Color image pixel permutation not reversible

Question

I performed color image permutation using 2D sine-map for RGB image. The code uses this map to perform pixel location permutation for each RGB channel in the image. Then, I used the same map with the same initial parameters to inverse the permutation. The problem is the code only perform correct inverse permutation for one channel only the other channels is not recovered. See the attached images of the permuted and the recovered image.

%% Image Encryption Demo - Encryption and Decryption
clear all
close all
clc

%% 1. Load plaintext images
% Image 1
I = imread('D:\1\1.jpg');
Ir = I(:,:,1);
Ig = I(:,:,2);
Ib = I(:,:,3);
K=1;
%% 2. Encryption
%[CI,K] = Logistic2D_ImageCipher(I,'encryption');
[CIb,K] = Logistic2D_ImageCipher(Ib,'encryption');
clearvars -except CIb Ir Ig Ib K I;
[CIr,K] = Logistic2D_ImageCipher(Ir,'encryption');
clearvars -except CIb CIr Ir Ig Ib K I;
[CIg,K] = Logistic2D_ImageCipher(Ig,'encryption');
clearvars -except CIb CIr CIg Ir Ig Ib K I;

CI = cat(3,CIr,CIg,CIb);
%% 3. Decryption
%DI = Logistic2D_ImageCipher(CI,'decryption',K);
DIb = Logistic2D_ImageCipher(CIb,'decryption',K);
clearvars -except CIb CIr CIg Ir Ig Ib K I DIb CI;
DIg = Logistic2D_ImageCipher(CIg,'decryption',K);
clearvars -except CIb CIr CIg Ir Ig Ib K I DIb DIg CI;
DIr = Logistic2D_ImageCipher(CIr,'decryption',K);
clearvars -except CIb CIr CIg Ir Ig Ib K I DIb DIg DIr CI;
DI = cat(3,DIr,DIg,DIb);
%% 4. Analaysis
% Histogram
%title('aaa');
figure,subplot(221),imshow(I,[]),subplot(222),imshow(CI,[])
subplot(223),imhist(I),subplot(224),imhist(CI)
title('aaa2');
figure,subplot(221),imshow(DI,[])

function varargout = Logistic2D_ImageCipher(P,para,K)

%% 1. Initialization
% 1.1. Genereate Random Key if K is not given
if ~exist('K','var') && strcmp(para,'encryption') 
    K = round(rand(1,256));
    varOutN = 2;
elseif ~exist('K','var') && strcmp(para,'decryption') 
    error('Cannot Complete Decryption without Encryption Key')
else
    varOutN = 1;
end
% 1.2. Translate K to map formats
transFrac = @(K,st,ed) sum(K(st:ed).*2.^(-(1:(ed-st+1))));
x0 = transFrac(K,1,52);
y0 = transFrac(K,53,104);
a=0.8;
b =0.3;

r = transFrac(K,105,156)*.08+1.11;
T = transFrac(K,157,208);
turb = blkproc(K(209:256),[1,8],@(x) bi2de(x));

MN = numel(P);

Logistic2D = @(x,y,a) [sin(pi*a*(y+3)*x*(1-x)), sin(pi*a*(x+3)*y*(1-y))];
format long eng
%% 2. Estimate cipher rounds
if max(P(:))>1
    F = 256;
    S = 4;
else
    F = 2;
    S = 32;
end
P = double(P);
iter = 1;
%iter = ceil(log2(numel(P))/log2(S));

