How to prove bitcoin ownership without revealing amount? Is it possible to use some cryptographic scheme to prove bitcoin ownership without revealing any information about value held in addresses?
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.