Logistic混沌置乱，先不说有多复杂，其实很简单。

Logistic函数是源于一个人口统计的动力学系统，其系统方程形式如下：

 X(k+1) = u * X(k) * [1 - X(k)],（k=0,1,…,n）

先不用管这个方程是怎么得出来的，觉得不舒服的话自己百度去。可以看出这个方程是非线性的，迭代的形式。要使用的话，我们需要知道两个东西：

①    初值：X(0)

②    参数：u

为什么这个方程可以称作混沌呢？它什么时候是一个混沌系统呢？这个也是有条件的：

①    0  < X(0) < 1

②   3.5699456...  <  u <=4

当满足上述两个条件时，Logistic函数工作于混沌状态。这两个条件是怎么来的请百度，我们这里只说算法和实现。什么是混沌状态：顾名思义就是一种无序的、不可预测的、混乱的、摸不到头、摸不到尾的状态。混沌状态时会出现什么现象，我们以下面的参数为例：

①    X(0) = 0.1

②    u = 4

当迭代n次后，我们就得到了X(1)、X(2)、…，X(n)这么n个值。那么这就是一个混沌序列，是一维的暂且称作序列A，也就是我们想要得到的序列，在MATLAB中，可以看出X(i)（i=1,2,…,n）的取值是在(0,1)之间的——这是一个很好地特性，就像图像灰度值是在(0,255)之间一样。那么我们把这个一维序列归一化到(0,255)之间得到序列B。

再来看加密过程。对于一幅M*N大小的图像（暂且称为Picture），我们需要产生一个同样大小的矩阵来对其进行加密。如此说来，只需要迭代M*N次得到序列A，再转成序列B，此时序列B是一维的，将其转化成M*N的二维矩阵（暂且称为Fuck）。因此，用Fuck与Picutre进行异或，便可得到一幅新的图像，称作Rod，如此便完成了一次图像加密，加密后的图像为Rod。

Rod=Picture⊕Fuck（⊕表示异或）

这样我们手中的秘钥是：u，X(0)

此种加密方式称作序列加密，可以看出这种加密方式改变了下像素的灰度（直方图变了），没有改变位置。解密同样道理：Picture = Rod⊕Fuck。

function varargout = encrypt(varargin)
% ENCRYPT MATLAB code for encrypt.fig
%      ENCRYPT, by itself, creates a new ENCRYPT or raises the existing
%      singleton*.
%
%      H = ENCRYPT returns the handle to a new ENCRYPT or the handle to
%      the existing singleton*.
%
%      ENCRYPT('CALLBACK',hObject,eventData,handles,...) calls the local
%      function named CALLBACK in ENCRYPT.M with the given input arguments.
%
%      ENCRYPT('Property','Value',...) creates a new ENCRYPT or raises the
%      existing singleton*.  Starting from the left, property value pairs are
%      applied to the GUI before encrypt_OpeningFcn gets called.  An
%      unrecognized property name or invalid value makes property application
%      stop.  All inputs are passed to encrypt_OpeningFcn via varargin.
%
%      *See GUI Options on GUIDE's Tools menu.  Choose "GUI allows only one
%      instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES
 
% Edit the above text to modify the response to help encrypt
 
% Last Modified by GUIDE v2.5 24-Dec-2019 21:56:19
 
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...
                   'gui_Singleton',  gui_Singleton, ...
                   'gui_OpeningFcn', @encrypt_OpeningFcn, ...
                   'gui_OutputFcn',  @encrypt_OutputFcn, ...
                   'gui_LayoutFcn',  [] , ...
                   'gui_Callback',   []);
if nargin && ischar(varargin{1})
    gui_State.gui_Callback = str2func(varargin{1});
end
 
if nargout
    [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
    gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT
 
 
% --- Executes just before encrypt is made visible.
function encrypt_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject    handle to figure
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
% varargin   command line arguments to encrypt (see VARARGIN)
 
% Choose default command line output for encrypt
handles.output = hObject;
 
% Update handles structure
guidata(hObject, handles);
 
% UIWAIT makes encrypt wait for user response (see UIRESUME)
% uiwait(handles.figure1);
 
 
% --- Outputs from this function are returned to the command line.
function varargout = encrypt_OutputFcn(hObject, eventdata, handles) 
% varargout  cell array for returning output args (see VARARGOUT);
% hObject    handle to figure
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
 
% Get default command line output from handles structure
varargout{1} = handles.output;
 
 
% --- Executes on button press in pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton1 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
[filename,filepath] = uigetfile({'*.bmp;*.jpg;*.png;*.jpeg;*.tif','文件类型 (*.bmp,*.jpg,*.png,*.jpeg,*.tif)';'*.*', '所有文件(*.*)'},'Pick an image');
file = strcat(filepath,filename);
im = imread(file);
axes(handles.axes1);
imshow(im);
imwrite(im,'snap.bmp'); 
 
