I don't see how proving the Riemann Hypothesis would help cracking RSA? If it helps, couldn't you just assume it is true and start cracking RSA today? If you ever hit a point where it doesn't work then BOOOM: Riemann Hypothesis disproven!
I think it is the other way around--disproving the RH might break some things.
Most mathematicians believe RH is true, and generally when doing industrial number theory people operate under the assumption that RH is indeed true and so if they need to use X to justify something and there is a theorem of the form "if RH is true then X" they use X.
Thus a proof of RH is not a problem. It just confirms that what people applying number theory already assumed was correct.
A disproof means that those X's might not be true and their use would need to be reassessed.
