Modification and Performance Improvement of Paillier Homomorphic Cryptosystem

Data security and privacy have become an important problem while big data systems are growing dramatically fast in various application fields. Paillier additive homomorphic cryptosystem is widely used in information security fields such as big data security, communication security, cloud computing security, and artificial intelligence security. However, how to improve its computational performance is one of the most critical problems in practice. In this paper, we propose two modifications to improve the performance of the Paillier cryptosystem. Firstly, we introduce a key generation method to generate the private key with low Hamming weight, and this can be used to accelerate the decryption computation of the Paillier cryptosystem. Secondly, we propose an acceleration method based on Hensel lifting in the Paillier cryptosystem. This method can obtain a faster and improved decryption process by showing the mathematical analysis of the decryption algorithm.