Let's say that I'm developing an iOS RPG where the player gains 1 point per monster kill.

The amount of monsters killed is persistent data: it is an endless adventure, and the score keeps on growing. It isn't a "session score" like Fruit Ninja, but rather a "reputation score".

There are Game Center leaderboards for that score. Keep killing monsters, your score goes up, and the leaderboards are updated.

My problem is that, technically, you can log out and log in using a different Game Center account, kill one monster, and the leaderboards will be updated for the new GC account.

Supposing that this score is a big deal, this could be considered as cheating, because if you have a score of 2000, any of your friends who have never played the game can simply log into your iPhone, play the game, and the system will update the score for their accounts, essentially giving them 2000 points in the leaderboards for doing nothing.

I have considered linking one GC account to a specific save game. It won't update your score unless you're using the linked GC account. But what if the player actually needs to change their GC account? Technically they would be forced to start a new game and link their account to that profile.

How should I prevent this kind of cheat? Essentially, I don't want someone to distribute a high schore to multiple GC accounts, given the fact that the game updates the score constantly since it isn't a "session score".

I do realize that it isn't quite a big deal. But I'm curious about how to avoid this.