Expanding on that, zk-snarks[0], a kind of non-interactive zero-knowledge proof[1] are really interesting. They're used as the basis for the anonymous cryptocurrency zcash[2], where one can prove they haven't already spent an input without actually revealing which input they are spending.
[0]: https://z.cash/technology/zksnarks.html
[1]: https://en.wikipedia.org/wiki/Non-interactive_zero-knowledge...
[2]: https://z.cash/