Ask HN: What are the attack vectors for a mobile app?

I've got an idea for an app that would require it to keep a private key. If this key were compromised it would have severe security implications for the user.

I'm wondering how possible it would be to make such an app secure. What attack vectors should I be thinking about? Is this something that should only be attempted on a hardened handset... or not at all? Any ideas or feedback greatly appriciated.