Paillier cryptosystem enhancement for Homomorphic Encryption technique

Homomorphic Encryption (HE) is one of the most popular technologies which assists for keeping the confidentiality and privacy of user data on cloud storage. It can apply a mathematical computation to the ciphertext and return the result as if the operation was performed on the corresponding plaintext. Many of algorithms are known as a class of this interested technology, one of them is Paillier cryptosystem. This paper offers two solutions (MPEA-A and MPEA-B) for Paillier's cryptosystem bottleneck problem which causes delay in Paillier decrypting procedures. MPEA-A and MPEA-B algorithms are based on the Chinese Reminder Theorem CRT with appended principles to achieve the desired goal. Practical implementations are applied to the proposed algorithms, The results show that the two algorithms succeeded in reducing the decryption time with various ratios. The practical implementation proved that MPEA-A can be useful for encrypting with a medium Paillier key size, whereas MPEA-B is preferred for encrypting in a large key size value.