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There has always been a contentious trade-off between extracting utility from a user’s data and preserving their privacy— what if you could do both? This article gives an introduction to Fully Homomorphic Encryption (FHE), a family of encryption schemes that allows users to perform computations on encrypted data, upending the utility-privacy trade-offs.

The theory was first floated around in the late 70s (notably, by R and A of the RSA encryption team) but the first functional scheme was only proposed in 2009 by Craig Gentry. It was offensively inefficient, with multiplications of two encrypted numbers taking minutes. Since then, the pace of improvements and iterations has been ramping up and FHE has gone from prohibitively expensive to just impractical. With all it promises— whether in privacy-preserving ML, encrypted blockchains, or others— it’s becoming an important part of the conversation on privacy. So, read on!

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