[FRIAM] *-sovereignty

[Jon Zingale]

I suppose the slogan could be:
"Proofs are to propositions as identities are to agents",
and in the context of zero knowledge protocols, the parallel extends to:

φ: Verifying a proof without exposing the proof.
ψ: Verifying an identity without exposing the identity.

To the degree that φ is the case and that the formal analogy connecting
φ to ψ holds, I suspect ZKP is sufficient for establishing self-sovereign
identity.

In practice, I imagine that to each agent a provable proposition (of
some significant computational complexity[κ]) is assigned. The statement
is then converted into a 3-coloring problem[З] while the proof is
transformed into an instance of one such 3-coloring. The rest is pressing
plates. It seems worth mentioning that just as a proposition may have
many proofs, an agent may have many identities.

A thing that has always impressed me about ZKP is that the verification
process is constrained to be a local process. That is, at no point does
the verifier get a global picture[λ] of the proof (as that would give the
proof away) and instead, in the spirit of a Las Vegas algorithm, one
verifies only up to taste.

For those interested, I highly recommend this numberphile episode:
https://www.youtube.com/watch?v=5ovdoxnfFVc&ab_channel=Numberphile2

[κ] Where the proposition is about products of RSA group elements, some
discrete log problem, or some other trapdoor function.

[λ] In my much earlier post to Nick on limits of inference, I attempted
to connect this locality to physical limitations such as light cones,
and propositions to phenomena like spin. Unfortunately, EricC shrugged
and nothing more came of it ;)

[З]
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.419.8132&rep=rep1&type=pdf
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