Why is RSA unsafe if N=pq can be factored? I just started learning about cryptography and specifically RSA, and the texts I have read don't have a proof or explanation for why RSA is unsafe if you can factor N=pq, it merely asserted this. Is there a formal reason for this?
Thank you in advance :)
Let's assume RSA works.
There is a person, who created the key. He chooses 2 primes, multiplied them, and publishes the modulus with another number he can choose almost freely (it has to be coprime to $(p-1)(q-1)$).
So if you give the attackers the factorization, what else is there, that the attackers does not know? There isn't anything.
There is not much to put formally. If the attackers knows all secret information, there can not be any security. What should it be based on? Unless we allow security to be based on magic fairy dust.