I am aiming to find out if this problem/puzzle can be solved with cryptography at all. Say there are these two parties:
- Subject S which has a master private/public key pair (MPriv, MPub) and a set of key pairs derived from MPriv. Each of the derived pairs has its own public ID, and the private keys are merely the concatenation of MPriv and the ID (this appears to be achievable);
- Trusted party T which issues proofs/certificates to subjects like S. These proofs are linked to the subjects' public keys and are used to demonstrate to the whole world that whoever has the corresponding private key is such-and-such-and-such (which T would have verified by appropriate means before issuing the proof; let's call this proof content).
So, say S has obtained a proof from T for one of his public keys (either MPub or one of the derived ones). Is there a way for S to "relay" the proof to another derived key from the same set? That said, could S, without going to T again, somehow use the proof he has already got to derive a proof of the same content for another key in the same set? From the point of view of the public, the original proof and the derived proof would appear unrelated — apart from that they have the same content and are issued by T.