%% 3. Image Cipher
C = double(P);
switch para
    case 'encryption'
        for i = 1:iter
            tx0 = mod(log(turb(mod(i-1,6)+1)+i)*x0+T,1);
            ty0 = mod(log(turb(mod(i-1,6)+1)+i)*y0+T,1);
            xy = zeros(MN,2);
            for n = 1:MN
                if n == 1
                    xy(n,:) = (Logistic2D(tx0,ty0,a)); 
                else
                    xy(n,:) = (Logistic2D(xy(n-1,1),xy(n-1,2),a));
                end
            end
            R = cat(3,reshape(xy(:,1),size(P,1),size(P,2)),reshape(xy(:,2),size(P,1),size(P,2)));
            C = LogisticPermutation(C,R,'encryption');
        end
    case 'decryption'
        for i = iter:-1:1
            tx0 = mod(log(turb(mod(i-1,6)+1)+i)*x0+T,1);
            ty0 = mod(log(turb(mod(i-1,6)+1)+i)*y0+T,1);
            xy = zeros(MN,2);
            for n = 1:MN
                if n == 1
                    xy(n,:) = (Logistic2D(tx0,ty0,a)); 
                else
                    xy(n,:) = (Logistic2D(xy(n-1,1),xy(n-1,2),a));
                end
            end
            R = cat(3,reshape(xy(:,1),size(P,1),size(P,2)),reshape(xy(:,2),size(P,1),size(P,2)));
            C = LogisticPermutation(C,R,'decryption'); 
        end
end

%% 4. Output
switch F
    case 2
        C = logical(C);
    case 256
        C = uint8(C);
end

switch varOutN
    case 1
        varargout{1} = C;
    case 2
        varargout{1} = C;
        varargout{2} = K;
end

function C = LogisticPermutation(P,R,para)

C0 = zeros(size(P));
C = C0;
switch para
    case 'encryption'
        % 1. Shuffling within a Column
        [v,Epix] = sort(R(:,:,1),1);
        for i = 1:size(R,1)
            C0(:,i) = P(Epix(:,i),i);
        end
        % 2. Shuffling within a Row
        [v,Epiy] = sort(R(:,:,2),2);
        for j = 1:size(R,2)
            C(j,:) = C0(j,Epiy(j,:));
        end
    case 'decryption'
        % 1. Shuffling within a Row
        [v,Epiy] = sort(R(:,:,2),2);
        for j = 1:size(R,2)
            C0(j,Epiy(j,:)) = P(j,:);
        end
        % 2. Shuffling within a Column
        [v,Epix] = sort(R(:,:,1),1);
        for i = 1:size(R,1)
            C(Epix(:,i),i) = C0(:,i);
        end
end

Answer 1

It didn't work because you overwrote K in the encryption stage, and it was different for each channel, so the decryption only worked correctly for the last channel that created K. If you're using the MATLAB editor, you should pay attention to the mlint warnings (square at the top right that should be always be green) - you could say that this is what told me the answer to your problem.

Here's a fixed version of the first part of the script:

function q50823167
%% 1. Load plaintext images
% Image 1
I = imread(fullfile(matlabroot, 'examples', 'wavelet', 'mandrill.jpg'));
Ir = I(:,:,1);
Ig = I(:,:,2);
Ib = I(:,:,3);
%% 2. Encryption
%[CI,K] = Logistic2D_ImageCipher(I,'encryption');
[CIb,Kb] = Logistic2D_ImageCipher(Ib,'encryption');
[CIr,Kr] = Logistic2D_ImageCipher(Ir,'encryption');
[CIg,Kg] = Logistic2D_ImageCipher(Ig,'encryption');

CI = cat(3,CIr,CIg,CIb);
%% 3. Decryption
%DI = Logistic2D_ImageCipher(CI,'decryption',K);
DIb = Logistic2D_ImageCipher(CIb,'decryption',Kb);
DIg = Logistic2D_ImageCipher(CIg,'decryption',Kg);
DIr = Logistic2D_ImageCipher(CIr,'decryption',Kr);
DI = cat(3,DIr,DIg,DIb);
%% 4. Analaysis
% Histogram
%title('aaa');
figure,subplot(221),imshow(I,[]),subplot(222),imshow(CI,[])
subplot(223),imhist(I),subplot(224),imhist(CI)
title('aaa2');
figure,subplot(221),imshow(DI,[])

Note that you don't have to clear variables every time.