An overview of torus fully homomorphic encryption

Document Type : Ischia Group Theory 2022

Authors

1 Dipartimento di Matematica e Fisica, Università della Campania “Luigi Vanvitelli”, viale Lincoln, 5 - 81100, Italy

2 Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, 132 - 84084 - Fisciano (SA), Italy

Abstract

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.

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Articles in Press, Corrected Proof
Available Online from 23 November 2023
  • Receive Date: 05 September 2023
  • Revise Date: 20 November 2023
  • Accept Date: 23 November 2023
  • Published Online: 23 November 2023