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
.-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn UTC-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/
