The right to bear arms

In another example of Anthony Kennedy's omnipotence, the Supreme Court ruled today that individuals have the right to own firearms outside the realm of an organized militia. Though I still don't really see how this interpretation arises from the text of the second amendment, the troubling issue arises from Scalia: From the NYTimes:

Scalia said nothing in Thursday's ruling should "cast doubt on long-standing prohibitions on the possession of firearms by felons or the mentally ill, or laws forbidding the carrying of firearms in sensitive places such as schools and government buildings."

But where does this assurance arise? If carrying a weapon is a constitutionally protected right and there are no explicit measures for removing that right, I don't see where Scalia can argue that longstanding restrictions to gun possession are safe. Maybe he expands on his reasoning later on in his opinion, but I don't know where he could get it from.