# Chaos encrypt system

Contents

## 虫口模型 Logistic 混沌映射

$X_{n+1}=X_n \times \mu \times (1-X_n)$

$\mu \in[0,4];X\in[0,1]$

## 一种像素灰度值替代设计图像加密

$I′(i,j)=((r1(i,j)⊕I(i,j)⊕r2(i,j)+L−r3(i,j)));mod;L);mod;256$

$L$表示图像的颜色深度

$r1,r2,r3$表示的是混沌序列值，替换变换的密钥由$r1,r2,r3$对应的混沌系统提供，变换可多次进行，如此加密效果更好。设重复次数为 n ，与混沌模型的初值和参数共同作为这一部分的密钥，增大了密钥的空间

## 混沌理论Chaos theory

Chaos theory is a branch of mathematics focusing on the study of chaos — dynamical systems whose apparently random states of disorder and irregularities are actually governed by underlying patterns and deterministic laws that are highly sensitive to initial conditions