an overview of torus fully homomorphic encryption

The homomorphic encryption allows us to operate on encrypted data, making any action less vulnerable to hacking. the implementation of a fully homomorphic cryptosystem has long been impracticable. a breakthrough was achieved only in 2009 thanks to gentry [c. gentry, fully homomorphic encryption using ideal lattices, stoc ’09: proceedings of the forty-first annual acm symposium on theory of computing, association for computing machinery, new york, (2009) 169--178.] with his innovative idea of bootstrapping. tfhe is a torus-based fully homomorphic cryptosystem using the bootstrapping technique. this paper aims to present tfhe from an algebraic point of view.