Distinguishing Original VS Fake Products Let's assume that we want to distinguish original vs fake products when a customer receives them. I was thinking about using a protocol similar to digital signature. 

My question is can this problem be mapped to digital signature? 
If not, what other security protocol can we use?

More details:
I was thinking about using the digital signature. Let's assume the original company writes a pair of digital signature and plain text on the product. Then, when customer receives it, (s)he can verifies it using the protocol (you may refer to here (3' 56'') for the protocol), and understands if the item is coming from the original sender or not.
However, the attacker can come in the middle, make a product, and copy the digital signature and the plaintext from original one!
This problem is well defined for supply chain management, and generally you use a challenge-response.  In RFID, you an use asymmetric or symmetric schemes to verify that a product is authentic.  I give RFID as an example because you should be able find a lot of documentation on them.

In the asymmetric case:


A authentic product public key is on the interrogator and the product sends a unique id  (UID).
The interrogator responds with the created signature
The product sends it's signature


In the symmetric case:


The product sends a UID to the interrogator
The interrogator sends a challenge to the product
The product sends a response.


The asymmetric case allows you verify the authenticity of a class of product without a network to know the key for each device.  The symmetric case requires some method to get the key to the interrogator to verify the response because usually the key and the challenge verification are on a server somewhere.

Grab any notes on verifying a supply chain and these schemes will be described in detail.

Update:  An example from NXP.