Analysis on DGHV and NTRU Fully Homomorphic Encryption Schemes

  • B. Santhiya
  • K. Anitha Kumari
Conference paper


Homomorphic encryption (HE) is an emerging scheme that allows computation over encrypted data. The standard encryption algorithms like RSA, Elgamal, etc. help in protecting confidential data from attackers rather than performing computation over encrypted data. Fully homomorphic encryption (FHE) permits computation to perform upon encrypted data unlimitedly in server side than in computational node. In this paper, the basic DGHV FHE scheme and NTRU FHE scheme are analyzed to preserve the security and privacy of the data. DGHV performs computing over real integers, while NTRU in a truncated polynomial ring. A detailed investigation of both the schemes is based on the storage and noise reduction that best suits for a real-world application.


Homomorphic encryption Fully homomorphic encryption DGHV NTRU 



Homomorphic encyrption


Rivest, Shamir, and Adleman


Elliptic curve cryptography


Fully homomorphic encryption


Diji Gentry Halevi Vaikuntanathan


Nth degree truncated polynomial ring units


Lattice-based encryption


Partial homomorphic encryption


Somewhat homomorphic encryption


Linear feedback shift register


Public key


Secret key


  1. 1.
    Boneh D, Gentry C, Gorbunov S, Halevi S, Nikolaenko V, Segev G, Vaikuntanathan V, Vinayagamurthy D (2014) Fully key-homomorphic encryption, arithmetics circuit ABE, and compact garbled circuits. Cryptology ePrint Archive. Report 2014/356, 2014.
  2. 2.
    Ramotsoela TD, Hancke GP (2015). Data aggregation using homomorphic encryption in wireless sensor networks. In: 2015 Information Security for South Africa (ISSA), Johannesburg, pp 1–8.
  3. 3.
    Rivest R, Shamir A, Adelman L (1978) A method for obtaining digital signatures and public-key cryptosystems. Commun ACM 21(2):120126MathSciNetCrossRefGoogle Scholar
  4. 4.
    Nassar M, Erradi A, Malluhi Q (2015) Pallier’s encryption: implementation and clouds applications. Applied Research in Computer Science and Engineering (ICAR), 2015 international conference on, Beirut, pp 1–5.
  5. 5.
    Gentry C (2009) A fully homomorphic encryption scheme. PhD thesis, Stanford University, Department of Computer ScienceGoogle Scholar
  6. 6.
    Gentry C (2009) Fully homomorphic encryption using ideal lattices. In: Proceedings of the forty-first annual ACM symposium on Theory of Computing (STOC’09). ACM, New York. pp 169–178.
  7. 7.
    Brakerski Z, Vaikuntanathan V (2011) Fully homomorphic encryption from ring-LWE and security for key dependent messages. In: Rogaway P (ed) Proceedings of the 31st annual conference on Advances incryptology (CRYPTO’11). Springer, Berlin/Heidelberg, pp 505–524Google Scholar
  8. 8.
    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 (STOC ’05). ACM, New York, pp 84–93. Scholar
  9. 9.
    Hariss K, Chamoun M, Samhat AE (2017) On DGHV and BGV fully homomorphic encryption schemesGoogle Scholar
  10. 10.
    Sattar NS, Adnan MA, Kali MB (2017) Secured aerial photography using homomorphic encryptionGoogle Scholar
  11. 11.
    Hu J, Vasilakos AV (2016) Energy big data analytics and security: challenges and opportunitiesCrossRefGoogle Scholar
  12. 12.
    Liu B, Wu H (2016) Efficient multiplication architecture over ring for NTRU encrypt systemGoogle Scholar
  13. 13.
    Ferrer JD (1996) A new privacy homomorphism and applications. Inf Process Lett 60(5):277–282MathSciNetCrossRefGoogle Scholar
  14. 14.
    Xiao, Liangliang, Bastani, Osbert and Yen (2012) An efficient homomorphic encryption protocol for multi-user systems. Citeseer, IACR Cryptology ePrint Archive, vol 2012, p 193Google Scholar
  15. 15.
    Kipnis, Aviad, Hibshoosh, Eliphaz (2012) Efficient methods for practical fully homomorphic symmetric-key encryption, randomization and verification. IACR Cryptology ePrint Archive, vol 2012, p 637Google Scholar
  16. 16.
    Hariss K, Noura H, Samhat AE (2017) Fully enhanced homomorphic encryption algorithm of MORE approach for real world applications. J Inf Secur Appl 34:233–242. ISSN:2214-2126CrossRefGoogle Scholar
  17. 17.
    van Dijk M, Gentry C, Halevi S, Vaikuntanathan V (2010) Fully homomorphic encryption over the integers. EURO-CRYPT (LNCS) 6110:24–43MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • B. Santhiya
    • 1
  • K. Anitha Kumari
    • 1
  1. 1.Department of Information TechnologyPSG College of TechnologyCoimbatoreIndia

Personalised recommendations