An overview of torus fully homomorphic encryption

Ferrara, Maria; Tortora, Antonio; Tota, Maria

doi:10.22108/ijgt.2023.139030.1869

تعداد نشریات	43
تعداد شماره‌ها	1,652
تعداد مقالات	13,415
تعداد مشاهده مقاله	30,345,296
تعداد دریافت فایل اصل مقاله	12,096,066

	An overview of torus fully homomorphic encryption
International Journal of Group Theory
دوره 14، شماره 2، شهریور 2025، صفحه 59-73 اصل مقاله (448.42 K)
نوع مقاله: Ischia Group Theory 2022
شناسه دیجیتال (DOI): 10.22108/ijgt.2023.139030.1869
نویسندگان
Maria Ferrara¹؛ Antonio Tortora^* ¹؛ Maria Tota²
¹Dipartimento di Matematica e Fisica, Università della Campania “Luigi Vanvitelli”, viale Lincoln, 5 - 81100, Italy
²Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, 132 - 84084 - Fisciano (SA), Italy
چکیده
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.
کلیدواژه‌ها
TFHE؛ fully homomorphic encryption؛ bootstrapping؛ learning with errors

مراجع
[1] A. Acar, H. Aksu, A. S. Uluagac and M. Conti, A survey on homomorphic encryption schemes: theory and implementation, ACM Comput. Surv., 51 no. 4 (2019) 1–35. [2] I. Chillotti, N. Gama, M. Georgieva and M. Izabachene, TFHE: fast fully homomorphic encryption over the torus, J. Cryptology, 33 (2020) no. 1 34–91. [3] I. Chillotti, M. Joye, D. Ligier, J.-B. Orfila and S. Tap, CONCRETE: Concrete Operates oN Ciphertexts Rapidly by Extending TfhE, WAHC 2020 - 8th Workshop on Encrypted Computing & Applied Homomorphic Cryptography, (2020), [Virtual], France. [4] I. Chillotti, M. Joye and P. Paillier, Programmable bootstrapping enables efficient homomorphic inference of deep neural networks, Cyber Security Cryptography and Machine Learning (CSCML 2021), Lecture Notes in Comput. Sci., Springer, (2021) 1–19. [5] L. Ducas and D. Micciancio, FHEW: Bootstrapping homomorphic encryption in less than a second, Advances in cryptology—EUROCRYPT 2015, Part I, Lecture Notes in Comput. Sci., 9056, Springer, Heidelberg, (2015) 617–640. [6] C. Gentry, Computing arbitrary functions on encrypted data, Communications of the ACM, 53 (2010) no. 3 97–105. [7] 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. [8] C. Gentry, A. Sahai and B. Waters, Homomorphic encryption from learning with errors: conceptuallysimpler, asymptotically-faster, attribute-based, Advances in Cryptology – CRYPTO 2013, Lecture Notes in Comput. Sci., Springer, Berlin, Heidelberg, 75–92. [9] V. Lyubashevsky, C. Peikert and O. Regev, On ideal lattices and learning with errors over rings, J. ACM, 60 (2013) no. 6 35 pp. [10] D. Micciancio and C. Peikert, Trapdoors for lattices: simpler, tighter, faster, smaller, Advances in Cryptology – EUROCRYPT 2012, Lecture Notes in Comput. Sci., Springer, Heidelberg, (2012) 700–718. [11] O. Regev, On lattices, learning with errors, random linear codes, and cryptography, J. ACM, 56 (2009) no. 6 40 pp. [12] R. L. Rivest, L. Adleman and M. L. Dertouzos, On data banks and privacy homomorphism, Foundations of secure computation (Workshop, Georgia Inst. Tech., Atlanta, Ga., 1977), Academic, New York, (1978) 169–179.
آمار تعداد مشاهده مقاله: 146 تعداد دریافت فایل اصل مقاله: 242

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

اخبار و اعلانات

آمار

An overview of torus fully homomorphic encryption