Error using bitxor Inputs must have the same size.

Hello there,

i have a proplem with bitxor function :

Error using bitxor Inputs must have the same size.

the first input " original " & the second input " cipher " has the following sizes like below :

How can i make original & cipher variable of same size ?

and here is my code :

%Using Logistic chaotic mapping, sequence encryption of grayscale images
original = imread('pp.jpg');
figure(1);
subplot(1,3,1);
imshow(original);
title('original');

[M,N]=size(original);
x=0.1;
u=4;
% %Iterative200Second, achieve full chaotic state
 for i=1:200
     x=u*x*(1-x);
 end
% %Generate a single-dimensional chaotic encryption sequence
 A=zeros(1,M*N);                                                            %generate1*Mn zero matrix
 A(1)=x;
 %Generate chaotic sequence
for i=1:M*N-1
A(i+1)=u*A(i)*(1-A(i));
end
%Normalized sequence
B=uint8(255*A);                                                            %Convert to 255 type of data 
% %Transforming into two-dimensional chaotic encryption sequence
Cipher=reshape(B,M,N);                                                     %Reshape changes the shape of the specified matrix, but the number of elements does not change; here B is converted to M line, N columns
Encrypted =bitxor(original ,Cipher);                                       %Tone or operation encryption
figure(1);
subplot(1,3,2);
imshow(Encrypted);
title('Encrypted');

%Decryption
Decrypted=bitxor(Encrypted,Cipher);                                        %Different or operation decryption
figure(1);
subplot(1,3,3);
imshow(Decrypted);
title('Decrypted');

%Draw a histogram of original Image and Encrypted Image
figure(2);
subplot(1,3,1);
imhist(original);
title(' original ');
figure(2);
subplot(1,3,2);
imhist(Encrypted);
title('Encrypted');
figure(2);
subplot(1,3,3);
imhist(Decrypted);
title('Decrypted');

Thanks in advance.

Answer 1

[Jan]

The mistake happens here:

[M,N]=size(original);

The original image is an RGB image, not a grey-scale image as the comments imply, which store its data in [nRows x nColumns x 3] array. With [M, N] = size(img) the N is nColumns*3.

Note:

[M, N] = size(X)
% is not the same as:
M = size(X, 1)
N = size(X, 2)

Better:

nByte = numel(original);  % instead of: [M,N]=size(original);
... Modify code to use nByte instead of M*N
    
Cipher    = reshape(B, size(original));                                                     %Reshape changes the shape of the specified matrix, but the number of elements does not change; here B is converted to M line, N columns
Encrypted = bitxor(original ,Cipher); 

[Muhammad Abdulrazek]

I appreciate your response MR. Jan

it worked, thanks

[Muhammad Abdulrazek]

@Jan

When I tried to implement your solution to my project this error appeared again

here is the entire code , Hope you can help me sir

THX in Advance

%NOMA images Logistic chaotic mapping sequence encryption 
clc;
clear variables;
close all;
rand('state',32768);
randn('state',86723);
warning('off','comm:obsolete:randint')

N = 128*128*8;                                                             %Data lenghth
Pt = 0:2:40;                                                               %transmit power (dBm)
pt = (10^-3)*10.^(Pt/10);                                                  %transmit power (linear scale)
BW = 1*10^6;                                                               %BandWidth = 1MHZ
No = -174 + 10*log10(BW);                                                  %Noise power (dBm)
no = (10^-3) *10.^(No/10);                                                 %Noise power (linear scale)
d1 = 500;  d2 = 200;  d3 = 70;                                             %Distances
a1 = 0.8;  a2 = 0.15;  a3 = 0.05;                                          %power allocation coefficients
eta = 4;                                                                   %path loss 

% Generate Rayleigh fading channel for the three users 
h1 = sqrt(d1^-eta)*(randn(N/2,1) + 1i*randn(N/2,1))/sqrt(2);
g1 = (abs(h1)).^2;
h2 = sqrt(d2^-eta)*(randn(N/2,1) + 1i*randn(N/2,1))/sqrt(2);
g2 = (abs(h2)).^2;
h3 = sqrt(d3^-eta)*(randn(N/2,1) + 1i*randn(N/2,1))/sqrt(2);
g3 = (abs(h3)).^2;

