Low Noise Homomorphic Encryption Scheme Supporting Multi-Bit Encryption

Fully homomorphic encryption (FHE) provides effective security assurance for privacy computing in cloud environments. But the existing FHE schemes are generally faced with challenges including using single-bit encryption and large ciphertext noise, which greatly affects the encryption efficiency and practicability. In this paper, a low-noise FHE scheme supporting multi-bit encryption is proposed based on the HAO scheme. The new scheme redesigns the encryption method without changing the system parameters and expands the plaintext space to support the encryption of integer matrices. In the process of noise reduction, we introduce a PNR method and use the subGaussian distribution theory to analyze the ciphertext noise. The security and the efficiency analysis show that the improved scheme can resist the chosen plaintext attack and effectively reduce the noise expansion rate. Comparative experiments show that the scheme has high encryption efficiency and is suitable for the privacy-preserving computation of integer matrices.