More Practical Fully Homomorphic Encryption

In this paper, we first modify the Smart-Vercauteren’s fully homomorphic encryption scheme [SV10] by applying self-loop bootstrappable technique. The security of the modified scheme only depends on the hardness of the polynomial coset problem, removing the assumption of the sparse subset sum problem in the original paper in [SV10]. Moreover, we construct a non-self-loop in FHE by using cycle keys. Then, we further improve our scheme to make it be practical. The securities of our improving FHE’s are respectively based on the hardness of factoring integer problem, solving Diophantine equation problem, and finding approximate greatest common divisor problem.