""" Could the verifier be allowed a global understanding using something akin to homomorphic encryption, though? """
In some sense I would suppose yes for FHE, but the method of verification in ZKP seems not to be. Again, you mentioned playing fast and loose with the bindings. It would be great to really understand FHE systems better, and there is always plowing through the Gentry paper or checking in on how far Google has publicly gotten with it. From what I understand about FHE, one encrypts some data (whole databases, perhaps) and then one can operate on that data in its encrypted form via homomorphisms. Now one can operate meaningfully on the data without having access to the data. I would suspect it is necessary to present a limited DSL of homomorphic actions to make this privacy truly work. One wouldn't want one of those accessible homomorphic actions to be to simply decode the database. """ So, I would have said: Just like propositions participate in many proofs, identities can employ many agents. But we're playing fast and loose with our bindings. "Agent" often means the object/thing, whereas "identity" means the attributes of that object/thing. So, maybe you accidentally flipped that as you went along in the post? """ I am considering the bipartite (hyper?) graph at the top of Stephen's earlier Wikipedia reference[ω]. There they use the word entity instead of the word agent. I do mean many proofs for a proposition, for instance, the proposition could be that there are an infinite number of primes. A piece that I could easily be missing is in the "colorings" formal analogy. There, do different formal proofs of a statement give different colorings? Is there ultimately an isomorphism between possible proofs and possible colorings? This part doesn't seem right to me, I would be surprised. So, I know I am missing something. [ω] https://en.wikipedia.org/wiki/File:Identity-concept.svg
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