At the moment, producing a zero knowledge proof has roughly a million-fold overhead compared to running a program directly. So there aren't many applications where that's acceptable. So I am very grateful that the blockchain people are more than happy to throw money at the math here. Very generous of them.
In principle, you can use ZKP for privacy preserving compliance work in real (ie traditional) finance.
To quote myself (https://news.ycombinator.com/item?id=41422250):
> Eg Goldman Sachs could encode all their compliance rules in a program, and publish a proof that their books pass the check by that program, without revealing anything about their accounting.
> In a banking context, you could in theory also run your know-your-customer (KYC) rules against customer provided data, store the proof, and delete the original data. That way, you still have proof that your customers don't have ties to North Korea or Russia, but you can't be compelled by anyone to reveal the data later (nor accidentally leak that data, etc).
> Of course, for that latter application, you need a sharp lawyer to make sure that storing the proof instead of the original data is enough for your KYC obligations.
> If you want to go further, you could have your customers run the KYC rules locally, so that their data never leaves their premises.
> (For all these applications, you still have to have a mechanism that connects the real world to the inputs of the programs whose execution you are proving.
> So eg Goldman Sachs would still need an auditor that checks that the assets and obligations they have in their balance sheet actually exist, but the auditor does not otherwise need to make judgement calls or apply any rules.)
