University of Isfahan International Journal of Group Theory 2251-7650 14 2 2023 12 29 An overview of torus fully homomorphic encryption 59 73 28010 10.22108/ijgt.2023.139030.1869 EN Maria Ferrara Dipartimento di Matematica e Fisica, Università della Campania “Luigi Vanvitelli”, viale Lincoln, 5 - 81100, Italy Antonio Tortora Dipartimento di Matematica e Fisica, Università della Campania “Luigi Vanvitelli”, viale Lincoln, 5 - 81100, Italy Maria Tota Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, 132 - 84084 - Fisciano (SA), Italy Journal Article 2023 09 05 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,<em> STOC '09: Proceedings of the forty-first annual ACM symposium on Theory of computing</em>, 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.

https://ijgt.ui.ac.ir/article_28010_ce3bd36fdffff4ea67a1dd4de2776590.pdf