Thing which leaps out at me:

You assume PGP encryption is secure. I believe that - at a very basic level - PGP encryption is mathematically similar to the problem of factorising large prime numbers, which is currently computationally "difficult". If an AI spent time working on number theory (given that it has access to all of our world as an input, it would certainly be up to date with our most advanced techniques) there's a danger it would simply be able to prove the Riemann Hypothesis and enter the world having already learned to quickly decrypt all of our communications.

This doesn't affect this as a thought experiment, but please don't try to implement this as stated.