Top

Published in:

2024 | OriginalPaper | Chapter

Enhancing FHE Over the Integers: Beyond Binary Numbers and Batch Processing

Authors : Rohitkumar R. Upadhyay, Sahadeo Padhye

Published in: Cryptology and Network Security with Machine Learning

Publisher: Springer Nature Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Fully Homomorphic Encryption (FHE) schemes enable secure computations on encrypted data. Following Gentry’s groundbreaking result, the AGCD problem-based FHE scheme, also known as Fully Homomorphic Encryption over the Integers (FHE-OI), was introduced by Dijk et al. Over the time, several improvements have been made to FHE-OI, including the CS scheme proposed by Cheon and Stehlé. This paper presents two significant enhancements to CS scheme. The first contribution involves extending their FHE scheme to support message space \(\mathbb {Z}_g\), removing the previous constraint limited to binary numbers as described in Cheon and Stehlé’s work. Building upon this advancement, the second enhancement further extends the scheme to encompass batch fully homomorphic encryption. This extension empowers the scheme to efficiently encrypt and perform homomorphic operations on entire vectors of plaintext bits using a single ciphertext, thereby enhancing its applicability and utility in various practical scenarios.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter A Secure RSA-Based Image Encryption Method

next chapter A Study on Designated Verifier Signature Schemes and Their Variants

Boneh D, Goh EJ, Nissim K (2005) Evaluating 2-DNF formulas on ciphertexts. In: TCC, vol 3378. Springer, pp 325–341

Brakerski Z, Gentry C, Vaikuntanathan V (2014) Fully homomorphic encryption without bootstrapping. ACM Trans Comput Theor (TOCT) 6(3):1–36MathSciNetCrossRef

Brakerski Z, Vaikuntanathan V (2011) Efficient fully homomorphic encryption from (standard) lWE. In: 2011 IEEE 52nd annual symposium on foundations of computer science. IEEE Computer Society, pp 97–106

Brakerski Z, Vaikuntanathan V (2011) Fully homomorphic encryption from ring-LWE and security for key dependent messages. In: Advances in cryptology—CRYPTO 2011: 31st annual cryptology conference proceedings 31. Springer, pp 505–524

Cheon JH, Coron JS, Kim J, Lee MS, Lepoint T, Tibouchi M, Yun A (2013) Batch fully homomorphic encryption over the integers. In: Advances in Cryptology—EUROCRYPT 2013: 32nd annual international conference on the theory and applications of cryptographic techniques, proceedings 32. Springer, pp 315–335

Cheon JH, Stehlé D (2015) Fully homomophic encryption over the integers revisited. In: Advances in cryptology—EUROCRYPT 2015: 34th annual international conference on the theory and applications of cryptographic techniques proceedings, part I. Springer, pp 513–536

Coron JS, Lepoint T, Tibouchi M (2014) Scale-invariant fully homomorphic encryption over the integers. In: Public-key cryptography—PKC 2014: 17th international conference on practice and theory in public-key cryptography proceedings 17. Springer, pp 311–328

Coron JS, Mandal A, Naccache D, Tibouchi M (2011) Fully homomorphic encryption over the integers with shorter public keys. In: Advances in cryptology—CRYPTO 2011: 31st annual cryptology conference, proceedings 31. Springer, pp 487–504

Coron JS, Naccache D, Tibouchi M (2012) Public key compression and modulus switching for fully homomorphic encryption over the integers. In: Advances in cryptology—EUROCRYPT 2012: 31st annual international conference on the theory and applications of cryptographic techniques, proceedings 31. Springer, pp 446–464

10.

ElGamal T (1985) A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans Inf Theor 31(4):469–472MathSciNetCrossRef

11.

Gentry C (2009) Fully homomorphic encryption using ideal lattices. In: Proceedings of the forty-first annual ACM symposium on theory of computing, pp 169–178

12.

Gentry C, Sahai A, Waters B (2013) Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Advances in cryptology—CRYPTO 2013: 33rd annual cryptology conference proceedings, part I. Springer, pp 75–92

13.

Goldwasser S, Micali S (1984) Probabilistic encryption. J Comput Syst Sci 28(2):270–299MathSciNetCrossRef

14.

Howgrave-Graham N (2001) Approximate integer common divisors. In: Cryptography and lattices: international conference, CaLC 2001 providence, revised papers. Springer, pp 51–66

15.

López-Alt A, Tromer E, Vaikuntanathan V (2012) On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption. In: Proceedings of the forty-fourth annual ACM symposium on theory of computing, pp 1219–1234

16.

Lyubashevsky V, Peikert C, Regev O (2010) On ideal lattices and learning with errors over rings. In: 29th in the series of European conferences on the theory and application of cryptographic techniques, Eurocrypt, pp 1–23

17.

Paillier P (1999) Public-key cryptosystems based on composite degree residuosity classes. In: Advances in cryptology-EUROCRYPT’99: international conference on the theory and application of cryptographic techniques Prague, proceedings 18. Springer, pp 223–238

18.

Regev O (2005) On lattices, learning with errors, random linear codes, and cryptography. In: Proceedings of the thirty-seventh annual ACM symposium on theory of computing, pp 84–93

19.

Rivest RL, Adleman L, Dertouzos ML (1978) On data banks and privacy homomorphisms. Foundations Secur Comput 4(11):169–180MathSciNet

20.

Smart NP, Vercauteren F (2014) Fully homomorphic SIMD operations. Des Codes Cryptogr 71:57–81CrossRef

21.

Van Dijk M, Gentry C, Halevi S, Vaikuntanathan V (2010) Fully homomorphic encryption over the integers. In: Advances in cryptology—EUROCRYPT 2010: 29th annual international conference on the theory and applications of cryptographic techniques, proceedings 29. Springer, pp 24–43

22.

Xu J, Sarkar S, Hu L (2022) Revisiting orthogonal lattice attacks on approximate common divisor problems. Theor Comput Sci 911:55–69MathSciNetCrossRef

Title: Enhancing FHE Over the Integers: Beyond Binary Numbers and Batch Processing
Authors: Rohitkumar R. Upadhyay
Sahadeo Padhye
Publisher: Springer Nature Singapore
Book: Cryptology and Network Security with Machine Learning
Print ISBN: 978-981-9706-40-2

Electronic ISBN: 978-981-9706-41-9

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-981-97-0641-9_22

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"