It would be pretty easy to design a hard-to-spoof system using public key cryptography. Each ship and traffic control system broadcasts its public key. Signals in either direction are encrypted using the public key, and decrypted using the private key. Combine that with a wide distribution system for known public keys (presumably as part of the shipping registry) and it's trivial to authenticate that anyone is either (a) who they say they are, or (b) obtained the private key of the entity they're pretending to be. Grabbing private keys and outrunning their invalidation update message might be a good motive for piracy or espionage.
Note that this removes the need for a sealed black-box transponder. Everything can be open and accessible. The private key and the subsystem that handles encryption/decryption are the only things that need to be carefully protected.