The security aspect is based on the fact that it's difficult to factor it back into p and q Now, since rsa keys are so large (often 1024 bits and above), the primes have to be at least half that (at least 512 bits then). It is hard to imagine very big numbers So what would be your way to explain the difference to someone who doesn't know much about cryptography? I know that the sizes are standardized to $1024$, $2048$ etc By the way, it's not clear if your question is about the correctness of rsa or the security of rsa (i.e
Does rsa need to have a modulus with two prime factors to be correct vs does rsa need to have a modulus with two prime factors to be secure). Rsa encryption whose security is based on the infeasibility of solving the factoring of big primes problem and the elgamal encryption which is as secure as the discrete logarithmic problem The question is whether or not there are specific circumstances where you must use elgamal instead rsa and vice versa. Its relationship to security level is more complex than in ecc Is there much difference in security between the two Why is prime number size important for rsa security
