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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).
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  • $\begingroup$ Is it required that the third party doing the verification does not need to hold confidential data allowing whoever holds that data (including the third party) to forge a Unique Non-Reproducible ID? Is it required that a serial number (perhaps, sequential) is A) a subfield of the UNRID? B) recoverable by some other public process from UNRID? C) hidden but recoverable by some other process requiring a secret key? D) not needed? $\endgroup$ – fgrieu Nov 26 '19 at 10:06
  • $\begingroup$ @kelalaka: I'm not familiar with RFC 4122, but I do not see that its UUIDs are verifiable as thought by the question. $\endgroup$ – fgrieu Nov 26 '19 at 10:09
  • $\begingroup$ @fgrieu Not sure I understand the first question. I am interested in two cases: (1) The genuineness of the label should be publicly verifiable, and (2) The genuineness of the label should be verifiable by an entity given some secret information by the manufacturer. A serial number can be used if needed, but in my eyes it should be possible to avoid it. $\endgroup$ – Chipotle Nov 26 '19 at 10:25
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It is desired a Unique Non-Reproducible ID (UNRID) which genuineness is publicly verifiable.

I know no standard for that. But we can take as UNRID the signature of a public fixed message (e.g. empty), if the signature scheme is randomized and EUF-CMA secure. Verification simply checks the signature. If probability of collision among signatures is satisfactorily low, security follows from EUF-CMA.

The signature scheme could be RSASSA-PSS of PKCS#1v2.2, with the advantage of fast signature verification. But for modern security that requires 256 bytes (342 Base64 characters), which is a lot.

A more compact option is a slight variant of ECDSA, where a signature $(r,s)$ becomes the UNRID $(r,\min(s,n-s))$, which is presented as EUF-CMA secure there, without proof but plausibly: EUF-CMA security of the signature scheme matters in Bitcoin, and was repaired with apparent success, in a manner equivalent to what's proposed. That would make the UNRID 64-byte (86 Base64 characters).

Using a signature scheme with message recovery, we can embed a serial number or other small ancillary information in the UNRID, without making it bigger. For RSA, ISO/IEC 9796-2 Scheme 2 would do (it's essentially RSASSA-PSS with message recovery). There are ECC-based randomized signature schemes with message recovery as compact as ECDSA, see bibliography.

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