Guide to Fully Homomorphic Encryption over the [discretized] Torus.

First posed as a challenge in 1978 by Rivest et al. [RAD78], fully homomorphic encryption—the ability to evaluate any function over encrypted data— was only solved in 2009 in a breakthrough result by Gentry [Gen09, Gen10]. After a decade of intense research, practical solutions have emerged and are being pushed for standardization. This guide is intended to practitioners. It explains the inner-workings of TFHE [CGGI20], a torus-based fully homomorphic encryption scheme. More exactly, it describes its implementation on a discretized version of the torus. It also explains in detail the technique of the programmable bootstrapping.