Secured Paillier Homomorphic Encryption Scheme Based on the Residue Number System

Abstract

In this paper, we present an improved Paillier Cryptosystem for a secured data transmission based on the Residue Number System (RNS). The current state of Paillier Cryptosystem allows the computation of the plaintext from the cipher text without solving its security assumption of Decisional Composite Residuosity or the knowledge of its private keys under mathematical attacks. The proposed RNS based cryptosystem involving two stages of encryption and two stages of decryption has never been adequately studied before. This paper attempts to solve by introducing two stages of encryption and two stages of decryption. The first stage of the encryption process maintains the traditional Paillier encryption process and the second stage process is the encryption using the recommended moduli set – by the RNS Forward converter. At the first stage of the decryption process, our proposed RNS based reverse converter is adopted and finally, the traditional Paillier decryption process will be used at the second stage of the decryption process. Because the entire encryption technique is randomized, it can withstand chosen bruteforce attacks. The suggested algorithm's security study reveals that it has a wide key space ( , a high level resistance to key sensitivity attacks, and an acceptable level of resilience. In terms of security, it has been discovered that the proposed system outperforms the present algorithm.