> Cracking the RSA algorithm itself is basically equivalent to turning r back into p and q.
This has not been proven. RSA encrypts by taking C=m^e (MOD N). The normal way of decrypting is to take C^d (MOD N), where d can be efficiently computed if you know the factors of N. However, all you need to do to decrypt C is to take the e`th root (mod n). It has not been shown that the ability to do so allows you to factor N.
In fact, it appears (after a few minutes of research, so someone please correct me if I'm wrong), that their is evidence that breaking RSA is easier than factoring [1]
This has not been proven. RSA encrypts by taking C=m^e (MOD N). The normal way of decrypting is to take C^d (MOD N), where d can be efficiently computed if you know the factors of N. However, all you need to do to decrypt C is to take the e`th root (mod n). It has not been shown that the ability to do so allows you to factor N.
In fact, it appears (after a few minutes of research, so someone please correct me if I'm wrong), that their is evidence that breaking RSA is easier than factoring [1]
[1]http://crypto.stanford.edu/~dabo/pubs/papers/no_rsa_red.pdf