I think I roughly understand how the RSA alorithm is working.
However, I don't understand why we need the $N$, which we use as a modulus, to be $pq$ for some large primes $p, q$.
I vaguely know it has something to do with factorization, but I am kind of lost. So, hypothetical questions.
- What would happen if the $N$ was not $pq$, but just a big prime?
- What if $N$ would be some random composite (that's easy to factor)?
The other parts of RSA would stay the same.