I was reading CLRS and is said:If factoring large integers is easy, then breaking the RSA  cryptosystem is easy.Which makes sense to me because with the knowledge of $p$ and $q$, it is easy to create the secret key which the knowledge of the public key. Though, it explains the converse statement, which I don't quite understand:The converse statement, that if factoring large integers is hard, then  breaking RSA is hard, is unproven.What does the statement above formally mean? If we assume factoring is hard (in some formal way), why does that not imply that breaking the RSA crypto system is hard?Now consider that if we assumed that factoring is hard...and that we discovered that it meant that the RSA cryptosystem is hard to break. What would that formally mean?
Meaning of: 'If factoring large integers is hard, then breaking RSA is hard,' is unproven
cryptography