Fast fully homomorphic encryption (FHE) based on GSW and its ring variants

In this seminar, we present a fast fully homomorphic encryption (FHE) based on GSW and its ring variants. The cryptosystem relies on the hardness of lattice problems in the unique domain (e.g. the LWE family). After a brief presentation of these lattice problems, with a few notes on their asymptotic and practical average case hardness, we will present our homomorphic cryptosystem TFHE, based on a ring variant of GSW. TFHE can operate in two modes: The first one is a leveled homomorphic mode, which has the ability to evaluate deterministic automata (or branching programs) at a rate of 1 transition every 50microseconds. For the second mode, we also show that this scheme can evaluate its own decryption in only 20milliseconds, improving on the the construction by Ducas-Micciancio, and of Brakerski-Perlman. This makes the scheme fully homomorphic by Gentry's bootstrapping principle, and for instance, suitable for representing fully dynamic encrypted databases in the cloud.