Classification of Lattice-based Fully Homomorphic Encryption from Noisy Polly Cracker*

Lattices have been used to construct many cryptographic primitives after Ajtai’s seminal paper in 1996. The goal of this paper is to design novel cryptographic primitives using lattices, which are still found to be no polynomial time attack by quantum computers. For achieving this, we survey the known lattice-based cryptography and lattice-based fully homomorphic encryption schemes as a first step. We focus on the hard problems in lattice and the relationship between known fully homomorphic encryption scheme and noisy polly cracker model.