% Generate noise samples for the three users
n1 = sqrt(no)*(randn(N/2,1) + 1i*randn(N/2,1))/sqrt(2);
n2 = sqrt(no)*(randn(N/2,1) + 1i*randn(N/2,1))/sqrt(2);
n3 = sqrt(no)*(randn(N/2,1) + 1i*randn(N/2,1))/sqrt(2);

%Generate binary message data ((image)) for the three Users----------------

original1_image = imread('pp2.jpeg');
%%%%%%%%%[M1,N1]=size(original1_image);
nByte1 = numel(original1_image); 
[original1_Data,row_im, col_im, third_im] = image2data(original1_image, 2);%image 2 Data conversion
x1=0.1;
u1=4;
%Iterative200Second, achieve full chaotic state
for i1=1:200
    x1=u1*x1*(1-x1);
end
%Generate a single-dimensional chaotic encryption sequence
A1=zeros(1,nByte1);                                                         %generate1*Mn zero matrix                                                          
A1(1)=x1;
%Generate chaotic sequence
for i1=1:nByte1-1
A1(i1+1)=u1*A1(i1)*(1-A1(i1));
end
%Normalized sequence
B1=uint8(255*A1);                                                          %Convert to 255 type of data 
%Transforming into two-dimensional chaotic encryption sequence
%%%%%%%%%%5Cipher1 =reshape(B1,M1,N1);                                                %Reshape changes the shape of the specified matrix, but the number of elements does not change; here B is converted to M line, N column
Cipher1 = reshape(B1, size(original1_image));                                                     %Reshape changes the shape of the specified matrix, but the number of elements does not change; here B is converted to M line, N columns

Encry1 =bitxor(original1_Data',Cipher1);                                   %Tone or operation encryption
Encrypted1 = reshape (Encry1,N,1);
Encrypted1_image =  data2image(Encrypted1', row_im, col_im, third_im, 2);  %Data 2 image conversion

%--------------------------------------------------------------------------
original2_image = imread('Woman.bmp');
%%%%%%%%%%%%5[M2,N2]=size(original2_image);
nByte2 = numel(original2_image); 
[original2_Data,row_im, col_im, third_im] = image2data(original2_image, 2);%image 2 Data conversion
x2=0.1;
u2=4;
%Iterative200Second, achieve full chaotic state
for i2=1:200
    x2=u2*x2*(1-x2);
end
%Generate a single-dimensional chaotic encryption sequence
A2=zeros(1,nByte2);                                                         %generate1*Mn zero matrix                                                           
A2(1)=x2;
%Generate chaotic sequence
for i2=1:nByte2-1
A2(i2+1)=u2*A2(i2)*(1-A2(i2));
end
%Normalized sequence
B2=uint8(255*A2);                                                          %Convert to 255 type of data
%Transforming into two-dimensional chaotic encryption sequence
%%%%%Cipher2=reshape(B2,M2,N2);  %Reshape changes the shape of the specified matrix, but the number of elements does not change; here B is converted to M line, N columns
Cipher2 = reshape(B2, size(original2_image));                                                     %Reshape changes the shape of the specified matrix, but the number of elements does not change; here B is converted to M line, N columns
Encry2 =bitxor(original2_Data' ,Cipher2);                                  %Tone or operation encryption
Encrypted2 = reshape (Encry2,N,1);
Encrypted2_image =  data2image(Encrypted2', row_im, col_im, third_im, 2);  %Data 2 image conversion

%--------------------------------------------------------------------------
original3_image = imread('Clock.bmp');
%%%%%5[M3,N3]=size(original3_image);
nByte3 = numel(original3_image); 
[original3_Data,row_im, col_im, third_im] = image2data(original3_image, 2);%image 2 Data conversion
x3=0.1;
u3=4;
%Iterative200Second, achieve full chaotic state
for i3=1:200
    x3=u3*x3*(1-x3);
end
%Generate a single-dimensional chaotic encryption sequence
A3=zeros(1,nByte3);                                                         %generate1*Mn zero matrix                                                         
A3(1)=x3;
%Generate chaotic sequence
for i3=1:nByte3-1
A3(i3+1)=u3*A3(i3)*(1-A3(i3));
end
%Normalized sequence
B3=uint8(255*A3);                                                          %Convert to 255 type of data
%%%%Cipher3=reshape(B3,M3,N3); %Reshape changes the shape of the specified matrix, but the number of elements does not change; here B is converted to M line, N columns                                                 
Cipher2 = reshape(B3, size(original3_image));                                                     %Reshape changes the shape of the specified matrix, but the number of elements does not change; here B is converted to M line, N columns
Encry3 =bitxor(original3_Data' ,Cipher3);                                  %Tone or operation encryption
Encrypted3 = reshape (Encry3,N,1);
Encrypted3_image =  data2image(Encrypted3', row_im, col_im, third_im, 2);  %Data 2 image conversion


