>How do you prevent leaks?
By leaking things, Tyrion Lannister style. Each potential leaker (Littlefinger/Varys/Pycelle) is given different pieces of information (Arryn/Greyjoy/Martell), and whichever piece reaches its intended target (Cersei) reveals the leaker.
In this case, we the public are Cersei, and the leak bait provided by POTUS/MI reveals the leaker via the media.