The Doghouse: SecureRF
Claims to offer the first feasible security for RFIDs. Conventional public key cryptography (such as RSA) is far too computationally intensive for an RFID. SecureRF provides a similar technology at far lower footprint by harnessing a relatively obscure area of mathematics: infinite group theory, which comes (of all places) from knot theory, a branch of topology.
Their website claims to have “white papers” on the theory, but you have to give them your personal information to get it. Of course, they reference no actual published cryptography papers. “New mathematics” is my Snake-Oil Warning Sign #2—and I strongly suspect their documentation displays several other of the warning signs, too. I’d stay away from this one.