Total views : 250

A Novice’s Perception of Partial Homomorphic Encryption Schemes


  • School of Information Technology and Engineering, VIT University, Vellore - 632014, Tamil Nadu, India


Objectives: Homomorphic Encryption is a way of performing computations on encrypted data. In this paper, we explore two famous Homomorphic Encryption schemes (RSA and ElGamal) with illustrations and related security issues. Methods/ Analysis: Both RSA and ElGamal encryption techniques possess multiplicative homomorphic property. These algorithms support only one operation (multiplication) on encrypted data and so they are termed as partial homomorphic encryption schemes. By using RSA and ElGamal, the encrypted data could be multiplied together without performing decryption. If needed, the results after such computations could be returned in decrypted form. This scheme reduces computation time and increases security and privacy of data being processed. Findings: It has been described how RSA and ElGamal algorithms perform key generation, encryption and decryption with simple illustrations. It has also been proved that RSA and ElGamal algorithms support multiplication operation on encrypted data with examples. Improvement/Applications: Many organizations rely on third party to outsource their large amount of electronic data for storage. It may be needed to perform some computations on the encrypted data on the server side provided by untrusted third party. Homomorphic Encryption will be much useful in such applications.


Cryptography, El Gamal, Homomorphic Encryption, Partial Homomorphic Encryption, RSA.

Full Text:

 |  (PDF views: 385)


  • Caroline FCF, Fabien GFG. A survey of homomorphic encryption for nonspecialists. Journal of Information Security. 2009; 1:41-50.
  • Rivest RL, Shamir A, Adleman L. A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM. 1983; 26(19):96-9.
  • Gamal TE. A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory. 1985; 31(4):469-72.
  • Shafi GG, Silvio MSM. Probabilistic encryption and how to play mental poker keeping secret all partial information. Proceedings of the 14th Annual ACM Symposium on Theory of Computing; USA. 1982; p. 365-77.
  • Josh D, Cohen, Michael J, Fischer. A robust and verifiable cryptographically secure election scheme (extended abstract). IEEE Proceedings of 26th Annual Symposium on Foundations of Computer Science; Connecticut. 1985. p. 372-82.
  • Pascal PP. Public-key cryptosystems based on composite degree residuosity classes. Advances in Cryptology-EUROCRYPT, LNCS. 1999; 1592:223-38.
  • Dan Boneh DB, Eu Jin Goh EG, Kobbi Nissim KN. Evaluating 2-DNF formulas on cipher texts. Proceedings of Theory of Cryptography, LNCS 3378; 2005. p. 325-41.
  • Craig Gentry CG. Fully homomorphic encryption using ideal lattices. Proceedings of the 41st Annual ACM Symposium on Theory of Computing; BUSA. 2009. p. 169-78.
  • Dijk M, Craig Gentry CG, Shai Halevi SH, Vinod VVV. Fully homomorphic encryption over the integers. Advances in Cryptology-EUROCRYPT, LNCS. 2010; 6110:24-43.
  • Nigel P, Frederik VFV. Fully homomorphic encryption with relatively small key and ciphertext sizes. Public Key Cryptography, LNCS. 2010; 6056:420-43.
  • Damien Stehle DS, Ron Steinfeld RS. Faster fully homomorphic encryption. Advances in Cryptology-ASIACRYPT, LNCS. 2010; 6477:377-94.
  • ZvikaBrakerski ZB, Vinod VVV. Efficient fully homomorphic encryption from (standard) LWE. Proceedings of the IEEE 52nd Annual Symposium on Foundations of Computer Science, LWE, FOCS; 2011. p. 97-106.
  • Zvika Brakerski ZB, Vinod Vaikuntanathan VV. Fully homomorphic encryption from ring-LWE and security for key dependent messages. Advances in Cryptology-CRYPTO, LNCS. 2011; 6841:505-24.


  • »

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.