Recent Results in Lattice-Based Cryptography

In this report we describe a fully homomorphic encryption (FHE) scheme based on the learning with errors (LWE) problem. Firstly we introduce some definitions related to lattices and some operators which will be needed to build an efficient fully homomorphic encryption system base on LWE. The main focus in this report is to explain the new technique to building FHE schemes that is called the approximate eigenvector method, Also we show that how this approach can make the Gentry et. al.’s scheme as an efficient FHE scheme.