 
 
% --- Executes on button press in pushbutton2.
function pushbutton2_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton2 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
obj = videoinput('winvideo',1,'YUY2_1280x720')%1280x720 160x120 176x144 320x240 352x288 640x480 
% vidRes = get(obj, 'VideoResolution');
% nBands = get(obj, 'NumberOfBands');
% preview(obj);%getsnapshot(obj);
vidRes = get(obj, 'VideoResolution');
nBands = get(obj, 'NumberOfBands');
hImage = image( zeros(vidRes(2), vidRes(1), nBands),'parent',handles.axes1);
preview(obj, hImage);
frame = getsnapshot(obj);
frame = ycbcr2rgb(frame);
imwrite(frame,'snap.bmp','bmp');
pic = imread('snap.bmp');
axes(handles.axes1);
imshow(pic);
title(date,'color','r');
 
 
 
function edit1_Callback(hObject, eventdata, handles)
% hObject    handle to edit1 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
 
% Hints: get(hObject,'String') returns contents of edit1 as text
%        str2double(get(hObject,'String')) returns contents of edit1 as a double
% input = str2num(get(hObject,'String'));%这里get后面要注意
% if(isempty(input))
%     set(hObject,'String','0')
% end
guidata(hObject,handles)
 
 
% --- Executes during object creation, after setting all properties.
function edit1_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit1 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called
 
% Hint: edit controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end
 
 
% --- Executes on button press in pushbutton3.
function pushbutton3_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton3 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
a=imread('snap.bmp');
R=a(:,:,1);                           %取图像的R层像素
G=a(:,:,2);                           %取图像的G层像素
B=a(:,:,3);                           %取图像的B层像素
[M1,N1]=size(R);
[M2,N2]=size(G);
[M3,N3]=size(B);
h=0.01;    %混沌序列初始化 
x=zeros(1,40001);x(1)= str2num(get(handles.edit1,'String')); 
y=zeros(1,40001);y(1)=0; 
z=zeros(1,40001);z(1)=0; 
w=zeros(1,40001);w(1)=0; 
v=zeros(1,40001);v(1)=0; 
for n=1:40000         %产生混沌序列初始化,欧拉法 
  x(n+1)=x(n)+h*(3.5*(y(n)-x(n)-(-1.2+0.3*(w(n)*w(n)))*x(n))); 
  y(n+1)=y(n)+h*(2.1*y(n)-z(n)-0.2*(y(n)-x(n))-0.2*(1.2+7*abs(v(n)))*y(n)); 
  z(n+1)=z(n)+h*(2.1*y(n)-z(n));
  w(n+1)=w(n)+h*(x(n));
  v(n+1)=v(n)+h*(y(n)); 
end 
for n=1:40000  %对3个序列进行改进 
    x(n)=x(n)*1000000-round(x(n)*1000000); 
    y(n)=y(n)*1000000-round(y(n)*1000000); 
    z(n)=z(n)*1000000-round(z(n)*1000000);
    w(n)=w(n)*1000000-round(w(n)*1000000); 
    v(n)=v(n)*1000000-round(v(n)*1000000); 
end 
 
% %对R通道进行加密
 
for j=1:N1  %用位异或法对像素进行置乱 
    aa=(uint8((M1*N1*(x(N1+j)+0.5))*ones(M1,1))); 
    g1(:,j)=bitxor(R(:,j),aa); 
    h1(:,j)=bitxor(g1(:,j),aa); %对像素置乱进行解密 
end 
for i=1:M1 %行置乱
    t(1:N1)=y(1:N1);
    [t1,index1]=sort(t(1:N1));
    t1=flipud(t1);
    g2(i,:)=g1(i,index1);
    h2(i,index1)=g2(i,:);
end
for j=1:N1 %列置乱
    t(1:M1)=z(1:M1);
    [t1,index1]=sort(t(1:M1));
    index1=flipud(index1);
    g3(:,j)=g2(index1,j);
    h3(index1,j)=g3(:,j);
end
 
% %对G通道进行加密
 
for j=1:N2  %用位异或法对像素进行置乱 
    bb=(uint8((M2*N2*(x(N2+j)+0.5))*ones(M2,1))); 
    j1(:,j)=bitxor(G(:,j),bb); 
    k1(:,j)=bitxor(j1(:,j),bb); %对像素置乱进行解密 
end 
for i=1:M2 %行置乱
    t(1:N2)=x(1:N2);
    [t2,index2]=sort(t(1:N2));
    t2=flipud(t2);
    j2(i,:)=j1(i,index2);
    k2(i,index2)=j2(i,:);
end