Blockchain-Based Secure Outsourcing of Fully Homomorphic Encryption Using Hidden Ideal Lattice

摘要

The efficiency of homomorphic encryption has always affected its practicality. With the dawn of internet of things, the demand for computation and encryption on lightweight devices is increasing. Complex cryptographic computing is an important burden for lightweight devices, but outsourcing provides great convenience for them. In this paper, based on blockchain, we propose a secure outsourcing scheme for Fully Homomorphic Encryption using Hidden Ideal Lattice (FHEHIL). in which the time-consuming operations (including modular exponentiation and polynomial multiplication) are outsourced. For polynomial multiplication, we propose a secure outsourcing algorithm that reduces the local computation cost to O(n). Previous work based on Fast Fourier Transform can only achieve O(nlog(n)) for the local cost. Through security analysis, our scheme achieves the goals of privacy protection against passive attackers and cheating detection against active attackers. Experiments also demonstrate our scheme is more efficient in comparison with the non-outsourcing FHEHIL.