What does Riemann's hypothesis have to do with encryption?

Riemann's hypothesis does not facilitate the factorization of composite numbers (which is required for some types of encryption). The hypothesis "corrects" the error term for the current estimation of distribution of primes. Further, it is not a matter of "solving" RH which suggests it is some sort of high school algebra problem. Rather, it is proving (or disproving) the conjecture that the RH proposes; namely the location of the zeros of the Zeta function. Besides, if the RH could be used in the manner you are worried about you would not need a "proof" of it. Many constructs or theorems in mathematics are created assuming the RH is true. Some have suggested that the RH is, in fact, undecidable which is an even deeper and more squiggly can of worms.