|English: Encrypted message authentication (Photo credit: Wikipedia)|
Cryptographers have devised a way to perform any mathematical operation on encrypted text, allowing processing of this encrypted text without decrypting it. Think of it like this: You run a jewelry store but dont trust your employees to manage precious jewels and not steal them. So, you lock raw materials in a box, they have gloves into this box, and they can create rings/pendants using the gloves, but never steal the contents once they finish because its locked. Later on, you unlock the boxes yourself, without risk of anyone stealing it.
What does this mean for us? We can perform any mathematical circuit of functions on our encrypted, private data on untrusted systems (see: “The Cloud”), without ever exposing that encrypted data to untrusted users, servers or machines. Online banking, where you transfer/add/remove funds on an account without ever showing the account number? Check. Google Docs / text processing in the cloud without ever revealing what you are writing to the people who own those servers? Check.
The issues right now is that it takes a long time to generate keys and perform these functions. But to be able to live in a time where this was correctly implemented is mindblowing.