Bitcoin the network is fully transparent, which makes BTC not really fungible - it can and is traced, which creates better/worse BTC. This is why coinbase (small c) BTC is sold at premium.
Bitcoin should and will die, but in its place a thousand flowers will bloom.
FYI, you can have BTC asset without Bitcoin network in trust-less manner TODAY. See recent paper by Leona Hioki on the way to do it using Witness Encryption cryptographic scheme.
Financial privacy is a must-have, not a nice-to-have feature. Financial privacy does not prevent one from being able to pay taxes. But it definitely prevents this type of attacks.
1) pepesza finds "42424242" <- that is the solution that needs to be hidden from the world
2) Signature = sign("42424242", privk_pepesza)
3) Witness = Circuit("42424242", Signature, pubk_pepesza). `Circuit` program will validate things I've mentioned. a) is 42424242 a correct solution to the puzzle? b) is signature correct for "42424242" as msg and pubk_pepesza as signer? It will return a computation trace - the Witness.
4) Proof = Prove(Witness). This `Prove` program is specific to a zksnark flavor that is being used. Some flavors will produce Proof of constant size.
Now pepesza sends the Proof and pubk_pepesza to zamadatix. Zamadatix runs:
Result = Validate(Proof, pubk_pepesza). If Result is true, both a) and b) are correct. This allows zamadatix to learn if pepesza actually has a solution to the puzzle. Note that Validate(Proof, pubk_zamadatix) will return false.
`Validate` is the program which can be automatically compiled from the Circuit (and things that are dependent on the flavor of zksnarks used).
The whole thing revolves around two properties of zksnarks. First - they allow to prove any(*) computation. Second - they allow to use so-called hidden inputs. In example above `pubk_pepesza` is the only public input. "42424242" and Signature are both hidden inputs and don't have to be revealed. Thus Zamadatix can create a Proof' that will result in true = Validate(Proof', pukb_zamadatix), but that would require an independent discovery of "42424242" string. Or a hack of pepesza's machine.
The trick is to sign the secret, not the proof. And than to prove inside the circuit following claims:
1) secret (provided as a hidden input) is correct a solution to the puzzle
2) signature that signs the secret is correct (signature is provided as a hidden input)
3) signature corresponds to a public key (which is provided as a public input)
You don't need blockchain or interaction for that. You just provide the proof and you are done. As long as other people are not able to steal the secret and your private key - world knows that you are the only holder of the secret.
I think we are talking about three different scenarios.
You are describing attribution problem. "Solution to the puzzle is no longer a secret, it is a public knowledge. Who was the original finder?". This problem is not really concerned with the proof - there is nothing more to hide, milk has been spilled.
GP is speaking about a different problem. Thief is not stealing the secret - they are stealing the proof that secret exists. In GP's scenario thief hacks GP's machine - which is not necessary, since GP is likely to show the proof to the world himself.
> That means if someone snoops my machine and tries to use my proof to claim that they know the answer, I can spot it as a stolen proof. However, without revealing the treasure, I wouldn't be able to prove that they stole it, because it is equally possible that I stole it from them.
And I was specifically addressing the situation when GP has made proof public. In such scenario thief can point the finger at the proof and claim that they have produced it. Solution described by me prevents thief from doing it, since proof will contain a public key from a keypair thief does not possess.
Why would it? Both signatures and snarks are non-interactive. And since you prove any(*) computation with a snark, you can prove that computation that verifies something (signature or snark proof) went well.
There are multiple ways of pulling this off. Signatures are zk-proof systems, just a very specialized ones. So you do it every time you sign a message.
Sign the puzzle solution with your private key. Check signature inside the circuit. This obviously can't be applied to this particular game since it has a circuit that does not employ such measures. Alternatively, if used snark is recursive - create a new circuit that will both validate original proof and check the signature.
Think of Kessler syndrome. One can imagine that blowing (small) N of them would create a cloud of shrapnel posing danger for the whole network. Birds are on really low orbits, so it would clear after some time, but network might not survive this.
Don't give them any info. Write something along the lines of "transfer of money", always. Use separate channel to communicate "why". Every bit of information you give them will be used against you.
Bitcoin should and will die, but in its place a thousand flowers will bloom.
FYI, you can have BTC asset without Bitcoin network in trust-less manner TODAY. See recent paper by Leona Hioki on the way to do it using Witness Encryption cryptographic scheme.