So I want to create a zero-knowledge proving system for numbers (think loans and bank accounts, I want to prove my paycheck is more than x dollars per month).
I was thinking about using a zero-knowledge proof for the preimage of a hash. So let's say my employer hashes my paycheck in such a way (e.g. using merkle trees) that my net received is hashed individually. I can use a preimage proof to prove I know the preimage of the hash, but that does not get me anywhere. I want to prove the preimage of the hash is bigger than some set amount.
But that also is not very useful as I don't want to disclose the hash of my paycheck, because it's not difficult to hash all possible amounts (let's say 500.00-5000.00, that's only 450k options) and check if it's equal.
So what I thought about doing is append a random string to the amount, and hash that. Is there a way I can prove that a hash of a string containing a number is bigger than some amount? Or am I thinking about this the wrong way?