%create QPSKModulator and QPSKDemodulator objects
QPSKmod = comm.QPSKModulator('BitInput',true);
QPSKdemod = comm.QPSKDemodulator('BitOutput',true);


%perform QPSK modulation
mod1 = step(QPSKmod,Encrypted1);
mod2 = step(QPSKmod,Encrypted2);
mod3 = step(QPSKmod,Encrypted3);

%Do superposition coding
x = sqrt(a1)*mod1 + sqrt(a2)*mod2 + sqrt(a3)*mod3 ;



for u = 1:length(Pt)
    %received signals
    y1 = sqrt(pt(u))*x.*h1 + n1;
    y2 = sqrt(pt(u))*x.*h2 + n2;
    y3 = sqrt(pt(u))*x.*h3 + n3;
    
    %perform equalization
    eq1 = y1./h1;                                                          %At user 1
    eq2 = y2./h2;                                                          %At user 2
    eq3 = y3./h3;                                                          %At user 3
    
    %Demode at user1 (direct decoding)
    dem1 = step(QPSKdemod, eq1);
    demodulated1_image = data2image(dem1', row_im, col_im, third_im, 2);   %Data 2 image conversion
    
    %Demode at user2 
    dem12 = step(QPSKdemod, eq2);                                          %Direct demodulation to get user1’s data
    dem12_remod = step(QPSKmod, dem12);                                    %Remodulation of user1’s data 
    rem2 = eq2 - sqrt(a1*pt(u))*dem12_remod;                               %SIC to remove user1’s data
    dem2 = step(QPSKdemod, rem2);                                          %direct demodulation of remaining signal
    demodulated2_image = data2image(dem2', row_im, col_im, third_im, 2);   %Data 2 image conversion
    
    %Demode at user3
    dem13 = step(QPSKdemod, eq3);                                          %direct demodulation to get user1’s data
    dem13_remod = step(QPSKmod, dem13);                                    %Remodulation of user1’s data 
    rem31 = eq3 - sqrt(a1*pt(u))*dem13_remod;                              %SIC to remove user1’s data 
    dem23 = step(QPSKdemod, rem31);                                        %direct demodulation of remaining signal to get user2’s data
    dem23_remod = step(QPSKmod, dem23);                                    %Remodulation of user2’s data 
    rem3 = rem31 - sqrt(a2*pt(u))*dem23_remod;                             %SIC to remove user2’s data 
    dem3 = step(QPSKdemod, rem3);                                          %demodulate of remaining signal to get user3’s data
    demodulated3_image = data2image(dem3', row_im, col_im, third_im, 2);   %Data 2 image conversion
    
    %BER calculation
    ber1(u) = biterr(dem1, Encrypted1)/N;
    ber2(u) = biterr(dem2, Encrypted2)/N;
    ber3(u) = biterr(dem3, Encrypted3)/N;
    

end
 


 Decrypted1=bitxor(dem1,Cipher1);                                          %Decryption(XOR operation)
 Decrypted1_image =  data2image(Decrypted1', row_im, col_im, third_im, 2); %Data 2 image conversion
 
 Decrypted2=bitxor(dem2,Cipher2);                                          %Decryption(XOR operation)
 Decrypted2_image =  data2image(Decrypted2', row_im, col_im, third_im, 2); %Data 2 image conversion
 
