Biblio

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.

Fully homomorphic encryption (FHE) makes it easier for cloud computing to be consistent with privacy. But the efficiency of existing FHE schemes is still far from the actual needs. The main cause is that most of existing FHE schemes are single-bit encryption. Hiromasa, Abe and Okamoto (PKC 2015) reached the major milestone by constructing the first fully homomorphic encryption (FHE) scheme that encrypted message matrices (with single-bit matrices components) and supported homomorphic matrix addition and multiplication. In this paper, we propose a more efficient variant of Hiromasa, Abe and Okamoto with a lower factor noise-expansion factor for homomorphic multiplication from $\Theta$(poly(n)) to $\Theta$(1) and multi-bit matrices components.