I want to prove that I own an amount of ETH without revealing the address which holds it. I don't know if this is possible at all, whether with zk-snarks technology or any other way. I've found nothing on this and I'm not knowledgeable enough to figure out by myself. Does anyone can shed some light on this? Thanks!
It should be possible with a ZKP.
without revealing the address
That's the "zero-knowledge" part.
The ZKP part will be challenging in itself but I foresee another problem.
prove that I own an amount
An account balance will tend to leak meta-data. A precise balance will narrow the field to addresses that have exactly the same balance which would often be exactly one. Oh oh ... it is probably merely a matter of searching for the account with the balance that matches the "secret". So, you will need to obfuscate that further. For example, "balance of at least x". This will further complicate the ZKP you would need to construct.
Not trivial. I might summarize the challenge by saying that Ethereum is optimized for transparency so this sort of thing is awkward.
Hope it helps.