Paper 2022/594

A CONCRETE approach to torus fully homomorphic encryption

Maria Ferrara and Antonio Tortora

Abstract

The homomorphic encryption allows 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 and 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, starting from the CONCRETE library which implements TFHE.