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From what I can tell this is still an unsolved problem for Lightning, and it's not clear how to solve it
This is a solvable problem. You can do something similiair to how monero works where you give a signature that is valid over many utxos, so the verifiier knows that you own 1 of the utxos but it could be any of the ones you provided
Hmm interesting, but couldn't you potentially produce a lot of such "proofs". And how would you effectively blacklist a certain utxo/proof? Would all the utxos involved in that proof be tainted?
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Monero has something called key image to solve it. It ensures that each proof has an identical component based on the key. So you can know if two proofs are to the same key and discard duplicates but still don't know which one it is. I don't remember the details enough to say if it's possible to use on Bitcoin. Probably yes.
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