Say that a manufacturer wants to label her products in such a way that a third party could verify that the manufacturer is the one that labeled the product, meaning it's not a counterfeit.
The manufacturer could have a serial number to each product, and have it signed with some signature scheme. However, this introduces some redundancy, as a verifier would have to use both the manufacture's public key and the serial number.
Is there a different, more efficiently method create such labels?
Two cases are of special interest:
- The label should be publicly verifiable.
- The label should only be verifiable by an entity that share some secret information with the manufacturer (so perhaps encryption schemes are relevant).