Indian Journal of Science and Technology

Abstract

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