I would imagine existing cryptography could work. Each card could have a unique private key, and the public key would be associated with the students ID. At thi

I would imagine existing cryptography could work. Each card could have a unique private key, and the public key would be associated with the students ID. At this point, someone can verify a card is who it says it is by asking the card to encrypt a randomly generated message. Assuming we are using the method I described (as apposed to a crypto-system optimized for identification), the card would only need to be able to encrypt 1 block (probably 512-bits) for each identification. This seems quite doable.