基于无退化混沌系统的序列密码研究

针对连续时间混沌系统的退化问题,提出一种基于矩阵特征值配置的方法来构造具有多个正Lyapunov指数的连续时间混沌系统。提出一种基于特征值定义的特征值配置方法,通过设计一个线性反馈控制器,可以配置任何系统为以稳定焦点为原点的渐近稳定线性系统;通过设计一个非线性反馈控制器来配置多个正Lyapunov指数。相比于现有算法,对于任意受控系统,该方法都能系统地配置该受控系统的Lyapunov指数,使之成为无退化混沌系统。将该方法得到的无退化混沌系统转换为二进制序列,对得到的混沌序列进行分析后证明该序列具有良好的加密特性。

STREAM CIPHER ALGORITHM BASED ON NON-DEGENERATE CHAOTIC SYSTEM

Aiming at the degradation problem of continuous-time chaotic systems,this paper proposes a method based on matrix eigenvalue configuration to construct a continuous time chaotic system with multiple positive Lyapunov exponents.A method for configuring feature values by definition of eigenvalues was proposed.By designing a linear feedback controller,any system could be configured as an asymptotically stable linear system with a stable focus as its origin.Then the positive Lyapunov exponent was configured by designing a nonlinear feedback controller.Compared with the existing algorithms,for any controlled system,this method can systematically configure the Lyapunov exponents of the controlled system to make it a non-degenerate chaotic system.The non-degenerate chaotic system obtained by this method is transformed into binary sequence,and the analysis of the obtained chaotic sequence proves that the sequence has good encryption characteristics.