why do I get NaN result

I am trying to code a RSA encryption and I either get a Nan result where I should get a number or Matlab doesn't create that variable at all. Can somebody help me? The code is below:

fid = fopen('input.txt', 'r');   % We have to first open the file 'Input.txt'
plain = fscanf(fid, '%s', [5,1]);  % We write the 5 letter word in the file as a 5x1 matrix
fclose(fid); % We close the file

plainascii = double(plain);   % Now we have the numeric values of the letters depending on ASCII code

% We reduce the numbers in such a way that A=0, B=1, ... Z=25.
for i = 1:5
    plainmod(i) = plainascii(i) - 65;
end 

% We add the numbers in Z_26 and make it ready for encyption 
plainnumbers = 26^4*plainmod(1) + 26^3*plainmod(2) + 26^2*plainmod(3) + 26^1*plainmod(2) + 26^0*plainmod(1);

% Now, we move on to the key. We select two prime numbers between 100.000
% and 1.000.000. 

p = 459817;
q = 459817; 
n = p*q;

% We need to have a key set (n, e). To find e, we ask the user for a number. 
% We test that gcd(e, phi(n)) = 1. We define phi(n) as phin. 

phin = n - p - q + 1;

e = input('Please provide a number between 100.000 to 1.000.000 to use as key:\n');

if gcd(e, phin) == 1
    continue
else 
    e = input('This number is not valid. Please pick another:\n');
    
end 


ciphernumbers = mod(plainnumbers^e,n);
display(ciphernumbers);

[Andreas Bernatzky]

Because you get an overflow with plannumbers^e which is "inf".

I do not know the rsa algorithm well enough but a simple solution could be choose a value from e in a much smaller range something between 10 and 100 for example. But as I say I am not an expert for crypthography.

[Nazli Demir]

I was wondering if that was it, but they told us to choose p and q large. But, now that you mention it, they didn't say anything about e. I will try with a different value for e. Thank you.

Answer 1

[Andreas Bernatzky]

Hey Nazil,

I can just remember the RSA really roughly but I did some researches yesterday evening and I read at several points to choose p and q large. But I did just some quick researches on it.

But fact u get an INF for plannumbers^e and that is the problem.

Also you could use this for allowing extra high numbers:

https://www.mathworks.com/matlabcentral/answers/489112-how-to-use-large-numbers

Greets Andreas

[Nazli Demir]

Thank you for this Andreas!