RSA algorithm for image encryption

c

lc;
clear all;
format longE
disp('RSA algorithm');
p=input('Enter the prime no. for p: ');%23
q=input('Enter the prime no. for q: ');%13
n=p*q;
fprintf('\n n=%d',n);
phi=(p-1)*(q-1);
fprintf('\n phi(%d) = %d',n,phi);
e=input('\n Enter the value for e relatively prime to phi:');%23

%% find inverse for e
for d=1:phi
    f=mod(e*d,phi);
    if f==1
      break
    end
    
end


c=[2 254 123;214 231 189;241 253 3]% image matrix
A=[];
B=[];
%% cipher image
for i=1:3
    for j=1:3
        A(i,j)=mod(c(i,j)^(e),n);
    end
end
%% decrypted image
for i=1:3
    for j=1:3
        B(i,j)=mod(A(i,j)^(d),n);
    end
end

[Ameer Hamza]

This question might not be appropriate for this forum: https://www.mathworks.com/matlabcentral/answers/438831-is-discussion-of-cryptography-allowed

Answer 1

[Madhu]

Dear Parveiz Lone

still you have the same doubt? Follow this code as it is.

img=imread('Lenna.jpg'); %Reading an RGB image
img=rgb2gray(img); % converting RBG image into grayscale image
img=imresize(img,[128,128]); % Resizing the image
img=reshape(img,1,numel(img)); % Reshaping 2D array into 1D array
img=double(img);
cip=zeros(1,numel(img));
ct=zeros(1,numel(img));
primenumbers=primes(1000);
p=primenumbers(randi(numel(primenumbers),1,1));
q=primenumbers(randi(numel(primenumbers),1,1));
n=p*q;
phi=(p-1)*(q-1);
e = randi([2, phi-1]);
while (gcd(e,phi)~=1)
    x = randi([2, phi-1]);
    if gcd(x, phi) == 1
        e = x;
    end
end
d=multiplicativeInverse(e, phi);
for i=1:1:numel(img)
    cip(i)=powermod(img(i),e,n);
    ct(i)=mod(cip(i),255); %Limiting cip to values less than 255.
end
ct=reshape(ct,128,128);
imshow(ct,[]);
pt=zeros(1,numel(img));
for i=1:1:numel(img)
    pt(i)=powermod(cip(i),d,n);
end
pt=reshape(pt,128,128);
imshow(pt,[]);
function result = multiplicativeInverse(a, m)
[g, result, ~] = extended_gcd(a, m);
if g ~= 1
    error('Inverse does not exist.');
end

result = mod(result, m);
end

function [g, x, y] = extended_gcd(a, b)
% Extended Euclidean Algorithm

if b == 0
    g = a;
    x = 1;
    y = 0;
else
    [g, x, y] = extended_gcd(b, mod(a, b));
    temp = x;
    x = y;
    y = temp - floor(a/b) * y;
end

[Madhu]

This code consists of both encryption and decryption of an image using RSA

[Madhu]

Further any doubts mail me to [e-mail]

[Kajal Chawla]

Respected mam, I have gone through your code and have a doubt regarding decryption of this code. When a reciever wants to decrypt the image he has the access to encrypted image matrix that is ct, but decryption code needs the matrix cip. Can you please clarify that?