 Decrypted3=bitxor(dem3,Cipher3);                                          %Decryption(XOR operation)
 Decrypted3_image =  data2image(Decrypted3', row_im, col_im, third_im, 2); %Data 2 image conversion
%--------------------------------------------------------------------------  
 figure(1)
 subplot(1,4,1);
 imshow(original1_image,[]);
 subplot(1,4,2);
 imshow(Encrypted1_image,[]);
 subplot(1,4,3);
 imshow(demodulated1_image,[]);
 subplot(1,4,4);
 imshow(Decrypted1_image,[]);
 
 figure(2)
 subplot(1,4,1);
 imshow(original2_image,[]);
 subplot(1,4,2);
 imshow(Encrypted2_image,[]);
 subplot(1,4,3);
 imshow(demodulated2_image,[]);
 subplot(1,4,4);
 imshow(Decrypted2_image,[]);
 
 figure(3)
 subplot(1,4,1);
 imshow(original3_image,[]);
 subplot(1,4,2);
 imshow(Encrypted3_image,[]);
 subplot(1,4,3);
 imshow(demodulated3_image,[]);
 subplot(1,4,4);
 imshow(Decrypted3_image,[]);
 
 figure (4)
 semilogy(Pt, ber1, 'b-o', 'linewidth', 2);
 hold on;  grid on ;
 semilogy(Pt, ber2, 'r-s', 'linewidth', 2);
 semilogy(Pt, ber3, 'k->', 'linewidth', 2);
 xlabel('Transmit power (dBm)');
 ylabel('BER');
 legend('User 1 (Weakest user)', 'User 2', 'User 3 (Strongest user)');
 

[Jan]

Now you are using

Encry1 = bitxor(original1_Data',Cipher1);

The tranpspose operator ' works with matrices only. In the first example your data was an RGB image, which is imported as 3D array. Not the original data are a 2D matrix. Why do you transpose it?

I cannot run your code due to themissing images and the functions "data2image" and "image2data". But you can use the debugger to examine, what's going on: Set a break point in the first line and step through the code. The problem concerns the dimension of the image data and the cipher. Clarify what happens with RGB and grayscale images.

[Muhammad Abdulrazek]

data2image:

%--------------------------------------------------------------------------
%this function is to transfer data type back to image for display
%
%Chen Zhifeng
%2007-05-19
[e-mail]
%I left this function as is since I'm clueless and a neophyte in image
%processing. JC 7/16/08
%--------------------------------------------------------------------------

function im = data2image(Data, row_im, col_im, third_im, M);%changed data to Data
% M =4;
data = Data';%changed data' to Data'
l = length(data);
col =ceil( 8/log2(M) ); %in case M = 8, 32, 64, 128, we need ceil
row= l/col;
Tm = zeros(row,col);
for i = 1:col,
    Tm(:,i) = num2str(data((i-1)*row+1 : i*row));
end
%temp = char(Tm);
%Tmn = num2str(temp);

V_im = base2dec(Tm,M);
im = zeros(row_im, col_im, third_im);
for i=1:third_im,
    for j=1:col_im,
        im(:,j,i) = V_im((i-1)*row_im*col_im+(j-1)*row_im +1 : (i-1)*row_im*col_im+j*row_im);
    end
end

image2data:

%--------------------------------------------------------------------------
%this function is to transfer image to data suitable for transmission
%
%Chen Zhifeng
%2007-05-19
[e-mail]
%%I left this function as is since I'm clueless and a neophyte in image
%processing. JC 7/16/08
%--------------------------------------------------------------------------

function [data, row_im, col_im, third_im] = image2data(im, M)
% im = imread('photo.bmp');
% M =4;
[row_im, col_im, third_im] =size(im);
V_im = zeros(1, row_im*col_im*third_im);
for i=1:third_im,
    for j=1:col_im,
        V_im((i-1)*row_im*col_im+(j-1)*row_im +1 : (i-1)*row_im*col_im+j*row_im) = im(:,j,i);
    end
end

%I use dec2base here, then if M>8, for example M=16, the result string may
%include characters, this is not appropriate to use str2num below. However,
%due to the time limit, I will not add function here to deal with this.
%Actually, this may be done by dec2bin function.
Tm = dec2base(V_im,M);
[row, col] = size(Tm);
% data = [];
% for i = 1:col,
%     data = [data; Tm(:,i)];
% end
% 
%data=[];
for i =1:col,
    data(row*(i-1)+1:row*i)=str2num(Tm(:,i));   %very important to add str2num here
end
%Tm = str2num(Tm_char);

%data = str2num(data);

Images are normal grey scale images , i used rgb by mistake

my problem is : how to get the image data & the cipher of the same dimensions to accomplish the bitxor function ?