In A fully homomorphic encryption scheme, Gentry provides a plausible candidate construction of a fully homomorphic (FHE) scheme, answering the problem posed in 1978 by Rivest, Adleman, and Dertouzos in On Data Banks and Privacy Homomorphisms.

A FHE cryptosystem is one that is homomorphic under both addition and multiplication and yet still secure. FHE makes it possible to perform arbitrary computations (mathematical operations like sum or product as well as more complicated operations) on encrypted data while it remains encrypted — and without needing a secret key.

To put everything online “in the cloud,” unencrypted, is to risk an Orwellian future.”
— Craig Gentry

Although FHE is not yet practical for widespread implementation, Gentry’s breakthrough has enormous implications for making cloud computing more secure and compatible with the data privacy for individuals.