International Association
for Cryptologic Research

This paper explores advancements in the Gentry-Sahai-Waters (GSW) fully homomorphic encryption scheme, addressing challenges related to message data range limitations and ciphertext size constraints. We introduce a novel approach utilizing the Chinese Remainder Theorem (CRT) for message decomposition, significantly expanding the allowable message range to the entire plaintext space. This method enables unrestricted message selection and supports parallel homomorphic operations without intermediate decryption. Additionally, we adapt existing ciphertext compression techniques, such as the PVW-like scheme, to reduce memory overhead associated with ciphertexts. Our experimental results demonstrate the effectiveness of the CRT-based decomposition in increasing the upper bound of message values and improving the scheme's capacity for consecutive homomorphic operations. However, compression introduces a trade-off, necessitating a reduced message range due to error accumulation. This research contributes to enhancing the practicality and efficiency of the GSW encryption scheme for complex computational scenarios while managing the balance between expanded message range, computational complexity, and storage requirements.