How can a computer calculate on data it is not allowed to read?

A computer can calculate on data it cannot read if that data is locked with homomorphic encryption. This is a form of encryption that allows computations to be performed on encrypted data without first decrypting it. The answer comes back still locked, and when its owner finally unlocks it, it is identical to what the same operations would have produced on the unlocked data. You hand over a sealed box, the other side does the work through the walls, and only you ever see the result.

That solves a real dilemma. Predictive analytics in healthcare is hard to run through an outside company because of medical privacy concerns. But if the provider can operate on encrypted data without having the decryption keys, those concerns shrink. And even if the provider's system is broken into, the data would remain secure. The same trick lets data be encrypted and sent to commercial cloud services for processing, all while staying encrypted.

Some schemes only go part of the way. These are called partially homomorphic, because they support circuits made of only one type of gate, such as addition or multiplication. The dream was fully homomorphic encryption, which can evaluate any computation at all. The problem was first proposed in 1978, within a year of the publication of RSA, and then for more than 30 years it was unclear whether a solution existed.

In 2009 Craig Gentry used lattice-based cryptography to describe the first plausible way to build it. It was painfully slow: the first implementation of his original scheme took about 30 minutes for a single basic bit operation. Years of work have since sped it up by many orders of magnitude, and in 2017 researchers from IBM, Microsoft, Intel, NIST and others formed a consortium that maintains a community security standard for it.