ABC Conjecture's Impact on RSA Encryption
There are no known implications of the ABC Conjecture to RSA.  The ABC problem doesn't have even a superficial resemblance to the security of RSA.

(The only point of connection is the fact that they both relate to prime numbers, but that is extremely thin.  Much of number theory can say it is somehow related to prime numbers.  It'd be like assuming that recent improvements in building fast sailboats for the America's Cup has implications for the possible future availability of a flying car, since they both involve fluids.)