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Is it possible to use some cryptographic scheme to prove bitcoin ownership without revealing any information about value held in addresses?
How to prove bitcoin ownership without revealing amount?
Answers
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Dagher et al. Provisions privacy-preserving proofs of solvency may be what you are looking for:
The objective of Provisions is to enable an exchange E to publicly prove that it owns enough bitcoin to cover all its customers’ balances such that (1) all customer accounts remain fully confidential, (2) no account contains a negative balance, (3) the exchange does not reveal its total liabilities or total assets, and (4) the exchange does not reveal its Bitcoin addresses.
Full version of the paper available in J. Bonneau's web page.
Are you asking how to prove that you are the owner of a specific Bitcoin address without revealing the amount of bitcoins at that address? This would be inherently impossible since Bitcoin has a public ledger: as soon as you state "I am the owner of Bitcoin address foobar" then someone can look up "address foobar" independently on the public ledger and see the amount of bitcoins at it. – Vilhelm Gray – 2017-10-13T15:20:29.263
Alternatively, are you asking instead if there is a way to prove that you have access to a specified amount of bitcoins without revealing their source addresses (i.e. that you are capable of funding a transaction of a certain amount of bitcoins if you so desired)? – Vilhelm Gray – 2017-10-13T15:27:22.413