This article has details about how cards using the EMV protocl work, and discusses a vulnerability that seems to have been exploited in the wild regarding predictability of a nonce (called the "unpredictable number", funny enough).

http://www.cl.cam.ac.uk/~sjm217/papers/oakland14chipandskim....

Chip and Skim: cloning EMV cards with the pre-play attack Mike Bond, Omar Choudary, Steven J. Murdoch, Sergei Skorobogatov, Ross Anderson Computer Laboratory, University of Cambridge, UK