It lets you to prove a program without having to execute it, and without needing to send the potentially private bytes over the wire.
Privacy and identity is one example; like having a proof of some record of your identity that you can submit to an app (ie: age, citizenship, # of followers on twitter), without the need to share your personal details.
Succinct proofs is another application. If you have a distributed compute environment (think folding@home), you may want receipts that proves a user in the network correctly executed a program. With ZK, the idea is that it can be cheaper to prove a program executed correctly, rather than re-execute it.
Privacy and identity is one example; like having a proof of some record of your identity that you can submit to an app (ie: age, citizenship, # of followers on twitter), without the need to share your personal details.
Succinct proofs is another application. If you have a distributed compute environment (think folding@home), you may want receipts that proves a user in the network correctly executed a program. With ZK, the idea is that it can be cheaper to prove a program executed correctly, rather than re-execute it.