Would you happen to know of a good reference for this? I have a Proxmark and I'd like to learn how the encryption works so I can play around with (and maybe clone) some of my cards.
These systems usually do mutual authentication, and that's as much a side effect of the cryptographic primitives used as it is an intentional feature:
They're often using symmetric cryptography (even ECC is orders of magnitude more complex than a simple block cipher), and you get mutual authentication "for free" that way, in exchange for having to guard the keys on both the card and the reader to prevent a total compromise.