的计算结果和系统运动轨迹的仿真结果验证了系统的超混沌性。安全性分析和测试结果表明，新算法对密钥非常敏感，具有较好的扩散性及安全性，能抵抗蛮力攻击、已知明文攻击和选择明文攻击。

关键词: 混沌, 四维超混沌系统, Lorenz系统, 数字图像加密, Lyapunov指数

Abstract: There are some problems for digital image encryption algorithm of low dimensional chaotic system such as small key space and low safety. On the basis of three-dimensional Lorenz system, by adding a new variable w to construct a four-dimension differential equations and adding a nonlinear term campaign to increase the complexity of the system, this paper establishes a novel four-dimensional hyperchaotic system. And an image encryption algorithm based on this hyperchaotic system is proposed and implemented. The system’s hyperchaotic properties is verified by the Lyapunov exponents calculation and simulation result of the trajectory of the system. By analyzing the security performance of the algorithm, it finds that the algorithm is extremely sensitive to key, has good diffusivity, and it can resist all kinds of attacks effectively such as brute force attack and known-plaintext attack.

Key words: chaotic, four-dimensional hyperchaotic system, Lorenz system, digital image encryption, Lyapunov exponents

中图分类号: 

• TP309.2