RLWE-Based Homomorphic Encryption and Private Information Retrieval

A multi-bit somewhat homomorphic encryption scheme based on Learning With Errors over Rings (RLWE) assumption is provided, which use canonical embedding to transform elements over a ring into vectors, thus the operation of polynomial multiplication can be performed within O(nlog n) scalar operations, and cipher text size is reduced as well. CPA security of this scheme can be reduced into RLWE assumption. Moreover, an efficient private information retrieval protocol that employs this scheme is presented.