# Dereks Time Travel Note Books: III Zero Knowledge Proof Paradoxes

For reasons not entirely clear, Derek had a rake of notes about Zero Knowledge Proofs.

The notes began in the 1986 Diary, in January, and ended in the 1987 Diary in December.

January 1st 1986 read as follows:

A Zero Knowledge Proof has three strict requirements:

First completeness: if a statement is true, the Honest Verifier will be convinced of this truth by an Honest Prover and that proof will be by following the proof protocol correctly.

Second soundness: if the statement is false, no Dishonest Prover can convince the Honest Verifier that it is true, except with some small probability.

Zero Knowledge: if the statement is true, no Verifier learns anything other than the fact that the statement is true.

Derek began with a Sketch For A Truth Protocol For Time Travellers.

A pair of Time Travellers, the Honest Verifier Time Traveller and the Honest Prover Time Traveller meet at some space time coordinates which they agree is the Present. The Present must be travelled to from the Future or the Past, which is to say, from the Future Light Cone or the Past Light Cone but not from Absolute Elsewhere of the Present.

Derek began: a Pair of Time Travellers have travelled from the Other to the Absolute Elsewhere of the Now - and then crossed it out. Beginning again, Derek wrote: a pair of Time Travellers have travelled from the Past to the Future which is the Present or from the Future to the Past which is the Present. These two Time Travellers are the Honest Prover and the Honest Verifier.

The Honest Prover must be able to provide the Honest Verifier with a true statement that is Complete, Sound and Zero Knowledge. This must amount to the statement "I am from the Future and am here in the Present" or "I am from the Past and am here in the Present".

The claim of originating in the Future or in the Past is an important part of the statement which is not separable from the claim about being here in the Future.

There are Four Scenarios: Future Honest Prover and Future Honest Verifier (I); Past Honest Prover and Future Honest Verifier (II); Past Honest Prover and Past Honest Verifier (III); and, Future Honest Prover and Past Honest Verifier (IV). Each scenario has slightly different constraints and, because Time is relational, these four scenarios have further constraints.

In Scenario (I), the Future Honest Prover might come from the Future or the Past of the Future Honest Verifier and both come from the Future of the Present. This adds a level of subtleness to the Zero Knowledge Proof. The Prover must make a statement that is sound, complete and zero knowledge that encapsulates the temporal relationship to the Verifier as well as the temporal relationship to the Present. Similar constraints arise for Scenarios (I), (II), (III), and (IV).

The key to all of the scenarios is, quite literally, a key.

The Future of the Present has an intrinsically higher Entropy than the Present. The Past of the Present has intrinsically lower Entropy than the Present. The Four scenarios amount to the Honest Prover being able to say, I know more information than you; or I know less information than you. The main barrier this runs into is the Liar Paradox. When the Liar Says "This Statement Is False" there is a problem. If the statement is, in fact, False then it must be True and therefore the Statement must be False. This Liar Paradox forms the basis of the conversation between the Honest Prover and the Honest Verifier. The entire Paradox enables both the Prover and Verifier to provide Zero Knowledge Proof, switch roles and again provide Zero Knowledge Proof.

The key to all of the scenarios is a Blockchain Ledger with the Liar Paradox as the mechanism of Proof.

Derek's first sketch of a Protocol ended there. He returned to it several times, annotating, revising, and even replacing and going back to earlier versions. His key to all of the scenarios was never far from a Blockchain Structure.

Which seemed to precede the actual invention of the Blockchain Ledger by some years. Yet, if the marginal notes are to be believed, this is just a matter of not understanding the History of Blockchain. In the Margin of the First of April 1987 was a note: "read David Chaum's Dissertation on 'Computer Systems Established, Maintained, and Trusted by Mutually Suspicious Groups' again. It is five years old, but still fresh."

The consensus element of the Blockchain Ledger came later. Satoshi was never that concerned with time travel. Which is a bit of a shame as, according to Derek, all Currency Exchanges amount to some kind of Zero Knowledge Proof of one kind or another.

Imagine being colour blind. I tell you that there are red and green balls. I show you a pair of balls. One, I say is Red. The Other, I say is Green. You say that I need to prove it. Which requires me to prove to something that you cannot experience. So I hand you both Balls. I do not tell you which colour each one is but, instead, say, hide them behind your back. Show me one and then hide it behind your back. Then swap them - or do not swap them - and show me a ball. I will tell you if they have been swapped. You will know if they have been swapped because you did the swapping. We repeat this process a large number of times and keep a tally of how many times I get the answer "swapped" correct. If I am guessing then I will guess correctly half the time. So long as I get my answer correct each time then I cannot be guessing: I know you swapped them and I can tell because one is green and the other is red. This is a zero knowledge proof.

Which is what happens at an Exchange, according to Derek. Indeed, it is the basis of the Consensus mechanism. Which makes all that talk about the Liar Paradox seem futile.

Hubert Huzzah

An ongoing manifestation of Thee Surrealerpool Collage of Alchymical, Flâneurial and ’Pataphysical Studies. An Institutuion with membership by invitation, coercion and accident only. Hawkers, Traders and Carlists not welcome except by exception.

Derek has given up Time Travel.

Derek has given up Time Travels for reasons of practical expedience and to devote more time to a particularly important project. Episode #1 of an intermittent series on Surrealism, Technology, and Science.

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