Maria Ferrara - Dipartimento di Matematica e Fisica, Università della Campania “Luigi Vanvitelli”, viale Lincoln, ۵ - ۸۱۱۰۰, Italy
Antonio Tortora - Dipartimento di Matematica e Fisica, Università della Campania “Luigi Vanvitelli”, viale Lincoln, ۵ - ۸۱۱۰۰, Italy
Maria Tota - Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, ۱۳۲ - ۸۴۰۸۴ - Fisciano (SA), Italy

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 ۲۰۰۹ thanks to Gentry [C. Gentry, Fully homomorphic encryption using ideal lattices, STOC '۰۹: Proceedings of the forty-first annual ACM symposium on Theory of computing, Association for Computing Machinery, New York, (۲۰۰۹) ۱۶۹--۱۷۸.] 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.

TFHE, fully homomorphic encryption, Bootstrapping, learning with errors