What chips can be used to design an Anti-Counterfeit /Authentication circuit?
Use whatever $0.25 micro-controller you want.  Put one controller in your power supply and another one in each device you want to attach.

The controller in both devices (supply and attached peripheral) contain a 128-bit secret key K.

The supply sends out a 128-bit random challenge word W that never repeats.  The seed for the challenge word W should be stored using non-volatile memory in such a way that the seed does not reset if you loose power (to avoid play-back attacks).

The device sends back the SHA-512 hash H1 of K xor W.

The controller in the supply also computes the same hash H2.  If H1 and H2 match then the attached device knows the secret key and is therefore authenticated.  If H1 does not match H2 then the attached device is either broken or counterfeit.

This scheme avoids ever sending the secret key K between the devices.  Therefore no-one can record it.

Any code-protection in the controller in both devices should be turned on so no-one can read out your secret key by opening the boxes.