This is a follow-up to this answer. The context & vocabulary used is that of a decentralized identity system.
Let $I$ be the issuer of a credential, $H$ the holder and $V$ the verifier. In this setting, $I$ signs a credential $C$ with their private key, and hands it over to $H$ for storage, who may then present it to $V$ to prove their identity.
One flaw remains in this system: if such were the intentions of $V$, nothing prevents them from giving the signed data contained in $C$ to a third-party, who could then verify & attest that the credential is authentic even though $H$ didn't give the credential themself.
How could this be avoided?
Note: regarding the link between this question and the answer cited above, I'm not sure if the question I asked about deniable authentication was formulated well enough: I wasn't interested in making the ZKP unreadable to third parties (I fear this is impossible if Bob / $V$ is part of the conspiracy), but my goal was to make the whole credential (passport, in that case) no longer provably authentic.